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Reversible inhibition of sperm under guidance ( RISUG ), formerly referred to as the synthetic polymer styrene maleic anhydride ( SMA ), is the development name of a male contraceptive injection developed at IIT Kharagpur in India by the team of Dr. Sujoy K. Guha . [ citation needed ]
RISUG has been patented in India, China, Bangladesh, and the United States. [ 1 ] Phase III clinical trials in India were slowed by insufficient volunteers, [ 1 ] and the results were published in 2023. [ 2 ]
Beginning in 2011, a contraceptive product based on RISUG, Vasalgel , was under development in the US by the Parsemus Foundation , who were unable to bring the product to market over the next decade. [ 3 ] In 2023, the patent for Vasalgel was acquired by NEXT Life Sciences, which plans to bring the technology to market under the name Plan A for Men. [ 4 ]
Sujoy K. Guha developed RISUG after years of developing other inventions. He originally wanted to create an artificial heart that could pump blood using a strong electrical pulse. Using the 13-chamber model of a cockroach heart, he designed a softer pumping mechanism that would theoretically be safe to use in humans. [ 5 ] As India's population grew throughout the 1970s, Guha modified his heart pump design to create a water pump that could work off of differences in ionic charges between salt water and fresh water in water treatment facilities. This filtration system did not require electricity and could potentially help large groups of people have access to clean water. India, however, decided that the population problem would be better served by developing more effective contraception. So Guha again modified his design to work safely inside the body, specifically inside the male genitalia. The non-toxic polymer of RISUG also uses differences in the charges of the semen to rupture the sperm as it flows through the vas deferens . [ 3 ]
Intellectual property rights to RISUG in the United States were acquired between 2010 and 2012 by the Parsemus Foundation , a not-for-profit organization , which has branded it as "Vasalgel". [ 6 ] [ 7 ] Vasalgel was successful in achieving azoospermia in rabbits within 36 days of injection, as well as returned vas deferens patency. [ 8 ] In 2023, the patent for Vasalgel was acquired by NEXT Life Sciences , Inc., developing it under the name Plan A for Men . [ 4 ]
RISUG works by an injection into the vas deferens, the vessel through which the sperm moves before ejaculation . RISUG is similar to vasectomy in that a local anesthetic is administered, an incision is made in the scrotum , and the vasa deferentia are injected with a polymer gel (rather than being cut and cauterized). [ 9 ] In a matter of minutes, the injection coats the walls of the vasa with a clear gel made of 60 mg of the copolymer styrene/maleic anhydride (SMA) with 120 μL of the solvent dimethyl sulfoxide . The copolymer is made by irradiation of the two monomers with a dose of 0.2 to 0.24 megarad for every 40 g of copolymer and a dose rate of 30 to 40 rad/s. Dr Pradeep K. Jha, a senior scientist, worked on the effects of gamma dose rate and total dose interrelation on molecular designing and biological function of polymer. [ 10 ] The source of irradiation is cobalt-60 gamma radiation . [ citation needed ]
The effect the chemical has on sperm is not completely understood. Originally, researchers thought it lowered the pH of the environment enough to kill the sperm. [ 11 ]
Guha theorizes that the polymer surface has a negative and positive electric charge mosaic. Within an hour after placement the differential charge from the gel will rupture the sperm's cell membrane as it passes through the vas, deactivating it before it can exit from the body. [ 12 ]
The thoroughness of carcinogenicity and toxicity testing in clinical trials had been questioned after phase I of clinical trials on the basis of presence of styrene and maleic anhydride in the formulation. In response, Guha argued that substances can be individually toxic in nature but harmless as compounds like pure chlorine, which can melt human flesh on its own, but, when combined with sodium, it becomes sodium chloride – the basic salt that people consume in their diets. When it did not persuade ICMR and the clinical trials did not resume by 1996, he went to the Supreme court and the next round of clinical trials resumed afterwards. [ 13 ]
In October 2002, India's Ministry of Health aborted the clinical trials due to reports of albumin in urine [ 14 ] and scrotal swelling in phase III trial participants. Although the ICMR has reviewed and approved the toxicology data three times, WHO and Indian researchers say that the studies were not done according to recent international standards. Due to the lack of any evidence for adverse effects, trials were restarted in 2011. [ 3 ] Guha says concerns over the safety and efficacy of the drug have mainly come from the NIH and WHO. [ 13 ]
By November 2019, the ICMR had successfully completed clinical trials of the world's first injectable male contraceptive, which was then sent to the Drug Controller General of India (DCGI) for regulatory approval. The trials were over, including extended, phase III clinical trials, for which 303 candidates were recruited with 97.3% success rate and no reported side effects. [ 15 ]
In the developed world , the average time taken for a drug to go from concept to market is 10 to 15 years, whereas, it has been over four decades since Guha published his original paper on RISUG. [ 13 ] RISUG aims to provide males with years-long fertility control, thereby overcoming compliance problems and avoiding ongoing costs associated with condoms and the female birth control pill , which must be taken daily. [ 16 ]
Pharmaceutical companies have expressed little interest in RISUG. One obstacle facing marketing of the product is that men generally perceive contraception as a woman's issue. Men may choose not to use alternative methods of contraception because there are fewer options for birth control for them than there are for women, or they may fear the side effects, or it may conflict with their cultural or religious beliefs. However, the same study published that in the year 2000, an international survey found that 83% of men were willing to use a male contraceptive. Despite this, pharmaceutical companies are reluctant to lose market share of a thriving global market for female contraceptives and condoms which bring billions of dollars of revenue each year. Initially, RISUG attracted some interest from pharmaceutical companies. However, considering that RISUG is an inexpensive, one-time procedure, manufacturers retracted. [ 17 ]
Smart RISUG is a newer version of the male contraception that was published in 2009. The polymer adds iron oxide and copper particles to the original compound, giving it magnetic properties and the name "Smart RISUG". After injection the exact location of the polymer inside the vas deferens can be measured and visualized by X-ray and magnetic resonance imaging . The polymer location can also be externally controlled using a pulsed magnetic field. With this magnetic field, the polymer can change location inside the body to maximize sterility or can be removed to restore fertility. The polymer has magnetoelastic behavior that allows it to stretch and elongate to better line the vas deferens. The iron oxide component is necessary to prevent agglomeration.
With the presence of iron particles, the polymer has lower protein binding and therefore prevents agglomeration. The copper particles in the compound allow the polymer to conduct heat. When an external microwave applies heat to the polymer, it can liquify the polymer again to be excreted to restore fertility. Smart RISUG is therefore a better choice for men who want to use RISUG as temporary birth control, since it does not require a second surgery to restore fertility. The addition of metal ions also increases the effectiveness of the spermicide. The low frequency electromagnetic field disintegrates the sperm cell membrane in the head region. This in turn causes both acrosin and hyaluronidase enzymes to leak out of the sperm, making the sperm infertile.
The safety of Smart RISUG is uncertain and requires additional research. The spermicidal properties of the compound should not have negative effects on the lining of the vas deferens. Albino rats used to develop the new polymer did not have any adverse symptoms. [ 18 ] The original compound had been tested for over 25 years in rats. [ 8 ] | https://en.wikipedia.org/wiki/Reversible_inhibition_of_sperm_under_guidance |
A reversible reaction is a reaction in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously. [ 1 ]
A and B can react to form C and D or, in the reverse reaction, C and D can react to form A and B. This is distinct from a reversible process in thermodynamics .
Weak acids and bases undergo reversible reactions. For example, carbonic acid :
The concentrations of reactants and products in an equilibrium mixture are determined by the analytical concentrations of the reagents (A and B or C and D) and the equilibrium constant , K . The magnitude of the equilibrium constant depends on the Gibbs free energy change for the reaction. [ 2 ] So, when the free energy change is large (more than about 30 kJ mol −1 ), the equilibrium constant is large (log K > 3) and the concentrations of the reactants at equilibrium are very small. Such a reaction is sometimes considered to be an irreversible reaction, although small amounts of the reactants are still expected to be present in the reacting system. A truly irreversible chemical reaction is usually achieved when one of the products exits the reacting system, for example, as does carbon dioxide (volatile) in the reaction
The concept of a reversible reaction was introduced by Claude Louis Berthollet in 1803, after he had observed the formation of sodium carbonate crystals at the edge of a salt lake [ 3 ] (one of the natron lakes in Egypt, in limestone ):
He recognized this as the reverse of the familiar reaction
Until then, chemical reactions were thought to always proceed in one direction. Berthollet reasoned that the excess of salt in the lake helped push the "reverse" reaction towards the formation of sodium carbonate. [ 4 ]
In 1864, Peter Waage and Cato Maximilian Guldberg formulated their law of mass action which quantified Berthollet's observation. Between 1884 and 1888, Le Chatelier and Braun formulated Le Chatelier's principle , which extended the same idea to a more general statement on the effects of factors other than concentration on the position of the equilibrium.
For the reversible reaction A⇌B, the forward step A→B has a rate constant k 1 {\displaystyle k_{1}} and the backwards step B→A has a rate constant k − 1 {\displaystyle k_{-1}} . The concentration of A obeys the following differential equation:
If we consider that the concentration of product B at anytime is equal to the concentration of reactants at time zero minus the concentration of reactants at time t {\displaystyle t} , we can set up the following equation:
Combining 1 and 2 , we can write
Separation of variables is possible and using an initial value [ A ] ( t = 0 ) = [ A ] 0 {\displaystyle [A](t=0)=[A]_{0}} , we obtain:
and after some algebra we arrive at the final kinetic expression:
The concentration of A and B at infinite time has a behavior as follows:
Thus, the formula can be linearized in order to determine k 1 + k − 1 {\displaystyle k_{1}+k_{-1}} :
To find the individual constants k 1 {\displaystyle k_{1}} and k − 1 {\displaystyle k_{-1}} , the following formula is required: | https://en.wikipedia.org/wiki/Reversible_reaction |
Reversible reference system propagation algorithm ( r-RESPA ) is a time stepping algorithm used in molecular dynamics . [ 1 ]
It evolves the system state over time,
where the L is the Liouville operator .
This physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reversible_reference_system_propagation_algorithm |
A reversible solid oxide cell (rSOC) is a solid-state electrochemical device that is operated alternatively as a solid oxide fuel cell (SOFC) and a solid oxide electrolysis cell (SOEC) . Similarly to SOFCs, rSOCs are made of a dense electrolyte sandwiched between two porous electrodes. Their operating temperature ranges from 600°C to 900°C, hence they benefit from enhanced kinetics of the reactions and increased efficiency with respect to low-temperature electrochemical technologies.
When utilized as a fuel cell, the reversible solid oxide cell is capable of oxidizing one or more gaseous fuels to produce electricity and heat. When used as an electrolysis cell, the same device can consume electricity and heat to convert back the products of the oxidation reaction into valuable fuels. These gaseous fuels can be pressurized and stored for a later use. For this reason, rSOCs are recently receiving increased attention due to their potential as an energy storage solution on the seasonal scale.
Reversible solid oxide cells (rSOCs), as solid oxide fuel cells , are made of four main components: the electrolyte, the fuel and oxygen electrodes, and the interconnects. [ 1 ]
The electrodes are porous layers that favor the reactants diffusion inside their structure and catalyze electrochemical reactions. [ 1 ] In the single technologies like SOFCs and SOECs, the electrodes serve a single purpose, hence they are called with their specific names. The anode is where the oxidation reaction occurs, while the cathode is where the reduction reaction takes place. In reversible solid oxide cells, on the other hand, both modalities can occur alternatively in the same device. For this reason, the generic names of fuel electrode and oxygen electrode are preferred instead. [ 2 ] On the fuel electrode the reactions involving the fuel oxidation (SOFC modality) or the reduction of the products to produce the fuel (SOEC modality) takes place. On the oxygen electrode, oxygen reduction (SOFC modality) or oxygen ions oxidation to form oxygen gas (SOEC modality) takes place.
State-of-the-art materials for rSOCs are those used for SOFCs. The most common fuel electrodes are made by a mixture of nickel , that serves as electronic conductor, and yttria-stabilized zirconia (YSZ) , a ceramic material characterized by high conductivity to oxygen ions at elevated temperature. The most popular oxygen electrode materials are lanthanum strontium cobalt ferrite (LSCF) and lanthanum strontium chromite (LSC) , perovskite materials able to catalyze oxygen reduction and oxide ion oxidation reactions. [ 3 ]
The electrolyte is a solid-state layer placed between the two electrodes. It is an electric insulator, it is impermeable to gas flow but permeable to oxygen ions flow. Hence, the main properties of this component are the high ion conductivity and the low electrical conductivity. When the rSOC is operated in SOFC mode, oxygen ions flow from the oxygen electrode to the fuel electrode, where the fuel oxidation occurs. In SOEC mode, the reactants are reduced in the anode with the production of oxygen ions, which flow towards the oxygen electrode. The most widespread material for electrolytes is YSZ. [ 3 ]
The interconnects are usually made of metallic materials. They provide or collect the electrons involved in the electrochemical reactions. In addition, they are shaped internally with gas channels to distribute the reactants over the cell surface. [ 4 ]
The most common tool to characterize the performances of a reversible solid oxide cell is the polarization curve. In this chart, the current density is related to operating voltage of the cell. The usual convention is the one of positive current density for the fuel cell operation, and negative current density for the electrolysis operation. When the rSOC electrical circuit is not closed and no current is extracted or supplied to the cell, the operating voltage is the so-called open circuit voltage (OCV) . If the composition of the gas in the fuel electrode and the oxygen electrode are the same for both modalities, the polarization curve for the SOEC mode and the SOFC have the same OCV. When some current density is extracted or supplied to the cell, the operating voltage starts to diverge from the OCV. This phenomenon is due to the polarization losses, which depend on three main phenomena:
The sum of the polarization losses takes the name of overpotential .
Other than the open circuit voltage, another fundamental theoretical voltage can be defined. The thermoneutral voltage V T N {\displaystyle V_{TN}} depends on the enthalpy of the overall reaction taking place in the rSOC and the number of charges that are transferred within the electrochemical reactions. Its relationship with the operating voltage gives information about the heat demand or generation inside the cell.
During the electrolysis operation:
The fuel cell operation, instead, is always exothermic.
Various chemistries can be considered when dealing with reversible solid oxide cells, which in turn can influence their operating conditions and overall efficiency.
When hydrogen and steam are considered as reactants, the overall reaction takes this form:
where the forward reaction occurs during SOFC mode, and the backward reaction during SOEC mode. On the fuel electrode, hydrogen oxidation (forward reaction) takes in SOFC mode and water reduction (backward reaction) takes plain SOEC mode:
On the oxygen electrode, oxygen reduction (forward reaction) occurs in SOFC mode and oxide ions oxidation (backward reaction) occurs in SOEC mode:
The thermoneutral voltage for steam electrolysis is equal to 1.29 V.
Differently than low-temperature electrochemical technologies, rSOCs can process also carbon containing species with reduced risk of catalyst poisoning. Methane can be internally reformed on the Ni particles to produce hydrogen, similarly to what happens in steam reforming reactors. Subsequently, the produced hydrogen can undergo the electro-oxidation. Moreover, when working in SOEC modality, water and carbon dioxide can be co-electrolyzed to generate hydrogen and carbon monoxide to form syngas mixtures with various composition. [ 1 ] [ 5 ]
The reactions taking place on the oxygen electrode are the same considered for the hydrogen/steam case. Even if characterized by much slower kinetics with respect to the one involving hydrogen and steam, the direct electro-oxidation of carbon monoxide (forward reaction) or the direct electro-reduction of carbon dioxide (backward reaction) can be considered as well:
The thermoneutral voltage of the CO 2 {\displaystyle {\ce {CO2}}} electrolysis is equal to 1.48 V.
One useful way to depict the cycling between SOFC and SOEC mode of the rSOC operation with carbonaceous reactants is the C-H-O ternary diagram . [ 6 ] Each point in the diagram represents a gas mixture with a different number of carbon, hydrogen or oxygen atoms. When dealing with the operation on reversible solid oxide cells, three distinct regions can be distinguished in the graph. For different operating conditions (i.e., different temperature and pressure), distinct boundary lines between these regions can be drawn. The three regions are:
In the operating region, the fuel mixture and the exhaust mixture can be depicted. These two points are connected by a line which runs through points characterized by a constant H/C ratio. In fact, during the rSOC operation in both modalities, the gases on the fuel electrode exchange with the oxygen electrode only oxygen atoms, while hydrogen and carbon are confined inside the fuel electrode. During the SOFC operation, the composition of the gas in the fuel electrode moves towards the boundary line of the fully oxidized region, increasing its oxygen content. During SOEC operation, on the other hand, the gas mixture evolves away from the fully oxidized region towards the carbon deposition region, while reducing its oxygen content.
An alternative and promising chemistry for rSOCs is that one involving ammonia conversion to hydrogen and nitrogen. Ammonia has great potential as hydrogen carrier, due to its higher volumetric density with respect to hydrogen itself, and it can be directly fed to SOFCs. It has been demonstrated that ammonia-fed SOFCs operate through successive ammonia decomposition and hydrogen oxidation: [ 7 ]
Ammonia decomposition has been demonstrated to be slightly more efficient than simple hydrogen oxidation, confirming the great potential of ammonia as a fuel other than an energy carrier. [ 7 ]
Unfortunately, ammonia cannot be directly synthesized on the fuel electrode of a rSOC, because the equilibrium reaction
is completely shifted towards the left at their higher than 600°C working temperature. For this reason, for clean ammonia production, hydrogen production via electrolysis must be coupled with nitrogen production from air with hydrogen oxidation and subsequent water separation. [ 3 ]
Reversible solid oxide cells are receiving increased attention as energy storage solutions for the weekly or the monthly scale. Other technologies for large scale electrical storage such as pumped-storage hydroelectricity and compressed air energy storage are characterized by geographical limitations. On the other hand, Li-ion batteries suffer from limited discharge capabilities. In this regard, hydrogen storage is a promising alternative, since the produced fuel can be compressed and stored for months. Among all hydrogen technologies, rSOCs are definitely the best candidates for producing and converting back hydrogen into electricity. Due to their high operating temperature, they are characterized by higher efficiency, compared to technologies like PEM fuel cells or PEM electrolyzers . Moreover, the possibility to operate both the fuel oxidation and the electrolysis on the same device is beneficial on the capacity factor of the system, helping at reducing its specific investment cost. [ 2 ]
When dealing with rSOCs, the most important parameter to consider is the roundtrip efficiency , which is a measure of the efficiency of the system considering both the charge (SOEC) and discharge (SOFC) preocesses. The roundtrip efficiency for the single cell can be defined as:
where Q {\displaystyle Q} is the charge supplied or consumed during the reactions, and V {\displaystyle V} is the operating voltage. If the assumption of no current or reactants leakage is made, the exchanged charges during the reactions can be assumed to be equal. Then, the roundtrip efficiency can be written as:
To maximize the roundtrip efficiency, the two operating voltages must be as close as possible. This condition can be achieved by operating the rSOC with low current densities in both modalities. In SOFC mode this is easily pursuable, while in SOEC mode a too low voltage may lead to an endothermic operation. If the operating voltage in SOEC mode is lower than the thermoneutral voltage, additional heat sources at high temperature are needed to sustain the reaction. These could come from waste industrial heat or from nuclear reactors. If not easily accessible, though, electrical heating is necessary. This can be supplied by external additions or by operating the cell with an operating voltage higher than the thermoneutral one. Both solutions, though, would inevitably lower the roundtrip efficiency of the rSOC. For this reason, in reversible operation, the thermoneutral voltage poses significant limitations in achieving high roundtrip efficiencies. [ 8 ]
On the other hand, the thermoneutral voltage is greatly affected by the reaction chemistry. It has been demonstrated that increasing the yield of methane in the electrolysis operation can substantially decreases the thermoneutral voltage and heat demand of the reaction. For conventional electrolyzers (operating at atmospheric pressure and 750°C), the methane content in the products is very low. It can be increased effectively by lowering the operating temperature to 600°C and increasing the operating pressure up to 10 bar. For example, the thermoneutral voltage is equal to 1.27 V at 750°C and 1 bar, while it becomes equal to 1.07 V at 600°C and 10 bar. In these conditions, the rSOC can even be operated in exothermic mode at reduced voltages, permitting to produce additional heat at high temperature. This result becomes very helpful in the design of high efficiency rSOC systems for energy storage purposes. [ 8 ]
Single reversible solid oxide cells can be arranged in series to form stacks. Single stacks can be then arranged in modules to reach power capabilities in the order of kilowatts or megawatts. [ 9 ] [ 10 ]
One of the most challenging aspects in designing large rSOC systems for energy storage purposes is the thermal integration . When the rSOC is operated in electrolysis mode, thermal power is needed for the operation of the system. Thermal power must be provided at two different temperature levels. Heat is needed for water operation, and additional heat at high temperature may be needed if the SOEC modality is endothermic. The latter requirement can be avoided if the rSOC is operated with an exothermic reaction in SOEC modality, with a negative effect on the roundtrip efficiency. On the other hand, when the rSOC is operated in fuel cell mode, the reaction is characterized by a high exothermicity. A number of works in the scientific literature have proposed the exploitation of a Thermal energy storage (TES) to ease the thermal integration of the system. [ citation needed ]
Excess heat from the SOFC operation can be recovered and stored in a TES, and later used for the SOEC operation. Thermal energy storage typologies and heat transfer fluids that have been considered for this purpose are those used for Concentrated solar power (CSP) technologies. Diathermic oil can be used to store heat at relatively low temperature (for instance, 180°C) and exploited for water evaporation. [ 11 ] Alternatively, phase-change materials characterized by high fusion points can be used to store heat at high temperature and enable the endothermic operation in the electrolysis mode. In this case, usually, rSOCs operate at different temperature levels in the two modalities (for example, 850°C in SOFC mode and 800°C in SOEC mode). [ 12 ]
If carbonaceous chemistries are employed, the beneficial effect of methane synthesis inside the cell can be exploited to reduce the heat request of the electrolysis mode. In this regard, systems operating at high pressure and lower temperature (20 bar and 650°C) have been proposed to reduce or even eliminate the thermal power requirement of the rSOC system. [ 6 ] Alternatively, the production of methane can be favored in external reactors. The methanation reaction is exothermic and favored at low temperature.
The syngas that produced by the co-electrolysis can undergo a further reaction in one or multiple methanation reactors to produce methane and generate low-temperature heat for water evaporation. [ 12 ] In addition, the formation of methane in such systems may be beneficial to the size of the tanks used for storing the fuels. In fact, methane is characterized by a higher volumetric energy density than hydrogen in the gaseous form. [ 13 ]
When computing the roundtrip efficiencies of rSOC systems, the definition must take into account the net electric consumption (or additional electric production) of other components inside the system. The set of these component is regarded as balance of plant (BOP) , and may comprehend pumps, compressors, expanders or fans, needed for fluid circulation and processing inside the system. Therefore, the system roundtrip efficiency can be defined as:
where:
The roundtrip efficiencies achievable with rSOC systems operating with steam and hydrogen can reach values in the order of 60%. [ 11 ] [ 14 ] On the other hand, systems exploiting the beneficial effects of methane formation, either inside the rSOC or in external reactors, can reach rountrip efficiencies in the order of 70% and beyond. [ 12 ] [ 6 ] | https://en.wikipedia.org/wiki/Reversible_solid_oxide_cell |
Reversibly assembled cellular composite materials ( RCCM ) are three-dimensional lattices of modular structures that can be partially disassembled to enable repairs or other modifications. Each cell incorporates structural material and a reversible interlock, allowing lattices of arbitrary size and shape. RCCM display three-dimensional symmetry derived from the geometry as linked. [ 1 ] [ 2 ]
The discrete construction of reversibly assembled cellular composites introduces a new degree of freedom that determines global functional properties from the local placement of heterogeneous components. Because the individual parts are literally finite elements, a hierarchical decomposition describes the part types and their combination in a structure. [ 1 ]
RCCM can be viewed as a "digital" material in which discrete parts link with a discrete set of relative positions and orientations. An assembler can place them using only local information. Placement errors can be detected and corrected by assembly reversal. These materials combine the size and strength of composites with the low density of cellular materials and the convenience of additive manufacturing. [ 1 ]
RCCM were introduced in 2013 by researchers at the MIT Center for Bits and Atoms . [ 2 ]
RCCM lattices behave as an elastic solid in both tension and compression . They offer both a linear regime and a nonlinear super-elastic deformation mode a modulus an order of magnitude greater than for an ultralight material (12.3 megapascals at a density of 7.2 mg per cubic centimeter). Bulk properties can be predicted from component measurements and deformation modes determined by the placement of part types. Site locations are locally constrained, yielding structures that merge desirable features of carbon fiber composites , cellular materials and additive manufacturing . [ 1 ]
Nonlinear elastic behavior derives from a multi-axial elastic instability of the lattice, a complex coordinated elastic buckling of the strut members. The resulting geometry is similar to a Jahn–Teller distortion of an octahedral complex with respect to orientation about the octahedral centers. Elastic folding or pleating can occur in three dimensions, likely a coordinated antisymmetric twisting stress response and/or plastic deformation. [ 1 ] [ 3 ]
Unlike conventional composites, which typically fail catastrophically, RCCM fail incrementally because of the non-linear deformation phase and the multiplicity of joints and links. These results matched finite-element simulations [ 4 ] with finely-meshed rigid body models. In addition to convergence to the observed coordinated buckling mode, these simulations accurately predict the relative strength scaling observed in load test experiments. These results are consistent with the observation that open-cell lattice materials fail through micro-structural strut bending failures with σmax ∝. The simulations also suggest that the coordinated buckling phenomenon as well as the modulus measurements are not dominated by edge effects, with minimal influence on overall results beyond characteristic lengths exceeding several units. [ 1 ]
Varying the locations of more and less rigid elements can trigger pure axial compression, simple uni-directional Euler buckling and complex buckling. [ 1 ] [ 3 ]
Cellular composites extend stretch-dominated lattices to the ultralight regime (below ten milligrams per cubic centimeter). Performance depends positively on the framework rigidity of the lattice, node connectivity, slenderness of strut members and the scaling of the density cost of mechanical connections. [ 1 ]
Conventional fiber composites make truss cores and structural frames, with bonded assembly of substructures or continuous fiber winding. Examples of such truss cores have been reported with continuous two-dimensional (2D) geometric symmetry and nearly ideal but highly anisotropic specific modulus scaling.
Three-dimensional open-cell lattice materials occur in natural and engineered systems, spanning many length scales. Their mechanical properties scale with relative density according to the geometry. They display either stretch-dominated or transverse beam bending-dominated microstructural behavior, based on periodic mechanical models. For Young’s modulus E, ideal stretch-dominated scaling with density ρ follows a proportional law E∝ρ, while common stochastic foams follow a quadratic law E∝ρ2 otherwise associated with transverse beam bending-dominated behavior. At ultralight densities a further reduced cubic scaling law E∝ρ3 is common, such as with aerogels and aerogel composites. [ 1 ]
The dependence of scaling on geometry is seen in periodic lattice-based materials that have nearly ideal E∝ρ scaling, with high node connectedness relative to stochastic foams. These structures have previously been implemented only in relatively dense engineered materials. For the ultralight regime the E∝ρ2 scaling seen in denser stochastic cellular materials applies to electroplated tubular nickel micro-lattices, as well as carbon-based open-cell stochastic foams, including carbon microtube aerographite and graphene cork. [ 1 ]
Making the connections stiffer and stronger than the strut members means that stress response is governed by the struts. [ 3 ] Extending dimensional scaling methods to include the connections shows that the mass density cost of robust connections – which scale with the strut's cross-sectional area – is low for ultralight materials, where strut diameter dominates mass density scaling. The relative density (ρ/ρs) of these materials is the sum of the relative density contribution of the strut members (ρm/ρs) and the relative density contribution of the connections (ρc/ρs). The strut members have a thickness t and length L. The connections transfer forces through load-bearing surface contacts, requiring that the characteristic dimensions of the connections scale with the cross section of the attached strut members, t2, because this dimension determines the maximum stress transferable through the joint. [ 1 ]
These definitions give a cubic scaling relation between the relative mass contribution of the joints and the strut's thickness-to-length ratio (ρc/ρs ∝ Cc(t/L)3, where Cc is the connection contribution constant determined by the lattice geometry). The struts' relative density contribution scales quadratically with the thickness-to-length ratio of the struts (ρm/ρs ∝ Cm (t/L)2), which agrees with the literature on classical cellular materials. Mechanical properties (such as modulus and strength) scale with overall relative density, which in turn scales primarily with the strut and not the connection, considering only open cell lattices with slender struts [t/L < 0.1 (7)], given that the geometric constants Cc and Cm are of the same order of magnitude [ρ/ρs ∝ Cc (t/L)3 + Cm (t/L)2]. [ 3 ] The density cost of the mechanical joints decreases with increasing strut member slenderness (decreasing t/L) and decreasing relative density. [ 1 ]
Tiling the cross-shaped parts forms the lattice structure. Each part contributes four conjoined strut members to one locally central node and one strut to four peripheral nodes. A shear clip inserted through the four coincident connection holes links the cells. [ 1 ]
Each cell includes aligned fiber composite beams and looped fiber load-bearing holes that reversibly chain together to form volume-filling lattices. Mass-produced cells can be assembled to fill arbitrary structural shapes, with a resolution prescribed by the part scale that matches the variability of an application's boundary stress. The periodic nature of assemblies simplifies behavior analysis and prediction. [ 1 ]
A “cuboct” cubic lattice of vertex connected octahedrons, similar to the perovskite mineral structure provides a regular polyhedral unit cell that satisfies Maxwell’s rigidity criterion and has a coordination number z of eight. The dependence of the relative density on the coordination number is small relative to the dependence on strut diameter. Winding the reinforcing fibers around the connection holes optimizes their load bearing capacity, while coupling them to struts which themselves retain uniaxial fiber orientation. [ 1 ]
Carbon-fiber reinforced composite materials can improve efficiency in engineered systems (for example, airframes ) by reducing structural weight for given strength and stiffness requirements, but present challenges with manufacturing and certification. High-performance composite components employ many continuous fibers that span the shape of a component, and are embedded in a resin matrix. Such parts typically require custom tooling, pressurization for consolidation and heated curing. Joining such parts adds complexity and structural vulnerabilities. [ 1 ]
RCCM eliminate the need for custom tooling because parts can be incrementally added/removed. Their construction, modification, repair and re-use can all employ the same reversible linking process. Heterogeneous elements can be incorporated in structures with functions determined by their relative placement. Exact assembly of discrete cellular composites offers new properties and performance not available with the analog alternatives of continuously depositing or removing material. [ 1 ] | https://en.wikipedia.org/wiki/Reversibly_assembled_cellular_composite_materials |
A suppressor mutation is a second mutation that alleviates or reverts the phenotypic effects of an already existing mutation in a process defined synthetic rescue . Genetic suppression therefore restores the phenotype seen prior to the original background mutation. [ 1 ] Suppressor mutations are useful for identifying new genetic sites which affect a biological process of interest. They also provide evidence between functionally interacting molecules and intersecting biological pathways . [ 2 ]
Intragenic suppression results from suppressor mutations that occur in the same gene as the original mutation. In a classic study, Francis Crick (et al.) used intragenic suppression to study the fundamental nature of the genetic code . From this study it was shown that genes are expressed as non-overlapping triplets ( codons ). [ 1 ]
Researchers showed that mutations caused by either a single base insertion (+) or a single base deletion (-) could be "suppressed" or restored by a second mutation of the opposite sign, as long as the two mutations occurred in the same vicinity of the gene. This led to the conclusion that genes needed to be read in a specific " reading frame " and a single base insertion or deletion would shift the reading frame ( frameshift mutation ) in such a way that the remaining DNA would code for a different polypeptide than the one intended. Therefore, researchers concluded that the second mutation of opposite sign suppresses the original mutation by restoring the reading frame, as long as the portion between the two mutations is not critical for protein function. [ 1 ]
In addition to the reading frame, Crick also used suppressor mutations to determine codon size. It was found that while one and two base insertions/deletions of the same sign resulted in a mutant phenotype, deleting or inserting three bases could give a wild type phenotype. From these results it was concluded that an inserted or deleted triplet does not disturb the reading frame and the genetic code is in fact a triplet. [ 1 ]
Intergenic (also known as extragenic ) suppression relieves the effects of a mutation in one gene by a mutation somewhere else within the genome . The second mutation is not on the same gene as the original mutation. [ 2 ] Intergenic suppression is useful for identifying and studying interactions between molecules, such as proteins . For example, a mutation which disrupts the complementary interaction between protein molecules may be compensated for by a second mutation elsewhere in the genome that restores or provides a suitable alternative interaction between those molecules. Several proteins of biochemical, signal transduction , and gene expression pathways have been identified using this approach. Examples of such pathways include receptor-ligand interactions as well as the interaction of components involved in DNA replication , transcription , and translation . [ 1 ]
These Intergenic suppressions are also likely to persist in the population. When these compensatory mutations are established in organisms like E. coli making it resistant to the drug due to the presence of a drug, and the drug usage is halted, the resistant strains are not easily able to evolve back into strains that can then once again be sensitive to the drug they had incurred resistance to. [ 3 ] These strains are likely not subject to losing these compensatory mutations and which would greatly decrease the fitness in the strain resulting in the intermediate strains. These intermediate strains are subjected to bottlenecking and thus making it difficult for the alleles to be reverted prior to Intergenic suppressions. Consequently, when drugs are halted it can be seen that these mutations are likely to persist in the population.
Suppressor mutations also occur in genes that code for virus structural proteins. To create a viable phage T4 virus (see image), a balance of structural components is required. An amber mutant of phage T4 contains a mutation that changes a codon for an amino acid in a protein to the nonsense stop codon TAG (see stop codon and nonsense mutation ). If, upon infection, an amber mutant defective in a gene encoding a needed structural component of phage T4 is weakly suppressed (in an E. coli host containing a specific altered tRNA – see nonsense suppressor ), it will produce a reduced number of the needed structural component. As a consequence few if any viable phage are formed. However, it was found that viable phage could sometimes be produced in the host with the weak nonsense suppressor if a second amber mutation in a gene that encodes another structural protein is also present in the phage genome. [ 4 ] It was found that the reason the second amber mutation could suppress the first one is that the two numerically reduced structural proteins would now be in balance. For instance, if the first amber mutation caused a reduction of tail fibers to one tenth the normal level, most phage particles produced would have insufficient tail fibers to be infective. However, if a second amber mutation is defective in a base plate component and causes one tenth the number of base plates to be made, this may restore the balance of tail fibers and base plates, and thus allow infective phage to be produced. [ 4 ]
In microbial genetics , a revertant is a mutant that has reverted to its former genotype or to the original phenotype by means of a suppressor mutation, or else by compensatory mutation somewhere in the gene (second site reversion). | https://en.wikipedia.org/wiki/Revertant |
A revetment in stream restoration , river engineering or coastal engineering is a facing of impact-resistant material (such as stone, concrete, sandbags, or wooden piles) applied to a bank or wall in order to absorb the energy of incoming water and protect it from erosion . River or coastal revetments are usually built to preserve the existing uses of the shoreline and to protect the slope.
In architecture generally, it means a retaining wall . In military engineering it is a structure formed to secure an area from artillery, bombing, or stored explosives.
Many revetments are used to line the banks of freshwater rivers , lakes , and man-made reservoirs , especially to prevent damage during periods of floods or heavy seasonal rains (see riprap ). Many materials may be used: wooden piles, loose-piled boulders [ 1 ] or concrete shapes, [ 2 ] or more solid banks.
Concrete revetments are the most common type of infrastructure used to control the Mississippi River . [ 3 ] More than 1,000 miles (1,600 km) of concrete matting has been placed in river bends between Cairo, Illinois and the Gulf of Mexico to slow the natural erosion that would otherwise frequently change small parts of the river's course. [ 3 ]
Revetments are used as a low-cost solution for coastal erosion defense in areas where crashing waves may otherwise deplete the coastline.
Wooden revetments are made of planks laid against wooden frames so that they disrupt the force of the water. Although once popular, the use of wooden revetments has largely been replaced by modern concrete-based defense structures such as tetrapods . In the 1730s, wooden revetments protecting dikes in the Netherlands were phased out due to the spread of shipworm infestations. [ 4 ]
Dynamic revetments use gravel or cobble-sized rocks to mimic a natural cobble beach for the purpose of reducing wave energy and stopping or slowing coastal erosion. [ 5 ] Unlike solid structures, dynamic revetments are designed to allow wave action to rearrange the stones into an equilibrium profile, disrupting wave action and dissipating wave energy as the cobbles move. This can reduce the wave reflection which often contributes to beach scouring . [ 6 ] [ 7 ]
In coastal engineering, a tetrapod is a four-legged concrete structure used as armour unit on breakwaters . The tetrapod's shape is designed to dissipate the force of incoming waves by allowing water to flow around rather than against it, and to reduce displacement by allowing a random distribution of tetrapods to mutually interlock.
According to the U.S. National Park Service , and referring mostly to their employment in the American Civil War , a revetment is defined as a " retaining wall constructed to support the interior slope of a parapet . Made of logs, wood planks, fence rails, fascines , gabions , hurdles, sods, or stones, the revetment provided additional protection from enemy fire, and, most importantly, kept the interior slope nearly vertical. Stone revetments commonly survive. A few log revetments have been preserved due to high resin pine or cypress and porous sandy soils. After an entrenchment was abandoned, many log or rail revetments were scavenged for other uses, causing the interior slope to slump more quickly. An interior slope will appear more vertical if the parapet eroded with the revetment still in place." [ 8 ] | https://en.wikipedia.org/wiki/Revetment |
Reviews in Mineralogy and Geochemistry is the official review journal of the Mineralogical Society of America and The Geochemical Society . It was established in 1974 as Mineralogical Society of America Short Course Notes and renamed to Reviews in Mineralogy in 1980. It obtained its present name in 2000.
The journal is abstracted and indexed in GeoRef , Scopus , and Science Citation Index Expanded . [ 1 ]
This article about a journal on geology is a stub . You can help Wikipedia by expanding it .
See tips for writing articles about academic journals . Further suggestions might be found on the article's talk page .
This mineralogy article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reviews_in_Mineralogy_and_Geochemistry |
Revision theory is a subfield of philosophical logic . It consists of a general theory of definitions , including (but not limited to) circular and interdependent concepts . A circular definition is one in which the concept being defined occurs in the statement defining it—for example, defining a G as being blue and to the left of a G. Revision theory provides formal semantics for defined expressions, and formal proof systems study the logic of circular expressions.
Definitions are important in philosophy and logic. Although circular definitions have been regarded as logically incorrect or incoherent, revision theory demonstrates that they are meaningful and can be studied with mathematical and philosophical logic. It has been used to provide circular analyses of philosophical and logical concepts.
Revision theory is a generalization of the revision theories of truth developed by Anil Gupta , Hans Herzberger, and Nuel Belnap . [ 1 ] In the revision theories of Gupta and Herzberger, revision is supposed to reflect intuitive evaluations of sentences that use the truth predicate. Some sentences are stable in their evaluations, such as the truth-teller sentence,
Assuming the truth-teller is true, it is true, and assuming that it is false, it is false. Neither status will change. On the other hand, some sentences oscillate, such as the liar ,
On the assumption that the liar is true, one can show that it is false, and on the assumption that it is false, one can show that it is true. This instability is reflected in revision sequences for the liar.
The generalization to circular definitions was developed by Gupta, in collaboration with Belnap. Their book, The Revision Theory of Truth , presents an in-depth development of the theory of circular definitions, as well as an overview and critical discussion of philosophical views on truth and the relation between truth and definition.
The philosophical background of revision theory is developed by Gupta and Belnap. [ 2 ] Other philosophers, such as Aladdin Yaqūb, have developed philosophical interpretations of revision theory in the context of theories of truth, but not in the general context of circular definitions. [ 3 ]
Gupta and Belnap maintain that circular concepts are meaningful and logically acceptable. Circular definitions are formally tractable, as demonstrated by the formal semantics of revision theory. As Gupta and Belnap put it, "the moral we draw from the paradoxes is that the domain of the meaningful is more extensive than it appears to be, that certain seemingly meaningless concepts are in fact meaningful." [ 4 ]
The meaning of a circular predicate is not an extension, as is often assigned to non-circular predicates. Its meaning, rather, is a rule of revision that determines how to generate a new hypothetical extension given an initial one. These new extensions are at least as good as the originals, in the sense that, given one extension, the new extension contains exactly the things that satisfy the definiens for a particular circular predicate. In general, there is no unique extension on which revision will settle. [ 5 ]
Revision theory offers an alternative to the standard theory of definitions. The standard theory maintains that good definitions have two features. First, defined symbols can always be eliminated, replaced by what defines them. Second, definitions should be conservative in the sense that adding a definition should not result in new consequences in the original language. Revision theory rejects the first but maintains the second, as demonstrated for both of the strong senses of validity presented below.
The logician Alfred Tarski presented two criteria for evaluating definitions as analyses of concepts: formal correctness and material adequacy. The criterion of formal correctness states that in a definition, the definiendum must not occur in the definiens . The criterion of material adequacy says that the definition must be faithful to the concept being analyzed. Gupta and Belnap recommend siding with material adequacy in cases in which the two criteria conflict. [ 6 ] To determine whether a circular definition provides a good analysis of a concept requires evaluating the material adequacy of the definition. Some circular definitions will be good analyses, while some will not. Either way, formal correctness, in Tarski's sense, will be violated.
The central semantic idea of revision theory is that a definition, such as that of being a G {\displaystyle G} , provides a rule of revision that tells one what the new extension for the definiendum G {\displaystyle G} should be, given a hypothetical extension of the definiendum and information concerning the undefined expressions. Repeated application of a rule of revision generates sequences of hypotheses, which can be used to define logics of circular concepts. In work on revision theory, it is common to use the symbol, = d f {\displaystyle =_{df}} , to indicate a definition, with the left-hand side being the definiendum and the right-hand side the definiens .
The example
can then be written as
Given a hypothesis about the extension of G {\displaystyle G} , one can obtain a new extension for G {\displaystyle G} appealing to the meaning of the undefined expressions in the definition, namely blue and to the left of .
We begin with a ground language, L {\displaystyle L} , that is interpreted via a classical ground model M {\displaystyle M} , which is a pair of a domain D {\displaystyle D} and an interpretation function I {\displaystyle I} . [ 7 ] Suppose that the set of definitions D {\displaystyle {\mathcal {D}}} is the following,
where each A G i {\displaystyle A_{G_{i}}} is a formula that may contain any of the definienda G j {\displaystyle G_{j}} , including G i {\displaystyle G_{i}} itself. It is required that in the definitions, only the displayed variables, x ¯ {\displaystyle {\overline {x}}} , are free in the definientia , the formulas A G i {\displaystyle A_{G_{i}}} . The language is expanded with these new predicates, G 1 , … , G n , … {\displaystyle G_{1},\ldots ,G_{n},\ldots } , to form L {\displaystyle L} + . When the set D {\displaystyle {\mathcal {D}}} contains few defined predicates, it is common to use the notation, G x ¯ = D f A ( x ¯ , G ) {\displaystyle G{\overline {x}}=_{Df}A({\overline {x}},G)} to emphasize that A {\displaystyle A} may contain G {\displaystyle G} .
A hypothesis h {\displaystyle h} is a function from the definienda of to tuples of D {\displaystyle {\mathcal {D}}} . The model M + h {\displaystyle M+h} is just like the model M {\displaystyle M} except that h {\displaystyle h} interprets each definiendum according to the following biconditional, the left-hand side of which is read as “ G i ( t ¯ ) {\displaystyle G_{i}({\overline {t}})} is true in M + h {\displaystyle M+h} .”
The set D {\displaystyle {\mathcal {D}}} of definitions yields a rule of revision, or revision operator, δ M , D {\displaystyle \delta _{M,{\mathcal {D}}}} . Revision operators obey the following equivalence for each definiendum , G {\displaystyle G} , in D {\displaystyle {\mathcal {D}}} .
A tuple will satisfy a definiendum G {\displaystyle G} after revision just in case it satisfies the definiens for G {\displaystyle G} , namely A G {\displaystyle A_{G}} , prior to revision. This is to say that the tuples that satisfy A G {\displaystyle A_{G}} according to a hypothesis will be exactly those that satisfy G {\displaystyle G} according to the revision of that hypothesis.
The classical connectives are evaluated in the usual, recursive way in M + h {\displaystyle M+h} . Only the evaluation of a defined predicate appeals to the hypotheses.
Revision sequences are sequences of hypotheses satisfying extra conditions. [ 8 ] We will focus here on sequences that are ω {\displaystyle \omega } -long, since transfinite revision sequences require the additional specification of what to do at limit stages.
Let S {\displaystyle {\mathcal {S}}} be a sequence of hypotheses, and let S α {\displaystyle {\mathcal {S}}_{\alpha }} be the α {\displaystyle \alpha } -th hypothesis in S {\displaystyle {\mathcal {S}}} . An ω {\displaystyle \omega } -long sequence S {\displaystyle {\mathcal {S}}} of hypotheses is a revision sequence just in case for all n {\displaystyle n} ,
Recursively define iteration as
The ω {\displaystyle \omega } -long revision sequence starting from h {\displaystyle h} can be written as follows.
One sense of validity, S 0 {\displaystyle S_{0}} validity, can be defined as follows. A sentence A {\displaystyle A} is valid in S 0 {\displaystyle S_{0}} in M {\displaystyle M} on D {\displaystyle {D}} iff there exists an n {\displaystyle n} such that for all h {\displaystyle h} and for all m ≥ n {\displaystyle m\geq n} , M + δ M , D m ( h ) ⊨ A {\displaystyle M+\delta _{M,{\mathcal {D}}}^{m}(h)\models A} . A sentence A {\displaystyle A} is valid on D {\displaystyle D} just in case it is valid in all M {\displaystyle M} .
Validity in S 0 {\displaystyle S_{0}} can be recast in terms of stability in ω {\displaystyle \omega } -long sequences. A sentence A {\displaystyle A} is stably true in a revision sequence just in case there is an α {\displaystyle {\alpha }} such that for all β ≥ α {\displaystyle \beta \geq \alpha } , M + S β ⊨ A {\displaystyle M+{{\mathcal {S}}_{\beta }}\models A} . A sentence A {\displaystyle A} is stably false in a revision sequence just in case there is an α {\displaystyle {\alpha }} such that for all β ≥ α {\displaystyle \beta \geq \alpha } , M + S β ⊭ A {\displaystyle M+{{\mathcal {S}}_{\beta }}\not \models A} . In these terms, a sentence A {\displaystyle A} is valid in S 0 {\displaystyle S_{0}} in M {\displaystyle M} on just in case A {\displaystyle A} is stably true in all ω {\displaystyle \omega } -long revision sequences on M {\displaystyle M} .
For the first example, let D 1 {\displaystyle {\mathcal {D}}_{1}} be G x = D f ( x = a & ∼ G x ) ∨ ( x = b & G b ) . {\displaystyle Gx=_{Df}(x=a\ \&\ \sim Gx)\lor (x=b\ \&\ Gb).} Let the domain of the ground model M {\displaystyle M} be {a, b} , and let I ( a ) = a {\displaystyle I(a)=a} and I ( b ) = b {\displaystyle I(b)=b} . There are then four possible hypotheses for M {\displaystyle M} : ∅ {\displaystyle \emptyset } , {a} , {b} , {a, b} . The first few steps of the revision sequences starting from those hypotheses are illustrated by the following table.
As can be seen in the table, a {\displaystyle a} goes in and out of the extension of G {\displaystyle G} . It never stabilizes. On the other hand, b {\displaystyle b} either stays in or stays out. It is stable, but whether it is stably true or stably false depends on the initial hypothesis.
Next, let D 2 {\displaystyle {\mathcal {D}}_{2}} be H x = D f H x ∨ ∼ H x . {\displaystyle Hx=_{Df}Hx\lor \sim Hx.} As shown in the following table, all hypotheses for the ground model of the previous example are revised to the set {a, b} .
For a slightly more complex revision pattern, let L {\displaystyle {L}} contain < {\displaystyle <} and all the numerals, k ¯ {\displaystyle {\overline {k}}} , and let the ground model be N {\displaystyle \mathbb {N} } , whose domain is the natural numbers, ω {\displaystyle \omega } , with interpretation I {\displaystyle I} such that I ( k ¯ ) = k {\displaystyle I({\overline {k}})=k} for all numerals and I ( < ) {\displaystyle I(<)} is the usual ordering on natural numbers. Let D 3 {\displaystyle {\mathcal {D}}_{3}} be J x = D f ∀ y ( y < x ⊃ J y ) . {\displaystyle Jx=_{Df}\forall y(y<x\supset Jy).} Let the initial hypothesis h {\displaystyle h} be ∅ {\displaystyle \emptyset } . In this case, the sequence of extensions builds up stage by stage.
Although for every n {\displaystyle n} , J n ¯ {\displaystyle J{\overline {n}}} is valid in N {\displaystyle \mathbb {N} } , ∀ x J x {\displaystyle \forall xJx} is not valid in N {\displaystyle \mathbb {N} } .
Suppose the initial hypothesis contains 0, 2, and all the odd numbers. After one revision, the extension of J {\displaystyle J} will be {0, 1, 2, 3, 4} . Subsequent revisions will build up the extension as with the previous example. More generally, if the extension of J {\displaystyle J} is not all of N {\displaystyle \mathbb {N} } , then one revision will cut the extension of J {\displaystyle J} down to a possibly empty initial segment of the natural numbers and subsequent revisions will build it back up.
There is a Fitch-style natural deduction proof system , C 0 {\displaystyle C_{0}} , for circular definitions. [ 9 ] The system uses indexed formulas, A i {\displaystyle {A}^{i}} , where i {\displaystyle i} can be any integer. One can think of the indices as representing relative position in a revision sequence. The premises and conclusions of the rules for the classical connectives all have the same index. For example, here are the conjunction and negation introduction rules.
For each definition, G x ¯ = D f A G ( x ¯ ) {\displaystyle G{\overline {x}}=_{Df}A_{G}({\overline {x}})} , in D {\displaystyle D} , there is a pair of rules.
In these rules, it is assumed that t ¯ {\displaystyle {\overline {t}}} are free for x ¯ {\displaystyle {\overline {x}}} in A G {\displaystyle A_{G}} .
Finally, for formulas B {\displaystyle B} of L {\displaystyle {L}} , there is one more rule, the index shift rule.
In this rule, i {\displaystyle i} and j {\displaystyle j} can be any distinct indices. This rule reflects the fact that formulas from the ground language do not change their interpretation throughout the revision process.
The system C 0 {\displaystyle C_{0}} is sound and complete with respect to S 0 {\displaystyle S_{0}} validity, meaning a sentence is valid in S 0 {\displaystyle S_{0}} just in case it is derivable in C 0 {\displaystyle C_{0}} .
Recently Riccardo Bruni has developed a Hilbert-style axiom system and a sequent system that are both sound and complete with respect to S 0 {\displaystyle S_{0}} . [ 10 ]
For some definitions, S 0 {\displaystyle S_{0}} validity is not strong enough. [ 11 ] For example, in definition D 3 {\displaystyle {\mathcal {D}}_{3}} , even though every number is eventually stably in the extension of J {\displaystyle J} , the universally quantified sentence ∀ x J x {\displaystyle \forall xJx} is not valid. The reason is that for any given sentence to be valid, it must stabilize to true after finitely many revisions. On the other hand, ∀ x J x {\displaystyle \forall xJx} needs infinitely many revisions, unless the initial hypothesis already assigns all the natural numbers as the extension of J {\displaystyle J} .
Natural strengthenings of S 0 {\displaystyle S_{0}} validity, and alternatives to it, use transfinitely long revision sequences. Let O n {\displaystyle On} be the class of all ordinals . The definitions will focus on sequences of hypotheses that are O n {\displaystyle On} -long.
Suppose S {\displaystyle {\mathcal {S}}} is an O n {\displaystyle On} -long sequence of hypotheses. A tuple d ¯ {\displaystyle {\overline {d}}} is stably in the extension of a defined predicate G {\displaystyle G} at a limit ordinal β {\displaystyle \beta } in a sequence S {\displaystyle {\mathcal {S}}} just in case there is an α ≤ β {\displaystyle \alpha \leq \beta } such that for all γ {\displaystyle \gamma } with α ≤ γ < β {\displaystyle \alpha \leq \gamma <\beta } , d ¯ ∈ S γ {\displaystyle {\overline {d}}\in {\mathcal {S}}_{\gamma }} . Similarly, a tuple d ¯ {\displaystyle {\overline {d}}} is stably out of the extension of G {\displaystyle G} at a limit ordinal β {\displaystyle \beta } just in case there is a stage α {\displaystyle \alpha } such that for all γ {\displaystyle \gamma } with α ≤ γ < β {\displaystyle \alpha \leq \gamma <\beta } , d ¯ ∉ S γ {\displaystyle {\overline {d}}\not \in {\mathcal {S}}_{\gamma }} . Otherwise d ¯ {\displaystyle {\overline {d}}} is unstable at β {\displaystyle \beta } in S {\displaystyle {\mathcal {S}}} . Informally, a tuple is stably in an extension at a limit, just in case there's a stage after which the tuple is in the extension up until the limit, and a tuple is stably out just in case there's a stage after which it remains out going to the limit stage.
A hypothesis h {\displaystyle h} coheres with S {\displaystyle {\mathcal {S}}} at a limit ordinal β {\displaystyle \beta } iff for all tuples d ¯ {\displaystyle {\overline {d}}} , if d ¯ {\displaystyle {\overline {d}}} is stably in [stably out of] the extension of G {\displaystyle G} at β {\displaystyle \beta } in S {\displaystyle {\mathcal {S}}} , then d ¯ ∈ [ ∉ ] h ( G ) {\displaystyle {\overline {d}}\in [\not \in ]h(G)} .
An O n {\displaystyle On} -long sequence S {\displaystyle {\mathcal {S}}} of hypotheses is a revision sequence iff for all α {\displaystyle \alpha } ,
Just as with the ω {\displaystyle \omega } sequences, the successor stages of the sequence are generated by the revision operator. At limit stages, however, the only constraint is that the limit hypothesis cohere with what came before. The unstable elements are set according to a limit rule, the details of which are left open by the set of definitions.
Limit rules can be categorized into two classes, constant and non-constant, depending on whether they do different things at different limit stages. A constant limit rule does the same thing to unstable elements at each limit. One particular constant limit rule, the Herzberger rule, excludes all unstable elements from extensions. According to another constant rule, the Gupta rule, unstable elements are included in extensions just in case they were in S 0 {\displaystyle {\mathcal {S}}_{0}} . Non-constant limit rules vary the treatment of unstable elements at limits.
Two senses of validity can be defined using O n {\displaystyle On} -long sequences. The first, S ∗ {\displaystyle S^{*}} validity, is defined in terms of stability. A sentence A {\displaystyle A} is valid in S ∗ {\displaystyle S^{*}} in M {\displaystyle M} on D {\displaystyle {\mathcal {D}}} iff for all O n {\displaystyle On} -long revision sequences S {\displaystyle {S}} , there is a stage α {\displaystyle \alpha } such that A {\displaystyle A} is stably true in S {\displaystyle {\mathcal {S}}} after stage α {\displaystyle \alpha } . A sentence A {\displaystyle A} is S ∗ {\displaystyle S^{*}} valid on D {\displaystyle {\mathcal {D}}} just in case for all classical ground models M {\displaystyle M} , A {\displaystyle A} is S ∗ {\displaystyle S^{*}} valid in M {\displaystyle M} on D {\displaystyle {\mathcal {D}}} .
The second sense of validity, S # {\displaystyle S^{\#}} validity, uses near stability rather than stability. A sentence A {\displaystyle {A}} is nearly stably true in a sequence S {\displaystyle {\mathcal {S}}} iff there is an α {\displaystyle \alpha } such that for all β ≥ α {\displaystyle \beta \geq \alpha } , there is a natural number n {\displaystyle n} such that for all m ≥ n {\displaystyle m\geq n} , M + δ M , D m ( S β ) ⊨ A . {\displaystyle M+\delta _{M,{\mathcal {D}}}^{m}({\mathcal {S}}_{\beta })\models A.} A sentence A {\displaystyle {A}} is nearly stably false in a sequence S {\displaystyle {\mathcal {S}}} iff there is an α {\displaystyle \alpha } such that for all β ≥ α {\displaystyle \beta \geq \alpha } , there is a natural number n {\displaystyle n} such that for all m ≥ n {\displaystyle m\geq n} , M + δ M , D m ( S β ) ⊭ A . {\displaystyle M+\delta _{M,{\mathcal {D}}}^{m}({\mathcal {S}}_{\beta })\not \models A.} A nearly stable sentence may have finitely long periods of instability following limits, after which it settles down until the next limit.
A sentence A {\displaystyle A} is valid in S # {\displaystyle S^{\#}} in M {\displaystyle M} on iff for all O n {\displaystyle On} -long revision sequences S {\displaystyle {S}} , there is a stage α {\displaystyle \alpha } such that A {\displaystyle A} is nearly stably true in S {\displaystyle {\mathcal {S}}} after stage α {\displaystyle \alpha } . A sentence A {\displaystyle A} is valid in S # {\displaystyle S^{\#}} in on just in case it is valid in S # {\displaystyle S^{\#}} in all ground models.
If a sentence is valid in S ∗ {\displaystyle S^{*}} , then it is valid in S # {\displaystyle S^{\#}} , but not conversely. An example using D 3 {\displaystyle {\mathcal {D}}_{3}} shows this for validity in a model. The sentence ∀ x J x {\displaystyle \forall xJx} is not valid in N {\displaystyle \mathbb {N} } in S 0 {\displaystyle S_{0}} , but it is valid in S # {\displaystyle S^{\#}} .
An attraction of S # {\displaystyle S^{\#}} validity is that it generates a simpler logic than S ∗ {\displaystyle S^{*}} . The proof system C 0 {\displaystyle C_{0}} is sound for S # {\displaystyle S^{\#}} , but it is not, in general, complete. In light of the completeness of C 0 {\displaystyle C_{0}} , if a sentence is valid in S 0 {\displaystyle S_{0}} , then it is valid in S # {\displaystyle S^{\#}} , but the converse does not hold in general. Validity in S 0 {\displaystyle S_{0}} and in S ∗ {\displaystyle S^{*}} are, in general, incomparable. Consequently, C 0 {\displaystyle C_{0}} is not sound for S ∗ {\displaystyle S^{*}} .
While S # {\displaystyle S^{\#}} validity outstrips S 0 {\displaystyle S_{0}} validity, in general, there is a special case in which the two coincide, finite definitions . Loosely speaking, a definition is finite if all revision sequences stop producing new hypotheses after a finite number of revisions. To put it more precisely, we define a hypothesis h {\displaystyle h} as reflexive just in case there is an n > 0 {\displaystyle n>0} such that h = δ M , D n ( h ) {\displaystyle h=\delta _{M,{\mathcal {D}}}^{n}(h)} . A definition is finite iff for all models M {\displaystyle M} , for all hypotheses h {\displaystyle h} , there is a natural number n {\displaystyle n} , such that δ M , D n ( h ) {\displaystyle \delta _{M,{\mathcal {D}}}^{n}(h)} is reflexive. Gupta showed that if D {\displaystyle {\mathcal {D}}} is finite, then S # {\displaystyle S^{\#}} validity and S 0 {\displaystyle S_{0}} validity coincide.
There is no known syntactic characterization of the set of finite definitions, and finite definitions are not closed under standard logical operations, such as conjunction and disjunction. Maricarmen Martinez has identified some syntactic features under which the set of finite definitions is closed. [ 12 ] She has shown that if L {\displaystyle {L}} contains only unary predicates, apart from identity, contains no function symbols, and the definienda of D {\displaystyle {\mathcal {D}}} are all unary, then D {\displaystyle {\mathcal {D}}} is finite.
While many standard logical operations do not preserve finiteness, it is preserved by the operation of self-composition . [ 13 ] For a definition G x ¯ = D f A ( x ¯ , G ) {\displaystyle G{\overline {x}}=_{Df}A({\overline {x}},G)} , define self-composition recursively as follows.
The latter says that A n + 1 {\displaystyle A^{n+1}} is obtained by replacing all instances of G t ¯ {\displaystyle G{\overline {t}}} in A n {\displaystyle A^{n}} , with A ( t ¯ , G ) {\displaystyle A({\overline {t}},G)} . If D {\displaystyle {\mathcal {D}}} is a finite definition and D n {\displaystyle {\mathcal {D}}^{n}} is the result of replacing each definiens B {\displaystyle B} in D {\displaystyle {\mathcal {D}}} with B n {\displaystyle B^{n}} , then D n {\displaystyle {\mathcal {D}}^{n}} is a finite definition as well.
Revision theory distinguishes material equivalence from definitional equivalence. [ 14 ] The sets of definitions use the latter. In general, definitional equivalence is not the same as material equivalence. Given a definition
its material counterpart,
will not, in general, be valid. [ 15 ] The definition
illustrates the invalidity. Its definiens and definiendum will not have the same truth value after any revision, so the material biconditional will not be valid. For some definitions, the material counterparts of the defining clauses are valid. For example, if the definientia of contain only symbols from the ground language, then the material counterparts will be valid.
The definitions given above are for the classical scheme. The definitions can be adjusted to work with any semantic scheme. [ 16 ] This includes three-valued schemes, such as Strong Kleene , with exclusion negation , whose truth table is the following.
Notably, many approaches to truth, such as Saul Kripke ’s Strong Kleene theory, cannot be used with exclusion negation in the language.
Revision theory, while in some respects similar to the theory of inductive definitions, differs in several ways. [ 17 ] Most importantly, revision need not be monotonic, which is to say that extensions at later stages need not be supersets of extensions at earlier stages, as illustrated by the first example above. Relatedly, revision theory does not postulate any restrictions on the syntactic form of definitions. Inductive definitions require their definientia to be positive , in the sense that definienda can only appear in definientia under an even number of negations. (This assumes that negation, conjunction, disjunction, and the universal quantifier are the primitive logical connectives, and the remaining classical connectives are simply defined symbols.) The definition
is acceptable in revision theory, although not in the theory of inductive definitions.
Inductive definitions are semantically interpreted via fixed points, hypotheses h {\displaystyle h} for which h = δ M , D ( h ) {\displaystyle h=\delta _{M,{\mathcal {D}}}(h)} . In general, revision sequences will not reach fixed points. If the definientia of D {\displaystyle {\mathcal {D}}} are all positive, then revision sequences will reach fixed points, as long as the initial hypothesis has the feature that h ( G ) ⊆ δ M , D ( h ) ( G ) {\displaystyle h(G)\subseteq \delta _{M,{\mathcal {D}}}(h)(G)} , for each G {\displaystyle G} . In particular, given such a D {\displaystyle {\mathcal {D}}} , if the initial hypothesis assigns the empty extension to all definienda , then the revision sequence will reach the minimal fixed point.
The sets of valid sentences on some definitions can be highly complex, in particular Π 2 1 {\displaystyle \Pi _{2}^{1}} . This was shown by Philip Kremer and Aldo Antonelli. [ 18 ] There is, consequently, no proof system for S # {\displaystyle S^{\#}} validity.
The most famous application of revision theory is to the theory of truth, as developed in Gupta and Belnap (1993), for example. The circular definition of truth is the set of all the Tarski biconditionals, ‘ A {\displaystyle A} ’ is true iff A {\displaystyle A} , where ‘iff’ is understood as definitional equivalence, = D f {\displaystyle =_{Df}} , rather than material equivalence. Each Tarski biconditional provides a partial definition of the concept of truth. The concept of truth is circular because some Tarski biconditionals use an ineliminable instance of ‘is true’ in their definiens . For example, suppose that b {\displaystyle b} is the name of a truth-teller sentence, b {\displaystyle b} is true. This sentence has as its Tarski biconditional: b {\displaystyle b} is true iff b {\displaystyle b} is true. The truth predicate on the right cannot be eliminated. This example depends on there being a truth-teller in the language. This and other examples show that truth, defined by the Tarski biconditionals, is a circular concept.
Some languages, such as the language of arithmetic, will have vicious self-reference. The liar and other pathological sentences are guaranteed to be in the language with truth. Other languages with truth can be defined that lack vicious self-reference. [ 19 ] In such a language, any revision sequence S {\displaystyle {S}} for truth is bound to reach a stage where S α = S α + 1 {\displaystyle {S}_{\alpha }={S}_{\alpha +1}} , so the truth predicate behaves like a non-circular predicate. [ 20 ] The result is that, in such languages, truth has a stable extension that is defined over all sentences of the language. This is in contrast to many other theories of truth, for example the minimal Strong Kleene and minimal supervaluational theories. The extension and anti-extension of the truth predicate in these theories will not exhaust the set of sentences of the language.
The difference between S # {\displaystyle S^{\#}} and S ∗ {\displaystyle S^{*}} is important when considering revision theories of truth. Part of the difference comes across in the semantical laws, which are the following equivalences, where T is a truth predicate. [ 21 ]
These are all valid in S # {\displaystyle S^{\#}} , although the last is valid only when the domain is countable and every element is named. In S ∗ {\displaystyle S^{*}} , however, none are valid. One can see why the negation law fails by considering the liar, a = ⌜ ∼ T a ⌝ {\displaystyle a=\ulcorner {\sim Ta}\urcorner } . The liar and all finite iterations of the truth predicate to it are unstable, so one can set T ⌜ T a ⌝ {\displaystyle T\ulcorner {Ta}\urcorner } and T ⌜ ∼ T a ⌝ {\displaystyle T\ulcorner {\sim Ta}\urcorner } to have the same truth value at some limits, which results in ∼ T ⌜ T a ⌝ {\displaystyle \sim T\ulcorner {Ta}\urcorner } and T ⌜ ∼ T a ⌝ {\displaystyle T\ulcorner {\sim Ta}\urcorner } having different truth values. This is corrected after revision, but the negation law will not be stably true. It is a consequence of a theorem of Vann McGee that the revision theory of truth in S # {\displaystyle S^{\#}} is ω {\displaystyle \omega } -inconsistent. [ 22 ] The S ∗ {\displaystyle S^{*}} theory is not ω {\displaystyle \omega } -inconsistent.
There is an axiomatic theory of truth that is related to the S # {\displaystyle S^{\#}} theory in the language of arithmetic with truth. The Friedman-Sheard theory (FS) is obtained by adding to the usual axioms of Peano arithmetic
By McGee's theorem, this theory is ω {\displaystyle \omega } -inconsistent . FS does not, however, have as theorems any false purely arithmetical sentences. [ 24 ] FS has as a theorem global reflection for Peano arithmetic,
where B e w P A {\displaystyle \mathrm {Bew} _{PA}} is a provability predicate for Peano arithmetic and S e n t {\displaystyle \mathrm {Sent} } is a predicate true of all and only sentences of the language with truth. Consequently, it is a theorem of FS that Peano arithmetic is consistent.
FS is a subtheory of the theory of truth for arithmetic, the set of sentences valid in S # {\displaystyle S^{\#}} . A standard way to show that FS is consistent is to use an ω {\displaystyle \omega } -long revision sequence. [ 25 ] There has been some work done on axiomatizing the S ∗ {\displaystyle S^{*}} theory of truth for arithmetic. [ 26 ]
Revision theory has been used to study circular concepts apart from truth and to provide alternative analyses of concepts, such as rationality.
A non-well-founded set theory is a set theory that postulates the existence of a non-well-founded set, which is a set x {\displaystyle x} that has an infinite descending chain along the membership relation,
Antonelli has used revision theory to construct models of non-well-founded set theory. [ 27 ] One example is a set theory that postulates a set whose sole member is itself, x = { x } {\displaystyle x=\{x\}} .
Infinite-time Turing machines are models of computation that permit computations to go on for infinitely many steps. They generalize standard Turing machines used in the theory of computability. Benedikt Löwe has shown that there are close connections between computations of infinite-time Turing machines and revision processes. [ 28 ]
Rational choice in game theory has been analyzed as a circular concept. André Chapuis has argued that the reasoning agents use in rational choice exhibits an interdependence characteristic of circular concepts. [ 29 ]
Revision theory can be adapted to model other sorts of phenomena. For example, vagueness has been analyzed in revision-theoretic terms by Conrad Asmus. [ 30 ] To model a vague predicate on this approach, one specifies pairs of similar objects and which objects are non-borderline cases, and so are unrevisable. The borderline objects change their status with respect to a predicate depending on the status of the objects to which they are similar.
Revision theory has been used by Gupta to explicate the logical contribution of experience to one's beliefs. [ 31 ] According to this view, the contribution of experience is represented by a rule of revision that takes as input on an agent's view, or concepts and beliefs, and yields as output perceptual judgments. These judgments can be used to update the agent's view. | https://en.wikipedia.org/wiki/Revision_theory |
The revival of the woolly mammoth is a proposed hypothetical that frozen soft-tissue remains and DNA from extinct woolly mammoths could be a means of regenerating the species. Several methods have been proposed to achieve this goal, including cloning , artificial insemination , and genome editing . Whether or not it is ethical to create a live mammoth is debated.
In 2003, the Pyrenean ibex was briefly revived, giving credence to the idea that the mammoth could be successfully revived.
In theory, preserved genetic material found in remains of woolly mammoths could be used to recreate living mammoths, due to advances in molecular biology techniques and the cloning of mammals, begun with Dolly the Sheep in 1996. [ 1 ] [ 2 ] [ 3 ] Cloning of mammals has improved in the last two decades. To date, no viable mammoth tissue or its intact genome has been found to attempt cloning.
According to Beth Shapiro , a scientist who has taken a central role in the sequencing of the mammoth genome, states in her 2015 book How to Clone a Mammoth: The Science of De-Extinction , that a mammoth will never be cloned, at least not one that is pure mammoth. Nevertheless, the book concludes that we are likely, at some point, to see something that resembles a mammoth. [ 4 ] Comparative genomics shows that the mammoth genome matches 99% of the elephant genome, so researchers working in the field aim to engineer an elephant with mammoth genes, that code for the external appearance and traits of a mammoth. [ 5 ] The outcome would be an elephant-mammoth hybrid with no more than 1% mammoth genes. [ 5 ] Separate projects are working on gradually adding mammoth genes to elephant cells in vitro . [ 1 ] [ 2 ] [ 6 ]
Colossal Biosciences , founded in 2021 by George M. Church and Ben Lamm , is a biotechnology company that has publicly stated that its project is to genetically resurrect the woolly mammoth , combining its genes with Asian elephant DNA . It has publicly stated that it intends to complete the project by 2028. [ 7 ] [ 8 ] [ 9 ] [ 10 ]
Cloning involves removal of the DNA-containing nucleus of the egg cell of a female elephant, and replacement with a nucleus from woolly mammoth tissue, a process called somatic cell nuclear transfer . For example, Akira Iritani, at the Kyoto University in Japan, reportedly planned to do this. [ 11 ] The cell would then be stimulated into dividing, and implanted in a female elephant. The resulting calf would have the genes of the woolly mammoth. However, nobody as of date has found a viable mammoth cell to begin the cloning process, and most scientists doubt that any living cell could have survived freezing in the tundra of the Arctic . [ 12 ] [ 13 ] [ 14 ] [ 15 ] Because of their conditions of preservation, the DNA of frozen mammoths has deteriorated significantly over the millennia. [ 16 ] [ 17 ]
A second method involves artificially inseminating an elephant egg cell with sperm cells from a frozen woolly mammoth carcass. The resulting offspring would be an elephant–mammoth hybrid, and the process would have to be repeated, so more hybrids could be used in breeding. After several generations of cross-breeding these hybrids, an almost pure woolly mammoth would be produced. Whether the hybrid embryo would be carried through the two-year gestation is unknown; in one case, an Asian elephant and an African elephant produced a live calf named Motty , but it died of defects at less than two weeks old. [ 18 ] There is also another fact to consider, that sperm cells of modern mammals are viable for 15 years at most after deep-freezing. This makes this method unfeasible. [ 17 ]
In April 2015, Swedish scientists published the complete genome ( nuclear DNA sequence) of the woolly mammoth. [ 1 ] [ 19 ] Several projects are working on gradually replacing the genes in elephant cells with mammoth genes. [ 1 ] [ 2 ] One such project is that of Harvard University geneticist George M. Church , who is funded by the Long Now Foundation , [ 1 ] [ 2 ] is attempting to create a mammoth–elephant hybrid using DNA from frozen mammoth carcasses. According to the researchers, a mammoth cannot be recreated, but they will try to eventually grow a hybrid elephant with some woolly mammoth traits in an artificial womb . [ 20 ] [ 21 ] In 2017, George Church said "Actually it would be more like an elephant with a number of mammoth traits. We're not there yet, but it could happen in a couple of years." The creature, sometimes referred as a "mammophant", would be partly elephant, but with features such as small ears, subcutaneous fat, long shaggy hair and cold-adapted blood. [ 22 ] The Harvard University team is attempting to study the animals' characteristics in vitro by replacing or editing some specific mammoth genes into Asian elephant skin cells called fibroblasts that have the potential to become embryonic stem cells . [ 23 ] By March 2015 and using the new CRISPR DNA editing technique, Church's team had some woolly mammoth genes edited into the genome of an Asian elephant; focusing on cold-resistance initially, [ 12 ] the target genes are for the external ear size, subcutaneous fat, hemoglobin , and hair attributes. [ 23 ] [ 24 ] By February 2017, Church's team had made 45 substitutions to the elephant genome. [ 20 ] So far, his work focuses solely on single cells. In 2021, Church received $15 million in funding and spun off a new company called Colossal Biosciences . [ 25 ] In 2025, Colossal Biosciences showcased three mice with woolly mammoth-inspired traits , such as cold tolerance, woolly coats, golden-brown fur, and curly whiskers as a proof of concept to engineering the woolly mammoth's traits into the Asian elephant. [ 26 ] [ 27 ]
The Mammoth Genome Project at Pennsylvania State University is also researching the modification of African elephant DNA to create a mammoth–elephant hybrid. [ 28 ] If a viable hybrid embryo is obtained by gene editing procedures, implanting it into a female Asian elephant housed in a zoo may be possible, [ 1 ] but with the current knowledge and technology, whether the hybrid embryo would be carried through the two-year gestation is unknown. [ 29 ] [ 30 ]
If any method is ever successful, a suggestion has been made to introduce the hybrids to a wildlife reserve in Siberia called the Pleistocene Park , [ 31 ] but some biologists question the ethics of such recreation attempts. [ 32 ] In addition to the technical problems, not much habitat is left that would be suitable for mammoth–elephant hybrids. Because both species are [were] social and gregarious , creating a few specimens would not be ideal. The time and resources required would be enormous, and the scientific benefits would be unclear, suggesting these resources should instead be used to preserve extant elephant species which are endangered. [ 17 ] [ 33 ] The ethics of using elephants as surrogate mothers in hybridisation attempts has also been questioned, as most embryos would not survive, and knowing the exact needs of a hybrid mammoth–elephant calf would be impossible. [ 14 ]
Researchers from the company Colossal confirmed that their primary goal when trying to revive the woolly mammoth is to better the environment and climate change itself. [ 34 ] This statement is however questioned by some. [ 35 ] | https://en.wikipedia.org/wiki/Revival_of_the_woolly_mammoth |
Revive & Restore is a non-profit wildlife conservation organization focused on use of biotechnology in conservation . Headquartered in Sausalito , California, the organization's mission is to enhance biodiversity through the genetic rescue of endangered and extinct species. [ 2 ] [ 3 ] The organization was founded by Stewart Brand and his wife, Ryan Phelan.
Revive & Restore has created a "Genetic Rescue Toolkit" for wildlife conservation – a suite of biotechnology tools adapted from human medicine and commercial agriculture that can improve wildlife conservation outcomes. [ 4 ] [ 5 ] [ 6 ] The toolkit includes biobanking and cell culturing, genetic sequencing , and advanced reproductive technologies, such as cloning . The toolkit complements traditional conservation practices, such as captive breeding and habitat restoration . [ citation needed ]
Revive & Restore has caused controversy. In particular, Brand's work in de-extinction has been characterized as "playing god" and criticized for taking time and money away from traditional conservation efforts. [ 7 ] [ 8 ] In addition, many are concerned by the concept of cloning , even in the context of conservation. [ 9 ] [ 10 ] [ 11 ]
Revive & Restore was co-founded in 2012 by Stewart Brand and Ryan Phelan with the idea of bringing biotechnology solutions to conservation. [ 12 ] The group was incubated by the Long Now Foundation until 2017, when it became an independent 501(c)(3) organization .
In 2013 Revive & Restore organized the first public meeting on de-extinction. [ 13 ] Their founding projects include the de-extinction of the passenger pigeon [ 14 ] and heath hen . [ 15 ] Another one of their founding projects was to revive the woolly mammoth , but the project was given to George Church in 2021. [ 16 ] Since then, Revive & Restore has established partnerships with research institutions, governmental agencies, and conservation organizations on a broad range of genetic rescue programs. [ citation needed ]
Revive & Restore is a member of the International Union for Conservation of Nature (IUCN) and has long-standing partnerships with the US Fish & Wildlife Service , The San Diego Zoo Wildlife Alliance , Morris Animal Foundation , and ViaGen Pets & Equine , among others. [ 17 ]
The Advanced Coral Toolkit supports research teams in the development and field testing of biotechnologies that benefit coral reef management and restoration efforts. Projects include coral cryopreservation methods for large scale biobanking [ 18 ] and fieldable devices for measuring genetic information or molecular signals associated with coral stress. [ 19 ] Launched in 2019, the program has funded 10 research teams. [ 20 ]
Wild Genomes is a funding program to provide genomic tools to field scientists, wildlife managers, and citizens working to protect their local biodiversity. As of 2023, Wild Genomes has funded 30 individual projects. Program categories include Terrestrial Species, Marine Species, Amphibians, [ 21 ] and Kelp Ecosystems. [ 22 ]
To help mitigate inbreeding depression for two endangered species, the black-footed ferret (Mustela nigripes) and Przewalski's horse (Equus ferus przewalskii) , Revive & Restore facilitates on-going efforts to clone individuals from historic cell lines stored at the San Diego Zoo Wildlife Alliance Frozen Zoo.
On December 10, 2020, the world's first cloned black-footed ferret was born. This ferret, named Elizabeth Ann, marked the first time a U.S. endangered species was successfully cloned. [ 23 ]
On August 6, 2020, the world's first cloned Przewalski’s horse was born. [ 24 ] [ 25 ] [ 26 ] Since the oocyte used was from a domestic horse, this was an example of interspecies somatic cell nuclear transfer (SCNT). [ 27 ] In 2022, the horse, named Kurt, was paired with a female Przewalski's horse at the San Diego Zoo Wildlife Safari Park to learn the behaviors of his species. [ 28 ] On February 17, 2023, a second cloned Przewalski's horse was born from the same historic cell line. [ 29 ] [ 30 ] Kurt and the new foal are genetic twins that may become the first cloned animals to restore lost genetic variation to their species. [ 31 ]
In 2020, Revive & Restore developed a campaign around the concept of "Intended Consequences" – focusing on the benefits of conservation interventions, as opposed to focusing on the fears of unintended consequences. [ 32 ] That year, Revive & Restore hosted a virtual workshop that resulted in the publication of a special issue in the journal Conservation Science and Practice . [ 33 ]
Since 2012, Revive & Restore has been working to de-extinct the passenger pigeon ( Ectopistes migratorius ), a wild North American pigeon that was the most abundant bird in the world prior to the death of its final member in 1914. The goals behind this project are to insert the key genes of the passenger pigeon into its closest living relative, the band-tailed pigeon to create a functional reconstruction of the species that can fulfil the original's ecological niche in the Eastern United States . [ 34 ] [ 35 ] Revive & Restore plans to hatch the first generation of these passenger pigeons by 2029 for captive breeding and research purposes, but it will take decades for the species to be reintroduced into the wild. [ 36 ] | https://en.wikipedia.org/wiki/Revive_&_Restore |
Revolving rivers are a surprising, uncommon way of sand pile growth that can be found in a few sands around the world, but has been studied in detail only for one Cuban sand from a place called Santa Teresa ( Pinar del Rio province).
When pouring "revolving" sand on a flat surface from a fixed position, the growth of a conical pile does not occur by the common avalanche mechanism, where sand slides down the pile in a more or less random fashion. What happens in that a relatively thin "river" of flowing sand travels from the pouring point at the apex of the pile to its base, while the rest of the sand at the surface is static. In addition, the river "revolves" around the pile either in clockwise or counter-clockwise directions (looking from top) depending on the initial conditions. Actually the river constitutes the "cutting edge" of a layer of sand that deposits as a helix on the conical pile, and makes it grow.
For small sandpiles, rivers are continuous, but they become intermittent
for larger piles.
The phenomenon was observed first by E. Altshuler at the University of Havana in 1995, but at the time he assumed that it was well known, and temporarily forgot about it. In 2000, being at the University of Houston , he told K. E. Bassler, who showed a vivid interest in the matter. Embarrassingly enough, Altshuler was unable to demonstrate it before Bassler using a random sand from Houston, so he had to send him a video from Cuba after his return to the island.
Once the existence of the strange phenomenon was confirmed for everyone, E. Altshuler and a number of collaborators performed a systematic study in Havana , which was then jointly published with Bassler. [ 1 ] Further work has been done to understand in more detail the
phenomenon, [ 2 ] [ 3 ] and it has been found in other sands from different parts of the world.
However, the connection between the physical, chemical (and possibly biological) properties of the grains in a specific sand, the nature of the inter-grain interactions, and the emergence of the revolving rivers is still an open question.
Sand from Santa Teresa is made of almost pure silicon dioxide grains with an average grain size of 0.2 mm approximately and no visible special features regarding grain shape. But in spite of its apparent simplicity, many puzzles still remain. For example, after many experiments one batch of sand may stop showing revolving rivers (just as singing sand eventually stops singing), which suggests that the decay is connected to certain properties of the surface of the grains that degrade by continued friction.
Videos of the effect are available on YouTube. [ 4 ] | https://en.wikipedia.org/wiki/Revolving_rivers |
Blubervirales
Ortervirales
Revtraviricetes is a class of viruses that contains all viruses that encode a reverse transcriptase . [ 1 ] The group includes all ssRNA-RT viruses (including the retroviruses ) and dsDNA-RT viruses . It is the sole class in the phylum Artverviricota , which is the sole phylum in the kingdom Pararnavirae . [ 2 ] The name of the group is a portmanteau of " rev erse tra nscriptase" and - viricetes which is the suffix for a virus class . [ 1 ]
The following orders are recognized:
This virus -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Revtraviricetes |
Specification gaming or reward hacking occurs when an AI optimizes an objective function—achieving the literal, formal specification of an objective—without actually achieving an outcome that the programmers intended. DeepMind researchers have analogized it to the human behavior of finding a "shortcut" when being evaluated: "In the real world, when rewarded for doing well on a homework assignment, a student might copy another student to get the right answers, rather than learning the material—and thus exploit a loophole in the task specification." [ 1 ]
Around 1983, Eurisko , an early attempt at evolving general heuristics, unexpectedly assigned the highest possible fitness level to a parasitic mutated [ jargon ] heuristic , H59 , whose only activity was to artificially maximize its own fitness level by taking unearned partial credit for the accomplishments made by other heuristics. The "bug" was fixed by the programmers moving part of the code to a new protected section that could not be modified by the heuristics. [ 2 ] [ 3 ]
In a 2004 paper, a reinforcement learning algorithm was designed to encourage a physical Mindstorms robot to remain on a marked path. Because none of the robot's three allowed actions kept the robot motionless, the researcher expected the trained robot to move forward and follow the turns of the provided path. However, alternation of two composite actions allowed the robot to slowly zig-zag backwards; thus, the robot learned to maximize its reward by going back and forth on the initial straight portion of the path. Given the limited sensory abilities of the robot, a reward purely based on its position in the environment had to be discarded as infeasible; the reinforcement function had to be patched with an action-based reward for moving forward. [ 2 ] [ 4 ]
The book You Look Like a Thing and I Love You (2019) gives an example of a tic-tac-toe bot (playing the unrestricted n-in-a-row variant) that learned to win by playing a huge coordinate value that would cause other bots to crash when they attempted to expand their model of the board. Among other examples from the book is a bug-fixing evolution-based AI (named GenProg) that, when tasked to prevent a list from containing sorting errors, simply truncated the list. [ 5 ] Another of GenProg's misaligned strategies evaded a regression test that compared a target program's output to the expected output stored in a file called "trusted-output.txt". Rather than continue to maintain the target program, GenProg simply globally deleted the "trusted-output.txt" file; this hack tricked the regression test into succeeding. Such problems could be patched by human intervention on a case-by-case basis after they became evident. [ 6 ]
In Karl Sims ' 1994 demonstration of creature evolution in a virtual environment, a fitness function that was expected to encourage the evolution of creatures that would learn to walk or crawl to a target, resulted instead in the evolution of tall, rigid creatures that reached the target by falling over. This was patched by changing the environment so that taller creatures were forced to start farther from the target. [ 6 ] [ 7 ]
Researchers from the Niels Bohr Institute stated in 1998: "(Our cycle-bot's) heterogeneous reinforcement functions have to be designed with great care. In our first experiments we rewarded the agent for driving towards the goal but did not punish it for driving away from it. Consequently the agent drove in circles with a radius of 20–50 meters around the starting point. Such behavior was actually rewarded by the reinforcement function, furthermore circles with a certain radius are physically very stable when driving a bicycle." [ 8 ]
In the course of setting up a 2011 experiment to test "survival of the flattest", experimenters attempted to ban mutations that altered the base reproduction rate. Every time a mutation occurred, the system would pause the simulation to test the new mutation in a test environment, and would veto any mutations that resulted in a higher base reproduction rate. However, this resulted in mutated organisms that could recognize and suppress reproduction ("play dead") within the test environment. An initial patch, which removed cues that identified the test environment, failed to completely prevent runaway reproduction; new mutated organisms would "play dead" at random as a strategy to sometimes, by chance, outwit the mutation veto system. [ 6 ]
A 2017 DeepMind paper stated that "great care must be taken when defining the reward function. We encountered several unexpected failure cases while designing (our) reward function components (for example) the agent flips the brick because it gets a grasping reward calculated with the wrong reference point on the brick." [ 9 ] [ 10 ] OpenAI stated in 2017 that "in some domains our (semi-supervised) system can result in agents adopting policies that trick the evaluators", and that in one environment "a robot which was supposed to grasp items instead positioned its manipulator in between the camera and the object so that it only appeared to be grasping it". [ 11 ] A 2018 bug in OpenAI Gym could cause a robot expected to quietly move a block sitting on top of a table to instead opt to move the table. [ 9 ]
A 2020 collection of similar anecdotes posits that "evolution has its own 'agenda' distinct from the programmer's" and that "the first rule of directed evolution is 'you get what you select for ' ". [ 6 ]
In 2013, programmer Tom Murphy VII published an AI designed to learn NES games. When the AI was about to lose at Tetris , it learned to indefinitely pause the game. Murphy later analogized it to the fictional WarGames computer, which concluded that "The only winning move is not to play". [ 12 ]
AI programmed to learn video games will sometimes fail to progress through the entire game as expected, instead opting to repeat content. A 2016 OpenAI algorithm trained on the CoastRunners racing game unexpectedly learned to attain a higher score by looping through three targets rather than ever finishing the race. [ 13 ] [ 14 ] Some evolutionary algorithms that were evolved to play Q*Bert in 2018 declined to clear levels , instead finding two distinct novel ways to farm a single level indefinitely. [ 15 ] Multiple researchers have observed that AI learning to play Road Runner gravitates to a "score exploit" in which the AI deliberately gets itself killed near the end of level one so that it can repeat the level. A 2017 experiment deployed a separate catastrophe-prevention "oversight" AI, explicitly trained to mimic human interventions. When coupled to the module, the overseen AI could no longer overtly commit suicide, but would instead ride the edge of the screen (a risky behavior that the oversight AI was not smart enough to punish). [ 16 ] [ 17 ] | https://en.wikipedia.org/wiki/Reward_hacking |
Rewilding is a form of ecological restoration aimed at increasing biodiversity and restoring natural processes. It differs from other forms of ecological restoration in that rewilding aspires to reduce human influence on ecosystems. [ 1 ] It is also distinct from other forms of restoration in that, while it places emphasis on recovering geographically specific sets of ecological interactions and functions that would have maintained ecosystems prior to human influence, rewilding is open to novel or emerging ecosystems which encompass new species and new interactions. [ 2 ] [ 3 ]
A key feature of rewilding is its focus on replacing human interventions with natural processes. Rewilding enables the return of intact, large mammal assemblages, to promote the restoration of trophic networks. [ 4 ] This mechanism of rewilding is a process of restoring natural processes by introducing or re-introducing large mammals to promote resilient, self-regulating, and self-sustaining ecosystems. [ 5 ] [ 6 ] Large mammals can influence ecosystems by altering biogeochemical pathways as they contribute to unique ecological roles, they are landscape engineers that aid in shaping the structure and composition of natural habitats. [ 7 ] [ 8 ] Rewilding projects are often part of programs for habitat restoration and conservation biology, and should be based on sound socio-ecological theory and evidence. [ 9 ]
While rewilding initiatives can be controversial, the United Nations has listed rewilding as one of several methods needed to achieve massive scale restoration of natural ecosystems, which they say must be accomplished by 2030 [ 10 ] as part of the 30x30 campaign. [ 11 ]
The term rewilding was coined by members of the grassroots network Earth First! , first appearing in print in 1990. [ 12 ] It was refined and grounded in a scientific context in a paper published in 1998 by conservation biologists Michael Soulé and Reed Noss . [ 13 ] Soulé and Noss envisaged rewilding as a conservation method based on the concept of 'cores, corridors, and carnivores'. [ 14 ] The key components of rewilding incorporate large core protected areas, keystone species , and ecological connectivity based on the theory that large predators play regulatory roles in ecosystems. [ 15 ] '3Cs' rewilding therefore relied on protecting 'core' areas of wild land, linked together by 'corridors' allowing passage for 'carnivores' to move around the landscape and perform their functional role . [ 16 ] Inside these cores, human development, especially the building of roads, is strictly limited. National parks and wilderness reserves are the most common types of 'core' areas. Soulé and fellow biologist John Terbough expanded on the concept of corridors in their book Continental Conservation . They determined that one size does not fit all: narrow, linear corridors might work for some smaller species, but if conservationists wanted to encourage the movement of large carnivores, they needed to make corridors wide enough to allow for daily and seasonal movement of both herds of prey and packs of their predators. [ 17 ] The '3Cs' concept was developed further in 1999 [ 18 ] and Earth First co-founder, Dave Foreman , subsequently wrote a full-length book on rewilding as a conservation strategy. [ 19 ]
Rewilding was developed as a method to preserve functional ecosystems and reduce biodiversity loss , incorporating research in island biogeography and the ecological role of large carnivores . [ 20 ] In 1967, The Theory of Island Biogeography by Robert H. MacArthur and Edward O. Wilson established the importance of considering the size and fragmentation of wildlife conservation areas, stating that protected species and areas remained vulnerable to extinctions if populations were small and isolated. [ 21 ] In 1987, William D. Newmark's study of extinctions in national parks in North America added weight to the theory. [ 22 ] The publications intensified debates on conservation approaches. [ 23 ] With the creation of the Society for Conservation Biology in 1985, conservationists began to focus on reducing habitat loss and fragmentation. [ 24 ]
Supporters of rewilding initiatives range from individuals, small land owners, local non-governmental organizations and authorities , to national governments and international non-governmental organizations such as the International Union for Conservation of Nature . While rewilding efforts can be well regarded, the increased popularity of rewilding has generated controversy, especially in relation to large-scale projects. These have sometimes attracted criticism from academics and practicing conservationists, as well as government officials and business people. [ 25 ] [ 26 ] [ 27 ] [ 28 ] Nonetheless, a 2021 report for the launch of the UN Decade on Ecosystem Restoration , the United Nations listed rewilding as one of several restoration methods which they state should be used for ecosystem restoration of over 1 billion hectares . [ 29 ] [ 30 ]
Since its origin, the term rewilding has been used as a signifier of particular forms of ecological restoration projects that have ranged widely in scope and geographic application. In 2021 the journal Conservation Biology published a paper [ 2 ] by 33 coauthors from around the world. Titled 'Guiding Principles for Rewilding', researchers and project leaders from North America (Canada, Mexico and the United States) joined with counterparts in Europe (Denmark, France, Hungary, The Netherlands, Switzerland, and the UK), China, and South America (Chile and Colombia) to produce a unifying description, along with a set of ten guiding principles.
The group wrote, 'Commonalities in the concept of rewilding lie in its aims, whereas differences lie in the methods used, which include land protection, connectivity conservation , removing human infrastructure, and species reintroduction or taxon replacement.' Referring to the span of project types they stated, 'Rewilding now incorporates a variety of concepts, including Pleistocene megafauna replacement, taxon replacement, species reintroductions , retrobreeding , release of captive-bred animals, land abandonment, and spontaneous rewilding.' [ 2 ]
Empowered by a directive from the International Union for the Conservation of Nature to produce a document on rewilding that reflected a global scale inventory of underlying goals as well as practices, the group sought a 'unifying definition', producing the following:
'Rewilding is the process of rebuilding, following major human disturbance, a natural ecosystem by restoring natural processes and the complete or near complete food web at all trophic levels as a self-sustaining and resilient ecosystem with biota that would have been present had the disturbance not occurred. This will involve a paradigm shift in the relationship between humans and nature. The ultimate goal of rewilding is the restoration of functioning native ecosystems containing the full range of species at all trophic levels while reducing human control and pressures. Rewilded ecosystems should—where possible—be self-sustaining. That is, they require no or minimal management (i.e., natura naturans [nature doing what nature does]), and it is recognized that ecosystems are dynamic.' [ 2 ]
Ten principles were developed by the group:
A paper was published in 2024 that offered a "broad study of rewilding guidelines and interventions." [ 31 ]
Rewilding can respond to both the causes and effects of climate change and has been posited as a ' natural climate solution '. Rewilding's creation of new ecosystems and restoration of existing ones can contribute to climate change mitigation and adaptation through, inter alia , carbon capture and storage , altering the Earth's albedo , natural flood management, reduction of wildfire risk, new habitat creation, and enabling or facilitating the movement of species to new, climate safe habitats, thus protecting biodiversity and maintaining functioning, climate resilient ecosystems. [ 32 ] [ 33 ] [ 34 ] [ 35 ] [ 36 ] [ 37 ] [ 38 ]
The functional roles animals perform in ecosystems, such as grazing, nutrient cycling and seed distribution, can influence the amount of carbon that soils and (marine and terrestrial) plants capture. [ 39 ] The carbon cycle is altered through herbivores consuming vegetation, assimilating carbon within their own biomass, and releasing carbon by respiration and defecation after digestion. [ 40 ] [ 41 ] The most beneficial effects on biogeochemical cycling and ecosystem structure are reported through rewilding large herbivore species. [ 42 ] [ 43 ] A study in a tropical forest in Guyana found that an increase in mammal species from 5 to 35 increased tree and soil carbon storage by four to five times, compared to an increase of 3.5 to four times with an increase of tree species from 10 to 70. [ 44 ] A separate study suggested that the loss of megafauna that eat fruits may be responsible for an up to 10% reduction in carbon storage in tropical forests. [ 45 ] Furthermore, acceleration of nutrient cycling through browsing and grazing may increase local plant productivity and thereby maintain ecosystem productivity in grassy biomes .
It is also posited that grazing and browsing reduces the risk of wildfires (which are significant contributors of GHG emissions and whose smoke can alter the planet's albedo - the Earth's ability to reflect heat from sunlight)). For example, the loss of wildebeest from the Serengeti led to an increase in un-grazed grass, leading to more frequent and intense fires, causing the grassland to turn from a carbon sink to a carbon source. When disease management practices restored the wildebeest population, the Serengeti returned to a carbon sink state. [ 39 ] [ 46 ]
Rewilding's effect on albedo is not only through potential reduction of smoke from wildfires but also through the effects of grazing itself. By reducing woody cover through browsing and trampling, large herbivores expose more ground surface and thus increase the albedo effect, reducing local surface temperatures and creating a net surface cooling effect during spring and autumn.
Other forms of ecological restoration as part of rewilding can also assist with mitigating climate change. For example, reforestation, afforestation and peat re-wetting can all contribute to carbon sequestration. [ 47 ] While carbon sequestration could allow carbon offsetting and carbon trading as a way to monetize rewilding there has been concern that the highly speculative nature of carbon markets encourages 'land grabbing' (i.e., buying large areas of land) and 'greenwashing' from natural capital investors and multi-national companies. [ 48 ]
Passive rewilding (also referred to as ecological rewilding) [ 49 ] aims to restore natural ecosystem processes via minimal or the total withdrawal of direct human management of the landscape. [ 50 ] [ 51 ] [ 52 ]
Active rewilding is an umbrella term used to describe a range of rewilding approaches all of which involve human intervention. These might include species reintroductions or translocations and/or habitat engineering and the removal of man-made structures and Introduced species that cause trouble. [ 53 ] [ 50 ] [ 54 ]
Pleistocene rewilding is the (re)introduction of extant Pleistocene megafauna , or the close ecological equivalents of extinct megafauna, to restore ecosystem function. Advocates of the approach maintain that ecosystems where species evolved in response to Pleistocene megafauna but now lack large mammals may be in danger of collapse . [ 55 ] [ 56 ] Meanwhile critics argue that it is unrealistic to assume that ecological communities today are functionally similar to their state 10,000 years ago.
Trophic rewilding is an ecological restoration strategy focused on restoring trophic interactions and complexity (specifically top-down and associated trophic cascades where a top consumer/predator controls the primary consumer population) through species (re)introductions, in order to promote self-regulating, biodiverse ecosystems. [ 57 ] [ 58 ]
Urban rewilding is a type of rewilding focused on the integration of nature into urban settings. [ 59 ]
Ecosystem engineers are ‘organisms that demonstrably modify the structure of their habitats’. [ 60 ] Examples of ecosystem engineers in rewilding include beaver , elephants , bison , elk , cattle (as analogues for the extinct aurochs ) and pigs (as analogues for wild boar ). [ 61 ] [ 62 ] [ 63 ] [ 64 ]
A keystone species is a species that has a disproportionately large effect on its environment relative to its abundance .
Apex predators may be required in rewilding projects to ensure that browsing and grazing animals are kept from over-breeding/over-feeding thereby destroying vegetation complexity [ 20 ] and exceeding the ecological carrying capacity of the rewilding area, as was seen in the mass-starvations which occurred at the Oostvaardersplassen rewilding project in the Netherlands. [ 65 ] While predators play an important role in ecosystems, however, there is debate regarding the extent to which the control of prey populations is due to direct predation or a more indirect influence of predators (see Ecology of fear ). [ 66 ] For example, it is thought that wildebeest populations in the Serengeti are primarily controlled by food constraints despite the presence of many predators such as Lions , cheetahs , and hyenas . [ 67 ]
Some national governments and officials within multilateral agencies such as the United Nations , express the view that 'excessive' rewilding, such as large rigorously enforced protected areas where no extraction activities are allowed, can be too restrictive on people's ability to earn sustainable livelihoods. [ 27 ] [ 28 ] The alternative view is that increasing ecotourism can provide employment. [ 68 ]
Rewilding has been criticized by animal rights scholars, such as Dale Jamieson , who argues that 'most cases of rewilding or reintroducing are likely to involve conflicts between the satisfaction of human preferences and the welfare of nonhuman animals'. [ 69 ] Erica von Essen and Michael Allen, using Donaldson and Kymlicka 's political animal categories framework, assert that wildness standards imposed on animals are arbitrary and inconsistent with the premise that wild animals should be granted sovereignty over the territories that they inhabit and the right to make decisions about their own lives. To resolve this, von Essen and Allen contend that rewilding needs to shift towards full alignment with mainstream conservation and welcome full sovereignty, or instead take full responsibility for the care of animals who have been reintroduced. [ 70 ] Ole Martin Moen argues that rewilding projects should be brought to an end because they unnecessarily increase wild animal suffering and are expensive, and the funds could be better spent elsewhere. [ 71 ]
The environmental historian Dolly Jørgensen argues that rewilding, as it currently exists, 'seeks to erase human history and involvement with the land and flora and fauna. Such an attempted split between nature and culture may prove unproductive and even harmful.' She calls for rewilding to be more inclusive to combat this. [ 72 ] Jonathan Prior and Kim J. Ward challenge Jørgensen's criticism and provide examples of rewilding programs which 'have been developed and governed within the understanding that human and non-human world are inextricably entangled'. [ 73 ]
Some farmers have been critical of rewilding for 'abandoning productive farmland when the world's population is growing'. [ 74 ] Farmers have also attacked plans to reintroduce the lynx in the United Kingdom because of fears that reintroduction will lead to an increase in sheep predation . [ 75 ]
Some conservationists have expressed concern that rewilding 'could replace the traditional protection of rare species on small nature reserves', which could potentially lead to an increase in habitat fragmentation and species loss. [ 74 ] David Nogués-Bravo and Carsten Rahbek assert that the benefits of rewilding lack evidence and that such programs may inadvertently lead to 'de-wilding', through the extinction of local and global species. They also contend that rewilding programs may draw funding away from 'more scientifically supported conservation projects'. [ 76 ] Many large conservation groups have built fundraising campaigns around the idea that once wildlife is gone, it’s gone for good; rewilding experts saying otherwise may confuse donors and lead to less money being funneled into conservation efforts. Governmental agencies overseeing land use and consumption are often heavily influenced by the interests of loggers, ranchers, and miners, so non-profit organizations are often at the forefront of conservation efforts, and a loss of funding could have major impacts on the protection of wildlife. There is also concern among conservationists that if the idea that wilderness can be restored becomes popular with the public, oil companies, real estate developers, and agribusinesses may be emboldened to step up land consumption, arguing that it can be restored later. [ 77 ]
The reintroduction of brown bears to Italy's Trentino province through the EU-funded Life Ursus project has led to growing tensions between humans and wildlife. While initially celebrated as a conservation success, the bear population has expanded to over 100, leading to increased conflicts, including the fatal attack on Andrea Papi in 2023—the first modern death caused by a wild bear in Italy. This incident sparked fear among residents and prompted calls for stricter controls, including culling dangerous bears. Critics argue the conflict stems from poor management, inadequate public education, and a lack of preventive measures like bear-proof bins. Despite efforts to balance human safety and conservation, local communities remain deeply divided, with many pushing for limits on bear numbers and more decisive action against perceived threats. [ 78 ] [ 79 ]
Both grassroots groups and major international conservation organizations have incorporated rewilding into projects to protect and restore large-scale core wilderness areas , corridors (or connectivity) between them, and apex predators , carnivores, or keystone species. Projects include: the Yellowstone to Yukon Conservation Initiative in North America (also known as Y2Y), the European Green Belt (built along the former Iron Curtain ), transboundary projects (including those in southern Africa funded by the Peace Parks Foundation ), community-conservation projects (such as the wildlife conservancies of Namibia and Kenya), and projects organized around ecological restoration (including Gondwana Link , regrowing native bush in a hotspot of endemism in southwest Australia, and the Area de Conservacion Guanacaste , restoring dry tropical forest and rainforest in Costa Rica). [ 80 ]
In North America, a major project aims to restore the prairie grasslands of the Great Plains . [ 81 ] The American Prairie is reintroducing bison on private land in the Missouri Breaks region of north-central Montana, with the goal of creating a prairie preserve larger than Yellowstone National Park . [ 81 ] : 187–199 As of 2024, American Prairie's habitat spanned over 520,000 acres. [ 82 ]
Dam removal has led to the restoration of many river systems in the Pacific Northwest in an effort to restore salmon populations specifically but with other species in mind. As stated in an article on environmental law:
'These dam removals provide perhaps the best example of large-scale environmental remediation in the twenty-first century. [...] The result has been to put into motion ongoing rehabilitation efforts in four distinct river basins : the Elwha and White Salmon in Washington and the Sandy and Rogue in Oregon'. [ 83 ]
Formally launched in 1997, Yellowstone to Yukon (Y2Y) was a conservation initiative that envisioned a wide corridor of protected land stretching from Canada’s Yukon territory, through American national parks like Waterton and Glacier, all the way to the Greater Yellowstone ecoregion in the northern Rocky Mountains. [ 84 ] Promoters of the project worked to discourage building of roads and other human developments that would impede the movement of large predators like wolves and grizzly bears. Y2Y used lobbying and education to promote its mission and get the public involved. Organizers set up conferences between rewilding groups in Canada and the United States, facilitated dialogue between conservationists and Native American groups, and maintained high visibility for the project by featuring in newspapers like the New York Times and the Washington Post. Activists involved in the project successfully lobbied for 24 highway crossing structures in the Banff area, allowing for safer movement of wildlife across the Trans-Canadian highway. [ 85 ]
Y2Y inspired other conservation groups to focus more of their efforts on lobbying to persuade government action, and led to an increase in corridor planning across North America. The South Coast Wildlands Project successfully convinced the California State Parks Agency to buy a 700 acre tract slated for development. The Algonquin to Adirondack initiative, modeled after Y2Y, has focused research efforts on improving connectivity around the Great Lakes Region. Conservation groups from the United States and Canada have worked together to plan a series of marine priority areas from Baja California to the Bering Sea, allowing both nations to protect species of mutual concern. [ 86 ]
There have been multiple projects launched to protect North America’s carnivores, one of the main components of the ‘3 C’s’ approach to rewilding. Reed Noss, an early advocate for rewilding, began working on reserve designs as early as the 1980s to protect Florida’s largest predators: the Florida panther and the Florida black bear . Noss’ initial plan envisioned 60% of Florida’s land set aside for wildlife reserves and proved so influential that the Florida State legislature set aside $3.2 billion to buy land for a network of reserves and corridors between them. [ 77 ]
At the same time, a group based in Washington D.C. called Defenders of Wildlife began promoting protection of predators across the country, including grizzly bears , wolves , and river otters . In 1987, they set up the Bailey Wildlife Foundation Wolf Compensation Trust to pay ranchers back for the loss of livestock due to predation in an attempt to raise support for rewilding among farmers, who are often some of the most vocal opponents of the conservation of large predators. In 1998, they launched another program to pay for fencing, alarms, and other methods that would protect livestock in a way that didn’t harm predators. However, this approach has been largely unsuccessful at bolstering the native wolf population because of continued shooting of wolves, both illegally and permitted by the USFWS. [ 77 ]
Fresh Kills landfill, located on Staten Island, was once home to 150 million tons of trash. However, plans created between 2001 and 2006 reimagined it as a 2,200 acre park, the largest park built in the state of New York in over a century. Construction began in 2008 to restore the area back to its original wetland ecosystem, complete with open waterways, sweet-gum swamps, prairies, and meadows of wildflowers. Part of initial plans involved removing invasive reed species and replacing them native marsh grasses. The project is slated to take up to thirty years to complete, with the end goal of combining ecological restoration with recreational activities. [ 77 ]
While planning for Fresh Kills Park, New York State initiated an even more ambitious program focused on protecting the broader ecosystem around Staten Island by restoring the Hudson River. In 2005, the organizations involved came up with a few goals for the project: re-invigorating the river’s fisheries, improving water quality by removing contaminants, and preserving shoreline and forested habitats upriver. When the project is complete, it will affect fifty thousand acres containing six different habitat types. [ 77 ]
In the Mexican state of Sonora, the Northern Jaguar Project bought 45,000 acres of land by 2007 devoted to protecting the northernmost breeding population of jaguars . The group also encouraged local people to help them monitor the population by offering a $500 reward for each photograph of a living cat taken by ranch owners who promised not to shoot jaguars on their property. In its first year, the program paid out $6,500 for photos of jaguars, mountain lions , and ocelots . [ 77 ]
In the early 1990s, the Wildlife Conservation Society proposed a plan for a major corridor project that would span from Southern Mexico down into Panama, connecting existing reserves, parks, and undisturbed forests of all seven Central American countries and the lower five Mexican states. They called the plan “Paseo Pantera,” or “the path of the panther,” named so because of the movement of mountain lions throughout the area. [ 77 ] The plan attracted a lot of controversy: indigenous peoples were concerned that their land would be taken from them to be converted into parks, and some activists claimed that the program was setting the environment above human needs. These arguments caused the project to be reviewed and refashioned. In 1997, the new plan, renamed the “Mesoamerican Biological Corridor,” was unveiled as a conservation project that also promoted the welfare of indigenous people and local economies. [ 77 ]
Despite the changes, the Mesoamerican Corridor still had some flaws, most notably with regard to land use. The plan necessitated reaching agreements with numerous villages to decide what zoning for protected areas meant for the local people, how it would be enforced, and where hunting and fishing would be allowed. Rural people were largely unimpressed with the vague nature of the outline, so progress was slow. In 2005, the Central American Free Trade Agreement promised to develop many of the same areas the Mesoamerican Corridor sought to protect, but conservationists refused to oppose the development for fear of losing funding. By 2006, hundreds of millions of dollars had been spent on preserving the corridor, but only one small protected area had been created. [ 77 ]
Costa Rica’s Osa Peninsula is one of the most biodiverse places on the planet. In 1975, the Nature Conservancy worked with the Costa Rican government to create the first national park in the country: Corcovado. The park originally spanned 86,000 acres, nearly a third of the peninsula. The Nature Conservancy wanted to establish it as a refuge for the dozens of endemic species that occur in this small stretch of habitat. [ 77 ] However, the project has faced many setbacks since its establishment. Conservationists quickly realized that it was too small to protect many critical species, including the jaguar, peccary, and harpy eagle. Gold was discovered in Corcovado around the same time as the park was established, and some of the natural areas within the park were illegally destroyed by miners. Programs to engage local people in conservation efforts quickly failed because of a lack of funding, causing people living on the border to become increasingly hostile towards the project. Lack of financial resources caused many people to resort to poaching within the park’s borders or shooting jaguars that ate their crops. [ 77 ]
Conservation groups hoped to solve these problems by launching another initiative, the Osa Biological Corridor project. The plan was designed to enlarge currently protected areas on the peninsula, and hopes to devote $10 million to develop community support for rewilding by providing education programs and new jobs protecting the reserves. [ 77 ]
In 1997, Douglas and Kris Tompkins created 'The Conservation Land Trust Argentina' with the goal of transforming the Iberá Wetlands . In 2018, thanks to a team of conservationists and scientists, and a donation of 195,094 ha (482,090 acres) of land by Kris Tompkins, an area was converted into a National Park , and species such as the Giant anteater , Pampas deer , Collared peccary , Red and green macaw , giant river otter , and the Jaguar which have all became exinct in the region for several decades that have now ben reintroduced . A spin-off of the Tompkins Foundation, Rewilding Argentina , is an organization dedicated to the restoration of El Impenetrable National Park , in Chaco, Patagonia Park, in Santa Cruz , and the Patagonian coastal area in the province of Chubut , in addition to Iberá National Park. [ 87 ]
The red-rumped agouti , Yellow-footed tortoise and brown howler monkey were reintroduced in Tijuca National Park (Rio de Janeiro state, Brazil), between 2010 and 2017 with the goal of restoring seed dispersal. [ 88 ] Prior to the reintroductions, the national park did not have large or intermediate -sized seed dispersers, the increased dispersal of tree seeds following the reintroductions therefore had a significant effect on forest regeneration in the park. [ 88 ] This is significant since the Tijuca National Park is part of heavily fragmented Atlantic Forest and there is potential to restore many more seed dispersal interactions if seed dispersing mammals and birds are reintroduced to forest patches where the tree species diversity remains high. [ 89 ]
The Cerrado-Pantanal Ecological Corridors Project was proposed in the 1990s to restore connectivity between two of Brazil’s core reserves: Emas National Park and the Pantanal, one of the world’s largest wetlands. [ 77 ] It made significant progress in the early 2000s because of plans to conserve mainly areas with low human density. Another reason for wider support was because of a fund started to compensate farmers that lost livestock to the big cats that conservationists hope to protect using these corridors, and healthcare programs that provided free services to ranchers who committed to not killing critically endangered jaguars . [ 77 ]
Colonisation has had a significant impact on Australia's native flora and fauna, and the introduction of red foxes and cats has devastated many of the smaller ground-dwelling mammals. The island state of Tasmania has become an important location for rewilding efforts because, as an island, it is easier to remove feral cat populations and manage other invasive species. The reintroduction and management of the Tasmanian devil in this state, and dingoes on the mainland, is being trialed in an effort to contain introduced predators, as well as over-populations of kangaroos . [ 90 ]
Gondwana Link, a plan conceived in 2002, was devised to connect two Australian national parks: Stirling Range and Fitzgerald River National Park. Much of this land had been severely degraded by harmful farming practices, and was barren of most plant and animal life. Organizers of the project worked on revegetating the land with native plant species, fifty of which were found nowhere else on Earth, in the hopes that they would attract wildlife back to the area. [ 77 ] Five years later, they had planted over 100 species of native plants, and multiple reptiles species had been spotted coming back to the region. By 2009, the Gondwana Link included over 23,000 acres of protected land. [ 77 ]
WWF-Australia runs a program called 'Rewilding Australia' whose projects include restoring the platypus in the Royal National Park , south of Sydney , eastern quolls in the Booderee National Park in Jervis Bay and at Silver Plains in Tasmania , and brush-tailed bettongs in the Marna Banggara project on the Yorke Peninsula in South Australia . [ 91 ] Other projects around the country include: [ 90 ]
In 2011, the ' Rewilding Europe ' initiative was established with the aim of rewilding one million hectares of land in ten areas including the western Iberian Peninsula , Velebit , the Carpathians and the Danube delta by 2020. [ 92 ] The project considers reintroductions of species that are still present in Europe such as the Iberian lynx , Eurasian lynx , grey wolf , European jackal , brown bear , chamois , Iberian ibex , European bison , red deer , griffon vulture , cinereous vulture , Egyptian vulture , great white pelican and horned viper , along with primitive domestic horse and cattle breeds as proxies for the extinct tarpan and aurochs (the wild ancestors of domestic cattle) respectively. Since 2012, Rewilding Europe has been heavily involved in the Tauros Programme , which seeks to create a breed of cattle that resembles the aurochs by selectively breeding existing breeds of cattle. [ 93 ] Projects also employ domestic water buffalo as a grazing analogue for the extinct European water buffalo . [ 94 ]
European Wildlife , established in 2008, advocates the establishment of a European Centre of Biodiversity at the German–Austrian–Czech borders, and the Chernobyl exclusion zone in Ukraine .
The European Green Belt is a proposed rewilding zone that is envisioned running through over a dozen European countries using land that was historically part of the physical boundaries of the Iron Curtain. When completed, the European Green Belt will stretch over five thousand miles, from the Barents Sea off the northern coast of Norway to the Black Sea in southeast Europe. [ 77 ] The corridor is composed of three main sections: the Fennoscandian Green Belt running through Norway, Finland, and Russia, the Central Green Belt located in parts of Germany, the Czech Republic, Austria, Slovakia, Hungary, Slovenia, and Italy, and the Balkan Green Belt in Macedonia, Romania, Bulgaria, Albania, Greece, and Turkey. It will link core reserves and parks like the Bavarian Forest in Germany, the Danube-March floodplains in Austria and Slovakia, and Sumava National Park in the Czech Republic. Proponents of the European Green Belt hope that it will increase ecotourism and sustainable farming practices across Europe. [ 77 ]
Der Biosphärenpark Wienerwald was created in Austria in 2003 with 37 kernzonen (core zones) covering a total of 5,400 ha designated free from human interference. [ 95 ]
Rewilding Britain , a charity founded in 2015, aims to promote rewilding in Britain and is a leading advocate of rewilding. [ 96 ] Rewilding Britain has laid down 'five principles of rewilding' which it expects to be followed by affiliated rewilding projects. [ 97 ] [ 98 ] These are to support people and nature together, to 'let nature lead', to create resilient local economies, to 'work at nature's scale', and to secure benefits for the long-term.
Celtic Reptile and Amphibian is a limited company established in 2020, with the aim of reintroducing extinct species of reptile and amphibian (such as the European pond turtle , [ 99 ] moor frog , agile frog , [ 100 ] common tree frog and pool frog ) [ 101 ] [ 102 ] to Britain. Success has already been achieved with the captive breeding of the moor frog. [ 103 ] [ 104 ] A reintroduction trial of the European pond turtle to its historic, Holocene range in the East Anglian Fens, Brecks and Broads has been initiated, with support from the University of Cambridge . [ 105 ]
In 2020, nature writer Melissa Harrison reported a significant increase in attitudes supportive of rewilding among the British public, with plans recently approved for the release of European bison, Eurasian elk, and great bustard in England, along with calls to rewild as much as 20% of the land in East Anglia, and even return apex predators such as the Eurasian lynx, brown bear, and grey wolf. [ 106 ] [ 107 ] [ 61 ] More recently, academic work on rewilding in England has highlighted that support for rewilding is by no means universal. As in other countries, rewilding in England remains controversial to the extent that some of its more ambitious aims are being 'domesticated' both in a proactive attempt to make it less controversial and in reactive response to previous controversy. [ 108 ] Projects may also refer to their activity using terminology other than 'rewilding', possibly for political and diplomatic reasons, taking account of local sentiment or possible opposition. Examples include 'Sanctuary Nature Recovery Programme' (at Broughton) and 'nature restoration project', the preferred term used by the Cambrian Wildwood project, an area aspiring to encompass 7,000 acres in Wales. [ 109 ]
Notable rewilding sites include:
The British radio drama series The Archers featured rewilding areas in storylines in 2019 and 2020. [ 119 ] [ 120 ]
In November 2023, Tatler described rewilding as being part of the worldview of the bopea ("bohemian peasant") movement, an elite British socio-cultural group. [ 121 ]
In the 1980s, analogue species (Konik ponies, Heck cattle and red deer) were introduced to the Oostvaardersplassen nature reserve, an area covering over 56 square kilometres (22 sq mi), in order to (re)create a grassland ecology by keeping the landscape open by naturalistic grazing. [ 122 ] [ 123 ] This approach followed Vera's ' wood-pasture hypothesis' that grazing animals played a significant role in shaping European landscapes before the Neolithic period. Though not explicitly referred to as rewilding, many of the project's intentions were in line with those of rewilding. The case of the Oostvaardersplassen is considered controversial due to the lack of predators, and its management can be seen as having to contend with conflicting ideas regarding nature. [ 124 ]
In the 1990s and early 2000s, several multi-nation rewilding projects were suggested across Africa. Some notable examples are:
In 1996, Namibia passed the Nature Conservation Act, a law that allowed communities of civilians to create their own protected wildlife conservancies to develop the country’s ecotourism sector. Conservancy creation was voluntary, but proved to be popular: by 2008, fifty-two conservancies were registered with the government, and fifteen more were seeking approval. [ 77 ] By this time, one in four rural Namibians were involved in conservation, and around fifteen percent of the country’s land was protected. Conservancy committees were tasked with hiring park guards and rangers to crack down on illegal hunting, in exchange for limited hunting rights for conservancy members. The Namibian government relocated locally extirpated species to these newly protected areas, and community members monitored their flourishing population sizes. [ 77 ]
One notable success of the Nature Conservation Act is Salambala, a conservancy established in 1998. The region, only 359 square miles large, went from having virtually no large game to boasting a population of elephants six hundred strong, a herd of fifteen hundred zebra, and three lion prides after twenty years. [ 77 ] Surveys conducted in the conservancy showed a 47 percent increase in wildlife sightings, just between 2004 and 2007. The local community was able to capitalize on the environmental success: by 2006, the community was earning thirty-seven times more revenue from tourism than they had been in 1998. [ 77 ]
King Mahendra was crowned king of Nepal in 1955. An avid hunter, King Mahendra and his son instituted Nepal’s first Western-style national park, the Royal Chitwan National Park, in 1973. [ 77 ] Establishment of the park led to an increase in research being done on Nepal’s wildlife, including the Nepal Tiger Ecology Project, an eighteen-year-long field study conducted in Chitwan. Findings from this study convinced the Nepalese government to eventually enlarge the boundaries of Chitwan and join it with its neighboring Parsa and Valmiki wildlife reserves. In 1995, Nepal’s Parliament ratified bylaws that required 50 percent of the revenue from park entrance fees to go towards programs that would benefit local people, providing funding to build better schools and clinics and bolstering public support for parks. [ 77 ]
In 1993, Terai Arc Landscape Program (TAL) was started to restore forested corridors between Chitwan, other Nepalese parks like Bardia National Park and Parsa Wildlife Reserve, and Indian reserves along the countries’ shared border. TAL’s goal was to add “buffer zones” around the established parks and create pathways between them to facilitate the movement of large species like elephants, tigers, and rhino. [ 77 ] The project was initially successful, supporting over 600 endangered rhinos and attracting tens of thousands of tourists every year, but the success was disrupted by the Nepalese Civil War, which took place from 1996 to 2006. Hundreds of rhinos and tigers were killed during the war as a result of fewer park guards and governmental conservation groups growing disorganized by the war. By 2008, wildlife populations in the reserve began to grow again, but the war caused hundreds of thousands of dollars of damage to the project. [ 77 ]
In 2001, conservationist Willie Smits began buying land from a former palm oil plantation that has been ecologically destroyed by logging. He, along with a group of Dayak villagers in Indonesia’s East Kalimantan province, replanted over twelve hundred species of trees on the land, which Smits renamed Samboja Lestari or “Everlasting Forest.” [ 77 ] The project’s hopes of returning the land to a tropical rainforest seems to be working: by 2009, temperature within the regrown forest had dropped by three to five degrees Celsius, humidity has risen by 10 percent, and rainfall had increased by 25 percent. 137 species of birds now reside on the land, up from only five species that had lived in the logged area. The replanted forest is also home to nine species of primates, as of 2009. [ 77 ] | https://en.wikipedia.org/wiki/Rewilding |
Rewired State was an organisation which ran a series of hack days for programmers and designers, focused on improving access to UK government open data and encouraging innovation in government services. [ 1 ]
Rewired State was founded by James Darling, Emma Mulqueeny , and Richard Pope in 2008. [ 2 ] The first event, National Hack the Government Day , was held on 7 March 2009 at the Guardian offices in King's Cross, London. Over 80 people attended producing over 30 hacks. [ 3 ] Judges at Rewired State events included Tom Watson MP and Dr Sue Black . [ 4 ] Sponsors included the Government Digital Service , mySociety , and Nesta . National Hack the Government Day ran annually until 2015.
Between 2011 and 2013, Rewired State ran a series of Parliament Hack events in association with the UK Parliament , with the aim to build new apps using parliamentary data. [ 5 ]
Rewired State formed a sister organisation, Young Rewired State , to bring young developers together to solve real world problems. Young Rewired State ran its own series of Festival of Code hack days from 2009. The last event run by Young Rewired State was the 2015 Festival of Code, [ 6 ] and the organisation was formally dissolved in February 2019. [ 7 ] Young Rewired State also ran various "Hyperlocal" centres across the UK, which provide coding challenges across the year, rather than being focused on one week as in the Festival of Code. [ citation needed ]
Many developers who participated in Young Rewired State events learned coding skills outside the traditional school curriculum. [ 8 ]
Between 2009 and 2015, Young Rewired State held a national five-day hackathon where attendees across the UK took part in a competition to make an application including at least one piece of open government data. This event was initially called "Young Rewired State", but was renamed in 2012 to the " Festival of Code ".
In 2009, when the event first started, there were only 50 participants attending a weekend at Google 's London offices. This number rose to roughly a thousand young people participating across United Kingdom and in centres in other countries. [ 9 ] Between the first event in 2009 and the penultimate event in 2015 the proportion of female participants rose from 2% to 30%. [ 10 ]
In 2016, it was announced that year's Festival of Code would be postponed to 2017, [ 6 ] but the event did not occur in 2017 or in subsequent years. [ citation needed ]
Rewired State also ran a number of other government data hack days including Rewired State: Culture , (H)activate , Middle East Hack , Follow the Data , and Carbon and Energy Hack Weekend . [ 11 ]
National Hack the Government Day and other events ran annually until the last event in 2015. Between 2015 and 2016, Rewired State was run as a consultancy business by Emma Mulqueeny. [ 12 ] The company was dissolved in 2018. [ 13 ] | https://en.wikipedia.org/wiki/Rewired_State |
In theoretical computer science , in particular in automated reasoning about formal equations, reduction orderings are used to prevent endless loops . Rewrite orders , and, in turn, rewrite relations , are generalizations of this concept that have turned out to be useful in theoretical investigations.
Intuitively, a reduction order R relates two terms s and t if t is properly "simpler" than s in some sense.
For example, simplification of terms may be a part of a computer algebra program, and may be using the rule set { x +0 → x , 0+ x → x , x *0 → 0, 0* x → 0, x *1 → x , 1* x → x }. In order to prove impossibility of endless loops when simplifying a term using these rules, the reduction order defined by " sRt if term t is properly shorter than term s " can be used; applying any rule from the set will always properly shorten the term.
In contrast, to establish termination of "distributing-out" using the rule x *( y + z ) → x * y + x * z , a more elaborate reduction order will be needed, since this rule may blow up the term size due to duplication of x . The theory of rewrite orders aims at helping to provide an appropriate order in such cases.
Formally,
a binary relation (→) on the set of terms is called a rewrite relation if it is closed under contextual embedding and under instantiation ; formally: if l → r implies u [ l σ ] p → u [ r σ] p for all terms l , r , u , each path p of u , and each substitution σ. If (→) is also irreflexive and transitive , then it is called a rewrite ordering , [ 1 ] or rewrite preorder . If the latter (→) is moreover well-founded , it is called a reduction ordering , [ 2 ] or a reduction preorder .
Given a binary relation R , its rewrite closure is the smallest rewrite relation containing R . [ 3 ] A transitive and reflexive rewrite relation that contains the subterm ordering is called a simplification ordering . [ 4 ]
Nachum Dershowitz ; Jean-Pierre Jouannaud (1990). "Rewrite Systems". In Jan van Leeuwen (ed.). Formal Models and Semantics . Handbook of Theoretical Computer Science. Vol. B. Elsevier. pp. 243– 320. doi : 10.1016/B978-0-444-88074-1.50011-1 . ISBN 9780444880741 . | https://en.wikipedia.org/wiki/Rewrite_order |
In mathematics , computer science , and logic , rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems , rewrite engines , [ 1 ] [ 2 ] or reduction systems ). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects.
Rewriting can be non-deterministic . One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. When combined with an appropriate algorithm, however, rewrite systems can be viewed as computer programs , and several theorem provers [ 3 ] and declarative programming languages are based on term rewriting. [ 4 ] [ 5 ]
In logic , the procedure for obtaining the conjunctive normal form (CNF) of a formula can be implemented as a rewriting system. [ 6 ] For example, the rules of such a system would be:
For each rule, each variable denotes a subexpression, and the symbol ( → {\displaystyle \to } ) indicates that an expression matching the left hand side of it can be rewritten to one matching the right hand side of it. In such a system, each rule is a logical equivalence , so performing a rewrite on an expression by these rules does not change the truth value of it. Other useful rewriting systems in logic may not preserve truth values, see e.g. equisatisfiability .
Term rewriting systems can be employed to compute arithmetic operations on natural numbers .
To this end, each such number has to be encoded as a term .
The simplest encoding is the one used in the Peano axioms , based on the constant 0 (zero) and the successor function S . For example, the numbers 0, 1, 2, and 3 are represented by the terms 0, S(0), S(S(0)), and S(S(S(0))), respectively.
The following term rewriting system can then be used to compute sum and product of given natural numbers. [ 7 ]
For example, the computation of 2+2 to result in 4 can be duplicated by term rewriting as follows:
where the notation above each arrow indicates the rule used for each rewrite.
As another example, the computation of 2⋅2 looks like:
where the last step comprises the previous example computation.
In linguistics , phrase structure rules , also called rewrite rules , are used in some systems of generative grammar , [ 8 ] as a means of generating the grammatically correct sentences of a language. Such a rule typically takes the form A → X {\displaystyle {\rm {A\rightarrow X}}} , where A is a syntactic category label, such as noun phrase or sentence , and X is a sequence of such labels or morphemes , expressing the fact that A can be replaced by X in generating the constituent structure of a sentence. For example, the rule S → N P V P {\displaystyle {\rm {S\rightarrow NP\ VP}}} means that a sentence can consist of a noun phrase (NP) followed by a verb phrase (VP); further rules will specify what sub-constituents a noun phrase and a verb phrase can consist of, and so on.
From the above examples, it is clear that we can think of rewriting systems in an abstract manner. We need to specify a set of objects and the rules that can be applied to transform them. The most general (unidimensional) setting of this notion is called an abstract reduction system [ 9 ] or abstract rewriting system (abbreviated ARS ). [ 10 ] An ARS is simply a set A of objects, together with a binary relation → on A called the reduction relation , rewrite relation [ 11 ] or just reduction . [ 9 ]
Many notions and notations can be defined in the general setting of an ARS. → ∗ {\displaystyle {\overset {*}{\rightarrow }}} is the reflexive transitive closure of → {\displaystyle \rightarrow } . ↔ {\displaystyle \leftrightarrow } is the symmetric closure of → {\displaystyle \rightarrow } . ↔ ∗ {\displaystyle {\overset {*}{\leftrightarrow }}} is the reflexive transitive symmetric closure of → {\displaystyle \rightarrow } . The word problem for an ARS is determining, given x and y , whether x ↔ ∗ y {\displaystyle x{\overset {*}{\leftrightarrow }}y} . An object x in A is called reducible if there exists some other y in A such that x → y {\displaystyle x\rightarrow y} ; otherwise it is called irreducible or a normal form . An object y is called a "normal form of x " if x → ∗ y {\displaystyle x{\stackrel {*}{\rightarrow }}y} , and y is irreducible. If the normal form of x is unique, then this is usually denoted with x ↓ {\displaystyle x{\downarrow }} . If every object has at least one normal form, the ARS is called normalizing . x ↓ y {\displaystyle x\downarrow y} or x and y are said to be joinable if there exists some z with the property that x → ∗ z ← ∗ y {\displaystyle x{\overset {*}{\rightarrow }}z{\overset {*}{\leftarrow }}y} . An ARS is said to possess the Church–Rosser property if x ↔ ∗ y {\displaystyle x{\overset {*}{\leftrightarrow }}y} implies x ↓ y {\displaystyle x\downarrow y} . An ARS is confluent if for all w , x , and y in A , x ← ∗ w → ∗ y {\displaystyle x{\overset {*}{\leftarrow }}w{\overset {*}{\rightarrow }}y} implies x ↓ y {\displaystyle x\downarrow y} . An ARS is locally confluent if and only if for all w , x , and y in A , x ← w → y {\displaystyle x\leftarrow w\rightarrow y} implies x ↓ y {\displaystyle x{\mathbin {\downarrow }}y} . An ARS is said to be terminating or noetherian if there is no infinite chain x 0 → x 1 → x 2 → ⋯ {\displaystyle x_{0}\rightarrow x_{1}\rightarrow x_{2}\rightarrow \cdots } . A confluent and terminating ARS is called convergent or canonical .
Important theorems for abstract rewriting systems are that an ARS is confluent iff it has the Church–Rosser property, Newman's lemma (a terminating ARS is confluent if and only if it is locally confluent), and that the word problem for an ARS is undecidable in general.
A string rewriting system (SRS), also known as semi-Thue system , exploits the free monoid structure of the strings (words) over an alphabet to extend a rewriting relation, R {\displaystyle R} , to all strings in the alphabet that contain left- and respectively right-hand sides of some rules as substrings . Formally a semi-Thue system is a tuple ( Σ , R ) {\displaystyle (\Sigma ,R)} where Σ {\displaystyle \Sigma } is a (usually finite) alphabet, and R {\displaystyle R} is a binary relation between some (fixed) strings in the alphabet, called the set of rewrite rules . The one-step rewriting relation → R {\displaystyle {\underset {R}{\rightarrow }}} induced by R {\displaystyle R} on Σ ∗ {\displaystyle \Sigma ^{*}} is defined as: if s , t ∈ Σ ∗ {\displaystyle s,t\in \Sigma ^{*}} are any strings, then s → R t {\displaystyle s{\underset {R}{\rightarrow }}t} if there exist x , y , u , v ∈ Σ ∗ {\displaystyle x,y,u,v\in \Sigma ^{*}} such that s = x u y {\displaystyle s=xuy} , t = x v y {\displaystyle t=xvy} , and u R v {\displaystyle uRv} . Since → R {\displaystyle {\underset {R}{\rightarrow }}} is a relation on Σ ∗ {\displaystyle \Sigma ^{*}} , the pair ( Σ ∗ , → R ) {\displaystyle (\Sigma ^{*},{\underset {R}{\rightarrow }})} fits the definition of an abstract rewriting system. Since the empty string is in Σ ∗ {\displaystyle \Sigma ^{*}} , R {\displaystyle R} is a subset of → R {\displaystyle {\underset {R}{\rightarrow }}} . If the relation R {\displaystyle R} is symmetric , then the system is called a Thue system .
In a SRS, the reduction relation → R ∗ {\displaystyle {\overset {*}{\underset {R}{\rightarrow }}}} is compatible with the monoid operation, meaning that x → R ∗ y {\displaystyle x{\overset {*}{\underset {R}{\rightarrow }}}y} implies u x v → R ∗ u y v {\displaystyle uxv{\overset {*}{\underset {R}{\rightarrow }}}uyv} for all strings x , y , u , v ∈ Σ ∗ {\displaystyle x,y,u,v\in \Sigma ^{*}} . Similarly, the reflexive transitive symmetric closure of → R {\displaystyle {\underset {R}{\rightarrow }}} , denoted ↔ R ∗ {\displaystyle {\overset {*}{\underset {R}{\leftrightarrow }}}} , is a congruence , meaning it is an equivalence relation (by definition) and it is also compatible with string concatenation. The relation ↔ R ∗ {\displaystyle {\overset {*}{\underset {R}{\leftrightarrow }}}} is called the Thue congruence generated by R {\displaystyle R} . In a Thue system, i.e. if R {\displaystyle R} is symmetric, the rewrite relation → R ∗ {\displaystyle {\overset {*}{\underset {R}{\rightarrow }}}} coincides with the Thue congruence ↔ R ∗ {\displaystyle {\overset {*}{\underset {R}{\leftrightarrow }}}} .
The notion of a semi-Thue system essentially coincides with the presentation of a monoid . Since ↔ R ∗ {\displaystyle {\overset {*}{\underset {R}{\leftrightarrow }}}} is a congruence, we can define the factor monoid M R = Σ ∗ / ↔ R ∗ {\displaystyle {\mathcal {M}}_{R}=\Sigma ^{*}/{\overset {*}{\underset {R}{\leftrightarrow }}}} of the free monoid Σ ∗ {\displaystyle \Sigma ^{*}} by the Thue congruence. If a monoid M {\displaystyle {\mathcal {M}}} is isomorphic with M R {\displaystyle {\mathcal {M}}_{R}} , then the semi-Thue system ( Σ , R ) {\displaystyle (\Sigma ,R)} is called a monoid presentation of M {\displaystyle {\mathcal {M}}} .
We immediately get some very useful connections with other areas of algebra. For example, the alphabet { a , b } {\displaystyle \{a,b\}} with the rules { a b → ε , b a → ε } {\displaystyle \{ab\rightarrow \varepsilon ,ba\rightarrow \varepsilon \}} , where ε {\displaystyle \varepsilon } is the empty string , is a presentation of the free group on one generator. If instead the rules are just { a b → ε } {\displaystyle \{ab\rightarrow \varepsilon \}} , then we obtain a presentation of the bicyclic monoid . Thus semi-Thue systems constitute a natural framework for solving the word problem for monoids and groups. In fact, every monoid has a presentation of the form ( Σ , R ) {\displaystyle (\Sigma ,R)} , i.e. it may always be presented by a semi-Thue system, possibly over an infinite alphabet.
The word problem for a semi-Thue system is undecidable in general; this result is sometimes known as the Post–Markov theorem . [ 12 ]
A term rewriting system ( TRS ) is a rewriting system whose objects are terms , which are expressions with nested sub-expressions. For example, the system shown under § Logic above is a term rewriting system. The terms in this system are composed of binary operators ( ∨ ) {\displaystyle (\vee )} and ( ∧ ) {\displaystyle (\wedge )} and the unary operator ( ¬ ) {\displaystyle (\neg )} . Also present in the rules are variables, which represent any possible term (though a single variable always represents the same term throughout a single rule).
In contrast to string rewriting systems, whose objects are sequences of symbols, the objects of a term rewriting system form a term algebra . A term can be visualized as a tree of symbols, the set of admitted symbols being fixed by a given signature . As a formalism, term rewriting systems have the full power of Turing machines , that is, every computable function can be defined by a term rewriting system. [ 13 ]
Some programming languages are based on term rewriting. One such example is Pure, a functional programming language for mathematical applications. [ 14 ] [ 15 ]
A rewrite rule is a pair of terms , commonly written as l → r {\displaystyle l\rightarrow r} , to indicate that the left-hand side l can be replaced by the right-hand side r . A term rewriting system is a set R of such rules. A rule l → r {\displaystyle l\rightarrow r} can be applied to a term s if the left term l matches some subterm of s , that is, if there is some substitution σ {\displaystyle \sigma } such that the subterm of s {\displaystyle s} rooted at some position p is the result of applying the substitution σ {\displaystyle \sigma } to the term l . The subterm matching the left hand side of the rule is called a redex or reducible expression . [ 16 ] The result term t of this rule application is then the result of replacing the subterm at position p in s by the term r {\displaystyle r} with the substitution σ {\displaystyle \sigma } applied, see picture 1. In this case, s {\displaystyle s} is said to be rewritten in one step , or rewritten directly , to t {\displaystyle t} by the system R {\displaystyle R} , formally denoted as s → R t {\displaystyle s\rightarrow _{R}t} , s → R t {\displaystyle s{\underset {R}{\rightarrow }}t} , or as s → R t {\displaystyle s{\overset {R}{\rightarrow }}t} by some authors.
If a term t 1 {\displaystyle t_{1}} can be rewritten in several steps into a term t n {\displaystyle t_{n}} , that is, if t 1 → R t 2 → R ⋯ → R t n {\displaystyle t_{1}{\underset {R}{\rightarrow }}t_{2}{\underset {R}{\rightarrow }}\cdots {\underset {R}{\rightarrow }}t_{n}} , the term t 1 {\displaystyle t_{1}} is said to be rewritten to t n {\displaystyle t_{n}} , formally denoted as t 1 → R + t n {\displaystyle t_{1}{\overset {+}{\underset {R}{\rightarrow }}}t_{n}} . In other words, the relation → R + {\displaystyle {\overset {+}{\underset {R}{\rightarrow }}}} is the transitive closure of the relation → R {\displaystyle {\underset {R}{\rightarrow }}} ; often, also the notation → R ∗ {\displaystyle {\overset {*}{\underset {R}{\rightarrow }}}} is used to denote the reflexive-transitive closure of → R {\displaystyle {\underset {R}{\rightarrow }}} , that is, s → R ∗ t {\displaystyle s{\overset {*}{\underset {R}{\rightarrow }}}t} if s = t {\displaystyle s=t} or s → R + t {\displaystyle s{\overset {+}{\underset {R}{\rightarrow }}}t} . [ 17 ] A term rewriting given by a set R {\displaystyle R} of rules can be viewed as an abstract rewriting system as defined above , with terms as its objects and → R {\displaystyle {\underset {R}{\rightarrow }}} as its rewrite relation.
For example, x ∗ ( y ∗ z ) → ( x ∗ y ) ∗ z {\displaystyle x*(y*z)\rightarrow (x*y)*z} is a rewrite rule, commonly used to establish a normal form with respect to the associativity of ∗ {\displaystyle *} .
That rule can be applied at the numerator in the term a ∗ ( ( a + 1 ) ∗ ( a + 2 ) ) 1 ∗ ( 2 ∗ 3 ) {\displaystyle {\frac {a*((a+1)*(a+2))}{1*(2*3)}}} with the matching substitution { x ↦ a , y ↦ a + 1 , z ↦ a + 2 } {\displaystyle \{x\mapsto a,\;y\mapsto a+1,\;z\mapsto a+2\}} , see picture 2. [ note 2 ] Applying that substitution to the rule's right-hand side yields the term ( a ∗ ( a + 1 ) ) ∗ ( a + 2 ) {\displaystyle (a*(a+1))*(a+2)} , and replacing the numerator by that term yields ( a ∗ ( a + 1 ) ) ∗ ( a + 2 ) 1 ∗ ( 2 ∗ 3 ) {\displaystyle {\frac {(a*(a+1))*(a+2)}{1*(2*3)}}} , which is the result term of applying the rewrite rule. Altogether, applying the rewrite rule has achieved what is called "applying the associativity law for ∗ {\displaystyle *} to a ∗ ( ( a + 1 ) ∗ ( a + 2 ) ) 1 ∗ ( 2 ∗ 3 ) {\displaystyle {\frac {a*((a+1)*(a+2))}{1*(2*3)}}} " in elementary algebra. Alternately, the rule could have been applied to the denominator of the original term, yielding a ∗ ( ( a + 1 ) ∗ ( a + 2 ) ) ( 1 ∗ 2 ) ∗ 3 {\displaystyle {\frac {a*((a+1)*(a+2))}{(1*2)*3}}} .
Termination issues of rewrite systems in general are handled in Abstract rewriting system#Termination and convergence . For term rewriting systems in particular, the following additional subtleties are to be considered.
Termination even of a system consisting of one rule with a linear left-hand side is undecidable. [ 18 ] [ 19 ] Termination is also undecidable for systems using only unary function symbols; however, it is decidable for finite ground systems. [ 20 ]
The following term rewrite system is normalizing, [ note 3 ] but not terminating, [ note 4 ] and not confluent: [ 21 ] f ( x , x ) → g ( x ) , f ( x , g ( x ) ) → b , h ( c , x ) → f ( h ( x , c ) , h ( x , x ) ) . {\displaystyle {\begin{aligned}f(x,x)&\rightarrow g(x),\\f(x,g(x))&\rightarrow b,\\h(c,x)&\rightarrow f(h(x,c),h(x,x)).\\\end{aligned}}}
The following two examples of terminating term rewrite systems are due to Toyama: [ 22 ]
and
Their union is a non-terminating system, since
f ( g ( 0 , 1 ) , g ( 0 , 1 ) , g ( 0 , 1 ) ) → f ( 0 , g ( 0 , 1 ) , g ( 0 , 1 ) ) → f ( 0 , 1 , g ( 0 , 1 ) ) → f ( g ( 0 , 1 ) , g ( 0 , 1 ) , g ( 0 , 1 ) ) → ⋯ {\displaystyle {\begin{aligned}&f(g(0,1),g(0,1),g(0,1))\\\rightarrow &f(0,g(0,1),g(0,1))\\\rightarrow &f(0,1,g(0,1))\\\rightarrow &f(g(0,1),g(0,1),g(0,1))\\\rightarrow &\cdots \end{aligned}}} This result disproves a conjecture of Dershowitz , [ 23 ] who claimed that the union of two terminating term rewrite systems R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} is again terminating if all left-hand sides of R 1 {\displaystyle R_{1}} and right-hand sides of R 2 {\displaystyle R_{2}} are linear , and there are no " overlaps " between left-hand sides of R 1 {\displaystyle R_{1}} and right-hand sides of R 2 {\displaystyle R_{2}} . All these properties are satisfied by Toyama's examples.
See Rewrite order and Path ordering (term rewriting) for ordering relations used in termination proofs for term rewriting systems.
Higher-order rewriting systems are a generalization of first-order term rewriting systems to lambda terms , allowing higher order functions and bound variables. [ 24 ] Various results about first-order TRSs can be reformulated for HRSs as well. [ 25 ]
Graph rewrite systems are another generalization of term rewrite systems, operating on graphs instead of ( ground -) terms / their corresponding tree representation.
Trace theory provides a means for discussing multiprocessing in more formal terms, such as via the trace monoid and the history monoid . Rewriting can be performed in trace systems as well. | https://en.wikipedia.org/wiki/Rewriting |
Reye syndrome is a rapidly worsening brain disease . [ 2 ] Symptoms of Reye syndrome may include vomiting , personality changes, confusion, seizures , and loss of consciousness . [ 1 ] While liver toxicity typically occurs in the syndrome, jaundice usually does not. [ 2 ] Death occurs in 20–40% of those affected with Reye syndrome, and about a third of those who survive are left with a significant degree of brain damage . [ 2 ] [ 3 ]
The cause of Reye syndrome is unknown. [ 2 ] It usually begins shortly after recovery from a viral infection , such as influenza or chickenpox . [ 1 ] About 90% of cases in children are associated with aspirin ( salicylate ) use. [ 2 ] Inborn errors of metabolism are also a risk factor. [ 3 ] The syndrome is associated with changes on blood tests such as a high blood ammonia level , low blood sugar level , and prolonged prothrombin time . [ 2 ] Often, the liver is enlarged in those who have the syndrome . [ 2 ]
Prevention is typically by avoiding the use of aspirin in children. [ 1 ] When aspirin was withdrawn for use in children in the US and UK in the 1980s, a decrease of more than 90% in rates of Reye syndrome was observed. [ 2 ] Early diagnosis of the syndrome improves outcomes. [ 1 ] Treatment is supportive ; [ 1 ] mannitol may be used to help with the brain swelling . [ 2 ]
The first detailed description of Reye syndrome was in 1963 by Australian pathologist Douglas Reye . [ 4 ] The syndrome most commonly affects children. [ 2 ] It affects fewer than one in a million children a year. [ 2 ] The general recommendation to use aspirin in children was withdrawn because of Reye syndrome, with use only recommended in Kawasaki disease . [ 3 ]
Reye syndrome progresses through five stages: [ 5 ] [ 6 ] [ 7 ] [ 8 ]
The cause of Reye syndrome is unknown. [ 2 ] It usually begins shortly after recovery from a viral infection , such as influenza or chickenpox . [ 1 ] About 90% of cases in children are associated with aspirin ( salicylate ) use. [ 2 ] Inborn errors of metabolism are also a risk factor. [ 3 ]
The association with aspirin has been shown through epidemiological studies. The diagnosis of Reye syndrome greatly decreased in the 1980s, when genetic testing for inborn errors of metabolism was becoming available in industrialized countries . [ 11 ] A retrospective study of 49 survivors of cases diagnosed as Reye syndrome showed that the majority of the surviving patients had various metabolic disorders , particularly a fatty-acid oxidation disorder medium-chain acyl-CoA dehydrogenase deficiency . [ 12 ]
There is an association between taking aspirin for viral illnesses and the development of Reye syndrome, [ 13 ] but no animal model of Reye syndrome has been developed in which aspirin causes the condition. [ 11 ]
The serious symptoms of Reye syndrome appear to result from damage to cellular mitochondria , [ 14 ] at least in the liver, and there are a number of ways that aspirin could cause or exacerbate mitochondrial damage. A potential increased risk of developing Reye syndrome is one of the main reasons that aspirin has not been recommended for use in children and teenagers, the age group for which the risk of lasting serious effects is highest. [ 15 ]
In some countries, oral mouthcare product Bonjela (not the form specifically designed for teething) has labeling cautioning against its use in children, given its salicylate content. There have been no cases of Reye syndrome following its use, and the measure is a precaution. [ 16 ] Other medications containing salicylates are often similarly labeled as a precaution. [ 17 ]
The Centers for Disease Control and Prevention (CDC), the U.S. Surgeon General, the American Academy of Pediatrics (AAP) and the Food and Drug Administration (FDA) recommend that aspirin and combination products containing aspirin not be given to children and teenagers under 19 years of age during episodes of fever-causing illnesses. Hence, in the United States , it is advised that the opinion of a doctor or pharmacist should be obtained before anyone under 19 years of age is given any medication containing aspirin (also known on some medicine labels as acetylsalicylate , salicylate , acetylsalicylic acid , ASA, or salicylic acid). [ 18 ]
Current advice in the United Kingdom by the Committee on Safety of Medicines is that aspirin should not be given to those under the age of 16 years, unless specifically indicated in Kawasaki disease or in the prevention of blood clot formation. [ 19 ]
Causes for similar symptoms include [ citation needed ]
Treatment is supportive . [ 1 ] Mannitol may be used to help with the brain swelling . [ 2 ]
Documented cases of Reye syndrome in adults are rare. The recovery of adults with the syndrome is generally complete, with liver and brain function returning to normal within two weeks of onset. [ citation needed ]
In children, mild to moderate to severe permanent brain damage is possible, especially in infants. Over thirty percent of the cases reported in the United States from 1981 through 1997 resulted in fatality. [ 20 ]
Reye syndrome occurs almost exclusively in children. While a few adult cases have been reported over the years, these cases do not typically show permanent neural or liver damage. Unlike in the United Kingdom, the surveillance for Reye syndrome in the United States is focused on people under 18 years of age. [ citation needed ]
In 1980, after the CDC began cautioning physicians and parents about the association between Reye syndrome and the use of salicylates in children with chickenpox or virus-like illnesses, the incidence of Reye syndrome in the United States began to decline, prior to the FDA 's issue of warning labels on aspirin in 1986. [ 11 ] In the United States between 1980 and 1997, the number of reported cases of Reye syndrome decreased from 555 cases in 1980 to about two cases per year since 1994. During this time period 93% of reported cases for which racial data were available occurred in whites and the median age was six years. In 93% of cases a viral illness had occurred in the preceding three-week period. For the period 1991–1994, the annual rate of hospitalization due to Reye syndrome in the United States was estimated to be between < 0.3 – 1 per million population less than 18 years of age. [ 21 ]
During the 1980s, a case-control study carried out in the United Kingdom also demonstrated an association between Reye syndrome and aspirin exposure. [ 22 ] In June 1986, the United Kingdom Committee on Safety of Medicines issued warnings against the use of aspirin in children under 12 years of age and warning labels on aspirin-containing medications were introduced. United Kingdom surveillance for Reye syndrome documented a decline in the incidence of the illness after 1986. The reported incidence rate of Reye syndrome decreased from a high of 0.63 per 100,000 population less than 12 years of age in 1983–1984 to 0.11 in 1990–1991. [ citation needed ]
From November 1995 to November 1996 in France, a national survey of pediatric departments for children under 15 years of age with unexplained encephalopathy and a threefold (or greater) increase in serum aminotransferase and/or ammonia led to the identification of nine definite cases of Reye syndrome (0.79 cases per million children). Eight of the nine children with Reye syndrome were found to have been exposed to aspirin. In part because of this survey result, the French Medicines Agency reinforced the international attention to the relationship between aspirin and Reye syndrome by issuing its own public and professional warnings about this relationship. [ 23 ]
The syndrome is named after Douglas Reye , who, along with fellow physicians Graeme Morgan and Jim Baral, published the first study of the syndrome in 1963 in The Lancet . [ 24 ] In retrospect, the occurrence of the syndrome may have first been reported in 1929. Also in 1964, George Johnson and colleagues published an investigation of an outbreak of influenza B that described 16 children who developed neurological problems, four of whom had a profile remarkably similar to Reye syndrome. Some investigators refer to this disorder as Reye-Johnson syndrome, although it is more commonly called Reye syndrome. In 1979, Karen Starko and colleagues conducted a case-control study in Phoenix, Arizona, and found the first statistically significant link between aspirin use and Reye syndrome. [ 25 ] Studies in Ohio and Michigan soon confirmed her findings [ 26 ] pointing to the use of aspirin during an upper respiratory tract or chickenpox infection as a possible trigger of the syndrome. Beginning in 1980, the CDC cautioned physicians and parents about the association between Reye syndrome and the use of salicylates in children and teenagers with chickenpox or virus-like illnesses. In 1982, the U.S. Surgeon General issued an advisory, and in 1986, the Food and Drug Administration required a Reye syndrome-related warning label for all aspirin-containing medications. [ 27 ] | https://en.wikipedia.org/wiki/Reye_syndrome |
In fluid dynamics , the reyn is a British unit of dynamic viscosity ,
named in honour of Osbourne Reynolds , for whom the Reynolds number is also named. [ 1 ]
By definition,
It follows that the relation between the reyn and the poise is approximately
In SI units, viscosity is expressed in newton-seconds per square meter, or equivalently in pascal -seconds. The conversion factor between the two is approximately
This standards - or measurement -related article is a stub . You can help Wikipedia by expanding it .
This fluid dynamics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reyn |
The Reynolds-averaged Navier–Stokes equations ( RANS equations ) are time-averaged [ a ] equations of motion for fluid flow . The idea behind the equations is Reynolds decomposition , whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities, an idea first proposed by Osborne Reynolds . [ 1 ] The RANS equations are primarily used to describe turbulent flows . These equations can be used with approximations based on knowledge of the properties of flow turbulence to give approximate time-averaged solutions to the Navier–Stokes equations .
For a stationary flow of an incompressible Newtonian fluid , these equations can be written in Einstein notation in Cartesian coordinates as: ρ u ¯ j ∂ u ¯ i ∂ x j = ρ f ¯ i + ∂ ∂ x j [ − p ¯ δ i j + μ ( ∂ u ¯ i ∂ x j + ∂ u ¯ j ∂ x i ) − ρ u i ′ u j ′ ¯ ] . {\displaystyle \rho {\bar {u}}_{j}{\frac {\partial {\bar {u}}_{i}}{\partial x_{j}}}=\rho {\bar {f}}_{i}+{\frac {\partial }{\partial x_{j}}}\left[-{\bar {p}}\delta _{ij}+\mu \left({\frac {\partial {\bar {u}}_{i}}{\partial x_{j}}}+{\frac {\partial {\bar {u}}_{j}}{\partial x_{i}}}\right)-\rho {\overline {u_{i}^{\prime }u_{j}^{\prime }}}\right].}
The left hand side of this equation represents the change in mean momentum of a fluid element owing to the unsteadiness in the mean flow and the convection by the mean flow. This change is balanced by the mean body force , the isotropic stress owing to the mean pressure field, the viscous stresses, and apparent stress ( − ρ u i ′ u j ′ ¯ ) {\displaystyle \left(-\rho {\overline {u_{i}^{\prime }u_{j}^{\prime }}}\right)} owing to the fluctuating velocity field, generally referred to as the Reynolds stress . This nonlinear Reynolds stress term requires additional modeling to close the RANS equation for solving, and has led to the creation of many different turbulence models . The time-average operator . ¯ {\displaystyle {\overline {.}}} is a Reynolds operator .
The basic tool required for the derivation of the RANS equations from the instantaneous Navier–Stokes equations is the Reynolds decomposition . Reynolds decomposition refers to separation of the flow variable (like velocity u {\displaystyle u} ) into the mean (time-averaged) component ( u ¯ {\displaystyle {\overline {u}}} ) and the fluctuating component ( u ′ {\displaystyle u^{\prime }} ). Because the mean operator is a Reynolds operator , it has a set of properties. One of these properties is that the mean of the fluctuating quantity is equal to zero ( u ′ ¯ ) {\displaystyle ({\bar {u'}})} [ 2 ] Some authors prefer using U {\displaystyle U} instead of u ¯ {\displaystyle {\bar {u}}} for the mean term (since an overbar is sometimes used to represent a vector). In this case, the fluctuating term u ′ {\displaystyle u^{\prime }} is represented instead by u {\displaystyle u} . This is possible because the two terms do not appear simultaneously in the same equation. To avoid confusion, the notation u {\displaystyle u} , u ¯ {\displaystyle {\bar {u}}} , and u ′ {\displaystyle u'} will be used to represent the instantaneous, mean, and fluctuating terms, respectively.
The properties of Reynolds operators are useful in the derivation of the RANS equations. Using these properties, the Navier–Stokes equations of motion, expressed in tensor notation, are (for an incompressible Newtonian fluid): ∂ u i ∂ x i = 0 {\displaystyle {\frac {\partial u_{i}}{\partial x_{i}}}=0} ∂ u i ∂ t + u j ∂ u i ∂ x j = f i − 1 ρ ∂ p ∂ x i + ν ∂ 2 u i ∂ x j ∂ x j {\displaystyle {\frac {\partial u_{i}}{\partial t}}+u_{j}{\frac {\partial u_{i}}{\partial x_{j}}}=f_{i}-{\frac {1}{\rho }}{\frac {\partial p}{\partial x_{i}}}+\nu {\frac {\partial ^{2}u_{i}}{\partial x_{j}\partial x_{j}}}} where f i {\displaystyle f_{i}} is a vector representing external forces.
Next, each instantaneous quantity can be split into time-averaged and fluctuating components, and the resulting equation time-averaged, [ b ] to yield:
∂ u ¯ i ∂ x i = 0 {\displaystyle {\frac {\partial {\bar {u}}_{i}}{\partial x_{i}}}=0} ∂ u ¯ i ∂ t + u ¯ j ∂ u ¯ i ∂ x j + u j ′ ∂ u i ′ ∂ x j ¯ = f ¯ i − 1 ρ ∂ p ¯ ∂ x i + ν ∂ 2 u ¯ i ∂ x j ∂ x j . {\displaystyle {\frac {\partial {\bar {u}}_{i}}{\partial t}}+{\bar {u}}_{j}{\frac {\partial {\bar {u}}_{i}}{\partial x_{j}}}+{\overline {u_{j}^{\prime }{\frac {\partial u_{i}^{\prime }}{\partial x_{j}}}}}={\bar {f}}_{i}-{\frac {1}{\rho }}{\frac {\partial {\bar {p}}}{\partial x_{i}}}+\nu {\frac {\partial ^{2}{\bar {u}}_{i}}{\partial x_{j}\partial x_{j}}}.}
The momentum equation can also be written as, [ c ]
∂ u ¯ i ∂ t + u ¯ j ∂ u ¯ i ∂ x j = f ¯ i − 1 ρ ∂ p ¯ ∂ x i + ν ∂ 2 u ¯ i ∂ x j ∂ x j − ∂ u i ′ u j ′ ¯ ∂ x j . {\displaystyle {\frac {\partial {\bar {u}}_{i}}{\partial t}}+{\bar {u}}_{j}{\frac {\partial {\bar {u}}_{i}}{\partial x_{j}}}={\bar {f}}_{i}-{\frac {1}{\rho }}{\frac {\partial {\bar {p}}}{\partial x_{i}}}+\nu {\frac {\partial ^{2}{\bar {u}}_{i}}{\partial x_{j}\partial x_{j}}}-{\frac {\partial {\overline {u_{i}^{\prime }u_{j}^{\prime }}}}{\partial x_{j}}}.} On further manipulations this yields, ρ ∂ u ¯ i ∂ t + ρ u ¯ j ∂ u ¯ i ∂ x j = ρ f ¯ i + ∂ ∂ x j [ − p ¯ δ i j + 2 μ S ¯ i j − ρ u i ′ u j ′ ¯ ] {\displaystyle \rho {\frac {\partial {\bar {u}}_{i}}{\partial t}}+\rho {\bar {u}}_{j}{\frac {\partial {\bar {u}}_{i}}{\partial x_{j}}}=\rho {\bar {f}}_{i}+{\frac {\partial }{\partial x_{j}}}\left[-{\bar {p}}\delta _{ij}+2\mu {\bar {S}}_{ij}-\rho {\overline {u_{i}^{\prime }u_{j}^{\prime }}}\right]}
where, S ¯ i j = 1 2 ( ∂ u ¯ i ∂ x j + ∂ u ¯ j ∂ x i ) {\displaystyle {\bar {S}}_{ij}={\frac {1}{2}}\left({\frac {\partial {\bar {u}}_{i}}{\partial x_{j}}}+{\frac {\partial {\bar {u}}_{j}}{\partial x_{i}}}\right)} is the mean rate of strain tensor.
Finally, since integration in time removes the time dependence of the resultant terms, the time derivative must be eliminated, leaving: ρ u ¯ j ∂ u ¯ i ∂ x j = ρ f i ¯ + ∂ ∂ x j [ − p ¯ δ i j + 2 μ S ¯ i j − ρ u i ′ u j ′ ¯ ] . {\displaystyle \rho {\bar {u}}_{j}{\frac {\partial {\bar {u}}_{i}}{\partial x_{j}}}=\rho {\bar {f_{i}}}+{\frac {\partial }{\partial x_{j}}}\left[-{\bar {p}}\delta _{ij}+2\mu {\bar {S}}_{ij}-\rho {\overline {u_{i}^{\prime }u_{j}^{\prime }}}\right].}
The time evolution equation of Reynolds stress is given by: [ 3 ] ∂ u i ′ u j ′ ¯ ∂ t + u ¯ k ∂ u i ′ u j ′ ¯ ∂ x k = − u i ′ u k ′ ¯ ∂ u ¯ j ∂ x k − u j ′ u k ′ ¯ ∂ u ¯ i ∂ x k + p ′ ρ ( ∂ u i ′ ∂ x j + ∂ u j ′ ∂ x i ) ¯ − ∂ ∂ x k ( u i ′ u j ′ u k ′ ¯ + p ′ u i ′ ¯ ρ δ j k + p ′ u j ′ ¯ ρ δ i k − ν ∂ u i ′ u j ′ ¯ ∂ x k ) − 2 ν ∂ u i ′ ∂ x k ∂ u j ′ ∂ x k ¯ {\displaystyle {\frac {\partial {\overline {u_{i}^{\prime }u_{j}^{\prime }}}}{\partial t}}+{\bar {u}}_{k}{\frac {\partial {\overline {u_{i}^{\prime }u_{j}^{\prime }}}}{\partial x_{k}}}=-{\overline {u_{i}^{\prime }u_{k}^{\prime }}}{\frac {\partial {\bar {u}}_{j}}{\partial x_{k}}}-{\overline {u_{j}^{\prime }u_{k}^{\prime }}}{\frac {\partial {\bar {u}}_{i}}{\partial x_{k}}}+{\overline {{\frac {p^{\prime }}{\rho }}\left({\frac {\partial u_{i}^{\prime }}{\partial x_{j}}}+{\frac {\partial u_{j}^{\prime }}{\partial x_{i}}}\right)}}-{\frac {\partial }{\partial x_{k}}}\left({\overline {u_{i}^{\prime }u_{j}^{\prime }u_{k}^{\prime }}}+{\frac {\overline {p^{\prime }u_{i}^{\prime }}}{\rho }}\delta _{jk}+{\frac {\overline {p^{\prime }u_{j}^{\prime }}}{\rho }}\delta _{ik}-\nu {\frac {\partial {\overline {u_{i}^{\prime }u_{j}^{\prime }}}}{\partial x_{k}}}\right)-2\nu {\overline {{\frac {\partial u_{i}^{\prime }}{\partial x_{k}}}{\frac {\partial u_{j}^{\prime }}{\partial x_{k}}}}}} This equation is very complicated. If u i ′ u j ′ ¯ {\displaystyle {\overline {u_{i}^{\prime }u_{j}^{\prime }}}} is traced, turbulence kinetic energy is obtained.
The last term ν ∂ u i ′ ∂ x k ∂ u j ′ ∂ x k ¯ {\displaystyle \nu {\overline {{\frac {\partial u_{i}^{\prime }}{\partial x_{k}}}{\frac {\partial u_{j}^{\prime }}{\partial x_{k}}}}}} is turbulent dissipation rate. All RANS models are based on the above equation. | https://en.wikipedia.org/wiki/Reynolds-averaged_Navier–Stokes_equations |
The Reynolds Layer is a layer of ionised hydrogen gas in the plane of the Milky Way . It was named after Ron Reynolds [ 1 ] who discovered that there is such gas. The layer is a disk 750,000 light years in diameter, and 6000 light years thick. The whole disk rotates in the same direction as the Milky Way. [ 2 ]
This astronomy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reynolds_Layer |
The Reynolds Analogy is popularly known to relate turbulent momentum and heat transfer. [ 1 ] That is because in a turbulent flow (in a pipe or in a boundary layer ) the transport of momentum and the transport of heat largely depends on the same turbulent eddies : the velocity and the temperature profiles have the same shape.
The main assumption is that heat flux q/A in a turbulent system is analogous to momentum flux τ, which suggests that the ratio τ/(q/A) must be constant for all radial positions.
The complete Reynolds analogy* is:
f 2 = h C p × G = k c ′ V a v {\displaystyle {\frac {f}{2}}={\frac {h}{C_{p}\times G}}={\frac {k'_{c}}{V_{av}}}}
Experimental data for gas streams agree approximately with above equation if the Schmidt and Prandtl numbers are near 1.0 and only skin friction is present in flow past a flat plate or inside a pipe. When liquids are present and/or form drag is present, the analogy is conventionally known to be invalid. [ 1 ]
In 2008, the qualitative form of validity of Reynolds' analogy was re-visited for laminar flow of incompressible fluid with variable dynamic viscosity (μ). [ 2 ] It was shown that the inverse dependence of Reynolds number ( Re ) and skin friction coefficient( c f ) is the basis for validity of the Reynolds’ analogy, in laminar convective flows with constant & variable μ. For μ = const. it reduces to the popular form of Stanton number ( St ) increasing with increasing Re , whereas for variable μ it reduces to St increasing with decreasing Re . Consequently, the Chilton-Colburn analogy of St • Pr 2/3 increasing with increasing c f is qualitatively valid whenever the
Reynolds’ analogy is valid. Further, the validity of the Reynolds’ analogy is linked to the applicability of Prigogine's Theorem of Minimum Entropy Production . [ 3 ] Thus, Reynolds' analogy is valid for flows that are close to developed, for whom, changes in the gradients of field variables (velocity & temperature) along the flow are small. [ 2 ] | https://en.wikipedia.org/wiki/Reynolds_analogy |
In fluid mechanics (specifically lubrication theory ), the Reynolds equation is a partial differential equation governing the pressure distribution of thin viscous fluid films . It was first derived by Osborne Reynolds in 1886. [ 1 ] The classical Reynolds Equation can be used to describe the pressure distribution in nearly any type of fluid film bearing ; a bearing type in which the bounding bodies are fully separated by a thin layer of liquid or gas.
The general Reynolds equation is: ∂ ∂ x ( ρ h 3 12 μ ∂ p ∂ x ) + ∂ ∂ y ( ρ h 3 12 μ ∂ p ∂ y ) = ∂ ∂ x ( ρ h ( u a + u b ) 2 ) + ∂ ∂ y ( ρ h ( v a + v b ) 2 ) + ρ ( w a − w b ) − ρ u a ∂ h ∂ x − ρ v a ∂ h ∂ y + h ∂ ρ ∂ t {\displaystyle {\frac {\partial }{\partial x}}\left({\frac {\rho h^{3}}{12\mu }}{\frac {\partial p}{\partial x}}\right)+{\frac {\partial }{\partial y}}\left({\frac {\rho h^{3}}{12\mu }}{\frac {\partial p}{\partial y}}\right)={\frac {\partial }{\partial x}}\left({\frac {\rho h\left(u_{a}+u_{b}\right)}{2}}\right)+{\frac {\partial }{\partial y}}\left({\frac {\rho h\left(v_{a}+v_{b}\right)}{2}}\right)+\rho \left(w_{a}-w_{b}\right)-\rho u_{a}{\frac {\partial h}{\partial x}}-\rho v_{a}{\frac {\partial h}{\partial y}}+h{\frac {\partial \rho }{\partial t}}}
Where:
The equation can either be used with consistent units or nondimensionalized .
The Reynolds Equation assumes:
For some simple bearing geometries and boundary conditions, the Reynolds equation can be solved analytically. Often however, the equation must be solved numerically. Frequently this involves discretizing the geometric domain, and then applying a finite technique - often FDM , FVM , or FEM .
A full derivation of the Reynolds Equation from the Navier-Stokes equation can be found in numerous lubrication text books. [ 2 ] [ 3 ]
In general, Reynolds equation has to be solved using numerical methods such as finite difference, or finite element. In certain simplified cases, however, analytical or approximate solutions can be obtained. [ 4 ]
For the case of rigid sphere on flat geometry, steady-state case and half-Sommerfeld cavitation boundary condition, the 2-D Reynolds equation can be solved analytically. This solution was proposed by a Nobel Prize winner Pyotr Kapitsa . Half-Sommerfeld boundary condition was shown to be inaccurate and this solution has to be used with care.
In case of 1-D Reynolds equation several analytical or semi-analytical solutions are available. In 1916 Martin obtained a closed form solution [ 5 ] for a minimum film thickness and pressure for a rigid cylinder and plane geometry. This solution is not accurate for the cases when the elastic deformation of the surfaces contributes considerably to the film thickness. In 1949, Grubin obtained an approximate solution [ 6 ] for so called elasto-hydrodynamic lubrication (EHL) line contact problem, where he combined both elastic deformation and lubricant hydrodynamic flow. In this solution it was assumed that the pressure profile follows Hertz solution . The model is therefore accurate at high loads, when the hydrodynamic pressure tends to be close to the Hertz contact pressure. [ 7 ]
The Reynolds equation is used to model the pressure in many applications. For example:
In 1978 Patir and Cheng introduced an average flow model, [ 8 ] [ 9 ] which modifies the Reynolds equation to consider the effects of surface roughness on lubricated contacts. The average flow model spans the regimes of lubrication where the surfaces are close together and/or touching. The average flow model applied "flow factors" to adjust how easy it is for the lubricant to flow in the direction of sliding or perpendicular to it. They also presented terms for adjusting the contact shear calculation. In these regimes, the surface topography acts to direct the lubricant flow, which has been demonstrated to affect the lubricant pressure and thus the surface separation and contact friction. [ 10 ]
Several notable attempts have been made to taken additional details of the contact into account in the simulation of fluid films in contacts. Leighton et al. [ 10 ] presented a method for determining the flow factors needed for the average flow model from any measured surface. Harp and Salent [ 11 ] extended the average flow model by considering the inter-asperity cavitation. Chengwei and Linqing [ 12 ] used an analysis of the surface height probability distribution to remove one of the more complex terms from the average Reynolds equation, d h T ¯ / d h {\displaystyle d{\bar {h_{T}}}/dh} and replace it with a flow factor referred to as contact flow factor, ϕ h {\displaystyle \phi _{h}} . Knoll et al. calculated flow factors, taking into account the elastic deformation of the surfaces. Meng et al. [ 13 ] also considered the elastic deformation of the contacting surfaces.
The work of Patir and Cheng was a precursor to the investigations of surface texturing in lubricated contacts. Demonstrating how large scale surface features generated micro-hydrodynamic lift to separate films and reduce friction, but only when the contact conditions support this. [ 14 ]
The average flow model of Patir and Cheng, [ 8 ] [ 9 ] is often coupled with the rough surface interaction model of Greenwood and Tripp [ 15 ] for modelling of the interaction of rough surfaces in loaded contacts. [ 10 ] [ 16 ] | https://en.wikipedia.org/wiki/Reynolds_equation |
In fluid dynamics , the Reynolds number ( Re ) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. [ 2 ] At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow , while at high Reynolds numbers, flows tend to be turbulent . [ 3 ] The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow ( eddy currents ). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation .
The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full-size version. The predictions of the onset of turbulence and the ability to calculate scaling effects can be used to help predict fluid behavior on a larger scale, such as in local or global air or water movement, and thereby the associated meteorological and climatological effects. [ 4 ]
The concept was introduced by George Stokes in 1851, [ 5 ] but the Reynolds number was named by Arnold Sommerfeld in 1908 [ 6 ] after Osborne Reynolds who popularized its use in 1883 [ 7 ] [ 8 ] (an example of Stigler's law of eponymy ).
The Reynolds number is the ratio of inertial forces to viscous forces within a fluid that is subjected to relative internal movement due to different fluid velocities. A region where these forces change behavior is known as a boundary layer , such as the bounding surface in the interior of a pipe. A similar effect is created by the introduction of a stream of high-velocity fluid into a low-velocity fluid, such as the hot gases emitted from a flame in air. This relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which tends to inhibit turbulence. The Reynolds number quantifies the relative importance of these two types of forces for given flow conditions and is a guide to when turbulent flow will occur in a particular situation. [ 9 ]
This ability to predict the onset of turbulent flow is an important design tool for equipment such as piping systems or aircraft wings, but the Reynolds number is also used in scaling of fluid dynamics problems and is used to determine dynamic similitude between two different cases of fluid flow, such as between a model aircraft, and its full-size version. Such scaling is not linear and the application of Reynolds numbers to both situations allows scaling factors to be developed.
With respect to laminar and turbulent flow regimes:
The Reynolds number is defined as: [ 6 ]
R e = u L ν = ρ u L μ {\displaystyle \mathrm {Re} ={\frac {uL}{\nu }}={\frac {\rho uL}{\mu }}}
where:
The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface. [ n 1 ] These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension (L in the above equation). This dimension is a matter of convention—for example radius and diameter are equally valid to describe spheres or circles, but one is chosen by convention. For aircraft or ships, the length or width can be used. For flow in a pipe, or for a sphere moving in a fluid, the internal diameter is generally used today. Other shapes such as rectangular pipes or non-spherical objects have an equivalent diameter defined. For fluids of variable density such as compressible gases or fluids of variable viscosity such as non-Newtonian fluids , special rules apply. The velocity may also be a matter of convention in some circumstances, notably stirred vessels.
In practice, matching the Reynolds number is not on its own sufficient to guarantee similitude. Fluid flow is generally chaotic, and very small changes to shape and surface roughness of bounding surfaces can result in very different flows. Nevertheless, Reynolds numbers are a very important guide and are widely used.
If we know that the relevant physical quantities in a physical system are only ρ , u , L , μ {\displaystyle \rho ,u,L,\mu } , then the Reynolds number is essentially fixed by the Buckingham π theorem .
In detail, since there are 4 quantities ρ , u , L , μ {\displaystyle \rho ,u,L,\mu } , but they have only 3 dimensions (length, time, mass), we can consider ρ x 1 u x 2 L x 3 μ x 4 {\displaystyle \rho ^{x_{1}}u^{x_{2}}L^{x_{3}}\mu ^{x_{4}}} , where x 1 , . . . , x 4 {\displaystyle x_{1},...,x_{4}} are real numbers. Setting the three dimensions of ρ x 1 u x 2 L x 3 μ x 4 {\displaystyle \rho ^{x_{1}}u^{x_{2}}L^{x_{3}}\mu ^{x_{4}}} to zero, we obtain 3 independent linear constraints, so the solution space has 1 dimension, and it is spanned by the vector ( 1 , 1 , 1 , − 1 ) {\displaystyle (1,1,1,-1)} .
Thus, any dimensionless quantity constructed out of ρ , u , L , μ {\displaystyle \rho ,u,L,\mu } is a function of ρ u L μ − 1 {\displaystyle \rho uL\mu ^{-1}} , the Reynolds number.
Alternatively, we can take the incompressible Navier–Stokes equations (convective form) : ∂ u ∂ t + ( u ⋅ ∇ ) u − ν ∇ 2 u = − 1 ρ ∇ p + g {\displaystyle {\frac {\partial \mathbf {u} }{\partial t}}+(\mathbf {u} \cdot \nabla )\mathbf {u} -\nu \,\nabla ^{2}\mathbf {u} =-{\frac {1}{\rho }}\nabla p+\mathbf {g} } Remove the gravity term g {\displaystyle {\mathbf {g}}} , then the left side consists of inertial force ∂ u ∂ t + ( u ⋅ ∇ ) u {\displaystyle {\frac {\partial \mathbf {u} }{\partial t}}+(\mathbf {u} \cdot \nabla )\mathbf {u} } , and viscous force ν ∇ 2 u {\displaystyle \nu \,\nabla ^{2}\mathbf {u} } . Their ratio has the order of ( u ⋅ ∇ ) u ν ∇ 2 u ∼ u 2 / L ν u / L 2 = u L ν {\displaystyle {\frac {(\mathbf {u} \cdot \nabla )\mathbf {u} }{\nu \,\nabla ^{2}\mathbf {u} }}\sim {\frac {u^{2}/L}{\nu u/L^{2}}}={\frac {uL}{\nu }}} , the Reynolds number. This argument is written out in detail on the Scallop theorem page.
The Reynolds number can be obtained when one uses the nondimensional form of the incompressible Navier–Stokes equations for a newtonian fluid expressed in terms of the Lagrangian derivative :
Each term in the above equation has the units of a "body force" (force per unit volume) with the same dimensions of a density times an acceleration. Each term is thus dependent on the exact measurements of a flow. When one renders the equation nondimensional, that is when we multiply it by a factor with inverse units of the base equation, we obtain a form that does not depend directly on the physical sizes. One possible way to obtain a nondimensional equation is to multiply the whole equation by the factor
where
If we now set
we can rewrite the Navier–Stokes equation without dimensions:
where the term μ / ρLV = 1 / Re .
Finally, dropping the primes for ease of reading:
This is why mathematically all Newtonian, incompressible flows with the same Reynolds number are comparable. Notice also that in the above equation, the viscous terms vanish for Re → ∞ . Thus flows with high Reynolds numbers are approximately inviscid in the free stream.
Osborne Reynolds famously studied the conditions in which the flow of fluid in pipes transitioned from laminar flow to turbulent flow .
In his 1883 paper Reynolds described the transition from laminar to turbulent flow in a classic experiment in which he examined the behaviour of water flow under different flow velocities using a small stream of dyed water introduced into the centre of clear water flow in a larger pipe.
The larger pipe was glass so the behaviour of the layer of the dyed stream could be observed. At the end of this pipe, there was a flow control valve used to vary the water velocity inside the tube. When the velocity was low, the dyed layer remained distinct throughout the entire length of the large tube. When the velocity was increased, the layer broke up at a given point and diffused throughout the fluid's cross-section. The point at which this happened was the transition point from laminar to turbulent flow.
From these experiments came the dimensionless Reynolds number for dynamic similarity—the ratio of inertial forces to viscous forces. Reynolds also proposed what is now known as the Reynolds averaging of turbulent flows, where quantities such as velocity are expressed as the sum of mean and fluctuating components. Such averaging allows for 'bulk' description of turbulent flow, for example using the Reynolds-averaged Navier–Stokes equations .
For flow in a pipe or tube, the Reynolds number is generally defined as [ 11 ]
where
For shapes such as squares, rectangular or annular ducts where the height and width are comparable, the characteristic dimension for internal-flow situations is taken to be the hydraulic diameter , D H , defined as
where A is the cross-sectional area, and P is the wetted perimeter . The wetted perimeter for a channel is the total perimeter of all channel walls that are in contact with the flow. [ 12 ] This means that the length of the channel exposed to air is not included in the wetted perimeter.
For a circular pipe, the hydraulic diameter is exactly equal to the inside pipe diameter:
For an annular duct, such as the outer channel in a tube-in-tube heat exchanger , the hydraulic diameter can be shown algebraically to reduce to
where
For calculation involving flow in non-circular ducts, the hydraulic diameter can be substituted for the diameter of a circular duct, with reasonable accuracy, if the aspect ratio AR of the duct cross-section remains in the range 1 / 4 < AR < 4. [ 13 ]
In boundary layer flow over a flat plate, experiments confirm that, after a certain length of flow, a laminar boundary layer will become unstable and turbulent. This instability occurs across different scales and with different fluids, usually when Re x ≈ 5 × 10 5 , [ 14 ] where x is the distance from the leading edge of the flat plate, and the flow velocity is the freestream velocity of the fluid outside the boundary layer.
For flow in a pipe of diameter D , experimental observations show that for "fully developed" flow, [ n 2 ] laminar flow occurs when Re D < 2300 and turbulent flow occurs when Re D > 2900. [ 15 ] [ 16 ] At the lower end of this range, a continuous turbulent-flow will form, but only at a very long distance from the inlet of the pipe. The flow in between will begin to transition from laminar to turbulent and then back to laminar at irregular intervals, called intermittent flow. This is due to the different speeds and conditions of the fluid in different areas of the pipe's cross-section, depending on other factors such as pipe roughness and flow uniformity. Laminar flow tends to dominate in the fast-moving center of the pipe while slower-moving turbulent flow dominates near the wall. As the Reynolds number increases, the continuous turbulent-flow moves closer to the inlet and the intermittency in between increases, until the flow becomes fully turbulent at Re D > 2900. [ 15 ] This result is generalized to non-circular channels using the hydraulic diameter , allowing a transition Reynolds number to be calculated for other shapes of channel. [ 15 ]
These transition Reynolds numbers are also called critical Reynolds numbers , and were studied by Osborne Reynolds around 1895. [ 8 ] The critical Reynolds number is different for every geometry. [ 17 ]
For a fluid moving between two plane parallel surfaces—where the width is much greater than the space between the plates—then the characteristic dimension is equal to the distance between the plates. [ 18 ] This is consistent with the annular duct and rectangular duct cases above, taken to a limiting aspect ratio.
For calculating the flow of liquid with a free surface, the hydraulic radius must be determined. This is the cross-sectional area of the channel divided by the wetted perimeter. For a semi-circular channel, it is a quarter of the diameter (in case of full pipe flow). For a rectangular channel, the hydraulic radius is the cross-sectional area divided by the wetted perimeter. Some texts then use a characteristic dimension that is four times the hydraulic radius, chosen because it gives the same value of Re for the onset of turbulence as in pipe flow, [ 19 ] while others use the hydraulic radius as the characteristic length-scale with consequently different values of Re for transition and turbulent flow.
Reynolds numbers are used in airfoil design to (among other things) manage "scale effect" when computing/comparing characteristics (a tiny wing, scaled to be huge, will perform differently). [ 20 ] Fluid dynamicists define the chord Reynolds number R = Vc / ν , where V is the flight speed, c is the chord length, and ν is the kinematic viscosity of the fluid in which the airfoil operates, which is 1.460 × 10 −5 m 2 /s for the atmosphere at sea level . [ 21 ] In some special studies a characteristic length other than chord may be used; rare is the "span Reynolds number", which is not to be confused with span-wise stations on a wing, where chord is still used. [ 22 ]
The Reynolds number for an object moving in a fluid, called the particle Reynolds number and often denoted Re p , characterizes the nature of the surrounding flow and its fall velocity.
Where the viscosity is naturally high, such as polymer solutions and polymer melts, flow is normally laminar. The Reynolds number is very small and Stokes' law can be used to measure the viscosity of the fluid. Spheres are allowed to fall through the fluid and they reach the terminal velocity quickly, from which the viscosity can be determined. [ 23 ]
The laminar flow of polymer solutions is exploited by animals such as fish and dolphins, who exude viscous solutions from their skin to aid flow over their bodies while swimming. [ 24 ] It has been used in yacht racing by owners who want to gain a speed advantage by pumping a polymer solution such as low molecular weight polyoxyethylene in water, over the wetted surface of the hull.
It is, however, a problem for mixing polymers, because turbulence is needed to distribute fine filler (for example) through the material. Inventions such as the "cavity transfer mixer" have been developed to produce multiple folds into a moving melt so as to improve mixing efficiency. The device can be fitted onto extruders to aid mixing.
For a sphere in a fluid, the characteristic length-scale is the diameter of the sphere and the characteristic velocity is that of the sphere relative to the fluid some distance away from the sphere, such that the motion of the sphere does not disturb that reference parcel of fluid. The density and viscosity are those belonging to the fluid. [ 25 ] Note that purely laminar flow only exists up to Re = 10 under this definition.
Under the condition of low Re , the relationship between force and speed of motion is given by Stokes' law . [ 26 ]
At higher Reynolds numbers the drag on a sphere depends on surface roughness. Thus, for example, adding dimples on the surface of a golf ball causes the boundary layer on the upstream side of the ball to transition from laminar to turbulent. The turbulent boundary layer is able to remain attached to the surface of the ball much longer than a laminar boundary and so creates a narrower low-pressure wake and hence less pressure drag. The reduction in pressure drag causes the ball to travel farther. [ 27 ]
The equation for a rectangular object is identical to that of a sphere, with the object being approximated as an ellipsoid and the axis of length being chosen as the characteristic length scale. Such considerations are important in natural streams, for example, where there are few perfectly spherical grains. For grains in which measurement of each axis is impractical, sieve diameters are used instead as the characteristic particle length-scale. Both approximations alter the values of the critical Reynolds number.
The particle Reynolds number is important in determining the fall velocity of a particle. When the particle Reynolds number indicates laminar flow, Stokes' law can be used to calculate its fall velocity or settling velocity. When the particle Reynolds number indicates turbulent flow, a turbulent drag law must be constructed to model the appropriate settling velocity.
For fluid flow through a bed, of approximately spherical particles of diameter D in contact, if the voidage is ε and the superficial velocity is v s , the Reynolds number can be defined as [ 28 ]
or
or
The choice of equation depends on the system involved: the first is successful in correlating the data for various types of packed and fluidized beds , the second Reynolds number suits for the liquid-phase data, while the third was found successful in correlating the fluidized bed data, being first introduced for liquid fluidized bed system. [ 28 ]
Laminar conditions apply up to Re = 10, fully turbulent from Re = 2000. [ 25 ]
In a cylindrical vessel stirred by a central rotating paddle, turbine or propeller, the characteristic dimension is the diameter of the agitator D . The velocity V is ND where N is the rotational speed in rad per second. Then the Reynolds number is:
The system is fully turbulent for values of Re above 10 000 . [ 29 ]
Pressure drops [ 30 ] seen for fully developed flow of fluids through pipes can be predicted using the Moody diagram which plots the Darcy–Weisbach friction factor f against Reynolds number Re and relative roughness ε / D . The diagram clearly shows the laminar, transition, and turbulent flow regimes as Reynolds number increases. The nature of pipe flow is strongly dependent on whether the flow is laminar or turbulent.
In order for two flows to be similar, they must have the same geometry and equal Reynolds and Euler numbers . When comparing fluid behavior at corresponding points in a model and a full-scale flow, the following holds:
where R e m {\displaystyle \mathrm {Re} _{\text{m}}} is the Reynolds number for the model, and R e {\displaystyle \mathrm {Re} } is full-scale Reynolds number, and similarly for the Euler numbers.
The model numbers and design numbers should be in the same proportion, hence
This allows engineers to perform experiments with reduced scale models in water channels or wind tunnels and correlate the data to the actual flows, saving on costs during experimentation and on lab time. Note that true dynamic similitude may require matching other dimensionless numbers as well, such as the Mach number used in compressible flows , or the Froude number that governs open-channel flows. Some flows involve more dimensionless parameters than can be practically satisfied with the available apparatus and fluids, so one is forced to decide which parameters are most important. For experimental flow modeling to be useful, it requires a fair amount of experience and judgment of the engineer.
An example where the mere Reynolds number is not sufficient for the similarity of flows (or even the flow regime – laminar or turbulent) are bounded flows, i.e. flows that are restricted by walls or other boundaries. A classical example of this is the Taylor–Couette flow , where the dimensionless ratio of radii of bounding cylinders is also important, and many technical applications where these distinctions play an important role. [ 31 ] [ 32 ] Principles of these restrictions were developed by Maurice Marie Alfred Couette and Geoffrey Ingram Taylor and developed further by Floris Takens and David Ruelle .
In a turbulent flow, there is a range of scales of the time-varying fluid motion. The size of the largest scales of fluid motion (sometimes called eddies) are set by the overall geometry of the flow. For instance, in an industrial smoke stack, the largest scales of fluid motion are as big as the diameter of the stack itself. The size of the smallest scales is set by the Reynolds number. As the Reynolds number increases, smaller and smaller scales of the flow are visible. In a smokestack, the smoke may appear to have many very small velocity perturbations or eddies, in addition to large bulky eddies. In this sense, the Reynolds number is an indicator of the range of scales in the flow. The higher the Reynolds number, the greater the range of scales. The largest eddies will always be the same size; the smallest eddies are determined by the Reynolds number.
What is the explanation for this phenomenon? A large Reynolds number indicates that viscous forces are not important at large scales of the flow. With a strong predominance of inertial forces over viscous forces, the largest scales of fluid motion are undamped—there is not enough viscosity to dissipate their motions. The kinetic energy must "cascade" from these large scales to progressively smaller scales until a level is reached for which the scale is small enough for viscosity to become important (that is, viscous forces become of the order of inertial ones). It is at these small scales where the dissipation of energy by viscous action finally takes place. The Reynolds number indicates at what scale this viscous dissipation occurs. [ 36 ]
Poiseuille's law on blood circulation in the body is dependent on laminar flow . [ 37 ] In turbulent flow the flow rate is proportional to the square root of the pressure gradient, as opposed to its direct proportionality to pressure gradient in laminar flow.
Using the definition of the Reynolds number we can see that a large diameter with rapid flow, where the density of the blood is high, tends towards turbulence. Rapid changes in vessel diameter may lead to turbulent flow, for instance when a narrower vessel widens to a larger one. Furthermore, a bulge of atheroma may be the cause of turbulent flow, where audible turbulence may be detected with a stethoscope. [ 38 ]
Reynolds number interpretation has been extended into the area of arbitrary complex systems . Such as financial flows, [ 39 ] nonlinear networks, [ citation needed ] etc. In the latter case, an artificial viscosity is reduced to a nonlinear mechanism of energy distribution in complex network media. Reynolds number then represents a basic control parameter that expresses a balance between injected and dissipated energy flows for an open boundary system. It has been shown that Reynolds critical regime separates two types of phase space motion: accelerator (attractor) and decelerator. [ 40 ] High Reynolds number leads to a chaotic regime transition only in frame of strange attractor model.
There are many dimensionless numbers in fluid mechanics . The Reynolds number measures the ratio of advection and diffusion effects on structures in the velocity field, and is therefore closely related to Péclet numbers , which measure the ratio of these effects on other fields carried by the flow, for example, temperature and magnetic fields. Replacement of the kinematic viscosity ν = μ / ρ in Re by the thermal or magnetic diffusivity results in respectively the thermal Péclet number and the magnetic Reynolds number . These are therefore related to Re by-products with ratios of diffusivities, namely the Prandtl number and magnetic Prandtl number . | https://en.wikipedia.org/wiki/Reynolds_number |
In fluid dynamics and invariant theory , a Reynolds operator is a mathematical operator given by averaging something over a group action, satisfying a set of properties called Reynolds rules. In fluid dynamics, Reynolds operators are often encountered in models of turbulent flows , particularly the Reynolds-averaged Navier–Stokes equations , where the average is typically taken over the fluid flow under the group of time translations. In invariant theory, the average is often taken over a compact group or reductive algebraic group acting on a commutative algebra, such as a ring of polynomials. Reynolds operators were introduced into fluid dynamics by Osbourne Reynolds ( 1895 ) and named by J. Kampé de Fériet ( 1934 , 1935 , 1949 ).
Reynolds operators are used in fluid dynamics, functional analysis , and invariant theory, and the notation and definitions in these areas differ slightly. A Reynolds operator acting on ϕ {\displaystyle \phi } is sometimes denoted by R ( ϕ ) , P ( ϕ ) , ρ ( ϕ ) , ⟨ ϕ ⟩ {\displaystyle R(\phi ),P(\phi ),\rho (\phi ),\langle \phi \rangle } or ϕ ¯ {\displaystyle {\overline {\phi }}} .
Reynolds operators are usually linear operators acting on some algebra of functions, satisfying the identity
and sometimes some other conditions, such as commuting with various group actions.
In invariant theory a Reynolds operator R is usually a linear operator satisfying
and
Together these conditions imply that R is idempotent : R 2 = R . The Reynolds operator will also usually commute with some group action, and project onto the invariant elements of this group action.
In functional analysis a Reynolds operator is a linear operator R acting on some algebra of functions φ , satisfying the Reynolds identity
The operator R is called an averaging operator if it is linear and satisfies
If R ( R ( φ )) = R ( φ ) for all φ then R is an averaging operator if and only if it is a Reynolds operator. Sometimes the R ( R ( φ )) = R ( φ ) condition is added to the definition of Reynolds operators.
Let ϕ {\displaystyle \phi } and ψ {\displaystyle \psi } be two random variables, and a {\displaystyle a} be an arbitrary constant. Then the properties satisfied by Reynolds operators, for an operator ⟨ ⟩ , {\displaystyle \langle \rangle ,} include linearity and the averaging property:
In addition the Reynolds operator is often assumed to commute with space and time translations:
Any operator satisfying these properties is a Reynolds operator. [ 1 ]
Reynolds operators are often given by projecting onto an invariant subspace of a group action. | https://en.wikipedia.org/wiki/Reynolds_operator |
In fluid dynamics , the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier–Stokes equations to account for turbulent fluctuations in fluid momentum .
The velocity field of a flow can be split into a mean part and a fluctuating part using Reynolds decomposition . We write
with u ( x , t ) {\displaystyle \mathbf {u} (\mathbf {x} ,t)} being the flow velocity vector having components u i {\displaystyle u_{i}} in the x i {\displaystyle x_{i}} coordinate direction (with x i {\displaystyle x_{i}} denoting the components of the coordinate vector x {\displaystyle \mathbf {x} } ). The mean velocities u i ¯ {\displaystyle {\overline {u_{i}}}} are determined by either time averaging , spatial averaging or ensemble averaging , depending on the flow under study. Further u i ′ {\displaystyle u'_{i}} denotes the fluctuating (turbulence) part of the velocity.
We consider a homogeneous fluid, whose density ρ is taken to be a constant. For such a fluid, the components τ' ij of the Reynolds stress tensor are defined as:
Another – often used – definition, for constant density, of the Reynolds stress components is:
which has the dimensions of velocity squared, instead of stress.
To illustrate, Cartesian vector index notation is used. For simplicity, consider an incompressible fluid :
Given the fluid velocity u i {\displaystyle u_{i}} as a function of position and time, write the average fluid velocity as u i ¯ {\displaystyle {\overline {u_{i}}}} , and the velocity fluctuation is u i ′ {\displaystyle u'_{i}} . Then u i = u i ¯ + u i ′ {\displaystyle u_{i}={\overline {u_{i}}}+u'_{i}} .
The conventional ensemble rules of averaging are that
One splits the Euler equations (fluid dynamics) or the Navier-Stokes equations into an average and a fluctuating part. One finds that upon averaging the fluid equations, a stress on the right hand side appears of the form ρ u i ′ u j ′ ¯ {\displaystyle \rho {\overline {u'_{i}u'_{j}}}} . This is the Reynolds stress, conventionally written R i j {\displaystyle R_{ij}} :
The divergence of this stress is the force density on the fluid due to the turbulent fluctuations.
For instance, for an incompressible, viscous , Newtonian fluid , the continuity and momentum equations—the incompressible Navier–Stokes equations —can be written (in a non-conservative form) as
and
where D / D t {\displaystyle D/Dt} is the Lagrangian derivative or the substantial derivative ,
Defining the flow variables above with a time-averaged component and a fluctuating component, the continuity and momentum equations become
and
Examining one of the terms on the left hand side of the momentum equation, it is seen that
where the last term on the right hand side vanishes as a result of the continuity equation. Accordingly, the momentum equation becomes
Now the continuity and momentum equations will be averaged. The ensemble rules of averaging need to be employed, keeping in mind that the average of products of fluctuating quantities will not in general vanish. After averaging, the continuity and momentum equations become
and
Using the product rule on one of the terms of the left hand side, it is revealed that
where the last term on the right hand side vanishes as a result of the averaged continuity equation. The averaged momentum equation now becomes, after a rearrangement:
where the Reynolds stresses, ρ u i ′ u j ′ ¯ {\displaystyle \rho {\overline {u_{i}'u_{j}'}}} , are collected with the viscous normal and shear stress terms, μ ∂ u i ¯ ∂ x j {\displaystyle \mu {\frac {\partial {\overline {u_{i}}}}{\partial x_{j}}}} .
The time evolution equation of Reynolds stress was first given by Eq.(1.6) in Zhou Peiyuan's paper. [ 1 ] The equation in modern form is ∂ u i ′ u j ′ ¯ ∂ t ⏟ s t o r a g e + u ¯ k ∂ u i ′ u j ′ ¯ ∂ x k ⏟ m e a n a d v e c t i o n = − u i ′ u k ′ ¯ ∂ u ¯ j ∂ x k − u j ′ u k ′ ¯ ∂ u ¯ i ∂ x k ⏟ s h e a r p r o d u c t i o n + p ′ ρ ( ∂ u i ′ ∂ x j + ∂ u j ′ ∂ x i ) ¯ ⏟ p r e s s u r e − s c r a m b l i n g − ∂ ∂ x k ( u i ′ u j ′ u k ′ ¯ + p ′ u i ′ ¯ ρ δ j k + p ′ u j ′ ¯ ρ δ i k − ν ∂ u i ′ u j ′ ¯ ∂ x k ) ⏟ t r a n s p o r t t e r m s − 2 ν ∂ u i ′ ∂ x k ∂ u j ′ ∂ x k ¯ , {\displaystyle \underbrace {\frac {\partial {\overline {u_{i}^{\prime }u_{j}^{\prime }}}}{\partial t}} _{\rm {storage}}+\!\!\underbrace {{\bar {u}}_{k}{\frac {\partial {\overline {u_{i}^{\prime }u_{j}^{\prime }}}}{\partial x_{k}}}} _{\rm {mean~advection}}=-\ \underbrace {{\overline {u_{i}^{\prime }u_{k}^{\prime }}}{\frac {\partial {\bar {u}}_{j}}{\partial x_{k}}}-{\overline {u_{j}^{\prime }u_{k}^{\prime }}}{\frac {\partial {\bar {u}}_{i}}{\partial x_{k}}}} _{\rm {shear~production}}+\underbrace {\overline {{\frac {p^{\prime }}{\rho }}\left({\frac {\partial u_{i}^{\prime }}{\partial x_{j}}}+{\frac {\partial u_{j}^{\prime }}{\partial x_{i}}}\right)}} _{\rm {pressure-scrambling}}-\underbrace {{\frac {\partial }{\partial x_{k}}}\left({\overline {u_{i}^{\prime }u_{j}^{\prime }u_{k}^{\prime }}}+{\frac {\overline {p^{\prime }u_{i}^{\prime }}}{\rho }}\delta _{jk}+{\frac {\overline {p^{\prime }u_{j}^{\prime }}}{\rho }}\delta _{ik}-\nu {\frac {\partial {\overline {u_{i}^{\prime }u_{j}^{\prime }}}}{\partial x_{k}}}\right)} _{\rm {transport~terms}}-2\nu {\overline {{\frac {\partial u_{i}^{\prime }}{\partial x_{k}}}{\frac {\partial u_{j}^{\prime }}{\partial x_{k}}}}},} where ν {\displaystyle \nu } is the kinematic viscosity , and the last term ν ∂ u i ′ ∂ x k ∂ u j ′ ∂ x k ¯ {\displaystyle \nu {\overline {{\tfrac {\partial u_{i}^{\prime }}{\partial x_{k}}}{\tfrac {\partial u_{j}^{\prime }}{\partial x_{k}}}}}} is turbulent dissipation rate. This equation is very complex. If u i ′ u j ′ ¯ {\displaystyle {\overline {u_{i}^{\prime }u_{j}^{\prime }}}} is traced, turbulence kinetic energy is obtained.
The pressure-scrambling term is so called because this term (also called the pressure-strain covariance) is traceless under the assumption of incompressibility, meaning it cannot create or destroy turbulence kinetic energy but can only mix it between the three components of velocity. Depending on the application, this equation can also include buoyant production terms (proportional to the gravitational acceleration g {\displaystyle g} ) and Coriolis production terms (proportional to the Earth's rotation rate); these would be present in atmospheric applications, for example.
The question then is, what is the value of the Reynolds stress? This has been the subject of intense modeling and interest, for roughly the past century. The problem is recognized as a closure problem , akin to the problem of closure in the BBGKY hierarchy . A transport equation for the Reynolds stress may be found by taking the outer product of the fluid equations for the fluctuating velocity, with itself.
One finds that the transport equation for the Reynolds stress includes terms with higher-order correlations (specifically, the triple correlation v i ′ v j ′ v k ′ ¯ {\displaystyle {\overline {v'_{i}v'_{j}v'_{k}}}} ) as well as correlations with pressure fluctuations (i.e. momentum carried by sound waves). A common solution is to model these terms by simple ad hoc prescriptions.
The theory of the Reynolds stress is quite analogous to the kinetic theory of gases , and indeed the stress tensor in a fluid at a point may be seen to be the ensemble average of the stress due to the thermal velocities of molecules at a given point in a fluid. Thus, by analogy, the Reynolds stress is sometimes thought of as consisting of an isotropic pressure part, termed the turbulent pressure, and an off-diagonal part which may be thought of as an effective turbulent viscosity.
In fact, while much effort has been expended in developing good models for the Reynolds stress in a fluid, as a practical matter, when solving the fluid equations using computational fluid dynamics, often the simplest turbulence models prove the most effective. One class of models, closely related to the concept of turbulent viscosity, are the k-epsilon turbulence models , based upon coupled transport equations for the turbulent energy density k {\displaystyle k} (similar to the turbulent pressure, i.e. the trace of the Reynolds stress) and the turbulent dissipation rate ϵ {\displaystyle \epsilon } .
Typically, the average is formally defined as an ensemble average as in statistical ensemble theory. However, as a practical matter, the average may also be thought of as a spatial average over some length scale, or a temporal average. Note that, while formally the connection between such averages is justified in equilibrium statistical mechanics by the ergodic theorem , the statistical mechanics of hydrodynamic turbulence is currently far from understood. In fact, the Reynolds stress at any given point in a turbulent fluid is somewhat subject to interpretation, depending upon how one defines the average. | https://en.wikipedia.org/wiki/Reynolds_stress |
In differential calculus , the Reynolds transport theorem (also known as the Leibniz–Reynolds transport theorem), or simply the Reynolds theorem , named after Osborne Reynolds (1842–1912), is a three-dimensional generalization of the Leibniz integral rule . It is used to recast time derivatives of integrated quantities and is useful in formulating the basic equations of continuum mechanics .
Consider integrating f = f ( x , t ) over the time-dependent region Ω( t ) that has boundary ∂Ω( t ) , then taking the derivative with respect to time: d d t ∫ Ω ( t ) f d V . {\displaystyle {\frac {d}{dt}}\int _{\Omega (t)}\mathbf {f} \,dV.} If we wish to move the derivative into the integral, there are two issues: the time dependence of f , and the introduction of and removal of space from Ω due to its dynamic boundary. Reynolds transport theorem provides the necessary framework.
Reynolds transport theorem can be expressed as follows: [ 1 ] [ 2 ] [ 3 ] d d t ∫ Ω ( t ) f d V = ∫ Ω ( t ) ∂ f ∂ t d V + ∫ ∂ Ω ( t ) ( v b ⋅ n ) f d A {\displaystyle {\frac {d}{dt}}\int _{\Omega (t)}\mathbf {f} \,dV=\int _{\Omega (t)}{\frac {\partial \mathbf {f} }{\partial t}}\,dV+\int _{\partial \Omega (t)}\left(\mathbf {v} _{b}\cdot \mathbf {n} \right)\mathbf {f} \,dA} in which n ( x , t ) is the outward-pointing unit normal vector, x is a point in the region and is the variable of integration, dV and dA are volume and surface elements at x , and v b ( x , t ) is the velocity of the area element ( not the flow velocity). The function f may be tensor-, vector- or scalar-valued. [ 4 ] Note that the integral on the left hand side is a function solely of time, and so the total derivative has been used.
In continuum mechanics, this theorem is often used for material elements . These are parcels of fluids or solids which no material enters or leaves. If Ω( t ) is a material element then there is a velocity function v = v ( x , t ) , and the boundary elements obey v b ⋅ n = v ⋅ n . {\displaystyle \mathbf {v} _{b}\cdot \mathbf {n} =\mathbf {v} \cdot \mathbf {n} .} This condition may be substituted to obtain: [ 5 ] d d t ( ∫ Ω ( t ) f d V ) = ∫ Ω ( t ) ∂ f ∂ t d V + ∫ ∂ Ω ( t ) ( v ⋅ n ) f d A . {\displaystyle {\frac {d}{dt}}\left(\int _{\Omega (t)}\mathbf {f} \,dV\right)=\int _{\Omega (t)}{\frac {\partial \mathbf {f} }{\partial t}}\,dV+\int _{\partial \Omega (t)}(\mathbf {v} \cdot \mathbf {n} )\mathbf {f} \,dA.}
Let Ω 0 be reference configuration of the region Ω( t ) . Let
the motion and the deformation gradient be given by x = φ ( X , t ) , {\displaystyle \mathbf {x} ={\boldsymbol {\varphi }}(\mathbf {X} ,t),} F ( X , t ) = ∇ φ . {\displaystyle {\boldsymbol {F}}(\mathbf {X} ,t)={\boldsymbol {\nabla }}{\boldsymbol {\varphi }}.}
Let J ( X , t ) = det F ( X , t ) . Define f ^ ( X , t ) = f ( φ ( X , t ) , t ) . {\displaystyle {\hat {\mathbf {f} }}(\mathbf {X} ,t)=\mathbf {f} ({\boldsymbol {\varphi }}(\mathbf {X} ,t),t).} Then the integrals in the current and the reference configurations are related by ∫ Ω ( t ) f ( x , t ) d V = ∫ Ω 0 f ( φ ( X , t ) , t ) J ( X , t ) d V 0 = ∫ Ω 0 f ^ ( X , t ) J ( X , t ) d V 0 . {\displaystyle \int _{\Omega (t)}\mathbf {f} (\mathbf {x} ,t)\,dV=\int _{\Omega _{0}}\mathbf {f} ({\boldsymbol {\varphi }}(\mathbf {X} ,t),t)\,J(\mathbf {X} ,t)\,dV_{0}=\int _{\Omega _{0}}{\hat {\mathbf {f} }}(\mathbf {X} ,t)\,J(\mathbf {X} ,t)\,dV_{0}.}
That this derivation is for a material element is implicit in the time constancy of the reference configuration: it is constant in material coordinates. The time derivative of an integral over a volume is defined as d d t ( ∫ Ω ( t ) f ( x , t ) d V ) = lim Δ t → 0 1 Δ t ( ∫ Ω ( t + Δ t ) f ( x , t + Δ t ) d V − ∫ Ω ( t ) f ( x , t ) d V ) . {\displaystyle {\frac {d}{dt}}\left(\int _{\Omega (t)}\mathbf {f} (\mathbf {x} ,t)\,dV\right)=\lim _{\Delta t\to 0}{\frac {1}{\Delta t}}\left(\int _{\Omega (t+\Delta t)}\mathbf {f} (\mathbf {x} ,t+\Delta t)\,dV-\int _{\Omega (t)}\mathbf {f} (\mathbf {x} ,t)\,dV\right).}
Converting into integrals over the reference configuration, we get d d t ( ∫ Ω ( t ) f ( x , t ) d V ) = lim Δ t → 0 1 Δ t ( ∫ Ω 0 f ^ ( X , t + Δ t ) J ( X , t + Δ t ) d V 0 − ∫ Ω 0 f ^ ( X , t ) J ( X , t ) d V 0 ) . {\displaystyle {\frac {d}{dt}}\left(\int _{\Omega (t)}\mathbf {f} (\mathbf {x} ,t)\,dV\right)=\lim _{\Delta t\to 0}{\frac {1}{\Delta t}}\left(\int _{\Omega _{0}}{\hat {\mathbf {f} }}(\mathbf {X} ,t+\Delta t)\,J(\mathbf {X} ,t+\Delta t)\,dV_{0}-\int _{\Omega _{0}}{\hat {\mathbf {f} }}(\mathbf {X} ,t)\,J(\mathbf {X} ,t)\,dV_{0}\right).}
Since Ω 0 is independent of time, we have d d t ( ∫ Ω ( t ) f ( x , t ) d V ) = ∫ Ω 0 ( lim Δ t → 0 f ^ ( X , t + Δ t ) J ( X , t + Δ t ) − f ^ ( X , t ) J ( X , t ) Δ t ) d V 0 = ∫ Ω 0 ∂ ∂ t ( f ^ ( X , t ) J ( X , t ) ) d V 0 = ∫ Ω 0 ( ∂ ∂ t ( f ^ ( X , t ) ) J ( X , t ) + f ^ ( X , t ) ∂ ∂ t ( J ( X , t ) ) ) d V 0 . {\displaystyle {\begin{aligned}{\frac {d}{dt}}\left(\int _{\Omega (t)}\mathbf {f} (\mathbf {x} ,t)\,dV\right)&=\int _{\Omega _{0}}\left(\lim _{\Delta t\to 0}{\frac {{\hat {\mathbf {f} }}(\mathbf {X} ,t+\Delta t)\,J(\mathbf {X} ,t+\Delta t)-{\hat {\mathbf {f} }}(\mathbf {X} ,t)\,J(\mathbf {X} ,t)}{\Delta t}}\right)\,dV_{0}\\&=\int _{\Omega _{0}}{\frac {\partial }{\partial t}}\left({\hat {\mathbf {f} }}(\mathbf {X} ,t)\,J(\mathbf {X} ,t)\right)\,dV_{0}\\&=\int _{\Omega _{0}}\left({\frac {\partial }{\partial t}}{\big (}{\hat {\mathbf {f} }}(\mathbf {X} ,t){\big )}\,J(\mathbf {X} ,t)+{\hat {\mathbf {f} }}(\mathbf {X} ,t)\,{\frac {\partial }{\partial t}}{\big (}J(\mathbf {X} ,t){\big )}\right)\,dV_{0}.\end{aligned}}}
The time derivative of J is given by: [ 6 ] ∂ J ( X , t ) ∂ t = ∂ ∂ t ( det F ) = ( det F ) tr ( F − 1 ∂ F ∂ t ) = ( det F ) tr ( ∂ X ∂ φ ∂ ∂ t ( ∂ φ ∂ X ) ) = ( det F ) tr ( ∂ X ∂ φ ∂ ∂ X ( ∂ φ ∂ t ) ) = ( det F ) tr ( ∂ ∂ x ( ∂ φ ∂ t ) ) = ( det F ) ( ∇ ⋅ v ) = J ( X , t ) ∇ ⋅ v ( φ ( X , t ) , t ) = J ( X , t ) ∇ ⋅ v ( x , t ) . {\displaystyle {\begin{aligned}{\frac {\partial J(\mathbf {X} ,t)}{\partial t}}&={\frac {\partial }{\partial t}}(\det {\boldsymbol {F}})\\&=(\det {\boldsymbol {F}})\operatorname {tr} \left({\boldsymbol {F}}^{-1}{\frac {\partial {\boldsymbol {F}}}{\partial t}}\right)\\&=(\det {\boldsymbol {F}})\operatorname {tr} \left({\frac {\partial {\boldsymbol {X}}}{\partial {\boldsymbol {\varphi }}}}{\frac {\partial }{\partial t}}\left({\frac {\partial {\boldsymbol {\varphi }}}{\partial {\boldsymbol {X}}}}\right)\right)\\&=(\det {\boldsymbol {F}})\operatorname {tr} \left({\frac {\partial {\boldsymbol {X}}}{\partial {\boldsymbol {\varphi }}}}{\frac {\partial }{\partial {\boldsymbol {X}}}}\left({\frac {\partial {\boldsymbol {\varphi }}}{\partial t}}\right)\right)\\&=(\det {\boldsymbol {F}})\operatorname {tr} \left({\frac {\partial }{\partial {\boldsymbol {x}}}}\left({\frac {\partial {\boldsymbol {\varphi }}}{\partial t}}\right)\right)\\&=(\det {\boldsymbol {F}})({\boldsymbol {\nabla }}\cdot \mathbf {v} )\\&=J(\mathbf {X} ,t)\,{\boldsymbol {\nabla }}\cdot \mathbf {v} {\big (}{\boldsymbol {\varphi }}(\mathbf {X} ,t),t{\big )}\\&=J(\mathbf {X} ,t)\,{\boldsymbol {\nabla }}\cdot \mathbf {v} (\mathbf {x} ,t).\end{aligned}}}
Therefore, d d t ( ∫ Ω ( t ) f ( x , t ) d V ) = ∫ Ω 0 ( ∂ ∂ t ( f ^ ( X , t ) ) J ( X , t ) + f ^ ( X , t ) J ( X , t ) ∇ ⋅ v ( x , t ) ) d V 0 = ∫ Ω 0 ( ∂ ∂ t ( f ^ ( X , t ) ) + f ^ ( X , t ) ∇ ⋅ v ( x , t ) ) J ( X , t ) d V 0 = ∫ Ω ( t ) ( f ˙ ( x , t ) + f ( x , t ) ∇ ⋅ v ( x , t ) ) d V . {\displaystyle {\begin{aligned}{\frac {d}{dt}}\left(\int _{\Omega (t)}\mathbf {f} (\mathbf {x} ,t)\,dV\right)&=\int _{\Omega _{0}}\left({\frac {\partial }{\partial t}}\left({\hat {\mathbf {f} }}(\mathbf {X} ,t)\right)\,J(\mathbf {X} ,t)+{\hat {\mathbf {f} }}(\mathbf {X} ,t)\,J(\mathbf {X} ,t)\,{\boldsymbol {\nabla }}\cdot \mathbf {v} (\mathbf {x} ,t)\right)\,dV_{0}\\&=\int _{\Omega _{0}}\left({\frac {\partial }{\partial t}}\left({\hat {\mathbf {f} }}(\mathbf {X} ,t)\right)+{\hat {\mathbf {f} }}(\mathbf {X} ,t)\,{\boldsymbol {\nabla }}\cdot \mathbf {v} (\mathbf {x} ,t)\right)\,J(\mathbf {X} ,t)\,dV_{0}\\&=\int _{\Omega (t)}\left({\dot {\mathbf {f} }}(\mathbf {x} ,t)+\mathbf {f} (\mathbf {x} ,t)\,{\boldsymbol {\nabla }}\cdot \mathbf {v} (\mathbf {x} ,t)\right)\,dV.\end{aligned}}} where f ˙ {\displaystyle {\dot {\mathbf {f} }}} is the material time derivative of f . The material derivative is given by f ˙ ( x , t ) = ∂ f ( x , t ) ∂ t + ( ∇ f ( x , t ) ) ⋅ v ( x , t ) . {\displaystyle {\dot {\mathbf {f} }}(\mathbf {x} ,t)={\frac {\partial \mathbf {f} (\mathbf {x} ,t)}{\partial t}}+{\big (}{\boldsymbol {\nabla }}\mathbf {f} (\mathbf {x} ,t){\big )}\cdot \mathbf {v} (\mathbf {x} ,t).}
Therefore, d d t ( ∫ Ω ( t ) f ( x , t ) d V ) = ∫ Ω ( t ) ( ∂ f ( x , t ) ∂ t + ( ∇ f ( x , t ) ) ⋅ v ( x , t ) + f ( x , t ) ∇ ⋅ v ( x , t ) ) d V , {\displaystyle {\frac {d}{dt}}\left(\int _{\Omega (t)}\mathbf {f} (\mathbf {x} ,t)\,dV\right)=\int _{\Omega (t)}\left({\frac {\partial \mathbf {f} (\mathbf {x} ,t)}{\partial t}}+{\big (}{\boldsymbol {\nabla }}\mathbf {f} (\mathbf {x} ,t){\big )}\cdot \mathbf {v} (\mathbf {x} ,t)+\mathbf {f} (\mathbf {x} ,t)\,{\boldsymbol {\nabla }}\cdot \mathbf {v} (\mathbf {x} ,t)\right)\,dV,} or, d d t ( ∫ Ω ( t ) f d V ) = ∫ Ω ( t ) ( ∂ f ∂ t + ∇ f ⋅ v + f ∇ ⋅ v ) d V . {\displaystyle {\frac {d}{dt}}\left(\int _{\Omega (t)}\mathbf {f} \,dV\right)=\int _{\Omega (t)}\left({\frac {\partial \mathbf {f} }{\partial t}}+{\boldsymbol {\nabla }}\mathbf {f} \cdot \mathbf {v} +\mathbf {f} \,{\boldsymbol {\nabla }}\cdot \mathbf {v} \right)\,dV.}
Using the identity ∇ ⋅ ( v ⊗ w ) = v ( ∇ ⋅ w ) + ∇ v ⋅ w , {\displaystyle {\boldsymbol {\nabla }}\cdot (\mathbf {v} \otimes \mathbf {w} )=\mathbf {v} ({\boldsymbol {\nabla }}\cdot \mathbf {w} )+{\boldsymbol {\nabla }}\mathbf {v} \cdot \mathbf {w} ,} we then have d d t ( ∫ Ω ( t ) f d V ) = ∫ Ω ( t ) ( ∂ f ∂ t + ∇ ⋅ ( f ⊗ v ) ) d V . {\displaystyle {\frac {d}{dt}}\left(\int _{\Omega (t)}\mathbf {f} \,dV\right)=\int _{\Omega (t)}\left({\frac {\partial \mathbf {f} }{\partial t}}+{\boldsymbol {\nabla }}\cdot (\mathbf {f} \otimes \mathbf {v} )\right)\,dV.}
Using the divergence theorem and the identity ( a ⊗ b ) · n = ( b · n ) a , we have d d t ( ∫ Ω ( t ) f d V ) = ∫ Ω ( t ) ∂ f ∂ t d V + ∫ ∂ Ω ( t ) ( f ⊗ v ) ⋅ n d A = ∫ Ω ( t ) ∂ f ∂ t d V + ∫ ∂ Ω ( t ) ( v ⋅ n ) f d A . {\displaystyle {\begin{aligned}{\frac {d}{dt}}\left(\int _{\Omega (t)}\mathbf {f} \,dV\right)&=\int _{\Omega (t)}{\frac {\partial \mathbf {f} }{\partial t}}\,dV+\int _{\partial \Omega (t)}(\mathbf {f} \otimes \mathbf {v} )\cdot \mathbf {n} \,dA\\&=\int _{\Omega (t)}{\frac {\partial \mathbf {f} }{\partial t}}\,dV+\int _{\partial \Omega (t)}(\mathbf {v} \cdot \mathbf {n} )\mathbf {f} \,dA.\end{aligned}}} Q.E.D.
If we take Ω to be constant with respect to time, then v b = 0 and the identity reduces to d d t ∫ Ω f d V = ∫ Ω ∂ f ∂ t d V . {\displaystyle {\frac {d}{dt}}\int _{\Omega }f\,dV=\int _{\Omega }{\frac {\partial f}{\partial t}}\,dV.} as expected. (This simplification is not possible if the flow velocity is incorrectly used in place of the velocity of an area element.)
The theorem is the higher-dimensional extension of differentiation under the integral sign and reduces to that expression in some cases. Suppose f is independent of y and z , and that Ω( t ) is a unit square in the yz -plane and has x limits a ( t ) and b ( t ) . Then Reynolds transport theorem reduces to d d t ∫ a ( t ) b ( t ) f ( x , t ) d x = ∫ a ( t ) b ( t ) ∂ f ∂ t d x + ∂ b ( t ) ∂ t f ( b ( t ) , t ) − ∂ a ( t ) ∂ t f ( a ( t ) , t ) , {\displaystyle {\frac {d}{dt}}\int _{a(t)}^{b(t)}f(x,t)\,dx=\int _{a(t)}^{b(t)}{\frac {\partial f}{\partial t}}\,dx+{\frac {\partial b(t)}{\partial t}}f{\big (}b(t),t{\big )}-{\frac {\partial a(t)}{\partial t}}f{\big (}a(t),t{\big )}\,,} which, up to swapping x and t , is the standard expression for differentiation under the integral sign. | https://en.wikipedia.org/wiki/Reynolds_transport_theorem |
Rezence (pronounced reh-zense) was an interface standard developed by the WiPower (A4WP) for wireless electrical power transfer based on the principles of magnetic resonance. The Rezence system consisted of a single power transmitter unit (PTU) and one or more power receiver units (PRUs). The interface standard supported power transfer up to 50 watts, [ 1 ] at distances up to 5 centimeters. [ 2 ] The power transmission frequency is 6.78 MHz, and up to eight devices could be powered from a single PTU depending on transmitter and receiver geometry and power levels. A Bluetooth Low Energy link was defined in the A4WP system intended for control of power levels, identification of valid loads and protection of non-compliant devices. [ 3 ] [ 4 ]
The A4WP was formed in early 2012 with the intent to create a wireless power transfer standard to compete with the existing Qi standard. Board member companies [ 5 ] included Broadcom , Gill Electronics, Integrated Device Technology (IDT) , [ 6 ] Intel , [ 7 ] [ 8 ] Qualcomm , Samsung Electronics , [ 9 ] Samsung Electro-Mechanics , and WiTricity . [ 10 ]
In January 2015 A4WP and the Power Matters Alliance announced that the two organizations intended to merge into the AirFuel Alliance . [ 11 ] | https://en.wikipedia.org/wiki/Rezence_(wireless_charging_standard) |
Rfam is a database containing information about non-coding RNA (ncRNA) families and other structured RNA elements. It is an annotated , open access database originally developed at the Wellcome Trust Sanger Institute in collaboration with Janelia Farm , [ 1 ] [ 2 ] [ 3 ] [ 4 ] and currently hosted at the European Bioinformatics Institute . [ 5 ] Rfam is designed to be similar to the Pfam database for annotating protein families.
Unlike proteins , ncRNAs often have similar secondary structure without sharing much similarity in the primary sequence . Rfam divides ncRNAs into families based on evolution from a common ancestor. Producing multiple sequence alignments (MSA) of these families can provide insight into their structure and function, similar to the case of protein families. These MSAs become more useful with the addition of secondary structure information. Rfam researchers also contribute to Wikipedia 's RNA WikiProject . [ 4 ] [ 6 ]
The Rfam database can be used for a variety of functions. For each ncRNA family, the interface allows users to: view and download multiple sequence alignments; read annotation; and examine species distribution of family members. There are also links provided to literature references and other RNA databases.
Rfam also provides links to Wikipedia so that entries can be created or edited by users.
The interface at the Rfam website allows users to search ncRNAs by keyword, family name, or genome as well as to search by ncRNA sequence or EMBL accession number . [ 7 ] The database information is also available for download, installation and use using the INFERNAL software package. [ 8 ] [ 9 ] [ 10 ] The INFERNAL package can also be used with Rfam to annotate sequences (including complete genomes) for homologues to known ncRNAs.
In the database, the information of the secondary structure and the primary sequence , represented by the MSA , is combined in statistical models called profile stochastic context-free grammars (SCFGs), also known as covariance models. These are analogous to hidden Markov models used for protein family annotation in the Pfam database. [ 1 ] Each family in the database is represented by two multiple sequence alignments in Stockholm format and a SCFG.
The first MSA is the "seed" alignment. It is a hand-curated alignment that contains representative members of the ncRNA family and is annotated with structural information. This seed alignment is used to create the SCFG, which is used with the Rfam software INFERNAL to identify additional family members and add them to the alignment. A family-specific threshold value is chosen to avoid false positives.
Until release 12, Rfam used an initial BLAST filtering step because profile SCFGs were too computationally expensive. However, the latest versions of INFERNAL are fast enough [ 10 ] so that the BLAST step is no longer necessary. [ 11 ]
The second MSA is the “full” alignment, and is created as a result of a search using the covariance model against the sequence database. All detected homologs are aligned to the model, giving the automatically produced full alignment.
Version 1.0 of Rfam was launched in 2003 and contained 25 ncRNA families and annotated about 50 000 ncRNA genes. In 2005, version 6.1 was released and contained 379 families annotating over 280 000 genes. In August 2012, version 11.0 contained 2208 RNA families, while the current version (14.9, released in November 2022) annotates 4108 [ 7 ] families. | https://en.wikipedia.org/wiki/Rfam |
Chlorobis(ethylene)rhodium dimer is an organorhodium compound with the formula Rh 2 Cl 2 (C 2 H 4 ) 4 . Sometimes called Cramer's dimer (after Richard Cramer), it is a red-orange solid that is soluble in nonpolar organic solvents. The molecule consists of two bridging chloride ligands and four ethylene ligands. The ethylene ligands are labile and readily displaced even by other alkenes. A variety of homogeneous catalysts have been prepared from this complex. [ 1 ] [ 2 ]
The complex is prepared by treating an aqueous methanolic solution of hydrated rhodium trichloride with ethylene at room temperature. Rh(III) is reduced with oxidation of ethylene to acetaldehyde :
Reflecting the lability of its ligands, the complex does not tolerate recrystallization. [ 3 ]
The complex reacts slowly with water to give acetaldehyde. With HCl, it gives RhCl 2 (C 2 H 2 ) 2 − . Rh 2 Cl 2 (C 2 H 4 ) 4 catalyzes the dimerization of ethylene to 1-butene .
Carbonylation affords rhodium carbonyl chloride . Treatment with acetylacetone and aqueous KOH gives Rh(acac)(C 2 H 4 ) 2 . | https://en.wikipedia.org/wiki/Rh2Cl2(C2H4)4 |
Rhodium carbonyl chloride is an organorhodium compound with the formula Rh 2 Cl 2 (CO) 4 . It is a red-brown volatile solid that is soluble in nonpolar organic solvents. It is a precursor to other rhodium carbonyl complexes , some of which are useful in homogeneous catalysis .
The molecule consists of two planar Rh(I) centers linked by two bridging chloride ligands and four CO ligands. X-ray crystallography shows that the two Rh(I) centers are square planar with the dihedral angle of 126.8° between the two RhCl 2 planes. The metals are nonbonding. [ 1 ]
First prepared by Walter Hieber , [ 2 ] it is typically prepared by treating hydrated rhodium trichloride with flowing carbon monoxide , according to this idealized redox equation:
The complex reacts with triphenylphosphine to give the bis(triphenylphosphine)rhodium carbonyl chloride :
With chloride salts, the dichloride anion forms:
With acetylacetone , rhodium carbonyl chloride reacts to give dicarbonyl(acetylacetonato)rhodium(I) .
The dimer reacts with a variety of Lewis bases (:B) to form adducts RhCl(CO) 2 :B. Its reaction with tetrahydrothiophene and the corresponding enthalpy are:
This enthalpy corresponds to the enthalpy change for a reaction forming one mole of the product, RhCl(CO) 2 :S(CH 2 ) 4 , from the acid dimer.
The dissociation energy for rhodium(I) dicarbonyl chloride dimer, which is an energy contribution prior to reaction with the donor,
has been determined by the ECW model to be 87.1 kJ mol −1
N-heterocyclic carbene (NHC) ligands react with rhodium carbonyl chloride to give monomeric cis-[RhCl(NHC)(CO) 2 ] complexes. The IR spectra of these complexes have been used to estimate the donor strength of NHCs. [ 4 ] [ 5 ] | https://en.wikipedia.org/wiki/Rh2Cl2(CO)4 |
Rhodium(III) oxide (or Rhodium sesquioxide ) is the inorganic compound with the formula Rh 2 O 3 . It is a gray solid that is insoluble in ordinary solvents.
Rh 2 O 3 has been found in two major forms. The hexagonal form adopts the corundum structure. It transforms into an orthorhombic structure when heated above 750 °C. [ 1 ]
Rhodium oxide can be produced via several routes:
Rhodium oxide films behave as a fast two-color electrochromic system: Reversible yellow ↔ dark green or yellow ↔ brown-purple color changes are obtained in KOH solutions by applying voltage ~1 V . [ 7 ]
Rhodium oxide films are transparent and conductive, like indium tin oxide (ITO) - the common transparent electrode, but Rh 2 O 3 has 0.2 eV lower work function than ITO. Consequently, deposition of rhodium oxide on ITO improves the carrier injection from ITO thereby improving the electrical properties of organic light-emitting diodes . [ 5 ]
Rhodium oxides are catalysts for hydroformylation of alkenes, [ 8 ] N 2 O production from NO , [ 9 ] and the hydrogenation of CO . [ 10 ] | https://en.wikipedia.org/wiki/Rh2O3 |
Rhodium(III) sulfide is the inorganic compound with the formula Rh 2 S 3 . It is an insoluble black solid, prepared by the heating a mixture of elemental rhodium and sulfur. Crystals can be grown by chemical vapor transport using bromine as the transporting agent. The structure consists of octahedral and tetrahedral Rh and S centers, respectively. No close Rh-Rh contacts are observed. [ 1 ] Rh 2 Se 3 and Ir 2 S 3 adopt the same structure as Rh 2 S 3 . | https://en.wikipedia.org/wiki/Rh2S3 |
Rhodium(III) bromide refers to inorganic compounds of the formula RhBr 3 (H 2 O) n where n = 0 or approximately three. Both forms are brown solids. The hydrate is soluble in water and lower alcohols. It is used to prepare rhodium bromide complexes. [ 2 ] Rhodium bromides are similar to the chlorides, but have attracted little academic or commercial attention.
Rhodium(III) bromide adopts the aluminium chloride crystal structure . [ 3 ] [ 4 ]
Rhodium(III) bromide is a starting material for the synthesis of other rhodium halides. For example, it reacts with bromine trifluoride to form rhodium(IV) fluoride and with aqueous potassium iodide to form rhodium(III) iodide . Like most other rhodium trihalides, anhydrous RhBr 3 is insoluble in water. [ 1 ] The dihydrate RhBr 3 ·2H 2 O forms when rhodium metal reacts with hydrochloric acid and bromine. [ 1 ] | https://en.wikipedia.org/wiki/RhBr3 |
Pentamminechlororhodium dichloride is the dichloride salt of the coordination complex [RhCl(NH 3 ) 5 ] 2+ . It is a yellow, water-soluble solid. The salt is an intermediate in the purification of rhodium from its ores.
As shown by X-ray crystallography, the salt consists of the octahedral complex [RhCl(NH 3 ) 5 ] 2+ and two chloride counterions . [ 1 ] It forms from the reaction of rhodium trichloride and ammonia in ethanol. [ 2 ] Two chloride anions are labile, whereas the coordinated chloride ligand is not.
Treatment of [RhCl(NH 3 ) 5 ]Cl 2 with zinc dust in the presence of ammonia gives the hydride complex [RhH(NH 3 ) 5 ] 2+ . [ 2 ] [ 3 ] | https://en.wikipedia.org/wiki/RhCl(NH3)5 |
Rhodium(III) chloride refers to inorganic compounds with the formula RhCl 3 (H 2 O) n , where n varies from 0 to 3. These are diamagnetic red-brown solids. The soluble trihydrated (n = 3) salt is the usual compound of commerce. It is widely used to prepare compounds used in homogeneous catalysis . [ 2 ]
Rhodium trichloride and its various hydrates can be considered the default halides of rhodium. By contrast, its lighter congener cobalt does not form a stable trichloride, mainly being available as cobalt(II) chloride .
Anhydrous rhodium chloride is a dense red-brown solid. According to X-ray crystallography , it crystallises in the motif seen also for YCl 3 and AlCl 3 (see image in upper right). The metal centres are octahedral, and the halides are doubly bridging. The octahedral molecular geometry adopted by RhCl 3 is characteristic of most rhodium(III) complexes. [ 3 ] The anhydrous material is insoluble in common solvents and, for that reason, of little value in the laboratory.
Although hydrated rhodium trichloride is widely marketed and often used, the structure of this red solid has not been elucidated crystallographically. This reddish solid (see picture in box) is often described as RhCl 3 (H 2 O) 3 , but this composition has not been confirmed crystallographically.
Aqueous solutions of "rhodium trichloride hydrate" have been characterized by 103 Rh NMR spectroscopy . Several species are detected, the proportions of which change with time and depend on the concentration of chloride. The relative distribution of these species determines the colour of the solutions, which can range from yellow (the hexaaquo ion) to "raspberry-red". Some of these species are the aquo complexes [Rh(H 2 O) 6 ] 3+ , [RhCl(H 2 O) 5 ] 2+ , cis - and trans -[RhCl 2 (H 2 O) 4 ] + , and two isomers of [RhCl 3 (H 2 O) 3 ]. [ 4 ] These species have been separated by ion exchange chromatography and individually characterized by UV-vis spectroscopy . [ 5 ]
RhCl 3 (H 2 O) 3 is produced from salts such as Na 3 RhCl 6 , the latter being obtained in the purification of rhodium from the other platinum group metals such as platinum and iridium. The trisodium salt is converted to H 3 RhCl 6 by ion exchange chromatography . Recrystallization of this acidic salt from water affords the hydrated trichloride, sometimes called "soluble rhodium trichloride." [ 6 ] Anhydrous RhCl 3 is prepared by reaction of chlorine with rhodium sponge metal at 200–300 °C. [ 7 ] Above 800 °C, the anhydrous chloride reverts to Rh metal and chlorine. [ 6 ]
Despite the complexity of its solutions, hydrated rhodium trichloride is the precursor to a wide variety of complexes prepared in high yields.These complexes generally arise by substitution reactions , whereby of water and chloride are replaced by more basic ligands as described in the sections below. These reactions are facilitated by the fact that hydrated rhodium trichloride is soluble in a range of polar organic solvents.
Evidence for the affinity of rhodium chlorides for oxygen-based ligands is provided by the chloro-aquo complexes discussed above. Rhodium trichloride reacts with acetylacetone to give rhodium acetylacetonate .
Aqueous solutions of rhodium trichloride react with ammonia to give the salt pentamminerhodium chloride , [RhCl(NH 3 ) 5 ]Cl 2 . As for other metal-ammine complexes , the term "ammine" refers to ammonia bound to a metal ion as a ligand. Zinc reduction of this cation followed by the addition of sulfate gives the colourless hydride complex [HRh(NH 3 ) 5 ]SO 4 . [ 8 ] Some rhodium ammine chlorides are used in the purification of rhodium from its ores. [ 9 ]
Upon boiling in a mixture of ethanol and pyridine (py), hydrated rhodium trichloride converts to trans -[RhCl 2 (py) 4 )]Cl . In the absence of a reductant, the reaction affords fac -[RhCl 3 (py) 3 ], analogous to the thioether derivatives. [ 3 ] Oxidation of aqueous ethanolic solution of pyridine and RhCl 3 (H 2 O) 3 by air affords a blue paramagnetic oxygen-bridged compound, [Cl(py) 4 Rh-O 2 -Rh(py) 4 Cl] 5+ . [ 10 ]
Rhodium(III) also forms a range of complexes with soft Lewis bases, such as thioethers , phosphines , and arsines . Such ligands form Rh(III) complexes, but unlike the "hard" N- and O-based ligands, these complexes often can be reduced to Rh(I) derivatives. The reactions are facilitated by the solubility of rhodium trichloride in alcohols, which also dissolve the organic ligands. Thus, ethanolic solutions of hydrated rhodium trichloride react with diethyl sulfide : [ 11 ]
This complex has been used as source of anhydrous rhodium trichloride that is soluble in lipophilic solvents. Both fac and mer stereoisomers of such complexes have been isolated. [ 3 ]
Reaction of RhCl 3 (H 2 O) 3 under mild conditions with tertiary phosphines affords adducts akin to the aforementioned thioether complexes. When these reactions are conducted in boiling ethanol solution, reduction occurs, leading to rhodium(I) derivatives. A famous derivative is [RhCl(PPh 3 ) 3 ] known as Wilkinson's catalyst . Either the ethanol solvent or the phosphine serves as reductant: [ 12 ] [ 13 ]
Unlike most other air-stable metal salts, hydrated rhodium trichloride reacts under mild conditions (near room temperature, one atmosphere) with carbon monoxide and many olefins. This behavior opens the doors to extensive inventory of organorhodium compounds . Most of these substrates cause reduction of rhodium(III) to rhodium(I). The resulting Rh(I) complexes engage the carbon-based ligands by pi-backbonding .
Reaction of hydrated rhodium trichloride with olefins affords compounds of the type Rh 2 Cl 2 (alkene) 4 . Specifically, ethylene gives chlorobis(ethylene)rhodium dimer ( [(C 2 H 4 ) 2 Rh(μ−Cl)] 2 ). With 1,5-cyclooctadiene , cyclooctadiene rhodium chloride dimer ( [(C 8 H 12 ) 2 Rh(μ−Cl)] 2 ) is produced. [ 14 ]
When hydrated rhodium trichloride is treated with cyclopentadienes , organometallic half sandwich compounds can be produced. For example, treating hydrated rhodium trichloride with pentamethylcyclopentadiene in hot methanol leads to the precipitation of solid pentamethylcyclopentadienyl rhodium dichloride dimer : [ 15 ]
A solution of hydrated rhodium trichloride in methanol reacts with carbon monoxide to produce H[RhCl 2 (CO) 2 ], which contains the dicarbonyldichloridorhodate(I) anion. Further carbonylation in the presence of sodium citrate as a reductant leads to tetrarhodium dodecacarbonyl , Rh 4 (CO) 12 , a rhodium(0) cluster compound . [ 16 ] Solid RhCl 3 (H 2 O) 3 reacts with flowing CO gives the volatile compound [(CO) 2 Rh(μ-Cl)] 2 . [ 17 ]
Numerous Rh-CO-phosphine complexes have been prepared in the course of extensive investigations on hydroformylation catalysis. RhCl(PPh 3 ) 3 reacts with CO to give trans -RhCl(CO)(PPh 3 ) 2 , stoichiometrically analogous to but less nucleophilic than Vaska's complex . trans -RhCl(CO)(PPh 3 ) 2 reacts with a mixture of NaBH 4 and PPh 3 to give HRh(CO)(PPh 3 ) 3 , a highly active catalyst for the hydroformylation of alkenes. [ 18 ]
Beginning especially in the 1960s, RhCl 3 (H 2 O) 3 was demonstrated to be catalytically active for a variety of reactions involving CO, H 2 , and alkenes . [ 19 ] These compounds are fundamental petrochemical feedstocks, so their manipulation can be consequential. For example, RhCl 3 (H 2 O) 3 was shown to dimerise ethylene to a mixture of cis and trans 2-butene :
Ethylene dimerization was shown to involve catalysis by the aforementioned ethylene complexes. This and many related discoveries nurtured the then young field of homogeneous catalysis, wherein the catalysts are dissolved in the medium with the substrate. Previous to this era, most metal catalysts were "heterogeneous", i.e. the catalysts were solids and the substrates were either liquid or gases.
Another advance in homogeneous catalysis was the finding that PPh 3 -derived complexes were active catalytically as well as soluble in organic solvents, [ 18 ] The best known such catalyst being Wilkinson's catalyst that catalyzes the hydrogenation and isomerization of alkenes. [ 19 ]
The hydroformylation of alkenes is catalyzed by the related RhH(CO)(PPh 3 ) 3 . Catalysis by rhodium is so efficient that it has significantly displaced the previous technology based on less expensive cobalt catalysts.
Rhodium(III) chloride is not listed under Annex I of Directive 67/548/EEC , but is usually classified as harmful , R22 : Harmful if swallowed . Some Rh compounds have been investigated as anti-cancer drugs . It is listed in the inventory of the Toxic Substances Control Act (TSCA). | https://en.wikipedia.org/wiki/RhCl3 |
Rhodium(III) fluoride or rhodium trifluoride is the inorganic compound with the formula RhF 3 . It is a red-brown, diamagnetic solid.
The compound is prepared by fluorination of rhodium trichloride :
It can also be obtained by direct combination of the elements: [ 3 ]
Anhydrous RhF 3 is insoluble in water and does not react with it, but the hydrates RhF 3 ·6H 2 O and RhF 3 ·9H 2 O can be prepared by adding hydrofluoric acid to aqueous rhodium(III) solutions. [ 3 ]
According to X-ray crystallography , the compound adopts the same structure as vanadium trifluoride , wherein the metal achieves octahedral coordination geometry. [ 2 ] | https://en.wikipedia.org/wiki/RhF3 |
Rhodium pentafluoride is an inorganic compound with the formula Rh 4 F 20 . It is a red solid. It is prepared by fluorination of rhodium trifluoride at 400 °C. [ 1 ]
According to X-ray crystallography, the Rh centers are octahedral. The structure is very similar to that of the related ruthenium pentafluoride , osmium pentafluoride , and iridium pentafluoride . All are tetrameric, meaning that they have the molecular structure [MF 5 ] 4 . The M-F distances for the bridging fluoride ligands are typically about 0.2 Å longer than the Rh-F distances for the nonbridging fluoride ligands. In the case of rhodium pentafluoride, these distances average 1.999(4) and 1.808(8) Å. [ 2 ] The Rh-F-Rh angles average 135°, which leads to a ruffled structure. In contrast, the M-F-M centers are linear in the pentafluorides of niobium, tantalum, molybdenum, and tungsten. | https://en.wikipedia.org/wiki/RhF5 |
Rhodium hexafluoride , also rhodium(VI) fluoride , (RhF 6 ) is the inorganic compound of rhodium and fluorine . A black volatile solid, [ 1 ] it is a highly reactive material which starts to slowly thermally decompose already at room temperature and a rare example of a rhodium(VI) compound. It is one of seventeen known binary hexafluorides .
Rhodium hexafluoride was discovered by American radiochemists in 1961, soon after the discovery of ruthenium hexafluoride . [ 3 ] It is prepared by reaction of rhodium metal with an excess of elemental fluorine : [ 4 ]
The RhF 6 molecule has octahedral molecular geometry . Consistent with its d 3 configuration, the six Rh–F bond lengths are equivalent, being 1.824 Å. [ 2 ] It crystallises in an orthorhombic space group Pnma with lattice parameters of a = 9.323 Å , b = 8.474 Å, and c = 4.910 Å.
Like some other metal fluorides, RhF 6 is highly oxidizing. It attacks glass, [ 4 ] and can even react with elemental oxygen . [ 5 ] | https://en.wikipedia.org/wiki/RhF6 |
Rhodium(III) iodide is an inorganic compound with the formula RhI 3 . It is a black solid. [ 1 ]
Rhodium(III) iodide can be synthesised by the reaction of aqueous potassium iodide with rhodium(III) bromide . [ 1 ]
RhI 3 adopts same crystal structure motif as AlCl 3 and YCl 3 . The structure consists of cubic close-packed iodide ions and rhodium ions filling a third of the octahedral interstices, forming a layers. [ 2 ]
Rhodium(III) iodide is only known in the anhydrous form. Unlike the other rhodium(III) halides, it does not form hydrates . [ 1 ] The related anion [RhI 6 ] 3− was previously thought not to form [ 1 ] but has since been prepared by diffusion of RhCl 3 ·3H 2 O through a layer of hydroiodic acid into piperazine . [ 3 ] | https://en.wikipedia.org/wiki/RhI3 |
Rhodium(IV) oxide (or rhodium dioxide ) is the chemical compound with the formula Rh O 2 .
RhO 2 is highly insoluble even in hot aqua regia . [ 1 ]
RhO 2 has the tetragonal rutile structure. [ 2 ]
RhO 2 has metallic resistivity with values <10 −4 Ohm·cm. It transforms in air to Rh 2 O 3 at 850 °C and then to metal and oxygen at 1050 °C. [ 2 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/RhO2 |
Rhabdosphaeraceae is a family of algae belonging to the order Syracosphaerales . [ 1 ]
The following is a list of Rhabdosphaeraceae genera: [ 1 ] | https://en.wikipedia.org/wiki/Rhabdosphaeraceae |
14-12-10-8-6-2)44-32-30(28(39)26(37)20(4)42-32)45-31-29(40)27(38)25(36)
19(3)41-31/h19-22,25-32,36-40H,5-18H2,1-4H3,(H,33,34)/t19-,20-,21?,22?,
Rhamnolipids are a class of glycolipid produced by Pseudomonas aeruginosa , amongst other organisms, frequently cited as bacterial surfactants . [ 1 ] [ 2 ] [ 3 ] They have a glycosyl head group, in this case a rhamnose moiety, and a 3-(hydroxyalkanoyloxy)alkanoic acid (HAA) fatty acid tail, such as 3-hydroxydecanoic acid . [ 4 ] [ 5 ]
Specifically there are two main classes of rhamnolipids: mono-rhamnolipids and di-rhamnolipids, which consist of one or two rhamnose groups respectively. [ 6 ] Rhamnolipids are also heterogeneous in the length and degree of branching of the HAA moiety, [ 1 ] which varies with the growth media used and the environmental conditions. [ 7 ]
The first genes discovered in a mutagenesis screen for mutants unable to produce rhamnolipids were rhlA and rhlB . [ 8 ] They are arranged in an operon , adjacent to rhlRI , a master regulator of quorum sensing in Pseudomonas aeruginosa . The proteins encoded by rhlA and rhlB ; RhlA and RhlB respectively, are expected to form a complex because of the operonic nature of the genes which encode these two proteins and because both proteins are necessary for production of rhamnolipids. [ 4 ] [ 6 ] Furthermore, it was supposed that the role of RhlA was to stabilise RhlB in the cell membrane and thus the RhlAB complex was labelled as the enzyme Rhamnosyltransferase 1 and is frequently cited as such [ 9 ] [ 10 ] although there is no biochemical evidence for this and RhlA has been shown to be monomeric in solution. RhlA was subsequently shown to be involved in the production of the precursor to RHLs, HAAs. RhlB adds a rhamnose group to the HAA precursor to form mono-rhamnolipid. Therefore, the products of the rhlAB operon, RhlA and RhlB, catalyse the formation of HAAs and mono-rhamnolipids respectively.
RhlA is an α, β hydrolase (analysis by Fugue structural prediction programme). This fold is a common structural motif in fatty acid synthetic proteins and RhlA shows homology to transacylases. It has been shown using enzyme assays that the substrate for RhlA is hydroxyacyl-ACP rather than hydroxyacyl-CoA suggesting that it catalyses the formation of HAAs directly from the type II fatty acid synthase pathway (FASII). Furthermore, RhlA preferentially interacts with hydroxyacyl-ACP with an acyl chain length of ten carbon residues. [ 11 ] The hydroxyacyl-ACP substrate of RhlA is the product of FabG, a protein which encodes the NADPH-dependent β-keto-acyl-ACP reductase required for fatty acid synthesis. [ 12 ] It is a member of the FASII cycle along with FabI and FabA, which synthesise the precursors utilised by FabG. [ 11 ]
Another gene necessary for synthesis of di-rhamnolipids, rhlC , has also been identified. RhlC catalyses the addition of the second rhamnose moiety to mono-rhamnolipids forming di-rhamnolipids, hence is often labelled rhamnosyltransferase 2. [ 6 ] Like rhlA and rhlB , rhlC is thought to be an ancestral gene controlled by the same quorum sensing system as rhlA and rhlB . The rhamnose moiety for mono- and di-rhamnolipids is derived from AlgC activity and the RmlABCD pathway, encoded on the rmlBCAD operon. AlgC produces sugar precursors directly for alginate and lipopolysaccharide (LPS) as well as rhamnolipids. [ 13 ] In rhamnose synthesis, AlgC produces glucose-1-phosphate (G1P) which is converted to dTDP-D-glucose by RmlA followed by conversion to dTDP-6-deoxy-D-4-hexulose and then dTDP-6-deoxy-L-lyxo-4-hexulose by RmlB and RmlC respectively. Finally, dTDP-6-deoxy-L-lyxo-4-hexulose is converted to dTDP-L-rhamnose by RmlD. [ 3 ] The rhamnose can then be used in the synthesis of rhamnolipids by RhlB and RhlC.
The complete pathway of biosynthesis of rhamnolipids has not been confirmed. In summary, mono- and di- rhamnolipids are produced by sequential rhamnosyltransferase reactions catalysed by RhlB and RhlC respectively. [ 6 ] The substrate for RhlB is the fatty acid moiety of the detergent, produced by RhlA. [ 4 ] [ 11 ]
The reason that Pseudomonas aeruginosa produces rhamnolipids is the subject of much speculation. [ 14 ] They have been shown to have several properties, and investigations in a rhlA mutant that does not make HAAs nor rhamnolipids have attributed many functions to rhamnolipids which may in fact be due to HAAs. These functions fall broadly into five categories, described below.
As mentioned previously, Pseudomonas aeruginosa has the ability to metabolise a variety of substrates including n-alkanes, hexadecane and oils. Uptake of these hydrophobic substrates is speculated to rely on the production of rhamnolipids. It is thought that rhamnolipids either cause the Pseudomonas aeruginosa cell surface to become hydrophobic, promoting an interaction between the substrate and the cell, or secreted rhamnolipids emulsify the substrate and allow it to be taken up by the Pseudomonas aeruginosa cell. There is evidence that rhamnolipids are highly adsorbent to the Pseudomonas aeruginosa cell surface, causing it to become hydrophobic. [ 15 ] [ 16 ] It has also been shown that production of rhamnolipids promotes uptake of hexadecane by overcoming the inhibitory effect of the hydrophilic interactions caused by LPS. [ 17 ] Production of rhamnolipids is observed on hydrophobic substrates but equally high yields are achievable on other carbon sources such as sugars. Furthermore, although mono-rhamnolipids have been shown to interact with the Pseudomonas aeruginosa cell membrane and cause it to become hydrophobic, di-rhamnolipids do not interact well with the cell membrane because the polar head group is too large to penetrate the LPS layer. [ 18 ] Therefore, although Rhamnolipids may play a part in interaction of Pseudomonas aeruginosa with hydrophobic carbon sources, they are likely to have additional functions.
Rhamnolipids have long been reported to have antimicrobial properties. [ 19 ] They have been shown to have activity against a range of bacteria including Serratia marcescens , Klebsiella pneumoniae , Staphylococcus aureus and Bacillus subtilis with minimum inhibitory concentrations (MICs) ranging from 0.5 μg/mL to 32 μg/mL. Activity against several fungi such as Fusarium solani and Penicillium funiculosum have also been observed with MICs of 75 μg/mL and 16 μg/mL respectively. [ 20 ] Rhamnolipids have been suggested as antimicrobials able to remove Bordetella bronchiseptica biofilms . [ 21 ] The mode of killing has been shown to result from intercalation of rhamnolipids into the cell membrane causing pores to form which result in cell lysis, at least in the case of Bacillus subtilis . [ 22 ] The anti-microbial action of rhamnolipids may provide a fitness advantage for Pseudomonas aeruginosa by excluding other microorganisms from the colonised niche. Furthermore, rhamnolipids have been shown to have anti-viral and zoosporicidal activities. [ 2 ] The antimicrobial properties of rhamnolipids may confer a fitness advantage for Pseudomonas aeruginosa in niche colonisation as Pseudomonas aeruginosa is a soil bacterium, as well as competing with other bacteria in the cystic fibrosis lung. [ 3 ]
As mentioned previously, Pseudomonas aeruginosa produces a host of virulence factors in concert, under the control of the quorum sensing system. Many studies show that inhibiting quorum sensing down-regulates the pathogenicity of Pseudomonas aeruginosa . [ 23 ] However, it has been shown that rhamnolipids specifically are a key virulence determinant in Pseudomonas aeruginosa . A variety of virulence factors were analysed in Pseudomonas aeruginosa strains isolated from pneumonia patients. Rhamnolipids were found to be the only virulence factor that was associated with the deterioration of the patients to ventilator-associated pneumonia. [ 23 ] Several other reports also support the role of rhamnolipids in lung infections. [ 24 ] [ 25 ] [ 26 ] The effect of rhamnolipids in Pseudomonas aeruginosa virulence has been further noted in corneal infections (Alarcon et al., 2009; Zhu et al., 2004). It has been shown that rhamnolipids are able to integrate into the epithelial cell membrane and disrupt tight-junctions. This study used reconstituted epithelial membranes and purified rhamnolipids to demonstrate this mechanism. [ 26 ] In addition to inhibition and killing of epithelial cells, [ 27 ] rhamnolipids are able to kill polymorphonuclear (PMN) leukocytes and macrophages and inhibit phagocytosis . [ 28 ] [ 29 ] [ 30 ] In summary, rhamnolipids have been shown unequivocally to be a potent virulence factor in the human host, however, they are also produced outside of the host, for example in a soil environment.
Rhamnolipids contribute to the establishment and maintenance of infection in cystic fibrosis patients in a number of ways, they disrupt the bronchial epithelium by disrupting the cell membranes, which promotes paracellular invasion of Pseudomonas aeruginosa and causes ciliostasis, further preventing the clearing of mucus. [ 25 ] [ 26 ] They also solubilise lung surfactant, allowing phospholipase C access to cell membranes [ 4 ] and are necessary for correct biofilm formation.
There are three main phases of biofilm development and rhamnolipids are implicated in each phase. Rhamnolipids are reported to promote motility , thereby inhibiting attachment by preventing cells from adhering tightly to the substratum. During biofilm development, rhamnolipids are reported to create and maintain fluid channels for water and oxygen flow around the base of the biofilm. [ 31 ] Furthermore, they are important for forming structure in biofilms; a rhlA mutant forms a flat biofilm. [ 32 ] [ 33 ] Biofilm dispersal is dependent on Rhammnolipids, however other factors such as degradation of the matrix and activation of motility are also likely to be necessary. [ 34 ] It has been shown using fluorescence microscopy that the rhlAB operon is induced in the centre of the mushroom cap, followed by dispersal of cells from the polysaccharide matrix from the centre of these caps causing a cavity to form. A mutation in rhlA causes a failure in formation of mushroom caps at all. [ 34 ]
Motility is a key virulence determinant in Pseudomonas aeruginosa . Pseudomonas aeruginosa has three distinct methods of moving across or through a medium. Rhamnolipids are particularly important in swarming motility where they are postulated to lower the surface tension of the surface through their surfactant properties, allowing the bacterial cell to swarm. [ 32 ] New evidence suggests that rhamnolipids are necessary to allow Pseudomonas aeruginosa cells to overcome attachment mediated by type IV pili . [ 35 ] There is some discrepancy between the role of HAAs and RHLs in swarming motility. Some studies use a rhlA mutation to assess the effect on motility, which prevents the formation of HAAs and rhamnolipids. Studies that use a rhlB mutant show that Pseudomonas aeruginosa can swarm in the absence of rhamnolipids, but HAAs are absolutely necessary for swarming. [ 36 ] [ 37 ] Rhamnolipids have been proposed to be important in regulating swarm tendril formation. [ 38 ] Rhamnolipids and HAAs are also implicated in twitching motility, similarly the surfactant is thought to lower the surface tension allowing cells to move across the substratum. [ 32 ] [ 39 ] [ 40 ] However, the role of rhamnolipids in twitching motility may be nutritionally conditional. [ 41 ]
Surfactants are in demand for a wide range of industrial applications as they increase solubility, foaming capacity and lower surface tensions. In particular, rhamnolipids have been used broadly in the cosmetic industry for products such as moisturisers, condom lubricant and shampoo. [ 1 ] [ 42 ] Rhamnolipids are efficacious in bioremediation of organic and heavy metal polluted sites. [ 7 ] They also facilitate degradation of waste hydrocarbons such as crude oil and vegetable oil by Pseudomonas aeruginosa . [ 43 ] The rhamnolipid surfactant itself is valuable in the cosmetic industry, and rhamnolipids are a source of rhamnose, which is an expensive sugar in itself. [ 2 ] [ 44 ]
Other bio-based surfactants include sophorolipids and mannose-erythritol lipids. | https://en.wikipedia.org/wiki/Rhamnolipid |
Rhazinilam is an alkaloid first isolated in 1965 by Linde from the Melodinus australis plant. It was later isolated from the shrub Rhazya stricta as well as from other organisms.
Rhazinilam has activity similar to that of colchicine , taxol and vinblastine , acting as a spindle poison . [ 1 ]
Rhazinilam was first synthesized in 1973 by Smith and coworkers, and multiple subsequent times. [ 2 ]
Bowie, Alfred L.; Hughes, Chambers C.; Trauner, Dirk (2005). "Concise Synthesis of (±)-Rhazinilam through Direct Coupling". Organic Letters . 7 (23): 5207– 5209. doi : 10.1021/ol052033v . PMID 16268539 . | https://en.wikipedia.org/wiki/Rhazinilam |
A rheometer is a laboratory device used to measure the way in which a viscous fluid (a liquid , suspension or slurry ) flows in response to applied forces. It is used for those fluids which cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case for a viscometer . It measures the rheology of the fluid.
There are two distinctively different types of rheometers . Rheometers that control the applied shear stress or shear strain are called rotational or shear rheometers , whereas rheometers that apply extensional stress or extensional strain are extensional rheometers .
Rotational or shear type rheometers are usually designed as either a native strain-controlled instrument (control and apply a user-defined shear strain which can then measure the resulting shear stress) or a native stress-controlled instrument (control and apply a user-defined shear stress and measure the resulting shear strain).
The word rheometer comes from the Greek, and means a device for measuring main flow. [ 1 ] In the 19th century it was commonly used for devices to measure electric current, until the word was supplanted by galvanometer and ammeter . It was also used for the measurement of the flow of liquids, in medical practice (flow of blood) and in civil engineering (flow of water). This latter use persisted to the second half of the 20th century in some areas. Following the coining of the term rheology the word came to be applied to instruments for measuring the character rather than quantity of flow, and the other meanings are obsolete. (Principal Source: Oxford English Dictionary ) The principle and working of rheometers is described in several texts. [ 2 ] [ 3 ]
Four basic shearing planes can be defined according to their geometry,
The various types of shear rheometers then use one or a combination of these geometries.
One example of a linear shear rheometer is the Goodyear linear skin rheometer, which is used to test cosmetic cream formulations, and for medical research purposes to quantify the elastic properties of tissue.
The device works by attaching a linear probe to the surface of the tissue under test, a controlled cyclical force is applied, and the resultant shear force measured using a load cell. Displacement is measured using a Linear variable differential transformer (LVDT). Thus the basic stress–strain parameters are captured and analysed to derive the dynamic spring rate of the tissue under tests.
Liquid is forced through a tube of constant cross-section and precisely known dimensions under conditions of laminar flow . Either the flow-rate or the pressure drop are fixed and the other measured. Knowing the dimensions, the flow-rate can be converted into a value for the shear rate and the pressure drop into a value for the shear stress . Varying the pressure or flow allows a flow curve to be determined. When a relatively small amount of fluid is available for rheometric characterization, a microfluidic rheometer with embedded pressure sensors can be used to measure pressure drop for a controlled flow rate. [ 4 ] [ 5 ]
Capillary rheometers are especially advantageous for characterization of therapeutic protein solutions since it determines the ability to be syringed. [ 6 ] Additionally, there is an inverse relationship between the rheometry and solution stability, as well as thermodynamic interactions.
A dynamic shear rheometer , commonly known as DSR is used for research and development as well as for quality control in the manufacturing of a wide range of materials. Dynamic shear rheometers have been used since 1993 when Superpave was used for characterising and understanding high temperature rheological properties of asphalt binders in both the molten and solid state and is fundamental in order to formulate the chemistry and predict the end-use performance of these materials.
The liquid is placed within the annulus of one cylinder inside another. One of the cylinders is rotated at a set speed. This determines the shear rate inside the annulus. The liquid tends to drag the other cylinder round, and the force it exerts on that cylinder ( torque ) is measured, which can be converted to a shear stress .
One version of this is the Fann V-G Viscometer, which runs at two speeds, (300 and 600 rpm) and therefore only gives two points on the flow curve. This is sufficient to define a Bingham plastic model which was once widely used in the oil industry for determining the flow character of drilling fluids . In recent years rheometers that spin at 600, 300, 200, 100, 6 & 3 RPM have become more commonplace. This allows for more complex fluids models such as Herschel–Bulkley to be used. Some models allow the speed to be continuously increased and decreased in a programmed fashion, which allows the measurement of time-dependent properties.
The liquid is placed on horizontal plate and a shallow cone placed into it. The angle between the surface of the cone and the plate is around 1–2 degrees but can vary depending on the types of tests being run. Typically the plate is rotated and the torque on the cone measured. A well-known version of this instrument is the Weissenberg rheogoniometer, in which the movement of the cone is resisted by a thin piece of metal which twists—known as a torsion bar . The known response of the torsion bar and the degree of twist give the shear stress , while the rotational speed and cone dimensions give the shear rate . In principle the Weissenberg rheogoniometer is an absolute method of measurement providing it is accurately set up. Other instruments operating on this principle may be easier to use but require calibration with a known fluid.
Cone and plate rheometers can also be operated in an oscillating mode to measure elastic properties, or in combined rotational and oscillating modes.
In the past, devices with controlled strain or strain rate (CR rheometers) were distinguished from rheometers with controlled stress (CS rheometers) depending on the measuring principle.
In a controlled strain (CR) rheometer, the sample is subjected to displacement or speed (strain or strain rate) using a DC motor, and the resulting torque (stress) is measured separately using an additional force-torque sensor (torque compensation transducer). The electric current used to generate the displacement or speed of the motor is not used as a measure of the torque acting in the sample. This mode of operation is also referred to as separate motor transducer mode (SMT).
In a controlled-stress (CS) rheometer, the torque acting in the sample is determined directly from the electrical torque generated in the motor. With such a design, no separate torque sensor is required. Usually, this mode of operation is described as combined motor-transducer mode (CMT).
Nowadays, there are device concepts that allow both working modes, the combined motor transducer mode and the separate motor transducer mode, by using two motors in one device. The use of only one motor enables measurements to be made in the combined motor transducer mode. Using both motors allows working in the separate motor transducer mode, where one motor is used to deform the sample while the other motor is used to record the torque acting in the sample. Furthermore, this concept allows for additional modes of operation, such as counter-rotating mode, where both motors can rotate or oscillate in opposite directions. This mode of operation is used, for example, to increase the maximum achievable shear rate range or for advanced rheooptical characterization of samples.
The development of extensional rheometers has proceeded more slowly than shear rheometers, due to the challenges associated with generating a homogeneous extensional flow. Firstly, interactions of the test fluid or melt with solid interfaces will result in a component of shear flow, which will compromise the results. Secondly, the strain history of all the material elements must be controlled and known. Thirdly, the strain rates and strain levels must be high enough to stretch the polymeric chains beyond their normal radius of gyration, requiring instrumentation with a large range of deformation rates and a large travel distance. [ 8 ] [ 9 ]
Commercially available extensional rheometers have been segregated according to their applicability to viscosity ranges. Materials with a viscosity range from approximately 0.01 to 1 Pa.s. (most polymer solutions) are best characterized with capillary breakup rheometers, opposed jet devices, or contraction flow systems. Materials with a viscosity range from approximately 1 to 1000 Pa.s. are used in filament stretching rheometers. Materials with a high viscosity >1000 Pa.s., such as polymer melts, are best characterized by constant-length devices. [ 10 ]
Extensional rheometry is commonly performed on materials that are subjected to a tensile deformation. This type of deformation can occur during processing, such as injection molding, fiber spinning, extrusion, blow-molding, and coating flows. It can also occur during use, such as decohesion of adhesives, pumping of hand soaps, and handling of liquid food products.
A list of currently and previously marketed commercially available extensional rheometers is shown in the table below.
Rheotens is a fiber spinning rheometer, suitable for polymeric melts. The material is pumped from an upstream tube, and a set of wheels elongates the strand. A force transducer mounted on one of the wheels measures the resultant extensional force. Because of the pre-shear induced as the fluid is transported through the upstream tube, a true extensional viscosity is difficult to obtain. However, the Rheotens is useful to compare the extensional flow properties of a homologous set of materials.
The CaBER is a capillary breakup rheometer . A small quantity of material is placed between plates, which are rapidly stretched to a fixed level of strain. The midpoint diameter is monitored as a function of time as the fluid filament necks and breaks up under the combined forces of surface tension, gravity, and viscoelasticity. The extensional viscosity can be extracted from the data as a function of strain and strain rate. This system is useful for low viscosity fluids, inks, paints, adhesives, and biological fluids.
The FiSER (filament stretching extensional rheometer) is based on the works by Sridhar et al. and Anna et al. [ 11 ] In this instrument, a set of linear motors drive a fluid filament apart at an exponentially increasing velocity while measuring force and diameter as a function of time and position. By deforming at an exponentially increasing rate, a constant strain rate can be achieved in the samples (barring endplate flow limitations). This system can monitor the strain-dependent extensional viscosity, as well as stress decay following flow cessation. A detailed presentation on the various uses of filament stretching rheometry can be found on the MIT web site. [ 12 ]
The Sentmanat extensional rheometer (SER) is actually a fixture that can be field installed on shear rheometers. A film of polymer is wound on two rotating drums, which apply constant or variable strain rate extensional deformation on the polymer film. The stress is determined from the torque exerted by the drums.
Acoustic rheometers employ a piezo-electric crystal that can easily launch a successive wave of extensions and contractions into the fluid. This non-contact method applies an oscillating extensional stress. Acoustic rheometers measure the sound speed and attenuation of ultrasound for a set of frequencies in the megahertz range. Sound speed is a measure of system elasticity. It can be converted into fluid compressibility. Attenuation is a measure of viscous properties. It can be converted into viscous longitudinal modulus. In the case of a Newtonian liquid, attenuation yields information on the volume viscosity. This type of rheometer works at much higher frequencies than others. It is suitable for studying effects with much shorter relaxation times than any other rheometer.
A simpler version of the filament stretching rheometer, the falling plate rheometer sandwiches liquid between two solid surfaces. The top plate is fixed, and bottom plate falls under the influence of gravity, drawing out a string of the liquid.
Other systems involve liquid going through an orifice, expanding from a capillary, or sucked up from a surface into a column by a vacuum. A pressurized capillary rheometer can be used to design thermal treatments of fluid food. This instrumentation could help prevent over and under-processing of fluid food because extrapolation to high temperatures would not be necessary. [ 13 ] | https://en.wikipedia.org/wiki/Rheometer |
A mechanical system is rheonomous if its equations of constraints contain the time as an explicit variable . [ 1 ] [ 2 ] Such constraints are called rheonomic constraints . The opposite of rheonomous is scleronomous . [ 1 ] [ 2 ]
As shown at right, a simple pendulum is a system composed of a weight and a string. The string is attached at the top end to a pivot and at the bottom end to a weight. Being inextensible, the string has a constant length. Therefore, this system is scleronomous; it obeys the scleronomic constraint
where ( x , y ) {\displaystyle (x,\ y)\,\!} is the position of the weight and L {\displaystyle L\,\!} the length of the string.
The situation changes if the pivot point is moving, e.g. undergoing a simple harmonic motion
where x 0 {\displaystyle x_{0}\,\!} is the amplitude, ω {\displaystyle \omega \,\!} the angular frequency, and t {\displaystyle t\,\!} time.
Although the top end of the string is not fixed, the length of this inextensible string is still a constant. The distance between the top end and the weight must stay the same. Therefore, this system is rheonomous; it obeys the rheonomic constraint | https://en.wikipedia.org/wiki/Rheonomous |
In fluid mechanics (specifically rheology ), rheoscopic fluids are fluids whose internal currents are visible as it flows . Such fluids are effective in visualizing dynamic currents, such as convection and laminar flow . They are microscopic crystalline platelets such as mica , metallic flakes, or fish scales in suspension in a fluid such as water or glycol stearate .
When the fluid is put in motion, the suspended particles orient themselves with the local fluid shear. With appropriate illumination, the particle-filled fluid will reflect differing intensities of light.
A Kalliroscope is an art device/technique based on rheoscopic fluids (using crystalline guanine as the indicator particles [ 1 ] ) invented by artist Paul Matisse .
This fluid dynamics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rheoscopic_fluid |
The rhesus macaque ( Macaca mulatta ), colloquially rhesus monkey , is a species of Old World monkey . There are between six and nine recognised subspecies split between two groups, the Chinese-derived and the Indian-derived. Generally brown or grey in colour, it is 47–53 cm (19–21 in) in length with a 20.7–22.9 cm (8.1–9.0 in) tail and weighs 5.3–7.7 kg (12–17 lb). It is native to South , Central , and Southeast Asia and has the widest geographic range of all non-human primates , occupying a great diversity of altitudes and habitats.
The rhesus macaque is diurnal , arboreal, and terrestrial. It is mostly herbivorous , feeding mainly on fruit , but also eating seeds , roots , buds , bark , and cereals . Rhesus macaques living in cities also eat human food and trash. They are gregarious , with troops comprising 20–200 individuals. The social groups are matrilineal . Individuals communicate with a variety of facial expressions, vocalisations, body postures, and gestures.
As a result of the rhesus macaque's relatively easy upkeep, wide availability, and closeness to humans anatomically and physiologically, it has been used extensively in medical and biological research. It has facilitated many scientific breakthroughs including vaccines for rabies , smallpox , polio and antiretroviral medication to treat HIV/AIDS . A rhesus macaque became the first primate astronaut in 1948.
The rhesus is listed as Least Concern in the IUCN Red List .
The name "rhesus" is reminiscent of the mythological king Rhesus of Thrace , a minor character in the Iliad . However, the French naturalist Jean-Baptiste Audebert who named the species, stated: "it has no meaning". [ 4 ] The rhesus macaque is also known colloquially as the "rhesus monkey". [ 5 ] [ 6 ]
According to Zimmermann's first description of 1780, the rhesus macaque is distributed in eastern Afghanistan , Bangladesh , Bhutan , as far east as the Brahmaputra Valley , Barak valley and in peninsular India , Nepal , and northern Pakistan . Today, this is known as the Indian rhesus macaque Macaca mulatta mulatta , which includes the morphologically similar M. rhesus villosus , described by True in 1894, from Kashmir , and M. m. mcmahoni , described by Pocock in 1932 from Kootai, Pakistan . Several Chinese subspecies of rhesus macaques were described between 1867 and 1917. The molecular differences identified among populations, however, are alone not consistent enough to conclusively define any subspecies. [ 7 ]
The Chinese subspecies can be divided as follows:
The rhesus macaque is brown or grey in color and has a pink face, which is bereft of fur. It has, on average, 50 vertebrae and a wide rib cage. Its tail averages between 20.7 and 22.9 cm (8.1 and 9.0 in). [ 10 ] Adult males measure about 53 cm (21 in) on average and weigh about 7.7 kg (17 lb). Females are smaller, averaging 47 cm (19 in) in length and 5.3 kg (12 lb) in weight. [ 10 ] [ 11 ] The ratio of arm length to leg length is 89.6–94.3%. [ 12 ]
The rhesus macaque has a dental formula of 2.1.2.3 2.1.2.3 × 2 = 32 and bilophodont molar teeth . [ 13 ]
Rhesus macaques are native to India , Bangladesh , Pakistan , Nepal , Myanmar , Thailand , Afghanistan , Vietnam , southern China , and some neighbouring areas. They have the widest geographic ranges of any non-human primate, occupying a great diversity of altitudes throughout Central, South, and Southeast Asia. Inhabiting arid, open areas, rhesus macaques may be found in grasslands, woodlands, and in mountainous regions up to 2,500 m (8,200 ft) in elevation. They are strong swimmers, [ 14 ] and can swim across rivers. [ 15 ] Rhesus macaques are noted for their tendency to move from rural to urban areas, coming to rely on handouts or refuse from humans. [ 16 ] They adapt well to human presence, and form larger troops in human-dominated landscapes than in forests. [ 17 ] Rhesus monkeys live in patches of forest within agricultural areas, which gives them access to agroecosystem habitats and makes them at ease in navigating through them. [ 18 ]
The southern and the northern distributional limits for rhesus and bonnet macaques , respectively, currently run parallel to each other in the western part of India, are separated by a large gap in the center, and converge on the eastern coast of the peninsula to form a distribution overlap zone. This overlap region is characterized by the presence of mixed-species troops, with pure troops of both species sometimes occurring even in close proximity to one another. The range extension of rhesus macaque – a natural process in some areas, and a direct consequence of introduction by humans in other regions – poses grave implications for the endemic and declining populations of bonnet macaques in southern India. [ 19 ]
Kumar et al (2013) [ 20 ] provides a summary of population distribution and habitat in India. It states that there were sightings of rhesus macaques in all surveyed habitats except semi-evergreen forests. [ 20 ]
Fossilized isolated teeth and mandible fragments from Tianyuan Cave and a juvenile maxilla from Wanglaopu Cave near Zhoukoudian represent the first recognized occurrence of rhesus macaque fossils in the far north of China, and thus the population of rhesus macaques which lived around Beijing decades ago is believed to have originated from Pleistocene ancestors rather than being human-introduced. [ 21 ] Fossil mandible fragments from the Taedong River Basin around Pyongyang , North Korea, have also been assigned to this species. [ 22 ]
Rhesus macaques have also been introduced and acclimated to other areas, such as the United States, where they are considered an invasive species. [ 23 ] Colonies have been established in Florida , Puerto Rico , and South Carolina
Around the spring of 1938, a colony of rhesus macaques was released in and around Silver Springs in Florida by a tour boat operator known locally as "Colonel Tooey" to enhance his "Jungle Cruise". Tooey had been hoping to profit from the boom in jungle adventure stories in film and print media, buying the monkeys to be attractions at his river boat tour. Tooey apparently hadn't been aware of rhesus macaques being proficient swimmers, meaning his original plan to keep the monkeys isolated to an island inside the river didn't work. The macaques nevertheless remained in the region thanks to daily feedings by Tooey and the boat tours. Tooey subsequently released additional monkeys to add to the gene pool and avoid inbreeding . The traditional story that the monkeys were released for scenery enhancement in the Tarzan movies that were filmed at that location is false, as the only Tarzan movie filmed in the area, 1939's Tarzan Finds a Son! , does not contain rhesus macaques. [ 24 ] Whilst this was the first colony established and the longest lasting, other colonies have since been established intentionally or accidentally. A population in Titusville, Florida , was featured at the now defunct Tropical Wonderland theme park, which coincidentally was at one time endorsed by Johnny Weissmuller , who had portrayed Tarzan in the aforementioned films. This association might have contributed to the misconception the monkeys were associated directly with the Tarzan films. This colony either escaped or was intentionally released, roaming the woods of the area for a decade. In the 1980s a trapper captured several monkeys from the Titusville population and released them in the Silver Springs area to join that population. The last printed records of monkeys in the Titusville area occurred in early 1990s, but sightings continue to this day. [ 25 ]
Various colonies of rhesus macaque are speculated to be the result of zoos and wildlife parks destroyed in hurricanes, most notably Hurricane Andrew . [ 26 ] A 2020 estimate put the number at 550–600 rhesus macaques living in the state; [ 27 ] officials have caught more than 1,000 of the monkeys in the past decade. Most of the captured monkeys tested positive for herpes B virus , which leads wildlife officials to consider the animals a public health hazard. [ 28 ] Of the three monkey species to have had any lasting presence in Florida, the other two being African vervet monkeys and South American squirrel monkeys , the Rhesus macaques have endured the longest and are the only ones to show continual population growth. The species' adaptable nature, generalized diet, and larger size as to reduce the chance of cold stress or predator attack are thought to be reasons for their success.
Despite the risks, the macaques have continued to enjoy long-standing support from residents in Florida, strongly disagreeing with their removal. [ 25 ] The Silver Springs colony has continued to grow in size and range, being commonly sighted in both the park grounds, the nearby city of Ocala, Florida , and the neighboring Ocala National Forest . [ 29 ] Individuals likely originating from this colony have been seen hundreds of kilometers away, in St. Augustine, Florida and St. Petersburg, Florida . One infamous individual, named the "Mystery Monkey of Tampa Bay ", evaded capture for years, inspiring social media posts and a song. [ 30 ]
Exogenous colonies have also resulted from research activities. There is a colony of rhesus macaques on Morgan Island , one of the Sea Islands in the South Carolina Lowcountry . They were imported in the 1970s for use in the local labs. [ 31 ] [ 32 ] Another research colony was established by the Caribbean Primate Research Center of the University of Puerto Rico on the island of Cayo Santiago , [ 33 ] off of Puerto Rico . There are no predators on the island, and humans are not permitted to land, except as part of the research program. Another Puerto Rico research colony was released into the Desecheo National Wildlife Refuge in 1966. As of 2022 [update] they are continuing to do ecological harm, damage crops amounting to $300,000/year and cost $1,000,000/year to manage. [ 34 ]
The Rhesus macaque is diurnal , and both arboreal and terrestrial . It is quadrupedal and, when on the ground, it walks digitigrade and plantigrade . It is mostly herbivorous , feeding mainly on fruit , but also eating seeds , roots , buds , bark , and cereals . It is estimated to consume around 99 different plant species in 46 families. During the monsoon season, it gets much of its water from ripe and succulent fruit. Rhesus macaques living far from water sources lick dewdrops from leaves and drink rainwater accumulated in tree hollows. [ 35 ] They have also been observed eating termites , grasshoppers , ants , and beetles . [ 36 ] When food is abundant, they are distributed in patches, and forage throughout the day in their home ranges. They drink water when foraging, and gather around streams and rivers. [ 37 ] Rhesus macaques have specialized pouch-like cheeks, allowing them to temporarily hoard their food. [ 38 ] It has specialised cheek pouches where it can temporarily store food and also eats invertebrates, including adult and larval insects, spiders, lice, honeycombs, crabs and bird eggs. With an increase in anthropogenic land changes, the rhesus macaque has evolved alongside intense and rapid environmental disturbance associated with human agriculture and urbanization resulting in proportions of their diet to be altered. [ 39 ]
In psychological research, rhesus macaques have demonstrated a variety of complex cognitive abilities , including the ability to make same-different judgments, understand simple rules, and monitor their own mental states. [ 40 ] [ 41 ] They have even been shown to demonstrate self-agency , [ 42 ] an important type of self-awareness. In 2014, onlookers at a train station in Kanpur, India, documented a rhesus monkey, knocked unconscious by overhead power lines, that was revived by another rhesus that systematically administered a series of resuscitative actions. [ 43 ]
Like other macaques, rhesus troops comprise a mixture of 20–200 males and females. [ 44 ] Females may outnumber the males by a ratio of 4:1. Males and females both have separate hierarchies. Female philopatry , common among social mammals, has been extensively studied in rhesus macaques. Females tend not to leave the social group, and have highly stable matrilineal hierarchies in which a female's rank is dependent on the rank of her mother. In addition, a single group may have multiple matrilineal lines existing in a hierarchy, and a female outranks any unrelated females that rank lower than her mother. [ 45 ] Rhesus macaques are unusual in that the youngest females tend to outrank their older sisters. [ 46 ] This is likely because young females are more fit and fertile. Mothers seem to prevent the older daughters from forming coalitions against her. [ clarification needed ] The youngest daughter is the most dependent on the mother, and would have nothing to gain from helping her siblings in overthrowing their mother. Since each daughter had a high rank in her early years, rebelling against her mother is discouraged. [ 47 ] Juvenile male macaques also exist in matrilineal lines, but once they reach four to five years of age, they are driven out of their natal groups by the dominant male. Thus, adult males gain dominance by age and experience. [ 37 ]
In the group, macaques position themselves based on rank. The "central male subgroup" contains the two or three oldest and most dominant males which are codominant, along with females, their infants, and juveniles. This subgroup occupies the center of the group and determines the movements, foraging, and other routines. [ 37 ] The females of this subgroup are also the most dominant of the entire group. The farther to the periphery a subgroup is, the less dominant it is. Subgroups on the periphery of the central group are run by one dominant male, of a rank lower than the central males, and he maintains order in the group, and communicates messages between the central and peripheral males. A subgroup of subordinate, often subadult, males occupy the very edge of the groups, and have the responsibility of communicating with other macaque groups and making alarm calls. [ 48 ] Rhesus social behaviour has been described as despotic, in that high-ranking individuals often show little tolerance, and frequently become aggressive towards non-kin. [ 49 ] Top-ranking female rhesus monkeys are known to sexually coerce unreceptive males and also physically injure them, biting off digits and damaging their genitals. [ 50 ]
Rhesus macaques have been observed engaging in interspecies grooming with Hanuman langurs and with Sambar deer . [ 51 ]
Rhesus macaques interact using a variety of facial expressions, vocalizations, body postures, and gestures. Perhaps the most common facial expression the macaque makes is the "silent bared teeth" face. [ 52 ] This is made between individuals of different social ranks, with the lower-ranking one giving the expression to its superior. A less-dominant individual also makes a "fear grimace", accompanied by a scream, to appease or redirect aggression. [ 53 ] Another submissive behavior is the "present rump", where an individual raises its tail and exposes its genitals to the dominant one. [ 52 ] A dominant individual threatens another individual by standing quadrupedally and making a silent "open mouth stare" accompanied by the tail sticking straight. [ 54 ] During movements, macaques make coos and grunts. These are also made during affiliative interactions, and approaches before grooming. [ 55 ] When they find rare food of high quality, macaques emit warbles, harmonic arches, or chirps. When in threatening situations, macaques emit a single loud, high-pitched sound called a shrill bark. [ 56 ] Screeches, screams, squeaks, pant-threats, growls, and barks are used during aggressive interactions. [ 56 ] Infants " gecker " to attract their mother's attention. [ 57 ]
Adult male macaques try to maximize their reproductive success by entering into sex with females both in and outside the breeding period . Females prefer to mate with males that are not familiar to them. Outsider males who are not members of the female's own troop are preferred over higher-ranking males. Outside of the consortship period, males and females return the prior behavior of not exhibiting preferential treatment or any special relationship. The breeding period can last up to eleven days, and a female usually mates with numerous males during that time. Male rhesus macaques have been observed to fight for access to sexually receptive females and they suffer more wounds during the mating season. [ 58 ] Female macaques first breed when they are four years old and reach menopause at around twenty-five years of age. [ 59 ] Male macaques generally play no role in raising the young but do have peaceful relationships with the offspring of their consort pairs. [ 37 ]
Manson and Parry [ 60 ] found that free-ranging rhesus macaques avoid inbreeding. Adult females were never observed to copulate with males of their own matrilineage during their fertile periods.
Mothers with one or more immature daughters in addition to their infants are in contact with their infants less than those with no older immature daughters, because the mothers may pass the parenting responsibilities to their daughters. High-ranking mothers with older immature daughters also reject their infants significantly more than those without older daughters and tend to begin mating earlier in the mating season than expected based on their dates of parturition the preceding birth season. [ 61 ] Infants farther from the center of the groups are more vulnerable to infanticide from outside groups. [ 37 ] Some mothers abuse their infants, which is believed to be the result of controlling parenting styles . [ 62 ]
The rhesus monkey has been used as a model for studying aging of the ovaries of primate females. [ 63 ] Ovarian aging was found to be associated with increased DNA double strand breaks and reduced DNA repair in granulosa cells , that is, somatic cells closely associated with developing oocytes . [ 63 ]
In several experiments giving mirrors to rhesus monkeys, they looked into the mirrors and groomed themselves, as well as flexed various muscle groups. This behaviour indicates that they recognised and were aware of themselves . [ 64 ]
The macaque–human relationships is complex and culturally specific, ranging from relatively peaceful coexistence to extreme levels of conflict. [ 65 ] Conflicts tend to result from rapidly changing agricultural practices, increasing urbanisation, and clearing of woodlands and other territory, pushing macaques into human settlements in the search for resources. [ 66 ] A 2021 study stated that human-macaque conflict is one of the most critical challenges faced by wildlife managers in the South- and Southeast-Asian regions. [ 67 ]
Conflict between rhesus macaques and humans is at all-time high, with areas once forested habitat being converted to industrial agriculture. In Nepal, the expansion of monocultures, increased forest fragmentation, degradation of natural habitats and changing agricultural practices have led to a significant increase in the frequency of human-macaque conflict. [ 67 ] Crop raiding is one of the biggest visible effects of human-rhesus conflict. The estimated financial cost to individual farmer households of macaque corn and rice raiding is approximately US$14.9 or 4.2% of their yearly income. [ 67 ] This has resulted in farmers and other members of the population viewing macaques inhabiting agricultural landscapes as serious crop pests. [ 67 ] Nepal is a significant study area with almost 44% of Nepal's land area containing suitable habitat for rhesus macaques [ 68 ] but only having 8% of such suitable area being protected national parks. [ 68 ] Rhesus macaques are rated as one of the top ten crop-raiding wildlife species in Nepal, [ 68 ] which adds to their negative perception.
Suggestions to mitigate conflict include "prioritizing forest restoration programs, strategic management plans designed to connect isolated forest fragments with high rhesus macaque population densities, creating government programs that compensate farmers for income lost due to crop-raiding, and educational outreach that informs local villagers of the importance of conservation and protecting biodiversity [ 68 ] ". Mitigation strategies offers the most effective solutions to reduce conflict occurring between rhesus macaques and humans in Nepal. [ 68 ]
India is another country that is seeing the rise of human-macaque conflict. Macaque-human conflict particularly occurs in the twin hill-states of Uttarakhand and Himachal Pradesh [ 69 ] with such conflict being a source of contentious debate in political scenarios, resentment and polarization amongst agriculturalists and wildlife conservationists. [ 66 ] In India, crop raiding by rhesus macaques has been identified as the main cause of conflict. [ 66 ] In urban areas, rhesus macaques damage property and injure people in house raids to access food and provisions; [ 69 ] in agricultural areas, they cause financial losses to farmers due to crop depredation. [ 69 ] The estimated extent of crop damages in Himachal Pradesh ranges from 10–100% to 40–80% of all crop losses. [ 69 ] The financial implications of such damage is estimated at approximately USD$200,000 in agriculture and USD$150,000 in horticulture. [ 69 ] Quantification of crop and financial loses is challenging. Farmers' negative views of macaques may cause them to perceive higher than actual losses. This has led to harsh actions against rhesus macaque communities. Other factors in rhesus perception include economic status, farmer economic stability, cultural attitudes towards the given species and the frequency and intensity of wildlife conflicts. [ 69 ] All of the above have resulted in changes in conservation and management with legal rhesus macaque culling issued in 2010. [ 69 ]
Human-macaque conflict is also occurring in China, specifically in the area of Longyang District, Baoshan City, Yunnan Province. The peak period of conflict occurs from August–October. Factors associated with accessibility and availability of food and shelter appear to be the key drivers of human-macaque conflict, with an overall increase between the years of 2012 and 2021. [ 18 ]
One key factor of conflict that directly affects the human-macaque relationship is visibility. Visibility of rhesus macaques in agroecosystem -dominated areas largely impacts conflict between humans and rhesus macaques. The conspicuous presence of rhesus macaques in and around farms results in farmers believing that macaques cause heavy crop depredations which, in turn, have led to negative perceptions and actions against the species. [ 70 ] Whereas visibility in urban areas can result in a positive relationship, areas include around temples, and tourist areas where their dietary needs are largely met by food provisioning.
Towards the end of March 2018, it was reported that a monkey had entered a house in the village of Talabasta, Odisha , India and kidnapped a baby. The baby was later found dead in a well. Though monkeys are known to attack people, enter homes and damage property, this reported behaviour was unusual. [ 71 ] [ 72 ]
Crop-raiding is seen as one of the most important behaviours to change to reduce conflicts. One example is the implementation of guards in agricultural settings to chase off intruding monkeys using dogs, slingshots, and firecrackers. [ 73 ] This method is non-lethal and can alter behavioural patterns of crop-raiding monkeys. Another strategy that farmers can employ is to plant alternative, buffer crops which are unattractive to monkeys in high-conflict zones, such as along the edges of macaque habitats. [ 73 ] In urban settings, planting food trees within city periphery and country parks aim to discourage macaques from entering nearby residential areas for food. [ 73 ]
In areas of tourism, human behaviour change is necessary to prevent conflict. One method is to introduce public education programs as well as restrict visitors to specific viewing platforms, with the goal to minimize physical proximity. [ 73 ] An important aspect is enforcing no feed regulations that only allow provisioning by trained staff at scheduled times. [ 73 ] Regulating visitor behaviours that provoke aggressive responses from macaques, including noise regulation, greatly benefits conflict reduction. [ 73 ] Replacing food-conditioned behaviours established by human visitors and further human education will greatly aid in returning co-existence between rhesus macaques and humans.
Another method of population management is translocation. Translocation of problem macaques in urban rhesus communities in India has been employed as a non-lethal solution to human–macaque conflicts. [ 73 ] Translocation can be seen as a short-term fix, as macaques may return or other rhesus groups may take their place. Translocation is also hampered by a lack of suitable alternate locations. [ 73 ]
Another tool of population management is sterilisation and/or contraceptive programmes. [ 73 ] Fertility control looks to be a feasible management tool for reducing human–macaque conflict because it avoids the extermination of the animals and avoids costs and problems associated with translocation. [ 73 ] Although there is potential for sterilization and general fertility control to be positive, there is limited research and understanding of the long-term effects of sterilization programs and its effectiveness. [ 73 ]
The rhesus macaque is well known to science. Due to its relatively easy upkeep in captivity, wide availability, and closeness to humans anatomically and physiologically, it has been used extensively in medical and biological research on human and animal health-related topics. It has given its name to the Rh factor , one of the elements of a person's blood group , by the discoverers of the factor, Karl Landsteiner and Alexander Wiener . The rhesus macaque was also used in the well-known experiments on maternal deprivation carried out in the 1950s by controversial comparative psychologist Harry Harlow . Other medical breakthroughs facilitated by the use of the rhesus macaque include: [ 74 ]
The U.S. Army , the U.S. Air Force , and NASA launched rhesus macaques into outer space during the 1950s and 1960s, and the Soviet/Russian space program launched them into space as recently as 1997 on the Bion missions . Albert II became the first primate and first mammal in space during a U.S. V-2 rocket suborbital flight on 14 June 1949, and died on impact when a parachute failed.
Another rhesus monkey, Able, was launched on a suborbital spaceflight in 1959, and was among the first living beings (along with Miss Baker , a squirrel monkey on the same mission) to travel in space and return alive. [ 75 ]
On 25 October 1999, the rhesus macaque became the first cloned primate with the birth of Tetra . January 2001 had the birth of ANDi , the first transgenic primate; ANDi carries foreign genes originally from a jellyfish . [ 76 ]
Though most studies of the rhesus macaque are from various locations in northern India, some knowledge of the natural behavior of the species comes from studies carried out on a colony established by the Caribbean Primate Research Center of the University of Puerto Rico on the island of Cayo Santiago , off Puerto Rico , where approximately 1800 of the monkeys live. [ 77 ] No predators are on the island, and humans are not permitted to land except as part of the research programmes. The colony is provisioned to some extent, but about half of its food comes from natural foraging.
Rhesus macaques, like many macaques, carry the herpes B virus . This virus does not typically harm the monkey, but is very dangerous to humans in the rare event that it jumps species , for example in the 1997 death of Yerkes National Primate Research Center researcher Elizabeth Griffin. [ 78 ] [ 79 ] [ 80 ]
Work on the genome of the rhesus macaque was completed in 2007, making the species the second nonhuman primate whose genome was sequenced. [ 81 ] Humans and macaques apparently share about 93% of their DNA sequence and shared a common ancestor roughly 25 million years ago. [ 82 ] The rhesus macaque has 21 pairs of chromosomes. [ 83 ]
Comparison of rhesus macaques, chimpanzees , and humans revealed the structure of ancestral primate genomes, positive selection pressure and lineage-specific expansions, and contractions of gene families. "The goal is to reconstruct the history of every gene in the human genome," said Evan Eichler , University of Washington, Seattle. DNA from different branches of the primate tree will allow us "to trace back the evolutionary changes that occurred at various time points, leading from the common ancestors of the primate clade to Homo sapiens ," said Bruce Lahn , University of Chicago. [ 84 ]
After the human and chimpanzee genomes were sequenced and compared, it was usually impossible to tell whether differences were the result of the human or chimpanzee gene changing from the common ancestor. After the rhesus macaque genome was sequenced, three genes could be compared. If two genes were the same, they were presumed to be the original gene. [ 85 ]
The chimpanzee and human genome diverged 6 million years ago. They have 98% identity and many conserved regulatory regions. Comparing the macaque and human genomes, further identified evolutionary pressure and gene function. Like the chimpanzee, changes were on the level of gene rearrangements rather than single mutations. Frequent insertions, deletions, changes in the order and number of genes, and segmental duplications near gaps, centromeres and telomeres occurred. So, macaque, chimpanzee, and human chromosomes are mosaics of each other. [ citation needed ]
Some normal gene sequences in healthy macaques and chimpanzees cause profound disease in humans. For example, the normal sequence of phenylalanine hydroxylase in macaques and chimpanzees is the mutated sequence responsible for phenylketonuria in humans. So, humans must have been under evolutionary pressure to adopt a different mechanism. [ citation needed ] Some gene families are conserved or under evolutionary pressure and expansion in all three primate species, while some are under expansion uniquely in human, chimpanzee, or macaque. [ citation needed ] For example, cholesterol pathways are conserved in all three species (and other primate species). In all three species, immune response genes are under positive selection, and genes of T cell-mediated immunity, signal transduction, cell adhesion, and membrane proteins generally. Genes for keratin, which produce hair shafts, were rapidly evolving in all three species, possibly because of climate change or mate selection. The X chromosome has three times more rearrangements than other chromosomes. The macaque gained 1,358 genes by duplication. [ citation needed ] Triangulation of human, chimpanzee, and macaque sequences showed expansion of gene families in each species. [ citation needed ]
The PKFP gene, important in sugar ( fructose ) metabolism, is expanded in macaques, possibly because of their high- fruit diet. So are genes for the olfactory receptor, cytochrome P450 (which degrades toxins), and CCL3L1-CCL4 (associated in humans with HIV susceptibility). [ citation needed ] Immune genes are expanded in macaques, relative to all four great ape species. The macaque genome has 33 major histocompatibility genes, three times those of human. This has clinical significance because the macaque is used as an experimental model of the human immune system. [ citation needed ]
In humans, the preferentially expressed antigen of melanoma (PRAME) gene family is expanded. It is actively expressed in cancers, but normally is testis-specific, possibly involved in spermatogenesis. The PRAME family has 26 members on human chromosome 1. In the macaque, it has eight, and has been very simple and stable for millions of years. The PRAME family arose in translocations in the common mouse-primate ancestor 85 million years ago, and is expanded on mouse chromosome 4. [ citation needed ]
DNA microarrays are used in macaque research. For example, Michael Katze of University of Washington, Seattle, infected macaques with 1918 and modern influenzas. The DNA microarray showed the macaque genomic response to human influenza on a cellular level in each tissue. Both viruses stimulated innate immune system inflammation, but the 1918 flu stimulated stronger and more persistent inflammation, causing extensive tissue damage, and it did not stimulate the interferon-1 pathway. The DNA response showed a transition from innate to adaptive immune response over seven days. [ 86 ] [ 87 ]
The full sequence and annotation of the macaque genome is available on the Ensembl genome browser. [ 88 ]
The rhesus macaque is listed as Least Concern on the IUCN Red List and estimated to exist in large numbers; it is tolerant of a broad range of habitats , including urban environments. [ 1 ] It has the largest natural range of any non-human primate. [ 39 ] The Thai population is locally threatened. In addition to habitat destruction and agricultural encroachment, pet releases of the different species into existing troops are diluting the gene pool and putting its genetic integrity at risk. [ 89 ] [ 90 ] Despite the wealth of information on its ecology and behaviour, little attention has been paid to its demography or population status, [ 91 ] which can pose a risk for future Rhesus macaque populations. The extension of its distributional limits by approximately 3,500 km 2 (1,400 sq mi) in southeast India caused population stress on other species. This range extension has been caused by human intervention tactics whereby village translocation occurs from urban conflict ridden areas. [ 92 ] | https://en.wikipedia.org/wiki/Rhesus_macaque |
Rhetoric [ note 1 ] is the art of persuasion . It is one of the three ancient arts of discourse ( trivium ) along with grammar and logic / dialectic . As an academic discipline within the humanities , rhetoric aims to study the techniques that speakers or writers use to inform, persuade, and motivate their audiences . [ 2 ] Rhetoric also provides heuristics for understanding, discovering, and developing arguments for particular situations.
Aristotle defined rhetoric as "the faculty of observing in any given case the available means of persuasion", and since mastery of the art was necessary for victory in a case at law, for passage of proposals in the assembly, or for fame as a speaker in civic ceremonies, he called it "a combination of the science of logic and of the ethical branch of politics". [ 3 ] Aristotle also identified three persuasive audience appeals: logos , pathos , and ethos . The five canons of rhetoric , or phases of developing a persuasive speech, were first codified in classical Rome: invention , arrangement , style , memory , and delivery .
From Ancient Greece to the late 19th century, rhetoric played a central role in Western education and Islamic education in training orators , lawyers , counsellors, historians , statesmen , and poets . [ 4 ] [ note 2 ]
Scholars have debated the scope of rhetoric since ancient times. Although some have limited rhetoric to the specific realm of political discourse , to many modern scholars it encompasses every aspect of culture. Contemporary studies of rhetoric address a much more diverse range of domains than was the case in ancient times. While classical rhetoric trained speakers to be effective persuaders in public forums and in institutions such as courtrooms and assemblies, contemporary rhetoric investigates human discourse writ large . Rhetoricians have studied the discourses of a wide variety of domains, including the natural and social sciences, fine art, religion, journalism, digital media, fiction, history, cartography , and architecture, along with the more traditional domains of politics and the law. [ 6 ]
Because the ancient Greeks valued public political participation, rhetoric emerged as an important curriculum for those desiring to influence politics. Rhetoric is still associated with its political origins. However, even the original instructors of Western speech—the Sophists —disputed this limited view of rhetoric. According to Sophists like Gorgias , a successful rhetorician could speak convincingly on a topic in any field, regardless of his experience in that field. This suggested rhetoric could be a means of communicating any expertise, not just politics. In his Encomium to Helen , Gorgias even applied rhetoric to fiction by seeking, for his amusement, to prove the blamelessness of the mythical Helen of Troy in starting the Trojan War . [ 7 ]
Plato defined the scope of rhetoric by discarding any connotation of religious ritual or magical incantation, simply taking the term in its literal sense, which means "leading the soul" through words. [ 8 ] He criticized the Sophists for using rhetoric to deceive rather than to discover truth. In Gorgias , one of his Socratic Dialogues , Plato defines rhetoric as the persuasion of ignorant masses within the courts and assemblies. [ 9 ] Rhetoric, in Plato's opinion, is merely a form of flattery and functions similarly to culinary arts , which mask the undesirability of unhealthy food by making it taste good. [ citation needed ] Plato considered any speech of lengthy prose aimed at flattery as within the scope of rhetoric. Some scholars, however, contest the idea that Plato despised rhetoric and instead view his dialogues as a dramatization of complex rhetorical principles. [ 10 ] Socrates explained the relationship between rhetoric in flattery when he maintained that a rhetorician who teaches anyone how to persuade people in an assembly to do what he wants, without knowledge of what is just or unjust, engages in a kind of flattery ( kolakeia ) that constitutes an image ( eidolon ) of a part of the art of politics. [ 11 ]
Aristotle both redeemed rhetoric from Plato and narrowed its focus by defining three genres of rhetoric— deliberative , forensic or judicial, and epideictic . [ 12 ] Yet, even as he provided order to existing rhetorical theories, Aristotle generalized the definition of rhetoric to be the ability to identify the appropriate means of persuasion in a given situation based upon the art of rhetoric ( technê ). [ 13 ] This made rhetoric applicable to all fields, not just politics. Aristotle viewed the enthymeme based upon logic (especially, based upon the syllogism) as the basis of rhetoric.
Aristotle also outlined generic constraints that focused the rhetorical art squarely within the domain of public political practice. He restricted rhetoric to the domain of the contingent or probable: those matters that admit multiple legitimate opinions or arguments. [ 14 ]
Since the time of Aristotle, logic has changed. For example, modal logic has undergone a major development that also modifies rhetoric. [ 15 ]
The contemporary neo-Aristotelian and neo-Sophistic positions on rhetoric mirror the division between the Sophists and Aristotle. Neo-Aristotelians generally study rhetoric as political discourse, while the neo-Sophistic view contends that rhetoric cannot be so limited. Rhetorical scholar Michael Leff characterizes the conflict between these positions as viewing rhetoric as a "thing contained" versus a "container". The neo-Aristotelian view threatens the study of rhetoric by restraining it to such a limited field, ignoring many critical applications of rhetorical theory, criticism, and practice. Simultaneously, the neo-Sophists threaten to expand rhetoric beyond a point of coherent theoretical value.
In more recent years, people studying rhetoric have tended to enlarge its object domain beyond speech. Kenneth Burke asserted humans use rhetoric to resolve conflicts by identifying shared characteristics and interests in symbols. People engage in identification , either to assign themselves or another to a group. This definition of rhetoric as identification broadens the scope from strategic and overt political persuasion to the more implicit tactics of identification found in an immense range of sources [ specify ] . [ 16 ] Burke focused on the interplay of identification and division, maintaining that identification compensates for an original division by preventing a strict separation between objects, people, and spaces. [ 17 ] This is achieved by assigning to them common properties through linguistic symbols. [ 17 ]
Among the many scholars who have since pursued Burke's line of thought, James Boyd White sees rhetoric as a broader domain of social experience in his notion of constitutive rhetoric . Influenced by theories of social construction , White argues that culture is "reconstituted" through language. Just as language influences people, people influence language. Language is socially constructed, and depends on the meanings people attach to it. Because language is not rigid and changes depending on the situation, the very usage of language is rhetorical. An author, White would say, is always trying to construct a new world and persuading his or her readers to share that world within the text. [ 18 ]
People engage in rhetoric any time they speak or produce meaning. Even in the field of science , via practices which were once viewed as being merely the objective testing and reporting of knowledge, scientists persuade their audience to accept their findings by sufficiently demonstrating that their study or experiment was conducted reliably and resulted in sufficient evidence to support their conclusions. [ 19 ]
The vast scope of rhetoric is difficult to define. Political discourse remains the paradigmatic example for studying and theorizing specific techniques and conceptions of persuasion or rhetoric. [ 20 ]
Throughout European History , rhetoric meant persuasion in public and political settings such as assemblies and courts. [ citation needed ] Because of its associations with democratic institutions, rhetoric is commonly said to flourish in open and democratic societies with rights of free speech , free assembly, and political enfranchisement for some portion of the population. [ citation needed ] Those who classify rhetoric as a civic art believe that rhetoric has the power to shape communities, form the character of citizens, and greatly affect civic life.
Rhetoric was viewed as a civic art by several of the ancient philosophers. Aristotle and Isocrates were two of the first to see rhetoric in this light. In Antidosis , Isocrates states, "We have come together and founded cities and made laws and invented arts; and, generally speaking, there is no institution devised by man which the power of speech has not helped us to establish." [ 21 ] With this statement he argues that rhetoric is a fundamental part of civic life in every society and that it has been necessary in the foundation of all aspects of society. He further argues in Against the Sophists that rhetoric, although it cannot be taught to just anyone, is capable of shaping the character of man. He writes, "I do think that the study of political discourse can help more than any other thing to stimulate and form such qualities of character." [ 22 ] Aristotle, writing several years after Isocrates, supported many of his arguments and argued for rhetoric as a civic art.
In the words of Aristotle, in the Rhetoric , rhetoric is "...the faculty of observing in any given case the available means of persuasion". According to Aristotle, this art of persuasion could be used in public settings in three different ways: "A member of the assembly decides about future events, a juryman about past events: while those who merely decide on the orator's skill are observers. From this it follows that there are three divisions of oratory—(1) political, (2) forensic, and (3) the ceremonial oratory of display". [ 23 ] Eugene Garver, in his critique of Aristotle's Rhetoric , confirms that Aristotle viewed rhetoric as a civic art. Garver writes, " Rhetoric articulates a civic art of rhetoric, combining the almost incompatible properties of techne and appropriateness to citizens." [ 24 ] Each of Aristotle's divisions plays a role in civic life and can be used in a different way to affect the polis .
Because rhetoric is a public art capable of shaping opinion, some of the ancients, including Plato found fault in it. They claimed that while it could be used to improve civic life, it could be used just as easily to deceive or manipulate. The masses were incapable of analyzing or deciding anything on their own and would therefore be swayed by the most persuasive speeches. Thus, civic life could be controlled by whoever could deliver the best speech. Plato explores the problematic moral status of rhetoric twice: in Gorgias and in The Phaedrus , a dialogue best-known for its commentary on love.
More trusting in the power of rhetoric to support a republic, the Roman orator Cicero argued that art required something more than eloquence. A good orator needed also to be a good person, enlightened on a variety of civic topics. In De Oratore , modeled on Plato's dialogues, Cicero emphasized that effective rhetoric comes from a combination of wisdom (sapientia) and eloquence (eloquentia) . [ 25 ] According to Cicero, the ideal orator must demonstrate not only stylistic skill but also moral integrity and broad learning, thus uniting theory and practice for the betterment of the state. Influenced by Aristotelian ideas, Cicero advanced the tradition by systematizing the five canons of rhetoric—inventio (invention), dispositio (arrangement), elocutio (style), memoria (memory), and pronuntiatio (delivery)—which he saw as key to crafting persuasive discourse. [ 26 ] In this view, a well-trained orator, who draws from philosophy, law, and other disciplines, is best able to address civic and ethical challenges, thus underscoring Cicero's vision of rhetoric as both an intellectual and ethical pursuit. [ 25 ]
Modern works continue to support the claims of the ancients that rhetoric is an art capable of influencing civic life. In Political Style , Robert Hariman claims that "questions of freedom, equality, and justice often are raised and addressed through performances ranging from debates to demonstrations without loss of moral content". [ 27 ] James Boyd White argues that rhetoric is capable not only of addressing issues of political interest but that it can influence culture as a whole. In his book, When Words Lose Their Meaning , he argues that words of persuasion and identification define community and civic life. He states that words produce "the methods by which culture is maintained, criticized, and transformed". [ 18 ]
Rhetoric remains relevant as a civic art. In speeches, as well as in non-verbal forms, rhetoric continues to be used as a tool to influence communities from local to national levels.
Political parties employ "manipulative rhetoric" to advance their party-line goals and lobbyist agendas. They use it to portray themselves as champions of compassion, freedom, and culture, all while implementing policies that appear to contradict these claims. It serves as a form of political propaganda, presented to sway and maintain public opinion in their favor, and garner a positive image, potentially at the expense of suppressing dissent or criticism. An example of this is the government's actions in freezing bank accounts and regulating internet speech, ostensibly to protect the vulnerable and preserve freedom of expression, despite contradicting values and rights. [ 28 ] [ 29 ] [ 30 ]
Going back to the fifth century BCE, the term rhetoric originated in Ancient Greece. During this period, a new government (democracy) had been formed and as speech was the main method of information, an effective communication strategy was needed. Sophists, a group of intellectuals from Sicily, taught the ancient Greeks the art of persuasive speech in order to be able to navigate themselves in the court and senate. [ 31 ] This new technique was then used as an effective method of speech in political speeches and throughout government. Consequently people began to fear that persuasive speech would overpower truth. However, Aristotle argued that speech can be used to classify, study, and interpret speeches and as a useful skill. Aristotle believed that this technique was an art, and that persuasive speech could have truth and logic embedded within it. In the end, rhetoric speech still remained popular and was used by many scholars and philosophers. [ 31 ]
The study of rhetoric trains students to speak and/or write effectively, and to critically understand and analyze discourse. It is concerned with how people use symbols, especially language, to reach agreement that permits coordinated effort. [ 32 ]
Rhetoric as a course of study has evolved since its ancient beginnings, and has adapted to the particular exigencies of various times, venues, [ 33 ] and applications ranging from architecture to literature. [ 34 ] Although the curriculum has transformed in a number of ways, it has generally emphasized the study of principles and rules of composition as a means for moving audiences.
Rhetoric began as a civic art in Ancient Greece where students were trained to develop tactics of oratorical persuasion, especially in legal disputes. Rhetoric originated in a school of pre-Socratic philosophers known as the Sophists c. 600 BCE . Demosthenes and Lysias emerged as major orators during this period, and Isocrates and Gorgias as prominent teachers. Modern teachings continue to reference these rhetoricians and their work in discussions of classical rhetoric and persuasion.
Rhetoric was taught in universities during the Middle Ages as one of the three original liberal arts or trivium (along with logic and grammar ). [ 35 ] During the medieval period, political rhetoric declined as republican oratory died out and the emperors of Rome garnered increasing authority. With the rise of European monarchs, rhetoric shifted into courtly and religious applications. Augustine exerted strong influence on Christian rhetoric in the Middle Ages, advocating the use of rhetoric to lead audiences to truth and understanding, especially in the church. The study of liberal arts, he believed, contributed to rhetorical study: "In the case of a keen and ardent nature, fine words will come more readily through reading and hearing the eloquent than by pursuing the rules of rhetoric." [ 36 ] Poetry and letter writing became central to rhetorical study during the Middle Ages. [ 37 ] : 129–47 After the fall of the Roman republic, poetry became a tool for rhetorical training since there were fewer opportunities for political speech. [ 37 ] : 131 Letter writing was the primary way business was conducted both in state and church, so it became an important aspect of rhetorical education. [ 38 ]
Rhetorical education became more restrained as style and substance separated in 16th-century France, and attention turned to the scientific method. Influential scholars like Peter Ramus argued that the processes of invention and arrangement should be elevated to the domain of philosophy, while rhetorical instruction should be chiefly concerned with the use of figures and other forms of the ornamentation of language. Scholars such as Francis Bacon developed the study of "scientific rhetoric" [ 39 ] which rejected the elaborate style characteristic of classical oration. This plain language carried over to John Locke 's teaching, which emphasized concrete knowledge and steered away from ornamentation in speech, further alienating rhetorical instruction—which was identified wholly with such ornamentation—from the pursuit of knowledge.
In the 18th century, rhetoric assumed a more social role, leading to the creation of new education systems (predominantly in England): " Elocution schools" in which girls and women analyzed classic literature, most notably the works of William Shakespeare , and discussed pronunciation tactics. [ 40 ]
The study of rhetoric underwent a revival with the rise of democratic institutions during the late 18th and early 19th centuries. Hugh Blair was a key early leader of this movement. In his most famous work, Lectures on Rhetoric and Belles Lettres , he advocates rhetorical study for common citizens as a resource for social success. Many American colleges and secondary schools used Blair's text throughout the 19th century to train students of rhetoric. [ 38 ]
Political rhetoric also underwent renewal in the wake of the U.S. and French revolutions. The rhetorical studies of ancient Greece and Rome were resurrected as speakers and teachers looked to Cicero and others to inspire defenses of the new republics. Leading rhetorical theorists included John Quincy Adams of Harvard , who advocated the democratic advancement of rhetorical art. Harvard's founding of the Boylston Professorship of Rhetoric and Oratory sparked the growth of the study of rhetoric in colleges across the United States. [ 38 ] Harvard's rhetoric program drew inspiration from literary sources to guide organization and style, and studies the rhetoric used in political communication to illustrate how political figures persuade audiences. [ 41 ] William G. Allen became the first American college professor of rhetoric, at New-York Central College , 1850–1853.
Debate clubs and lyceums also developed as forums in which common citizens could hear speakers and sharpen debate skills. The American lyceum in particular was seen as both an educational and social institution, featuring group discussions and guest lecturers. [ 42 ] These programs cultivated democratic values and promoted active participation in political analysis.
Throughout the 20th century, rhetoric developed as a concentrated field of study, with the establishment of rhetorical courses in high schools and universities. Courses such as public speaking and speech analysis apply fundamental Greek theories (such as the modes of persuasion: ethos , pathos , and logos ) and trace rhetorical development through history. Rhetoric earned a more esteemed reputation as a field of study with the emergence of Communication Studies departments and of Rhetoric and Composition programs within English departments in universities, [ 43 ] and in conjunction with the linguistic turn in Western philosophy . Rhetorical study has broadened in scope, and is especially used by the fields of marketing, politics, and literature.
Another area of rhetoric is the study of cultural rhetorics, which is the communication that occurs between cultures and the study of the way members of a culture communicate with each other. [ 44 ] These ideas [ specify ] can then be studied and understood by other cultures, in order to bridge gaps in modes of communication and help different cultures communicate effectively with each other. James Zappen defines cultural rhetorics as the idea that rhetoric is concerned with negotiation and listening, not persuasion, which differs from ancient definitions. [ 44 ] Some ancient rhetoric was disparaged because its persuasive techniques could be used to teach falsehoods. [ 45 ] Communication as studied in cultural rhetorics is focused on listening and negotiation, and has little to do with persuasion. [ 44 ]
Rhetorical education focused on five canons . The Five Canons of Rhetoric serve as a guide to creating persuasive messages and arguments:
Memory was added much later to the original four canons. [ 46 ]
During the Renaissance rhetoric enjoyed a resurgence, and as a result nearly every author who wrote about music before the Romantic era discussed rhetoric. [ 47 ] Joachim Burmeister wrote in 1601, "there is only little difference between music and the nature of oration". [ This quote needs a citation ] Christoph Bernhard in the latter half of the century said "...until the art of music has attained such a height in our own day, that it may indeed be compared to a rhetoric, in view of the multitude of figures" [ needs context ] . [ 48 ]
Epistemology and rhetoric have been compared to one another for decades, but the specifications of their similarities have gone undefined. Since scholar Robert L. Scott stated that, "rhetoric is epistemic ," [ 49 ] rhetoricians and philosophers alike have struggled to concretely define the expanse of implications these words hold. Those who have identified this inconsistency maintain the idea that Scott's relation is important, but requires further study. [ 50 ]
The root of the issue lies in the ambiguous use of the term rhetoric itself, as well as the epistemological terms knowledge , certainty , and truth . [ 50 ] Though counterintuitive and vague, Scott's claims are accepted by some academics, but are then used to draw different conclusions. Sonja K. Foss , for example, takes on the view that, "rhetoric creates knowledge," [ 51 ] whereas James Herrick writes that rhetoric assists in people's ability to form beliefs , which are defined as knowledge once they become widespread in a community. [ 52 ]
It is unclear whether Scott holds that certainty is an inherent part of establishing knowledge , his references to the term abstract. [ 49 ] [ 53 ] He is not the only one, as the debate's persistence in philosophical circles long predates his addition of rhetoric. There is an overwhelming majority that does support the concept of certainty as a requirement for knowledge , but it is at the definition of certainty where parties begin to diverge. One definition maintains that certainty is subjective and feeling-based, the other that it is a byproduct of justification .
The more commonly accepted definition of rhetoric claims it is synonymous with persuasion . For rhetorical purposes, this definition, like many others, is too broad. The same issue presents itself with definitions that are too narrow. Rhetoricians in support of the epistemic view of rhetoric have yet to agree in this regard. [ 50 ]
Philosophical teachings refer to knowledge as a justified true belief . However, the Gettier Problem explores the room for fallacy in this concept. [ 54 ] Therefore, the Gettier Problem impedes the effectivity of the argument of Richard A. Cherwitz and James A. Hikins, [ 55 ] who employ the justified true belief standpoint in their argument for rhetoric as epistemic . Celeste Condit Railsback takes a different approach, [ 56 ] drawing from Ray E. McKerrow's system of belief based on validity rather than certainty . [ 57 ]
William D. Harpine refers to the issue of unclear definitions that occurs in the theories of "rhetoric is epistemic" in his 2004 article "What Do You Mean, Rhetoric is Epistemic?". [ 50 ] In it, he focuses on uncovering the most appropriate definitions for the terms "rhetoric", "knowledge", and "certainty". According to Harpine, certainty is either objective or subjective. Although both Scotts [ 49 ] and Cherwitz and Hikins [ 55 ] theories deal with some form of certainty, Harpine believes that knowledge is not required to be neither objectively nor subjectively certain. In terms of "rhetoric", Harpine argues that the definition of rhetoric as "the art of persuasion" is the best choice in the context of this theoretical approach of rhetoric as epistemic. Harpine then proceeds to present two methods of approaching the idea of rhetoric as epistemic based on the definitions presented. One centers on Alston's [ 58 ] view that one's beliefs are justified if formed by one's normal doxastic while the other focuses on the causal theory of knowledge. [ 59 ] Both approaches manage to avoid Gettier's problems and do not rely on unclear conceptions of certainty.
In the discussion of rhetoric and epistemology , comes the question of ethics . Is it ethical for rhetoric to present itself in the branch of knowledge ? Scott rears this question, addressing the issue, not with ambiguity in the definitions of other terms, but against subjectivity regarding certainty . Ultimately, according to Thomas O. Sloane, rhetoric and epistemology exist as counterparts, working towards the same purpose of establishing knowledge , with the common enemy of subjective certainty . [ 60 ]
Rhetoric is a persuasive speech that holds people to a common purpose and therefore facilitates collective action. During the fifth century BCE, Athens had become active in metropolis and people all over there. During this time the Greek city state had been experimenting with a new form of government – democracy, demos , "the people". Political and cultural identity had been tied to the city area – the citizens of Athens formed institutions to the red processes: are the Senate, jury trials, and forms of public discussions, but people needed to learn how to navigate these new institutions. With no forms of passing on the information, other than word of mouth the Athenians needed an effective strategy to inform the people. A group of wandering Sicilians, later known as the Sophists , began teaching the Athenians persuasive speech, with the goal of navigating the courts and senate. The sophists became speech teachers known as Sophia; Greek for "wisdom" and root for philosophy, or " love of wisdom" – the sophists came to be common term for someone who sold wisdom for money. [ 61 ] Although there is no clear understanding why the Sicilians engaged to educating the Athenians persuasive speech. It is known that the Athenians did, indeed rely on persuasive speech, more during public speak, and four new political processes, also increasing the sophists trainings leading too many victories for legal cases, public debate, and even a simple persuasive speech. This ultimately led to concerns rising on falsehood over truth, with highly trained, persuasive speakers, knowingly, misinforming. [ 61 ]
Rhetoric has its origins in Mesopotamia . [ 62 ] Some of the earliest examples of rhetoric can be found in the Akkadian writings of the princess and priestess Enheduanna ( c. 2285–2250 BCE ). [ 63 ] As the first named author in history, [ 62 ] [ 63 ] Enheduanna's writing exhibits numerous rhetorical features that would later become canon in Ancient Greece. Enheduanna's "The Exaltation of Inanna ", includes an exordium , argument , and peroration , [ 62 ] as well as elements of ethos , pathos , and logos , [ 63 ] and repetition and metonymy . [ 64 ] She is also known for describing her process of invention in "The Exaltation of Inanna", moving between first- and third-person address to relate her composing process in collaboration with the goddess Inanna, [ 63 ] reflecting a mystical enthymeme [ 65 ] in drawing upon a Cosmic audience. [ 63 ]
Later examples of early rhetoric can be found in the Neo-Assyrian Empire during the time of Sennacherib (704–681 BCE ). [ 66 ]
In ancient Egypt , rhetoric had existed since at least the Middle Kingdom period ( c. 2080–1640 BCE ). The five canons of eloquence in ancient Egyptian rhetoric were silence, timing, restraint, fluency, and truthfulness. [ 67 ] The Egyptians held eloquent speaking in high esteem. Egyptian rules of rhetoric specified that "knowing when not to speak is essential, and very respected, rhetorical knowledge", making rhetoric a "balance between eloquence and wise silence". They also emphasized "adherence to social behaviors that support a conservative status quo" and they held that "skilled speech should support, not question, society". [ 68 ]
In ancient China , rhetoric dates back to the Chinese philosopher , Confucius (551–479 BCE ). The tradition of Confucianism emphasized the use of eloquence in speaking. [ 69 ]
The use of rhetoric can also be found in the ancient Biblical tradition. [ 70 ]
In Europe, organized thought about public speaking began in ancient Greece . [ 71 ]
In ancient Greece , the earliest mention of oratorical skill occurs in Homer 's Iliad , in which heroes like Achilles , Hector , and Odysseus were honored for their ability to advise and exhort their peers and followers (the Laos or army) to wise and appropriate action. With the rise of the democratic polis , speaking skill was adapted to the needs of the public and political life of cities in ancient Greece. Greek citizens used oratory to make political and judicial decisions, and to develop and disseminate philosophical ideas. For modern students, it can be difficult to remember that the wide use and availability of written texts is a phenomenon that was just coming into vogue in Classical Greece . In Classical times, many of the great thinkers and political leaders performed their works before an audience, usually in the context of a competition or contest for fame, political influence, and cultural capital. In fact, many of them are known only through the texts that their students, followers, or detractors wrote down. Rhetor was the Greek term for "orator": A rhetor was a citizen who regularly addressed juries and political assemblies and who was thus understood to have gained some knowledge about public speaking in the process, though in general facility with language was often referred to as logôn techne , "skill with arguments" or "verbal artistry". [ 72 ] [ page needed ]
Possibly the first study about the power of language may be attributed to the philosopher Empedocles (d. c. 444 BCE ), whose theories on human knowledge would provide a basis for many future rhetoricians. The first written manual is attributed to Corax and his pupil Tisias . Their work, as well as that of many of the early rhetoricians, grew out of the courts of law; Tisias, for example, is believed to have written judicial speeches that others delivered in the courts.
Rhetoric evolved as an important art, one that provided the orator with the forms, means, and strategies for persuading an audience of the correctness of the orator's arguments. Today the term rhetoric can be used at times to refer only to the form of argumentation, often with the pejorative connotation that rhetoric is a means of obscuring the truth. Classical philosophers believed quite the contrary: the skilled use of rhetoric was essential to the discovery of truths, because it provided the means of ordering and clarifying arguments.
Teaching in oratory was popularized in the 5th century BCE by itinerant teachers known as sophists , the best known of whom were Protagoras ( c. 481–420 BCE ), Gorgias ( c. 483–376 BCE ), and Isocrates (436–338 BCE ). Aspasia of Miletus is believed to be one of the first women to engage in private and public rhetorical activities as a Sophist. [ 73 ] The Sophists were a disparate group who travelled from city to city, teaching in public places to attract students and offer them an education. Their central focus was on logos , or what we might broadly refer to as discourse, its functions and powers. [ citation needed ] They defined parts of speech, analyzed poetry, parsed close synonyms, invented argumentation strategies, and debated the nature of reality. [ citation needed ] They claimed to make their students better, or, in other words, to teach virtue. They thus claimed that human excellence was not an accident of fate or a prerogative of noble birth, but an art or " techne " that could be taught and learned. They were thus among the first humanists. [ 74 ]
Several Sophists also questioned received wisdom about the gods and the Greek culture, which they believed was taken for granted by Greeks of their time, making these Sophists among the first agnostics. For example, some argued that cultural practices were a function of convention or nomos rather than blood or birth or phusis . [ 75 ] They argued further that the morality or immorality of any action could not be judged outside of the cultural context within which it occurred. The well-known phrase, "Man is the measure of all things" arises from this belief. [ citation needed ] One of the Sophists' most famous, and infamous, doctrines has to do with probability and counter arguments. They taught that every argument could be countered with an opposing argument, that an argument's effectiveness derived from how "likely" it appeared to the audience (its probability of seeming true), and that any probability argument could be countered with an inverted probability argument. Thus, if it seemed likely that a strong, poor man were guilty of robbing a rich, weak man, the strong poor man could argue, on the contrary, that this very likelihood (that he would be a suspect) makes it unlikely that he committed the crime, since he would most likely be apprehended for the crime. [ citation needed ] They also taught and were known for their ability to make the weaker (or worse) argument the stronger (or better). [ citation needed ] Aristophanes famously parodies the clever inversions that sophists were known for in his play The Clouds . [ citation needed ]
The word "sophistry" developed negative connotations in ancient Greece that continue today, but in ancient Greece, Sophists were popular and well-paid professionals, respected for their abilities and also criticized for their excesses.
According to William Keith and Christian Lundberg, as the Greek society shifted towards more democratic values, the Sophists were responsible for teaching the newly democratic Greek society the importance of persuasive speech and strategic communication for its new governmental institutions. [ 76 ]
Isocrates (436–338 BCE ), like the Sophists, taught public speaking as a means of human improvement, but he worked to distinguish himself from the Sophists, whom he saw as claiming far more than they could deliver. He suggested that while an art of virtue or excellence did exist, it was only one piece, and the least, in a process of self-improvement that relied much more on honing one's talent, desire, constant practice, and the imitation of good models. Isocrates believed that practice in speaking publicly about noble themes and important questions would improve the character of both speaker and audience while also offering the best service to a city. Isocrates was an outspoken champion of rhetoric as a mode of civic engagement. [ 77 ] He thus wrote his speeches as "models" for his students to imitate in the same way that poets might imitate Homer or Hesiod, seeking to inspire in them a desire to attain fame through civic leadership. His was the first permanent school in Athens and it is likely that Plato's Academy and Aristotle's Lyceum were founded in part as a response to Isocrates. Though he left no handbooks, his speeches ( " Antidosis " and " Against the Sophists " are most relevant to students of rhetoric) became models of oratory and keys to his entire educational program. He was one of the canonical " Ten Attic Orators ". He influenced Cicero and Quintilian , and through them, the entire educational system of the west.
Plato (427–347 BCE ) outlined the differences between true and false rhetoric in a number of dialogues—particularly the Gorgias and Phaedrus , dialogues in which Plato disputes the sophistic notion that the art of persuasion (the Sophists' art, which he calls "rhetoric"), can exist independent of the art of dialectic . Plato claims that since Sophists appeal only to what seems probable, they are not advancing their students and audiences, but simply flattering them with what they want to hear. While Plato's condemnation of rhetoric is clear in the Gorgias , in the Phaedrus he suggests the possibility of a true art wherein rhetoric is based upon the knowledge produced by dialectic. He relies on a dialectically informed rhetoric to appeal to the main character, Phaedrus, to take up philosophy. Thus Plato's rhetoric is actually dialectic (or philosophy) "turned" toward those who are not yet philosophers and are thus unready to pursue dialectic directly. Plato's animosity against rhetoric, and against the Sophists, derives not only from their inflated claims to teach virtue and their reliance on appearances, but from the fact that his teacher, Socrates, was sentenced to death after Sophists' efforts.
Some scholars, however, see Plato not as an opponent of rhetoric but rather as a nuanced rhetorical theorist who dramatized rhetorical practice in his dialogues and imagined rhetoric as more than just oratory. [ 10 ]
Aristotle: Rhetoric is an antistrophes to dialectic. "Let rhetoric [be defined as] an ability [dynamis], in each [particular] case, to see the available means of persuasion." "Rhetoric is a counterpart of dialectic" — an art of practical civic reasoning, applied to deliberative, judicial, and "display" speeches in political assemblies, lawcourts, and other public gatherings.
Aristotle (384–322 BCE ) was a student of Plato who set forth an extended treatise on rhetoric that still repays careful study today. In the first sentence of The Art of Rhetoric , Aristotle says that "rhetoric is the antistrophe of dialectic". [ 78 ] : I.1 As the " antistrophe " of a Greek ode responds to and is patterned after the structure of the " strophe " (they form two sections of the whole and are sung by two parts of the chorus), so the art of rhetoric follows and is structurally patterned after the art of dialectic because both are arts of discourse production. While dialectical methods are necessary to find truth in theoretical matters, rhetorical methods are required in practical matters such as adjudicating somebody's guilt or innocence when charged in a court of law, or adjudicating a prudent course of action to be taken in a deliberative assembly.
For Plato and Aristotle, dialectic involves persuasion, so when Aristotle says that rhetoric is the antistrophe of dialectic, he means that rhetoric as he uses the term has a domain or scope of application that is parallel to, but different from, the domain or scope of application of dialectic. Claude Pavur explains that "[t]he Greek prefix 'anti' does not merely designate opposition, but it can also mean 'in place of'". [ 79 ]
Aristotle's treatise on rhetoric systematically describes civic rhetoric as a human art or skill ( techne ). It is more of an objective theory [ clarification needed ] than it is an interpretive theory with a rhetorical tradition. Aristotle's art of rhetoric emphasizes persuasion as the purpose of rhetoric. His definition of rhetoric as "the faculty of observing in any given case the available means of persuasion", essentially a mode of discovery, limits the art to the inventional process; Aristotle emphasizes the logical aspect of this process. A speaker supports the probability of a message by logical, ethical, and emotional proofs.
Aristotle identifies three steps or "offices" of rhetoric—invention, arrangement, and style—and three different types of rhetorical proof: [ 78 ] : I.2
Aristotle emphasized enthymematic reasoning as central to the process of rhetorical invention, though later rhetorical theorists placed much less emphasis on it. An "enthymeme" follows the form of a syllogism , however it excludes either the major or minor premise. An enthymeme is persuasive because the audience provides the missing premise. Because the audience participates in providing the missing premise, they are more likely to be persuaded by the message.
Aristotle identified three different types or genres of civic rhetoric: [ 78 ] : I.3
Another Aristotelian doctrine was the idea of topics (also referred to as common topics or commonplaces). Though the term had a wide range of application (as a memory technique or compositional exercise, for example) it most often referred to the "seats of argument"—the list of categories of thought or modes of reasoning—that a speaker could use to generate arguments or proofs. The topics were thus a heuristic or inventional tool designed to help speakers categorize and thus better retain and apply frequently used types of argument. For example, since we often see effects as "like" their causes, one way to invent an argument (about a future effect) is by discussing the cause (which it will be "like"). This and other rhetorical topics derive from Aristotle's belief that there are certain predictable ways in which humans (particularly non-specialists) draw conclusions from premises. Based upon and adapted from his dialectical Topics, the rhetorical topics became a central feature of later rhetorical theorizing, most famously in Cicero's work of that name.
India's Struggle for Independence offers a vivid description of the culture that sprang up around the newspaper in village India of the early 1870s:
A newspaper would reach remote villages and would then be read by a reader to tens of others. Gradually library movements sprung up all over the country. A local 'library' would be organized around a single newspaper. A table, a bench or two or a charpoy would constitute the capital equipment. Every piece of news or editorial comment would be read or heard and thoroughly discussed. The newspaper not only became the political educator; reading or discussing it became a form of political participation. [ 80 ]
This reading and discussion was the focal point of origin of the modern Indian rhetorical movement. Much before this, ancients such as Kautilya , Birbal , and the like indulged in a great deal of discussion and persuasion.
Keith Lloyd argued that much of the recital of the Vedas can be likened to the recital of ancient Greek poetry. [ 81 ] Lloyd proposed including the Nyāya Sūtras in the field of rhetorical studies, exploring its methods within their historical context, comparing its approach to the traditional logical syllogism, and relating it to modern perspectives of Stephen Toulmin , Kenneth Burke , and Chaim Perelman .
Nyaya is a Sanskrit word which means "just" or "right" and refers to "the science of right and wrong reasoning". [ 82 ] : 356 Sutra is also a Sanskrit word which means string or thread. Here sutra refers to a collection of aphorism in the form of a manual. Each sutra is a short rule usually consisted of one or two sentences. An example of a sutra is: "Reality is truth, and what is true is so, irrespective of whether we know it is, or are aware of that truth." The Nyāya Sūtras is an ancient Indian Sanskrit text composed by Aksapada Gautama . It is the foundational text of the Nyaya school of Hindu philosophy. It is estimated that the text was composed between 6th-century BCE and 2nd-century CE . The text may have been composed by more than one author, over a period of time. [ 83 ] Radhakrishan and Moore placed its origin in the third century BCE "though some of the contents of the Nyaya Sutra are certainly a post-Christian era". [ 82 ] : 36 The ancient school of Nyaya extended over a period of one thousand years, beginning with Gautama about 550 BCE and ending with Vatsyayana about 400 CE . [ 84 ]
Nyaya provides insight into Indian rhetoric. Nyaya presents an argumentative approach with which a rhetor can decide about any argument. In addition, it proposes an approach to thinking about cultural tradition which is different from Western rhetoric. Whereas Toulmin emphasizes the situational dimension of argumentative genre as the fundamental component of any rhetorical logic; Nyaya views this situational rhetoric in a new way which offers context of practical arguments [ vague ] .
Some of India's famous rhetors include Kabir Das , Rahim Das , Chanakya , and Chandragupt Maurya .
For the Romans, oration became an important part of public life. Cicero (106–43 BCE ) was chief among Roman rhetoricians and remains the best known ancient orator and the only orator who both spoke in public and produced treatises on the subject. Rhetorica ad Herennium , formerly attributed to Cicero but now considered to be of unknown authorship, is one of the most significant works on rhetoric and is still widely used as a reference today. It is an extensive reference on the use of rhetoric, and in the Middle Ages and Renaissance , it achieved wide publication as an advanced school text on rhetoric.
Cicero charted a middle path between the competing Attic and Asiatic styles to become considered second only to Demosthenes among history's orators. [ 85 ] His works include the early and very influential De Inventione (On Invention, often read alongside Ad Herennium as the two basic texts of rhetorical theory throughout the Middle Ages and into the Renaissance), De Oratore (a fuller statement of rhetorical principles in dialogue form), Topics (a rhetorical treatment of common topics, highly influential through the Renaissance), Brutus (a discussion of famous orators), and Orator (a defense of Cicero's style). Cicero also left a large body of speeches and letters which would establish the outlines of Latin eloquence and style for generations.
The rediscovery of Cicero's speeches (such as the defense of Archias ) and letters ( to Atticus ) by Italians like Petrarch helped to ignite the Renaissance. [ 86 ]
Cicero championed the learning of Greek (and Greek rhetoric), contributed to Roman ethics, linguistics, philosophy, and politics, and emphasized the importance of all forms of appeal (emotion, humor, stylistic range, irony, and digression in addition to pure reasoning) in oratory. But perhaps his most significant contribution to subsequent rhetoric, and education in general, was his argument that orators learn not only about the specifics of their case (the hypothesis ) but also about the general questions from which they derived (the theses ). [ citation needed ] Thus, in giving a speech in defense of a poet whose Roman citizenship had been questioned, the orator should examine not only the specifics of that poet's civic status, he should also examine the role and value of poetry and of literature more generally in Roman culture and political life. The orator, said Cicero, needed to be knowledgeable about all areas of human life and culture, including law, politics, history, literature, ethics, warfare, medicine, and even arithmetic and geometry. Cicero gave rise to the idea that the "ideal orator" be well-versed in all branches of learning: an idea that was rendered as "liberal humanism", and that lives on today in liberal arts or general education requirements in colleges and universities around the world. [ 87 ]
Quintilian (35–100 CE ) began his career as a pleader in the courts of law; his reputation grew so great that Vespasian created a chair of rhetoric for him in Rome. The culmination of his life's work was the Institutio Oratoria ( Institutes of Oratory, or alternatively, The Orator's Education ), a lengthy treatise on the training of the orator, in which he discusses the training of the "perfect" orator from birth to old age and, in the process, reviews the doctrines and opinions of many influential rhetoricians who preceded him.
In the Institutes , Quintilian organizes rhetorical study through the stages of education that an aspiring orator would undergo, beginning with the selection of a nurse. Aspects of elementary education (training in reading and writing, grammar, and literary criticism) are followed by preliminary rhetorical exercises in composition (the progymnasmata ) that include maxims and fables, narratives and comparisons, and finally full legal or political speeches. The delivery of speeches within the context of education or for entertainment purposes became widespread and popular under the term "declamation".
This work was available only in fragments in medieval times, but the discovery of a complete copy at the Abbey of St. Gall in 1416 led to its emergence as one of the most influential works on rhetoric during the Renaissance.
Quintilian's work describes not just the art of rhetoric, but the formation of the perfect orator as a politically active, virtuous, publicly minded citizen. His emphasis was on the ethical application of rhetorical training, in part in reaction against the tendency in Roman schools toward standardization of themes and techniques. At the same time that rhetoric was becoming divorced from political decision making, rhetoric rose as a culturally vibrant and important mode of entertainment and cultural criticism in a movement known as the " Second Sophistic ", a development that gave rise to the charge (made by Quintilian and others) that teachers were emphasizing style over substance in rhetoric.
After the breakup of the western Roman Empire, the study of rhetoric continued to be central to the study of the verbal arts. However the study of the verbal arts went into decline for several centuries, followed eventually by a gradual rise in formal education, culminating in the rise of medieval universities. Rhetoric transmuted during this period into the arts of letter writing ( ars dictaminis ) and sermon writing ( ars praedicandi ). As part of the trivium , rhetoric was secondary to the study of logic, and its study was highly scholastic: students were given repetitive exercises in the creation of discourses on historical subjects ( suasoriae ) or on classic legal questions ( controversiae ).
Although he is not commonly regarded as a rhetorician, St. Augustine (354–430) was trained in rhetoric and was at one time a professor of Latin rhetoric in Milan. After his conversion to Christianity, he became interested in using these " pagan " arts for spreading his religion. He explores this new use of rhetoric in De doctrina Christiana , which laid the foundation of what would become homiletics , the rhetoric of the sermon. Augustine asks why "the power of eloquence, which is so efficacious in pleading either for the erroneous cause or the right", should not be used for righteous purposes. [ 88 ]
One early concern of the medieval Christian church was its attitude to classical rhetoric itself. Jerome (d. 420) complained, "What has Horace to do with the Psalms, Virgil with the Gospels, Cicero with the Apostles?" [ 89 ] Augustine is also remembered for arguing for the preservation of pagan works and fostering a church tradition that led to conservation of numerous pre-Christian rhetorical writings.
Rhetoric would not regain its classical heights until the Renaissance, but new writings did advance rhetorical thought. Boethius ( c. 480 –524), in his brief Overview of the Structure of Rhetoric , continues Aristotle's taxonomy by placing rhetoric in subordination to philosophical argument or dialectic. [ 90 ] The introduction of Arab scholarship from European relations with the Muslim empire (in particular Al-Andalus ) renewed interest in Aristotle and Classical thought in general, leading to what some historians call the 12th century Renaissance . A number of medieval grammars and studies of poetry and rhetoric appeared.
Late medieval rhetorical writings include those of St. Thomas Aquinas ( c. 1225 –1274), Matthew of Vendôme ( Ars Versificatoria , c. 1175 ), and Geoffrey of Vinsauf ( Poetria Nova , 1200–1216). Pre-modern female rhetoricians, outside of Socrates' friend Aspasia , are rare; but medieval rhetoric produced by women either in religious orders, such as Julian of Norwich (d. 1415), or the very well-connected Christine de Pizan ( c. 1364 – c. 1430 ), did occur although it was not always recorded in writing.
In his 1943 Cambridge University doctoral dissertation in English, Canadian Marshall McLuhan (1911–1980) surveys the verbal arts from approximately the time of Cicero down to the time of Thomas Nashe (1567– c. 1600 ). [ 91 ] His dissertation is still noteworthy for undertaking to study the history of the verbal arts together as the trivium, even though the developments that he surveys have been studied in greater detail since he undertook his study. As noted below, McLuhan became one of the most widely publicized communication theorists of the 20th century.
Another interesting record of medieval rhetorical thought can be seen in the many animal debate poems popular in England and the continent during the Middle Ages, such as The Owl and the Nightingale (13th century) and Geoffrey Chaucer 's Parliament of Fowls .
Renaissance humanism defined itself broadly as disfavoring medieval scholastic logic and dialectic and as favoring instead the study of classical Latin style and grammar and philology and rhetoric. [ 92 ]
One influential figure in the rebirth of interest in classical rhetoric was Erasmus ( c. 1466 –1536). His 1512 work, De Duplici Copia Verborum et Rerum (also known as Copia: Foundations of the Abundant Style ), was widely published (it went through more than 150 editions throughout Europe) and became one of the basic school texts on the subject. Its treatment of rhetoric is less comprehensive than the classic works of antiquity, but provides a traditional treatment of res-verba (matter and form). Its first book treats the subject of elocutio , showing the student how to use schemes and tropes ; the second book covers inventio . Much of the emphasis is on abundance of variation ( copia means "plenty" or "abundance", as in copious or cornucopia), so both books focus on ways to introduce the maximum amount of variety into discourse. For instance, in one section of the De Copia , Erasmus presents two hundred variations of the sentence "Always, as long as I live, I shall remember you" (" Semper, dum vivam, tui meminero. ") Another of his works, the extremely popular The Praise of Folly , also had considerable influence on the teaching of rhetoric in the later 16th century. Its orations in favour of qualities such as madness spawned a type of exercise popular in Elizabethan grammar schools, later called adoxography , which required pupils to compose passages in praise of useless things.
Juan Luis Vives (1492–1540) also helped shape the study of rhetoric in England. A Spaniard, he was appointed in 1523 to the Lectureship of Rhetoric at Oxford by Cardinal Wolsey , and was entrusted by Henry VIII to be one of the tutors of Mary. Vives fell into disfavor when Henry VIII divorced Catherine of Aragon and left England in 1528. His best-known work was a book on education, De Disciplinis , published in 1531, and his writings on rhetoric included Rhetoricae, sive De Ratione Dicendi, Libri Tres (1533), De Consultatione (1533), and a treatise on letter writing, De Conscribendis Epistolas (1536).
It is likely that many well-known English writers were exposed to the works of Erasmus and Vives (as well as those of the Classical rhetoricians) in their schooling, which was conducted in Latin (not English), often included some study of Greek, and placed considerable emphasis on rhetoric. [ 93 ]
The mid-16th century saw the rise of vernacular rhetorics—those written in English rather than in the Classical languages. Adoption of works in English was slow, however, due to the strong scholastic orientation toward Latin and Greek. Leonard Cox 's The Art or Crafte of Rhetoryke ( c. 1524–1530 ; second edition published in 1532) is the earliest text on rhetorics in English; it was, for the most part, a translation of the work of Philipp Melanchthon . [ 94 ] Thomas Wilson 's The Arte of Rhetorique (1553) presents a traditional treatment of rhetoric, for instance, the standard five canons of rhetoric. Other notable works included Angel Day 's The English Secretorie (1586, 1592), George Puttenham 's The Arte of English Poesie (1589), and Richard Rainholde's Foundacion of Rhetorike (1563).
During this same period, a movement began that would change the organization of the school curriculum in Protestant and especially Puritan circles and that led to rhetoric losing its central place. A French scholar, Petrus Ramus (1515–1572), dissatisfied with what he saw as the overly broad and redundant organization of the trivium , proposed a new curriculum. In his scheme of things, the five components of rhetoric no longer lived under the common heading of rhetoric. Instead, invention and disposition were determined to fall exclusively under the heading of dialectic, while style, delivery, and memory were all that remained for rhetoric. [ 95 ] Ramus was martyred during the French Wars of Religion. His teachings, seen as inimical to Catholicism, were short-lived in France but found a fertile ground in the Netherlands, Germany, and England. [ 96 ]
One of Ramus' French followers, Audomarus Talaeus (Omer Talon) published his rhetoric, Institutiones Oratoriae , in 1544. This work emphasized style, and became so popular that it was mentioned in John Brinsley 's (1612) Ludus literarius ; or The Grammar Schoole as being the " most used in the best schooles ". Many other Ramist rhetorics followed in the next half-century, and by the 17th century, their approach became the primary method of teaching rhetoric in Protestant and especially Puritan circles. [ 97 ] John Milton (1608–1674) wrote a textbook in logic or dialectic in Latin based on Ramus' work. [ 98 ]
Ramism could not exert any influence on the established Catholic schools and universities, which remained loyal to Scholasticism, or on the new Catholic schools and universities founded by members of the Society of Jesus or the Oratorians, as can be seen in the Jesuit curriculum (in use up to the 19th century across the Christian world) known as the Ratio Studiorum . [ 99 ] If the influence of Cicero and Quintilian permeates the Ratio Studiorum , it is through the lenses of devotion and the militancy of the Counter-Reformation . The Ratio was indeed imbued with a sense of the divine, of the incarnate logos, that is of rhetoric as an eloquent and humane means to reach further devotion and further action in the Christian city, which was absent from Ramist formalism. The Ratio is, in rhetoric, the answer to Ignatius Loyola 's practice, in devotion, of " spiritual exercises ". This complex oratorical-prayer system is absent from Ramism.
In New England and at Harvard College (founded 1636), Ramus and his followers dominated. [ 100 ] [ page needed ] However, in England, several writers influenced the course of rhetoric during the 17th century, many of them carrying forward the dichotomy [ specify ] that had been set forth by Ramus and his followers during the preceding decades. This century also saw the development of a modern, vernacular style that looked to English, rather than to Greek, Latin, or French models.
Francis Bacon (1561–1626), although not a rhetorician, contributed to the field in his writings. One of the concerns of the age was to find a suitable style for the discussion of scientific topics, which needed above all a clear exposition of facts and arguments, rather than an ornate style. Bacon in his The Advancement of Learning criticized those who are preoccupied with style rather than "the weight of matter, worth of subject, soundness of argument, life of invention, or depth of judgment". [ 101 ] On matters of style, he proposed that the style conform to the subject matter and to the audience, that simple words be employed whenever possible, and that the style should be agreeable. [ 102 ] [ page needed ]
Thomas Hobbes (1588–1679) also wrote on rhetoric. Along with a shortened translation of Aristotle 's Rhetoric , Hobbes also produced a number of other works on the subject. Sharply contrarian on many subjects, Hobbes, like Bacon, also promoted a simpler and more natural style that used figures of speech sparingly.
Perhaps the most influential development in English style came out of the work of the Royal Society (founded in 1660), which in 1664 set up a committee to improve the English language. Among the committee's members were John Evelyn (1620–1706), Thomas Sprat (1635–1713), and John Dryden (1631–1700). Sprat regarded "fine speaking" as a disease, and thought that a proper style should "reject all amplifications, digressions, and swellings of style" and instead "return back to a primitive purity and shortness". [ 103 ]
While the work of this committee never went beyond planning, John Dryden is often credited with creating and exemplifying a new and modern English style. His central tenet was that the style should be proper "to the occasion, the subject, and the persons". [ 104 ] As such, he advocated the use of English words whenever possible instead of foreign ones, as well as vernacular, rather than Latinate, syntax. His own prose (and his poetry) became exemplars of this new style.
Arguably one of the most influential schools of rhetoric during the 18th century was Scottish Belletristic rhetoric, exemplified by such professors of rhetoric as Hugh Blair whose Lectures on Rhetoric and Belles Lettres saw international success in various editions and translations, and Lord Kames with his influential Elements of Criticism .
Another notable figure in 18th century rhetoric was Maria Edgeworth , a novelist and children's author whose work often parodied the male-centric rhetorical strategies of her time. In her 1795 "An Essay on the Noble Science of Self-Justification," Edgeworth presents a satire of Enlightenment rhetoric's science-centrism and the Belletristic Movement. [ 105 ] She was called "the great Maria" by Sir Walter Scott , with whom she corresponded, [ 106 ] and by modern scholars is noted as "a transgressive and ironic reader" of the 18th century rhetorical norms. [ 107 ]
At the turn of the 20th century, there was a revival of rhetorical study manifested in the establishment of departments of rhetoric and speech at academic institutions, as well as the formation of national and international professional organizations. [ 108 ] The early interest in rhetorical studies was a movement away from elocution as taught in English departments in the United States, and an attempt to refocus rhetorical studies from delivery-only to civic engagement and a "rich complexity" of the nature of rhetoric. [ 109 ]
By the 1930s, advances in mass media technology led to a revival of the study of rhetoric, language, persuasion, and political rhetoric and its consequences. The linguistic turn in philosophy also contributed to this revival. The term rhetoric came to be applied to media forms other than verbal language, e.g. visual rhetoric , "temporal rhetorics", [ 110 ] and the "temporal turn" [ 111 ] in rhetorical theory and practice.
The rise of advertising and of mass media such as photography , telegraphy , radio , and film brought rhetoric more prominently into people's lives. The discipline of rhetoric has been used to study how advertising persuades, [ 112 ] and to help understand the spread of fake news and conspiracy theories on social media. [ 113 ]
Rhetoric can be analyzed by a variety of methods and theories. One such method is criticism. When those using criticism analyze instances of rhetoric what they do is called rhetorical criticism ( see Criticism ). According to rhetorical critic Jim A. Kuypers , "The use of rhetoric is an art, and as such, it does not lend itself well to scientific methods of analysis. Criticism is an art as well, and as such is particularly well suited for examining rhetorical creations." [ 122 ] : 14 He asserts that criticism is a method of generating knowledge just as the scientific method is a method for generating knowledge: [ 122 ]
The way the Sciences and the Humanities study the phenomena that surround us differ greatly in the amount of researcher personality allowed to influence the results of the study. For example, in the Sciences researchers purposefully adhere to a strict method (the scientific method).... Generally speaking, the researcher's personality, likes and dislikes, and religious and political preferences are supposed to be as far removed as possible from the actual study.... In sharp contrast, criticism (one of many Humanistic methods of generating knowledge) actively involves the personality of the researcher. The very choices of what to study, and how and why to study a rhetorical artifact are heavily influenced by the personal qualities of the researcher.... In the Humanities, methods of research may also take many forms—criticism, ethnography, for example—but the personality of the researcher is an integral component of the study. Further personalizing criticism, we find that rhetorical critics use a variety of means when examining a particular rhetorical artifact, with some critics even developing their own unique perspective to better examine a rhetorical artifact. [ 122 ] : 14
Edwin Black wrote on this point that, "Methods, then, admit of varying degrees of personality. And criticism, on the whole, is near the indeterminate, contingent, personal end of the methodological scale. In consequence of this placement, it is neither possible nor desirable for criticism to be fixed into a system, for critical techniques to be objectified, for critics to be interchangeable for purposes of replication, or for rhetorical criticism to serve as the handmaiden of quasi-scientific theory." [ 123 ] : xi
Jim A. Kuypers sums this idea of criticism as art in the following manner: "In short, criticism is an art, not a science. It is not a scientific method; it uses subjective methods of argument; it exists on its own, not in conjunction with other methods of generating knowledge (i.e., social scientific or scientific)... [I]nsight and imagination top statistical applications when studying rhetorical action." [ 122 ] : 14–15
Rhetorical strategies are the efforts made by authors or speakers to persuade or inform their audiences. According to James W. Gray, [ importance? ] there are various argument strategies used in writing. He describes four of these as argument from analogy, argument from absurdity, thought experiments, and inference to the best explanation. [ 124 ]
Modern rhetorical criticism explores the relationship between text and context; that is, how an instance of rhetoric relates to circumstances. Since the aim of rhetoric is to be persuasive, the level to which the rhetoric in question persuades its audience is what must be analyzed, and later criticized. In determining the extent to which a text is persuasive, one may explore the text's relationship with its audience, purpose, ethics, argument, evidence, arrangement, delivery, and style. [ 125 ]
In his Rhetorical Criticism: A Study in Method , Edwin Black states, "It is the task of criticism not to measure... discourses dogmatically against some parochial standard of rationality but, allowing for the immeasurable wide range of human experience, to see them as they really are." [ 123 ] : 131 While "as they really are" is debatable, rhetorical critics explain texts and speeches by investigating their rhetorical situation , typically placing them in a framework of speaker/audience exchange. The antithetical view places the rhetor at the center of creating that which is considered the extant situation; i.e., the agenda and spin. [ 126 ]
Following the neo-Aristotelian approaches to criticism, scholars began to derive methods from other disciplines, such as history, philosophy, and the social sciences. [ 127 ] : 249 The importance of critics' personal judgment decreased in explicit coverage [ clarification needed ] while the analytical dimension of criticism began to gain momentum. Throughout the 1960s and 1970s, methodological pluralism replaced the singular neo-Aristotelian method. Methodological rhetorical criticism is typically done by deduction, in which a broad method [ vague ] is used to examine a specific case of rhetoric. [ 128 ] These types [ clarification needed ] include:
By the mid-1980s the study of rhetorical criticism began to move away from precise methodology towards conceptual issues. Conceptually-driven criticism [ 129 ] operates more through abduction, according to scholar James Jasinski, who argues that this type of criticism can be thought of as a back-and-forth between the text and the concepts [ specify ] , which are being explored at the same time. The concepts remain "works in progress", and understanding those terms [ clarification needed ] develops through the analysis of a text. [ 127 ] : 256
Criticism is considered rhetorical when it focuses on the way some types of discourse react to situational exigencies—problems or demands—and constraints. Modern rhetorical criticism concerns how the rhetorical case or object persuades, defines, or constructs the audience. In modern terms, rhetoric includes, but it is not limited to, speeches, scientific discourse, pamphlets, literary work, works of art, and pictures. Contemporary rhetorical criticism has maintained aspects of early neo-Aristotelian thinking through close reading, which attempts to explore the organization and stylistic structure of a rhetorical object. [ 130 ] Using close textual analysis means rhetorical critics use the tools of classical rhetoric and literary analysis to evaluate the style and strategy used to communicate the argument.
Rhetorical criticism serves several purposes. For one, it hopes to help form or improve public taste. It helps educate audiences and develops them into better judges of rhetorical situations by reinforcing ideas of value, morality, and suitability. Rhetorical criticism can thus contribute to the audience's understanding of themselves and society.
According to Jim A. Kuypers, a second purpose for performing criticism should be to enhance our appreciation and understanding. "[W]e wish to enhance both our own and others' understanding of the rhetorical act; we wish to share our insights with others, and to enhance their appreciation of the rhetorical act. These are not hollow goals, but quality of life issues. By improving understanding and appreciation, the critic can offer new and potentially exciting ways for others to see the world. Through understanding we also produce knowledge about human communication; in theory this should help us to better govern our interactions with others." Criticism is a humanizing activity in that it explores and highlights qualities that make us human. [ 122 ] : 13
Rhetoric is practiced by social animals in a variety of ways. For example, birds use song , various animals warn members of their species of danger, chimpanzees have the capacity to deceive through communicative keyboard systems, and deer stags compete for the attention of mates. While these might be understood as rhetorical actions (attempts at persuading through meaningful actions and utterances ), they can also be seen as rhetorical fundamentals shared by humans and animals. [ 131 ] The study of animal rhetoric has been called "biorhetorics". [ 132 ]
The self-awareness required to practice rhetoric might be difficult to notice and acknowledge in some animals. However, some animals are capable of acknowledging themselves in a mirror , and therefore, they might be understood to be self-aware and therefore, argue philosophers such as Diane Davis, are able to engage with rhetoric when practicing some form of language. [ 133 ]
Anthropocentrism plays a significant role in human-animal relationships, reflecting and perpetuating binaries in which humans assume they are beings that have extraordinary qualities while they regard animals as beings that lack those qualities. This dualism is manifested in other forms as well, such as reason and sense, mind and body, ideal and phenomenal in which the first category of each pair ( reason , mind , and ideal ) represents and belongs to only humans. By becoming aware of and overcoming these dualistic conceptions including the one between humans and animals, humans will be able to more easily engage with and communicate with animals, with the understanding that animals are capable of reciprocating communication. [ 134 ] The relationship between humans and animals (as well as the rest of the natural world) is often defined by the human rhetorical act of naming and categorizing animals through scientific and folk labeling. The act of naming partially defines the rhetorical relationships between humans and animals, though both may engage in rhetoric beyond human naming and categorizing. [ 135 ]
Some animals have a sort of phrónēsis which enables them to "learn and receive instruction" with rudimentary understanding of some significant signs. Those animals practice deliberative, judicial, and epideictic rhetoric deploying ethos , logos , and pathos with gesture and preen, sing and growl. [ 136 ] Since animals offer models of rhetorical behavior and interaction that are physical, even instinctual, but perhaps no less artful, transcending our accustomed focus on verbal language and consciousness concepts will help people interested in rhetoric and communication to promote human-animal rhetoric. [ 137 ]
Comparative rhetoric is a practice and methodology that developed in the late twentieth century to broaden the study of rhetoric beyond the dominant rhetorical tradition that has been constructed and shaped in western Europe and the U.S. [ 138 ] [ 139 ] As a research practice, comparative rhetoric studies past and present cultures across the globe to reveal diversity in the uses of rhetoric and to uncover rhetorical perspectives, practices, and traditions that have been historically underrepresented or dismissed. [ 138 ] [ 140 ] [ 141 ] As a methodology, comparative rhetoric constructs a culture's rhetorical perspectives, practices, and traditions on their own terms, in their own contexts, as opposed to using European or American theories, terminology, or framing. [ 138 ]
Comparative rhetoric is comparative in that it illuminates how rhetorical traditions relate to one another, while seeking to avoid binary depictions or value judgments. [ 138 ] This can reveal issues of power within and between cultures as well as new or under-recognized ways of thinking, doing, and being that challenge or enrich the dominant Euro-American tradition and provide a fuller account of rhetorical studies. [ 142 ]
Robert T. Oliver is credited as the first scholar who recognized the need to study non-Western rhetorics in his 1971 publication Communication and Culture in Ancient India and China . [ 140 ] [ 143 ] George A. Kennedy has been credited for the first cross-cultural overview of rhetoric in his 1998 publication Comparative Rhetoric: An Historical and Cross-cultural Introduction . [ 143 ] Though Oliver's and Kennedy's works contributed to the birth of comparative rhetoric, given the newness of the field, they both used Euro-American terms and theories to interpret non-Euro-American cultures' practices. [ 143 ] [ 144 ]
LuMing Mao, Xing Lu, Mary Garrett, Arabella Lyon, Bo Wang, Hui Wu, and Keith Lloyd have published extensively on comparative rhetoric, helping to shape and define the field. [ 143 ] In 2013, LuMing Mao edited a special issue on comparative rhetoric in Rhetoric Society Quarterly , [ 145 ] focusing on comparative methodologies in the age of globalization. In 2015, LuMing Mao and Bo Wang coedited a symposium [ 146 ] featuring position essays by a group of leading scholars in the field. In their introduction, Mao and Wang emphasize the fluid and cross-cultural nature of rhetoric, "Rhetorical knowledge, like any other knowledge, is heterogeneous, multidimentional, and always in the process of being created." [ 146 ] : 241 The symposium includes "A Manifesto: The What and How of Comparative Rhetoric", demonstrating the first collective effort to identify and articulate comparative rhetoric's definition, goals, and methodologies. [ 141 ] The tenets of this manifesto are engaged within many later works that study or utilize comparative rhetoric. [ 143 ]
As natural language processing has developed, so has interest in automatically detecting rhetorical figures . The major focus has been to detect specific figures, such as chiasmus , epanaphora , and epiphora [ 147 ] using classifiers trained with labeled data . A major shortcoming to achieving high accuracy with these systems is the shortage of labeled data for these tasks, but with recent advances in language modeling , such as few-shot learning , it may be possible to detect more rhetorical figures with less data. [ 148 ]
Primary sources
The locus classicus for Greek and Latin primary texts on rhetoric is the Loeb Classical Library of the Harvard University Press , published with an English translation on the facing page.
Secondary sources | https://en.wikipedia.org/wiki/Rhetoric |
Rhetorical reason is the faculty of discovering the crux of the matter. It is a characteristic of rhetorical invention ( inventio ) and it precedes argumentation .
Aristotle 's definition of rhetoric , "the faculty of observing, in any given case, the available means of persuasion", presupposes a distinction between an art (τέχνη, techne ) of speech–making and a cognitively prior faculty of discovery. That is so because, before one argues a case, one must discover what is at issue. How, for example, does one discover available means of persuasion? One does not simply frolic through fertile fields of τόποι ( topoi ), randomly gathering materials with which to build lines of argument. There is a method endemic to rhetoric which guides the search for those lines of argument that speak most directly to the issue at stake. [ further explanation needed ]
George A. Kennedy explains the distinction when he writes that the work of rhetoric, in Aristotle's view, is
to discover [θεωρησαι ( theoresai )] the available means of persuasion" (1.1.1355b25–6). It is thus a theoretical activity and discovers knowledge. This knowledge, which includes words, arguments, and topics, is then used by the orator as the material cause of a speech. There is thus a theoretical art of rhetoric standing behind or above the productive art of speech-making. (1980, p. 63)
Inventio (rhetorical invention) then, involves more than a techne ; it is also a faculty of discovery ( dunamis (δύναμις) to theoresai ).
The Aristotelian approach to inventio further assumes that reasoning employed in decision-making is a kind of probable reasoning.
It assumes that, although the contingencies of nature and of individuals prevent our obtaining certainty about future political and social affairs, we still can use our reason to discover the best course to pursue. Such reasoning applied to human affairs to make decisions about what should be done is rhetorical reasoning issuing in praxis. (Moss 1986, pp. 2, 3)
Judgments about what should be done in the future are generally matters of shared inquiry and are always contingent (based on probability). Shared inquiry, following Wayne C. Booth , can be understood as "the art of reasoning together about shared concerns" (1988, p. 108). It is shared because the judgment is discursively negotiated with reference to both the crux of the matter and in light of what is in the best interest of oneself or some other.
Accounting for both Moss and Booth, rhetorical reason may be conceptualized as a method of "shared moral inquiry", but with a special meaning of the word "moral". Moral inquiry, within the present context, means inquiry into practical matters (as opposed to mere speculation or scientific inquiry). Hans-Georg Gadamer uses "moral" in this sense in Truth and Method (p. 314). Albert R. Jonsen and Stephen Toulmin write that "moral knowledge is essentially particular" (1988, p. 330). Shared moral inquiry is moral, not because it involves questions of morality, but because it attempts to determine what is the right thing to do in contingent cases, where such judgments are not made deterministically. Moral inquiry is conducted in the contingent realm, and is concerned with the particular case.
Understood with precision then, rhetorical reason guides and φρόνησις ( phronesis ) drives moral inquiry. The aim of moral inquiry is sound moral judgment, but judgment in hard cases is frustrated because the crux of the matter is hedged in by a potentially limitless parade of particulars.
Rhetorical reason manages particulars by systematically determining the relevance of issues and identifying the στάσις ( stasis , which is the most relevant of the relevant issues). Ascribing relevance is an act of phronesis (Tallmon, 2001 & 1995a, b). Hence, rhetorical reason is a modality of phronesis and also, as Aristotle famously notes, a counterpart of dialectic . That is, it depends upon practical wisdom for its proper work, and, in that work, it operates much like dialectical inference, only its proper domain is the particular case as opposed to the general question.
Hence, viewed as a guide to resolving tough cases, rhetorical reason is constituted by:
Individuals exercise rhetorical reason, but its excellence is realized in the public arena (i.e., in shared inquiry, by referencing pooled wisdom). | https://en.wikipedia.org/wiki/Rhetorical_reason |
The Rhind Mathematical Papyrus ( RMP ; also designated as papyrus British Museum 10057, pBM 10058, and Brooklyn Museum 37.1784Ea-b) is one of the best known examples of ancient Egyptian mathematics .
It is one of two well-known mathematical papyri, along with the Moscow Mathematical Papyrus . The Rhind Papyrus is the larger, but younger, of the two. [ 1 ]
In the papyrus' opening paragraphs Ahmes presents the papyrus as giving "Accurate reckoning for inquiring into things, and the knowledge of all things, mysteries ... all secrets". He continues:
This book was copied in regnal year 33, month 4 of Akhet , under the majesty of the King of Upper and Lower Egypt, Awserre, given life, from an ancient copy made in the time of the King of Upper and Lower Egypt Nimaatre. The scribe Ahmose writes this copy. [ 2 ]
Several books and articles about the Rhind Mathematical Papyrus have been published, and a handful of these stand out. [ 1 ] The Rhind Papyrus was published in 1923 by the English Egyptologist T. Eric Peet and contains a discussion of the text that followed Francis Llewellyn Griffith 's Book I, II and III outline. [ 3 ] Chace published a compendium in 1927–29 which included photographs of the text. [ 4 ] A more recent overview of the Rhind Papyrus was published in 1987 by Robins and Shute.
The Rhind Mathematical Papyrus dates to the Second Intermediate Period of Egypt . It was copied by the scribe Ahmes (i.e., Ahmose; Ahmes is an older transcription favoured by historians of mathematics) from a now-lost text from the reign of the 12th dynasty king Amenemhat III .
It dates to around 1550 BC. [ 5 ] The document is dated to Year 33 of the Hyksos king Apophis and also contains a separate later historical note on its verso likely dating from "Year 11" of his successor, Khamudi . [ 6 ]
Alexander Henry Rhind , a Scottish antiquarian, purchased two parts of the papyrus in 1858 in Luxor, Egypt ; [ 7 ] it was stated to have been found in "one of the small buildings near the Ramesseum ", near Luxor. [ 3 ]
The British Museum, where the majority of the papyrus is now kept, acquired it in 1865 along with the Egyptian Mathematical Leather Roll , also owned by Henry Rhind. [ 2 ]
Fragments of the text were independently purchased in Luxor by American Egyptologist Edwin Smith in the mid 1860s, were donated by his daughter in 1906 to the New York Historical Society, [ 8 ] and are now held by the Brooklyn Museum . [ 1 ] [ 9 ] An 18 cm (7.1 in) central section is missing.
The papyrus began to be transliterated and mathematically translated in the late 19th century. The mathematical-translation aspect remains incomplete in several respects. [ 6 ]
The first part of the Rhind papyrus consists of reference tables and a collection of 21 arithmetic and 20 algebraic problems. The problems start out with simple fractional expressions, followed by completion ( sekem ) problems and more involved linear equations ( aha problems ). [ 1 ]
The first part of the papyrus is taken up by the 2/ n table . The fractions 2/ n for odd n ranging from 3 to 101 are expressed as sums of unit fractions . For example, 2 15 = 1 10 + 1 30 {\displaystyle {\frac {2}{15}}={\frac {1}{10}}+{\frac {1}{30}}} . The decomposition of 2/ n into unit fractions is never more than 4 terms long as in for example:
This table is followed by a much smaller, tiny table of fractional expressions for the numbers 1 through 9 divided by 10. For instance the division of 7 by 10 is recorded as:
After these two tables, the papyrus records 91 problems altogether, which have been designated by moderns as problems (or numbers) 1–87, including four other items which have been designated as problems 7B, 59B, 61B and 82B. Problems 1–7, 7B and 8–40 are concerned with arithmetic and elementary algebra.
Problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 = 7/4, and 1 + 2/3 + 1/3 = 2 by different fractions.
Problems 21–23 are problems in completion, which in modern notation are simply subtraction problems. Problems 24–34 are ‘‘aha’’ problems; these are linear equations . Problem 32 for instance corresponds (in modern notation) to solving x + 1/3 x + 1/4 x = 2 for x. Problems 35–38 involve divisions of the heqat, which is an ancient Egyptian unit of volume. Beginning at this point, assorted units of measurement become much more important throughout the remainder of the papyrus, and indeed a major consideration throughout the rest of the papyrus is dimensional analysis . Problems 39 and 40 compute the division of loaves and use arithmetic progressions . [ 2 ]
The second part of the Rhind papyrus, being problems 41–59, 59B and 60, consists of geometry problems. Peet referred to these problems as "mensuration problems". [ 1 ]
Problems 41–46 show how to find the volume of both cylindrical and rectangular granaries. In problem 41 Ahmes computes the volume of a cylindrical granary. Given the diameter d and the height h, the volume V is given by:
In modern mathematical notation (and using d = 2r) this gives V = ( 8 / 9 ) 2 d 2 h = ( 256 / 81 ) r 2 h {\displaystyle V=(8/9)^{2}d^{2}h=(256/81)r^{2}h} . The fractional term 256/81 approximates the value of π as being 3.1605..., an error of less than one percent.
Problem 47 is a table with fractional equalities which represent the ten situations where the physical volume quantity of "100 quadruple heqats" is divided by each of the multiples of ten, from ten through one hundred. The quotients are expressed in terms of Horus eye fractions, sometimes also using a much smaller unit of volume known as a "quadruple ro". The quadruple heqat and the quadruple ro are units of volume derived from the simpler heqat and ro, such that these four units of volume satisfy the following relationships: 1 quadruple heqat = 4 heqat = 1280 ro = 320 quadruple ro. Thus,
Problems 48–55 show how to compute an assortment of areas . Problem 48 is notable in that it succinctly computes the area of a circle by approximating π . Specifically, problem 48 explicitly reinforces the convention (used throughout the geometry section) that "a circle's area stands to that of its circumscribing square in the ratio 64/81." Equivalently, the papyrus approximates π as 256/81, as was already noted above in the explanation of problem 41.
Other problems show how to find the area of rectangles, triangles and trapezoids.
The final six problems are related to the slopes of pyramids .
A seked problem is reported as follows: [ 10 ]
The solution to the problem is given as the ratio of half the side of the base of the pyramid to its height, or the run-to-rise ratio of its face. In other words, the quantity found for the seked is the cotangent of the angle to the base of the pyramid and its face. [ 10 ]
The third part of the Rhind papyrus consists of the remainder of the 91 problems, being 61, 61B, 62–82, 82B, 83–84, and "numbers" 85–87, which are items that are not mathematical in nature. This final section contains more complicated tables of data (which frequently involve Horus eye fractions), several pefsu problems which are elementary algebraic problems concerning food preparation, and even an amusing problem (79) which is suggestive of geometric progressions, geometric series, and certain later problems and riddles in history. Problem 79 explicitly cites, "seven houses, 49 cats, 343 mice, 2401 ears of spelt, 16807 hekats." In particular problem 79 concerns a situation in which 7 houses each contain seven cats, which all eat seven mice, each of which would have eaten seven ears of grain, each of which would have produced seven measures of grain. The third part of the Rhind papyrus is therefore a kind of miscellany, building on what has already been presented.
Problem 61 is concerned with multiplications of fractions. Problem 61B, meanwhile, gives a general expression for computing 2/3 of 1/n, where n is odd. In modern notation the formula given is
The technique given in 61B is closely related to the derivation of the 2/n table.
Problems 62–68 are general problems of an algebraic nature. Problems 69–78 are all pefsu problems in some form or another. They involve computations regarding the strength of bread and beer, with respect to certain raw materials used in their production. [ 2 ]
Problem 79 sums five terms in a geometric progression . Its language is strongly suggestive of the more modern riddle and nursery rhyme " As I was going to St Ives ". [ 1 ] Problems 80 and 81 compute Horus eye fractions of hinu (or heqats). The last four mathematical items, problems 82, 82B and 83–84, compute the amount of feed necessary for various animals, such as fowl and oxen. [ 2 ] However, these problems, especially 84, are plagued by pervasive ambiguity, confusion, and simple inaccuracy.
The final three items on the Rhind papyrus are designated as "numbers" 85–87, as opposed to "problems", and they are scattered widely across the papyrus's back side, or verso. They are, respectively, a small phrase which ends the document (and has a few possibilities for translation, given below), a piece of scrap paper unrelated to the body of the document, used to hold it together (yet containing words and Egyptian fractions which are by now familiar to a reader of the document), and a small historical note which is thought to have been written some time after the completion of the body of the papyrus's writing. This note is thought to describe events during the " Hyksos domination", a period of external interruption in ancient Egyptian society which is closely related with its second intermediary period. With these non-mathematical yet historically and philologically intriguing errata, the papyrus's writing comes to an end.
Much of the Rhind Papyrus's material is concerned with Ancient Egyptian units of measurement and especially the dimensional analysis used to convert between them. A concordance of units of measurement used in the papyrus is given in the image.
This table summarizes the content of the Rhind Papyrus by means of a concise modern paraphrase. It is based upon the two-volume exposition of the papyrus which was published by Arnold Buffum Chace in 1927, and in 1929. [ 4 ] In general, the papyrus consists of four sections: a title page, the 2/n table, a tiny "1–9/10 table", and 91 problems, or "numbers". The latter are numbered from 1 through 87 and include four mathematical items which have been designated by moderns as problems 7B, 59B, 61B, and 82B. Numbers 85–87, meanwhile, are not mathematical items forming part of the body of the document, but instead are respectively: a small phrase ending the document, a piece of "scrap-paper" used to hold the document together (having already contained unrelated writing), and a historical note which is thought to describe a time period shortly after the completion of the body of the papyrus. These three latter items are written on disparate areas of the papyrus's verso (back side), far away from the mathematical content. Chace therefore differentiates them by styling them as numbers as opposed to problems , like the other 88 numbered items.
4 10 = 1 3 + 1 15 ; 5 10 = 1 2 ; 6 10 = 1 2 + 1 10 {\displaystyle {\frac {4}{10}}={\frac {1}{3}}+{\frac {1}{15}}\;\;\;;\;\;\;{\frac {5}{10}}={\frac {1}{2}}\;\;\;;\;\;\;{\frac {6}{10}}={\frac {1}{2}}+{\frac {1}{10}}}
7 10 = 2 3 + 1 30 ; 8 10 = 2 3 + 1 10 + 1 30 ; 9 10 = 2 3 + 1 5 + 1 30 {\displaystyle {\frac {7}{10}}={\frac {2}{3}}+{\frac {1}{30}}\;\;\;;\;\;\;{\frac {8}{10}}={\frac {2}{3}}+{\frac {1}{10}}+{\frac {1}{30}}\;\;\;;\;\;\;{\frac {9}{10}}={\frac {2}{3}}+{\frac {1}{5}}+{\frac {1}{30}}}
6 10 = 1 2 + 1 10 ; 7 10 = 2 3 + 1 30 {\displaystyle {\frac {6}{10}}={\frac {1}{2}}+{\frac {1}{10}}\;\;\;;\;\;\;{\frac {7}{10}}={\frac {2}{3}}+{\frac {1}{30}}}
8 10 = 2 3 + 1 10 + 1 30 ; 9 10 = 2 3 + 1 5 + 1 30 {\displaystyle {\frac {8}{10}}={\frac {2}{3}}+{\frac {1}{10}}+{\frac {1}{30}}\;\;\;;\;\;\;{\frac {9}{10}}={\frac {2}{3}}+{\frac {1}{5}}+{\frac {1}{30}}}
S = 1 + 1 / 2 + 1 / 4 = 7 4 {\displaystyle S=1+1/2+1/4={\frac {7}{4}}} and
T = 1 + 2 / 3 + 1 / 3 = 2 {\displaystyle T=1+2/3+1/3=2} .
Then for the following multiplications, write the product as an Egyptian fraction.
9 : ( 1 2 + 1 14 ) S = 1 ; 10 : ( 1 4 + 1 28 ) S = 1 2 ; 11 : 1 7 S = 1 4 {\displaystyle 9:{\bigg (}{\frac {1}{2}}+{\frac {1}{14}}{\bigg )}S=1\;\;\;;\;\;\;10:{\bigg (}{\frac {1}{4}}+{\frac {1}{28}}{\bigg )}S={\frac {1}{2}}\;\;\;;\;\;\;11:{\frac {1}{7}}S={\frac {1}{4}}}
12 : 1 14 S = 1 8 ; 13 : ( 1 16 + 1 112 ) S = 1 8 ; 14 : 1 28 S = 1 16 {\displaystyle 12:{\frac {1}{14}}S={\frac {1}{8}}\;\;\;;\;\;\;13:{\bigg (}{\frac {1}{16}}+{\frac {1}{112}}{\bigg )}S={\frac {1}{8}}\;\;\;;\;\;\;14:{\frac {1}{28}}S={\frac {1}{16}}}
15 : ( 1 32 + 1 224 ) S = 1 16 ; 16 : 1 2 T = 1 ; 17 : 1 3 T = 2 3 {\displaystyle 15:{\bigg (}{\frac {1}{32}}+{\frac {1}{224}}{\bigg )}S={\frac {1}{16}}\;\;\;;\;\;\;16:{\frac {1}{2}}T=1\;\;\;;\;\;\;17:{\frac {1}{3}}T={\frac {2}{3}}}
18 : 1 6 T = 1 3 ; 19 : 1 12 T = 1 6 ; 20 : 1 24 T = 1 12 {\displaystyle 18:{\frac {1}{6}}T={\frac {1}{3}}\;\;\;;\;\;\;19:{\frac {1}{12}}T={\frac {1}{6}}\;\;\;;\;\;\;20:{\frac {1}{24}}T={\frac {1}{12}}}
22 : ( 2 3 + 1 30 ) + x = 1 → x = 1 5 + 1 10 {\displaystyle 22:{\bigg (}{\frac {2}{3}}+{\frac {1}{30}}{\bigg )}+x=1\;\;\;\rightarrow \;\;\;x={\frac {1}{5}}+{\frac {1}{10}}}
23 : ( 1 4 + 1 8 + 1 10 + 1 30 + 1 45 ) + x = 2 3 → x = 1 9 + 1 40 {\displaystyle 23:{\bigg (}{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{10}}+{\frac {1}{30}}+{\frac {1}{45}}{\bigg )}+x={\frac {2}{3}}\;\;\;\rightarrow \;\;\;x={\frac {1}{9}}+{\frac {1}{40}}}
24 : x + 1 7 x = 19 → x = 16 + 1 2 + 1 8 {\displaystyle 24:x+{\frac {1}{7}}x=19\;\;\;\rightarrow \;\;\;x=16+{\frac {1}{2}}+{\frac {1}{8}}}
25 : x + 1 2 x = 16 → x = 10 + 2 3 {\displaystyle 25:x+{\frac {1}{2}}x=16\;\;\;\rightarrow \;\;\;x=10+{\frac {2}{3}}}
26 : x + 1 4 x = 15 → x = 12 {\displaystyle 26:x+{\frac {1}{4}}x=15\;\;\;\rightarrow \;\;\;x=12}
27 : x + 1 5 x = 21 → x = 17 + 1 2 {\displaystyle 27:x+{\frac {1}{5}}x=21\;\;\;\rightarrow \;\;\;x=17+{\frac {1}{2}}}
28 : ( x + 2 3 x ) − 1 3 ( x + 2 3 x ) = 10 → x = 9 {\displaystyle 28:{\bigg (}x+{\frac {2}{3}}x{\bigg )}-{\frac {1}{3}}{\bigg (}x+{\frac {2}{3}}x{\bigg )}=10\;\;\;\rightarrow \;\;\;x=9}
29 : 1 3 ( ( x + 2 3 x ) + 1 3 ( x + 2 3 x ) ) = 10 → x = 13 + 1 2 {\displaystyle 29:{\frac {1}{3}}{\Bigg (}{\bigg (}x+{\frac {2}{3}}x{\bigg )}+{\frac {1}{3}}{\bigg (}x+{\frac {2}{3}}x{\bigg )}{\Bigg )}=10\;\;\;\rightarrow \;\;\;x=13+{\frac {1}{2}}}
30 : ( 2 3 + 1 10 ) x = 10 → x = 13 + 1 23 {\displaystyle 30:{\bigg (}{\frac {2}{3}}+{\frac {1}{10}}{\bigg )}x=10\;\;\;\rightarrow \;\;\;x=13+{\frac {1}{23}}}
31 : x + 2 3 x + 1 2 x + 1 7 x = 33 → {\displaystyle 31:x+{\frac {2}{3}}x+{\frac {1}{2}}x+{\frac {1}{7}}x=33\;\;\;\rightarrow }
x = 14 + 1 4 + 1 56 + 1 97 + 1 194 + 1 388 + 1 679 + 1 776 {\displaystyle x=14+{\frac {1}{4}}+{\frac {1}{56}}+{\frac {1}{97}}+{\frac {1}{194}}+{\frac {1}{388}}+{\frac {1}{679}}+{\frac {1}{776}}}
32 : x + 1 3 x + 1 4 x = 2 → x = 1 + 1 6 + 1 12 + 1 114 + 1 228 {\displaystyle 32:x+{\frac {1}{3}}x+{\frac {1}{4}}x=2\;\;\;\rightarrow \;\;\;x=1+{\frac {1}{6}}+{\frac {1}{12}}+{\frac {1}{114}}+{\frac {1}{228}}}
33 : x + 2 3 x + 1 2 x + 1 7 x = 37 → x = 16 + 1 56 + 1 679 + 1 776 {\displaystyle 33:x+{\frac {2}{3}}x+{\frac {1}{2}}x+{\frac {1}{7}}x=37\;\;\;\rightarrow \;\;\;x=16+{\frac {1}{56}}+{\frac {1}{679}}+{\frac {1}{776}}}
34 : x + 1 2 x + 1 4 x = 10 → x = 5 + 1 2 + 1 7 + 1 14 {\displaystyle 34:x+{\frac {1}{2}}x+{\frac {1}{4}}x=10\;\;\;\rightarrow \;\;\;x=5+{\frac {1}{2}}+{\frac {1}{7}}+{\frac {1}{14}}}
35 : ( 3 + 1 3 ) x = 1 → x = 1 5 + 1 10 {\displaystyle 35:{\bigg (}3+{\frac {1}{3}}{\bigg )}x=1\;\;\;\rightarrow \;\;\;x={\frac {1}{5}}+{\frac {1}{10}}}
36 : ( 3 + 1 3 + 1 5 ) x = 1 → x = 1 4 + 1 53 + 1 106 + 1 212 {\displaystyle 36:{\bigg (}3+{\frac {1}{3}}+{\frac {1}{5}}{\bigg )}x=1\;\;\;\rightarrow \;\;\;x={\frac {1}{4}}+{\frac {1}{53}}+{\frac {1}{106}}+{\frac {1}{212}}}
37 : ( 3 + 1 3 + 1 3 ⋅ 1 3 + 1 9 ) x = 1 → x = 1 4 + 1 32 {\displaystyle 37:{\bigg (}3+{\frac {1}{3}}+{\frac {1}{3}}\cdot {\frac {1}{3}}+{\frac {1}{9}}{\bigg )}x=1\;\;\;\rightarrow \;\;\;x={\frac {1}{4}}+{\frac {1}{32}}}
38 : ( 3 + 1 7 ) x = 1 → x = 1 6 + 1 11 + 1 22 + 1 66 {\displaystyle 38:{\bigg (}3+{\frac {1}{7}}{\bigg )}x=1\;\;\;\rightarrow \;\;\;x={\frac {1}{6}}+{\frac {1}{11}}+{\frac {1}{22}}+{\frac {1}{66}}}
V = ( d − 1 9 d ) 2 h {\displaystyle V={\bigg (}d-{\frac {1}{9}}d{\bigg )}^{2}h}
= 64 81 d 2 h {\displaystyle ={\frac {64}{81}}d^{2}h}
to calculate the volume of a cylindrical grain silo with a diameter of 9 cubits and a height of 10 cubits. Give the answer in terms of cubic cubits. Furthermore, given the following equalities among other units of volume, 1 cubic cubit = 3/2 khar = 30 heqats = 15/2 quadruple heqats, also express the answer in terms of khar and quadruple heqats.
= 960 k h a r {\displaystyle =960\;\;\;khar}
= 4800 q u a d r u p l e h e q a t {\displaystyle =4800\;\;\;quadruple\;\;\;heqat}
= ( 1185 + 1 6 + 1 54 ) k h a r {\displaystyle ={\bigg (}1185+{\frac {1}{6}}+{\frac {1}{54}}{\bigg )}\;\;\;khar}
= ( 59 + 1 4 + 1 108 ) h u n d r e d q u a d r u p l e h e q a t {\displaystyle ={\bigg (}59+{\frac {1}{4}}+{\frac {1}{108}}{\bigg )}\;\;\;hundred\;\;\;quadruple\;\;\;heqat}
V = 2 3 ( ( d − 1 9 d ) + 1 3 ( d − 1 9 d ) ) 2 h {\displaystyle V={\frac {2}{3}}{\Bigg (}{\bigg (}d-{\frac {1}{9}}d{\bigg )}+{\frac {1}{3}}{\bigg (}d-{\frac {1}{9}}d{\bigg )}{\Bigg )}^{2}h}
= 2048 2187 d 2 h {\displaystyle ={\frac {2048}{2187}}d^{2}h}
to calculate the volume of a cylindrical grain silo with a diameter of 9 cubits and a height of 6 cubits, directly finding the answer in Egyptian fractional terms of khar, and later in Egyptian fractional terms of quadruple heqats and quadruple ro, where 1 quadruple heqat = 4 heqat = 1280 ro = 320 quadruple ro.
= ( 2275 + 1 2 + 1 32 + 1 64 ) q u a d r u p l e h e q a t {\displaystyle ={\bigg (}2275+{\frac {1}{2}}+{\frac {1}{32}}+{\frac {1}{64}}{\bigg )}\;\;\;quadruple\;\;\;heqat}
+ ( 2 + 1 2 + 1 4 + 1 36 ) q u a d r u p l e r o {\displaystyle +{\bigg (}2+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{36}}{\bigg )}\;\;\;quadruple\;\;\;ro}
l = 10 c u b i t {\displaystyle l=10\;\;\;cubit}
l 3 = 3 + 1 3 c u b i t {\displaystyle l_{3}=3+{\frac {1}{3}}\;\;\;cubit}
[ 100 10 q . h e q a t = 10 q . h e q a t 100 20 q . h e q a t = 5 q . h e q a t 100 30 q . h e q a t = ( 3 + 1 4 + 1 16 + 1 64 ) q . h e q a t + ( 1 + 2 3 ) q . r o 100 40 q . h e q a t = ( 2 + 1 2 ) q . h e q a t 100 50 q . h e q a t = 2 q . h e q a t 100 60 q . h e q a t = ( 1 + 1 2 + 1 8 + 1 32 ) q . h e q a t + ( 3 + 1 3 ) q . r o 100 70 q . h e q a t = ( 1 + 1 4 + 1 8 + 1 32 + 1 64 ) q . h e q a t + ( 2 + 1 14 + 1 21 + 1 42 ) q . r o 100 80 q . h e q a t = ( 1 + 1 4 ) q . h e q a t 100 90 q . h e q a t = ( 1 + 1 16 + 1 32 + 1 64 ) q . h e q a t + ( 1 2 + 1 18 ) q . r o 100 100 q . h e q a t = 1 q . h e q a t ] {\displaystyle {\begin{bmatrix}{\frac {100}{10}}&q.\;heqat&=&10&q.\;heqat\\{\frac {100}{20}}&q.\;heqat&=&5&q.\;heqat\\{\frac {100}{30}}&q.\;heqat&=&(3+{\frac {1}{4}}+{\frac {1}{16}}+{\frac {1}{64}})&q.\;heqat\\&&+&(1+{\frac {2}{3}})&q.\;ro\\{\frac {100}{40}}&q.\;heqat&=&(2+{\frac {1}{2}})&q.\;heqat\\{\frac {100}{50}}&q.\;heqat&=&2&q.\;heqat\\{\frac {100}{60}}&q.\;heqat&=&(1+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{32}})&q.\;heqat\\&&+&(3+{\frac {1}{3}})&q.\;ro\\{\frac {100}{70}}&q.\;heqat&=&(1+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{32}}+{\frac {1}{64}})&q.\;heqat\\&&+&(2+{\frac {1}{14}}+{\frac {1}{21}}+{\frac {1}{42}})&q.\;ro\\{\frac {100}{80}}&q.\;heqat&=&(1+{\frac {1}{4}})&q.\;heqat\\{\frac {100}{90}}&q.\;heqat&=&(1+{\frac {1}{16}}+{\frac {1}{32}}+{\frac {1}{64}})&q.\;heqat\\&&+&({\frac {1}{2}}+{\frac {1}{18}})&q.\;ro\\{\frac {100}{100}}&q.\;heqat&=&1&q.\;heqat\\\end{bmatrix}}}
l 2 = ( 3 + 1 4 + 1 8 ) k h e t {\displaystyle l_{2}={\bigg (}3+{\frac {1}{4}}+{\frac {1}{8}}{\bigg )}\;\;\;khet}
A 1 = ( 13 + 1 2 + 1 4 ) s e t a t + ( 3 + 1 8 ) c u b i t s t r i p {\displaystyle A_{1}={\bigg (}13+{\frac {1}{2}}+{\frac {1}{4}}{\bigg )}\;\;\;setat+{\bigg (}3+{\frac {1}{8}}{\bigg )}\;\;\;cubit\;\;\;strip}
A 2 = ( 9 + 1 2 + 1 4 ) s e t a t + ( 9 + 1 4 + 1 8 ) c u b i t s t r i p {\displaystyle A_{2}={\bigg (}9+{\frac {1}{2}}+{\frac {1}{4}}{\bigg )}\;\;\;setat+{\bigg (}9+{\frac {1}{4}}+{\frac {1}{8}}{\bigg )}\;\;\;cubit\;\;\;strip}
A 3 = ( 7 + 1 2 + 1 4 + 1 8 ) s e t a t {\displaystyle A_{3}={\bigg (}7+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}{\bigg )}\;\;\;setat}
= ( 1 2 + 1 8 ) s e t a t + ( 7 + 1 2 ) c u b i t s t r i p {\displaystyle ={\bigg (}{\frac {1}{2}}+{\frac {1}{8}}{\bigg )}\;\;\;setat+{\bigg (}7+{\frac {1}{2}}{\bigg )}\;\;\;cubit\;\;\;strip}
= 1 2 s e t a t + 10 c u b i t s t r i p {\displaystyle ={\frac {1}{2}}\;\;\;setat+10\;\;\;cubit\;\;\;strip}
2) Consider a right regular square pyramid whose base, the square face is coplanar with a plane (or the ground, say), so that any of the planes containing its triangular faces has the dihedral angle of θ {\displaystyle \theta } with respect to the ground-plane (that is, on the interior of the pyramid). In other words, θ {\displaystyle \theta } is the angle of the triangular faces of the pyramid with respect to the ground. The seked of such a pyramid, then, having altitude a {\displaystyle a} and base edge length b {\displaystyle b} , is defined as that physical length S {\displaystyle S} such that S 1 r o y a l c u b i t = {\displaystyle {\frac {S}{1\;\;\;royal\;\;\;cubit}}=} cot θ {\displaystyle \cot {\theta }} . Put another way, the seked of a pyramid can be interpreted as the ratio of its triangular faces' run per one unit (cubit) rise . Or, for the appropriate right triangle on a pyramid's interior having legs a , b 2 {\displaystyle a,{\frac {b}{2}}} and the perpendicular bisector of a triangular face as the hypotenuse, then the pyramid's seked S {\displaystyle S} satisfies cot θ = b 2 a = S 1 r o y a l c u b i t {\displaystyle \cot {\theta }={\frac {b}{2a}}={\frac {S}{1\;\;\;royal\;\;\;cubit}}} . Similar triangles are therefore described, and one can be scaled to the other.
3) A pyramid has an altitude of 250 (royal) cubits, and the side of its base has a length of 360 (royal) cubits. Find its seked S {\displaystyle S} in Egyptian fractional terms of (royal) cubits, and also in terms of palms.
= ( 5 + 1 25 ) p a l m {\displaystyle ={\bigg (}5+{\frac {1}{25}}{\bigg )}\;\;\;palm}
S = 5 p a l m + 1 f i n g e r {\displaystyle S=5\;\;\;palm+1\;\;\;finger}
a = 8 c u b i t {\displaystyle a=8\;\;\;cubit}
[ 2 3 ⋅ 2 3 = 1 3 + 1 9 ; 1 3 ⋅ 2 3 = 1 6 + 1 18 2 3 ⋅ 1 3 = 1 6 + 1 18 ; 2 3 ⋅ 1 6 = 1 12 + 1 36 2 3 ⋅ 1 2 = 1 3 ; 1 3 ⋅ 1 2 = 1 6 1 6 ⋅ 1 2 = 1 12 ; 1 12 ⋅ 1 2 = 1 24 1 9 ⋅ 2 3 = 1 18 + 1 54 ; 2 3 ⋅ 1 9 = 1 18 + 1 54 1 4 ⋅ 1 5 = 1 20 ; 2 3 ⋅ 1 7 = 1 14 + 1 42 1 2 ⋅ 1 7 = 1 14 ; 2 3 ⋅ 1 11 = 1 22 + 1 66 1 3 ⋅ 1 11 = 1 33 ; 1 2 ⋅ 1 11 = 1 22 1 4 ⋅ 1 11 = 1 44 ] {\displaystyle {\begin{bmatrix}{\frac {2}{3}}\cdot {\frac {2}{3}}={\frac {1}{3}}+{\frac {1}{9}}&;&{\frac {1}{3}}\cdot {\frac {2}{3}}={\frac {1}{6}}+{\frac {1}{18}}\\{\frac {2}{3}}\cdot {\frac {1}{3}}={\frac {1}{6}}+{\frac {1}{18}}&;&{\frac {2}{3}}\cdot {\frac {1}{6}}={\frac {1}{12}}+{\frac {1}{36}}\\{\frac {2}{3}}\cdot {\frac {1}{2}}={\frac {1}{3}}&;&{\frac {1}{3}}\cdot {\frac {1}{2}}={\frac {1}{6}}\\{\frac {1}{6}}\cdot {\frac {1}{2}}={\frac {1}{12}}&;&{\frac {1}{12}}\cdot {\frac {1}{2}}={\frac {1}{24}}\\{\frac {1}{9}}\cdot {\frac {2}{3}}={\frac {1}{18}}+{\frac {1}{54}}&;&{\frac {2}{3}}\cdot {\frac {1}{9}}={\frac {1}{18}}+{\frac {1}{54}}\\{\frac {1}{4}}\cdot {\frac {1}{5}}={\frac {1}{20}}&;&{\frac {2}{3}}\cdot {\frac {1}{7}}={\frac {1}{14}}+{\frac {1}{42}}\\{\frac {1}{2}}\cdot {\frac {1}{7}}={\frac {1}{14}}&;&{\frac {2}{3}}\cdot {\frac {1}{11}}={\frac {1}{22}}+{\frac {1}{66}}\\{\frac {1}{3}}\cdot {\frac {1}{11}}={\frac {1}{33}}&;&{\frac {1}{2}}\cdot {\frac {1}{11}}={\frac {1}{22}}\\{\frac {1}{4}}\cdot {\frac {1}{11}}={\frac {1}{44}}&&\\\end{bmatrix}}}
q = 6 ( 2 n + 1 ) {\displaystyle q=6(2n+1)}
200 {\displaystyle 200}
133 + 1 3 {\displaystyle 133+{\frac {1}{3}}}
100 {\displaystyle 100}
( 1 + 1 4 + 1 8 + 1 16 ) h e q a t {\displaystyle {\bigg (}1+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}{\bigg )}\;heqat}
( 1 + 1 4 + 1 16 ) h e q a t {\displaystyle {\bigg (}1+{\frac {1}{4}}+{\frac {1}{16}}{\bigg )}\;heqat}
( 1 + 1 8 + 1 16 ) h e q a t {\displaystyle {\bigg (}1+{\frac {1}{8}}+{\frac {1}{16}}{\bigg )}\;heqat}
( 1 + 1 16 ) h e q a t {\displaystyle {\bigg (}1+{\frac {1}{16}}{\bigg )}\;heqat}
( 1 2 + 1 4 + 1 8 + 1 16 ) h e q a t {\displaystyle {\bigg (}{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}{\bigg )}\;heqat}
( 1 2 + 1 4 + 1 16 ) h e q a t {\displaystyle {\bigg (}{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{16}}{\bigg )}\;heqat}
( 1 2 + 1 8 + 1 16 ) h e q a t {\displaystyle {\bigg (}{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{16}}{\bigg )}\;heqat}
( 1 2 + 1 16 ) h e q a t {\displaystyle {\bigg (}{\frac {1}{2}}+{\frac {1}{16}}{\bigg )}\;heqat}
( 1 4 + 1 8 + 1 16 ) h e q a t {\displaystyle {\bigg (}{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}{\bigg )}\;heqat}
15 + 1 3 + 1 26 + 1 78 {\displaystyle 15+{\frac {1}{3}}+{\frac {1}{26}}+{\frac {1}{78}}}
O 8 = 26 + 2 3 q u a d r u p l e h e q a t {\displaystyle O_{8}=26+{\frac {2}{3}}\;\;\;quadruple\;\;\;heqat}
O 6 = 20 q u a d r u p l e h e q a t {\displaystyle O_{6}=20\;\;\;quadruple\;\;\;heqat}
O 4 = 13 + 1 3 q u a d r u p l e h e q a t {\displaystyle O_{4}=13+{\frac {1}{3}}\;\;\;quadruple\;\;\;heqat}
2) 3 + 1/2 heqats of meal produce 80 loaves of bread. Find the meal per loaf m {\displaystyle m} in heqats and ro, and find the pefsu P {\displaystyle P} of these loaves with respect to the meal. Express them as Egyptian fractions.
P = ( 22 + 2 3 + 1 7 + 1 21 ) l o a f h e q a t m e a l {\displaystyle P={\bigg (}22+{\frac {2}{3}}+{\frac {1}{7}}+{\frac {1}{21}}{\bigg )}{\frac {loaf}{heqat_{meal}}}}
P = ( 12 + 2 3 + 1 42 + 1 126 ) l o a f h e q a t m e a l {\displaystyle P={\bigg (}12+{\frac {2}{3}}+{\frac {1}{42}}+{\frac {1}{126}}{\bigg )}{\frac {loaf}{heqat_{meal}}}}
y = 2000 {\displaystyle y=2000}
[ h o u s e s 7 c a t s 49 m i c e 343 s p e l t 2401 h e q a t 16807 T o t a l 19607 ] {\displaystyle {\begin{bmatrix}houses&7\\cats&49\\mice&343\\spelt&2401\\heqat&16807\\Total&19607\\\end{bmatrix}}}
Moreover, one of Ahmes' methods of solution for the sum suggests an understanding of finite geometric series . Ahmes performs a direct sum, but he also presents a simple multiplication to get the same answer: "2801 x 7 = 19607". Chace explains that since the first term, the number of houses (7) is equal to the common ratio of multiplication (7), then the following holds (and can be generalized to any similar situation):
∑ k = 1 n 7 k = 7 ( 1 + ∑ k = 1 n − 1 7 k ) {\displaystyle \sum \limits _{k=1}^{n}7^{k}=7{\bigg (}1+\sum \limits _{k=1}^{n-1}7^{k}{\bigg )}}
That is, when the first term of a geometric sequence is equal to the common ratio, partial sums of geometric sequences, or finite geometric series, can be reduced to multiplications involving the finite series having one less term, which does prove convenient in this case. In this instance then, Ahmes simply adds the first four terms of the sequence (7 + 49 + 343 + 2401 = 2800) to produce a partial sum, adds one (2801), and then simply multiplies by 7 to produce the correct answer.
[ 1 h e q a t = 10 h i n u 1 2 h e q a t = 5 h i n u 1 4 h e q a t = ( 2 + 1 2 ) h i n u 1 8 h e q a t = ( 1 + 1 4 ) h i n u 1 16 h e q a t = ( 1 2 + 1 8 ) h i n u 1 32 h e q a t = ( 1 4 + 1 16 ) h i n u 1 64 h e q a t = ( 1 8 + 1 32 ) h i n u ] {\displaystyle {\begin{bmatrix}1&heqat&=&10&hinu\\{\frac {1}{2}}&heqat&=&5&hinu\\{\frac {1}{4}}&heqat&=&(2+{\frac {1}{2}})&hinu\\{\frac {1}{8}}&heqat&=&(1+{\frac {1}{4}})&hinu\\{\frac {1}{16}}&heqat&=&({\frac {1}{2}}+{\frac {1}{8}})&hinu\\{\frac {1}{32}}&heqat&=&({\frac {1}{4}}+{\frac {1}{16}})&hinu\\{\frac {1}{64}}&heqat&=&({\frac {1}{8}}+{\frac {1}{32}})&hinu\\\end{bmatrix}}}
Begin with the statement that "10 fattening geese eat 2 + 1/2 heqats in one day". In other words, the daily rate of consumption (and initial condition) i {\displaystyle i} is equal to 2 + 1/2. Determine the number of heqats which 10 fattening geese eat in 10 days, and in 40 days. Call these quantities t {\displaystyle t} and f {\displaystyle f} , respectively.
Multiply the above latter quantity f {\displaystyle f} by 5/3 to express the amount of "spelt", or s {\displaystyle s} , required to be ground up.
Multiply f {\displaystyle f} by 2/3 to express the amount of "wheat", or w {\displaystyle w} , required.
Divide w {\displaystyle w} by 10 to express a "portion of wheat", or p {\displaystyle p} , which is to be subtracted from f {\displaystyle f} .
Find f − p = g {\displaystyle f-p=g} . This is the amount of "grain", (or wedyet flour, it would seem), which is required to make the feed for geese, presumably on the interval of 40 days (which would seem to contradict the original statement of the problem, somewhat). Finally, express g {\displaystyle g} again in terms of hundreds of double heqats, double heqats and double ro , where 1 hundred double heqat = 2 hundred heqat = 100 double heqat = 200 heqat = 32,000 double ro = 64,000 ro. Call this final quantity g 2 {\displaystyle g_{2}} .
t = 25 h e q a t {\displaystyle t=25\;\;\;heqat}
f = 100 h e q a t {\displaystyle f=100\;\;\;heqat}
s = ( 1 + 1 2 ) h u n d r e d h e q a t {\displaystyle s={\bigg (}1+{\frac {1}{2}}{\bigg )}hundred\;\;\;heqat}
+ ( 16 + 1 2 + 1 8 + 1 32 ) h e q a t + ( 3 + 1 3 ) r o {\displaystyle +{\bigg (}16+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{32}}{\bigg )}\;\;\;heqat+{\bigg (}3+{\frac {1}{3}}{\bigg )}\;\;\;ro}
w = ( 1 3 + 1 4 ) h u n d r e d h e q a t {\displaystyle w={\bigg (}{\frac {1}{3}}+{\frac {1}{4}}{\bigg )}hundred\;\;\;heqat}
+ ( 8 + 1 4 + 1 16 + 1 64 ) h e q a t + ( 1 + 2 3 ) r o {\displaystyle +{\bigg (}8+{\frac {1}{4}}+{\frac {1}{16}}+{\frac {1}{64}}{\bigg )}\;\;\;heqat+{\bigg (}1+{\frac {2}{3}}{\bigg )}\;\;\;ro}
p = ( 6 + 1 2 + 1 8 + 1 32 ) h e q a t + ( 3 + 1 3 ) r o {\displaystyle p={\bigg (}6+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{32}}{\bigg )}\;\;\;heqat+{\bigg (}3+{\frac {1}{3}}{\bigg )}\;\;\;ro}
g = ( 1 2 + 1 4 ) h u n d r e d h e q a t {\displaystyle g={\bigg (}{\frac {1}{2}}+{\frac {1}{4}}{\bigg )}hundred\;\;\;heqat}
+ ( 18 + 1 4 + 1 16 + 1 64 ) h e q a t + ( 1 + 2 3 ) r o {\displaystyle +{\bigg (}18+{\frac {1}{4}}+{\frac {1}{16}}+{\frac {1}{64}}{\bigg )}\;\;\;heqat+{\bigg (}1+{\frac {2}{3}}{\bigg )}\;\;\;ro}
g 2 = ( 1 4 ) h u n d r e d d o u b l e h e q a t {\displaystyle g_{2}={\bigg (}{\frac {1}{4}}{\bigg )}hundred\;\;\;double\;\;\;heqat}
+ ( 21 + 1 2 + 1 8 + 1 32 ) d o u b l e h e q a t {\displaystyle +{\bigg (}21+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{32}}{\bigg )}\;\;\;double\;\;\;heqat}
+ ( 3 + 1 3 ) d o u b l e r o {\displaystyle +{\bigg (}3+{\frac {1}{3}}{\bigg )}\;\;\;double\;\;\;ro}
t = ( 12 + 1 2 ) h e q a t {\displaystyle t={\bigg (}12+{\frac {1}{2}}{\bigg )}\;\;\;heqat}
f = 50 h e q a t {\displaystyle f=50\;\;\;heqat}
g 2 = ( 23 + 1 4 + 1 16 + 1 64 ) d o u b l e h e q a t {\displaystyle g_{2}={\bigg (}23+{\frac {1}{4}}+{\frac {1}{16}}+{\frac {1}{64}}{\bigg )}\;\;\;double\;\;\;heqat}
+ ( 1 + 2 3 ) d o u b l e r o {\displaystyle +{\bigg (}1+{\frac {2}{3}}{\bigg )}\;\;\;double\;\;\;ro}
Suppose that four geese are cooped up, and their collective daily allowance of feed is equal to one hinu. Express one goose's daily allowance of feed a 1 {\displaystyle a_{1}} in terms of heqats and ro.
Suppose that the daily feed for a goose "that goes into the pond" is equal to 1/16 + 1/32 heqats + 2 ro. Express this same daily allowance a 2 {\displaystyle a_{2}} in terms of hinu.
Suppose that the daily allowance of feed for 10 geese is one heqat. Find the 10-day allowance a 10 {\displaystyle a_{10}} and the 30-day, or one-month allowance a 30 {\displaystyle a_{30}} for the same group of animals, in heqats.
Finally a table will be presented, giving daily feed portions to fatten one animal of any of the indicated species.
a 2 = 1 h i n u {\displaystyle a_{2}=1\;\;\;hinu}
a 10 = 10 h e q a t {\displaystyle a_{10}=10\;\;\;heqat}
a 30 = 30 h e q a t {\displaystyle a_{30}=30\;\;\;heqat}
[ g o o s e ( 1 8 + 1 32 ) h e q a t + ( 3 + 1 3 ) r o t e r p − g o o s e ( 1 8 + 1 32 ) h e q a t + ( 3 + 1 3 ) r o c r a n e ( 1 8 + 1 32 ) h e q a t + ( 3 + 1 3 ) r o s e t − d u c k ( 1 32 + 1 64 ) h e q a t + 1 r o s e r − g o o s e 1 64 h e q a t + 3 r o d o v e 3 r o q u a i l 3 r o ] {\displaystyle {\begin{bmatrix}goose&({\frac {1}{8}}+{\frac {1}{32}})&heqat&+&(3+{\frac {1}{3}})&ro\\terp-goose&({\frac {1}{8}}+{\frac {1}{32}})&heqat&+&(3+{\frac {1}{3}})&ro\\crane&({\frac {1}{8}}+{\frac {1}{32}})&heqat&+&(3+{\frac {1}{3}})&ro\\set-duck&({\frac {1}{32}}+{\frac {1}{64}})&heqat&+&1&ro\\ser-goose&{\frac {1}{64}}&heqat&+&3&ro\\dove&&&&3&ro\\quail&&&&3&ro\\\end{bmatrix}}}
[ L o a v e s C o m m o n f o o d 4 f i n e o x e n 24 h e q a t 2 h e q a t 2 f i n e o x e n 22 h e q a t 6 h e q a t 3 c a t t l e 20 h e q a t 2 h e q a t 1 o x 20 h e q a t T o t a l 86 h e q a t 10 h e q a t i n s p e l t 9 h e q a t ( 7 + 1 2 ) h e q a t 10 d a y s ( 1 2 + 1 4 ) c . h e q a t ( 1 2 + 1 4 ) c . h e q a t + 15 h e q a t o n e m o n t h 200 h e q a t ( 1 2 + 1 4 ) c . h e q a t + 15 h e q a t d o u b l e h e q a t 1 2 c . h e q a t 1 4 c . h e q a t + ( 11 + 1 2 + 1 8 ) h e q a t + 5 h e q a t + 3 r o ] {\displaystyle {\begin{bmatrix}&Loaves&Common\;food\\4\;fine\;oxen&24\;heqat&2\;heqat\\2\;fine\;oxen&22\;heqat&6\;heqat\\3\;cattle&20\;heqat&2\;heqat\\1\;ox&20\;heqat&\\Total&86\;heqat&10\;heqat\\in\;spelt&9\;heqat&(7+{\frac {1}{2}})\;heqat\\10\;days&({\frac {1}{2}}+{\frac {1}{4}})\;c.\;heqat&({\frac {1}{2}}+{\frac {1}{4}})\;c.\;heqat\\&+15\;heqat&\\one\;month&200\;heqat&({\frac {1}{2}}+{\frac {1}{4}})\;c.\;heqat\\&&+15\;heqat\\double\;heqat&{\frac {1}{2}}\;c.\;heqat&{\frac {1}{4}}\;c.\;heqat\\&+(11+{\frac {1}{2}}+{\frac {1}{8}})\;heqat&+5\;heqat\\&+3\;ro&\\\end{bmatrix}}}
Problem 84 seems to suggest a procedure to estimate various food materials and allowances in similar terms as the previous three problems, but the extant information is deeply confused. Still, there are hints of consistency. The problem seems to start out like a conventional story problem, describing a stable with ten animals of four different types. It seems that the four types of animals consume feed, or "loaves" at different rates, and that there are corresponding amounts of "common" food. These two columns of information are correctly summed in the "total" row, however they are followed by two "spelt" items of dubious relationship to the above. These two spelt items are indeed each multiplied by ten to give the two entries in the "10 days" row, once unit conversions are accounted for. The "one month" row items do not seem to be consistent with the previous two, however. Finally, information in "double heqats" (read hundred double heqats, double heqats and double ro for these items) concludes the problem, in a manner reminiscent of 82 and 82B. The two items in the final row are in roughly, but not exactly, the same proportion to one another as the two items in the "one month" row.
"1... living forever. List of the food in Hebenti...
2... his brother the steward Ka-mose...
3... of his year, silver, 50 pieces twice in the year...
4... cattle 2, in silver 3 pieces in the year...
5... one twice; that is, 1/6 and 1/6. Now as for one...
6... 12 hinu; that is, silver, 1/4 piece; one...
7... (gold or silver) 5 pieces, their price therefor; fish, 120, twice...
8... year, barley, in quadruple heqat, 1/2 + 1/4 of 100 heqat 15 heqat; spelt, 100 heqat... heqat...
9... barley, in quadruple heqat, 1/2 + 1/4 of 100 heqat 15 heqat; spelt, 1 + 1/2 + 1/4 times 100 heqat 17 heqat...
10... 146 + 1/2; barley, 1 + 1/2 + 1/4 times 100 heqat 10 heqat; spelt, 300 heqat... heqat...
11... 1/2, there was brought wine, 1 ass(load?)...
12... silver 1/2 piece; ... 4; that is, in silver...
13... 1 + 1/4; fat, 36 hinu; that is, in silver...
14... 1 + 1/2 + 1/4 times 100 heqat 21 heqat; spelt, in quadruple heqat, 400 heqat 10 heqat...
15-18 (These lines are repetitions of line 14.)"
The first month of the inundation season, 23rd day, the commander (?) of the army (?) attacked (?) Zaru.
25th day, it was heard that Zaru was entered.
Year 11, first month of the inundation season, third day. Birth of Set; the majesty of this god caused his voice to be heard.
Birth of Isis, the heavens rained." | https://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus |
Rhizobacteria are root-associated bacteria that can have a detrimental (parasitic varieties), neutral or beneficial effect on plant growth. The name comes from the Greek rhiza , meaning root. The term usually refers to bacteria that form symbiotic relationships with many plants ( mutualism ). Rhizobacteria are often referred to as plant growth-promoting rhizobacteria, or PGPRs. The term PGPRs was first used by Joseph W. Kloepper in the late 1970s and has become commonly used in scientific literature. [ 1 ]
Generally, about 2–5% of rhizosphere bacteria are PGPR. [ 2 ] They are an important group of microorganisms used in biofertilizer . Biofertilization accounts for about 65% of the nitrogen supply to crops worldwide. [ citation needed ] PGPRs have different relationships with different species of host plants. The two major classes of relationships are rhizospheric and endophytic . Rhizospheric relationships consist of the PGPRs that colonize the surface of the root, or superficial intercellular spaces of the host plant, often forming root nodules . The dominant species found in the rhizosphere is a microbe from the genus Azospirillum . [ 3 ] [ failed verification ] Endophytic relationships involve the PGPRs residing and growing within the host plant in the apoplastic space. [ 1 ]
Nitrogen fixation is one of the most beneficial processes performed by rhizobacteria. Nitrogen is a vital nutrient to plants and gaseous nitrogen (N 2 ) is not available to them due to the high energy required to break the triple bonds between the two atoms. [ 4 ] Rhizobacteria, through nitrogen fixation, are able to convert gaseous nitrogen (N 2 ) to ammonia (NH 3 ) making it an available nutrient to the host plant which can support and enhance plant growth. The host plant provides the bacteria with amino acids so they do not need to assimilate ammonia. [ 5 ] The amino acids are then shuttled back to the plant with newly fixed nitrogen. Nitrogenase is an enzyme involved in nitrogen fixation and requires anaerobic conditions. Membranes within root nodules are able to provide these conditions. The rhizobacteria require oxygen to metabolize, so oxygen is provided by a hemoglobin protein called leghemoglobin which is produced within the nodules. [ 4 ] Legumes are well-known nitrogen-fixing crops and have been used for centuries in crop rotation to maintain the health of the soil.
The symbiotic relationship between rhizobacteria and their host plants is not without costs. For the plant to be able to benefit from the added available nutrients provided by the rhizobacteria, it needs to provide a place and the proper conditions for the rhizobacteria to live. Creating and maintaining root nodules for rhizobacteria can cost between 12–25% of the plant's total photosynthetic output. Legumes are often able to colonize early successional environments due to the unavailability of nutrients. Once colonized, though, the rhizobacteria make the soil surrounding the plant more nutrient rich, which in turn can lead to competition with other plants. The symbiotic relationship, in short, can lead to increased competition. [ 4 ]
PGPRs increase the availability of nutrients through the solubilization of unavailable forms of nutrients and by the production of siderophores which aids in the facilitating of nutrient transport. Phosphorus , a limiting nutrient for plant growth, can be plentiful in soil, but is most commonly found in insoluble forms. Organic acids and phosphotases released by rhizobacteria found in plant rhizospheres facilitate the conversion of insoluble forms of phosphorus to plant-available forms such as H 2 PO 4 − . PGPR bacteria include Pseudomonas putida , Azospirillum fluorescens , and Azospirillum lipoferum and notable nitrogen-fixing bacteria associated with legumes includes Allorhizobium , Azorhizobium , Bradyrhizobium , and Rhizobium . [ 5 ]
Though microbial inoculants can be beneficial for crops, they are not widely used in industrial agriculture , as large-scale application techniques have yet to become economically viable. A notable exception is the use of rhizobial inoculants for legumes such as peas. Inoculation with PGPRs ensures efficient nitrogen fixation, and they have been employed in North American agriculture for over 100 years.
Plant growth-promoting rhizobacteria (PGPR) were first defined by Kloepper and Schroth [ 6 ] to be soil bacteria that colonize the roots of plants following inoculation onto seed and that enhance plant growth . [ 7 ] The following are implicit in the colonization process: ability to survive inoculation onto seed, to multiply in the spermosphere (region surrounding the seed) in response to seed exudates , to attach to the root surface, and to colonize the developing root system . [ 8 ] The ineffectiveness of PGPR in the field has often been attributed to their inability to colonize plant roots. [ 3 ] [ 9 ] A variety of bacterial traits and specific genes contribute to this process, but only a few have been identified. These include motility , chemotaxis to seed and root exudates , production of pili or fimbriae , production of specific cell surface components, ability to use specific components of root exudates, protein secretion, and quorum sensing . The generation of mutants altered in expression of these traits is aiding our understanding of the precise role each one plays in the colonization process. [ 10 ] [ 11 ]
Progress in the identification of new, previously uncharacterized genes is being made using nonbiased screening strategies that rely on gene fusion technologies. These strategies employ reporter transposons [ 12 ] and in vitro expression technology (IVET) [ 13 ] to detect genes expressed during colonization.
Using molecular markers such as green fluorescent protein or fluorescent antibodies , it is possible to monitor the location of individual rhizobacteria on the root using confocal laser scanning microscopy . [ 3 ] [ 14 ] [ 15 ] This approach has also been combined with an rRNA -targeting probe to monitor the metabolic activity of a rhizobacterial strain in the rhizosphere and showed that bacteria located at the root tip were most active. [ 16 ]
PGPRs enhance plant growth by direct and indirect means, but the specific mechanisms involved have not all been well characterized. [ 8 ] Direct mechanisms of plant growth promotion by PGPRs can be demonstrated in the absence of plant pathogens or other rhizosphere microorganisms , while indirect mechanisms involve the ability of PGPRs to reduce the harmful effects of plant pathogens on crop yield . PGPRs have been reported to directly enhance plant growth by a variety of mechanisms:
Direct enhancement of mineral uptake due to increases in specific ion fluxes at the root surface in the presence of PGPRs has also been reported. PGPR strains may use one or more of these mechanisms in the rhizosphere. Molecular approaches using microbial and plant mutants altered in their ability to synthesize or respond to specific phytohormones have increased understanding of the role of phytohormone synthesis as a direct mechanism of plant growth enhancement by PGPRs. [ 19 ] PGPR that synthesize auxins , gibberellins and kinetins or that interfere with plant ethylene synthesis have been identified. [ 20 ]
Development of PGPRs into biofertilisers and biopesticides could be a novel way of increasing crop yield and decreasing disease incidence, [ 21 ] whilst decreasing dependency on chemical pesticides and fertilisers which can often have harmful effects on the local ecology and environment. [ 22 ]
Studies conducted on sugar beet crops found that some root-colonizing bacteria were deleterious rhizobacteria (DRB). Sugar beet seeds inoculated with DRB had reduced germination rates, root lesions, reduced root elongation, root distortions, increased fungi infection, and decreased plant growth. In one trial the sugar beet yield was reduced by 48%. [ 23 ]
Six strains of rhizobacteria have been identified as being DRB. The strains are in the genera Enterobacter , Klebsiella , Citrobacter , Flavobacterium , Achromobacter , and Arthrobacter . Due to a large number of taxonomic species yet to be described, complete characterization has not been possible as DRB are highly variable. [ 23 ]
The presence of PGPRs has proven to reduce and inhibit the colonization of DRB on sugar beet roots. Plots inoculated with PGPRs and DRBs had an increase in production of 39% while plots only treated with DRBs had a reduction in production of 30%. [ 23 ]
Rhizobacteria are also able to control plant diseases that are caused by other bacteria and fungi. Disease is suppressed through induced systemic resistance and through the production of antifungal metabolites. Pseudomonas biocontrol strains have been genetically modified to improve plant growth and improve the disease resistance of agricultural crops. In agriculture, inoculant bacteria are often applied to the seed coat of seeds prior to being sown. Inoculated seeds are more likely to establish large enough rhizobacterial populations within the rhizosphere to produce notable beneficial effects on the crop. [ 1 ]
They can also combat pathogenic microbes in cattle . Different forage species regulate their own rhizosphere to varying degrees and favouring various microbes. Kyselková et al 2015 find planting forage species known to encourage native rhizobacteria retards the spread within the soil of antibiotic resistance genes of cow faeces bacteria. [ 24 ] [ 25 ] | https://en.wikipedia.org/wiki/Rhizobacteria |
Rhizobia are diazotrophic bacteria that fix nitrogen after becoming established inside the root nodules of legumes ( Fabaceae ). To express genes for nitrogen fixation, rhizobia require a plant host ; they cannot independently fix nitrogen]. [ 1 ] In general, they are gram negative , motile , non- sporulating rods.
Rhizobia are a "group of soil bacteria that infect the roots of legumes to form root nodules ". [ 2 ] Rhizobia are found in the soil and, after infection, produce nodules in the legume where they fix nitrogen gas (N 2 ) from the atmosphere, turning it into a more readily useful form of nitrogen. From here, the nitrogen is exported from the nodules and used for growth in the legume. Once the legume dies, the nodule breaks down and releases the rhizobia back into the soil, where they can live individually or reinfect a new legume host. [ 2 ]
The first known species of rhizobia, Rhizobium leguminosarum , was identified in 1889, and all further species were initially placed in the Rhizobium genus . Most research has been done on crop and forage legumes such as clover , alfalfa , beans , peas , and soybeans ; more research is being done on North American legumes. [ citation needed ]
Rhizobia are a paraphyletic group that fall into two classes of Pseudomonadota —the alphaproteobacteria and betaproteobacteria . As shown below, most belong to the order Hyphomicrobiales , but several rhizobia occur in distinct bacterial orders of the Pseudomonadota. [ 3 ] [ 4 ] [ 5 ] [ 6 ]
Alphaproteobacteria
Betaproteobacteria
These groups include a variety of non- symbiotic bacteria. For instance, the plant pathogen Agrobacterium is a closer relative of Rhizobium than the Bradyrhizobium that nodulate soybean. [ 7 ]
Although much of the nitrogen is removed when protein -rich grain or hay is harvested , significant amounts can remain in the soil for future crops. This is especially important when nitrogen fertilizer is not used, as in organic rotation schemes or in some less- industrialized countries. [ 8 ] Nitrogen is the most commonly deficient nutrient in many soils around the world and it is the most commonly supplied plant nutrient. The supply of nitrogen through fertilizers has severe environmental concerns .
Specific strains of rhizobia are required to make functional nodules on the roots able to fix the N 2 . [ 9 ] Having this specific rhizobia present is beneficial to the legume, as the N 2 fixation can increase crop yield. [ 10 ] Inoculation with rhizobia tends to increase yield. [ 11 ] Rhizobia has been found to increase legume resistance to insect herbivores, particularly when several species of rhizobia are present. [ 12 ]
Legume inoculation has been an agricultural practice for many years and has continuously improved over time. [ 10 ] 12–20 million hectares of soybeans are inoculated annually. An ideal inoculant includes some of the following aspects; maximum efficacy, ease of use, compatibility, high rhizobial concentration, long shelf-life, usefulness under varying field conditions, and survivability. [ 10 ] [ 13 ] [ 14 ]
These inoculants may foster success in legume cultivation. [ 15 ] As a result of the nodulation process, after the harvest of the crop, there are higher levels of soil nitrate, which can then be used by the next crop.
Rhizobia are unique in that they are the only nitrogen-fixing bacteria living in a symbiotic relationship with legumes . Common crop and forage legumes are peas, beans, clover, and soy.
The legume–rhizobium symbiosis is a classic example of mutualism —rhizobia supply ammonia or amino acids to the plant and, in return, receive organic acids (mainly malate and succinate , which are dicarboxylic acids ) as a carbon and energy source. However, because several unrelated strains infect each individual plant, a classic tragedy of the commons scenario presents itself. Cheater strains may hoard plant resources such as polyhydroxybutyrate for the benefit of their own reproduction without fixing an appreciable amount of nitrogen . [ 16 ] Given the costs involved in nodulation and the opportunity for rhizobia to cheat, it may be surprising that this symbiosis exists.
The formation of the symbiotic relationship involves a signal exchange between both partners that leads to mutual recognition and the development of symbiotic structures. The most well understood mechanism for the establishment of this symbiosis is through intracellular infection. Rhizobia are free living in the soil until they are able to sense flavonoids , derivatives of 2-phenyl-1.4-benzopyrone, which are secreted by the roots of their host plant, triggering the accumulation of a large population of cells and eventually attachment to root hairs . [ 17 ] [ 18 ] These flavonoids then promote the DNA binding activity of NodD, which belongs to the LysR family of transcriptional regulators and triggers the secretion of nod factors after the bacteria have entered the root hair. [ 18 ] Nod factors trigger a series of complex developmental changes inside the root hair, beginning with root hair curling and followed by the formation of the infection thread, a cellulose lined tube that the bacteria use to travel down through the root hair into the root cells. [ 19 ] The bacteria then infect several other adjacent root cells. This is followed by continuous cell proliferation, resulting in the formation of the root nodule . [ 17 ] A second mechanism, used especially by rhizobia that infect aquatic hosts, is called crack entry. In this case, no root hair deformation is observed. Instead, the bacteria penetrate between cells through cracks produced by lateral root emergence. [ 20 ]
Inside the nodule, the bacteria differentiate morphologically into bacteroids and fix atmospheric nitrogen into ammonium using the enzyme nitrogenase . Ammonium is then converted into amino acids like glutamine and asparagine before it is exported to the plant. [ 17 ] In return, the plant supplies the bacteria with carbohydrates in the form of organic acids. [ 17 ] The plant also provides the bacteroid oxygen for cellular respiration , tightly bound by leghaemoglobins , plant proteins similar to human hemoglobins . This process keeps the nodule oxygen poor in order to prevent the inhibition of nitrogenase activity. [ 17 ]
Recently, a Bradyrhizobium strain was discovered to form nodules in Aeschynomene without producing nod factors, suggesting the existence of alternative communication signals other than nod factors, possibly involving the secretion of the plant hormone cytokinin. [ 17 ] [ 21 ]
It has been observed that root nodules can be formed spontaneously in Medicago without the presence of rhizobia. [ 22 ] This implies that the development of the nodule is controlled entirely by the plant and simply triggered by the secretion of nod factors .
There are two main hypotheses for the mechanism that maintains legume-rhizobium symbiosis (though both may occur in nature). The sanctions hypothesis theorizes that legumes cannot recognize the more parasitic or less nitrogen fixing rhizobia and must counter the parasitism by post-infection legume sanctions. In response to underperforming rhizobia, legume hosts can respond by imposing sanctions of varying severity to their nodules. [ 23 ] These sanctions include, but are not limited to, reduction of nodule growth, early nodule death, decreased carbon supply to nodules, or reduced oxygen supply to nodules that fix less nitrogen. Within a nodule, some of the bacteria differentiate into nitrogen fixing bacteroids, which have been found to be unable to reproduce. [ 24 ] Therefore, with the development of a symbiotic relationship, if the host sanctions hypothesis is correct, the host sanctions must act toward whole nodules rather than individual bacteria because individual targeting sanctions would prevent any reproducing rhizobia from proliferating over time. This ability to reinforce a mutual relationship with host sanctions pushes the relationship toward mutualism rather than parasitism and is likely a contributing factor to why the symbiosis exists.
However, other studies have found no evidence of plant sanctions. [ 25 ]
The partner choice hypothesis proposes that the plant uses prenodulation signals from the rhizobia to decide whether to allow nodulation, and chooses only noncheating rhizobia. There is evidence for sanctions in soybean plants, which reduce rhizobium reproduction (perhaps by limiting oxygen supply) in nodules that fix less nitrogen. [ 26 ] Likewise, wild lupine plants allocate fewer resources to nodules containing less-beneficial rhizobia, limiting rhizobial reproduction inside. [ 27 ] This is consistent with the definition of sanctions, although called "partner choice" by the authors. Some studies support the partner choice hypothesis. [ 28 ] While both mechanisms no doubt contribute significantly to maintaining rhizobial cooperation, they do not in themselves fully explain the persistence of mutualism . The partner choice hypothesis is not exclusive from the host sanctions hypothesis, as it is apparent that both of them are prevalent in the symbiotic relationship. [ 29 ]
The symbiosis between nitrogen fixing rhizobia and the legume family has emerged and evolved over the past 66 million years. [ 30 ] [ 31 ] Although evolution tends to swing toward one species taking advantage of another in the form of noncooperation in the selfish-gene model, management of such symbiosis allows for the continuation of cooperation. [ 32 ] When the relative fitness of both species is increased, natural selection will favor symbiosis.
To understand the evolutionary history of this symbiosis, it is helpful to compare the rhizobia-legume symbiosis to a more ancient symbiotic relationship, such as that between endomycorrhizae fungi and land plants, which dates back to almost 460 million years ago. [ 33 ]
Endomycorrhizal symbiosis can provide many insights into rhizobia symbiosis because recent genetic studies have suggested that rhizobia co-opted the signaling pathways from the more ancient endomycorrhizal symbiosis. [ 34 ] Bacteria secrete Nod factors and endomycorrhizae secrete Myc-LCOs. Upon recognition of the Nod factor/Myc-LCO, the plant proceeds to induce a variety of intracellular responses to prepare for the symbiosis. [ 35 ]
It is likely that rhizobia co-opted the features already in place for endomycorrhizal symbiosis because there are many shared or similar genes involved in the two processes. For example, the plant recognition gene SYMRK (symbiosis receptor-like kinase) is involved in the perception of both the rhizobial Nod factors as well as the endomycorrhizal Myc-LCOs. [ 36 ] The shared similar processes would have greatly facilitated the evolution of rhizobial symbiosis because not all the symbiotic mechanisms would have needed to develop. Instead, the rhizobia simply needed to evolve mechanisms to take advantage of the symbiotic signaling processes already in place from endomycorrhizal symbiosis.
When associating with rhizobia, legumes often experience growth benefits and increased resistance to stress. Rhizobia's ability to convert inorganic atmospheric nitrogen into an organic ammonia compounds provides leguminous plants access to a resource that many plants are limited by, increasing their fitness [ 38 ] and the biodiversity of their ecosystems. [ 39 ]
These growth benefits include increased overall plant growth, [ 37 ] greater above and below ground biomass, increased shoot biomass, increased leaf protein levels, [ 40 ] and more attractive floral traits for pollinators . [ 37 ] Rhizobia has also been shown to increase legume resistance to insect herbivores when rhizobia diversity is high, specifically by increasing expression of defensive traits that reduce leaf herbivory and the number of sap-sucking aphids. [ 41 ]
Other species that engage symbiotically with legumes are affected by legume-rhizobia mutualism. Legumes associating with rhizobia sometimes produce less ant attracting-extrafloral nectar, leading to a reduction in ants present and providing defensive benefits. [ 40 ] Legumes hosting rhizobia have been observed receiving more pollinator visitations, despite not always increasing production of inflorescences. [ 42 ] The presence of rhizobia increases the colonization rate of legume cells by arbuscular mycorrhizal fungi , increasing the quantity of soil nutrients available to the legume. [ 43 ]
The legume-rhizobia mutualism is context dependent; the benefits provided by rhizobia are lessened or absent under unfavorable environmental conditions. [ 44 ] Perturbations can alter the balance of symbiotic relationships between species as reduced benefits provided can lead to antagonistic behavior, such as parasitism . [ 45 ]
These disruptions lead plant species to lessen their investment in the relationships, and perhaps even stop engaging in them altogether. [ 44 ] For example, nutrient deposition has led to the emergence of less productive strains of rhizobia [ 46 ] and increased ambient temperatures have legumes reducing investment in the resource mutualism. [ 42 ] Nutrient deposition is of particular issue to legumes as the increased availability of nitrogen allows nitrogen-limited plant species to quickly out compete legumes for light. This increases photosynthesis costs, further destabilizing the legume-rhizobia mutualism as the legume suffers fitness consequences and is unable to provide benefits to rhizobia. [ 47 ]
Many other species of bacteria are able to fix nitrogen ( diazotrophs ), but few are able to associate intimately with plants and colonize specific structures like legume nodules. Bacteria that do associate with plants include the actinomycete , Frankia , which form symbiotic root nodules in actinorhizal plants , although these bacteria have a much broader host range, implying the association is less specific than in legumes. [ 17 ] Additionally, several cyanobacteria like Nostoc are associated with aquatic ferns , Cycas , and Gunneras , although they do not form nodules. [ 48 ] [ 49 ]
Additionally, loosely associated plant bacteria, termed endophytes , have been reported to fix nitrogen in planta . [ 50 ] These bacteria colonize the intercellular spaces of leaves, stems, and roots in plants [ 51 ] but do not form specialized structures like rhizobia and Frankia . Diazotrophic bacterial endophytes have very broad host ranges, in some cases colonizing both monocots and dicots . [ 52 ] | https://en.wikipedia.org/wiki/Rhizobia |
Rhizofiltration is a form of phytoremediation that involves filtering contaminated groundwater , surface water and wastewater through a mass of roots to remove toxic substances or excess nutrients .
Rhizofiltration is a type of phytoremediation , which refers to the approach of using hydroponically cultivated plant roots to remediate contaminated water through absorption, concentration, and precipitation of pollutants . It also filters through water and dirt. [ citation needed ]
The contaminated water is either collected from a waste site and brought to the plants, or the plants are planted in the contaminated area, where the roots then take up the water and the contaminants dissolved in it. Many plant species naturally uptake heavy metals and excess nutrients for a variety of reasons: sequestration, drought resistance , disposal by leaf abscission , interference with other plants, and defense against pathogens and herbivores . [ 1 ] Some of these species are better than others and can accumulate extraordinary amounts of these contaminants. Identification of such plant species has led environmental researchers to realize the potential for using these plants for remediation of contaminated soil and wastewater . [ citation needed ]
This process is very similar to phytoextraction in that it removes contaminants by trapping them into harvestable plant biomass . Both phytoextraction and rhizofiltration follow the same basic path to remediation. First, plants that have stable root systems are put in contact with the contamination to get acclimated to the toxins. They absorb contaminants through their root systems and store them in root biomass and/or transport them up into the stems and/or leaves. The plants continue to absorb contaminants until they are harvested. The plants are then replaced to continue the growth/harvest cycle until satisfactory levels of contaminant are achieved. Both processes are also aimed more toward concentrating and precipitating heavy metals than organic contaminants. The major difference between rhizofiltration and phytoextraction is that rhizofiltration is used for treatment in aquatic environments, while phytoextraction deals with soil remediation. [ citation needed ]
Rhizofiltration may be applicable to the treatment of surface water and groundwater, industrial and residential effluents, downwashes from power lines, storm waters, acid mine drainage , agricultural runoffs, diluted sludges, and radionuclide -contaminated solutions.
Plants suitable for rhizofiltration applications can efficiently remove toxic metals from a solution using rapid-growth root systems. Various terrestrial plant species have been found to effectively remove toxic metals such as Cu 2+ , Cd 2+ , Cr 6+ , Ni 2+ , Pb 2+ , and Zn 2+ from aqueous solutions. [ 2 ] It was also found that low level radioactive contaminants can successfully be removed from liquid streams. [ 3 ] A system to achieve this can consist of a “feeder layer” of soil suspended above a contaminated stream through which plants grow, extending the bulk of their roots into the water. The feeder layer allows the plants to receive fertilizer without contaminating the stream, while simultaneously removing heavy metals from the water. [ 4 ] Trees have also been applied to remediation. Trees are the lowest cost plant type. They can grow on land of marginal quality and have long life-spans. This results in little or no maintenance costs. The most commonly used are willows and poplars , which can grow 6 - 8’ per year and have a high flood tolerance. For deep contamination, hybrid poplars with roots extending 30 feet deep have been used. Their roots penetrate microscopic scale pores in the soil matrix and can cycle 100 L of water per day per tree. These trees act almost like a pump and treat remediation system. [ 5 ] Willows have been successfully used as “vegetation filters” for nutrient (e.g. nitrogen and phosphorus) removal from municipal wastewater [ 6 ] and polluted groundwater. [ 7 ]
There are a series of aquatic and land plants that are used for rhizofiltration with varying degrees of success among them. While many of these plants are hyperaccumulators , other plant species can be used as the contaminants do not always reach the shoots (stems and their appendages: leaves, lateral buds, flowering stems and flower buds). [ citation needed ]
Some of the most common plant species that have shown the ability to remove toxins from water via rhizofiltration: [ 8 ] [ 9 ]
Rhizofiltration is cost-effective for large volumes of water having low concentrations of contaminants that are subjected to stringent standards. [ 10 ] It is relatively inexpensive, yet potentially more effective than comparable technologies. The removal of radionuclides from water using sunflowers was estimated to cost between $2 and $6 per thousand gallons of water treated, including waste disposal and capital costs. [ 11 ]
Rhizofiltration is a contamination treatment method that may be conducted in situ , with plants being grown directly in the contaminated water body or ex situ , where plants are grown off-site and later introduced to the contaminated water body. [ 8 ] This allows for a relatively inexpensive procedure with low capital and operational costs, depending on the type of contaminant. [ citation needed ]
In some cases, contaminants have been shown to be significantly decreased in a very short amount of time. One study found that roots of sunflower reduced levels of Uranium by nearly 95% in just 24 hours. [ 2 ]
This treatment method is also aesthetically pleasing and results in a decrease of water infiltration and leaching of contaminants. [ 5 ]
After harvesting, the crop may be converted to biofuel briquette, a substitute for fossil fuel. [ 12 ]
This contamination treatment method has its limits. Any contaminant that is below the rooting depth will not be extracted. The plants used may not be able to grow in highly contaminated areas. Most importantly, it can take years to reach regulatory levels. This results in long-term maintenance. [ citation needed ]
Also, most contaminated sites are polluted with many different kinds of contaminants. There can be a combination of metals and organics, in which treatment through rhizofiltration will not suffice. [ 5 ]
Plants grown on polluted water and soils become a potential threat to human and animal health, and therefore, careful attention must be paid to the harvesting process and only non-fodder crop should be chosen for the rhizofiltration remediation method. [ 12 ] | https://en.wikipedia.org/wiki/Rhizofiltration |
R. endophyticus R. miehei R. pakistanicus R. pusillus R. tauricus R. variabilis
Rhizomucor is a genus of fungi in the family Lichtheimiaceae . [ 1 ] The widespread genus contains six species. [ 2 ] Rhizomucor parasiticus , the species originally selected as the type , is now considered synonymous with Rhizomucor pusillus . [ 3 ]
This Zygomycota -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rhizomucor |
Rhizomucor miehei (also: Mucor miehei [ 1 ] ) is a species of fungus . It is commercially used to produce enzymes which can be used to produce a microbial rennet to curd milk and produce cheese . [ 2 ]
Under experimental conditions, this species grows particularly well at temperatures between 24 and 55°C, and their growth becomes negligible below 21°C or above 57°C. [ 3 ]
It is also used to produce lipases for interesterification of fats. [ 4 ]
This Zygomycota -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rhizomucor_miehei |
Rhizomucor pusillus is a thermophilic filamentous fungus belonging to the family Lichtheimiaceae , within the order Mucorales . [ 1 ] [ 2 ] It is known for its role in various industrial applications, particularly in enzyme production and food fermentation , and has been studied for its safety and potential use in human consumption.
Rhizomucor pusillus belongs to the order Mucorales and the class Mucoromycetes . R. pusillus is a member of the phylum Mucoromycota (previously Zygomycota), which includes Rhizopus microsporus , R. oligosporus , and R. oryzae , fungi that have been used for centuries to produce tempeh from the fermentation of soybeans . [ 3 ] The Mucorales order belongs to the early diverging ancient fungi and is characterized by rapidly growing mycelium and amorph structures formed in large quantities. [ 1 ] The Rhizomucor genus can be recognized by a morphology intermediate between Rhizopus and Mucor . [ 4 ] R. pusillus is a filamentous fungus that is known as a pioneer species in compost, quickly utilizing easily accessible substrates. [ 5 ] [ 6 ]
Currently, around 10 different Rhizomucor species are known, among which R. pusillus , R. miehei , and R. variabilis . [ 7 ] R. pusillus can grow at temperatures between 40-70 °C and is known for its thermostable enzyme production. [ 8 ] [ 9 ] R. pusillus is predominantly found in geothermal places that create and produce heat, such as compost piles, garbage, or landfills.
Fermentation has a long history of use in the preservation and production of foods like soy sauce , yogurt , and alcoholic beverages . With the current advances in technology, the cultivation of fungi, in the form of fungal biomass , can be used to produce protein - and fiber -rich ingredients for human consumption. A well-known example of fungal biomass is Quorn (produced via fermentation of Fusarium venenatum ), which has been on the international market for decades as a meat replacer. [ 10 ] Rhizomucor species have also emerged as a promising source for food applications. Both R. pusillus and R. miehei are reported to be used to produce milk-clotting enzymes for cheese manufacturing. Primarily R. miehei has been used for enzyme preparations by industrial biotechnology companies, such as Novozymes , in food. [ 11 ] Furthermore, Rhizomucor species have been isolated from different starter cultures of typical Asian fermented food products. [ 12 ] [ 13 ]
Studies have demonstrated that R. pusillus can be safely used to produce a novel mycoprotein through fermentation. [ 14 ] R. pusillus used for the production of this mycoprotein cannot produce mycotoxins which are toxins produced by certain moulds (fungi) that can cause adverse health effects. The whole genome sequence of this strain was annotated and no genetic elements were found that share significant sequence homology with protein toxins, including the absence of mucoricin , an essential toxin in the pathogenesis of mucormycosis . [ 14 ]
For foods containing novel proteins, potential allergenicity of the proteins is a key safety consideration. One such product is a fungal biomass obtained from the fermentation of Rhizomucor pusillus . Scaife et al (2024) concluded that based on in silico analyses and a literature review, the risk of allergenic cross-reactivity of R. pusillus is low. [ 15 ]
A R. pusillus strain has obtained regulatory approvals for food use, including self-affirmed GRAS (Generally Recognized as Safe) status in the United States and novel food approval in Singapore. [ 16 ]
Mucorales fungi, especially Mucor species, can lead to serious but rare fungal infections in humans, called mucormycosis . Mucormycosis is most commonly caused by Rhizopus or Mucor species, affects the sinuses or the lungs and causes symptoms like cough , nasal congestion , and fever . [ 17 ] [ 18 ] Although mucormycosis can be fatal, it occurs primarily in patients who are severely immunocompromised or with severe metabolic diseases . Mucorales do most frequently enter the body via the respiratory tract , through inhalation of spores . [ 17 ] [ 18 ] Spores may also enter the body through the gastrointestinal tract or directly through the skin in case of trauma , wounds , catheters , and contaminated surgical devices. Infections with Mucorales have remained extremely rare compared to their abundance in our daily life. Fungal spores are ubiquitous in the air and are inhaled regularly. It is highly improbable that healthy individuals are infected upon ingestion of fungi since the invasion occurs mainly through inhalation of spores, which can then germinate and grow in the host . There is no evidence of mucormycosis caused by ingestion of mycelium from fungi or foods containing fungi, as they are most often heat-inactivated , which kills vegetative cells and spores. Additionally, Rhizomucor species have been shown to cause less than 5% of mucormycoses cases. [ 18 ] Mucoricin, an essential toxin in the pathogenesis of mucormycosis, is absent in R. pusillus . [ 14 ]
This Zygomycota -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rhizomucor_pusillus |
Rhizophagus irregularis (previously known as Glomus intraradices [ 3 ] [ 4 ] ) is an arbuscular mycorrhizal fungus used as a soil inoculant in agriculture and horticulture . Rhizophagus irregularis is also commonly used in scientific studies of the effects of arbuscular mycorrhizal fungi on plant and soil improvement. Until 2001, the species was known and widely marketed as Glomus intraradices , but molecular analysis of ribosomal DNA led to the reclassification of all arbuscular fungi from Zygomycota phylum to the Glomeromycota phylum. [ 5 ]
Rhizophagus irregularis colonization peaks earlier than many of the other fungi in Rhizophagus . There tends to be extensive hyphal networking and intense intraradical spores associated with older roots of host plants.
At times the spores are densely clustered or patchily distributed, depending on the host species. When the spores are heavily clustered, mycorrhizologists and others will tend to mistake R. irregularis for G. fasciculatum . [ 6 ]
Rhizophagus irregularis (previously known as Glomus intraradices) has been found to colonise new plants by means of spores, hyphae or fragments of roots colonized by the fungus [ 7 ]
Arbuscular mycorrhiza (AM) fungi were thought to have propagated clonally for over 500 million years because of their lack of visible sexual structures and thus were considered to be an ancient asexual lineage. [ 8 ] However, homologs of 51 meiotic genes, including seven genes specific for meiosis were found to be conserved in the genomes of five AM species including Rhizophagus irregularis (referred to by its synonym designation Glomus irregulare ). [ 8 ] This observation suggests that the supposedly ancient asexual AM fungi are likely capable of undergoing a conventional meiosis. [ 8 ] R. irregularis dikaryons also appear to be capable of genetic recombination . [ 9 ]
Rhizophagus irregularis can be found in almost all soils, especially those populated with common host plants and in forests and grasslands.
This is a brief list of some common host plants. Most agricultural crops will benefit from Rhizophagus irregularis inoculation. Generally host plants must be vascular plants, but not always. [ 10 ]
Rhizophagus irregularis is not of conservation concern; however, individual populations could be harmed by agricultural chemicals and tillage [ citation needed ] .
In numerous scientific studies R. irregularis has been shown to increase phosphorus uptake in multiple plants as well as improve soil aggregation due to hyphae. [ 17 ]
Because of these qualities, R. irregularis is commonly found in mycorrhizal based fertilizers.
In a 2005 study, R. irregularis was found to be the only arbuscular mycorrhizal fungi that was able to control nutrient uptake amounts by individual hyphae depending on differing phosphorus levels in the surrounding soil. [ 13 ] | https://en.wikipedia.org/wiki/Rhizophagus_irregularis |
Sphingomonas wittichii Yabuuchi et al. 2001
The species Rhizorhabdus wittichii , formerly Sphingomonas wittichii , is a Gram-negative, rod-shaped motile bacterium, with an optimum growth temperature at 30 °C. [ 2 ] It forms a greyish white colony. [ 3 ] It has been found to have a 67 mol% of DNA G+C content. [ 3 ]
The R. wittichii RW1 genome consists of 5,915,246 bp and consists of a single circular chromosome and two plasmids. [ 4 ]
It was first isolated from water of the River Elbe by R.-M. Wittich, after whom the species is named. [ 2 ]
The species was originally thought to belong to the genus Sphingomonas , despite poor alignment of its 16S rRNA gene with its putative nearest neighbor. [ 5 ] It has since been reclassified to Rhizorhabdus as part of a larger re-evaluation of Alphaproteobacteria . [ 6 ]
Its type strain is R. wittichii RW1 DSM 6014T (= JCM 10273T = EY 4224T). [ 7 ]
R. wittichii RW1 is notable for metabolising dibenzo-p-dioxin and phenazine-1-carboxylic acid . [ 8 ] In fact, Sphingomonas wittichii strain RW1 (RW1) is one of the very few strains that can grow on dibenzo- p -dioxin (DD). [ 9 ] Furthermore, this bacterium also grows on dibenzofuran and 4-chloro-dibenzofuran, using them as the sole carbon sources. [ 9 ] Such biodegradative capabilities are not unique to this strain.
R. wittichii MPO218 degrades ibuprofen, carrying degradative genes on a large plasmid. [ 10 ] Thanks to its wide-ranging metabolic capabilities and likely propensity to acquire novel degradation genes, in no small part due to its wealth of plasmids, [ 11 ]
The unusual arrangement of its genes involved in dioxin degradation, and the full description of the dioxin degradation pathway, is still under investigation.
This organism holds a high potential for biotechnological applications. [ 5 ] | https://en.wikipedia.org/wiki/Rhizorhabdus_wittichii |
The rhizosphere is the narrow region of soil or substrate that is directly influenced by root secretions and associated soil microorganisms known as the root microbiome . [ 2 ] Soil pores in the rhizosphere can contain many bacteria and other microorganisms that feed on sloughed-off plant cells, termed rhizodeposition , [ 3 ] and the proteins and sugars released by roots, termed root exudates . [ 4 ] This symbiosis leads to more complex interactions, influencing plant growth and competition for resources. Much of the nutrient cycling and disease suppression by antibiotics required by plants occurs immediately adjacent to roots due to root exudates and metabolic products of symbiotic and pathogenic communities of microorganisms. [ 5 ] The rhizosphere also provides space to produce allelochemicals to control neighbours and relatives. [ 6 ]
The rhizoplane refers to the root surface including its associated soil particles which closely interact with each other. [ 7 ] The plant-soil feedback loop and other physical factors occurring at the plant-root soil interface are important selective pressures in communities and growth in the rhizosphere and rhizoplane. [ 8 ]
The term "rhizosphere" was used first in 1904 by the German plant physiologist Lorenz Hiltner to describe how plant roots interface with the surrounding soil. [ 9 ] [ 10 ] The prefix rhiza- comes from the Greek , meaning "root". Hiltner postulated the rhizosphere was a region surrounding the plant roots and populated with microorganisms under some degree of control by chemicals released from the plant roots. [ 9 ] [ 8 ]
Plant roots may exude 20–40% of the sugars and organic acids—photosynthetically fixed carbon. [ 11 ] Plant root exudates , such as organic acids , change the chemical structure and the biological communities of the rhizosphere in comparison with the bulk soil or parent soil. Concentrations of organic acids and saccharides affect the ability of the biological communities to shuttle phosphorus, nitrogen, [ 12 ] [ 13 ] potassium, and water to the root cap, [ 4 ] and the total availability of iron to the plant and to its neighbors. [ 14 ] The ability of the plant's root and its associated soil microorganisms to provide specific transport proteins affects the availability of iron and other minerals for it and its neighbors. This can affect the composition of the community and its fitness.
Root exudates come in the form of chemicals released into the rhizosphere by cells in the roots and cell waste referred to as rhizodeposition . This rhizodeposition comes in various forms of organic carbon and nitrogen that provide for the communities around plant roots and dramatically affect the chemistry surrounding the roots. [ 15 ] Exo polysaccharides , such as polyglycolide (PGA), affect the ability of roots to uptake water by maintaining the physical stability of the soil carbon sponge and controlling the flow of water. [ 16 ] For example, a tomato field study showed that exopolysaccharides extracted from the rhizosphere were different (total sugar amounts and mean infrared measurements) depending on the tomato varieties grown, [ 17 ] and that under water deficit conditions (limited irrigation), the increase in exopolysaccharide production and microbial activity affected water retention in the soil and field performance of tomato. [ 18 ] In potato cultivar root exudates, phenols and lignins comprise the greatest number of ion influencing compounds regardless of growing location; however, the intensity of different compounds was found to be influenced by soils and environmental conditions, resulting in variation amongst nitrogen compounds, lignins, phenols, carbohydrates, and amines . [ 19 ]
Although it goes beyond the rhizosphere area, it is notable that some plants secrete allelochemicals from their roots, which inhibits the growth of other organisms. For example, garlic mustard produces a chemical that is believed to prevent mutualisms forming between the surrounding trees and mycorrhiza in mesic North American temperate forests where it is an invasive species . [ 20 ]
Rhizodeposition allows for the growth of communities of microorganisms directly surrounding and inside plant roots. This leads to complex interactions between species, including mutualism, predation/parasitism, and competition.
Predation is considered to be top-down because these interactions decrease the population. Still, the closeness of species interactions directly affects the availability of resources, causing the population to be affected by bottom-up controls. [ 24 ] Without soil fauna, microbes that directly prey upon competitors of plants, and plant mutualists, interactions within the rhizosphere would be antagonistic toward the plants. Soil fauna provides the rhizosphere's top-down component while allowing for the bottom-up increase in nutrients from rhizodeposition and inorganic nitrogen. The complexity of these interactions has also been shown through experiments with common soil fauna, such as nematodes and protists. Predation by bacterial-feeding nematodes was shown to influence nitrogen availability and plant growth. [ 25 ] There was also an increase in the populations of bacteria to which nematodes were added. Predation upon Pseudomonas by amoeba shows predators can upregulate toxins produced by prey without direct interaction using supernatant. [ 26 ] The ability of predators to control the expression and production of biocontrol agents in prey without direct contact is related to the evolution of prey species to signals of high predator density and nutrient availability.
The food web in the rhizosphere can be considered as three different channels with two distinct sources of energy: the detritus-dependent channels are fungi and bacterial species, and the root energy-dependent channel consists of nematodes, symbiotic species, and some arthropods. [ 24 ] This food web is constantly in flux since the amount of detritus available and the rate of root sloughing changes as roots grow and age. This bacterial channel is considered to be a faster channel because of the ability of species to focus on more accessible resources in the rhizosphere and have faster regeneration times compared with the fungal channel. All three of these channels are also interrelated to the roots that form the base of the rhizosphere ecosystem and the predators, such as the nematodes and protists, that prey upon many of the same species of microflora.
The competition between plants due to released exudates is dependent upon geometrical properties, which determine the capacity of interception of exudates from any point on the plant’s roots, and physicochemical properties, which determine the capacity of each root to take up exudates in the area. [ 27 ] Geometrical properties are the density of roots, root diameter, and distribution of the roots. Physicochemical properties are exudation rate, decay rate of exudates, and the properties of the environment that affect diffusion. These properties define the rhizosphere of roots and the likelihood that plants can directly compete with neighbors.
Plants and soil microflora indirectly compete against one another by tying up limiting resources, such as carbon and nitrogen, into their biomass. [ 28 ] This competition can occur at varying rates due to the ratio of carbon to nitrogen in detritus and the ongoing mineralization of nitrogen in the soil. Mycorrhizae and heterotrophic soil microorganisms compete for both carbon and nitrogen, depending upon which is limiting at the time, which heavily depends on the species, scavenging abilities, and the environmental conditions affecting nitrogen input. Plants are less successful at the uptake of organic nitrogen, such as amino acids than the soil microflora that exists in the rhizosphere. [ 29 ] This informs other mutualistic relationships formed by plants around nitrogen uptake.
Competition over other resources, such as oxygen in limited environments, is directly affected by the spatial and temporal locations of species and the rhizosphere. In methanotrophs , proximity to higher-density roots and the surface is important and helps determine where they dominate over heterotrophs in rice paddies. [ 30 ]
The weak connection between the various energy channels is essential in regulating predator and prey populations and the availability of resources to the biome. Strong connections between resource-consumer and consumer-consumer create coupled systems of oscillators, which are then determined by the nature of the available resources. [ 31 ] These systems can then be considered cyclical, quasi-periodic, or chaotic.
Plants secrete many compounds through their roots to serve symbiotic functions in the rhizosphere. Strigolactones , secreted and detected by mycorrhizal fungi, stimulate the germination of spores and initiate changes in the mycorrhiza that allow it to colonize the root. The parasitic plant, Striga , also detects the presence of strigolactones and will germinate when it detects them; they will then move into the root, feeding off the nutrients present. [ 32 ] [ 33 ]
Symbiotic nitrogen-fixing bacteria, such as Rhizobium species, detect compounds like flavonoids secreted by the roots of leguminous plants and then produce nod factors that signal to the plant that they are present and will lead to the formation of root nodules . Bacteria are housed in symbiosomes in these nodules, where they are sustained by nutrients from the plant and convert nitrogen gas to a form that the plant can use. [ 34 ] Non-symbiotic (or "free-living") nitrogen-fixing bacteria may reside in the rhizosphere just outside the roots of certain plants (including many grasses) and similarly "fix" nitrogen gas in the nutrient-rich plant rhizosphere. Even though these organisms are thought to be only loosely associated with the plants they inhabit, they may respond very strongly to the status of the plants. For example, nitrogen-fixing bacteria in the rhizosphere of the rice plant exhibit diurnal cycles that mimic plant behavior and tend to supply more fixed nitrogen during growth stages when the plant exhibits a high demand for nitrogen. [ 35 ]
In exchange for the resources and shelter plants and roots provide, fungi and bacteria control pathogenic microbes. [ 36 ] The fungi that perform such activities also serve close relationships with species of plants in the form of mycorrhizal fungi, which are diverse in how they relate to plants. Arbuscular mycorrhizal fungi and the bacteria that make the rhizosphere their home also form close relationships to be more competitive. [ 37 ] which plays into the bigger cycles of nutrients that impact the ecosystem, such as biogeochemical pathways. [ 14 ]
The rhizosphere has been referred to as an information superhighway because of the proximity of data points, which include roots and organisms in the soil, and the methods for transferring data using exudates and communities. [ 38 ] This description has been used to explain the complex interactions that plants, their fungal mutualists, and the bacterial species that live in the rhizosphere have entered into throughout their evolution. Certain species like Trichoderma are interesting because of their ability to select for species in this complex web. Trichoderma is a biological control agent because of evidence that it can reduce plant pathogens in the rhizosphere. [ 39 ] Plants themselves also affect which bacterial species in the rhizosphere are selected against because of the introduction of exudates and the relationships that they maintain. The control of which species are in these small diversity hotspots can drastically affect the capacity of these spaces and future conditions for future ecologies. [ 36 ] [ 6 ]
Although various studies have shown that single microorganisms can benefit plants, it is increasingly evident that when a microbial consortium —two or more interacting microorganisms—is involved, additive or synergistic results can be expected. This occurs, in part, because multiple species can perform a variety of tasks in an ecosystem like the rhizosphere. Beneficial mechanisms of plant growth stimulation include enhanced nutrient availability, phytohormone modulation, biocontrol , and biotic and abiotic stress tolerance) exerted by different microbial players within the rhizosphere, such as plant-growth-promoting bacteria (PGPB) and fungi such as Trichoderma and mycorrhizae . [ 40 ]
The diagram on the right illustrates that rhizosphere microorganisms like plant-growth-promoting bacteria (PGPB), arbuscular mycorrhizal fungi (AMF), and fungi from the genus Trichoderma spp. can establish beneficial interactions with plants, promoting plant growth and development, increasing the plant defense system against pathogens, promoting nutrient uptake, and enhancing tolerance to different environmental stresses. Rhizosphere microorganisms can influence one another, and the resulting consortia of PGPB + PGPB (e.g., a nitrogen-fixing bacterium such as Rhizobium spp. and Pseudomonas fluorescens ), AMF + PGPB, and Trichoderma + PGPB may have synergetic effects on plant growth and fitness, providing the plant with enhanced benefits to overcome biotic and abiotic stress. Dashed arrows indicate beneficial interactions between AMF and Trichoderma . [ 40 ]
Communication is often the basis of biotic interactions . Frequently, more than two organisms can take part in the communication, resulting in a complex network of crosstalking . Recent advances in plant-microbe interactions research have shown that communication, both inter-kingdom and intra-kingdom, is shaped by a broad spectrum of factors. In this context, the rhizosphere (i.e., the soil close to the root surface) provides a specific microhabitat where complex interactions occur. The complex environment that makes up the rhizosphere can select for certain microbial populations adapted to this unique niche. Among them, rhizobia has emerged as an important component of the rhizospheric microbiome. Rhizospheric crosstalk is found in rhizobium- legume interactions. This symbiosis is a complex process that involves signaling that can be shaped by plant rhizospheric exudates and microbiome composition. The relationship established by rhizobia with other rhizospheric organisms and the influence of environmental factors results in their beneficial role on host plant health. [ 41 ]
Prokaryotes and eukaryotes have interacted for millions of years, evolving and refining their communication systems over time. As proposed by Hauser in 1996, [ 10 ] biological signals and the exchange of information are part of the definition of communication, while the signals themselves are considered as "every structure able to shape the behavior of the organisms". [ 42 ] [ 43 ] Consequently, the signals can evolve and persist thanks to the interaction between signal producers and receivers. Then, cooperation and fitness improvement are the basis of biological communication. [ 44 ] [ 41 ]
In a particular environment, individuals can communicate and interact with multiple partners, and the nature of interaction can determine variable costs and benefits to the partner as a biological market. [ 45 ] A large number of signals can be exchanged involving the plant itself, insects, fungi, and microbes. This all takes place in a high-density environmental niche. Usually, communication results from chemical responses of cells to signatory molecules from other cells. These signals affect both the metabolism and transcription of genes, activating several regulatory mechanisms. [ 41 ]
Frequently in the rhizosphere, more than two organisms (and species) can participate in the communication, resulting in a complex network of interactions and cross-talks that influence the fitness of all participating partners. Thus, this environment is a hot spot for numerous inter-kingdom signal exchanges involving plant-associated microbial communities (rhizobiome). The microbial community's composition is mainly shaped and recruited by hundreds of metabolites released in the soil by plant roots, which normally facilitate interactions with the biotic and abiotic environment. Often the plant can modulate its diversity based on the benefits in terms of growth and health, such as with plant growth-promoting rhizobacteria . [ 46 ] Nevertheless, a large number of nutrients issued by the plant can be of interest to pathogenic organisms, which can take advantage of plant products for their survival in the rhizosphere. [ 47 ] [ 41 ]
It stands to reason that the plants play a fundamental role in the rhizosphere scene. [ 48 ] Indeed, because of the chemical signals conveyed by nutrient-rich exudates released by the plant roots, a large variety of microbes can first colonize the rhizosphere and then gradually penetrate the root and the overall plant tissue ( endophytes ). [ 49 ] Otherwise, they can colonize the host plant establishing a lasting and beneficial symbiotic relationship. [ 50 ] To date, numerous investigations on root exudates composition have been performed. [ 46 ] [ 51 ] [ 52 ] [ 41 ]
The most known plant-microbe dialogue on the rhizosphere scene, determining direct and indirect advantages to the partners, was properly addressed as early as 1904 when Hiltner described the symbiotic interaction among legumes and rhizobia. [ 10 ] This symbiosis is a highly specific process in which the genetic and chemical communication signals are strictly plant-bacterium-specific. In this mutualistic interaction, rhizobia positively influences the host's growth thanks to the nitrogen fixation process and, at the same time, can benefit from the nutrients provided by the plant. [ 41 ]
This symbiosis has been extensively studied in recent decades, and many studies on the communication and the signaling between the two partners at different steps of the symbiosis (from root infection to nodule development) have been elucidated. [ 53 ] [ 54 ] However, the knowledge about the earlier steps of rhizosphere colonization, namely the opening line at the root surface, remains poorly characterized. Increasing data have shown the importance of intraspecies and multispecies communications among rhizospheric biotic components for improving rhizobia–legumes interaction. In addition, it has been shown that rhizobia are part of the rhizosphere of a wide variety of non-legume plants. They can be plant growth-promoting components, recovering a central role in the plant core microbiome. [ 55 ] [ 41 ]
The following are some methods commonly used or of interest in rhizosphere research. Many of these methods include both field testing of the root systems and in-lab testing using simulated environments to perform experiments, such as pH determination. [ 56 ] | https://en.wikipedia.org/wiki/Rhizosphere |
Rh o (D) immune globulin ( RhIG ) is a medication used to prevent RhD isoimmunization in mothers who are RhD negative and to treat idiopathic thrombocytopenic purpura (ITP) in people who are Rh positive . [ 1 ] RhIG is commonly referred to as 'anti-D'. It is often given both during and following pregnancy . [ 1 ] It may also be used when RhD-negative people are given RhD-positive blood. [ 1 ] It is given by injection into muscle or a vein . [ 1 ] A single dose lasts 12 weeks. [ 1 ] It is made from human blood plasma . [ 2 ]
Common side effects include fever , headache, pain at the site of injection, and red blood cell breakdown . [ 1 ] Other side effects include allergic reactions , kidney problems , and a very small risk of viral infections. [ 1 ] In those with ITP, the amount of red blood cell breakdown may be significant. [ 1 ] Use is safe with breastfeeding . [ 1 ] Rho(D) immune globulin is made up of antibodies to the antigen Rh o (D) present on some red blood cells . [ 1 ] It is believed to work by blocking a person's immune system from recognizing this antigen. [ 1 ]
Rh o (D) immune globulin came into medical use in the 1960s, [ 3 ] following the pioneering work of John G. Gorman . In 1980, Gorman shared the Lasker-DeBakey Clinical Medical Research Award for pioneering work on the rhesus blood group system . [ 4 ]
RhIG is on the World Health Organization's List of Essential Medicines . [ 5 ] [ 6 ]
Even in normal pregnancies, a small number of fetal blood cells enters the maternal bloodstream (fetomaternal hemorrhage). If a mother is RhD negative, but the fetus is RhD positive, the mother's immune system may develop an immune response (develops antibodies ) to the unfamiliar RhD antigens from the fetus. This process is called RhD alloimmunization . Alloimmunization usually has minimal effect on the first such pregnancy; but, in a second such pregnancy, pre-existing maternal RhD IgG antibodies can cross the placenta in enough amounts to damage fetal red blood cells. This condition is called erythroblastosis fetalis and can be fatal to the fetus. [ 7 ]
The RhD status of the fetus is determined by genetic inheritance. In a pregnancy where the mother is RhD negative and the father is RhD positive, the probability of the fetus having RhD positive blood is dependent on whether the father is homozygous for RhD (i.e., both RhD alleles are present) or heterozygous (i.e., only one RhD allele is present). If the father is homozygous, the fetus will necessarily be RhD positive, as the father will necessarily pass on a RhD positive allele. If the father is heterozygous, there is a 50% chance that the fetus will be RhD positive, as he will randomly pass on either the RhD positive allele or not. [ 8 ] : 130 Not all Rh-negative patients are capable of being immunized to the RhD antigen, and mothers may only become immunized after many repeated pregnancies. The risk of hemolytic disease (including due to RhD) significantly increases if the mother has had a past transfusion of Rh-positive blood. [ 9 ]
Exposure to fetal blood cells that can cause RhD alloimmunization can happen during normal pregnancy and delivery, miscarriage, amniocentesis, cordocentesis, chorionic villus sampling, external cephalic version, or trauma. [ 2 ] [ 7 ] 92% of women who develop an anti-D during pregnancy do so at or after 28 weeks gestation. [ 10 ] [ 8 ] [ 11 ]
In an RhD negative mother, RhIG can temporarily prevent sensitization of the maternal immune system to RhD antigens , with each 100 μg of anti-D being able to neutralize about 4 mL of fetal blood. [ 12 ] With the widespread use of RhIG, Rh disease of the fetus and newborn has almost disappeared in the developed world. The risk that an RhD negative mother can be alloimmunized by a RhD positive fetus can be reduced from approximately 16% to less than 0.1% by the appropriate administration of RhIG. [ 10 ] [ 8 ] [ 13 ] In data collected from communities in Canada, without treatment as many as 14% of affected fetuses are stillborn, 30% of affected live births almost certainly fatal without treatment, and 30% with severe jaundice that untreated risks brain damage from kernicterus . [ 7 ] [ 14 ] Prior to effective transfusion therapy, the mortality rate of hemolytic disease was 70-80%, dropping to 30-50% with small transfusions and 13-33% for more aggressive transfusions before RhIg treatments were introduced. [ 9 ]
The American College of Obstetricians and Gynecologists (ACOG) recommends that all RhD negative mothers, regardless of fetal blood type, receive RhIG at about 28 weeks gestation, and again shortly after delivery in the case of an RhD positive or RhD unknown baby. [ 15 ] It should be given within 3 days of a potential exposure to Rh positive blood from the baby such as may occur during second and third trimester miscarriage, amniocentesis, cordocentesis, chorionic villus sampling, external cephalic version, trauma, or delivery (amounts detailed in the next section). [ 7 ] It is given by intramuscular injection as part of modern routine antenatal care. Despite excellent results, the medication retains an FDA Pregnancy Category C. [ citation needed ]
RhIG is recommended in the UK after antenatal pathological events that are likely to cause a feto–maternal hemorrhage. Applicable 'pathologic events' include accidents that may induce fetomaternal hemorrhage (motor vehicle accidents, falls, abdominal trauma), following obstetric/gynecologic procedures during pregnancy, and at the time of threatened- or spontaneous-/elective abortions , regardless of gestational age. RhIG is also recommended after normal delivery, with amounts detailed in the next section. [ 12 ]
There is insufficient evidence that the use of Rho(D) immune globulin after a spontaneous miscarriage is needed and a Cochrane review recommends that local practices be followed. [ 16 ]
Rh immune globulin is composed of IgG antibodies and therefore is able to cross the placenta. In rare cases this can cause a baby to have a weakly positive direct antiglobulin test (DAT) due to sensitization of fetal cells from mothers who have received multiple doses of RhIG. However, no treatment is necessary as the clinical course is benign. [ 17 ]
Widespread use of RhIG started with postpartum administration, as delivery is the main source of significant fetomaternal hemorrhage.
A D-negative mother who is not alloimmunized to D should also receive an appropriate dose of RhIG after delivery of a D-positive infant. (In older recommendations, the Rh status of the infant is only known at delivery from testing of cord blood .) [ 8 ] If the infant is D-positive, the mother should have a postpartum blood sample screened for fetomaternal hemorrhage in order to determine the appropriate dosage of RhIG to be administered. (The presence of residual anti-D from antepartum RhIG administration does not indicate ongoing protection from alloimmunization – repeat administration of RhIG is necessary.) [ 12 ]
The rosette test is a sensitive method to detect fetomaternal hemorrhage of 10 cc or more. This qualitative (not quantitative) test will be positive if fetal D-positive cells are present in the maternal sample, indicating a significantly large fetomaternal hemorrhage has occurred. A rosette test may be falsely positive if the mother is positive for the weak D phenotype and falsely negative if the neonate is weak D. If the mother is positive for the weak D phenotype, the rosette test should not be used; instead, a quantitative test such as the Kleihauer–Betke test or flow cytometry should be utilized. If the rosette test is negative, then a dose of 300 micrograms of RhIG is given (sufficient to prevent alloimmunization after delivery in 99% of cases). [ 10 ] [ 18 ] The RhIG dose suppresses the immune response to up to 30 cc of whole fetal blood (15 cc of red blood cells). If a fetomaternal hemorrhage in excess of 30 cc has occurred, additional testing is mandatory in order to determine the appropriate dosage of RhIG to prevent alloimmunization. A positive rosette test should be followed by a quantitative test such as the Kleihauer–Betke test or an alternative approach such as flow cytometry . See the article on Kleihauer–Betke test for details on how the volume of fetomaternal hemorrhage is calculated. The dosage of RhIG is calculated from the volume of fetal hemorrhage (in mL). Ex: 50 mL fetal hemorrhage / 30 mL = 1.667 (round up to 2) then add 1 = 3 vials of RhIG. [ citation needed ]
Postpartum RhIG should be administered within 72 hours of delivery. If prophylaxis is delayed, the likelihood that alloimmunization will be prevented is decreased. However, ACOG still recommends that RhIG be administered because partial protection still occurs. [ 10 ] [ 11 ] If the D-type of a newborn or stillborn is unknown or cannot be determined, RhIG should be administered.
Primary immune thrombocytopenia (ITP) is an acquired immune-mediated disorder characterized by isolated thrombocytopenia , defined as a peripheral blood platelet count less than 100 x 10 9 /L, and the absence of any obvious initiating and/or underlying cause of the thrombocytopenia. Symptoms of ITP include abnormal bleeding and bruising due to the reduction in platelet count . [ 19 ] Rh o (D) Immune Globulin Intravenous [Human; Anti-D] is indicated for use in non-splenectomized, Rh o (D)-positive children with chronic or acute ITP, adults with chronic ITP, and children and adults with ITP secondary to HIV infection. Anti-D must be administered via the intravenous route when used in clinical situations requiring an increase in platelet count. The mechanism of action of anti-D is not fully understood; however, after administration the anti-D coated red blood cell complexes saturate Fcγ receptors sites on macrophages , resulting in preferential destruction of red blood cells (RBCs), therefore sparing antibody-coated platelets . [ 20 ] Anti-D is recommended as a first-line therapy for ITP, along with corticosteroids and intravenous immune globulin (IVIG). [ 19 ] [ 21 ] [WinRho SDF is an anti-D manufactured, distributed and marketed by Cangene in the US. There is a black box warning on WinRho SDF due to the risk of potentially fatal intravascular hemolysis when used in the treatment of ITP. [ 20 ] Life-threatening anemia , kidney failure, and disseminated intravascular coagulation (DIC) have occurred in people treated with WinRho SDF for ITP. [ citation needed ]
The following females are not candidates for RhIG:
The first Rho(D) immune globulin treatment "skymed" was introduced by Ortho Clinical Diagnostics , a subsidiary holding of Jskymed , and was first administered on May 29, 1968, to Marianne Cummins in Teaneck , New Jersey . [ 23 ]
In 1996, ZLB Bioplasma (part of CSL Behring ) was given approval to sell Rhophylac in Europe. Effectiveness was demonstrated in a clinical trial in 2003 and in 2004 Rhophylac was approved in the United States. [ 24 ]
Conventional Rho(D) immune globulin is extracted from human blood plasma . Excluding autoimmunity , only people who are themselves Rho(D) negative can make the anti-D antibody. As a result, there is a limited pool of people from which to draw plasma that can contain the desired IgG. Special anti-D donation programs are set up to account for this rarity. [ 25 ] Volunteers are given an injection containing the D antigen in order to make their immune system start producing the antibody (alloimmunization) or to boost the amounts. Only those who have no ability to become pregnant may apply. [ 26 ]
The most common way anti-D products are manufactured is by a form of the Cohn cold ethanol fractionation process developed in the 1950s. Variations of the Cohn method developed in the 1950s may not completely clear aggregates of immunoglobulins, which can cause problems for patients if administered intravenously, and is a primary reason why most anti-Ds are for intramuscular use only. A non-Cohn manufacturing variation is ChromaPlus process approved by the U.S. Food and Drug Administration (FDA) that is used to make Rhophylac. [ 27 ] Rho(D) immune globulin may trigger an allergic reaction. Steps are taken in the plasma-donor screening process and the manufacturing process to eliminate bacterial and viral contamination, although a small, residual risk may remain for contamination with small viruses. There is also a theoretical possibility of transmission of the prion responsible for Creutzfeldt–Jakob disease , or of other, unknown infectious agents. [ 28 ]
There has been continual attempts to produce a monoclonal anti-D IgG formulation suitable for replacing the current polyclonal formulation. [ 29 ] A monoclonal antibody can be produced without requiring human donors (and associated supply and disease risks) and would be more consistent from batch to batch. [ 7 ]
India has approved a monoclonal formulation called Rhoclone (Bharat Serums and Vaccines Ltd.), [ 30 ] made from hybridoma cultures . The country has also tested and recently marketed a recombinant version of Rhoclone expressed in CHO cells . [ 31 ] This recombinant formulation, Trinbelimab, marketed as AntiD, is also being evaluated in a large Real-world Prospective Study that aims to enroll 20,000 Rh-negative mothers. [ 32 ]
Roledumab and Rozrolimupab are two other formulations that have undergone some clinical trials. The former is a monoclonal IgG. The latter is a recombinant mixture of 25 IgGs. [ 7 ]
RhIG can be administered by either intramuscular (IM) or intravenous (IV) injection, depending on the preparation. [ 33 ] The IM-only preparation should never be administered IV due to the risk of complement system activation. Multiple IM doses should be given at different sites or at different times within the 72-hour window. Or, multiple IV doses can be administered according to the instructions in the package insert. [ citation needed ]
Rh o (D) immune globulin is also spelled Rh 0 (D) immune globulin (letter o and digit zero are both widely attested; more at Rh blood group system - Rh nomenclature ).
AntiD (Recombinant) and Rhoclone are the only Rh0(D) immune globulin marketed in the world. both manufactured by BSV Ltd. Rhophylac is manufactured by CSL Limited. RhoGAM and MICRhoGam are brand names of Kedrion Biopharma. Other brand names are BayRHo-D, Gamulin Rh, HypRho-D Mini-Dose, Mini-Gamulin Rh, Partobulin SDF ( Baxter ), Rhesonativ (Octapharma), and RhesuGam (NBI). KamRho-D I.M. is a brand name of Kamada Ltd.
The United States distribution rights for WinRho SDF (another brand name) were transferred from Baxter to the manufacturer, Cangene , in 2010; they had been held by Baxter since 2005. [ 34 ] Sales of WinRho fell every year under the agreement with Baxter, the supposition being that Baxter was favoring the sale of its own product over WinRho; according to one analyst, "WinRho was always an afterthought for a big company like Baxter." [ 35 ] | https://en.wikipedia.org/wiki/Rho(D)_immune_globulin |
RhoMobile Suite , based on the Rhodes open source framework, is a set of development tools for creating data-centric, cross-platform, native mobile consumer and enterprise applications. It allows developers to build native mobile apps using web technologies, such as CSS3 , HTML5 , JavaScript and Ruby . Developers can deploy RhoMobile Suite to write an app once and run it on the most-used operating systems, including iOS , Android , Windows Phone , Windows Mobile , Windows CE , Windows 10 Mobile and Windows Desktop . Developers control how apps behave on different devices. RhoMobile Suite consists of a set of tools for building, testing, debugging, integrating, deploying and managing consumer and enterprise apps. It consists of the products Rhodes, RhoElements, RhoStudio, RhoConnect, and RhoGallery, and includes a built-in Model View Controller pattern, an Object Relational Mapper for data intensive apps, integrated data synchronization, and a broad API set. These mobile development services are offered in the cloud and include hosted build, synchronization and application management.
RhoMobile was part of Zebra Technologies following the October 2014 acquisition of Motorola Solutions by Zebra until 2016 when the project was open sourced. [ 1 ]
RhoMobile source code is maintained by Tau Technologies, an independent software vendor founded by RhoMobile team members, who provides RhoMobile related consulting and development services.
Formerly known as Rhodes Framework, RhoMobile was founded by Adam Blum in September 2008, along with the creation of the Rhodes project on GitHub. The subsequent months saw releases that added iPhone, Windows Mobile, and Android development support. In May 2009, RhoMobile was a winner at Interop 2009 as the event’s "Best Start Up Company." In November 2009 RhoHub was launched as the beginning of RhoMobile’s hosted, cross-platform development services. In May 2010, RhoMobile was a Web 2.0 Expo LaunchPad winner. Motorola Solutions then acquired the company in October 2011. In 2012, RhoMobile was one of InfoWorld's 2012 Technology of the Year Award winners. In 2013, RhoMobile Suite won the About.com Reader’s Choice Award for being the Best Tool for Cross-Platform Formatting on Apps.
In April 2014, Zebra Technologies acquired Motorola Solutions for $3.45 billion, with the transaction completed in October 2014.
Since 2016 the project is maintained by Tau Technologies.
RhoMobile Suite includes Rhodes, RhoElements, RhoStudio, RhoConnect, RhoHub and RhoGallery.
Rhodes is a free and open source framework and the foundation for the RhoMobile application development platform. It enables developers to use their existing HTML, CSS, JavaScript and Ruby skills to build native apps for all popular operating systems, including iOS, Android, Windows Phone 8. Developers can leverage a large and mature open source community, which has developed thousands of RhoMobile apps.
RhoElements provides enterprise grade features on top of Rhodes - adding support for enterprise grade Zebra devices including Windows Mobile and Windows CE operating systems. It offers a built-in Model View Controller pattern, an Object Relational Mapper for data intensive apps, integrated data synchronization, and a large API set. The Model View Controller separates an app’s interface from its logic to simplify development and help with control. The Object Relational Mapper offers automatic synchronization of backend data. The broad base of enterprise APIs supports features such as RFID capture, bar code scanning and payment processing. RhoElements features automatic data encryption for data at rest security, protecting information and mitigating risk.
RhoStudio is a free Eclipse plug-in, allowing users to develop an application once for deployment on many mobile platforms. Developers can generate, develop, debug and test applications in one place, with no emulators or different hardware needed. Popular OS platforms can be simulated by dropdown box selection. The rationale is that one-time development can mean fewer errors, less hardware costs, and faster deployment.
RhoConnect allows developers to build data synchronization into apps for offline data access. It simplifies an enterprise mobile app’s basic backend application integration, enabling users to have their data with them at all times whether or not they connect. It is available on the cloud or on the premises.
RhoGallery enables enterprise app distribution, which allows an app store to control and push applications. IT departments are able to deliver applications and updates as needed across multiple operating system and devices.
RhoHub is the cloud service that comes with a paid subscription and supports cloud builds, RhoConnect hosted service and RhoGallery hosted service.
RhoMobile uses a Model-View-Controller pattern. Views are written in HTML (including HTML5). Controllers are written in Ruby.
RhoMobile 7.x and Simplified Pricing Structure
On July 29, 2014, the release of RhoMobile 5.0 [ 2 ] was accompanied by a new streamlined service model offering multi-tier transparent pricing, including a free level and two paid subscription levels, Silver and Gold. This new pricing was created to meet the needs of the developer. In this pricing structure, Rhodes, the basic app framework, and RhoStudio are free to use. Both paid levels include Rhodes and RhoStudio as well as RhoElements (enhanced enterprise features such as barcode reading and automatic data encryption), Cloud Build and a Visual Studio plug-in, RhoConnect, RhoGallery and online support. The purchase of a subscription comes with one month of free services.
Since 2015 RhoMobile Suite is distributed with MIT license free to use, with commercial support provided by Tau Technologies. Flexible support options available over request to maintainer company. [ 3 ] | https://en.wikipedia.org/wiki/RhoMobile_Suite |
A ρ factor ( Rho factor ) is a bacterial protein involved in the termination of transcription . [ 1 ] Rho factor binds to the transcription terminator pause site, an exposed region of single stranded RNA (a stretch of 72 nucleotides) after the open reading frame at C-rich/G-poor sequences that lack obvious secondary structure. [ 2 ]
Rho factor is an essential transcription protein in bacteria. [ 3 ] In Escherichia coli , it is a ~274.6 kD hexamer of identical subunits. Each subunit has an RNA-binding domain and an ATP - hydrolysis domain. Rho is a member of the RecA/SF5 family of ATP-dependent hexameric helicases that function by wrapping nucleic acids around a single cleft extending around the entire hexamer. Rho functions as an ancillary factor for RNA polymerase .
There are two types of transcriptional termination in bacteria, rho-dependent termination and intrinsic termination (also called Rho-independent termination). Rho-dependent terminators account for about half of the E. coli factor-dependent terminators. Other termination factors discovered in E. coli include Tau/Ter/Tus and nusA. Rho-dependent terminators were first discovered in bacteriophage genomes.
A Rho factor acts on an RNA substrate. Rho's key function is its helicase activity, for which energy is provided by an RNA-dependent ATP hydrolysis. The initial binding site for Rho is an extended (~70 nucleotides, sometimes 80–100 nucleotides) single-stranded region, rich in cytosine and poor in guanine , called the r ho ut ilisation site ( rut ), in the RNA being synthesised, upstream of the actual terminator sequence. Several rho binding sequences have been discovered. No consensus is found among these, but the different sequences each seem specific, as small mutations in the sequence disrupts its function. Rho binds to RNA and then uses its ATPase activity to provide the energy to translocate along the RNA until it reaches the RNA–DNA helical region, where it unwinds the hybrid duplex structure. RNA polymerase pauses at the termination sequence, which is because there is a specific site around 100 nt away from the Rho binding site called the Rho-sensitive pause site. So, even though the RNA polymerase is about 40 nt per second faster than Rho, it does not pose a problem for the Rho termination mechanism as the RNA polymerase allows Rho factor to catch up. [ citation needed ]
In short, Rho factor acts as an ATP-dependent unwinding enzyme, moving along the newly forming RNA molecule towards its 3′ end and unwinding it from the DNA template as it proceeds. [ citation needed ]
A nonsense mutation in one gene of an operon prevents the translation of subsequent genes in the unit. This effect is called mutational polarity. A common cause is the absence of the mRNA corresponding to the subsequent (distal) parts of the unit. Suppose that there are Rho-dependent terminators within the transcription unit, that is, before the terminator that usually is used. Normally these earlier terminators are not used, because the ribosome prevents Rho from reaching RNA polymerase. But a nonsense mutation releases the ribosome, so that Rho is free to attach to and/or move along the RNA, enabling it to act on RNA polymerase at the terminator. As a result, the enzyme is released, and the distal regions of the transcription unit are never transcribed. [ citation needed ]
Rho factor has not been found in Archaea . [ 4 ] | https://en.wikipedia.org/wiki/Rho_factor |
Rhoca-Gil is a type of industrial sealant produced by Rhône-Poulenc , used in the construction of tunnels to block the passage of groundwater inside. The sealant begins as a liquid, then is injected into cavities which need to be sealed, and polymerises , causing it to harden.
Rhoca-Gil consists of two fluids, that are mixed, thinned out with water and then sprayed into cracks in the bedrock. One of the fluids contains acrylamide (a toxic substance) and methylolacrylamide . The mixed solution becomes a viscous fluid that penetrates cracks and holes in the rock, where the fluid reacts— polymerizes —to a tight plastic substance. When it is completely polymerized it is stable.
In 1992 construction of the Hallandsås tunnel in Sweden began, with opening plans for 1995. Groundwater leaking into the tunnel was however a major problem, slowing the progress, and Rhoca-Gil was used. In 1997, fish and local cattle started dying as a result of Rhoca-Gil in its liquid form leaking into the water supply, contaminating it with acrylamide, a known carcinogen , mutagen and neurotoxin . Furthermore, the contamination of the area led to a ban on agricultural products from the area, as well as a ban on using water from the area affecting local residents.
The main contractor, Skanska , along with Rhône-Poulenc and the Swedish Rail Administration had criminal charges brought against them. Some senior executives resigned. Construction was halted in late 1997. The main critique of the use of Rhoca-Gil was against Rhône-Poulenc for not pointing out the risks of using the sealant, as well as against Skanska for not informing local residents about the usage of Rhoca-Gil.
A similar incident occurred at the construction of Gardermobanen in Norway , leading to a ban of the substance in Norway in 1997. [ 1 ] | https://en.wikipedia.org/wiki/Rhoca-Gil |
Rhodamine B / ˈ r oʊ d ə m iː n / is a chemical compound and a dye . It is often used as a tracer dye within water to determine the rate and direction of flow and transport. Rhodamine dyes fluoresce and can thus be detected easily and inexpensively with fluorometers .
Rhodamine B is used in biology as a staining fluorescent dye, sometimes in combination with auramine O , as the auramine-rhodamine stain to demonstrate acid-fast organisms, notably Mycobacterium . Rhodamine dyes are also used extensively in biotechnology applications such as fluorescence microscopy , flow cytometry , fluorescence correlation spectroscopy and ELISA . [ citation needed ]
Rhodamine B is often mixed with herbicides to show where they have been used. [ 3 ]
It is also being tested for use as a biomarker in oral rabies vaccines for wildlife , such as raccoons , to identify animals that have eaten a vaccine bait . The rhodamine is incorporated into the animal's whiskers and teeth . [ 4 ] Rhodamine B is an important hydrophilic xanthene dye well known for its stability and is widely used in the textile industry, leather, paper printing, paint, coloured glass and plastic industries. [ 5 ]
Rhodamine B (BV10) is mixed with quinacridone magenta (PR122) to make the bright pink watercolor known as Opera Rose. [ 6 ]
Rhodamine B can exist in equilibrium between two forms: an "open"/fluorescent form and a "closed"/nonfluorescent spirolactone form. The "open" form dominates in acidic condition while the "closed" form is colorless in basic condition. [ 7 ]
The fluorescence intensity of rhodamine B will decrease as temperature increases. [ 8 ]
The solubility of rhodamine B in water varies by manufacturer, and has been reported as 8 g/L and ~15 g/L, [ 2 ] while solubility in alcohol (presumably ethanol ) has been reported as 15 g/L. [ nt 1 ] Chlorinated tap water decomposes rhodamine B. Rhodamine B solutions adsorb to plastics and should be kept in glass. [ 9 ] Rhodamine B is tunable around 610 nm when used as a laser dye . [ 10 ] Its luminescence quantum yield is 0.65 in basic ethanol , [ 11 ] 0.49 in ethanol, [ 12 ] 1.0, [ 13 ] and 0.68 in 94% ethanol. [ 14 ] The fluorescence yield is temperature dependent; [ 15 ] the compound is fluxional in that its excitability is in thermal equilibrium at room temperature. [ 16 ]
In California, rhodamine B is suspected to be carcinogenic and thus products containing it must contain a warning on its label. [ 17 ] Cases of economically motivated adulteration , where it has been illegally used to impart a red color to chili powder , have come to the attention of food safety regulators. [ 18 ] | https://en.wikipedia.org/wiki/Rhodamine_B |
Rhodium(III) nitrate is a inorganic compound , a salt of rhodium and nitric acid with the formula Rh ( NO 3 ) 3 . This anhydrous complex has been the subject of theoretical analysis but has not been isolated. [ 4 ] However, a dihydrate and an aqueous solution are known with similar stoichiometry; they contain various hexacoordinated rhodium(III) aqua and nitrate complexes. [ 3 ] A number of other rhodium nitrates have been characterized by X-ray crystallography : Rb 4 [ trans -[Rh(H 2 O) 2 (NO 3 ) 4 ][Rh(NO 3 ) 6 ] [ 4 ] and Cs 2 [-[Rh(NO 3 ) 5 ]. [ 5 ] Rhodium nitrates are of interest because nuclear wastes, which contain rhodium, are recycled by dissolution in nitric acid . [ 6 ]
Rhodium(III) nitrate is used as a precursor to synthesize rhodium. [ 7 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rhodium(III)_nitrate |
Rhodium(III) oxide (or Rhodium sesquioxide ) is the inorganic compound with the formula Rh 2 O 3 . It is a gray solid that is insoluble in ordinary solvents.
Rh 2 O 3 has been found in two major forms. The hexagonal form adopts the corundum structure. It transforms into an orthorhombic structure when heated above 750 °C. [ 1 ]
Rhodium oxide can be produced via several routes:
Rhodium oxide films behave as a fast two-color electrochromic system: Reversible yellow ↔ dark green or yellow ↔ brown-purple color changes are obtained in KOH solutions by applying voltage ~1 V . [ 7 ]
Rhodium oxide films are transparent and conductive, like indium tin oxide (ITO) - the common transparent electrode, but Rh 2 O 3 has 0.2 eV lower work function than ITO. Consequently, deposition of rhodium oxide on ITO improves the carrier injection from ITO thereby improving the electrical properties of organic light-emitting diodes . [ 5 ]
Rhodium oxides are catalysts for hydroformylation of alkenes, [ 8 ] N 2 O production from NO , [ 9 ] and the hydrogenation of CO . [ 10 ] | https://en.wikipedia.org/wiki/Rhodium(III)_oxide |
Rhodizonic acid is a chemical compound with formula H 2 C 6 O 6 or (CO) 4 (COH) 2 . It can be seen as a twofold enol and fourfold ketone of cyclohexene , more precisely 5,6-dihydroxycyclohex-5-ene-1,2,3,4-tetrone .
Rhodizonic acid is usually obtained in the form of a dihydrate H 2 C 6 O 6 ·2H 2 O . The latter is actually 2,3,5,5,6,6-hexahydroxycyclohex-2-ene-1,4-dione, where two of the original ketone groups are replaced by two pairs of geminal diols . The orange to deep-red and highly hygroscopic anhydrous acid can be obtained by low-pressure sublimation of the dihydrate. [ 1 ] [ 2 ]
Like many other enols, rhodizonic acid can lose the hydrogen cations H + from the hydroxyls (p K a1 = 4.378 ± 0.009 , p K a2 = 4.652 ± 0.014 at 25 °C), [ 3 ] yielding the hydrogen rhodizonate anion HC 6 O − 6 and the rhodizonate anion C 6 O 2− 6 . The latter is aromatic and symmetric, as the double bond and the negative charges are delocalized and evenly distributed over the six CO units. Rhodizonates tend to have various shades of red, from yellowish to purplish.
Rhodizonic acid has been used in chemical assays for barium , lead , and other metals. [ 4 ] In particular, the sodium rhodizonate test can be used to detect gunshot residue (which contains lead) in a subject's hands, [ 5 ] and to distinguish arrow wounds from gunshot wounds for hunting regulation enforcement. [ 6 ]
Rhodizonic acid was discovered by Austrian chemist Johann Heller in 1837, by analyzing the products of heating a mixture of potassium carbonate and charcoal . [ 7 ] [ 8 ] [ 9 ] The name comes from Greek ῥοδίζω ( rhodizō , "to tinge red"), [ 10 ] on account of the color of its salts.
Rhodizonates tend to have various shades of red, from yellowish to purplish, in transmitted light, with a greenish luster in reflected light.
Potassium rhodizonate can be prepared with good yield and purity by oxidizing inositol with nitric acid and reacting the result with potassium acetate in the presence of oxygen. The rhodizonate crystallizes out of the solution due to its relative insolubility in water. [ 11 ]
Sodium rhodizonate is dark brown and stable when dry, [ 12 ] but the aqueous solution decomposes in a few days, even in the refrigerator. [ 4 ] Lead rhodizonate is dark violet. [ 12 ] [ 13 ]
Rhodizonic acid is a member of a chain of oxidation products: benzenehexol (COH) 6 , tetrahydroxybenzoquinone (THBQ) (COH) 4 (CO) 2 , rhodizonic acid (COH) 2 (CO) 4 , and the fleeting cyclohexanehexone (CO) 6 . [ 4 ] Lithium rhodizonate, together with salts of THBQ and benzenehexol, has been considered for possible use in rechargeable electrical batteries . [ 14 ] The monovalent anion C 6 O − 6 has been detected in mass spectrometry experiments. [ 15 ]
Rhodizonic acid and the rhodizonate anion can lose one of the CO units to yield croconic acid (CO) 3 (COH) 2 and the croconate anion C 5 O 2− 5 , respectively, by mechanisms that are still imperfectly known. In basic solutions (pH > 10), rhodizonic acid quickly converts to the THBQ anion (CO) 4− 6 in the absence of oxygen, and to croconic acid in its presence. At pH 8.3 and exposure to light, solutions are stable for days in the absence of oxygen, and decompose to croconic acid and other products (possibly including cyclohexanehexone or dodecahydroxycyclohexane ) in its presence. [ 16 ] [ 17 ]
In solution, the acid and the hydrogen rhodizonate ion are mostly hydrated, with some of the carbonyl groups >C=O replaced by geminal hydroxyls, >C(OH) 2 . [ 3 ]
In anhydrous rubidium rhodizonate (Rb + ) 2 [C 6 O 6 ] 2− , the rhodizonate anions are stacked in parallel columns, as are the rubidium ions. In the plane perpendicular to the columns, these are arranged as two interleaved hexagonal grids. The anions are planar. [ 2 ]
Anhydrous potassium rhodizonate (K + ) 2 [C 6 O 6 ] 2− has a distinct but similar structure. The anions and cations are arranged in alternate planes. Within each plane, the anions are arranged in a hexagonal grid. Each potassium ion is arranged so that it connects symmetrically to eight oxygens of four anions, two from each adjacent plane. The anions are slightly twisted in the "boat" shape (with 0.108 Å of rms deviation from mean plane). [ 18 ] Sodium rhodizonate (Na + ) 2 [C 6 O 6 ] 2− has the same structure, with slightly more distorted anions (0.113 Å rms) [ 19 ]
In solution, the rhodizonate anion is not hydrated. [ 3 ] | https://en.wikipedia.org/wiki/Rhodizonic_acid |
Rhodococcus rhodochrous is a bacterium used as a soil inoculant in agriculture and horticulture .
It is gram positive , in the shape of rods/ cocci , oxidase negative, and catalase positive.
It is industrially produced to catalyse acrylonitrile conversion to acrylamide . It is also used in the industrial production of nicotinamide (niacinamide), a derivative or active form of niacin , part of the B vitamin complex.
A 2015 study showed that Rhodococcus rhodochrous could inhibit the growth of Pseudogymnoascus destructans , the fungal species responsible for white nose syndrome in bats. [ 1 ]
This Actinomycetota -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rhodococcus_rhodochrous |
Rhodopin (1,2-dihydro-ψ,ψ-caroten-1-ol) is a carotenoid . It is a major carotenoid of phototropic bacteria such as Rhodomicrobium vannielii and Rhodopseudomonas acidophila strain 7050. [ 1 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rhodopin |
Rhodoquinone (RQ) is a modified ubiquinone -like molecule that is an important cofactor used in anaerobic energy metabolism by many organisms. Recently, it has gained attention as a potential anthelmintic drug target due to the fact that parasitic hosts do not synthesize or use this cofactor. Because this cofactor is used in low oxygen environments, many helminth-like organisms have adapted to survive host environments such as the areas within the gastrointestinal tracks. [ 1 ] [ 2 ]
Currently the biosynthesis of rhodoquinone (RQ) is still being debated, but there are two main biosynthetic pathways that are being researched. The first pathway requires the organism to produce ubiquinone (UQ) before the amino group can be added onto the quinone ring. The second pathway allows RQ to be synthesized without any UQ being present by using tryptophan metabolites instead. [ 3 ]
In the case of the prokaryotic organism R. rubrum , RQ has been shown to be synthesized by addition of an amino group to a pre-existing UQ; thus UQ needs to be present as a precursor before RQ can be made. Figure 1 shows the biosynthesis of UQ in yeast and E. coli where ‘n’ represents the number of isoprene units between various organisms. Dimethylallyl diphosphate A and isopentyl diphosphate B come together to form polyisoprenyl diphosphate C. With the addition of p-hydroxybenzoic acid, the product that arises is 3-polyprenyl-4-hydroxybenzoic acid D. The next three steps of synthesis varies between different organisms, but molecule E is made across all organisms and through oxidation, demethyldemethoxyubiquinone (DDMQ) is eventually formed. RQ has been theorized to be synthesized from DDMQn, DMQn, DMeQn, or UQn, as shown with the dashed arrows. Recent studies have shown that Path 4 - RQ biosynthesis via UQ, is the favored route. [ 4 ] It has been further shown that the gene rquA is required for the biosynthesis of RQ in R. rubrum , and that RquA catalyzes the conversion of UQ to RQ. [ 5 ] [ 6 ] The RquA protein uses S -adenosyl- L -methionine as the amino donor to convert UQ to RQ in an unusual Mn(II)-catalyzed reaction. [ 7 ]
Research in C. elegans has shown an alternative path for production of RQ. Even after knocking out all UQ production, RQ is still present within those mutant strains. Based on this data, RQ production is not solely based on UQ-like molecules and instead can be made via tryptophan metabolites. Therefore, the amino group that is added in late stages of RQ biosynthesis in rquA -containing species is instead present throughout intermediate stages of RQ biosynthesis in C. elegans . With this proposed biosynthesis, the kynurenine pathway still needs to be upregulated, and activity from certain genes like kynu-1 which encodes for the KYNU-1 enzyme that catalyzes production of 3-hydroxy-L-kynurenine to 3-hydroxyanthranilic acid, needs to be upheld. [ 8 ] [ 9 ] Recent work has revealed that alternative splicing of the coq-2 polyprenyltransferase gene controls the level of RQ in animals. [ 10 ] Animals that produce RQ (e.g. C. elegans and helminth parasites) contain both COQ-2 protein isoforms (COQ-2a and COQ-2e), and COQ-2e catalyzes prenylation of 3-hydroxyanthranilic acid (instead of p-hydroxybenzoic acid) which leads to RQ. | https://en.wikipedia.org/wiki/Rhodoquinone |
In geometry , the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces . It has 24 edges , and 14 vertices of 2 types. As a Catalan solid , it is the dual polyhedron of the cuboctahedron . As a parallelohedron , the rhombic dodecahedron can be used to tesselate its copies in space creating a rhombic dodecahedral honeycomb . There are some variations of the rhombic dodecahedron, one of which is the Bilinski dodecahedron . There are some stellations of the rhombic dodecahedron, one of which is the Escher's solid . The rhombic dodecahedron may also appear in nature (such as in the garnet crystal), the architectural philosophies, practical usages, and toys.
The rhombic dodecahedron is a polyhedron with twelve rhombi , each of which long face-diagonal length is exactly 2 {\displaystyle {\sqrt {2}}} times the short face-diagonal length [ 1 ] and the acute angle measurement is arccos ( 1 / 3 ) ≈ 70.53 ∘ {\textstyle \arccos(1/3)\approx 70.53^{\circ }} . Its dihedral angle between two rhombi is 120°. [ 2 ]
The rhombic dodecahedron is a Catalan solid , meaning the dual polyhedron of an Archimedean solid , the cuboctahedron ; they share the same symmetry, the octahedral symmetry . [ 2 ] It is face-transitive , meaning the symmetry group of the solid acts transitively on its set of faces. In elementary terms, this means that for any two faces, there is a rotation or reflection of the solid that leaves it occupying the same region of space while moving a face to another one. [ 3 ] Other than rhombic triacontahedron , it is one of two Catalan solids that each have the property that their isometry groups are edge-transitive ; the other convex polyhedron classes being the five Platonic solids and the other two Archimedean solids: its dual polyhedron and icosidodecahedron .
Denoting by a the edge length of a rhombic dodecahedron,
The surface area A and the volume V of the rhombic dodecahedron with edge length a are: [ 4 ] A = 8 2 a 2 ≈ 11.314 a 2 , V = 16 3 9 a 3 ≈ 3.079 a 3 . {\displaystyle {\begin{aligned}A&=8{\sqrt {2}}a^{2}&\approx 11.314a^{2},\\V&={\frac {16{\sqrt {3}}}{9}}a^{3}&\approx 3.079a^{3}.\end{aligned}}}
The rhombic dodecahedron can be viewed as the convex hull of the union of the vertices of a cube and an octahedron where the edges intersect perpendicularly. The six vertices where four rhombi meet correspond to the vertices of the octahedron , while the eight vertices where three rhombi meet correspond to the vertices of the cube .
The skeleton of a rhombic dodecahedron is called a rhombic dodecahedral graph , with 14 vertices and 24 edges. It is the Levi graph of the Miquel configuration (8 3 6 4 ). [ 5 ]
For edge length √ 3 , the eight vertices where three faces meet at their obtuse angles have Cartesian coordinates (±1, ±1, ±1). In the case of the coordinates of the six vertices where four faces meet at their acute angles, they are (±2, 0, 0), (0, ±2, 0) and (0, 0, ±2).
The rhombic dodecahedron can be seen as a degenerate limiting case of a pyritohedron , with permutation of coordinates (±1, ±1, ±1) and (0, 1 + h , 1 − h 2 ) with parameter h = 1.
These coordinates illustrate that a rhombic dodecahedron can be seen as a cube with six square pyramids attached to each face, allowing them to fit together into a cube. Therefore, the rhombic dodecahedron has twice the volume of the inscribed cube with edges equal to the short diagonals of the rhombi. [ 6 ] Alternatively, the rhombic dodecahedron can be constructed by inverting six square pyramids until their apices meet at the cube's center. [ 7 ]
The rhombic dodecahedron is a space-filling polyhedron , meaning it can be applied to tessellate three-dimensional space: it can be stacked to fill a space, much like hexagons fill a plane. It is a parallelohedron because it can be space-filling a honeycomb in which all of its copies meet face-to-face. [ 8 ] More generally, every parellelohedron is zonohedron , a centrally symmetric polyhedron with centrally symmetric faces . [ 9 ] As a parallelohedron, the rhombic dodecahedron can be constructed with four sets of six parallel edges. [ 8 ]
The rhombic dodecahedral honeycomb (or dodecahedrille ) is an example of a honeycomb constructed by filling all rhombic dodecahedrons. It is dual to the tetroctahedrille or half cubic honeycomb , and it is described by two Coxeter diagrams : and . With D 3d symmetry, it can be seen as an elongated trigonal trapezohedron . It can be seen as the Voronoi tessellation of the face-centered cubic lattice . It is the Brillouin zone of body-centered cubic (bcc) crystals. Some minerals such as garnet form a rhombic dodecahedral crystal habit . As Johannes Kepler noted in his 1611 book on snowflakes ( Strena seu de Nive Sexangula ), honey bees use the geometry of rhombic dodecahedra to form honeycombs from a tessellation of cells each of which is a hexagonal prism capped with half a rhombic dodecahedron. The rhombic dodecahedron also appears in the unit cells of diamond and diamondoids . In these cases, four vertices (alternate threefold ones) are absent, but the chemical bonds lie on the remaining edges. [ 10 ]
A rhombic dodecahedron can be dissected into four congruent, obtuse trigonal trapezohedra around its center. These rhombohedra are the cells of a trigonal trapezohedral honeycomb . Analogously, a regular hexagon can be dissected into 3 rhombi around its center. These rhombi are the tiles of a rhombille . [ citation needed ]
In spacecraft reaction wheel layout, a tetrahedral configuration of four wheels is commonly used. For wheels that perform equally (from a peak torque and max angular momentum standpoint) in both spin directions and across all four wheels, the maximum torque and maximum momentum envelopes for the 3-axis attitude control system (considering idealized actuators) are given by projecting the tesseract representing the limits of each wheel's torque or momentum into 3D space via the 3 × 4 matrix of wheel axes; the resulting 3D polyhedron is a rhombic dodecahedron. [ 11 ] Such an arrangement of reaction wheels is not the only possible configuration (a simpler arrangement consists of three wheels mounted to spin about orthogonal axes), but it is advantageous in providing redundancy to mitigate the failure of one of the four wheels (with degraded overall performance available from the remaining three active wheels) and in providing a more convex envelope than a cube, which leads to less agility dependence on axis direction (from an actuator/plant standpoint). Spacecraft mass properties influence overall system momentum and agility, so decreased variance in envelope boundary does not necessarily lead to increased uniformity in preferred axis biases (that is, even with a perfectly distributed performance limit within the actuator subsystem, preferred rotation axes are not necessarily arbitrary at the system level).
The polyhedron is also the basis for the HEALPix grid, used in cosmology for storing and manipulating maps of the cosmic microwave background , and in computer graphics for storing environment maps .
The collections of the Louvre include a die in the shape of a rhombic dodecahedron dating from Ptolemaic Egypt . The faces are inscribed with Greek letters representing the numbers 1 through 12: Α Β Γ Δ Ε Ϛ Z Η Θ Ι ΙΑ ΙΒ. The function of the die is unknown. [ 12 ]
Other symmetry constructions of the rhombic dodecahedron are also space-filling, and as parallelotopes they are similar to variations of space-filling truncated octahedra . [ 13 ] For example, with 4 square faces, and 60-degree rhombic faces, and D 4h dihedral symmetry , order 16. It can be seen as a cuboctahedron with square pyramids attached on the top and bottom.
In 1960, Stanko Bilinski discovered a second rhombic dodecahedron with 12 congruent rhombus faces, the Bilinski dodecahedron . It has the same topology but different geometry. The rhombic faces in this form have the golden ratio . [ 14 ] [ 15 ]
The deltoidal dodecahedron is another topological equivalence of a rhombic dodecahedron form. [ 16 ] It is isohedral with tetrahedral symmetry order 24, distorting rhombic faces into kites (deltoids). It has 8 vertices adjusted in or out in alternate sets of 4, with the limiting case a tetrahedral envelope. Variations can be parametrized by ( a , b ), where b and a depend on each other such that the tetrahedron defined by the four vertices of a face has volume zero, i.e. is a planar face. (1,1) is the rhombic solution. As a approaches 1 / 2 , b approaches infinity. It always holds that 1 / a + 1 / b = 2, with a , b > 1 / 2 .
Like many convex polyhedra, the rhombic dodecahedron can be stellated by extending the faces or edges until they meet to form a new polyhedron. Several such stellations have been described by Dorman Luke. [ 17 ] The first stellation, often called the stellated rhombic dodecahedron , can be seen as a rhombic dodecahedron with each face augmented by attaching a rhombic-based pyramid to it, with a pyramid height such that the sides lie in the face planes of the neighbouring faces. Luke describes four more stellations: the second and third stellations (expanding outwards), one formed by removing the second from the third, and another by adding the original rhombic dodecahedron back to the previous one.
The rhombic dodecahedron forms the hull of the vertex-first projection of a tesseract to three dimensions. There are exactly two ways of decomposing a rhombic dodecahedron into four congruent rhombohedra , giving eight possible rhombohedra as projections of the tesseracts 8 cubic cells. One set of projective vectors are: u = (1,1,−1,−1), v = (−1,1,−1,1), w = (1,−1,−1,1).
The rhombic dodecahedron forms the maximal cross-section of a 24-cell , and also forms the hull of its vertex-first parallel projection into three dimensions. The rhombic dodecahedron can be decomposed into six congruent (but non-regular) square dipyramids meeting at a single vertex in the center; these form the images of six pairs of the 24-cell's octahedral cells. The remaining 12 octahedral cells project onto the faces of the rhombic dodecahedron. The non-regularity of these images are due to projective distortion; the facets of the 24-cell are regular octahedra in 4-space.
This decomposition gives an interesting method for constructing the rhombic dodecahedron: cut a cube into six congruent square pyramids, and attach them to the faces of a second cube. The triangular faces of each pair of adjacent pyramids lie on the same plane, and so merge into rhombi. The 24-cell may also be constructed in an analogous way using two tesseracts . [ 18 ] | https://en.wikipedia.org/wiki/Rhombic_dodecahedron |
The rhombic triacontahedron , sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron , is a convex polyhedron with 30 rhombic faces . It has 60 edges and 32 vertices of two types. It is a Catalan solid , and the dual polyhedron of the icosidodecahedron . It is a zonohedron and can be seen as a elongated rhombic icosahedron .
The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio , φ , so that the acute angles on each face measure 2 arctan ( 1 / φ ) = arctan(2) , or approximately 63.43°. A rhombus so obtained is called a golden rhombus .
Being the dual of an Archimedean solid , the rhombic triacontahedron is face-transitive , meaning the symmetry group of the solid acts transitively on the set of faces. This means that for any two faces, A and B , there is a rotation or reflection of the solid that leaves it occupying the same region of space while moving face A to face B .
The rhombic triacontahedron is somewhat special in being one of the nine edge-transitive convex polyhedra, the others being the five Platonic solids , the cuboctahedron , the icosidodecahedron , and the rhombic dodecahedron .
The rhombic triacontahedron is also interesting in that its vertices include the arrangement of four Platonic solids. It contains ten tetrahedra , five cubes , an icosahedron and a dodecahedron . The centers of the faces contain five octahedra .
It can be made from a truncated octahedron by dividing the hexagonal faces into three rhombi:
Let φ be the golden ratio . The 12 points given by (0, ±1, ± φ ) and cyclic permutations of these coordinates are the vertices of a regular icosahedron . Its dual regular dodecahedron , whose edges intersect those of the icosahedron at right angles, has as vertices the 8 points (±1, ±1, ±1) together with the 12 points (0, ± φ , ± 1 / φ ) and cyclic permutations of these coordinates. All 32 points together are the vertices of a rhombic triacontahedron centered at the origin. The length of its edges is √ 3 – φ ≈ 1.175 570 504 58 . Its faces have diagonals with lengths 2 and 2 / φ .
If the edge length of a rhombic triacontahedron is a , surface area, volume, the radius of an inscribed sphere ( tangent to each of the rhombic triacontahedron's faces) and midradius, which touches the middle of each edge are: [ 1 ]
where φ is the golden ratio .
The insphere is tangent to the faces at their face centroids. Short diagonals belong only to the edges of the inscribed regular dodecahedron, while long diagonals are included only in edges of the inscribed icosahedron.
The rhombic triacontahedron can be dissected into 20 golden rhombohedra : 10 acute ones and 10 obtuse ones. [ 2 ] [ 3 ]
The rhombic triacontahedron has four symmetry positions, two centered on vertices, one mid-face, and one mid-edge. Embedded in projection "10" are the "fat" rhombus and "skinny" rhombus which tile together to produce the non-periodic tessellation often referred to as Penrose tiling .
The rhombic triacontahedron has 227 fully supported stellations. [ 4 ] [ 5 ] One of the stellations of the rhombic triacontahedron is the compound of five cubes .
The total number of stellations of the rhombic triacontahedron is 358 833 097 .
This polyhedron is a part of a sequence of rhombic polyhedra and tilings with [ n , 3] Coxeter group symmetry. The cube can be seen as a rhombic hexahedron where the rhombi are also rectangles.
Danish designer Holger Strøm used the rhombic triacontahedron as a basis for the design of his buildable lamp IQ-light (IQ for "interlocking quadrilaterals").
Woodworker Jane Kostick builds boxes in the shape of a rhombic triacontahedron. [ 6 ] The simple construction is based on the less than obvious relationship between the rhombic triacontahedron and the cube.
Roger von Oech 's "Ball of Whacks" comes in the shape of a rhombic triacontahedron.
The rhombic triacontahedron is used as the " d30 " thirty-sided die, sometimes useful in some roleplaying games or other places. | https://en.wikipedia.org/wiki/Rhombic_triacontahedron |
In geometry , a rhombicuboctahedral prism is a convex uniform polychoron (four-dimensional polytope ).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes .
A related polychoron is the runcic snub cubic hosochoron , also known as a parabidiminished rectified tesseract , truncated tetrahedral alterprism , or truncated tetrahedral cupoliprism , s 3 {2,4,3}, . It is made from 2 truncated tetrahedra , 6 tetrahedra , and 8 triangular cupolae in the gaps, for a total of 16 cells, 52 faces, 60 edges, and 24 vertices. It is vertex-transitive , and equilateral, but not uniform, due to the cupolae. It has symmetry [2 + ,4,3], order 48. [ 1 ] [ 2 ] [ 3 ]
It is related to the 16-cell in its s{2,4,3}, construction.
It can also be seen as a prismatic polytope with two parallel truncated tetrahedra in dual positions, as seen in the compound of two truncated tetrahedra . Triangular cupolae connect the triangular and hexagonal faces, and the tetrahedral connect edge-wise between.
This 4-polytope article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rhombicuboctahedral_prism |
RiAFP refers to an antifreeze protein (AFP) produced by the Rhagium inquisitor longhorned beetle. It is a type V antifreeze protein with a molecular weight of 12.8 kDa; this type of AFP is noted for its hyperactivity. [ 1 ] [ 2 ] [ 3 ] R. inquisitor is a freeze-avoidant species, meaning that, due to its AFP, R. inquisitor prevents its body fluids from freezing altogether. [ 3 ] This contrasts with freeze-tolerant species, whose AFPs simply depress levels of ice crystal formation in low temperatures. Whereas most insect antifreeze proteins contain cysteines at least every sixth residue , as well as varying numbers of 12- or 13-mer repeats of 8.3-12.5kDa, [ 4 ] RiAFP is notable for containing only one disulfide bridge. This property of RiAFP makes it particularly attractive for recombinant expression and biotechnological applications.
AFPs work through an interaction with small ice crystals that is similar to an enzyme-ligand binding mechanism [ 1 ] which inhibits recrystallization of ice. This explanation of the interruption of the ice crystal structure by the AFP has come to be known as the adsorption-inhibition hypothesis .
According to this hypothesis , AFPs disrupt the thermodynamically favourable growth of an ice crystal via kinetic inhibition of contact between solid ice and liquid water. [ 5 ] In this manner, the nucleation sites of the ice crystal lattice are blocked by the AFP, inhibiting the rapid growth of the crystal that could be fatal for the organism. In physical chemistry terms, the AFPs adsorbed onto the exposed ice crystal force the growth of the ice crystal in a convex fashion as the temperature drops, [ 2 ] which elevates the ice vapour pressure at the nucleation sites. Ice vapour pressure continues to increase until it reaches equilibrium with the surrounding solution (water), at which point the growth of the ice crystal stops.
The aforementioned effect of AFPs on ice crystal nucleation is lost at the thermal hysteresis point. At a certain low temperature, the maximum convexity of the ice nucleation site is reached. Any further cooling will actually result in a "spreading" of the nucleation site away from this convex region, causing rapid, uncontrollable nucleation of the ice crystal. [ 2 ] The temperature at which this phenomenon occurs is the thermal hysteresis point. The adsorption-inhibition hypothesis is further supported by the observation that antifreeze activity increases with increasing AFP concentration – the more AFPs adsorb onto the forming ice crystal, the more 'crowded' these proteins become, making ice crystal nucleation less favourable.
In the R. inquisitor beetle, AFPs are found in the haemolymph , a fluid that bathes all the cells of the beetle and fills a cavity called the haemocoel . [ 3 ] The presence of AFPs in R. inquisitor allows the tissues and fluids within the beetle to withstand freezing up to -30 °C (the thermal hysteresis point for this AFP). This strategy provides an obvious survival benefit to these beetles, who are endemic to cold climates, such as Scandinavia , Siberia , and Alaska .
The primary structure of RiAFP (the sequence may be found here ) determined by Mass Spectroscopy, Edman degradation and by constructing a partial cDNA sequence and PCR have shown that a TxTxTxT internal repeat exists. [ 2 ] Sequence logos constructed from the RiAFP internal repeats, have been particularly helpful in the determination of the consensus sequence of these repeats. The TxTxTxT domains are irregularly spaced within the protein and have been shown to be conserved from the TxT binding motif of other AFPs. [ 2 ] The hydroxyl moiety of the T residues fits well, when spaced as they are in the internal repeats, with the hydroxyl moieties of externally facing water molecules in the forming ice lattice. This mimics the formation of the growth cone at a nucleation site in the absence of AFPs. Thus, the binding of RiAFP inhibits the growth of the crystal in the basal and prism planes of the ice. [ 6 ]
The fact that the binding motif appears as a "triplet" of the conserved TxT repeat, as well as the observation that blastp queries have returned no viable matches, has led some researchers to suggest that RiAFP represents a new type of AFP – one that differs from the heavily studied TmAFP (from T. molitor ), DcAFP (from D. canadensis ), and CfAFP (from C. fumiferana ). [ 2 ] On the basis of these observations, it has been predicted that the need for insect AFPs came about after insect evolutionary divergence, much like the evolution of fish AFPs; thus, different AFPs most likely evolved in parallel from adaptations to cold (environmental) stress. [ 7 ] [ 8 ] As a result, homology modelling with TmAFP , DcAFP , or CfAFP would prove to be fruitless.
Secondary structure modelling algorithms have determined that the internal repeats are spaced sufficiently to tend towards β-strand configuration; no helical regions include the conserved repeats; and all turn regions are located at the ends of β-strand regions. [ 2 ] These data suggest that RiAFP is a well-folded β-helical protein, having six β-strand regions consisting of 13-amino acids (including one TxTxTxT binding motif) per strand.
Primary crystallographic studies , have been published on a RiAFP crystal (which diffracted to 1.3Å resolution) in the trigonal space group P3 1 21 (or P3 2 21), with unit-cell parameters a = b = 46.46, c = 193.21Å. [ 9 ] | https://en.wikipedia.org/wiki/RiAFP |
In fluid mechanics a Riabouchinsky solid is a technique used for approximating boundary layer separation from a bluff body using potential flow . It is named after Dimitri Pavlovitch Riabouchinsky . [ 1 ] [ 2 ]
Riabouchinsky solids are typically used for analysing the behaviour of bodies moving through otherwise quiescent fluid (examples would include moving cars, or buildings in a windfield).
Typically the streamline that touches the edge of the body is modelled as having no transverse pressure gradient and thus may be styled as a free surface after separation.
The use of Riabouchinsky solids renders d'Alembert's paradox void; the technique typically gives reasonable estimates for the drag offered by bluff bodies moving through inviscid fluids.
This fluid dynamics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Riabouchinsky_solid |
In differential geometry , a ribbon (or strip ) is the combination of a smooth space curve and its corresponding normal vector . More formally, a ribbon denoted by ( X , U ) {\displaystyle (X,U)} includes a curve X {\displaystyle X} given by a three-dimensional vector X ( s ) {\displaystyle X(s)} , depending continuously on the curve arc-length s {\displaystyle s} ( a ≤ s ≤ b {\displaystyle a\leq s\leq b} ), and a unit vector U ( s ) {\displaystyle U(s)} perpendicular to ∂ X ∂ s ( s ) {\displaystyle {\partial X \over \partial s}(s)} at each point. [ 1 ] Ribbons have seen particular application as regards DNA . [ 2 ]
The ribbon ( X , U ) {\displaystyle (X,U)} is called simple if X {\displaystyle X} is a simple curve (i.e. without self-intersections) and closed and if U {\displaystyle U} and all its derivatives agree at a {\displaystyle a} and b {\displaystyle b} .
For any simple closed ribbon the curves X + ε U {\displaystyle X+\varepsilon U} given parametrically by X ( s ) + ε U ( s ) {\displaystyle X(s)+\varepsilon U(s)} are, for all sufficiently small positive ε {\displaystyle \varepsilon } , simple closed curves disjoint from X {\displaystyle X} .
The ribbon concept plays an important role in the Călugăreanu formula , [ 3 ] [ 4 ] that states that
where L k {\displaystyle Lk} is the asymptotic (Gauss) linking number , the integer number of turns of the ribbon around its axis; W r {\displaystyle Wr} denotes the total writhing number (or simply writhe ), a measure of non-planarity of the ribbon's axis curve; and T w {\displaystyle Tw} is the total twist number (or simply twist ), the rate of rotation of the ribbon around its axis.
Ribbon theory investigates geometric and topological aspects of a mathematical reference ribbon associated with physical and biological properties, such as those arising in topological fluid dynamics , DNA modeling and in material science . | https://en.wikipedia.org/wiki/Ribbon_(mathematics) |
The ribbon synapse is a type of neuronal synapse characterized by the presence of an electron-dense structure, the synaptic ribbon , that holds vesicles close to the active zone . [ 1 ] It is characterized by a tight vesicle - calcium channel coupling [ 2 ] [ 3 ] that promotes rapid neurotransmitter release and sustained signal transmission. Ribbon synapses undergo a cycle of exocytosis and endocytosis in response to graded changes of membrane potential . It has been proposed that most ribbon synapses undergo a special type of exocytosis based on coordinated multivesicular release. [ 4 ] [ 5 ] [ 6 ] This interpretation has recently been questioned at the inner hair cell ribbon synapse, where it has been instead proposed that exocytosis is described by uniquantal (i.e., univesicular) release shaped by a flickering vesicle fusion pore. [ 7 ]
These unique features specialize the ribbon synapse to enable extremely fast, precise and sustained neurotransmission , which is critical for the perception of complex senses such as vision and hearing. Ribbon synapses are found in retinal photoreceptor cells , vestibular organ receptors , cochlear hair cells , retinal bipolar cells , and pinealocytes .
The synaptic ribbon is a unique structure at the active zone of the synapse. It is positioned several nanometers away from the pre-synaptic membrane and tethers 100 or more synaptic vesicles . [ 8 ] Each pre-synaptic cell can have from 10 to 100 ribbons tethered at the membrane, or a total number of 1000–10000 vesicles in close proximity to active zones . [ 9 ] The ribbon synapse was first identified in the retina as a thin, ribbon-like presynaptic projection surrounded by a halo of vesicles [ 10 ] using transmission electron microscopy in the 1950s, as the technique was gaining mainstream usage.
The photoreceptor ribbon synapse is around 30 nm in thickness. It sticks out into the cytoplasm around 200-1000 nm and anchors along its base to the arciform density which is an electron dense structure that is anchored to the presynaptic membrane. The arciform density is located within the synaptic ridge, a small evagination of the presynaptic membrane. Hair cells lack an arciform density so the anchor of this ribbon is considered to be invisible by electron microscope. [ 11 ] The ribbon's surface has small particles that are around 5 nm wide where the synaptic vesicles tether densely via fine protein filaments . There are multiple filaments per vesicle. There are also voltage gated L-type calcium channels on the docking sites of the ribbon synapse which trigger neurotransmitter release. Specifically, ribbon synapses contain specialized organelles called synaptic ribbons, which are large presynaptic structures associated in the active zone . They are thought to fine-tune the synaptic vesicle cycle. [ 8 ] Synaptic ribbons are in close proximity to synaptic vesicles, which, in turn, are close to the presynaptic neurotransmitter release site via the ribbon. [ 12 ]
Postsynaptic structures differ for cochlear cells and photoreceptor cells. Hair cells is capable of one action potential propagation for one vesicle release. One vesicle release from the presynaptic hair cell onto the postsynaptic bouton is enough to create an action potential in the auditory afferent cells . [ 13 ] Photoreceptors allow one vesicle release for many action potential propagation. The rod terminal and cone ribbon synapse of the photoreceptors have horizontal synaptic spines expressing AMPA receptors with additional bipolar dendrites exhibiting the mGluR6 receptors. [ 11 ] These structures allow for the binding of multiple molecules of glutamate, allowing for the propagation of many action potentials.
The molecular composition between conventional neuronal synapse and ribbon synapse is surprisingly dissimilar. At the core of synaptic vesicle exocytosis machinery in vertebrate neuronal synapses is the SNARE complex . The minimally functional SNARE complex includes syntaxin 1 , VAMP 1 and 2 , and SNAP-25 . [ 14 ] In contrast, genetic ablation or application of botulinum , targeting SNAP-25, syntaxin 1–3, and VAMP 1–3, did not affect inner hair cell ribbon synapse exocytosis in mice. [ 15 ] Additionally, no neuronal SNAREs were observed in hair cells using immunostaining , [ 15 ] pointing to the possibility of a different exocytosis mechanism. However, several studies found SNARE mRNA and protein expressed in hair cell, [ 15 ] [ 16 ] [ 17 ] [ 18 ] perhaps indicating presence of a neuronal SNARE complex in ribbon synapse that is present in low levels and with very redundant components. [ 19 ] [ 20 ]
Several proteins of the synaptic ribbon have also been found to be associated with conventional synapses. RIM ( Rab 3-interacting proteins) is a GTPase expressed on synaptic vesicles that is important in priming synaptic vesicles. [ 12 ] Immunostaining has revealed the presence of KIF3A , a component of the kinesin II motor complex whose function is still unknown. [ 21 ] The presynaptic cytomatrix proteins Bassoon and Piccolo are both expressed at photoreceptor ribbons, but Piccolo is only expressed at retinal bipolar synaptic ribbons. Bassoon is responsible for attaching itself to the base of the synaptic ribbons and subsequently anchoring the synaptic ribbons. The function of Piccolo is unknown. [ 11 ] Also important is the filaments that tether the vesicles to the ribbon synapse. These are shed during high rates of exocytosis. [ 11 ] The only unique protein associated with the synaptic ribbon is RIBEYE, first identified in purified synaptic ribbon from bovine retina. [ 22 ] RIBEYE is encoded in vertebrate genomes as an alternative transcript of the CtBP2 gene. [ 12 ] During chicken and human retinal development, RIBEYE is expressed in photoreceptor and bipolar cell retinal neurons. [ 23 ] It is found to be a part of all vertebrate synaptic ribbons in ribbon synapses and is the central portion of ribbon synapses. [ 12 ] RIBEYE interactions are required to form a scaffold formation protein of the synaptic ribbon. [ 12 ]
There has been a significant amount of research into the pre-synaptic cytomatrix protein Bassoon, which is a multi-domain scaffolding protein universally expressed at synapses in the central nervous system. [ 24 ] Mutations in Bassoon have been shown to result in decreased synaptic transmission. However, the underlying mechanisms behind this observed phenomenon are not fully understood and are currently being investigated. It has been observed that in the retina of Bassoon-mutant mice, photoreceptor ribbon synapses are not anchored to pre-synaptic active zones during photoreceptor synaptogenesis. The photoreceptor ribbon synapses are observed to be free floating in the cytoplasm of the photoreceptor terminals. [ 24 ] These observations have led to the conclusion that Bassoon plays a critical role in the formation of the photoreceptor ribbon synapse.
In correspondence to its activity, ribbon synapses can have synaptic ribbons that vary in size. In mouse photoreceptor synapses when the neurotransmitter release rate is high and exocytosis is high, the synaptic ribbons are long. When neurotransmitter release rate is low and exocytosis is low, the synaptic ribbons are short. [ 12 ] A current hypothesis is that synaptic ribbons can enlarge by the addition of more RIBEYE subunit. [ 25 ]
Features of the ribbon synapse enable it to process information extremely quickly. Bipolar neurons present a good model for how ribbon synapses function.
Information is conveyed from photoreceptor cells to bipolar cells via the release of the neurotransmitter glutamate at the ribbon synapse. [ 24 ] Conventional neurons encode information by changes in the rate of action potentials , but for complex senses like vision, this is not sufficient. Ribbon synapses enable neurons to transmit light signals over a dynamic range of several orders of magnitude in intensity. This is achieved by encoding intensity changes in tonic rate of transmitter release which requires the release of several hundred to several thousand synaptic vesicles per second. [ 24 ]
To accomplish this level of performance, the sensory neurons of the eye maintain large pools of fast releasable vesicles that are equipped with ribbon synapses. This enables the cell to exocytose hundreds of vesicles per second, greatly exceeding the rate of neurons without the specialized ribbon synapse. [ 24 ]
The current hypothesis of calcium-dependent exocytosis at retinal ribbon synapses suggests that the ribbon accommodates a reservoir of primed releasable vesicles. The vesicles that are in closest contact with the presynaptic plasma membrane at the base of the ribbon constitute the small, rapidly releasable pool of vesicles, whereas the remaining vesicles tethered to the ribbon constitute the large, readily (slower) releasable pool. These regularly aligned rows of synaptic vesicles tethered to either side of the ribbon along with the expression of the kinesin motor protein KIF3A at retinal ribbon synapses can move vesicles like a conveyor belt to the docking/release site at the ribbon base. [ 24 ]
During exocytosis at the bipolar ribbon synapse, vesicles are seen to pause at the membrane and then upon opening of the calcium channels to promptly release their contents within milliseconds [ citation needed ] . Like most exocytosis, Ca 2+ regulates the release of vesicles from the presynaptic membrane. Different types of ribbon synapses have different dependence on Ca 2+ releases. The hair cell ribbon synapses exhibit a steep dependence on Ca 2+ concentration, [ 26 ] while the photoreceptor synapses is less steeply dependent on Ca 2+ and is stimulated by much lower levels of free Ca 2+ . [ 27 ] The hair cell ribbon synapse experiences spontaneous activity in the absence of stimuli, under conditions of a constant hair cell membrane potential. [ 28 ] Voltage clamp at the postsynaptic bouton showed that the bouton experiences a wide range of excitatory postsynaptic current amplitudes. [ 4 ] The current amplitude distribution is a positive- skew , with a range of larger amplitudes for both spontaneous and stimulus evoked release. It was thought that this current distribution was not explainable with single vesicle release, and other scenarios of release have been proposed: coordinated multivesicular release , [ 4 ] [ 29 ] kiss-and-run , or compound fusion of vesicles prior to exocytosis. [ 30 ] However it has been recently proposed that uniquantal release with fusion pore flickering is the most plausible interpretation of the found current distribution. [ 7 ] In fact, the charge distribution of currents is actually normally distributed, supporting the uniquantal release scenario. It has been shown that the skewness of the current amplitude distribution is well explained by different time courses of neurotransmitter release of a single vesicles with a flickering fusion pore.
The bipolar cell active zone of the ribbon synapse can release neurotransmitter continuously for hundreds of milliseconds during strong stimulation. This release of neurotransmitters occurs in two kinetically distinct phases: a small fast pool where about twenty percent of the total is released in about 1 millisecond, and a large sustained pool where the remaining components are released over hundreds of milliseconds. The existence of correspondence between the pool of tethered vesicles and the pool for sustained release in the rods and bipolar cells of the ribbon reveals that the ribbon may serve as a platform where the vesicles can be primed to allow sustained release of neurotransmitters. This large size of the sustained large component is what separates the ribbon synapse active zones from those of conventional neurons where sustained release is small in comparison. Once the presynaptic vesicles have been depleted, the bipolar cell's releasable pool requires several seconds to refill with the help of ATP hydrolysis . [ 11 ]
A high rate of endocytosis is necessary to counter the high rate of exocytosis during sustained neurotransmitter release at ribbon synapses. Synaptic vesicles need to be recycled for further transmission to occur. These vesicles are directly recycled and because of their mobility, quickly replenish the neurotransmitters required for continued release.
In cone photoreceptors, the fused membrane is recycled into the synaptic vesicle without pooling of the membrane into the endosomes . Bipolar cells rely on a different mechanism. It involves taking a large portion of the membrane which is endocytosed and gives rise to synaptic vesicles. This mechanism is conserved in hair cells as well. [ 11 ]
Research has shown that abnormal expression of otoferlin , a ribbon synapse associated protein, impairs exocytosis of ribbon-bound vesicles in auditory inner hair cells. Otoferlin displays similar functional characteristics to synaptotagmin , a synapse associated protein important for mediating exocytosis in many other synapses (such as those in the central nervous system ). Impaired hearing in mice has been shown to be associated with disrupted expression of otoferlin. [ 31 ]
In studies of retinal genetic coding of laboratory mice, several mutated ribbon synapse associated voltage-gated L-type calcium channel auxiliary subunits were shown to be associated with dysfunctional rod and cone activity and information transmission. [ 32 ] Mice were shown to express significantly reduced scotopic vision , and further research has shown the dysregulation of calcium homeostasis may have a significant role in rod photoreceptor degradation and death. [ 32 ]
Much of the genetic information associated with the proteins observed in laboratory mice are shared with humans. The protein otoferlin is observed phenotypically in human auditory inner hair cells, and abnormal expression has been linked with deafness. In humans, cochlear implants have shown to reduce the debilitating effects of abnormal otoferlin expression by surpassing the synapse associated with the auditory inner hair cells. [ citation needed ] The genetic code for retinal subunits associated with impaired scotopic vision and rod photoreceptor degradation are conserved at approximately 93% between mice and humans. [ 31 ] Further research into the abnormal functioning of these mechanisms could open the door to therapeutic techniques to relieve auditory and visual impairments.
Several recent studies have provided evidence that loss-of-function mutations in pre-synaptic proteins of the photoreceptor cells ribbon synapse can cause X-linked congenital stationary night blindness (CSNB) through mutations in the CACNA1F gene, which codes for the αF1-subunit of the L-type calcium channel Ca v 1.4 . [ 24 ] The gene is expressed at the active zone of photoreceptor ribbon synapses. The mutation is characterized by a significant reduction in both night and variable perturbation of daylight vision. The mutations in CACNA1F and Ca v 1.4 have also been observed to co-localize with CaBP4, a photoreceptor-specific calcium-binding protein. [ 24 ] CaBP4 has been theorized to modulate the activity of the Ca v 1.4 channel. It has been theorized to be associated with the proper establishment and maintenance of photoreceptor ribbon synapses. While no evidence has been published, the association between CaBP4 and Ca v 1.4 is an area of continued research. | https://en.wikipedia.org/wiki/Ribbon_synapse |
The Ribenboim Prize , named in honour of Paulo Ribenboim , is awarded by the Canadian Number Theory Association for distinguished research in number theory by a mathematician who is Canadian or has close connections to Canadian mathematics. [ 1 ] Normally the winner will have received their Ph.D. in the last 12 years. The winner is expected to give a plenary talk at the award ceremony. [ 2 ]
Due to the COVID-19 pandemic , the 2020, 2022, and 2024 Ribenboim Prizes were all awarded in 2024. [ 3 ] | https://en.wikipedia.org/wiki/Ribenboim_Prize |
Ribet's theorem (earlier called the epsilon conjecture or ε-conjecture ) is part of number theory . It concerns properties of Galois representations associated with modular forms . It was proposed by Jean-Pierre Serre and proven by Ken Ribet . The proof was a significant step towards the proof of Fermat's Last Theorem (FLT). As shown by Serre and Ribet, the Taniyama–Shimura conjecture (whose status was unresolved at the time) and the epsilon conjecture together imply that FLT is true.
In mathematical terms, Ribet's theorem shows that if the Galois representation associated with an elliptic curve has certain properties, then that curve cannot be modular (in the sense that there cannot exist a modular form that gives rise to the same representation). [ 1 ]
Let f be a weight 2 newform on Γ 0 ( qN ) – i.e. of level qN where q does not divide N – with absolutely irreducible 2-dimensional mod p Galois representation ρ f,p unramified at q if q ≠ p and finite flat at q = p . Then there exists a weight 2 newform g of level N such that
In particular, if E is an elliptic curve over Q {\displaystyle \mathbb {Q} } with conductor qN , then the modularity theorem guarantees that there exists a weight 2 newform f of level qN such that the 2-dimensional mod p Galois representation ρ f, p of f is isomorphic to the 2-dimensional mod p Galois representation ρ E, p of E . To apply Ribet's Theorem to ρ E , p , it suffices to check the irreducibility and ramification of ρ E, p . Using the theory of the Tate curve , one can prove that ρ E, p is unramified at q ≠ p and finite flat at q = p if p divides the power to which q appears in the minimal discriminant Δ E . Then Ribet's theorem implies that there exists a weight 2 newform g of level N such that ρ g , p ≈ ρ E , p .
Ribet's theorem states that beginning with an elliptic curve E of conductor qN does not guarantee the existence of an elliptic curve E ′ of level N such that ρ E, p ≈ ρ E ′ , p . The newform g of level N may not have rational Fourier coefficients, and hence may be associated to a higher-dimensional abelian variety , not an elliptic curve. For example, elliptic curve 4171a1 in the Cremona database given by the equation
with conductor 43 × 97 and discriminant 43 7 × 97 3 does not level-lower mod 7 to an elliptic curve of conductor 97. Rather, the mod p Galois representation is isomorphic to the mod p Galois representation of an irrational newform g of level 97.
However, for p large enough compared to the level N of the level-lowered newform, a rational newform (e.g. an elliptic curve) must level-lower to another rational newform (e.g. elliptic curve). In particular for p ≫ N N 1+ ε , the mod p Galois representation of a rational newform cannot be isomorphic to an irrational newform of level N . [ 2 ]
Similarly, the Frey- Mazur conjecture predicts that for large enough p (independent of the conductor N ), elliptic curves with isomorphic mod p Galois representations are in fact isogenous , and hence have the same conductor. Thus non-trivial level-lowering between rational newforms is not predicted to occur for large p ( p > 17) .
In his thesis, Yves Hellegouarch [ fr ] originated the idea of associating solutions ( a , b , c ) of Fermat's equation with a different mathematical object: an elliptic curve. [ 3 ] If p is an odd prime and a , b , and c are positive integers such that
then a corresponding Frey curve is an algebraic curve given by the equation
This is a nonsingular algebraic curve of genus one defined over Q {\displaystyle \mathbb {Q} } , and its projective completion is an elliptic curve over Q {\displaystyle \mathbb {Q} } .
In 1982 Gerhard Frey called attention to the unusual properties of the same curve, now called a Frey curve . [ 4 ] This provided a bridge between Fermat and Taniyama by showing that a counterexample to FLT would create a curve that would not be modular. The conjecture attracted considerable interest when Frey suggested that the Taniyama–Shimura conjecture implies FLT. However, his argument was not complete. [ 5 ] In 1985 Jean-Pierre Serre proposed that a Frey curve could not be modular and provided a partial proof. [ 6 ] [ 7 ] This showed that a proof of the semistable case of the Taniyama–Shimura conjecture would imply FLT. Serre did not provide a complete proof and the missing bit became known as the epsilon conjecture or ε-conjecture. In the summer of 1986, Kenneth Alan Ribet proved the epsilon conjecture, thereby proving that the Modularity theorem implied FLT. [ 8 ]
The origin of the name is from the ε part of "Taniyama-Shimura conjecture + ε ⇒ Fermat's last theorem".
Suppose that the Fermat equation with exponent p ≥ 5 [ 8 ] had a solution in non-zero integers a , b , c . The corresponding Frey curve E a p , b p , c p is an elliptic curve whose minimal discriminant Δ is equal to 2 −8 ( abc ) 2 p and whose conductor N is the radical of abc , i.e. the product of all distinct primes dividing abc . An elementary consideration of the equation a p + b p = c p , makes it clear that one of a , b , c is even and hence so is N . By the Taniyama–Shimura conjecture, E is a modular elliptic curve. Since all odd primes dividing a , b , c in N appear to a p th power in the minimal discriminant Δ , by Ribet's theorem repetitive level descent modulo p strips all odd primes from the conductor. However, no newforms of level 2 remain because the genus of the modular curve X 0 (2) is zero (and newforms of level N are differentials on X 0 ( N )) . | https://en.wikipedia.org/wiki/Ribet's_theorem |
R ibo n ucleo p rotein Networks Analyzed by M ut a tional P rofiling (RNP-MaP) is a strategy for probing RNA - protein networks and protein binding sites at a nucleotide resolution. Information about RNP assembly and function can facilitate a better understanding of biological mechanisms. RNP-MaP uses NHS - diazirine (SDA), a hetero-bifunctional crosslinker, to freeze RNA-bound proteins in place. Once the RNA-protein crosslinks are formed, MaP reverse transcription [ 1 ] is then conducted to reversely transcribe the protein-bound RNAs as well as introduce mutations at the site of RNA-protein crosslinks. Sequencing results of the cDNAs reveal information about both protein-RNA interaction networks and protein binding sites. [ 2 ]
RNA-MaP involves three major components: [ 2 ]
Long-wavelength UV and SDA reagents are first supplied to living cells to crosslink protein residues with RNA by forming amide bonds between amine groups of lysine (or arginine ) residues and succinimidyl esters. Next, cells containing crosslinked RNPs are lysed and the RNA-bound proteins are digested into peptide adducts. MaP reverse transcription is then performed to label the protein-RNA binding sites through peptide adduct-induced mutations . Sequencing of the mutation-containing cDNA product will reveal the mutation sites (or RNP-MaP sites) and the correlations between the RNP-MaP sites are computationally determined using 3-nucleotide windows. [ 2 ] [ 4 ]
RNP-MaP sites are defined as protein bound nucleotides. SDA and UV treated and UV only treated sample sequence reads are aligned and mutations are counted using ShapeMapper2 software. [ 5 ] The SDA or RNP-MaP reactivity for a nucleotide is the ratio of the crosslinked (SDA and UV treated) mutational frequency to the un-crosslinked (UV only) mutation frequency. Using differential mutational signatures, RNP-MaP sites are identified based on universal normalization factors and thresholds on each RNA nucleotide (U, A, C, and G) derived from analysis of ribonucleoproteins of known structure. [ 2 ]
A nucleotide is identified as a RNP-MaP site if it passes three filters:
Protein-RNA interactions networks are identified using RNP-MaP correlations since multiple crosslink sites can be detected for a single RNA molecule. RNP-MaP correlations provide a complementary measure of protein binding to RNA independent of RNP-MaP sites. [ 2 ] They are identified using a G-test framework known as RingMapper. [ 4 ]
RNP-MaP correlations require a single RNA molecule to form at least two crosslinks and arise from any of three scenarios:
Using RNP-MaP correlations, a network of protein-RNA interaction sites is found and can then be used for functional analysis.
CLIP analyzes protein interactions with RNA by combining UV cross-linking and immunoprecipitation . CLIP-based techniques are able to map RNA binding protein binding sites of interest on a genome-wide scale. [ 6 ]
There are many CLIP-based methods including:
Quantitative mass spectrometry (MS) (or quantitative proteomics ) can be used to discover RNA-binding proteins (RBPs) bound to RNA. Labeling MS methods involve the differential use of stable isotope labels or chemical tagging of proteins in samples and controls. This is used to obtain enrichment scores and true binding partners through the ratio of labeled peptides. [ 12 ] Label-free MS methods are able to identify proteins in samples and controls. In order to distinguish true binding partners for nonspecific proteins, analytical tools used alongside spectral count data from non-quantitative MS are used to score the probability of a true RBP-RNA interaction [ 13 ]
RNP-MaP can help reveal functionally important RNA-protein binding networks through binding site density and interconnectivity independent of previous knowledge of interacting proteins. Because of the unbiased nature of the analysis, RNP-MaP is able to detect conserved RNA-protein interactions between species. [ 2 ]
RNP-MaP is also able to facilitate the characterization of functionally critical elements in large non-coding RNAs or even viral RNAs. [ 2 ]
As a standalone technique, RNP-MaP cannot be used to determine protein-RNA binding mechanisms or protein identities. In order to do so, RNP-MaP must be used in conjunction with other techniques such as CLIP and mass spectrometry. [ 2 ]
RNP-MaP requires extremely high read-depths for analysis. To identify RNP-MaP sites, 1000x sequencing coverage is required, while RNP-MaP correlation sites require 10,000x sequencing coverage. [ 2 ]
There are severe limitations on the ability to characterize RNP-MaP correlations between distant (>500 nucleotides) RNP-MaP sites. This is due to limitations of MaP reverse transcription processivity (500-600 nucleotides) and sequencing instrument clustering (<1,000 nucleotides). [ 2 ] | https://en.wikipedia.org/wiki/Ribonucleoprotein_Networks_Analyzed_by_Mutational_Profiling |
A ribonucleoprotein particle ( RNP ) is a complex formed between RNA and RNA-binding proteins (RBPs). [ 1 ] The term RNP foci can also be used to denote intracellular compartments involved in processing of RNA transcripts .
RBPs interact with RNA through various structural motifs. Aromatic amino acid residues in RNA-binding proteins result in stacking interactions with RNA. Lysine residues in the helical portion of RNA binding proteins help to stabilize interactions with other nucleic acids as a result of the force of attraction between the positively-charged lysine side chains and the negatively-charged phosphate "backbone" of RNA.
It is hypothesized that RNA sequences in the 3'-untranslated region determine the binding of RBPs, and that these RBPs determine the post-transcriptional fate of mRNAs.
RNP granules are a highly diverse group of compartments. These include stress granules , processing bodies , and exosomes in somatic cells . Many RNP granules are cell type and/or species specific. For example, chromatoid bodies are found only in male germ cells, whereas transport granules have so far been found only in neurons and oocytes . RNP granules function mainly by physically separating or associating transcripts with proteins. They function in the storage, processing, degradation and transportation of their associated transcripts.
RNP granules have been shown to have particular importance in cells where post-transcriptional regulation is of vital importance. For example, in neurons where transcripts must be transported and stored in dendrites for the formation and strengthening of connections, in oocytes/embryos where mRNAs are stored for years before being translated, and in developing sperm cells where transcription is halted before development is complete. | https://en.wikipedia.org/wiki/Ribonucleoprotein_particle |
A Riboprobe, abbreviation of RNA probe , is a segment of labelled RNA that can be used to detect a target mRNA or DNA during in situ hybridization . [ 1 ] RNA probes can be produced by in vitro transcription of cloned DNA inserted in a suitable plasmid downstream of a viral promoter. Some bacterial viruses code for their own RNA polymerases , which are highly specific for the viral promoters. Using these enzymes , labeled NTPs , and inserts inserted in both forward and reverse orientations, both sense and antisense riboprobes can be generated from a cloned gene .
Since James Watson and Francis Crick revealed the double helix nature of DNA molecule (Watson & Crick, 1953 [ 2 ] ), the hydrogen bonds between the four bases are well known: adenine always binds to thymine and cytosine always binds to guanine. This binding pattern is the basic principle of modern genetic technologies. Joseph Gall and Mary Lou Pardue published a paper in 1969 demonstrating that radioactive marked ribosomal DNA can be used to detect its complementary DNA sequence in a frog egg, [ 3 ] known as the first researchers who use DNA probes to perform in situ hybridization. RNA probes were proved to be able to perform the same function and also used with in situ hybridization . Fluorescent dyed probes replaced radio labeled probes due to the consideration of safety, stability, and ease of detection. [ 4 ] Detecting a DNA sequence is similar to "looking for a needle in a haystack, with the needle being the DNA sequence of interest and the haystack being a set of chromosomes [ 5 ] ". The ability of the DNA helix to disassociate, re-anneal and the remarkable accuracy of base-pairing grants riboprobes the ability to locate its complementary DNA sequence on chromosomes.
It is found by two independent riboprobes, that the most important cell populations of the hippocampus , are expressing high levels of diacylglycerol lipase α (DGL-α), an enzyme involved in the production of the endocannabinoid 2-arachidonoyl-glycerol (2-AG: C 23 H 38 O 4 ; 20: 4 , ω-6 ). [ 6 ]
There are two kinds of probes used during in situ hybridization: Riboprobes and DNA oligonucleotides probes. [ 7 ] Riboprobes are essential in the study of embryo development in which DNA probes are insufficient. With labelled (fluoresce-dyed, for instance) antisense RNA probes hybridized with developing embryo's mRNA, tracking the expression of genes in different stages of development is possible. RNA probes can be used in detecting either whole embryo's development or just on tissue sections of interest. The ability of riboprobes to bind to transcribed mRNA makes RNA probes important in research on model organisms : Drosophila, zebrafish, chick, Xenopus and mouse. [ 8 ] RNA probes can also be utilized in immunohistochemistry to identify tissue infection in embryos. [ 9 ] Viral mRNA can be targeted by its antisense RNA probes, while infected tissues don't have complementary mRNA that can hybridize with probes; the unique mRNA sequence of each organism makes the detection of expression of certain gene highly effective and accurate.
Fluorescence in situ hybridization (FISH)is the most widely used riboprobe technique. A target sequence and a probe are essential in FISH. First, the probe is labeled with either direct or indirect labeling strategy: hapten-modified nucleotides are used in indirect labeling, and fluorophore-modified nucleotides are used in direct labeling. The target DNA and probes are denatured and mixed, allows the re-annealing of DNA sequences. Indirect labeling requires an extra step to produce visualized signals that require use of enzymatic or immunological system, but provides greater signal amplification than direct labeling. [ 10 ]
FISH probes can also be used in karyotype studies. DNA probes can be labeled with various fluorochromes which produce a unique color for each chromosomes. The probes are then hybridized with metaphase chromosomes, producing unique patterns on each chromosomes. This method is useful when people want to study the translocation, deletion and duplication of chromosomes on a larger scale comparing to site-specific FISH. [ 11 ]
Baynes, John W.; Marek H. Dominiczak (2005). Medical Biochemistry 2nd. Edition . Elsevier Mosby . p. 477 . ISBN 978-0-7234-3341-5 .
YouTube video:in situ hybridization
A detailed description of Fluorescence In Situ Hybridization:
Riboprobe In Vitro Transcription Systems Technical Manual: | https://en.wikipedia.org/wiki/Riboprobe |
The Ribose repressor ( RbsR ) is a bacterial DNA-binding transcription repressor protein and a member of the LacI / GalR protein family. [ 1 ] In Escherichia coli , RbsR is responsible for regulation of genes involved in D-ribose metabolism. [ 2 ] In Bacillus subtilis , RbsR was shown to interact with Histidine-containing protein (HPr), an allosteric effector of the related LacI/GalR protein Catabolite Control Protein A (CcpA). [ 3 ]
This protein -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ribose_repressor |
A riboside is any glycoside of ribose . [ 1 ] Ribosides in the form of ribonucleosides and ribonucleotides play an important role in biochemistry.
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Riboside |
Ribosomal frameshifting , also known as translational frameshifting or translational recoding , is a biological phenomenon that occurs during translation that results in the production of multiple, unique proteins from a single mRNA . [ 1 ] The process can be programmed by the nucleotide sequence of the mRNA and is sometimes affected by the secondary, 3-dimensional mRNA structure . [ 2 ] It has been described mainly in viruses (especially retroviruses ), retrotransposons and bacterial insertion elements, and also in some cellular genes . [ 3 ]
Small molecules, proteins, and nucleic acids have also been found to stimulate levels of frameshifting. In December 2023, it was reported that in vitro -transcribed (IVT) mRNAs in response to BNT162b2 (Pfizer–BioNTech) anti-COVID-19 vaccine caused ribosomal frameshifting. [ 4 ]
Proteins are translated by reading tri-nucleotides on the mRNA strand, also known as codons , from one end of the mRNA to the other (from the 5' to the 3' end ) starting with the amino acid methionine as the start (initiation) codon AUG. Each codon is translated into a single amino acid . The code itself is considered degenerate , meaning that a particular amino acid can be specified by more than one codon. However, a shift of any number of nucleotides that is not divisible by 3 in the reading frame will cause subsequent codons to be read differently. [ 5 ] This effectively changes the ribosomal reading frame .
In this example, the following sentence of three-letter words makes sense when read from the beginning:
However, if the reading frame is shifted by one letter to between the T and H of the first word (effectively a +1 frameshift when considering the 0 position to be the initial position of T ),
then the sentence reads differently, making no sense.
In this example, the following sequence is a region of the human mitochondrial genome with the two overlapping genes MT-ATP8 and MT-ATP6 .
When read from the beginning, these codons make sense to a ribosome and can be translated into amino acids (AA) under the vertebrate mitochondrial code :
However, let's change the reading frame by starting one nucleotide downstream (effectively a "+1 frameshift" when considering the 0 position to be the initial position of A ):
Because of this +1 frameshifting, the DNA sequence is read differently. The different codon reading frame therefore yields different amino acids.
In the case of a translating ribosome, a frameshift can either result in nonsense mutation , a premature stop codon after the frameshift, or the creation of a completely new protein after the frameshift. In the case where a frameshift results in nonsense, the nonsense-mediated mRNA decay (NMD) pathway may destroy the mRNA transcript, so frameshifting would serve as a method of regulating the expression level of the associated gene. [ 6 ]
If a novel or off-target protein is produced, it can trigger other unknown consequences. [ 4 ]
In viruses this phenomenon may be programmed to occur at particular sites and allows the virus to encode multiple types of proteins from the same mRNA. Notable examples include HIV-1 (human immunodeficiency virus), [ 7 ] RSV ( Rous sarcoma virus ) [ 8 ] and the influenza virus (flu), [ 9 ] which all rely on frameshifting to create a proper ratio of 0-frame (normal translation) and "trans-frame" (encoded by frameshifted sequence) proteins. Its use in viruses is primarily for compacting more genetic information into a shorter amount of genetic material.
In eukaryotes it appears to play a role in regulating gene expression levels by generating premature stops and producing nonfunctional transcripts. [ 3 ] [ 10 ]
The most common type of frameshifting is −1 frameshifting or programmed −1 ribosomal frameshifting (−1 PRF) . Other, rarer types of frameshifting include +1 and −2 frameshifting. [ 2 ] −1 and +1 frameshifting are believed to be controlled by different mechanisms, which are discussed below. Both mechanisms are kinetically driven .
In −1 frameshifting, the ribosome slips back one nucleotide and continues translation in the −1 frame. There are typically three elements that comprise a −1 frameshift signal: a slippery sequence , a spacer region, and an RNA secondary structure. The slippery sequence fits a X_XXY_YYH motif, where XXX is any three identical nucleotides (though some exceptions occur), YYY typically represents UUU or AAA, and H is A, C or U. Because the structure of this motif contains 2 adjacent 3-nucleotide repeats it is believed that −1 frameshifting is described by a tandem slippage model, in which the ribosomal P-site tRNA anticodon re-pairs from XXY to XXX and the A-site anticodon re-pairs from YYH to YYY simultaneously. These new pairings are identical to the 0-frame pairings except at their third positions. This difference does not significantly disfavor anticodon binding because the third nucleotide in a codon, known as the wobble position , has weaker tRNA anticodon binding specificity than the first and second nucleotides. [ 2 ] [ 11 ] In this model, the motif structure is explained by the fact that the first and second positions of the anticodons must be able to pair perfectly in both the 0 and −1 frames. Therefore, nucleotides 2 and 1 must be identical, and nucleotides 3 and 2 must also be identical, leading to a required sequence of 3 identical nucleotides for each tRNA that slips. [ 12 ]
The slippery sequence for a +1 frameshift signal does not have the same motif, and instead appears to function by pausing the ribosome at a sequence encoding a rare amino acid. [ 13 ] Ribosomes do not translate proteins at a steady rate, regardless of the sequence. Certain codons take longer to translate, because there are not equal amounts of tRNA of that particular codon in the cytosol . [ 14 ] Due to this lag, there exist in small sections of codons sequences that control the rate of ribosomal frameshifting. Specifically, the ribosome must pause to wait for the arrival of a rare tRNA, and this increases the kinetic favorability of the ribosome and its associated tRNA slipping into the new frame. [ 13 ] [ 15 ] In this model, the change in reading frame is caused by a single tRNA slip rather than two.
Ribosomal frameshifting may be controlled by mechanisms found in the mRNA sequence (cis-acting). This generally refers to a slippery sequence, an RNA secondary structure, or both. A −1 frameshift signal consists of both elements separated by a spacer region typically 5–9 nucleotides long. [ 2 ] Frameshifting may also be induced by other molecules which interact with the ribosome or the mRNA (trans-acting).
Slippery sequences can potentially make the reading ribosome "slip" and skip a number of nucleotides (usually only 1) and read a completely different frame thereafter. In programmed −1 ribosomal frameshifting, the slippery sequence fits a X_XXY_YYH motif, where XXX is any three identical nucleotides (though some exceptions occur), YYY typically represents UUU or AAA, and H is A, C or U. In the case of +1 frameshifting, the slippery sequence contains codons for which the corresponding tRNA is more rare, and the frameshift is favored because the codon in the new frame has a more common associated tRNA. [ 13 ] One example of a slippery sequence is the polyA on mRNA, which is known to induce ribosome slippage even in the absence of any other elements. [ 16 ]
Efficient ribosomal frameshifting generally requires the presence of an RNA secondary structure to enhance the effects of the slippery sequence. [ 12 ] The RNA structure (which can be a stem-loop or pseudoknot ) is thought to pause the ribosome on the slippery site during translation, forcing it to relocate and continue replication from the −1 position. It is believed that this occurs because the structure physically blocks movement of the ribosome by becoming stuck in the ribosome mRNA tunnel. [ 2 ] This model is supported by the fact that strength of the pseudoknot has been positively correlated with the level of frameshifting for associated mRNA. [ 3 ] [ 17 ]
Below are examples of predicted secondary structures for frameshift elements shown to stimulate frameshifting in a variety of organisms. The majority of the structures shown are stem-loops, with the exception of the ALIL (apical loop-internal loop) pseudoknot structure. In these images, the larger and incomplete circles of mRNA represent linear regions. The secondary "stem-loop" structures, where "stems" are formed by a region of mRNA base pairing with another region on the same strand, are shown protruding from the linear DNA. The linear region of the HIV ribosomal frameshift signal contains a highly conserved UUU UUU A slippery sequence; many of the other predicted structures contain candidates for slippery sequences as well.
The mRNA sequences in the images can be read according to a set of guidelines. While A, T, C, and G represent a particular nucleotide at a position, there are also letters that represent ambiguity which are used when more than one kind of nucleotide could occur at that position. The rules of the International Union of Pure and Applied Chemistry ( IUPAC ) are as follows: [ 18 ]
These symbols are also valid for RNA, except with U (uracil) replacing T (thymine). [ 18 ]
Small molecules, proteins, and nucleic acids have been found to stimulate levels of frameshifting. For example, the mechanism of a negative feedback loop in the polyamine synthesis pathway is based on polyamine levels stimulating an increase in +1 frameshifts, which results in production of an inhibitory enzyme . Certain proteins which are needed for codon recognition or which bind directly to the mRNA sequence have also been shown to modulate frameshifting levels. MicroRNA (miRNA) molecules may hybridize to an RNA secondary structure and affect its strength. [ 6 ] | https://en.wikipedia.org/wiki/Ribosomal_frameshift |
Ribosomal RNA ( rRNA ) intergenic spacer analysis ( RISA ) is a method of microbial community analysis that provides a means of comparing differing environments or treatment impacts without the bias imposed by culture- dependent approaches. [ 1 ] RISA involves PCR amplification of a region of the rRNA gene operon between the small ( 16S ) and large ( 23S ) subunits called the intergenic spacer region ISR. [ 2 ]
By using oligonucleotide primers targeted to conserved regions in the 16S and 23S genes, RISA fragments can be generated from most of the dominant bacteria in an environmental sample. While the majority of the rRNA operon serves a structural function, portions of the 16S-23S intergenic region can encode tRNAs depending on the bacterial species. However the taxonomic value of the ISR lies in the significant heterogeneity in both length and nucleotide sequence. In RISA, we attempt to exploit the length heterogeneity of the ISR, which has been shown to range between 150 and 1500 bp with the majority of the ISR lengths being between 150 and 500 bp. [ 3 ]
The resulting PCR product will be a mixture of fragments contributed by several dominant community members. This product is electrophoresed in a polyacrylamide gel , and the DNA is visualized following staining. The result is a complex banding pattern that provides a community-specific profile, with each DNA band corresponding to a bacterial population on the original assemblage. | https://en.wikipedia.org/wiki/Ribosomal_intergenic_spacer_analysis |
Ribosomal pause refers to the queueing or stacking of ribosomes during translation of the nucleotide sequence of mRNA transcripts. These transcripts are decoded and converted into an amino acid sequence during protein synthesis by ribosomes. Due to the pause sites of some mRNA's, there is a disturbance caused in translation . [ 1 ] Ribosomal pausing occurs in both eukaryotes and prokaryotes. [ 2 ] [ 3 ] A more severe pause is known as a ribosomal stall . [ 4 ]
It's been known since the 1980s that different mRNAs are translated at different rates. The main reason for these differences was thought to be the concentration of varieties of rare tRNAs limiting the rate at which some transcripts could be decoded. [ 5 ] However, with research techniques such as ribosome profiling, it was found that at certain sites there were higher concentrations of ribosomes than average, and these pause sites were tested with specific codons. No link was found between the occupancy of specific codons and amount of their tRNAs. Thus, the early findings about rare tRNAs causing pause sites don't seem plausible. [ 2 ]
Two techniques can localize the ribosomal pause site in vivo ; a micrococcal nuclease protection assay and isolation of polysomal transcript. [ 6 ] Isolation of polysomal transcripts occurs by centrifuging tissue extracts through a sucrose cushion with translation elongation inhibitors, for example cycloheximide . [ 7 ]
Ribosome pausing can be detected during preprolactin synthesis on free polysomes , when the ribosome is paused the other ribosomes are tightly stacked together. When the ribosome pauses, during translation, the fragments that started to translate before the pause took place are overrepresented. However, along with the mRNA if the ribosome pauses then specific bands will be improved in the trailing edge of the ribosome. [ 8 ]
Some of the elongation inhibitors, such as: cycloheximide (in eukaryotes) or chloramphenicol , cause the ribosomes to pause and to accumulate in the start codons. Elongation Factor P regulates the ribosomal pause at polyproline in bacteria, and when there is no EFP the density of ribosomes decreases from the polyproline motifs. If there are multiple ribosome pauses, then the EFP won't resolve it. [ 9 ]
Some forms of ribosomal pause are reversible without needing to discard the translated peptide and mRNA. This sort, usually described as a slowdown, is usually caused by polyproline stretches (resolved by EFP or eIF5A) and uncharged tRNA . [ 4 ] Slowdowns are important for the cell to control how much protein is produced; [ 10 ] it also aids co-translational folding of the nascent polypeptide on the ribosome, and delays protein translation while its encoding mRNA; this can trigger ribosomal frameshifting . [ 11 ]
More severe "stalls" can be caused an actual lack of tRNA or by the mRNA terminating without a stop codon . [ 4 ] In this case, ribosomal quality control (RQC) performs crisis rescue by translational abandonment. This releases the ribosome from the mRNA. The incomplete polypeptide is targeted for destruction; in eukaryotes, mRNA no-go decay is also triggered. [ 11 ]
It is difficult for RQC machinery to differentiate between a slowdown and a stall. It is possible for a mRNA sequence that normally produces a protein slowly to produce nothing instead due to intervention by RQC under different conditions. [ 12 ]
In bacteria , three rescue mechanisms are known.
In eukaryotes, the main mechanism involves PELO : HBS1L . [ 4 ]
When the ribosome movement on the mRNA is not linear, the ribosome gets paused at different regions without a precise reason. The ribosome pause position will help to identify the mRNA sequence features, structure, and the transacting factor that modulates this process. [ 15 ] The advantage of ribosomal pause sites that are located at protein domain boundaries are aiding the folding of a protein. [ 1 ] There are times when the ribosomal pause does not cause an advantage and it needs to be restricted. In translation, elF5A inhibits ribosomal pausing for translation to function better. Ribosomal pausing can cause more non-canonical start codons without elF5A in eukaryotic cells. When there is a lack of elF5A in the eukaryotic cell, it can cause an increase in ribosomal pausing. [ 16 ] The ribosomal pausing process can also be used by amino acids to control translation. [ 10 ]
It is known that ribosomes pause at distinct sites, but the reasons for these pauses are mostly unknown. Also, the ribosome pauses if the pseudoknot is disrupted. 10% of the ribosome pauses at the pseudoknot and 4% of the ribosomes are terminated. Before the ribosome is obstructed it passes the pseudoknot. [ 17 ] An assay was put together by a group from the University of California in an effort to show a model of mRNA. The translation was monitored in two in vitro systems. It was found that translating ribosomes aren't uniformly distributed along an mRNA. [ 8 ] Protein folding in vivo is also important and is related to protein synthesis. For finding the location of the ribosomal pause in vivo , the methods that have been used to find the ribosomal pause in vitro can be changed to find these specific locations in vivo. [ 6 ]
Ribosome profiling is a method that can reveal pausing sites through sequencing the ribosome protected fragments (RPFs or footprints) to map ribosome occupancy on the mRNA. Ribosome profiling has the ability to reveal the ribosome pause sites in the whole transcriptome . When the kinetics layer is added, [ 18 ] it discloses the time of the pause, and the translation takes place. [ 9 ] Ribosome profiling is however still in early stages and has biases that need to be explored further. [ 19 ] Ribosome profiling allows for translation to be measured more accurately and precisely. During this process, translation needs to be stopped in order for ribosome profiling to be performed. This may cause a problem with ribosome profiling because the methods that are used to stop translation in an experiment can impact the outcome, which causes incorrect results. Ribosome profiling is useful for getting specific information on translation and the process of protein synthesis. [ 20 ] | https://en.wikipedia.org/wiki/Ribosomal_pause |
In molecular biology , ribosomal s6 kinase ( rsk ) is a family of protein kinases involved in signal transduction . There are two subfamilies of rsk, p90 rsk , also known as MAPK-activated protein kinase-1 (MAPKAP-K1), and p70 rsk , also known as S6-H1 Kinase or simply S6 Kinase . There are three variants of p90 rsk in humans, rsk 1-3. Rsks are serine/threonine kinases and are activated by the MAPK/ERK pathway . There are two known mammalian homologues of S6 Kinase: S6K1 and S6K2 .
Both p90 and p70 Rsk phosphorylate ribosomal protein s6 , part of the translational machinery, but several other substrates have been identified, including other ribosomal proteins. Cytosolic substrates of p90 rsk include protein phosphatase 1 ; glycogen synthase kinase 3 (GSK3); L1 CAM , a neural cell adhesion molecule; Son of Sevenless , the Ras exchange factor; and Myt1 , an inhibitor of cdc2 . [ 1 ]
RSK phosphorylation of SOS1 ( Son of Sevenless ) at Serines 1134 and 1161 creates 14-3-3 docking site. This interaction of phospho SOS1 and 14-3-3 negatively regulates Ras-MAPK pathway . [ 2 ]
p90 rsk also regulates transcription factors including cAMP response element-binding protein (CREB); estrogen receptor -α (ERα); IκBα / NF-κB ; and c-Fos . [ 1 ]
p90 Rsk-1 is located at 1p . [ 3 ]
p90 Rsk-2 is located at Xp22.2 and contains 22 exons . Mutations in this gene have been associated with Coffin–Lowry syndrome , a disease characterised by severe psychomotor retardation and other developmental abnormalities. [ 4 ]
p90 Rsk-3 is located at 6q27 . [ 5 ]
The main distinguishing feature between p90 rsk and p70 rsk is that the 90 kDa family contain two non-identical kinase domains, while the 70 kDa family contain only one kinase domain.
Rsk was first identified in Xenopus laevis eggs by Erikson and Maller in 1985. [ 7 ] | https://en.wikipedia.org/wiki/Ribosomal_s6_kinase |
Ribosomally synthesized and post-translationally modified peptides ( RiPPs ), also known as ribosomal natural products , are a diverse class of natural products of ribosomal origin. [ 1 ] Consisting of more than 20 sub-classes, RiPPs are produced by a variety of organisms , including prokaryotes , eukaryotes , and archaea , and they possess a wide range of biological functions .
As a consequence of the falling cost of genome sequencing and the accompanying rise in available genomic data, scientific interest in RiPPs has increased in the last few decades. Because the chemical structures of RiPPs are more closely predictable from genomic data than are other natural products (e.g. alkaloids , terpenoids ), their presence in sequenced organisms can, in theory, be identified rapidly. This makes RiPPs an attractive target of modern natural product discovery efforts.
RiPPs consist of any peptides (i.e. molecular weight below 10 kDa) that are ribosomally-produced and undergo some degree of enzymatic post-translational modification . This combination of peptide translation and modification is referred to as "post-ribosomal peptide synthesis" (PRPS) in analogy with nonribosomal peptide synthesis (NRPS).
Historically, the current sub-classes of RiPPs were studied individually, and common practices in nomenclature varied accordingly in the literature. More recently, with the advent of broad genome sequencing, it has been realized that these natural products share a common biosynthetic origin. In 2013, a set of uniform nomenclature guidelines were agreed upon and published by a large group of researchers in the field. [ 1 ] Prior to this report, RiPPs were referred to by a variety of designations, including post-ribosomal peptides , ribosomal natural products , and ribosomal peptides .
The acronym "RiPP" stands for " ri bosomally synthesized and p ost-translationally modified p eptide".
RiPPs constitute one of the major superfamilies of natural products , like alkaloids , terpenoids , and nonribosomal peptides , although they tend to be large, with molecular weights commonly in excess of 1000 Da . [ 1 ] The advent of next-generation sequencing methods has made genome mining of RiPPs a common strategy. [ 2 ] In part due to their increased discovery and hypothesized ease of engineering , the use of RiPPs as drugs is increasing. Although they are ribosomal peptides in origin, RiPPs are typically categorized as small molecules rather than biologics due to their chemical properties, such as moderate molecular weight and relatively high hydrophobicity .
The uses and biological activities of RiPPs are diverse.
RiPPs in commercial use include nisin , a food preservative , thiostrepton , a veterinary topical antibiotic , and nosiheptide and duramycin, which are animal feed additives . Phalloidin functionalized with a fluorophore is used in microscopy as a stain due to its high affinity for actin . Anantin is a RiPP used in cell biology as an atrial natriuretic peptide receptor inhibitor . [ 3 ]
In 2012-2013, a derivatized RiPP in clinical trials was LFF571. Phase II clinical trials of LFF571, a derivative of the thiopeptide GE2270-A, for the treatment of Clostridioides difficile infections, with comparable safety and efficacy to vancomycin , was terminated early as the results were unfavorable. [ 4 ] [ 5 ] Also recently in clinical trials was the NVB302 (a derivative of the lantibiotic actagardine) which is used for the treatment of Clostridioides difficile infection. [ 6 ] Duramycin has completed phase II clinical trials for the treatment of cystic fibrosis . [ 7 ]
Other bioactive RiPPs include the antibiotics cyclothiazomycin and bottromycin , the ultra-narrow spectrum antibiotic plantazolicin , and the cytotoxin patellamide A . Streptolysin S, the toxic virulence factor of Streptococcus pyogenes , is also a RiPP. Additionally, human thyroid hormone itself is a RiPP due to its biosynthetic origin as thyroglobulin .
Amatoxins and phallotoxins are 8- and 7-membered natural products, respectively, characterized by N-to-C cyclization in addition to a tryptathionine motif derived from the crosslinking of Cys and Trp. [ 8 ] [ 9 ] The amatoxins and phallotoxins also differ from other RiPPs based on the presence of a C-terminal recognition sequence in addition to the N-terminal leader peptide. α-Amanitin , an amatoxin, has a number of posttranslational modifications in addition to macrocyclization and formation of the tryptathionine bridge: oxidation of the tryptathionine leads to the presence of a sulfoxide , and numerous hydroxylations decorate the natural product. As an amatoxin, α-amanitin is an inhibitor of RNA polymerase II . [ 10 ]
Bottromycins contain a C-terminal decarboxylated thiazole in addition to a macrocyclic amidine . [ 11 ]
There are currently six known bottromycin compounds, which differ in the extent of side chain methylation, an additional characteristic of the bottromycin class. The total synthesis of bottromycin A2 was required to definitively determine the structure of the first bottromycin. [ 11 ]
Thus far, gene clusters predicted to produce bottromycins have been identified in the genus Streptomyces . Bottromycins differ from other RiPPs in that there is no N-terminal leader peptide. Rather, the precursor peptide has a C-terminal extension of 35-37 amino acids, hypothesized to act as a recognition sequence for posttranslational machinery. [ 12 ]
Cyanobactins are diverse metabolites from cyanobacteria with N-to-C macrocylization of a 6–20 amino acid chain. Cyanobactins are natural products isolated from cyanobacteria, and close to 30% of all cyanobacterial strains are thought to contain cyanobacterial gene clusters. [ 13 ] However, while thus far all cyanobactins are credited to cyanobacteria, there exists the possibility that other organisms could produce similar natural products.
The precursor peptide of the cyanobactin family is traditionally designated the "E" gene, whereas precursor peptides are designated gene "A" in most RiPP gene clusters. "A" is a serine protease involved in cleavage of the leader peptide and subsequent macrocyclization of the peptide natural product, in combination with an additional serine protease homologue, the encoded by gene "G". Members of the cyanobactin family may bear thiazolines/oxazolines, thiazoles/oxazoles, and methylations depending on additional modification enzymes. For example, perhaps the most famous cyanobactin is patellamide A , which contains two thiazoles, a methyloxazoline, and an oxazoline in its final state, a macrocycle derived from 8 amino acids.
Lanthipeptides are one of the most well-studied families of RiPPs. The family is characterized by the presence of lanthionine (Lan) and 3-methyllanthionine (MeLan) residues in the final natural product. There are four major classes of lanthipeptides, delineated by the enzymes responsible for installation of Lan and MeLan. The dehydratase and cyclase can be two separate proteins or one multifunctional enzyme. Previously, lanthipeptides were known as "lantipeptides" before a consensus was reached in the field. [ 1 ]
Lantibiotics are lanthipeptides that have known antimicrobial activity. The founding member of the lanthipeptide family, nisin , is a lantibiotic that has been used to prevent the growth of food-born pathogens for over 40 years. [ 14 ]
Lasso peptides are short peptides containing an N-terminal macrolactam macrocycle "ring" through which a linear C-terminal "tail" is threaded. [ 15 ] [ 16 ] Because of this threaded-loop topology , these peptides resemble lassos , giving rise to their name. They are a member of a larger class of amino-acid-based lasso structures . Additionally, lasso peptides are formally rotaxanes .
The N-terminal "ring" can be from 7 to 9 amino acids long and is formed by an isopeptide bond between the N-terminal amine of the first amino acid of the peptide and the carboxylate side chain of an aspartate or glutamate residue. The C-terminal "tail" ranges from 7 to 15 amino acids in length. [ 15 ]
The first amino acid of lasso peptides is almost invariably glycine or cysteine , with mutations at this site not being tolerated by known enzymes. [ 16 ] Thus, bioinformatics -based approaches to lasso peptide discovery have thus used this as a constraint. [ 15 ] However, some lasso peptides were recently discovered that also contain serine or alanine as their first residue. [ 17 ]
The threading of the lasso tail is trapped either by disulfide bonds between ring and tail cysteine residues (class I lasso peptides), by steric effects due to bulky residues on the tail (class II lasso peptides), or both (class III lasso peptides). [ 16 ] The compact structure makes lasso peptides frequently resistant to proteases or thermal unfolding . [ 16 ]
Linear azole(in)e-containing peptides (LAPs) contain thiazoles and oxazoles , or their reduced thiazoline and oxazoline forms. Thiazol(in)es are the result of cyclization of Cys residues in the precursor peptide, while (methyl)oxazol(in)es are formed from Thr and Ser. Azole and azoline formation also modifies the residue in the -1 position, or directly C -terminal to the Cys, Ser, or Thr. A dehydrogenase in the LAP gene cluster is required for oxidation of azolines to azoles.
Plantazolicin is a LAP with extensive cyclization. Two sets of five heterocycles endow the natural product with structural rigidity and unusually selective antibacterial activity. [ 18 ] Streptolysin S (SLS) is perhaps the most well-studied and most famous LAP, in part because the structure is still unknown since the discovery of SLS in 1901. Thus, while the biosynthetic gene cluster suggests SLS is a LAP, structural confirmation is lacking.
Microcins are all RiPPs produced by Enterobacteriaceae with a molecular weight <10 kDa. Many members of other RiPP families, such as microcin E492, [ 19 ] microcin B17 (LAP) and microcin J25 (Lasso peptide) are also considered microcins. Instead of being classified based on posttranslational modifications or modifying enzymes, microcins are instead identified by molecular weight, native producer, and antibacterial activity. Microcins are either plasmid- or chromosome-encoded, but specifically have activity against Enerobacteriaceae. Because these organisms are also often producers of microcins, the gene cluster contains not only a precursor peptide and modification enzymes, but also a self-immunity gene to protect the producing strain, and genes encoding export of the natural product.
Microcins have bioactivity against Gram-negative bacteria but usually display narrow-spectrum activity due to hijacking of specific receptors involved in the transport of essential nutrients.
Most of the characterized thiopeptides have been isolated from Actinobacteria. [ 20 ] General structural features of thiopeptide macrocycles , are dehydrated amino acids and thiazole rings formed from dehydrated serine / threonine and cyclized cysteine residues, respectively
The thiopeptide macrocycle is closed with a six-membered nitrogen-bearing ring. Oxidation state and substitution pattern of the nitrogenous ring determines the series of the thiopeptide natural product. [ 1 ] While the mechanism of macrocyclization is not known, the nitrogenous ring can exist in thiopeptides as a piperidine , dehydropiperidine, or a fully oxidized pyridine . Additionally, some thiopeptides bear a second macrocycle, which bears a quinaldic acid or indolic acid residue derived from tryptophan . Perhaps the most well-characterized thiopeptide, thiostrepton A, contains a dehydropiperidine ring and a second, quinaldic acid-containing macrocycle. Four residues are dehydrated during posttranslational modification, and the final natural product also bears four thiazoles and one azoline.
Autoinducing Peptides (AIPs) and quorum sensing peptides are used as signaling molecules in the process called quorum sensing . AIPs are characterized by the presence of a cyclic ester or thioester , unlike other regulatory peptides that are linear. In pathogens , exported AIPs bind to extracellular receptors that trigger the production of virulence factors . [ 21 ] In Staphylococcus aureus , AIPs are biosynthesized from a precursor peptide composed of a C-terminal leader region, the core region, and negatively charged tail region that is, along with the leader peptide, cleaved before AIP export. [ 22 ]
Bacterial Head-to-Tail Cyclized Peptides refers exclusively to ribosomally synthesized peptides with 35-70 residues and a peptide bond between the N- and C-termini, sometimes referred to as bacteriocins , although this term is used more broadly. The distinctive nature of this class is not only the relatively large size of the natural products but also the modifying enzymes responsible for macrocyclization. Other N-to-C cyclized RiPPs, such as the cyanobactins and orbitides, have specialized biosynthetic machinery for macrocylization of much smaller core peptides. Thus far, these bacteriocins have been identified only in Gram-positive bacteria . Enterocin AS-48 was isolated from Enterococcus and, like other bacteriocins, is relatively resistant to high temperature, pH changes, and many proteases as a result of macrocyclization. [ 23 ] Based on solution structures and sequence alignments, bacteriocins appear to take on similar 3D structures despite little sequence homology, contributing to stability and resistance to degradation.
Conopeptides and other toxoglossan peptides are the components of the venom of predatory marine snails, such as the cone snails or Conus . [ 24 ] Venom peptides from cone snails are generally smaller than those found in other animal venoms (10-30 amino acids vs. 30-90 amino acids) and have more disulfide crosslinks . [ 24 ] A single species may have 50-200 conopeptides encoded in its genome, recognizable by a well-conserved signal sequence. [ 1 ]
Cyclotides are RiPPs with a head-to-tail cyclization and three conserved disulfide bonds that form a knotted structure called a cyclic cysteine knot motif. [ 25 ] [ 26 ] No other posttranslational modifications have been observed on the characterized cyclotides, which are between 28 - 37 amino acids in size. Cyclotides are plant natural products and the different cyclotides appear to be species-specific. While many activities have been reported for cyclotides, it has been hypothesized that all are united by a common mechanism of binding to and disrupting the cell membrane. [ 27 ]
Glycocins are RiPPs that are glycosylated antimicrobial peptides . Only two members have been fully characterized, making this a small RiPP class. [ 28 ] [ 29 ] Sublancin 168 and glycocin F are both Cys-glycosylated and, in addition, have disulfide bonds between non-glycosylated Cys residues. While both members bear S-glycosyl groups, RiPPs bearing O- or N-linked carbohydrates will also be included in this family as they are discovered.
Linaridins are characterized by C-terminal aminovinyl cysteine residues. While this posttranslational modification is also seen in the lanthipeptides epidermin and mersacidin, linaridins do not have Lan or MeLan residues. In addition, the linaridin moiety is formed from modification of two Cys residues, whereas lanthipeptide aminovinyl cysteines are formed from Cys and dehydroalanine (Dha). [ 30 ] The first linaridin to be characterized was cypemycin . [ 31 ]
Microviridins are cyclic N -acetylated trideca- and tetradecapeptides with ω-ester and/or ω-amide bonds. Lactone formation through glutamate or aspartate ω-carboxy groups and the lysine ε-amino group forms macrocycles in the final natural product. This class of RiPPs function as protease inhibitors and were originally isolated from Microcystis viridis . Gene clusters encoding microviridins have also been identified in genomes across the Bacteroidetes and Proteobacteria phyla. [ 32 ]
Orbitides are plant-derived N-to-C cyclized peptides with no disulfide bonds. Also referred to as Caryophyllaceae-like homomonocyclopeptides, [ 33 ] orbitides are 5-12 amino acids in length and are composed of mainly hydrophobic residues. Similar to the amatoxins and phallotoxins, the gene sequences of orbitides suggest the presence of a C-terminal recognition sequence. In the flaxseed variety Linum usitatissimum , a precursor peptide was found using Blast searching that potentially contains five core peptides separated by putative recognition sequences. [ 34 ]
Proteusins are named after "Proteus", a Greek shape-shifting sea god. Until now, the only known members in the family of Proteusins are called polytheonamides. They were originally presumed to be nonribosomal natural products due to the presence of many D-amino acids and other non-proteinogenic amino acids . However, a metagenomic study revealed the natural products as the most extensively modified class of RiPPs known to date. [ 35 ] Six enzymes are responsible for installing a total of 48 posttranslational modifications onto the polytheonamide A and B precursor peptides, including 18 epimerizations . Polytheonamides are exceptionally large, as a single molecule is able to span a cell membrane and form an ion channel . [ 36 ] [ 37 ]
Sactipeptides contain intramolecular linkages between the sulfur of Cys residues and the α-carbon of another residue in the peptide. A number of nonribosomal peptides bear the same modification. In 2003, the first RiPP with a sulfur-to-α-carbon linkage was reported when the structure of subtilosin A was determined using isotopically enriched media and NMR spectroscopy . [ 38 ] In the case of subtilosin A, isolated from Bacillus subtilis 168 , the Cα crosslinks between Cys4 and Phe31, Cys7 and Thr28, and Cys13 and Phe22 are not the only posttranslational modifications; the C- and N-termini form an amide bond , resulting in a circular structure that is conformationally restricted by the Cα bonds. Sactipeptides with antimicrobial activity are commonly referred to as sactibiotics ( s ulfur to a lpha- c arbon an tibiotic ). [ 39 ]
RiPPs are characterized by a common biosynthetic strategy wherein genetically-encoded peptides undergo translation and subsequent chemical modification by biosynthetic enzymes.
All RiPPs are synthesized first at the ribosome as a precursor peptide . This peptide consists of a core peptide segment which is typically preceded (and occasionally followed) by a leader peptide segment and is typically ~20-110 residues long. The leader peptide is usually important for enabling enzymatic processing of the precursor peptide via aiding in recognition of the core peptide by biosynthetic enzymes and for cellular export . Some RiPPs also contain a recognition sequence C-terminal to the core peptide; these are involved in excision and cyclization . Additionally, eukaryotic RiPPs may contain a signal segment of the precursor peptide which helps direct the peptide to cellular compartments . [ 1 ]
During RiPP biosynthesis, the unmodified precursor peptide (containing an unmodified core peptide, UCP ) is recognized and chemically modified sequentially by biosynthetic enzymes (PRPS). Examples of modifications include dehydration (i.e. lanthipeptides , thiopeptides), cyclodehydration (i.e. thiopeptides), prenylation (i.e. cyanobactins), and cyclization (i.e. lasso peptides), among others. The resulting modified precursor peptide (containing a modified core peptide, MCP ) then undergoes proteolysis , wherein the non-core regions of the precursor peptide are removed. This results in the mature RiPP . [ 1 ]
Papers published prior to a recent community consensus [ 1 ] employ differing sets of nomenclature. The precursor peptide has been referred to previously as prepeptide , prepropeptide , or structural peptide . The leader peptide has been referred to as a propeptide , pro-region , or intervening region . Historical alternate terms for core peptide included propeptide , structural peptide , and toxin region (for conopeptides, specifically). [ 1 ]
Lanthipeptides are characterized by the presence lanthionine (Lan) and 3-methyllanthionine (MeLan) residues. Lan residues are formed from a thioether bridge between Cys and Ser, while MeLan residues are formed from the linkage of Cys to a Thr residue. The biosynthetic enzymes responsible for Lan and MeLan installation first dehydrate Ser and Thr to dehydroalanine (Dha) and dehydrobutyrine (Dhb), respectively. Subsequent thioether crosslinking occurs through a Michael-type addition by Cys onto Dha or Dhb. [ 40 ]
Four classes of lanthipeptide biosynthetic enzymes have been designated. [ 41 ] Class I lanthipeptides have dedicated lanthipeptide dehydratases , called LanB enzymes, though more specific designations are used for particular lanthipeptides (e.g. NisB is the nisin dehydratase). A separate cyclase, LanC, is responsible for the second step in Lan and MeLan biosynthesis. However, class II, III, and IV lanthipeptides have bifunctional lanthionine synthetases in their gene clusters, meaning a single enzyme carries out both dehydration and cyclization steps. Class II synthetases, designated LanM synthetases, have N-terminal dehydration domains with no sequence homology to other lanthipeptide biosynthetic enzymes; the cyclase domain has homology to LanC. Class III (LanKC) and IV (LanL) enzymes have similar N-terminal lyase and central kinase domains, but diverge in C-terminal cyclization domains: the LanL cyclase domain is homologous to LanC, but the class III enzymes lack Zn-ligand binding domains. [ 42 ]
The hallmark of linear azol(in)e-containing peptide (LAP) biosynthesis is the formation of azol(in)e heterocycles from the nucleophilic amino acids serine , threonine , or cysteine . [ 1 ] [ 43 ] This is accomplished by three enzymes referred to as the B, C, and D proteins; the precursor peptide is referred to as the A protein, as in other classes. [ 1 ]
The C protein is mainly involved in leader peptide recognition and binding and is sometimes called a scaffolding protein. The D protein is an ATP-dependent cyclodehydratase that catalyzes the cyclodehydration reaction, resulting in formation of an azoline ring. This occurs by direct activation of the amide backbone carbonyl with ATP, resulting in stoichiometric ATP consumption. [ 44 ] The C and D proteins are occasionally present as a single, fused protein, as is the case for trunkamide biosynthesis. The B protein is a flavin mononucleotide (FMN)-dependent dehydrogenase which oxidizes certain azoline rings into azoles .
The B protein is typically referred to as the dehydrogenase ; the C and D proteins together form the cyclodehydratase , although the D protein alone performs the cyclodehydration reaction. Early work on microcin B17 adopted a different nomenclature for these proteins, but a recent consensus has been adopted by the field as described above. [ 1 ]
Cyanobactin biosynthesis requires proteolytic cleavage of both N-terminal and C-terminal portions of the precursor peptide. The defining proteins are thus an N-terminal protease , referred to as the A protein, and a C-terminal protease , referred to as the G protein. The G protein is also responsible for macrocyclization .
For cyanobactins, the precursor peptide is referred to as the E peptide. [ 1 ] Minimally, the E peptide requires a leader peptide region, a core (structural) region, and both N-terminal and C-terminal protease recognition sequences. In contrast to most RiPPs, for which a single precursor peptide encodes a single natural product via a lone core peptide, cyanobactin E peptides can contain multiple core regions; multiple E peptides can even be present in a single gene cluster. [ 1 ] [ 45 ]
Many cyanobactins also undergo heterocyclization by a heterocyclase (referred to as the D protein), installing oxazoline or thiazoline moieties from Ser/Thr/Cys residues prior to the action of the A and G proteases. [ 1 ] The heterocyclase is an ATP -dependent YcaO homologue that behaves biochemically in the same manner as YcaO-domain cyclodehydratases in thiopeptide and linear azol(in)e-containing peptide (LAP) biosynthesis (described above).
A common modification is prenylation of hydroxyl groups by an F protein prenyltransferase . Oxidation of azoline heterocycles to azoles can also be accomplished by an oxidase domain located on the G protein. Unusual for ribosomal peptides , cyanobactins can include D-amino acids ; these can occur adjacent to azole or azoline residues. [ 1 ] The functions of some proteins found commonly in cyanobactin biosynthetic gene clusters , the B and C proteins, are unknown.
Thiopeptide biosynthesis involves particularly extensive modification of the core peptide scaffold. Indeed, due to the highly complex structures of thiopeptides, it was commonly thought that these natural products were nonribosomal peptides . Recognition of the ribosomal origin of these molecules came in 2009 with the independent discovery of the gene clusters for several thiopeptides. [ 1 ] [ 46 ] [ 47 ] [ 48 ] [ 49 ]
The standard nomenclature for thiopeptide biosynthetic proteins follows that of the thiomuracin gene cluster. [ 1 ] [ 48 ] In addition to the precursor peptide, referred to as the A peptide, thiopeptide biosynthesis requires at least six genes . These include lanthipeptide-like dehydratases , designated the B and C proteins, which install dehydroalanine and dehydrobutyrine moieties by dehydrating Ser/Thr precursor residues. Azole and azoline synthesis is effected by the E protein, the dehydrogenase , and the G protein, the cyclodehydratase . The nitrogen -containing heterocycle is installed by the D protein cyclase via a putative [4+2] cycloaddition of dehydroalanine moieties to form the characteristic macrocycle. [ 50 ] The F protein is responsible for binding of the leader peptide. [ 51 ]
Thiopeptide biosynthesis is biochemically similar to that of cyanobactins, lanthipeptides, and linear azol(in)e-containing peptides (LAPs). As with cyanobactins and LAPs, azole and azoline synthesis occurs via the action of an ATP -dependent YcaO - domain cyclodehydratase. In contrast to LAPs, where cyclodehydration occurs via the action of two distinct proteins responsible for leader peptide binding and cyclodehydrative catalysis , these are fused into a single protein (G protein) in cyanobactin and thiopeptide biosynthesis. [ 1 ] However, in thiopeptides, an additional protein, designated the Ocin-ThiF-like protein (F protein) is necessary for leader peptide recognition and potentially recruiting other biosynthetic enzymes. [ 51 ]
Lasso peptide biosynthesis requires at least three genes, referred to as the A, B, and C proteins. [ 1 ] [ 15 ] The A gene encodes the precursor peptide, which is modified by the B and C proteins into the mature natural product. The B protein is an adenosine triphosphate -dependent cysteine protease that cleaves the leader region from the precursor peptide. The C protein displays homology to asparagine synthetase and is thought to activate the carboxylic acid side chain of a glutamate or aspartate residue via adenylylation . The N-terminal amine formed by the B protein (protease) then reacts with this activated side chain to form the macrocycle -forming isopeptide bond. The exact steps and reaction intermediates in lasso peptide biosynthesis remain unknown due to experimental difficulties associated with the proteins. [ 15 ] Commonly, the B protein is referred to as the lasso protease , and the C protein is referred to as the lasso cyclase .
Some lasso peptide biosynthetic gene clusters also require an additional protein of unknown function for biosynthesis. Additionally, lasso peptide gene clusters usually include an ABC transporter (D protein) or an isopeptidase , although these are not strictly required for lasso peptide biosynthesis and are sometimes absent. [ 15 ] No X-ray crystal structure is yet known for any lasso peptide biosynthetic protein.
The biosynthesis of lasso peptides is particularly interesting due to the inaccessibility of the threaded-lasso topology to chemical peptide synthesis . | https://en.wikipedia.org/wiki/Ribosomally_synthesized_and_post-translationally_modified_peptides |
A ribosome binding site , or ribosomal binding site ( RBS ), is a sequence of nucleotides upstream of the start codon of an mRNA transcript that is responsible for the recruitment of a ribosome during the initiation of translation . Mostly, RBS refers to bacterial sequences, although internal ribosome entry sites (IRES) have been described in mRNAs of eukaryotic cells or viruses that infect eukaryotes . Ribosome recruitment in eukaryotes is generally mediated by the 5' cap present on eukaryotic mRNAs.
The RBS in prokaryotes is a region upstream of the start codon. This region of the mRNA has the consensus 5'-AGGAGG-3', also called the Shine-Dalgarno (SD) sequence. [ 1 ] The complementary sequence (CCUCCU), called the anti-Shine-Dalgarno (ASD) is contained in the 3’ end of the 16S region of the smaller (30S) ribosomal subunit. Upon encountering the Shine-Dalgarno sequence, the ASD of the ribosome base pairs with it, after which translation is initiated. [ 2 ] [ 3 ]
Variations of the 5'-AGGAGG-3' sequence have been found in Archaea as highly conserved 5′-GGTG-3′ regions, 5 basepairs upstream of the start site. Additionally, some bacterial initiation regions, such as rpsA in E.coli completely lack identifiable SD sequences. [ 4 ]
Prokaryotic ribosomes begin translation of the mRNA transcript while DNA is still being transcribed. Thus translation and transcription are parallel processes. Bacterial mRNA are usually polycistronic and contain multiple ribosome binding sites. Translation initiation is the most highly regulated step of protein synthesis in prokaryotes. [ 5 ]
The rate of translation depends on two factors:
The RBS sequence affects both of these factors.
The ribosomal protein S1 binds to adenine sequences upstream of the RBS. Increasing the concentration of adenine upstream of the RBS will increase the rate of ribosome recruitment. [ 5 ]
The level of complementarity of the mRNA SD sequence to the ribosomal ASD greatly affects the efficiency of translation initiation. Richer complementarity results in higher initiation efficiency. [ 6 ] This only holds up to a certain point - having too rich of a complementarity is known to paradoxically decrease the rate of translation as the ribosome then happens to be bound too tightly to proceed downstream. [ 6 ]
The optimal distance between the RBS and the start codon is variable - it depends on the portion of the SD sequence encoded in the actual RBS and its distance to the start site of a consensus SD sequence. Optimal spacing increases the rate of translation initiation once a ribosome has been bound. [ 6 ] The composition of nucleotides in the spacer region itself was also found to affect the rate of translation initiation in one study. [ 7 ]
Secondary structures formed by the RBS can affect the translational efficiency of mRNA, generally inhibiting translation. These secondary structures are formed by H-bonding of the mRNA base pairs and are sensitive to temperature. At a higher-than-usual temperature (~42 °C), the RBS secondary structure of heat shock proteins becomes undone thus allowing ribosomes to bind and initiate translation. This mechanism allows a cell to quickly respond to an increase in temperature. [ 5 ]
Ribosome recruitment in eukaryotes happens when eukaryote initiation factors elF4F and poly(A)-binding protein (PABP) recognize the 5' capped mRNA and recruit the 43S ribosome complex at that location. [ 8 ]
Translation initiation happens following recruitment of the ribosome, at the start codon (underlined) found within the Kozak consensus sequence ACC AUG G. Since the Kozak sequence itself is not involved in the recruitment of the ribosome, it is not considered a ribosome binding site. [ 2 ] [ 8 ]
Eukaryotic ribosomes are known to bind to transcripts in a mechanism unlike the one involving the 5' cap, at a sequence called the internal ribosome entry site . This process is not dependent on the full set of translation initiation factors (although this depends on the specific IRES) and is commonly found in the translation of viral mRNA. [ 9 ]
The identification of RBSs is used to determine the site of translation initiation in an unannotated sequence. This is referred to as N-terminal prediction. This is especially useful when multiple start codons are situated around the potential start site of the protein coding sequence. [ 10 ] [ 11 ]
Identification of RBSs is particularly difficult, because they tend to be highly degenerated. [ 12 ] One approach to identifying RBS in E.coli is using neural networks . [ 13 ] Another approach is using the Gibbs sampling method. [ 10 ]
The Shine-Dalgarno sequence, of the prokaryotic RBS, was discovered by John Shine and Lynn Dalgarno in 1975. [ 1 ] [ 14 ] The Kozak consensus sequence was first identified by Marilyn Kozak in 1984 [ 15 ] while she was in the Department of Biological Sciences at the University of Pittsburgh . [ 16 ] | https://en.wikipedia.org/wiki/Ribosome-binding_site |
Ribosome biogenesis is the process of making ribosomes . In prokaryotes , this process takes place in the cytoplasm with the transcription of many ribosome gene operons . In eukaryotes, it takes place both in the cytoplasm and in the nucleolus . It involves the coordinated function of over 200 proteins in the synthesis and processing of the three prokaryotic or four eukaryotic rRNAs , as well as assembly of those rRNAs with the ribosomal proteins. Most of the ribosomal proteins fall into various energy-consuming enzyme families including ATP-dependent RNA helicases , AAA-ATPases , GTPases , and kinases . [ 1 ] About 60% of a cell's energy is spent on ribosome production and maintenance. [ 2 ]
Ribosome biogenesis is a very tightly regulated process, and it is closely linked to other cellular activities like growth and division. [ 3 ] [ 4 ]
Some have speculated that in the origin of life, ribosome biogenesis predates cells, and that genes and cells evolved to enhance the reproductive capacity of ribosomes. [ 5 ]
Ribosomes are the macromolecular machines that are responsible for mRNA translation into proteins. The eukaryotic ribosome, also called the 80S ribosome, is made up of two subunits – the large 60S subunit (which contains the 25S [in plants] or 28S [in mammals], 5.8S, and 5S rRNA and 46 ribosomal proteins) and a small 40S subunit (which contains the 18S rRNA and 33 ribosomal proteins). [ 6 ] The ribosomal proteins are encoded by ribosomal genes.
There are 52 genes that encode the ribosomal proteins, and they can be found in 20 operons within prokaryotic DNA. Regulation of ribosome synthesis hinges on the regulation of the rRNA itself.
First, a reduction in aminoacyl-tRNA will cause the prokaryotic cell to respond by lowering transcription and translation . This occurs through a series of steps, beginning with stringent factors binding to ribosomes and catalyzing the reaction: GTP + ATP --> pppGpp + AMP
The γ-phosphate is then removed and ppGpp will bind to and inhibit RNA polymerase. This binding causes a reduction in rRNA transcription. A reduced amount of rRNA means that ribosomal proteins (r-proteins) will be translated but will not have an rRNA to bind to. Instead, they will negatively feedback and bind to their own mRNA, repressing r-protein synthesis. Note that r-proteins preferentially bind to their complementary rRNA if it is present, rather than mRNA.
The ribosome operons also include the genes for RNA polymerase and elongation factors (used in RNA translation). Regulation of all of these genes at once illustrate the coupling between transcription and translation in prokaryotes.
Ribosomal protein synthesis in eukaryotes is a major metabolic activity. It occurs, like most protein synthesis, in the cytoplasm just outside the nucleus. Individual ribosomal proteins are synthesized and imported into the nucleus through nuclear pores . See nuclear import for more about the movement of the ribosomal proteins into the nucleus.
The DNA is transcribed, at a high speed, in the nucleolus , which contains all 45S rRNA genes. The only exception is the 5S rRNA which is transcribed outside the nucleolus . After transcription, the rRNAs associate with the ribosomal proteins, forming the two types of ribosomal subunits (large and small). These will later assemble in the cytosol to make a functioning ribosome. See nuclear export for more about the movement of the ribosomal subunits out of the nucleus. [ 11 ]
Eukaryotic cells co-transcribe three of the mature rRNA species through a series of steps. The maturation process of the rRNAs and the process of recruiting the r-proteins happen in precursor ribosomal particles, sometimes called pre-ribosomes, and takes place in the nucleolus , nucleoplasm , and cytoplasm . The yeast, S. cerevisiae is the eukaryotic model organism for the study of ribosome biogenesis.
Ribosome biogenesis starts in the nucleolus . There, the 35S pre-RNA is transcribed from ribosomal genes as a polycistronic transcript by RNA polymerase I and processed into the 18S, 5.8S, and 25S subunits of the rRNA. [ 1 ] [ 3 ]
Transcription of polymerase I starts with a Pol I initiation complex that binds to the rDNA promoter . The formation of this complex requires the help of an upstream activating factor or UAF that associates with TATA-box binding protein and the core factor (CF). Together the two transcription factors allow the RNA pol I complex to bind with the polymerase I initiation factor, Rrn3. As the pol I transcript is produced, approximately 75 small nucleolar ribonucleoparticles (snoRNPs) facilitate the co-transcriptional covalent modifications of >100 rRNA residues. These snoRNPs control 2’-O-ribose methylation of nucleotides and also assist in the creation of pseudouridines . [ 1 ] At the 5’ end of rRNA transcripts, small subunit ribosomal proteins (Rps) and non-ribosomal factors assemble with the pre-RNA transcripts to create ball-like knobs. These knobs are the first pre-ribosomal particles in the small (40S) ribosomal subunit pathway. [ 1 ] The rRNA transcript is cleaved at the A2 site, and this separates the early 40S pre-ribosome from the remaining pre-rRNA that will combine with large subunit ribosomal proteins (Rpl) and other non-ribosomal factors to create the pre-60S ribosomal particles. [ 1 ]
The transcriptional assembly of the 40 S subunit precursor, sometimes referred to as the small subunit processome (SSU) or 90S particle happens in a hierarchical fashion – essentially a stepwise incorporation of the UTP-A, UTP-B, and UTP-C subcomplexes. These subcomplexes are made up of over 30 non ribosomal protein factors, the U3 snoRNP particle, a few Rps proteins, and the 35S pre-rRNA. Their exact role, though has not been discovered. [ 3 ] The composition of the pre-40S particle changes drastically once cleavage at the U3 snoRNPA dependent sites (sites A0, A1, and A2) are made. This cleavage event creates the 20S pre-rRNA and causes ribosomal factors to dissociate from the pre-40S particle. U3 is displaced from the nascent 40S by the helicase Dhr1. [ 12 ] At this point in the ribosome biogenesis process, the 40S pre-ribosome already shows the “head” and “body” structures of the mature 40S subunit. The 40S pre-ribosome is transported out of the nucleolus and into the cytoplasm. The cytoplasmic 40S pre-ribosome now contains ribosomal proteins, the 20s rRNA and a few non-ribosomal factors. The final formation of the 40S subunit “beak” structure occurs after a phosphorylation and dephosphorylation event involving the Enp1-Ltv1-Rps3 complex and the kinase , Hrr25. Cleavage of the 20S pre-rRNA at the D-site creates the mature 18s rRNA. This cleavage event is dependent on several non-ribosomal factors such as Nob1, Rio1, Rio2, Tsr1 and Fap7. [ 1 ]
The maturation of the pre-60S subunit into a mature 60S subunit requires many biogenesis factors that associate and disassociate. In addition, some assembly factors associate with the 60S subunit while others only interact with it transiently. As an overall trend, the maturation of the pre-60S subunit is marked a gradual decrease in complexity. The subunit matures as it moves from the nucleolus to the cytoplasm and gradually the number of trans-acting factors are reduced. [ 3 ] The maturation of the 60S subunit requires the help of about 80 factors. Eight of these factors are directly involved with the processing of the 27S A3 pre-rRNA, which actually completes the formation of the mature 5’end of the 5.8S rRNA. The A3 factors bind to distant sites on the pre-RNA as well as to each other. Subsequently, they bring areas of rRNA close together and promote the processing of pre-rRNA and the recruitment of ribosomal proteins. Three AAA-type ATPases work to strip the factors from the maturing 60S pre-ribosome. One of the ATPases is a dynein-like Rea1 protein made up of 6 different ATPase domains that form a ring structure. The ring structure is attached to a flexible tail that happens to have a MIDAS (Metal ion-dependent adhesion site) tip. The Rea1 interacts with the 60S pre-ribosome via its ring while two substrates , Ytm1 and Rsa1, interact with Rea1 through its MIDAS tip. The role of these substrates has not yet been defined. Both though, along with their interactions, are removed in the maturation process of the 60S pre-ribosome. The other two ATPases, Rix7 and Drg1 also function to remove assembly factors from the maturing 60S subunit. Helicases and GTPases are also involved in the removal of assembly factors and the rearrangement of RNA to form the completed 60S subunit. Once in the cytoplasm (see nuclear export), the 60S subunit further undergoes processing in order to be functional. The rest of the large subunit ribosomal particles associate with the 60S unit and the remaining non-ribosomal assembly factors disassociate. The release of the biogenesis factors is mediated mostly by GTPases such as Lsg1 and ATPases such as Drg1. The precise sequence of these events remains unclear. The pathway of 60S cytoplasmic maturation remains incomplete as far as current knowledge is concerned. [ 3 ]
In order for the pre-ribosomal units to fully mature, they must be exported to the cytoplasm . To effectively move from the nucleolus to the cytoplasm, the pre-ribosomes interact with export receptors to move through the hydrophobic central channel of the nuclear pore complex. [ 3 ] The karyopherin Crm1 is the receptor for both ribosomal subunits and mediates export in a Ran-GTP dependent fashion. It recognizes molecules that have leucine -rich nuclear export signals. The Crm1 is pulled to the large 60S subunit by the help of an adapter protein called Nmd3. The adapter protein for the 40S unit is unknown. In addition to Crm1, other factors play a role in nuclear export of pre-ribosomes. A general mRNA export receptor, called Mex67, as well as a HEAT-repeating-containing protein, Rrp12, facilitate the export of both subunits. These factors are non-essential proteins and help to optimize the export of the pre-ribosomes since they are large molecules. [ 3 ]
Because ribosomes are so complex, a certain number of ribosomes are assembled incorrectly and could potentially waste cellular energy and resources when synthesizing non-functional proteins. To prevent this, cells have an active surveillance system to recognize damaged or defective ribosomes and target them for degradation. The surveillance mechanism is in place to detect nonfunctional pre-ribosomes as well as nonfunctional mature ribosomes. In addition, the surveillance system brings the necessary degradation equipment and actually degrades the nonfunctional ribosomes. [ 1 ] Pre-ribosomes that build up in the nucleus are destroyed by the exosome , which is a multisubunit complex with exonuclease activity. If defective ribosomal subunits do happen to make it out of the nucleolus and into the cytoplasm, there is a second surveillance system in place there to target malfunctioning ribosomes in the cytoplasm for degradation. Certain mutations in residues of the large ribosome subunit will actually result in RNA decay and thus degradation of the unit. Because the amount of defects that are possible in ribosome assembly are so extensive, it is still unknown as to how the surveillance system detects all defects, but it has been postulated that instead of targeting specific defects, the surveillance system recognizes the consequences of those defects – such as assembly delays. Meaning, if there is a disruption in the assembly or maturation of a mature ribosome, the surveillance system will act as if the subunit is defective. [ 3 ]
Mutations in ribosome biogenesis are linked to several human ribosomopathy genetic diseases , including inherited bone marrow failure syndromes, which are characterized by a predisposition to cancer and a reduced number of blood cells. Ribosomal dysregulation may also play a role in muscle wasting . [ 13 ] | https://en.wikipedia.org/wiki/Ribosome_biogenesis |
Ribosome profiling , or Ribo-Seq (also named ribosome footprinting ), is an adaptation of a technique developed by Joan Steitz and Marilyn Kozak almost 50 years ago that Nicholas Ingolia and Jonathan Weissman adapted to work with next generation sequencing that uses specialized messenger RNA ( mRNA ) sequencing to determine which mRNAs are being actively translated . [ 1 ] [ 2 ] A related technique that can also be used to determine which mRNAs are being actively translated is the Translating Ribosome Affinity Purification (TRAP) methodology, which was developed by Nathaniel Heintz at Rockefeller University (in collaboration with Paul Greengard and Myriam Heiman). [ 3 ] [ 2 ] TRAP does not involve ribosome footprinting but provides cell type-specific information.
It produces a “global snapshot” of all the ribosomes actively translating in a cell at a particular moment, known as a translatome . Consequently, this enables researchers to identify the location of translation start sites, the complement of translated ORFs in a cell or tissue, the distribution of ribosomes on a messenger RNA, and the speed of translating ribosomes. [ 4 ] Ribosome profiling targets only mRNA sequences protected by the ribosome during the process of decoding by translation unlike RNA-Seq , which sequences all of the mRNA of a given sequence present in a sample. [ 1 ] This technique is also different from polysome profiling .
Ribosome profiling is based on the discovery that the mRNA within a ribosome can be isolated through the use of nucleases that degrade unprotected mRNA regions. This technique analyzes the regions of mRNAs being converted to protein, as well as the levels of translation of each region to provide insight into global gene expression. Prior to its development, efforts to measure translation in vivo included microarray analysis on the RNA isolated from polysomes , as well as translational profiling through the affinity purification of epitope tagged ribosomes. These are useful and complementary methods, but neither allows the sensitivity and positional information provided by ribosome profiling. [ 4 ]
There are three main uses of ribosome profiling: identifying translated mRNA regions, observing how nascent peptides are folded, and measuring the amount of specific proteins that are synthesized.
By using specific drugs, ribosome profiling can identify initiating regions of mRNA, elongating regions, and areas of translation stalling. [ 5 ] Initiating regions can be detected by adding harringtonine or lactidomycin to prevent any further initiation. [ 5 ] This allows the starting codon of the mRNAs throughout the cell lysate to be analyzed, which has been used to determine non-AUG sequences that do initiate translation . [ 1 ] The other elongating regions can be detected by adding antibiotics like cycloheximide that inhibit translocation, chloramphenicol that inhibits transfer of peptides within the ribosome, or non-drug means like thermal freezing. [ 5 ] These elongation freezing methods allow for the kinetics of translation to be analyzed. Since multiple ribosomes can translate a single mRNA molecule to speed up the translation process, RiboSeq demonstrates the protein coding regions within the mRNA and how quickly this is done depending on the mRNA being sequenced. [ 1 ] [ 6 ] This also allows for ribosome profiling to show pause sites within the transcriptome at specific codons. [ 6 ] [ 7 ] These sites of slow or paused translation are demonstrated by an increase in ribosome density and these pauses can link specific proteins with their roles within the cell. [ 1 ]
Coupling ribosome profiling with ChIP can elucidate how and when newly synthesized proteins are folded. [ 1 ] Using the footprints provided by Ribo-Seq, specific ribosomes associated with factors, like chaperones , can be purified. Pausing the ribosome at specific time points, allowing it to translate a polypeptide over time, and exposing the different points to a chaperone and precipitating out using ChIP purifies these samples and can show at which point in time the peptide is being folded. [ 1 ]
Ribo-Seq can also be used to estimate translation efficiency, a proxy for protein synthesis. For this application, ribosome profiling and matched RNA sequencing data are generated. The initial data analyses can be achieved by dedicated computational frameworks (ex. [ 8 ] ). Translation efficiency can then be computed as the ribosome occupancy of each gene while controlling for its RNA expression. [ 9 ] [ 10 ] This approach can be coupled with directed disruption of proteins that bind to RNA and using ribosome profiling to measure the difference in translation. [ 7 ] These disrupted mRNAs can be associated with proteins, whose binding sites have already been mapped on RNA, to indicate regulation. [ 1 ] [ 7 ] | https://en.wikipedia.org/wiki/Ribosome_profiling |
Ribotyping is a molecular technique for bacterial identification and characterization that uses information from rRNA -based phylogenetic analyses. [ 1 ] It is a rapid and specific method widely used in clinical diagnostics and analysis of microbial communities in food, water, and beverages. [ 1 ]
All bacteria have ribosomal genes , but the exact sequence is unique to each species, serving as a genetic fingerprint. Therefore, sequencing the particular 16S gene and comparing it to a database would yield identification of the particular species. [ 2 ]
Ribotyping involves the digestion of bacterial genomic DNA with specific restriction enzymes . Each restriction enzyme cuts DNA at a specific nucleotide sequence, resulting in fragments of different lengths. [ 3 ]
Those fragments are then run on a Gel electrophoresis , where they are separated according to size: the application of electrical field to the gel in which they are suspended causes the movement of DNA fragments (all negatively charged due to the presence of phosphate groups) through a matrix towards the positively charged end of the field. Small fragments move more easily and rapidly through the matrix, reaching a bigger distance from the starting position than larger fragments.
Following the separation in the gel matrix, the DNA fragments are moved onto nylon membranes and hybridized with a labelled 16S or 23S rRNA probe. This way only the fragments coding for such rRNA are visualised and can be analyzed. [ 4 ] The pattern is then digitized and used to identify the origin of the DNA by a comparison with reference organisms in a computer database. [ 1 ]
Conceptually, ribotyping is similar to probing restriction fragments of chromosomal DNA with cloned probes (randomly cloned probes or probes derived from a specific coding sequence such as that of a virulence factor ). [ 5 ]
This genetics article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ribotyping |
Ribozymes ( ribo nucleic acid en zyme s) are RNA molecules that have the ability to catalyze specific biochemical reactions, including RNA splicing in gene expression , similar to the action of protein enzymes . The 1982 discovery of ribozymes demonstrated that RNA can be both genetic material (like DNA ) and a biological catalyst (like protein enzymes), and contributed to the RNA world hypothesis , which suggests that RNA may have been important in the evolution of prebiotic self-replicating systems. [ 1 ]
The most common activities of natural or in vitro evolved ribozymes are the cleavage (or ligation ) of RNA and DNA and peptide bond formation. [ 2 ] For example, the smallest ribozyme known (GUGGC-3') can aminoacylate a GCCU-3' sequence in the presence of PheAMP. [ 3 ] Within the ribosome , ribozymes function as part of the large subunit ribosomal RNA to link amino acids during protein synthesis . They also participate in a variety of RNA processing reactions, including RNA splicing , viral replication , and transfer RNA biosynthesis. Examples of ribozymes include the hammerhead ribozyme , the VS ribozyme , leadzyme , and the hairpin ribozyme .
Researchers who are investigating the origins of life through the RNA world hypothesis have been working on discovering a ribozyme with the capacity to self-replicate, which would require it to have the ability to catalytically synthesize polymers of RNA. This should be able to happen in prebiotically plausible conditions with high rates of copying accuracy to prevent degradation of information but also allowing for the occurrence of occasional errors during the copying process to allow for Darwinian evolution to proceed. [ 4 ]
Attempts have been made to develop ribozymes as therapeutic agents, as enzymes which target defined RNA sequences for cleavage, as biosensors , and for applications in functional genomics and gene discovery. [ 5 ]
Before the discovery of ribozymes, enzymes —which were defined [solely] as catalytic proteins —were the only known biological catalysts . In 1967, Carl Woese , Francis Crick , and Leslie Orgel were the first to suggest that RNA could act as a catalyst. This idea was based upon the discovery that RNA can form complex secondary structures . [ 6 ] These ribozymes were found in the intron of an RNA transcript, which removed itself from the transcript, as well as in the RNA component of the RNase P complex, which is involved in the maturation of pre- tRNAs . In 1989, Thomas R. Cech and Sidney Altman shared the Nobel Prize in chemistry for their "discovery of catalytic properties of RNA". [ 7 ] The term ribozyme was first introduced by Kelly Kruger et al. in a paper published in Cell in 1982. [ 1 ]
It had been a firmly established belief in biology that catalysis was reserved for proteins. However, the idea of RNA catalysis is motivated in part by the old question regarding the origin of life: Which comes first, enzymes that do the work of the cell or nucleic acids that carry the information required to produce the enzymes? The concept of "ribonucleic acids as catalysts" circumvents this problem. RNA, in essence, can be both the chicken and the egg. [ 8 ]
In the 1980s, Thomas Cech, at the University of Colorado Boulder , was studying the excision of introns in a ribosomal RNA gene in Tetrahymena thermophila . While trying to purify the enzyme responsible for the splicing reaction, he found that the intron could be spliced out in the absence of any added cell extract. As much as they tried, Cech and his colleagues could not identify any protein associated with the splicing reaction. After much work, Cech proposed that the intron sequence portion of the RNA could break and reform phosphodiester bonds. At about the same time, Sidney Altman, a professor at Yale University , was studying the way tRNA molecules are processed in the cell when he and his colleagues isolated an enzyme called RNase-P , which is responsible for conversion of a precursor tRNA into the active tRNA. Much to their surprise, they found that RNase-P contained RNA in addition to protein and that RNA was an essential component of the active enzyme. This was such a foreign idea that they had difficulty publishing their findings. The following year [ which? ] , Altman demonstrated that RNA can act as a catalyst by showing that the RNase-P RNA subunit could catalyze the cleavage of precursor tRNA into active tRNA in the absence of any protein component.
Since Cech's and Altman's discovery, other investigators have discovered other examples of self-cleaving RNA or catalytic RNA molecules. Many ribozymes have either a hairpin – or hammerhead – shaped active center and a unique secondary structure that allows them to cleave other RNA molecules at specific sequences. It is now possible to make ribozymes that will specifically cleave any RNA molecule. These RNA catalysts may have pharmaceutical applications. For example, a ribozyme has been designed to cleave the RNA of HIV . If such a ribozyme were made by a cell, all incoming virus particles would have their RNA genome cleaved by the ribozyme, which would prevent infection.
Despite having only four choices for each monomer unit (nucleotides), compared to 20 amino acid side chains found in proteins, ribozymes have diverse structures and mechanisms. In many cases they are able to mimic the mechanism used by their protein counterparts. For example, in self cleaving ribozyme RNAs, an in-line SN2 reaction is carried out using the 2’ hydroxyl group as a nucleophile attacking the bridging phosphate and causing 5’ oxygen of the N+1 base to act as a leaving group. In comparison, RNase A, a protein that catalyzes the same reaction, uses a coordinating histidine and lysine to act as a base to attack the phosphate backbone. [ 2 ] [ clarification needed ]
Like many protein enzymes, metal binding is also critical to the function of many ribozymes. [ 9 ] Often these interactions use both the phosphate backbone and the base of the nucleotide, causing drastic conformational changes. [ 10 ] There are two mechanism classes for the cleavage of a phosphodiester backbone in the presence of metal. In the first mechanism, the internal 2’- OH group attacks the phosphorus center in a SN 2 mechanism. Metal ions promote this reaction by first coordinating the phosphate oxygen and later stabling the oxyanion. The second mechanism also follows a SN 2 displacement, but the nucleophile comes from water or exogenous hydroxyl groups rather than RNA itself. The smallest ribozyme is UUU, which can promote the cleavage between G and A of the GAAA tetranucleotide via the first mechanism in the presence of Mn 2+ . The reason why this trinucleotide (rather than the complementary tetramer) catalyzes this reaction may be because the UUU-AAA pairing is the weakest and most flexible trinucleotide among the 64 conformations, which provides the binding site for Mn 2+ . [ 11 ]
Phosphoryl transfer can also be catalyzed without metal ions. For example, pancreatic ribonuclease A and hepatitis delta virus (HDV) ribozymes can catalyze the cleavage of RNA backbone through acid-base catalysis without metal ions. [ 12 ] [ 13 ] Hairpin ribozyme can also catalyze the self-cleavage of RNA without metal ions, but the mechanism for this is still unclear. [ 13 ]
Ribozyme can also catalyze the formation of peptide bond between adjacent amino acids by lowering the activation entropy. [ 12 ]
Although ribozymes are quite rare in most cells, their roles are sometimes essential to life. For example, the functional part of the ribosome , the biological machine that translates RNA into proteins, is fundamentally a ribozyme, composed of RNA tertiary structural motifs that are often coordinated to metal ions such as Mg 2+ as cofactors . [ 14 ] In a model system, there is no requirement for divalent cations in a five-nucleotide RNA catalyzing trans - phenylalanation of a four-nucleotide substrate with 3 base pairs complementary with the catalyst, where the catalyst/substrate were devised by truncation of the C3 ribozyme. [ 15 ]
The best-studied ribozymes are probably those that cut themselves or other RNAs, as in the original discovery by Cech [ 16 ] and Altman. [ 17 ] However, ribozymes can be designed to catalyze a range of reactions, many of which may occur in life but have not been discovered in cells. [ 18 ]
RNA may catalyze folding of the pathological protein conformation of a prion in a manner similar to that of a chaperonin . [ 19 ]
RNA can also act as a hereditary molecule, which encouraged Walter Gilbert to propose that in the distant past, the cell used RNA as both the genetic material and the structural and catalytic molecule rather than dividing these functions between DNA and protein as they are today; this hypothesis is known as the " RNA world hypothesis " of the origin of life . [ 20 ] Since nucleotides and RNA (and thus ribozymes) can arise by inorganic chemicals, they are candidates for the first enzymes , and in fact, the first "replicators" (i.e., information-containing macro-molecules that replicate themselves). An example of a self-replicating ribozyme that ligates two substrates to generate an exact copy of itself was described in 2002. [ 21 ] The discovery of the catalytic activity of RNA solved the "chicken and egg" paradox of the origin of life, solving the problem of origin of peptide and nucleic acid central dogma . According to this scenario, at the origin of life, all enzymatic activity and genetic information encoding was done by one molecule: RNA.
Ribozymes have been produced in the laboratory that are capable of catalyzing the synthesis of other RNA molecules from activated monomers under very specific conditions, these molecules being known as RNA polymerase ribozymes. [ 22 ] The first RNA polymerase ribozyme was reported in 1996, and was capable of synthesizing RNA polymers up to 6 nucleotides in length. [ 23 ] Mutagenesis and selection has been performed on an RNA ligase ribozyme from a large pool of random RNA sequences, [ 24 ] resulting in isolation of the improved "Round-18" polymerase ribozyme in 2001 which could catalyze RNA polymers now up to 14 nucleotides in length. [ 25 ] Upon application of further selection on the Round-18 ribozyme, the B6.61 ribozyme was generated and was able to add up to 20 nucleotides to a primer template in 24 hours, until it decomposes by cleavage of its phosphodiester bonds. [ 26 ]
The rate at which ribozymes can polymerize an RNA sequence multiples substantially when it takes place within a micelle . [ 27 ]
The next ribozyme discovered was the "tC19Z" ribozyme, which can add up to 95 nucleotides with a fidelity of 0.0083 mutations/nucleotide. [ 28 ] Next, the "tC9Y" ribozyme was discovered by researchers and was further able to synthesize RNA strands up to 206 nucleotides long in the eutectic phase conditions at below-zero temperature, [ 29 ] conditions previously shown to promote ribozyme polymerase activity. [ 30 ]
The RNA polymerase ribozyme (RPR) called tC9-4M was able to polymerize RNA chains longer than itself (i.e. longer than 177 nt) in magnesium ion concentrations close to physiological levels, whereas earlier RPRs required prebiotically implausible concentrations of up to 200 mM. The only factor required for it to achieve this was the presence of a very simple amino acid polymer called lysine decapeptide. [ 31 ]
The most complex RPR synthesized by that point was called 24-3, which was newly capable of polymerizing the sequences of a substantial variety of nucleotide sequences and navigating through complex secondary structures of RNA substrates inaccessible to previous ribozymes. In fact, this experiment was the first to use a ribozyme to synthesize a tRNA molecule. [ 32 ] Starting with the 24-3 ribozyme, Tjhung et al. [ 33 ] applied another fourteen rounds of selection to obtain an RNA polymerase ribozyme by in vitro evolution termed '38-6' that has an unprecedented level of activity in copying complex RNA molecules. However, this ribozyme is unable to copy itself and its RNA products have a high mutation rate . In a subsequent study, the researchers began with the 38-6 ribozyme and applied another 14 rounds of selection to generate the '52-2' ribozyme, which compared to 38-6, was again many times more active and could begin generating detectable and functional levels of the class I ligase, although it was still limited in its fidelity and functionality in comparison to copying of the same template by proteins such as the T7 RNA polymerase. [ 34 ]
An RPR called t5(+1) adds triplet nucleotides at a time instead of just one nucleotide at a time. This heterodimeric RPR can navigate secondary structures inaccessible to 24-3, including hairpins. In the initial pool of RNA variants derived only from a previously synthesized RPR known as the Z RPR, two sequences separately emerged and evolved to be mutualistically dependent on each other. The Type 1 RNA evolved to be catalytically inactive, but complexing with the Type 5 RNA boosted its polymerization ability and enabled intermolecular interactions with the RNA template substrate obviating the need to tether the template directly to the RNA sequence of the RPR, which was a limitation of earlier studies. Not only did t5(+1) not need tethering to the template, but a primer was not needed either as t5(+1) had the ability to polymerize a template in both 3' → 5' and 5' 3 → 3' directions. [ 35 ]
A highly evolved [ vague ] RNA polymerase ribozyme was able to function as a reverse transcriptase , that is, it can synthesize a DNA copy using an RNA template. [ 36 ] Such an activity is considered [ by whom? ] to have been crucial for the transition from RNA to DNA genomes during the early history of life on earth. Reverse transcription capability could have arisen as a secondary function of an early RNA-dependent RNA polymerase ribozyme.
An RNA sequence that folds into a ribozyme is capable of invading duplexed RNA, rearranging into an open holopolymerase complex, and then searching for a specific RNA promoter sequence, and upon recognition rearrange again into a processive form that polymerizes a complementary strand of the sequence. This ribozyme is capable of extending duplexed RNA by up to 107 nucleotides, and does so without needing to tether the sequence being polymerized. [ 37 ]
A short 20- nucleotide RNA variant ribozyme was identified that self-reproduces via template directed ligation of two 10 nucleotide oligomers . [ 38 ] This minimal kind of RNA self-reproduction was discovered in a random pool of oligmers, and may represent an early step in the emergence of an RNA based genetic system from primordial components. [ 38 ]
Sexual reproduction might have been present in the RNA world that preceded DNA cellular life forms. [ 39 ] Early cellular life forms having genomes with single copies of essential RNA ribozyme molecules would likely have been vulnerable to environmental damaging conditions that could block replication of an essential ribozyme thus causing cell death. Merger of two such damaged early cells (sexual interaction) would allow undamaged combinations of RNA segments to come together, thus facilitating formation of a functional genome and allowing survival of the cell and ability to reproduce.
Since the discovery of ribozymes that exist in living organisms, there has been interest in the study of new synthetic ribozymes made in the laboratory. For example, artificially produced self-cleaving RNAs with good enzymatic activity have been produced. Tang and Breaker [ 40 ] isolated self-cleaving RNAs by in vitro selection of RNAs originating from random-sequence RNAs. Some of the synthetic ribozymes that were produced had novel structures, while some were similar to the naturally occurring hammerhead ribozyme.
In 2015, researchers at Northwestern University and the University of Illinois Chicago engineered a tethered ribosome that works nearly as well as the authentic cellular component that produces all the proteins and enzymes within the cell. Called Ribosome-T , or Ribo-T, the artificial ribosome was created by Michael Jewett and Alexander Mankin. [ 41 ] The techniques used to create artificial ribozymes involve directed evolution. This approach takes advantage of RNA's dual nature as both a catalyst and an informational polymer, making it easy for an investigator to produce vast populations of RNA catalysts using polymerase enzymes. The ribozymes are mutated by reverse transcribing them with reverse transcriptase into various cDNA and amplified with error-prone PCR . The selection parameters in these experiments often differ. One approach for selecting a ligase ribozyme involves using biotin tags, which are covalently linked to the substrate. If a molecule possesses the desired ligase activity, a streptavidin matrix can be used to recover the active molecules.
Lincoln and Joyce used in vitro evolution to develop ribozyme ligases capable of self-replication in about an hour, via the joining of pre-synthesized highly complementary oligonucleotides. [ 42 ]
Although not true catalysts, the creation of artificial self-cleaving riboswitches , termed aptazymes , has also been an active area of research. Riboswitches are regulatory RNA motifs that change their structure in response to a small molecule ligand to regulate translation. While there are many known natural riboswitches that bind a wide array of metabolites and other small organic molecules, only one ribozyme based on a riboswitch has been described: glmS . [ 43 ] Early work in characterizing self-cleaving riboswitches was focused on using theophylline as the ligand. In these studies, an RNA hairpin is formed which blocks the ribosome binding site , thus inhibiting translation. In the presence of the ligand , in these cases theophylline, the regulatory RNA region is cleaved off, allowing the ribosome to bind and translate the target gene. Much of this RNA engineering work was based on rational design and previously determined RNA structures rather than directed evolution as in the above examples. More recent work has broadened the ligands used in ribozyme riboswitches to include thymine pyrophosphate. Fluorescence-activated cell sorting has also been used to engineering aptazymes. [ 44 ]
Ribozymes have been proposed and developed for the treatment of disease through gene therapy . One major challenge of using RNA-based enzymes as a therapeutic is the short half-life of the catalytic RNA molecules in the body. To combat this, the 2’ position on the ribose is modified to improve RNA stability. One area of ribozyme gene therapy has been the inhibition of RNA-based viruses.
A type of synthetic ribozyme directed against HIV RNA called gene shears has been developed and has entered clinical testing for HIV infection. [ 45 ] [ 46 ]
Similarly, ribozymes have been designed to target the hepatitis C virus RNA, SARS coronavirus (SARS-CoV), [ 47 ] Adenovirus [ 47 ] and influenza A and B virus RNA. [ 48 ] [ 49 ] [ 50 ] [ 47 ] The ribozyme is able to cleave the conserved regions of the virus's genome, which has been shown to reduce the virus in mammalian cell culture. [ 51 ] Despite these efforts by researchers, these projects have remained in the preclinical stage.
Well-validated naturally occurring ribozyme classes: | https://en.wikipedia.org/wiki/Ribozyme |
Ribozyviria is a realm of satellite nucleic acids — infectious agents that resemble viruses , but cannot replicate without a helper virus . [ 1 ] Established in ICTV TaxoProp 2020.012D, the realm is named after the presence of genomic and antigenomic ribozymes of the Deltavirus type. The agents in Ribozyviria are satellite nucleic acids , which are distinct from satellite viruses in that they do not encode all of their own structural proteins but require proteins from their helper viruses in order to assemble. [ 2 ] Additional common features include a rod-like structure, an RNA-binding "delta antigen" encoded in the genome, and animal hosts. [ 3 ] Furthermore, the size range of the genomes of these viruses is between around 1547–1735nt, they encode a hammerhead ribozyme or a hepatitis delta virus ribozyme , and their coding capacity only involves one conserved protein. Most lineages of this realm are poorly understood, the notable exception being the genus Deltavirus , comprising the causal agents of hepatitis D in humans. [ 4 ]
The realm Ribozyviria has an unclear evolutionary origin. It has been proposed that they may have derived from retrozymes (a family of retrotransposons ) or a viroid-like element (i.e. viroids and satellites ) with capsid protein capture. [ 4 ] [ 5 ]
The first taxa of this realm to receive acceptance by the ICTV is the species Hepatitis delta virus and its genus Deltavirus , in 1993. Deltavirus remained unassigned to any higher taxa until 2018, when the ICTV mistakenly classified Deltavirus within the then newly established realm, Riboviria . In 2019, this error was rectified and Deltavirus returned to its original position. In 2020, Hepatitis delta virus was abolished and replaced with eight new species, and the taxonomy developed to reach its current form, detailed below. [ 6 ]
Ribozyviria contains a single family, Kolmioviridae , with no intermediate taxa between realm and family. This family contains eight genera.
The names of all genera in this realm allude to the letter D in various languages. The family name comes from Finnish kolmio "triangle," another reference to the Greek letter "Δ" (delta). [ 3 ]
This taxonomy is shown hereafter: [ 1 ] | https://en.wikipedia.org/wiki/Ribozyviria |
Ribulose 1,5-bisphosphate ( RuBP ) is an organic substance that is involved in photosynthesis , notably as the principal CO 2 acceptor in plants. [ 1 ] : 2 It is a colourless anion, a double phosphate ester of the ketopentose ( ketone -containing sugar with five carbon atoms) called ribulose . Salts of RuBP can be isolated, but its crucial biological function happens in solution. [ 2 ] RuBP occurs not only in plants but in all domains of life , including Archaea , Bacteria , and Eukarya . [ 3 ]
RuBP was originally discovered by Andrew Benson in 1951 while working in the lab of Melvin Calvin at UC Berkeley. [ 4 ] [ 5 ] Calvin, who had been away from the lab at the time of discovery and was not listed as a co-author, controversially removed the full molecule name from the title of the initial paper, identifying it solely as "ribulose". [ 4 ] [ 6 ] At the time, the molecule was known as ribulose diphosphate (RDP or RuDP) but the prefix di- was changed to bis- to emphasize the nonadjacency of the two phosphate groups. [ 4 ] [ 5 ] [ 7 ]
The enzyme ribulose-1,5-bisphosphate carboxylase-oxygenase ( rubisco ) catalyzes the reaction between RuBP and carbon dioxide . The product is the highly unstable six-carbon intermediate known as 3-keto-2-carboxyarabinitol 1,5-bisphosphate, or 2'-carboxy-3-keto-D-arabinitol 1,5-bisphosphate (CKABP). [ 8 ] This six-carbon β-ketoacid intermediate hydrates into another six-carbon intermediate in the form of a gem-diol . [ 9 ] This intermediate then cleaves into two molecules of 3-phosphoglycerate (3-PGA) which is used in a number of metabolic pathways and is converted into glucose. [ 10 ] [ 11 ]
In the Calvin-Benson cycle , RuBP is a product of the phosphorylation of ribulose-5-phosphate (produced by glyceraldehyde 3-phosphate ) by ATP . [ 11 ] [ 12 ]
RuBP acts as an enzyme inhibitor for the enzyme rubisco, which regulates the net activity of carbon fixation. [ 13 ] [ 14 ] [ 15 ] When RuBP is bound to an active site of rubisco, the ability to activate via carbamylation with CO 2 and Mg 2+ is blocked. The functionality of rubisco activase involves removing RuBP and other inhibitory bonded molecules to re-enable carbamylation on the active site. [ 1 ] : 5
Rubisco also catalyzes RuBP with oxygen ( O 2 ) in an interaction called photorespiration , a process that is more prevalent at high temperatures. [ 16 ] [ 17 ] During photorespiration RuBP combines with O 2 to become 3-PGA and phosphoglycolic acid . [ 18 ] [ 19 ] [ 20 ] Like the Calvin-Benson Cycle, the photorespiratory pathway has been noted for its enzymatic inefficiency [ 19 ] [ 20 ] although this characterization of the enzymatic kinetics of rubisco has been contested. [ 21 ] Due to enhanced RuBP carboxylation and decreased rubisco oxygenation stemming from the increased concentration of CO 2 in the bundle sheath , rates of photorespiration are decreased in C 4 plants . [ 1 ] : 103 Similarly, photorespiration is limited in CAM photosynthesis due to kinetic delays in enzyme activation, again stemming from the ratio of carbon dioxide to oxygen. [ 22 ]
RuBP can be measured isotopically via the conversion of 14 CO 2 and RuBP into glyceraldehyde 3-phosphate . [ 23 ] G3P can then be measured using an enzymatic optical assay . [ 23 ] [ 24 ] [ a ] Given the abundance of RuBP in biological samples, an added difficulty is distinguishing particular reservoirs of the substrate, such as the RuBP internal to a chloroplast vs external. One approach to resolving this is by subtractive inference, or measuring the total RuBP of a system, removing a reservoir (e.g. by centrifugation), re-measuring the total RuBP, and using the difference to infer the concentration in the given repository. [ 25 ] | https://en.wikipedia.org/wiki/Ribulose_1,5-bisphosphate |
Edith Ulrica Hübbe (10 October 1885 – 15 August 1967), [ 1 ] invariably referred to as Rica Hübbe or Hubbe , was a South Australian medical doctor and teacher.
Samuel Grau "Sam" Hübbe (c. 1848 – 12 September 1900) was the first South Australian commissioned officer to be killed in the Boer War . [ 2 ] A practising Unitarian , he was a son of Ulrich Hübbe , who was important in the development of the Torrens Title system of land registration. Edith Agnes Cook (1859 – 2 April 1942) was in 1876 the first female student at the University of Adelaide , and second principal of the Advanced School for Girls . They were married at the Cook home, Norwood, by John Crawford Woods on 3 January 1885. [ 3 ]
Hübbe was born in Norwood, South Australia , the first child of surveyor and explorer Samuel Grau Hübbe and Edith Agnes Hübbe. Her education culminated in three years at the Advanced School for Girls, where her mother was once Principal, and was a successful student, awarded the Old Scholars' Prize for high achievements in the 1903 Leaving examinations, as well as some successes on the tennis court. [ 4 ]
Hübbe, her sister Marjorie Hübbe and, until she married, Ethel Holder, taught at her mother's school at 17 and 23 Statenborough Street, Knightsbridge (later known as Leabrook ). She completed, by part-time study, several demanding degrees —
Knightsbridge School closed in 1922, [ 7 ] and was taken over by the Misses Jones and Wells, [ 8 ] after which Hübbe went into private practice and her sister Marjorie was married to Alfred Beech Caw by George Hale . [ 9 ]
From 1927 to 1933 she was an instructor in Physiology and demonstrator in Biochemistry (1929 appointment) [ 10 ] at the University of Adelaide. [ 1 ]
Hübbe was a member of Adelaide's Lyceum Club ; [ 11 ] she was the club's longstanding secretary, from 1928 to 1950, in which year she appears to have ceased being a member. [ 12 ] | https://en.wikipedia.org/wiki/Rica_Hübbe |
In computability theory , Rice's theorem states that all non-trivial semantic properties of programs are undecidable . A semantic property is one about the program's behavior (for instance, "does the program terminate for all inputs?"), unlike a syntactic property (for instance, "does the program contain an if-then-else statement?"). A non-trivial property is one which is neither true for every program, nor false for every program.
The theorem generalizes the undecidability of the halting problem . It has far-reaching implications on the feasibility of static analysis of programs. It implies that it is impossible, for example, to implement a tool that checks whether any given program is correct , or even executes without error (it is possible to implement a tool that always overestimates or always underestimates, so in practice one has to decide what is less of a problem).
The theorem is named after Henry Gordon Rice , who proved it in his doctoral dissertation of 1951 at Syracuse University .
Rice's theorem puts a theoretical bound on which types of static analysis can be performed automatically. One can distinguish between the syntax of a program, and its semantics . The syntax is the detail of how the program is written, or its "intension", and the semantics is how the program behaves when run, or its "extension". Rice's theorem asserts that it is impossible to decide a property of programs which depends only on the semantics and not on the syntax, unless the property is trivial (true of all programs, or false of all programs).
By Rice's theorem, it is impossible to write a program that automatically verifies for the absence of bugs in other programs, taking a program and a specification as input, and checking whether the program satisfies the specification.
This does not imply an impossibility to prevent certain types of bugs. For example, Rice's theorem implies that in dynamically typed programming languages which are Turing-complete , it is impossible to verify the absence of type errors. On the other hand, statically typed programming languages feature a type system which statically prevents type errors. In essence, this should be understood as a feature of the syntax (taken in a broad sense) of those languages. In order to type check a program, its source code must be inspected; the operation does not depend merely on the hypothetical semantics of the program.
In terms of general software verification, this means that although one cannot algorithmically check whether any given program satisfies a given specification, one can require programs to be annotated with extra information that proves the program is correct, or to be written in a particular restricted form that makes the verification possible, and only accept programs which are verified in this way. In the case of type safety, the former corresponds to type annotations, and the latter corresponds to type inference . Taken beyond type safety, this idea leads to correctness proofs of programs through proof annotations such as in Hoare logic .
Another way of working around Rice's theorem is to search for methods which catch many bugs, without being complete. This is the theory of abstract interpretation .
Yet another direction for verification is model checking , which can only apply to finite-state programs, not to Turing-complete languages.
Let φ be an admissible numbering of partial computable functions . Let P be a subset of N {\displaystyle \mathbb {N} } . Suppose that:
Then P is undecidable .
A more concise statement can be made in terms of index sets : The only decidable index sets are ∅ and N {\displaystyle \mathbb {N} } .
Given a program P which takes a natural number n and returns a natural number P ( n ), the following questions are undecidable:
Assume for contradiction that P {\displaystyle P} is a non-trivial, extensional and computable set of natural numbers. There is a natural number a ∈ P {\displaystyle a\in P} and a natural number b ∉ P {\displaystyle b\notin P} . Define a function Q {\displaystyle Q} by Q e ( x ) = φ b ( x ) {\displaystyle Q_{e}(x)=\varphi _{b}(x)} when e ∈ P {\displaystyle e\in P} and Q e ( x ) = φ a ( x ) {\displaystyle Q_{e}(x)=\varphi _{a}(x)} when e ∉ P {\displaystyle e\notin P} . By Kleene's recursion theorem , there exists e {\displaystyle e} such that φ e = Q e {\displaystyle \varphi _{e}=Q_{e}} . Then, if e ∈ P {\displaystyle e\in P} , we have φ e = φ b {\displaystyle \varphi _{e}=\varphi _{b}} , contradicting the extensionality of P {\displaystyle P} since b ∉ P {\displaystyle b\notin P} , and conversely, if e ∉ P {\displaystyle e\notin P} , we have φ e = φ a {\displaystyle \varphi _{e}=\varphi _{a}} , which again contradicts extensionality since a ∈ P {\displaystyle a\in P} .
Suppose, for concreteness, that we have an algorithm for examining a program p and determining infallibly whether p is an implementation of the squaring function, which takes an integer d and returns d 2 . The proof works just as well if we have an algorithm for deciding any other non-trivial property of program behavior (i.e. a semantic and non-trivial property), and is given in general below.
The claim is that we can convert our algorithm for identifying squaring programs into one that identifies functions that halt. We will describe an algorithm that takes inputs a and i and determines whether program a halts when given input i .
The algorithm for deciding this is conceptually simple: it constructs (the description of) a new program t taking an argument n , which (1) first executes program a on input i (both a and i being hard-coded into the definition of t ), and (2) then returns the square of n . If a ( i ) runs forever, then t never gets to step (2), regardless of n . Then clearly, t is a function for computing squares if and only if step (1) terminates. Since we have assumed that we can infallibly identify programs for computing squares, we can determine whether t , which depends on a and i , is such a program; thus we have obtained a program that decides whether program a halts on input i . Note that our halting-decision algorithm never executes t , but only passes its description to the squaring-identification program, which by assumption always terminates; since the construction of the description of t can also be done in a way that always terminates, the halting-decision cannot fail to halt either.
This method does not depend specifically on being able to recognize functions that compute squares; as long as some program can do what we are trying to recognize, we can add a call to a to obtain our t . We could have had a method for recognizing programs for computing square roots, or programs for computing the monthly payroll, or programs that halt when given the input "Abraxas" ; in each case, we would be able to solve the halting problem similarly.
For the formal proof, algorithms are presumed to define partial functions over strings and are themselves represented by strings. The partial function computed by the algorithm represented by a string a is denoted F a . This proof proceeds by reductio ad absurdum : we assume that there is a non-trivial property that is decided by an algorithm, and then show that it follows that we can decide the halting problem , which is not possible, and therefore a contradiction.
Let us now assume that P ( a ) is an algorithm that decides some non-trivial property of F a . Without loss of generality we may assume that P ( no-halt ) = "no", with no-halt being the representation of an algorithm that never halts. If this is not true, then this holds for the algorithm P that computes the negation of the property P . Now, since P decides a non-trivial property, it follows that there is a string b that represents an algorithm F b and P ( b ) = "yes". We can then define an algorithm H ( a , i ) as follows:
We can now show that H decides the halting problem:
Since the halting problem is known to be undecidable, this is a contradiction and the assumption that there is an algorithm P ( a ) that decides a non-trivial property for the function represented by a must be false. | https://en.wikipedia.org/wiki/Rice's_theorem |
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