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Glycopegylation "is a site-selective PEGylation method developed for modifying complex glycoproteins ". [ 1 ] It can be useful to improve bioavailability and extend the half-life of various therapeutic proteins . [ 2 ] [ 1 ] [ 3 ] Examples of glycopegylated molecules include pegozafermin [ 4 ] and recombinant factor IX . [ 5 ]
This biotechnology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Glycopegylation |
Glycopeptides are peptides that contain carbohydrate moieties ( glycans ) covalently attached to the side chains of the amino acid residues that constitute the peptide.
Over the past few decades it has been recognised that glycans on cell surface (attached to membrane proteins or lipids ) and those bound to proteins ( glycoproteins ) play a critical role in biology. For example, these constructs have been shown to play important roles in fertilization , [ 1 ] the immune system , [ 2 ] brain development , [ 3 ] the endocrine system , [ 3 ] and inflammation . [ 3 ] [ 4 ] [ 5 ]
The synthesis of glycopeptides provides biological probes for researchers to elucidate glycan function in nature and products that have useful therapeutic and biotechnological applications. [ clarification needed ] [ citation needed ]
N -Linked glycans derive their name from the fact that the glycan is attached to an asparagine (Asn, N) residue, and are amongst the most common linkages found in nature. Although the majority of N-linked glycans take the form GlcNAc-β-Asn [ 6 ] other less common structural linkages such as GlcNac-α-Asn [ 7 ] and Glc-Asn [ 8 ] have been observed. In addition to their function in protein folding and cellular attachment, the N-liked glycans of a protein can modulate the protein's function, in some cases acting as an on-off switch. [ 5 ]
O -Linked glycans are formed by a linkage between an amino acid hydroxyl side chain (usually from serine or threonine ) with the glycan. The majority of O -linked glycans take the form GlcNac-β-Ser/Thr or GalNac-α-Ser/Thr. [ 6 ]
Of the three linkages the least common and least understood are C -linked glycans. The C-linkage refers to the covalent attachment of mannose to a tryptophan residue. An example of a C-linked glycan is α-mannosyl tryptophan. [ 9 ] [ 10 ]
Several methods have been reported in the literature for the synthesis of glycopeptides. Of these methods the most common strategies are listed below.
Within solid phase peptide synthesis (SPPS) there exist two strategies for the synthesis of glycopeptides, linear and convergent assembly. Linear assembly relies on the synthesis of building blocks and then the use of SPPS to attach the building block together. An outline of this approach is illustrated below.
Several methods exist for the synthesis of monosaccharide amino acid building block as illustrated below.
Provided the monosaccharide amino acid building block is stable to peptide coupling conditions, amine deprotection conditions and resin cleavage. Linear assembly remains a popular strategy for the synthesis of glycopeptides with many examples in the literature. [ 13 ] [ 14 ] [ 15 ]
In the convergent assembly strategy a peptide chain and glycan residue are first synthesis separately. Then the glycan is glycosylated onto a specific residue of the peptide chain. This approach is not as popular as the linear strategy due to the poor reaction yields in the glycosylation step. [ 16 ]
Another strategy to produce glycopeptide libraries is using Glyco-SPOT synthesis technique. [ 17 ] The technique extends the existing method of SPOT synthesis. [ 18 ] In this method, libraries of glycopeptides are produced on a cellulose surface (e.g. filter paper) which acts as the solid phase. The glycopeptides are produced by spotting FMOC protected amino acids allowing the synthesis to be performed at microgram (nanomole) scale using very small amounts of glycoamino acids. The scale of this technique can be an advantage for creating libraries for screening by using less amounts of glycoamino acids per peptide. However to produce larger quantities of glycopeptides traditional resin-based solid phase techniques would be better.
Native chemical ligation (NCL) is a convergent synthetic strategy based on the linear coupling of glycopeptide fragments. This technique makes use of the chemoselective reaction between a N-terminal cysteine residue on one peptide fragment with a thio-ester on the C-terminus of the other peptide fragment [ 19 ] as illustrated below.
Unlike standard SPPS (which is limited to 50 amino acid residue) NCL allows the construction of large glycopeptides. However the strategy is limited by the fact that it requires a cysteine residue at N-terminus , an amino acid residue that is rare in nature. [ 19 ] However this problem has partly been address by the selective desulfurization of the cysteine residue to an alanine . [ 20 ] | https://en.wikipedia.org/wiki/Glycopeptide |
Glycopeptide antibiotics are a class of drugs of microbial origin that are composed of glycosylated cyclic or polycyclic nonribosomal peptides . Significant glycopeptide antibiotics include the anti-infective antibiotics vancomycin , teicoplanin , telavancin , ramoplanin , avoparcin and decaplanin, corbomycin , complestatin and the antitumor antibiotic bleomycin . Vancomycin is used if infection with methicillin-resistant Staphylococcus aureus (MRSA) is suspected.
Some members of this class of drugs inhibit the synthesis of cell walls in susceptible microbes by inhibiting peptidoglycan synthesis. The core class (including vancomycin) binds to acyl- D -alanyl- D -alanine in lipid II , preventing the addition of new units to the peptidoglycan. [ 1 ] Of this core class, one may distinguish multiple generations: the first generation includes vancomycin and teicoplanin, while the semisynthetic second generation includes lipoglycopeptides like telavancin, oritavancin and dalbavancin. The extra lipophilicity not only enhances Lipid II binding but also creates a second mechanism of action whereby the antibiotic dissolves into the membrane and makes it more permeable. [ 1 ]
Corbomycin and complestatin are structurally and ancestrally related to vancomycin, but they work by inhibiting autolysins through binding to peptidoglycan, therefore preventing cell division, [ 2 ] neither is an approved drug.
Ramoplanin, although a "glycopeptide" in the literal sense, has a quite different structural core. It not only binds to Lipid II but also attacks MurG and transglycosylases (glycosyltransferases) which polymerize amino acid/sugar building blocks into peptidoglycan. [ 1 ] It has been described as a "first-in-class" antibiotic, representing glycolipodepsipeptide antibiotics . [ 3 ]
Bleomycin also has a different core. Its mode of action is also unrelated to the cell wall, instead causing DNA damage in tumor cells. [ 4 ]
Due to their toxicity, the use of first-generation glycopeptide antibiotics is restricted to patients who are critically ill, who have a demonstrated hypersensitivity to the β-lactams , or who are infected with β-lactam-resistant species, as in the case of methicillin-resistant Staphylococcus aureus . These antibiotics are effective principally against Gram-positive cocci. First-generation examples exhibit a narrow spectrum of action and are bactericidal only against the enterococci . Some tissues are not penetrated very well by glycopeptides, and they do not penetrate into the cerebrospinal fluid .
The second-generation glycopeptides, or "lipoglycopeptides", have better binding to Lipid II due to the lipophilic moieties, expanding the antibacterial spectrum. Telavancin also has a hydrophilic moiety attached to enhance tissue distribution and reduce nephrotoxicity. [ 1 ]
Vancomycin was isolated in 1953 and used clinically by 1958, while teicoplanin was discovered in 1978 and became clinically-available in 1984. [ 5 ] Telavancin is a semi-synthetic lipoglycopeptide derivative of vancomycin approved by FDA in 2009. [ citation needed ]
Teicoplanin has historically been more widely marketed - and thus more used - in Europe compared to the U.S. It has more fatty acid chains than vancomycin and is considered to be 50 to 100 times more lipophilic. Teicoplanin also has an increased half-life compared to vancomycin, as well as having better tissue penetration. It can be two to four times more active than vancomycin, but it does depend upon the organism. Teicoplanin is more acidic, forming water-soluble salts, so it can be given intramuscularly. Teicoplanin is much better at penetrating leukocytes and phagocytes than vancomycin. [ citation needed ]
Since 2002, isolates of vancomycin-resistant Staphylococcus aureus (VRSA) have been found in the USA and other countries. [ citation needed ]
Glycopeptides have typically been considered the last effective line of defense for cases of MRSA, however, several newer classes of antibiotics have proven to have activity against MRSA- including, in 2000, linezolid of the oxazolidinone class, and in 2003 daptomycin of the lipopeptide class. [ 6 ]
Several derivatives of vancomycin are currently being developed, including oritavancin and dalbavancin (both lipoglycopeptides ). Possessing longer half-lives than vancomycin, these newer candidates may demonstrate improvements over vancomycin due to less frequent dosing and activity against vancomycin-resistant bacteria. [ 7 ]
Vancomycin is usually given intravenously, as an infusion, and can cause tissue necrosis and phlebitis at the injection site if given too rapidly. Pain at the site of injection is indeed a common adverse event. One of the side effects is red man syndrome , an idiosyncratic reaction to bolus caused by histamine release. Some other side-effects of vancomycin are nephrotoxicity including kidney failure and interstitial nephritis, blood disorders including neutropenia, and deafness, which is reversible once therapy has stopped. Over 90% of the dose is excreted in the urine, therefore there is a risk of accumulation in patients with renal impairment, so therapeutic drug monitoring (TDM) is recommended. [ citation needed ]
Oral preparations of vancomycin are available, however, they are not absorbed from the lumen of the gut, so are of no use in treating systemic infections. The oral preparations are formulated for the treatment of infections within the gastrointestinal tract, Clostridioides difficile , for example. [ citation needed ] | https://en.wikipedia.org/wiki/Glycopeptide_antibiotic |
Glycopolymer is a synthetic polymer with pendant carbohydrates. [ 1 ] Glycopolymers play an important role in many biological recognition events such as cell–cell adhesion , the development of new tissues and the infectious behavior of virus and bacteria . They have high potential in targeted drug delivery, tissue engineering and synthesis of bio-compatible materials.
The first glycopolymer was synthesized in 1978 by free-radical polymerization . [ 2 ] Subsequent efforts have been devoted to synthesizing glycopolymers with various structures and sizes, and the synthesis techniques have widened to controlled/living radical polymerisation , ring-opening polymerization , ring-opening metathesis polymerization and post-functionalization. [ 3 ] | https://en.wikipedia.org/wiki/Glycopolymer |
Glycoproteins are proteins which contain oligosaccharide (sugar) chains covalently attached to amino acid side-chains. The carbohydrate is attached to the protein in a cotranslational or posttranslational modification . This process is known as glycosylation . Secreted extracellular proteins are often glycosylated.
In proteins that have segments extending extracellularly, the extracellular segments are also often glycosylated. Glycoproteins are also often important integral membrane proteins , where they play a role in cell–cell interactions. It is important to distinguish endoplasmic reticulum-based glycosylation of the secretory system from reversible cytosolic-nuclear glycosylation. Glycoproteins of the cytosol and nucleus can be modified through the reversible addition of a single GlcNAc residue that is considered reciprocal to phosphorylation and the functions of these are likely to be an additional regulatory mechanism that controls phosphorylation-based signalling. [ 2 ] In contrast, classical secretory glycosylation can be structurally essential. For example, inhibition of asparagine-linked, i.e. N-linked, glycosylation can prevent proper glycoprotein folding and full inhibition can be toxic to an individual cell. In contrast, perturbation of glycan processing (enzymatic removal/addition of carbohydrate residues to the glycan), which occurs in both the endoplasmic reticulum and Golgi apparatus , is dispensable for isolated cells (as evidenced by survival with glycosides inhibitors) but can lead to human disease (congenital disorders of glycosylation) and can be lethal in animal models. It is therefore likely that the fine processing of glycans is important for endogenous functionality, such as cell trafficking, but that this is likely to have been secondary to its role in host-pathogen interactions. A famous example of this latter effect is the ABO blood group system .
Though there are different types of glycoproteins, the most common are N -linked and O -linked glycoproteins. [ 3 ] These two types of glycoproteins are distinguished by structural differences that give them their names. Glycoproteins vary greatly in composition, making many different compounds such as antibodies or hormones. [ 4 ] Due to the wide array of functions within the body, interest in glycoprotein synthesis for medical use has increased. [ 5 ] There are now several methods to synthesize glycoproteins, including recombination and glycosylation of proteins. [ 5 ]
Glycosylation is also known to occur on nucleo cytoplasmic proteins in the form of O -GlcNAc . [ 6 ]
There are several types of glycosylation, although the first two are the most common.
Monosaccharides commonly found in eukaryotic glycoproteins include: [ 8 ] : 526
The sugar group(s) can assist in protein folding , improve proteins' stability and are involved in cell signalling.
The critical structural element of all glycoproteins is having oligosaccharides bonded covalently to a protein. [ 4 ] There are 10 common monosaccharides in mammalian glycans including: glucose (Glc), fucose (Fuc), xylose (Xyl), mannose (Man), galactose (Gal), N- acetylglucosamine (GlcNAc), glucuronic acid (GlcA), iduronic acid (IdoA), N-acetylgalactosamine (GalNAc), sialic acid , and 5- N-acetylneuraminic acid (Neu5Ac). [ 3 ] These glycans link themselves to specific areas of the protein amino acid chain.
The two most common linkages in glycoproteins are N -linked and O -linked glycoproteins. [ 3 ] An N -linked glycoprotein has glycan bonds to the nitrogen containing an asparagine amino acid within the protein sequence. [ 4 ] An O -linked glycoprotein has the sugar is bonded to an oxygen atom of a serine or threonine amino acid in the protein. [ 4 ]
Glycoprotein size and composition can vary largely, with carbohydrate composition ranges from 1% to 70% of the total mass of the glycoprotein. [ 4 ] Within the cell, they appear in the blood, the extracellular matrix , or on the outer surface of the plasma membrane, and make up a large portion of the proteins secreted by eukaryotic cells. [ 4 ] They are very broad in their applications and can function as a variety of chemicals from antibodies to hormones. [ 4 ]
Glycomics is the study of the carbohydrate components of cells. [ 4 ] Though not exclusive to glycoproteins, it can reveal more information about different glycoproteins and their structure. [ 4 ] One of the purposes of this field of study is to determine which proteins are glycosylated and where in the amino acid sequence the glycosylation occurs. [ 4 ] Historically, mass spectrometry has been used to identify the structure of glycoproteins and characterize the carbohydrate chains attached. [ 4 ] [ 10 ]
The unique interaction between the oligosaccharide chains have different applications. First, it aids in quality control by identifying misfolded proteins. [ 4 ] The oligosaccharide chains also change the solubility and polarity of the proteins that they are bonded to. [ 4 ] For example, if the oligosaccharide chains are negatively charged, with enough density around the protein, they can repulse proteolytic enzymes away from the bonded protein. [ 4 ] The diversity in interactions lends itself to different types of glycoproteins with different structures and functions. [ 5 ]
One example of glycoproteins found in the body is mucins , which are secreted in the mucus of the respiratory and digestive tracts. The sugars when attached to mucins give them considerable water-holding capacity and also make them resistant to proteolysis by digestive enzymes.
Glycoproteins are important for white blood cell recognition. [ citation needed ] Examples of glycoproteins in the immune system are:
H antigen of the ABO blood compatibility antigens.
Other examples of glycoproteins include:
Soluble glycoproteins often show a high viscosity , for example, in egg white and blood plasma .
Variable surface glycoproteins allow the sleeping sickness Trypanosoma parasite to escape the immune response of the host.
The viral spike of the human immunodeficiency virus is heavily glycosylated. [ 12 ] Approximately half the mass of the spike is glycosylation and the glycans act to limit antibody recognition as the glycans are assembled by the host cell and so are largely 'self'. Over time, some patients can evolve antibodies to recognise the HIV glycans and almost all so-called 'broadly neutralising antibodies (bnAbs) recognise some glycans. This is possible mainly because the unusually high density of glycans hinders normal glycan maturation and they are therefore trapped in the premature, high-mannose, state. [ 13 ] [ 14 ] This provides a window for immune recognition. In addition, as these glycans are much less variable than the underlying protein, they have emerged as promising targets for vaccine design. [ 15 ]
P-glycoproteins are critical for antitumor research due to its ability block the effects of antitumor drugs. [ 4 ] [ 16 ] P-glycoprotein, or multidrug transporter (MDR1), is a type of ABC transporter that transports compounds out of cells. [ 4 ] This transportation of compounds out of cells includes drugs made to be delivered to the cell, causing a decrease in drug effectiveness. [ 4 ] Therefore, being able to inhibit this behavior would decrease P-glycoprotein interference in drug delivery, making this an important topic in drug discovery. [ 4 ] For example, P-Glycoprotein causes a decrease in anti-cancer drug accumulation within tumor cells, limiting the effectiveness of chemotherapies used to treat cancer. [ 16 ]
Hormones that are glycoproteins include:
Quoting from recommendations for IUPAC: [ 17 ]
A glycoprotein is a compound containing carbohydrate (or glycan) covalently linked to protein. The carbohydrate may be in the form of a monosaccharide, disaccharide(s), oligosaccharide(s), polysaccharide(s), or their derivatives (e.g. sulfo- or phospho-substituted). One, a few, or many carbohydrate units may be present. Proteoglycans are a subclass of glycoproteins in which the carbohydrate units are polysaccharides that contain amino sugars. Such polysaccharides are also known as glycosaminoglycans.
A variety of methods used in detection, purification, and structural analysis of glycoproteins are [ 8 ] : 525 [ 18 ] [ 10 ]
The glycosylation of proteins has an array of different applications from influencing cell to cell communication to changing the thermal stability and the folding of proteins. [ 4 ] [ 19 ] Due to the unique abilities of glycoproteins, they can be used in many therapies. [ 19 ] By understanding glycoproteins and their synthesis, they can be made to treat cancer, Crohn's Disease , high cholesterol, and more. [ 3 ]
The process of glycosylation (binding a carbohydrate to a protein) is a post-translational modification , meaning it happens after the production of the protein. [ 3 ] Glycosylation is a process that roughly half of all human proteins undergo and heavily influences the properties and functions of the protein. [ 3 ] Within the cell, glycosylation occurs in the endoplasmic reticulum . [ 3 ]
There are several techniques for the assembly of glycoproteins. One technique utilizes recombination . [ 3 ] The first consideration for this method is the choice of host, as there are many different factors that can influence the success of glycoprotein recombination such as cost, the host environment, the efficacy of the process, and other considerations. [ 3 ] Some examples of host cells include E. coli, yeast, plant cells, insect cells, and mammalian cells. [ 3 ] Of these options, mammalian cells are the most common because their use does not face the same challenges that other host cells do such as different glycan structures, shorter half life, and potential unwanted immune responses in humans. [ 3 ] Of mammalian cells, the most common cell line used for recombinant glycoprotein production is the Chinese hamster ovary line. [ 3 ] However, as technologies develop, the most promising cell lines for recombinant glycoprotein production are human cell lines. [ 3 ]
The formation of the link between the glycan and the protein is key element of the synthesis of glycoproteins. [ 5 ] The most common method of glycosylation of N-linked glycoproteins is through the reaction between a protected glycan and a protected Asparagine. [ 5 ] Similarly, an O-linked glycoprotein can be formed through the addition of a glycosyl donor with a protected Serine or Threonine . [ 5 ] These two methods are examples of natural linkage. [ 5 ] However, there are also methods of unnatural linkages. [ 5 ] Some methods include ligation and a reaction between a serine-derived sulfamidate and thiohexoses in water. [ 5 ] Once this linkage is complete, the amino acid sequence can be expanded upon using solid-phase peptide synthesis. [ 5 ] | https://en.wikipedia.org/wiki/Glycoprotein |
Glycorandomization , is a drug discovery and drug development technology platform to enable the rapid diversification of bioactive small molecules, drug leads and/or approved drugs through the attachment of sugars. Initially developed as a facile method to manipulate carbohydrate substitutions of naturally occurring glycosides to afford the corresponding differentially glycosylated natural product libraries, [ 1 ] [ 2 ] [ 3 ] glycorandomization applications have expanded to include both small molecules (drug leads and approved drugs) and even macromolecules ( proteins ). [ 4 ] Also referred to as 'glycodiversification', [ 5 ] glycorandomization has led to the discovery of new glycoside analogs which display improvements in potency, selectivity and/or ADMET as compared to the parent molecule.
The traditional method for attaching sugars to natural products, drugs or drug leads is by chemical glycosylation . This classical approach typically requires multiple protection/deprotection steps in addition to the key anomeric activation/coupling reaction which, depending upon the glycosyl donor/acceptor pair, can lead to a mixture of anomers . Unlike classical chemical glycosylation, glycorandomization methods are divergent ( i.e. , diverge from a common starting material, see divergent synthesis ) and are not dependent upon sugar/ aglycon protection/deprotection or sugar anomeric activation. Two complementary strategies to achieve glycorandomization/diversification have been developed: an enzyme-based strategy referred to as 'chemoenzymatic glycorandomization' and a chemoselective method known as 'neoglycorandomization'. Both methods start with free reducing sugars and a target aglycon to afford a library of compounds which differ solely by the sugars appended to the target natural product, drug or drug lead.
Chemoenzymatic glycorandomization was inspired by the early pathway engineering work of Hutchinson and coworkers that suggested natural product glycosyltransferases were capable of utilizing non-native sugar nucleotide donors. [ 6 ] The initial platform for chemoenzymatic glycorandomization was based upon a set of two highly permissive sugar activation enzymes (a sugar anomeric kinase and sugar-1-phosphate nucleotidyltransferase ) to afford sugar nucleotide libraries as donors for these promiscuous glycosyltransferases where the permissivity of the corresponding sugar kinase [ 7 ] and nucleotidyltransferase [ 8 ] [ 9 ] was expanded by enzyme engineering and directed evolution . The first application of this three enzyme (kinase, nucleotidyltransferase and glycosyltransferase) strategy enabled the product of a set of >30 differentially glycosylated vancomycins , some members of which were further diversified chemoselectively by virtue of the installation of sugars bearing chemoselective handles. [ 10 ] [ 11 ] [ 12 ] This enzymatic platform has been further advanced through glycosyltransferase evolution [ 13 ] and capitalizing upon the discovery of the reversibility of glycosyltransferase-catalyzed reactions first discovered in the context of calicheamicin biosynthesis. [ 14 ] [ 15 ]
Neoglycorandomization is a chemoselective glycodiversification method inspired by the alkoxyamine-based ‘neoglycosylation’ reaction first described Peri and Dumy. [ 16 ] This reaction proceeds via an oxy-iminium intermediate to ultimately provide the more thermodynamically-favored closed ring neoglycoside. The neoglycosylation reaction is compatible with a wide range of saccharide and aglycon functionality where neoglycoside anomeric stereospecificity is a thermodynamically-driven. Importantly, structural and functional studies reveal neoglycosides to serve as good mimics of their O -glycosidic comparators. The first neoglycorandomization proof of concept focused upon digitoxin where the rapid generation and cancer cell line cytotoxicity screening of 78 digitoxigenin neoglycosides revealed unique analogs with improved anticancer activity and reduced potential for cardiotoxicity. [ 17 ] This platform has since been automated and used as an effective medicinal chemistry tool to modulate the properties of a range of natural products and pharmaceutical drugs . [ 18 ]
Both chemoenzymatic glycorandomization and neoglycorandomization use free reducing sugars and unprotected aglycons and are thereby a notable advance over classical glycosylation methods. A notable advantage of the enzymatic approach is the use of the corresponding genes encoding for the permissive kinases, nucleotidyltransferases and/or glycosyltransferases for in vivo synthetic biology applications to afford in vivo glycorandomization. [ 19 ] However, it is important to note the enzymatic platform is dependent upon the permissivity of the enzymes employed. In contrast, the main hurdle to chemoselective neoglycorandomization is installation of the alkoxylamine handle. Unlike the enzymatic approach, the anomeric stereoselectivity of the chemoselective method depends upon the reducing sugar used and can, in some cases, lead to anomeric mixtures.
Glycorandomization is used in the pharmaceutical industry and academic community to alter glycosylation patterns of sugar-containing natural products or to append sugars to drugs/drug leads. It provides a fast way to investigate the effect of subtle sugar modification on the pharmacological properties of the natural products analogues, [ 20 ] thus, affording a new approach to drug discovery. | https://en.wikipedia.org/wiki/Glycorandomization |
In chemistry , a glycoside / ˈ ɡ l aɪ k ə s aɪ d / is a molecule in which a sugar is bound to another functional group via a glycosidic bond . Glycosides play numerous important roles in living organisms. Many plants store chemicals in the form of inactive glycosides. These can be activated by enzyme hydrolysis , [ 1 ] which causes the sugar part to be broken off, making the chemical available for use. Many such plant glycosides are used as medications . Several species of Heliconius butterfly are capable of incorporating these plant compounds as a form of chemical defense against predators. [ 2 ] In animals and humans, poisons are often bound to sugar molecules as part of their elimination from the body.
In formal terms, a glycoside is any molecule in which a sugar group is bonded through its anomeric carbon to another group via a glycosidic bond . Glycosides can be linked by an O- (an O-glycoside ), N- (a glycosylamine ), S-(a thioglycoside ), or C- (a C-glycoside ) glycosidic bond. According to the IUPAC , the name " C -glycoside" is a misnomer ; the preferred term is " C -glycosyl compound". [ 3 ] The given definition is the one used by IUPAC , which recommends the Haworth projection to correctly assign stereochemical configurations. [ 4 ]
Many authors require in addition that the sugar be bonded to a non-sugar for the molecule to qualify as a glycoside, thus excluding polysaccharides . The sugar group is then known as the glycone and the non-sugar group as the aglycone or genin part of the glycoside. The glycone can consist of a single sugar group ( monosaccharide ), two sugar groups ( disaccharide ), or several sugar groups ( oligosaccharide ).
The first glycoside ever identified was amygdalin , by the French chemists Pierre Robiquet and Antoine Boutron-Charlard, in 1830. [ 5 ]
Molecules containing an N-glycosidic bond are known as glycosylamines . Many authors in biochemistry call these compounds N-glycosides and group them with the glycosides; this is considered a misnomer and is discouraged by the International Union of Pure and Applied Chemistry . Glycosylamines and glycosides are grouped together as glycoconjugates ; other glycoconjugates include glycoproteins , glycopeptides , peptidoglycans , glycolipids , and lipopolysaccharides . [ citation needed ]
Much of the chemistry of glycosides is explained in the article on glycosidic bonds . For example, the glycone and aglycone portions can be chemically separated by hydrolysis in the presence of acid and can be hydrolyzed by alkali . There are also numerous enzymes that can form and break glycosidic bonds. The most important cleavage enzymes are the glycoside hydrolases , and the most important synthetic enzymes in nature are glycosyltransferases . Genetically altered enzymes termed glycosynthases have been developed that can form glycosidic bonds in excellent yield. [ citation needed ]
There are many ways to chemically synthesize glycosidic bonds. Fischer glycosidation refers to the synthesis of glycosides by the reaction of unprotected monosaccharides with alcohols (usually as solvent) in the presence of a strong acid catalyst. The Koenigs-Knorr reaction is the condensation of glycosyl halides and alcohols in the presence of metal salts such as silver carbonate or mercuric oxide . [ citation needed ]
Glycosides can be classified by the glycone, by the type of glycosidic bond, and by the aglycone.
If the glycone group of a glycoside is glucose , then the molecule is a glucoside ; if it is fructose , then the molecule is a fructoside ; if it is glucuronic acid , then the molecule is a glucuronide ; etc. In the body, toxic substances are often bonded to glucuronic acid to increase their water solubility; the resulting glucuronides are then excreted. Compounds can also be generally defined based on the class of glycone; for example, biosides are glycosides with a disaccharide (biose) glycone.
Depending on whether the glycosidic bond lies "below" or "above" the plane of the cyclic sugar molecule, glycosides are classified as α-glycosides or β-glycosides . Some enzymes such as α-amylase can only hydrolyze α-linkages; others, such as emulsin , can only affect β-linkages.
There are four type of linkages present between glycone and aglycone:
Glycosides are also classified according to the chemical nature of the aglycone. For purposes of biochemistry and pharmacology, this is the most useful classification.
An example of an alcoholic glycoside is salicin , which is found in the genus Salix . Salicin is converted in the body into salicylic acid , which is closely related to aspirin and has analgesic , antipyretic , and anti-inflammatory effects.
These glycosides contain an aglycone group that is a derivative of anthraquinone . They have a laxative effect. They are mainly found in dicot plants except the family Liliaceae which are monocots . They are present in senna , rhubarb and Aloe species. Anthron and anthranol are reduced forms of anthraquinone.
Here, the aglycone is coumarin or a derivative. An example is apterin which is reported to dilate the coronary arteries as well as block calcium channels . Other coumarin glycosides are obtained from dried leaves of Psoralea corylifolia .
In this case, the aglycone is called benzo-gamma-pyrone.
In this case, the aglycone contains a cyanohydrin group. Plants that make cyanogenic glycosides store them in the vacuole , but, if the plant is attacked, they are released and become activated by enzymes in the cytoplasm . These remove the sugar part of the molecule, allowing the cyanohydrin structure to collapse and release toxic hydrogen cyanide . Storing them in inactive forms in the vacuole prevents them from damaging the plant under normal conditions. [ 6 ]
Along with playing a role in deterring herbivores, in some plants they control germination, bud formation, carbon and nitrogen transport, and possibly act as antioxidants. [ 6 ] The production of cyanogenic glycosides is an evolutionarily conserved function, appearing in species as old as ferns and as recent as angiosperms . [ 6 ] These compounds are made by around 3,000 species. In screens they are found in about 11% of cultivated plants but only 5% of plants overall; humans seem to have selected for them. [ 6 ]
Examples include amygdalin and prunasin which are made by the bitter almond tree; other species that produce cyanogenic glycosides are sorghum (from which dhurrin , the first cyanogenic glycoside to be identified, was first isolated), barley , flax , white clover , and cassava , which produces linamarin and lotaustralin . [ 6 ]
Amygdalin and a synthetic derivative, laetrile , were investigated as potential drugs to treat cancer and were heavily promoted as alternative medicine ; they are ineffective and dangerous. [ 7 ]
Some butterfly species, such as the Dryas iulia and Parnassius smintheus , have evolved to use the cyanogenic glycosides found in their host plants as a form of protection against predators through their unpalatability. [ 8 ] [ 9 ]
Here, the aglycone is a flavonoid . Examples of this large group of glycosides include:
Among the important effects of flavonoids are their antioxidant effect. They are also known to decrease capillary fragility.
Here, the aglycone is a simple phenolic structure. An example is arbutin found in the Common Bearberry Arctostaphylos uva-ursi . It has a urinary antiseptic effect.
These compounds give a permanent froth when shaken with water. They also cause hemolysis of red blood cells . Saponin glycosides are found in liquorice . Their medicinal value is due to their expectorant , corticoid and anti-inflammatory effects. Steroid saponins are important starting material for the production of semi-synthetic glucocorticoids and other steroid hormones such as progesterone ; for example in Dioscorea wild yam the sapogenin diosgenin , in the form of its glycoside dioscin. The ginsenosides are triterpene glycosides and ginseng saponins from Panax ginseng (Chinese ginseng) and Panax quinquefolius ( American ginseng ). In general, the use of the term saponin in organic chemistry is discouraged, because many plant constituents can produce foam , and many triterpene -glycosides are amphipolar under certain conditions, acting as a surfactant . More modern uses of saponins in biotechnology are as adjuvants in vaccines : Quil A and its derivative QS-21 , isolated from the bark of Quillaja saponaria Molina, to stimulate both the Th1 immune response and the production of cytotoxic T-lymphocytes (CTLs) against exogenous antigens make them ideal for use in subunit vaccines and vaccines directed against intracellular pathogens as well as for therapeutic cancer vaccines but with the aforementioned side-effect of hemolysis . [ 10 ] Saponins are also natural ruminal antiprotozoal agents that are potential to improve ruminal microbial fermentation reducing ammonia concentrations and methane production in ruminant animals . [ 11 ]
In these glycosides, the aglycone part is a steroid nucleus. These glycosides are found in the plant genera Digitalis , Scilla , and Strophanthus . They are used in the treatment of heart diseases , e.g., congestive heart failure (historically as now recognised does not improve survivability; other agents [ example needed ] are now preferred [ medical citation needed ] ) and arrhythmia .
These sweet glycosides found in the stevia plant Stevia rebaudiana Bertoni have 40–300 times the sweetness of sucrose . The two primary glycosides, stevioside and rebaudioside A, are used as natural sweeteners in many countries. These glycosides have steviol as the aglycone part. Glucose or rhamnose -glucose combinations are bound to the ends of the aglycone to form the different compounds.
These contain an iridoid group; e.g. aucubin , geniposidic acid , theviridoside, loganin , catalpol .
As the name contains the prefix thio- , these compounds contain sulfur . Examples include sinigrin , found in black mustard , and sinalbin , found in white mustard . | https://en.wikipedia.org/wiki/Glycoside |
In biochemistry , glycoside hydrolases (also called glycosidases or glycosyl hydrolases ) are a class of enzymes which catalyze the hydrolysis of glycosidic bonds in complex sugars . [ 1 ] [ 2 ] They are extremely common enzymes, with roles in nature including degradation of biomass such as cellulose ( cellulase ), hemicellulose , and starch ( amylase ), in anti-bacterial defense strategies (e.g., lysozyme ), in pathogenesis mechanisms (e.g., viral neuraminidases ) and in normal cellular function (e.g., trimming mannosidases involved in N -linked glycoprotein biosynthesis ). Together with glycosyltransferases , glycosidases form the major catalytic machinery for the synthesis and breakage of glycosidic bonds. [ 3 ]
Glycoside hydrolases are found in essentially all domains of life. In prokaryotes , they are found both as intracellular and extracellular enzymes that are largely involved in nutrient acquisition. One of the important occurrences of glycoside hydrolases in bacteria is the enzyme beta-galactosidase (LacZ), which is involved in regulation of expression of the lac operon in E. coli . In higher organisms glycoside hydrolases are found within the endoplasmic reticulum and Golgi apparatus where they are involved in processing of N-linked glycoproteins , and in the lysosome as enzymes involved in the degradation of carbohydrate structures. Deficiency in specific lysosomal glycoside hydrolases can lead to a range of lysosomal storage disorders that result in developmental problems or death. Glycoside hydrolases are found in the intestinal tract and in saliva where they degrade complex carbohydrates such as lactose , starch , sucrose and trehalose . In the gut they are found as glycosylphosphatidyl anchored enzymes on endothelial cells . The enzyme lactase is required for degradation of the milk sugar lactose and is present at high levels in infants, but in most populations will decrease after weaning or during infancy, potentially leading to lactose intolerance in adulthood. [ 4 ] [ 5 ] The enzyme O-GlcNAcase is involved in removal of N-acetylglucosamine groups from serine and threonine residues in the cytoplasm and nucleus of the cell. The glycoside hydrolases are involved in the biosynthesis and degradation of glycogen in the body.
Glycoside hydrolases are classified into EC 3.2.1 as enzymes catalyzing the hydrolysis of O- or S-glycosides. Glycoside hydrolases can also be classified according to the stereochemical outcome of the hydrolysis reaction: thus they can be classified as either retaining or inverting enzymes. [ 6 ] Glycoside hydrolases can also be classified as exo or endo acting, dependent upon whether they act at the (usually non-reducing) end or in the middle, respectively, of an oligo/polysaccharide chain. Glycoside hydrolases may also be classified by sequence or structure-based methods. [ 7 ]
Sequence-based classifications are one of the most powerful predictive methods for suggesting function for newly sequenced enzymes for which function has not been biochemically demonstrated. A classification system for glycosyl hydrolases, based on sequence similarity, has led to the definition of more than 100 different families. [ 8 ] [ 9 ] [ 10 ] This classification is available on the CAZy (CArbohydrate-Active EnZymes) web site. [ 7 ] [ 11 ] The database provides a series of regularly updated sequence based classification that allow reliable prediction of mechanism (retaining/inverting), active site residues and possible substrates. The online database is supported by CAZypedia, an online encyclopedia of carbohydrate active enzymes. [ 12 ] Based on three-dimensional structural similarities, the sequence-based families have been classified into 'clans' of related structure. Recent progress in glycosidase sequence analysis and 3D structure comparison has allowed the proposal of an extended hierarchical classification of the glycoside hydrolases. [ 13 ] [ 14 ]
Inverting enzymes utilize two enzymic residues, typically carboxylate residues, that act as acid and base respectively, as shown below for a β-glucosidase .
The product of the reaction has an axial position on C1, but some spontaneous changes of conformation can appear.
Retaining glycosidases operate through a two-step mechanism, with each step resulting in inversion , for a net retention of stereochemistry. Again, two residues are involved, which are usually enzyme-borne carboxylates . One acts as a nucleophile and the other as an acid/base. In the first step, the nucleophile attacks the anomeric centre, resulting in the formation of a glycosyl enzyme intermediate, with acidic assistance provided by the acidic carboxylate. In the second step, the now deprotonated acidic carboxylate acts as a base and assists a nucleophilic water to hydrolyze the glycosyl enzyme intermediate, giving the hydrolyzed product. The mechanism is illustrated below for hen egg white lysozyme . [ 15 ]
An alternative mechanism for hydrolysis with retention of stereochemistry can occur that proceeds through a nucleophilic residue that is bound to the substrate, rather than being attached to the enzyme. Such mechanisms are common for certain N-acetylhexosaminidases, which have an acetamido group capable of neighboring group participation to form an intermediate oxazoline or oxazolinium ion. This mechanism proceeds in two steps through individual inversions to lead to a net retention of configuration.
A variant neighboring group participation mechanism has been described for endo-α-mannanases that involves 2-hydroxyl group participation to form an intermediate epoxide. Hydrolysis of the epoxide leads to a net retention of configuration. [ 16 ]
Glycoside hydrolases are typically named after the substrate that they act upon. Thus glucosidases catalyze the hydrolysis of glucosides and xylanases catalyze the cleavage of the xylose based homopolymer xylan. Other examples include lactase , amylase , chitinase , sucrase , maltase , neuraminidase , invertase , hyaluronidase and lysozyme .
Glycoside hydrolases are predicted to gain increasing roles as catalysts in biorefining
applications in the future bioeconomy. [ 17 ] These enzymes have a variety of uses including degradation of plant materials (e.g., cellulases for degrading cellulose to glucose, which can be used for ethanol production), in the food industry ( invertase for manufacture of invert sugar, amylase for production of maltodextrins), and in the paper and pulp industry ( xylanases for removing hemicelluloses from paper pulp). Cellulases are added to detergents for the washing of cotton fabrics and assist in the maintenance of colours through removing microfibres that are raised from the surface of threads during wear.
In organic chemistry , glycoside hydrolases can be used as synthetic catalysts to form glycosidic bonds through either reverse hydrolysis (kinetic approach) where the equilibrium position is reversed; or by transglycosylation (kinetic approach) whereby retaining glycoside hydrolases can catalyze the transfer of a glycosyl moiety from an activated glycoside to an acceptor alcohol to afford a new glycoside.
Mutant glycoside hydrolases termed glycosynthases have been developed that can achieve the synthesis of glycosides in high yield from activated glycosyl donors such as glycosyl fluorides. Glycosynthases are typically formed from retaining glycoside hydrolases by site-directed mutagenesis of the enzymic nucleophile to some other less nucleophilic group, such as alanine or glycine. Another group of mutant glycoside hydrolases termed thioglycoligases can be formed by site-directed mutagenesis of the acid-base residue of a retaining glycoside hydrolase. Thioglycoligases catalyze the condensation of activated glycosides and various thiol-containing acceptors.
Various glycoside hydrolases have shown efficacy in degrading matrix polysaccharides within the extracellular polymeric substance (EPS) of microbial biofilms . [ 18 ] Medically, biofilms afford infectious microorganisms a variety of advantages over their planktonic, fre-floating counterparts, including greatly increased tolerances to antimicrobial agents and the host immune system. Thus, degrading the biofilm may increase antibiotic efficacy, and potentiate host immune function and healing ability. For example, a combination of alpha-amylase and cellulase was shown to degrade polymicrobial bacterial biofilms from both in vitro and in vivo sources, and increase antibiotic effectiveness against them. [ 19 ]
Many compounds are known that can act to inhibit the action of a glycoside hydrolase. Nitrogen-containing, 'sugar-shaped' heterocycles have been found in nature , including deoxynojirimycin , swainsonine , australine and castanospermine . From these natural templates many other inhibitors have been developed, including isofagomine and deoxygalactonojirimycin , and various unsaturated compounds such as PUGNAc. Inhibitors that are in clinical use include the anti-diabetic drugs acarbose and miglitol , and the antiviral drugs oseltamivir and zanamivir . Some proteins have been found to act as glycoside hydrolase inhibitors. | https://en.wikipedia.org/wiki/Glycoside_hydrolase |
A glycosidic bond or glycosidic linkage is a type of ether bond that joins a carbohydrate (sugar) molecule to another group, which may or may not be another carbohydrate.
A glycosidic bond is formed between the hemiacetal or hemiketal group of a saccharide (or a molecule derived from a saccharide) and the hydroxyl group of some compound such as an alcohol . A substance containing a glycosidic bond is a glycoside .
The term 'glycoside' is now extended to also cover compounds with bonds formed between hemiacetal (or hemiketal) groups of sugars and several chemical groups other than hydroxyls, such as -SR (thioglycosides), -SeR (selenoglycosides), -NR 1 R 2 (N-glycosides), or even -CR 1 R 2 R 3 (C-glycosides).
Particularly in naturally occurring glycosides, the compound ROH from which the carbohydrate residue has been removed is often termed the aglycone , and the carbohydrate residue itself is sometimes referred to as the 'glycone'.
Glycosidic bonds of the form discussed above are known as O-glycosidic bonds , in reference to the glycosidic oxygen that links the glycoside to the aglycone or reducing end sugar. In analogy, one also considers S-glycosidic bonds (which form thioglycosides ), where the oxygen of the glycosidic bond is replaced with a sulfur atom. In the same way, N-glycosidic bonds , have the glycosidic bond oxygen replaced with nitrogen . Substances containing N-glycosidic bonds are also known as glycosylamines . C-glycosyl bonds have the glycosidic oxygen replaced by a carbon ; the term "C-glycoside" is considered a misnomer by IUPAC and is discouraged. [ 1 ] All of these modified glycosidic bonds have different susceptibility to hydrolysis, and in the case of C-glycosyl structures, they are typically more resistant to hydrolysis.
When an anomeric center is involved in a glycosidic bond (as is common in nature) then one can distinguish between α- and β-glycosidic bonds by the relative stereochemistry of the anomeric position and the stereocenter furthest from C1 in the saccharide. [ 2 ]
Pharmacologists often join substances to glucuronic acid via glycosidic bonds in order to increase their water solubility ; this is known as glucuronidation . Many other glycosides have important physiological functions.
Nüchter et al. (2001) have shown a new approach to Fischer glycosidation . [ 3 ] [ 4 ] [ 5 ] Employing a microwave oven equipped with refluxing apparatus in a rotor reactor with pressure bombs , Nüchter et al. (2001) were able to achieve 100% yield of α- and β-D-glucosides. This method can be performed on a multi-kilogram scale.
Joshi et al. (2006) [ 6 ] propose the Koenigs-Knorr reaction in the stereoselective synthesis of alkyl D-glucopyranosides via glycosylation, with the exception of using lithium carbonate which is less expensive and toxic than the conventional method of using silver or mercury salts. D-glucose is first protected by forming the peracetate by addition of acetic anhydride in acetic acid , and then addition of hydrogen bromide which brominates at the 5-position. On addition of the alcohol ROH and lithium carbonate, the OR replaces the bromine and on deprotecting the acetylated hydroxyls the product is synthesized in relatively high purity. It was suggested by Joshi et al. (2001) that lithium acts as the nucleophile that attacks the carbon at the 5-position and through a transition state the alcohol is substituted for the bromine group. Advantages of this method as well as its stereoselectivity and low cost of the lithium salt include that it can be done at room temperature and its yield compares relatively well with the conventional Koenigs-Knorr method. [ 7 ]
Glycoside hydrolases (or glycosidases), are enzymes that break glycosidic bonds. Glycoside hydrolases typically can act either on α- or on β-glycosidic bonds, but not on both. This specificity allows researchers to obtain glycosides in high epimeric excess, one example being Wen-Ya Lu's conversion of D-Glucose to Ethyl β-D-glucopyranoside using naturally-derived glucosidase. Wen-Ya Lu utilized glucosidase in a reverse manner opposite to the enzyme's biological functionality: [ 8 ]
Before monosaccharide units are incorporated into glycoproteins, polysaccharides, or lipids in living organisms, they are typically first "activated" by being joined via a glycosidic bond to the phosphate group of a nucleotide such as uridine diphosphate (UDP), guanosine diphosphate (GDP), thymidine diphosphate (TDP), or cytidine monophosphate (CMP). These activated biochemical intermediates are known as sugar nucleotides or sugar donors. Many biosynthetic pathways use mono- or oligosaccharides activated by a diphosphate linkage to lipids, such as dolichol . These activated donors are then substrates for enzymes known as glycosyltransferases , which transfer the sugar unit from the activated donor to an accepting nucleophile (the acceptor substrate).
Different biocatalytic approaches have been developed toward the synthesis of glycosides in the past decades, which using "glycosyltransferases" and "glycoside hydrolases" are among the most common catalysis. The former often needs expensive materials and the later often shows low yields, De Winter et al. [ 10 ] investigated use of cellobiose phosphorylase (CP) toward synthesis of alpha-glycosides in ionic liquids. The best condition for use of CP was found to be in the presence of IL AMMOENG 101 and ethyl acetate.
Multiple chemical approaches exist to encourage selectivity of α- and β-glycosidic bonds. The highly substrate specific nature of the selectivity and the overall activity of the pyranoside can provide major synthetic difficulties. The overall specificity of the glycosylation can be improved by utilizing approaches which take into account the relative transition states that the anomeric carbon can undergo during a typical glycosylation. Most notably, recognition and incorporation of Felkin-Ahn-Eisenstein models into rationale chemical design can generally provide reliable results provided the transformation can undergo this type of conformational control in the transition state.
Fluorine directed glycosylations represent an encouraging handle for both B selectivity and introduction of a non-natural biomimetic C2 functionality on the carbohydrate. One innovative example provided by Bucher et al. provides a way to utilize a fluoro oxonium ion and the trichloroacetimidate to encourage B stereoselectivity through the gauche effect. [ 11 ] This reasonable stereoselectivity is clear through visualization of the Felkin-Ahn models of the possible chair forms.
This method represents an encouraging way to selectivity incorporate B-ethyl, isopropyl and other glycosides with typical trichloroacetimidate chemistry.
O-linked glycopeptides recently have been shown to exhibit excellent CNS permeability and efficacy in multiple animal models with disease states. In addition one of the most intriguing aspects thereof is the capability of O-glycosylation to extend half life, decrease clearance, and improve PK/PD thereof the active peptide beyond increasing CNS penetration. The innate utilization of sugars as solubilizing moieties in Phase II and III metabolism (glucuronic acids) has remarkably allowed an evolutionary advantage in that mammalian enzymes are not directly evolved to degrade O glycosylated products on larger moieties.
The peculiar nature of O-linked glycopeptides is that there are numerous examples which are CNS penetrant. The fundamental basis of this effect is thought to involve "membrane hopping" or "hop diffusion". The non-brownian motion driven "hop diffusion" process is thought to occur due to discontinuity of the plasma membrane. "Hop diffusion" notably combines free diffusion and intercomparmental transitions. Recent examples notably include high permeability of met-enkephalin analogs amongst other peptides. The full mOR agonist pentapeptide DAMGO is also CNS penetrant upon introduction of glycosylation. [ 12 ] [ 13 ] [ 14 ]
DNA molecules contain 5-membered carbon rings called deoxyriboses that are directly attached to two phosphate groups and a nucleobase that contains amino groups. The nitrogen atoms from the amino group in the nucleotides are covalently linked to the anomeric carbon of the ribose sugar structure through an N-glycosidic bond. Occasionally, the nucleobases attached to the ribose undergo deamination, alkylation, or oxidation which results in cytotoxic lesions along the DNA backbone. These modifications severely threaten the cohesiveness of the DNA molecule, leading to the development of diseases such as cancer. DNA glycosylases are enzymes that catalyze the hydrolysis the N-glycosidic bond to free the damaged or modified nucleobase from the DNA, by cleaving the carbon-nitrogen glycosidic bond at the 2' carbon, subsequently initiating the base excision repair (BER) pathway.
Monofunctional glycosylases catalyze the hydrolysis of the N-glycosidic bond via either a stepwise, S N 1 like mechanism, or a concerted, S N 2 like mechanism. The stepwise function, the nucleobase acts as a leaving group before the anomeric carbon gets attacked by the water molecule, producing a short-lived unstable oxacarbenium ion intermediate. This intermediate rapidly reacts with the nearby water molecule to substitute the N-glycosidic bond of the ribose and the nucleobase with an O-glycosidic bond with a hydroxy group. The concerted mechanism, the water acts as a nucleophile and attacks at the anomeric carbon before the nucelobase gets to act like a leaving group. The intermediate produced is a similar oxacarbenium ion where both the hydroxy groups and the nucleobase are still attached to the anomeric carbon. Both mechanisms theoretically yield the same product. Most ribonucleotides are hydrolyzed via the concerted S N 2 like mechanism, while most deoxyribonucleotides proceed through the stepwise like mechanism.
These reactions are practically irreversible. Due to the fact that the cleavage of the N-glycosidic bond from the DNA backbone can lead to detrimental mutagenic and cytotoxic responses in an organism , have [ clarify ] the ability to also catalyze the synthesis of N-glycosidic bonds by way of an abasic DNA site and a specific nucleobase. [ 15 ] | https://en.wikipedia.org/wiki/Glycosidic_bond |
The glycosome is a membrane -enclosed organelle that contains the glycolytic enzymes . The term was first used by Scott and Still in 1968 after they realized that the glycogen in the cell was not static but rather a dynamic molecule. [ 1 ] It is found in a few species of protozoa including the Kinetoplastida which include the suborders Trypanosomatida and Bodonina, most notably in the human pathogenic trypanosomes , which can cause sleeping sickness , Chagas's disease , and leishmaniasis . The organelle is bounded by a single membrane and contains a dense proteinaceous matrix. It is believed to have evolved from the peroxisome . [ 2 ] This has been verified by work done on Leishmania genetics. [ 3 ]
The glycosome is currently being researched as a possible target for drug therapies.
Glycosomes are unique to kinetoplastids and their sister diplonemids . The term glycosome is also used for glycogen-containing structures found in hepatocytes responsible for storing sugar, but these are not membrane bound organelles. [ 4 ]
Glycosomes are composed of glycogen and proteins. The proteins are the enzymes that are associated with the metabolism of glycogen. These proteins and glycogen form a complex to make a distinct and separate organelle. [ 1 ] The proteins for glycosomes are imported from free cytosolic ribosomes. The proteins imported into the organelle have a specific sequence, a PTS1 ending sequence to make sure they go to the right place. [ 5 ] They are similar to alpha-granules in the cytosol of a cell that are filled with glycogen. Glycosomes are typically round-to-oval shape with size varying in each cell. Although glycogen is found in the cytoplasm, that in the glycosome is separate, surrounded by membrane. The membrane is a lipid bilayer. The glycogen that is found within the glycosome is identical to glycogen found freely in the cytosol . [ 6 ] Glycosomes can be associated or attached to many different types of organelles. They have been found to be attached to the sarcoplasmic reticulum and its intermediate filaments. Other glycosomes have been found to be attached to myofibrils and mitochondria, rough endoplasmic reticulum, sarcolemma, polyribosomes, or the Golgi apparatus. Glycosome attachment may bestow a functional distinction between them; the glycosomes attached to the myofibrils seem to serve the myosin by providing energy substrates for generation of ATP through glycolysis. The glycosomes in the rough and smooth endoplasmic reticulum make use of its glycogen synthase and phosphorylase phosphatases. [ 1 ]
Glycosomes function in many processes in the cell. These processes include glycolysis, purine salvage , beta oxidation of fatty acids, and ether lipid synthesis. [ 5 ]
The main function that the glycosome serves is of the glycolytic pathway that is done inside its membrane. By compartmentalizing glycolysis inside of the glycosome, the cell can be more successful. In the cell, action in the cytosol, the mitochondria, and the glycosome are all completing the function of energy metabolism. This energy metabolism generates ATP through the process of glycolysis. The glycosome is a host of the main glycolytic enzymes in the pathway for glycolysis. This pathway is used to break down fatty acids for their carbon and energy. The entire process of glycolysis does not take place in the glycosome however. Rather, only the Embden-Meyerhof segment where the glucose enters into the glycosome. Importantly, the process in the organelle has no net ATP synthesis. This ATP comes later from processes outside of the glycosome. Inside of the glycosome does need NAD+ for functioning and its regeneration. Fructose 1,6-biphosphate is used in the glycosome as a way to help obtain oxidizing agents to help start glycolysis. The glycosome converts the sugar into 3-phosphoglycerate. [ 2 ]
Another function of glycosomes is purine salvage. The parasites which have glycosomes present in their cells cannot make purine de novo. This purine that is made in the glycosome is then exported out of the glycosome to be used in the cell in nucleic acid. In other cells the enzymes responsible for this are present in the cytosol. These enzymes found in the glycosome to help with synthesis are guanine and adenine phosphoribosyl transferase, hypoxanthine, and xanthine pho tran. All of these enzymes contain a PTS1 sequence at their carboxyl sequence so that they are sent to the glycosome. [ 5 ]
Microscopic techniques have revealed a lot about the glycosome in the cell and have indeed proven that there is a membrane-bound organelle in the cell for glycogen and its processes. Paul Erlich's findings as early as 1883 noted that from the microscope he could tell that glycogen in the cell was always found with what he called a carrier, later known to be protein. The glycogen itself was also always seen in the cell towards the lower pole in one group, fixed. When scientists tried to stain what was assumed was simple glycogen molecules, the staining had different outcomes. This is due to the fact that they weren't free glycogen molecules but really a glycosome. The glycosome was studied in the microscope by examining the glycosome that was stained with uranyl acetate . The U/Pb that was seen stained was the protein that was part of the glycosome. The glycogen in the glycosome in the cells is normally associated with protein that is two to four times the weight of the glycogen. The glycogen itself however, after purified, is found with very little protein, less than three percent normally, showing that the glycosome is responsible and functions by having the proteins and enzymes needed for the glycogen in the glycosome. With the uranyl staining, as an acid, it would cause dissociation of the protein from the glycogen. The glycogen without the protein would form large aggregates and the stain would be the protein. This gives the illusion of glycogen disappearing as it is not stained, but it dissociates from the protein that it is normally associated with in the glycosome. [ 1 ]
There has been a variety of evidence found biochemically to give evidence that glycosomes are present in cells. In the organelle that is assumed to be a glycosome, numerous proteins are found. These include glycogen synthase, phosphorylase, and branching and debranching enzymes for glycogen. All of these are regulatory enzymes that are needed in glycogen synthesis. The initiation of synthesis of glycogen requires glycogenin , found in glycosomes, a protein primer. Glycogen synthase as mentioned helps in glycogen elongation and the removal of the glucose from glycogen is aided by debranching enzymes and phosphorylase . All of these enzymes are found in the glycosome, showing that this organelle complete with glycogen as well is responsible for storing glycogen and separate from the cytosol. [ 1 ]
There are two types of glycosomes that are found in cells exhibiting these specialized organelles. These two groups are lyoglycosomes and desmoglycosomes. They differ in their association with other organelles in the cell, along with their relative abundance. Studies have shown that healthy cells have more lyoglycosomes while starved cells have more desmoglycosomes.
Lyoglycosomes are glycosomes that are free in the cytosol of the cell. These types of glycosomes are affected by acid. They tend to be less electron dense than the other type of glycosome. Lyoglycosomes also are usually found in chains in the cytosol. Because the lyoglycosomes are not bound to tissue, it is possible to extract these glycosomes with water that is boiling. [ 1 ]
Desmoglycosomes are not free in the cytosol but rather are with other organelles or structures in the cell. These structures relate to the other organelles mentioned such as the myofibrils, mitochondria, and endoplasmic reticulum. This accounts for why desmoglycosomes are found in muscle cells . These glycosomes are not affected by acid. These glycosomes are not found to form groups but rather stay separate as single organelles. Because of the high amount of protein that the glycosome associates with, a high electron density is usually observed. Desmoglycosomes are not extractable from boiling water as they are bound to tissue through their connection to protein. [ 1 ]
The glycosomes are the most divergent of the different types of organelles stemming from peroxisomes, especially as seen in the trypanosomes . Peroxisomes of higher eukaryotes are very similar to the glycosomes and the glyoxysomes that are found in some plants and fungi. The glycosome shares the same basic level structure of a single membrane and a very dense protein matrix. Some studies have shown that some of the enzymes and pathways that are found in the peroxisome are also seen in glycosomes of some species of the trypanosomes. Also, the targeting sequences on the proteins that are sent to the glycosome for the protein matrix are similar in sequence to those sequences on proteins being imported into the peroxisome. The same is seen in the actual sequences for the proteins going into the matrices for these two organelles, not just the targeting sequences. It has been speculated that the since it has been found that glycosomes possess plastid like proteins, a lateral gene transfer happened long ago from an organism capable of photosynthesis whose genes were transferred to have the resultant peroxisomes and glycosomes. The glycosome itself, along with the peroxisome, lacks a genome . [ 2 ]
Unlike peroxisomes, for most of the trypanosomes their glycosomes are needed for them to be able to survive. Because of this need for the glycosome, it has been suggested as a possible drug target to find a drug to halt its function. When the glycosome is not functioning correctly there is a severe lack of enzymes in the cell. These enzymes are those associated with ether-lipid synthesis or the beta oxidation of certain fatty acids. Cells without glycosomes are deficient in these enzymes as without the compartmentalization of the glycosome the enzymes are degraded in the cell in the cytosol. The organelle keeps metabolism of the enzymes from occurring. For parasites , ether-lipid synthesis is vital to be able to complete its life cycle, making the enzymes protected by the glycosome also vital. [ 2 ] In their life cycle, glycolysis partly through the glycosome is very high in the blood stream form comparatively to the pro-cyclic form. The glycosomal glycolysis pathway is necessary in stress situations for the pathogen as glycolysis can be started when the substrates for the pathway are available even when ATP is not available yet. So as this organelle is so essential for the trypanosome, if a drug could target this organelle, it could be a successful therapy as studies have shown without the glycosome parasite death occurs. [ 7 ] | https://en.wikipedia.org/wiki/Glycosome |
In organic chemistry , a glycosyl group is a univalent free radical or substituent structure obtained by removing the hydroxyl ( −OH ) group from the hemiacetal ( −CH(OH)O− ) group found in the cyclic form of a monosaccharide and, by extension, of a lower oligosaccharide . Glycosyl groups are exchanged during glycosylation from the glycosyl donor , the electrophile , to the glycosyl acceptor , the nucleophile . [ 1 ] The outcome of the glycosylation reaction is largely dependent on the reactivity of each partner. [ 2 ] Glycosyl also reacts with inorganic acids , such as phosphoric acid , forming an ester such as glucose 1-phosphate . [ 3 ]
In cellulose , glycosyl groups link together 1,4-β- D -glucosyl units to form chains of (1,4-β- D -glucosyl) n .
Other examples include ribityl in 6,7-Dimethyl-8-ribityllumazine , and glycosylamines .
Instead of the hemiacetal hydroxyl group, a hydrogen atom can be removed to form a substituent, for example the hydrogen from the C3 hydroxyl of a glucose molecule. Then the substituent is called D -glucopyranos-3- O -yl as it appears in the name of the drug Mifamurtide .
Recent detection of Au 3+ in vivo used C -glycosyl pyrene. Its fluorescence and permeability through cell membranes helped detect Au 3+ . [ 4 ] | https://en.wikipedia.org/wiki/Glycosyl |
A glycosyl acceptor is any suitable nucleophile -containing molecule that will react with a glycosyl donor to form a new glycosidic bond . By convention, the acceptor is the member of this pair which did not contain the resulting anomeric carbon of the new glycosidic bond. Since the nucleophilic atom of the acceptor is typically an oxygen atom, this can be remembered using the mnemonic of the acceptor is the alcohol. A glycosyl acceptor can be a mono- or oligosaccharide that contains an available nucleophile, such as an unprotected hydroxyl.
glucose to haemoglobin | https://en.wikipedia.org/wiki/Glycosyl_acceptor |
A glycosyl donor is a carbohydrate mono- or oligosaccharide that will react with a suitable glycosyl acceptor to form a new glycosidic bond . By convention, the donor is the member of this pair that contains the resulting anomeric carbon of the new glycosidic bond. [ 1 ] The resulting reaction is referred to as a glycosylation or chemical glycosylation .
In a glycosyl donor, a leaving group is required at the anomeric position. The simplest leaving group is the OH group that is naturally present in monosaccharides, but it requires activation by acid catalysis in order to function as leaving group (in the Fischer glycosylation). More effective leaving groups are in general used in the glycosyl donors employed in chemical synthesis of glycosides. Typical leaving groups are halides, thioalkyl groups, or imidates, but acetate, phosphate, and O-pentenyl groups are also employed. Natural glycosyl donors contain phosphates as leaving groups. [ 1 ]
The so-called "armed-disarmed" principle
The concept of armed and disarmed glycosyl donors refers to the increased reactivity of benzylated over benzoylated glycosyl donors, a phenomenon observed very early, [ 2 ] and which originates from the greater electron-withdrawing capability of ester blocking groups over ether blocking groups. However, it was Bertram Fraser-Reid who realised that benzylated glycosyl donors can be activated when benzoylated donors are not, and invented the terms armed glycosyl donor for the former, and disarmed glycosyl donor for the latter. He and his group showed that armed glycosyl donors could be coupled to a glycosyl acceptor, that was at the same time a disarmed glycosyl donor, without self-coupling of the disarmed donor/acceptor. [ 3 ] This approach allowed him to carry out a one-pot synthesis of a trisaccharide by the n-pentenyl glycoside method. [ 4 ]
The concept has been extended to superarmed glycosyl donor by Mikael Bols and his collaborators. He realised that the hydroxy groups of carbohydrates are less electron-withdrawing towards the anomeric center when they are axial than when they are equatorial, which means that glycosyl donor conformers with more axial oxy functions are more reactive. [ 5 ] Protection of a glycosyl donor with bulky silyl groups (tert-butyldimethylsilyl or triisopropyl) cause it to change conformation to a more axial-rich conformation that, as a consequence, is more reactive, which Bols and his group called superarmed. They showed that a superarmed donor can be coupled to an armed glycosyl donor/acceptor. [ 6 ] | https://en.wikipedia.org/wiki/Glycosyl_donor |
Glycosylamines are a class of biochemical compounds consisting of a glycosyl group attached to an amino group , -NR 2 . They are also known as N-glycosides, [ 1 ] as they are a type of glycoside . Glycosyl groups can be derived from carbohydrates . The glycosyl group and amino group are connected with a β-N-glycosidic bond , forming a cyclic hemiaminal ether bond (α-aminoether).
Examples include nucleosides such as adenosine .
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Glycosylamine |
Glycosylation is the reaction in which a carbohydrate (or ' glycan '), i.e. a glycosyl donor , is attached to a hydroxyl or other functional group of another molecule (a glycosyl acceptor ) in order to form a glycoconjugate . In biology (but not always in chemistry), glycosylation usually refers to an enzyme-catalysed reaction, whereas glycation (also 'non-enzymatic glycation' and 'non-enzymatic glycosylation') may refer to a non-enzymatic reaction. [ 1 ]
Glycosylation is a form of co-translational and post-translational modification . Glycans serve a variety of structural and functional roles in membrane and secreted proteins. [ 2 ] The majority of proteins synthesized in the rough endoplasmic reticulum undergo glycosylation. Glycosylation is also present in the cytoplasm and nucleus as the O -GlcNAc modification. Aglycosylation is a feature of engineered antibodies to bypass glycosylation. [ 3 ] [ 4 ] Five classes of glycans are produced:
Glycosylation is the process by which a carbohydrate is covalently attached to a target macromolecule , typically proteins and lipids . This modification serves various functions. [ 5 ] For instance, some proteins do not fold correctly unless they are glycosylated. [ 2 ] In other cases, proteins are not stable unless they contain oligosaccharides linked at the amide nitrogen of certain asparagine residues. The influence of glycosylation on the folding and stability of glycoprotein is twofold. Firstly, the highly soluble glycans may have a direct physicochemical stabilisation effect. Secondly, N -linked glycans mediate a critical quality control check point in glycoprotein folding in the endoplasmic reticulum. [ 6 ] Glycosylation also plays a role in cell-to-cell adhesion (a mechanism employed by cells of the immune system ) via sugar-binding proteins called lectins , which recognize specific carbohydrate moieties. [ 2 ] Glycosylation is an important parameter in the optimization of many glycoprotein-based drugs such as monoclonal antibodies . [ 6 ] Glycosylation also underpins the ABO blood group system. It is the presence or absence of glycosyltransferases which dictates which blood group antigens are presented and hence what antibody specificities are exhibited. This immunological role may well have driven the diversification of glycan heterogeneity and creates a barrier to zoonotic transmission of viruses. [ 7 ] In addition, glycosylation is often used by viruses to shield the underlying viral protein from immune recognition. A significant example is the dense glycan shield of the envelope spike of the human immunodeficiency virus . [ 8 ]
Overall, glycosylation needs to be understood by the likely evolutionary selection pressures that have shaped it. In one model, diversification can be considered purely as a result of endogenous functionality (such as cell trafficking ). However, it is more likely that diversification is driven by evasion of pathogen infection mechanism (e.g. Helicobacter attachment to terminal saccharide residues) and that diversity within the multicellular organism is then exploited endogenously. [ citation needed ]
Glycosylation can also modulate the thermodynamic and kinetic stability of the proteins. [ 9 ]
Glycosylation increases diversity in the proteome , because almost every aspect of glycosylation can be modified, including: [ citation needed ]
There are various mechanisms for glycosylation, although most share several common features: [ 2 ]
N -linked glycosylation is a very prevalent form of glycosylation and is important for the folding of many eukaryotic glycoproteins and for cell–cell and cell– extracellular matrix attachment. The N -linked glycosylation process occurs in eukaryotes in the lumen of the endoplasmic reticulum and widely in archaea , but very rarely in bacteria . In addition to their function in protein folding and cellular attachment, the N -linked glycans of a protein can modulate a protein's function, in some cases acting as an on/off switch. [ citation needed ]
O -linked glycosylation is a form of glycosylation that occurs in eukaryotes in the Golgi apparatus , [ 11 ] but also occurs in archaea and bacteria .
Xylose , fucose , mannose , and GlcNAc phosphoserine glycans have been reported in the literature. Fucose and GlcNAc have been found only in Dictyostelium discoideum , mannose in Leishmania mexicana , and xylose in Trypanosoma cruzi . Mannose has recently been reported in a vertebrate, the mouse, Mus musculus , on the cell-surface laminin receptor alpha dystroglycan 4 . It has been suggested this rare finding may be linked to the fact that alpha dystroglycan is highly conserved from lower vertebrates to mammals. [ 12 ]
A mannose sugar is added to the first tryptophan residue in the sequence W–X–X–W (W indicates tryptophan; X is any amino acid). A C-C bond is formed between the first carbon of the alpha-mannose and the second carbon of the tryptophan. [ 13 ] However, not all the sequences that have this pattern are mannosylated. It has been established that, in fact, only two thirds are and that there is a clear preference for the second amino acid to be one of the polar ones (Ser, Ala , Gly and Thr) in order for mannosylation to occur. Recently there has been a breakthrough in the technique of predicting whether or not the sequence will have a mannosylation site that provides an accuracy of 93% opposed to the 67% accuracy if we just consider the WXXW motif. [ 14 ]
Thrombospondins are one of the proteins most commonly modified in this way. However, there is another group of proteins that undergo C -mannosylation, type I cytokine receptors . [ 15 ] C -mannosylation is unusual because the sugar is linked to a carbon rather than a reactive atom such as nitrogen or oxygen . In 2011, the first crystal structure of a protein containing this type of glycosylation was determined—that of human complement component 8. [ 16 ] Currently it is established that 18% of human proteins , secreted and transmembrane undergo the process of C-mannosylation. [ 14 ] Numerous studies have shown that this process plays an important role in the secretion of Trombospondin type 1 containing proteins which are retained in the endoplasmic reticulum if they do not undergo C-mannosylation [ 14 ] This explains why a type of cytokine receptors , erythropoietin receptor remained in the endoplasmic reticulum if it lacked C-mannosylation sites. [ 17 ]
Glypiation is a special form of glycosylation that features the formation of a GPI anchor . In this kind of glycosylation a protein is attached to a lipid anchor, via a glycan chain. (See also prenylation .)
Glycosylation can also be effected using the tools of synthetic organic chemistry . Unlike the biochemical processes, synthetic glycochemistry relies heavily on protecting groups [ 18 ] (e.g. the 4,6- O -benzylidene) in order to achieve desired regioselectivity. The other challenge of chemical glycosylation is the stereoselectivity that each glycosidic linkage has two stereo-outcomes, α/β or cis / trans . Generally, the α- or cis -glycoside is more challenging to synthesis. [ 19 ] New methods have been developed based on solvent participation or the formation of bicyclic sulfonium ions as chiral-auxiliary groups. [ 20 ]
The non-enzymatic glycosylation is also known as glycation or non-enzymatic glycation. It is a spontaneous reaction and a type of post-translational modification of proteins meaning it alters their structure and biological activity. It is the covalent attachment between the carbonil group of a reducing sugar (mainly glucose and fructose) and the amino acid side chain of the protein. In this process the intervention of an enzyme is not needed. It takes place across and close to the water channels and the protruding tubules. [ 21 ]
At first, the reaction forms temporary molecules which later undergo different reactions ( Amadori rearrangements , Schiff base reactions, Maillard reactions , crosslinkings ...) and form permanent residues known as Advanced Glycation end-products (AGEs). [ citation needed ]
AGEs accumulate in long-lived extracellular proteins such as collagen [ 22 ] which is the most glycated and structurally abundant protein, especially in humans. Also, some studies have shown lysine may trigger spontaneous non-enzymatic glycosylation. [ 23 ]
AGEs are responsible for many things. These molecules play an important role especially in nutrition, they are responsible for the brownish color and the aromas and flavors of some foods. It is demonstrated that cooking at high temperature results in various food products having high levels of AGEs. [ 24 ]
Having elevated levels of AGEs in the body has a direct impact on the development of many diseases. It has a direct implication in diabetes mellitus type 2 that can lead to many complications such as: cataracts , renal failure , heart damage... [ 25 ] And, if they are present at a decreased level, skin elasticity is reduced which is an important symptom of aging. [ 22 ]
They are also the precursors of many hormones and regulate and modify their receptor mechanisms at the DNA level. [ 22 ]
There are different enzymes to remove the glycans from the proteins or remove some part of the sugar chain. [ citation needed ]
Notch signalling is a cell signalling pathway whose role is, among many others, to control the cell differentiation process in equivalent precursor cells . [ 26 ] This means it is crucial in embryonic development, to the point that it has been tested on mice that the removal of glycans in Notch proteins can result in embryonic death or malformations of vital organs like the heart. [ 27 ]
Some of the specific modulators that control this process are glycosyltransferases located in the endoplasmic reticulum and the Golgi apparatus . [ 28 ] The Notch proteins go through these organelles in their maturation process and can be subject to different types of glycosylation: N-linked glycosylation and O-linked glycosylation (more specifically: O-linked glucose and O-linked fucose). [ 26 ]
All of the Notch proteins are modified by an O-fucose, because they share a common trait: O-fucosylation consensus sequences . [ 26 ] One of the modulators that intervene in this process is the Fringe, a glycosyltransferase that modifies the O-fucose to activate or deactivate parts of the signalling, acting as a positive or negative regulator, respectively. [ 28 ]
There are three types of glycosylation disorders sorted by the type of alterations that are made to the glycosylation process: congenital alterations, acquired alterations and non-enzymatic acquired alterations.
All these diseases are difficult to diagnose because they do not only affect one organ, they affect many of them and in different ways. As a consequence, they are also hard to treat. However, thanks to the many advances that have been made in next-generation sequencing , scientists can now understand better these disorders and have discovered new CDGs. [ 31 ]
It has been reported that mammalian glycosylation can improve the therapeutic efficacy of biotherapeutics . For example, therapeutic efficacy of recombinant human interferon gamma , expressed in HEK 293 platform, was improved against drug-resistant ovarian cancer cell lines. [ 32 ] | https://en.wikipedia.org/wiki/Glycosylation |
Glycosyltransferases ( GTFs , Gtfs ) are enzymes ( EC 2.4 ) that establish natural glycosidic linkages . They catalyze the transfer of saccharide moieties from an activated nucleotide sugar (also known as the " glycosyl donor ") to a nucleophilic glycosyl acceptor molecule, the nucleophile of which can be oxygen - carbon -, nitrogen -, or sulfur -based. [ 1 ]
The result of glycosyl transfer can be a carbohydrate , glycoside , oligosaccharide , or a polysaccharide . Some glycosyltransferases catalyse transfer to inorganic phosphate or water . Glycosyl transfer can also occur to protein residues, usually to tyrosine , serine , or threonine to give O-linked glycoproteins , or to asparagine to give N-linked glycoproteins. Mannosyl groups may be transferred to tryptophan to generate C-mannosyl tryptophan , which is relatively abundant in eukaryotes. Transferases may also use lipids as an acceptor, forming glycolipids , and even use lipid-linked sugar phosphate donors, such as dolichol phosphates in eukaryotic organism, or undecaprenyl phosphate in bacteria.
Glycosyltransferases that use sugar nucleotide donors are Leloir enzymes , after Luis F. Leloir , the scientist who discovered the first sugar nucleotide and who received the 1970 Nobel Prize in Chemistry for his work on carbohydrate metabolism. Glycosyltransferases that use non-nucleotide donors such as dolichol or polyprenol pyrophosphate are non-Leloir glycosyltransferases .
Mammals use only 9 sugar nucleotide donors for glycosyltransferases: [ 2 ] UDP-glucose , UDP-galactose , UDP-GlcNAc , UDP-GalNAc , UDP-xylose , UDP-glucuronic acid , GDP-mannose , GDP-fucose , and CMP-sialic acid . The phosphate(s) of these donor molecules are usually coordinated by divalent cations such as manganese, however metal independent enzymes exist.
Many glycosyltransferases are single-pass transmembrane proteins , and they are usually anchored to membranes of Golgi apparatus [ 3 ]
Glycosyltransferases can be segregated into "retaining" or "inverting" enzymes according to whether the stereochemistry of the donor's anomeric bond is retained (α→α) or inverted (α→β) during the transfer. The inverting mechanism is straightforward, requiring a single nucleophilic attack from the accepting atom to invert stereochemistry.
The retaining mechanism has been a matter of debate, but there exists strong evidence against a double displacement mechanism (which would cause two inversions about the anomeric carbon for a net retention of stereochemistry) or a dissociative mechanism (a prevalent variant of which was known as SNi). An "orthogonal associative" mechanism has been proposed which, akin to the inverting enzymes, requires only a single nucleophilic attack from an acceptor from a non-linear angle (as observed in many crystal structures) to achieve anomer retention. [ 4 ]
The recent discovery of the reversibility of many reactions catalyzed by inverting glycosyltransferases served as a paradigm shift in the field and raises questions regarding the designation of sugar nucleotides as 'activated' donors. [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ]
Sequence-based classification methods have proven to be a powerful way of generating hypotheses for protein function based on sequence alignment to related proteins. The carbohydrate-active enzyme database presents a sequence-based classification of glycosyltransferases into over 90 families. [ 10 ] The same three-dimensional fold is expected to occur within each of the families. [ 11 ]
In contrast to the diversity of 3D structures observed for glycoside hydrolases , glycosyltransferase have a much smaller range of structures. [ 12 ] [ 13 ] In fact, according to the Structural Classification of Proteins database, only three different folds have been observed for glycosyltransferases [ 14 ] Very recently, a new glycosyltransferase fold was identified for the glycosyltransferases involved in the biosynthesis of the NAG-NAM polymer backbone of peptidoglycan . [ 15 ]
Many inhibitors of glycosyltransferases are known. Some of these are natural products, such as moenomycin , an inhibitor of peptidoglycan glycosyltransferases, the nikkomycins , inhibitors of chitin synthase, and the echinocandins , inhibitors of fungal β-1,3-glucan synthases . Some glycosyltransferase inhibitors are of use as drugs or antibiotics. Moenomycin is used in animal feed as a growth promoter. Caspofungin has been developed from the echinocandins and is in use as an antifungal agent. Ethambutol is an inhibitor of mycobacterial arabinotransferases and is used for the treatment of tuberculosis. Lufenuron is an inhibitor of insect chitin syntheses and is used to control fleas in animals. Imidazolium -based synthetic inhibitors of glycosyltransferases have been designed for use as antimicrobial and antiseptic agents. [ 16 ]
The ABO blood group system is determined by what type of glycosyltransferases are expressed in the body.
The ABO gene locus expressing the glycosyltransferases has three main allelic forms: A, B, and O. The A allele encodes 1-3-N-acetylgalactosaminyltransferase that bonds α- N-acetylgalactosamine to D-galactose end of H antigen, producing the A antigen. The B allele encodes 1-3-galactosyltransferase that joins α-D-galactose bonded to D-galactose end of H antigen, creating the B antigen. In case of O allele the exon 6 contains a deletion that results in a loss of enzymatic activity. The O allele differs slightly from the A allele by deletion of a single nucleotide - Guanine at position 261. The deletion causes a frameshift and results in translation of an almost entirely different protein that lacks enzymatic activity. This results in H antigen remaining unchanged in case of O groups.
The combination of glycosyltransferases by both alleles present in each person determines whether there is an AB, A, B or O blood type.
Glycosyltransferases have been widely used in both the targeted synthesis of specific glycoconjugates as well as the synthesis of differentially glycosylated libraries of drugs, biological probes or natural products in the context of drug discovery and drug development (a process known as glycorandomization ). [ 17 ] Suitable enzymes can be isolated from natural sources or produced recombinantly. As an alternative, whole cell-based systems using either endogenous glycosyl donors or cell-based systems containing cloned and expressed systems for synthesis of glycosyl donors have been developed. In cell-free approaches, the large-scale application of glycosyltransferases for glycoconjugate synthesis has required access to large quantities of the glycosyl donors. On the flip-side, nucleotide recycling systems that allow the resynthesis of glycosyl donors from the released nucleotide have been developed. The nucleotide recycling approach has a further benefit of reducing the amount of nucleotide formed as a by-product, thereby reducing the amount of inhibition caused to the glycosyltransferase of interest – a commonly observed feature of the nucleotide byproduct. | https://en.wikipedia.org/wiki/Glycosyltransferase |
The term glycosynthase refers to a class of proteins that have been engineered to catalyze the formation of a glycosidic bond . Glycosynthase are derived from glycosidase enzymes , which catalyze the hydrolysis of glycosidic bonds. [ 2 ] They were traditionally formed from retaining glycosidase by mutating the active site nucleophilic amino acid (usually an aspartate or glutamate ) to a small non-nucleophilic amino acid (usually alanine or glycine ). More modern approaches use directed evolution to screen for amino acid substitutions that enhance glycosynthase activity. [ 3 ]
Two discoveries led to the development of glycosynthase enzymes. The first was that a change of the active site nucleophile of a glycosidase from a carboxylate to another amino acid resulted in a properly folded protein that had no hydrolase activity. [ 4 ] The second discovery was that some glycosidase enzymes were able to catalyze the hydrolysis of glycosyl fluorides that had the incorrect anomeric configuration. [ 5 ] The enzymes underwent a transglycosidation reaction to form a disaccharide , which was then a substrate for hydrolase activity.
The first reported glycosynthase was a mutant of the Agrobacterium sp. β-glucosidase / galactosidase in which the nucleophile glutamate 358 was mutated to an alanine by site directed mutagenesis . [ 6 ] When incubated with α-glycosyl fluorides and an acceptor sugar it was found to catalyze the transglycosidation reaction without any hydrolysis. This glycosynthase was used to synthesize a series of di- and trisaccharide products with yields between 64% and 92%.
The mechanism of a glycosynthase is similar to the hydrolysis reaction of retaining glycosidases except no covalent-enzyme intermediate is formed. Mutation of the active site nucleophile to a non-nucleophilic amino acid prevents the formation of a covalent intermediate. An activated glycosyl donor with a good anomeric- leaving group (often a fluorine) is required. The leaving group is displaced by an alcohol of the acceptor sugar aided by the active site general base amino acid of the enzyme.
The first glycosynthase was a retaining exoglycosidase that catalyzed the formation of β 1-4 linked glycosides of glucose and galactose . Glycosynthase enzymes have since been expanded to include mutants of endoglycosidase , [ 7 ] as well as mutants of inverting glycosidase. [ 8 ] Substrates of glycosynthase include glucose, galactose, mannose , xylose , and glucuronic acid . [ 9 ] Modern methods to prepare glycosynthase use directed evolution to introduce modifications, which improve the enzymes function. This process was made available due to the development of high throughput screens for glycosynthase activity.
Glycosynthase have been useful for the preparation of oligosaccharides ; however, their use suffers from certain limitations. First, glycosynthase can only be used to synthesize glycosidic linkages for which there is a known glycosidase. That glycosidase must also be first converted into a glycosynthase, which is not always possible. Second, the product of the glycosynthase reaction is often a better substrate for the glycosynthase then the starting material, resulting in the formation of multiple products of varying lengths. Finally, glycosynthase are specific for the donor sugar but often have loose specificity for the acceptor sugar. This can result in different regioselectivity depending on the acceptor resulting in products with different glycosidic linkages. One example is the Agrobacterium sp. β-glucosynthase, which forms a β-1,4-glycoside with glucose as the acceptor, but forms a β-1,3-glycoside with xylose as the acceptor. | https://en.wikipedia.org/wiki/Glycosynthase |
Copper peptide GHK-Cu is a naturally occurring copper complex of the tripeptide glycyl- L -histidyl- L -lysine. The tripeptide has strong affinity for copper (II) and was first isolated from human plasma . It can be found also in saliva and urine .
Several copper(II)-peptide complexes occur naturally. [ 3 ] In human plasma, the level of GHK-Cu is about 200 ng/ml at age 20. By the age of 60, the level drops to 80 ng/ml. In humans, GHK-Cu is proposed to promote wound healing , attraction of immune cells , antioxidant and anti-inflammatory effects, stimulation of collagen and glycosaminoglycan synthesis in skin fibroblasts and promotion of blood vessels growth. Recent studies revealed its ability to modulate expression of a large number of human genes, generally reversing gene expression to a healthier state. Synthetic GHK-Cu is used in cosmetics as a reparative and anti-aging ingredient. [ 4 ]
Loren Pickart (1938–2023) isolated the copper peptide GHK-Cu from human plasma albumin in 1973. [ 5 ] It was noticed that liver tissue obtained from patients aged 60 to 80 years had an increased level of fibrinogen . However, when liver cells from old patients were incubated in the blood from the younger group, the older cells started functioning in nearly the same way as the younger liver tissue. [ 6 ] [ 7 ] It turned out that this effect was due to a small peptide factor that behaved similarly to the synthetic peptide glycyl-L-histidyl-L-lysine (GHK). Pickart proposed that this activity in human plasma albumin was a tripeptide glycyl-L-histidyl-L-lysine and that it might function by chelating metal ions. [ 8 ]
In 1977, the growth modulating peptide was shown to be a glycyl- L -histidyl- L -lysine. [ 9 ] It is proposed that GHK-Cu modulates copper intake into cells. [ 10 ]
In the late 1980s, copper peptide GHK-Cu started attracting attention as a promising wound healing agent. At picomolar to nanomolar concentrations, GHK-Cu stimulated the synthesis of collagen in skin fibroblasts , increased accumulation of total proteins, glycosaminoglycans (in a biphasic curve) and DNA in the dermal wounds in rats. They also found out that the GHK sequence is present in collagen and suggested that the GHK peptide is released after tissue injury. [ 11 ] [ 12 ] They proposed a class of emergency response molecules which are released from the extracellular matrix at the site of an injury. [ 13 ] GHK-Cu also increased synthesis of decorin – a small proteoglycan involved in the regulation of collagen synthesis, wound healing regulation and anti-tumor defense. [ 14 ]
It was also established that GHK-Cu stimulates both the synthesis of metalloproteinases , the enzymes which break down dermal proteins, and their inhibitors (anti-proteases). The fact that GHK-Cu not only stimulates the production of dermal components, but also regulates their breakdown suggests that it should be used with caution. [ 15 ]
A series of animal experiments established pronounced wound healing activity of GHK-Cu. In the dermal wounds of rabbits GHK-Cu facilitated wound healing, causing better wound contraction, faster development of granular tissue and improved angiogenesis . It also elevated the level of antioxidant enzymes . [ 16 ] [ 17 ]
GHK-Cu has been found to induce a systemic enhancement of healing in rats, mice, and pigs; that is, the GHK-Cu peptide injected in one area of the body (such as the thigh muscles) improved healing at distant body areas (such as the ears). These treatments strongly increased healing parameters such as collagen production, angiogenesis, and wound closure in both wound chambers and full thickness wounds. [ 18 ] In one study, full‐thickness wounds of 6 millimeters in diameter were created in an ischemic skin flap on the backs of rats, and for 13 days the wound sites were then treated daily with topical GHK or topical hydroxypropyl methylcellulose vehicle, or given no treatment. At the end of the study, the wound size had decreased by 64.5% in the GHK group; by 45.6% in the vehicle-treated group; and by 28.2% in the control group. [ 19 ] The difference between the GHK group's wounds and those of the control group was significant, and was accompanied by significantly lower levels of tumor necrosis factor alpha and elastin-degrading matrix metalloproteinases . [ 19 ]
Biotinylated GHK-Cu was incorporated into a collagen membrane, which was used as a wound dressing. This GHK-Cu enriched material stimulated wound contraction and cell proliferation , as well as increased expression of antioxidant enzymes. The same material was tested for wound healing in diabetic rats. GHK-Cu treatment resulted in faster wound contraction and epithelization, higher level of glutathione and ascorbic acid , increased synthesis of collagen, and activation of fibroblasts and mast cells . [ 20 ] Ischemic open wounds in rats treated with GHK-copper healed faster and had decreased concentration of metalloproteinases 2 and 9 as well as of tumor necrosis factor-beta (a major inflammatory cytokine) compared with vehicle alone or with untreated wounds. [ 19 ]
Copper peptide GHK-Cu is widely used in anti-aging cosmetics ( INCI name: Copper tripeptide-1). [ 21 ] Several controlled facial studies confirmed anti-aging , firming and anti-wrinkle activity of copper peptide GHK-Cu. [ 22 ]
Replacement of histidine with other amino acids showed that the glycine residue plays major role in copper binding, whereas lysine can interact with copper only at alkaline pH. At physiological pH, lysine is able to interact with a cellular receptor . The ability of GHK to interact both with copper and with a cellular receptor may allow it to transfer copper into and from cells. The small size of GHK permits speedy traveling in extracellular space and its easy access to cellular receptors. [ 23 ]
The molecular structure of the GHK copper complex (GHK-Cu) has been determined by X-ray crystallography, EPR spectroscopy, X-ray absorption spectroscopy, NMR spectroscopy, as well as other methods such as titration. In the GHK-Cu complex, the Cu (II) ion is coordinated by the nitrogen from the imidazole side chain of the histidine, another nitrogen from the alpha-amino group of glycine and the deprotonated amide nitrogen of the glycine–histidine peptide bond.
Since such a structure could not explain a high stability constant of the GHK-Cu complex (log 10 =16.44 vs. 8.68 of the GH copper complex, which is similar to the GHK-Cu structure), it was proposed that another amino group participates in the complex formation. Cu(II) is also coordinated by the oxygen from the carboxyl group of the lysine from the neighboring complex. Another carboxyl group of lysine from a neighboring complex provides the apical oxygen, resulting in the square-planar pyramid configuration. [ 24 ] Many researchers proposed that at the physiological pH, GHK-Cu complexes can form binary and ternary structures which may involve amino acid histidine and/or the copper binding region of the albumin molecule. Lau and Sarkar found also that GHK can easily obtain copper 2+ bound to other molecules such as the high affinity copper transport site on plasma albumin (albumin binding constant log 10 =16.2 vs. GHK binding constant 16 log 10 =16.44). It has been established that copper (II) redox activity is silenced when copper ions are complexed with the GHK tripeptide, which allows the delivery of non-toxic copper into the cell. [ 25 ]
Copper is vital for all eukaryotic organisms from microbes to humans. A dozen enzymes ( cuproenzymes ) use changes in copper oxidation state to catalyze important biochemical reactions including cellular respiration ( cytochrome c oxidase ), antioxidant defense (ceruloplasmin, superoxide dismutase (SOD), detoxification (metallothioneins), blood clotting (blood clotting factors V and VIII), melanin production (tyrosinase) and the connective tissue formation (lysyl peroxidase). Copper is required for iron metabolism, oxygenation, neurotransmission , embryonic development and many other essential biological processes. Another function of copper is signaling – for example, stem cells require a certain level of copper in the media to start their differentiation into cells needed for repair. Thus, GHK-Cu's ability to bind copper and to modulate its tissue level is a key factor determining its biological activity. [ 26 ] | https://en.wikipedia.org/wiki/Glycyl-L-histidyl-L-lysine |
The glyoxalase system is a set of enzymes that carry out the detoxification of methylglyoxal and the other reactive aldehydes that are produced as a normal part of metabolism . [ 1 ] [ 2 ] This system has been studied in both bacteria and eukaryotes . [ 2 ] [ 3 ] [ 4 ] This detoxification is accomplished by the sequential action of two thiol-dependent enzymes; firstly glyoxalase І , which catalyzes the isomerization of the spontaneously formed hemithioacetal adduct between glutathione and 2-oxoaldehydes (such as methylglyoxal) into S-2-hydroxyacylglutathione. [ 5 ] [ 6 ] Secondly, glyoxalase ІІ hydrolyses these thiolesters and in the case of methylglyoxal catabolism, produces D-lactate and GSH from S-D-lactoyl-glutathione. [ 7 ]
This system shows many of the typical features of the enzymes that dispose of endogenous toxins. Firstly, in contrast to the amazing substrate range of many of the enzymes involved in xenobiotic metabolism , it shows a narrow substrate specificity. [ 3 ] Secondly, intracellular thiols are required as part of its enzymatic mechanism and thirdly, the system acts to recycle reactive metabolites back to a form which may be useful to cellular metabolism.
Glyoxalase I (GLO1), glyoxalase II (GLO2), and reduced glutathione (GSH). In bacteria, there is an additional enzyme that functions if there is no GSH, it is called the third glyoxalase protein, glyoxalase 3 (GLO3). GLO3 has not been found in humans yet. [ 2 ] [ 8 ]
The pathway begins with methylglyoxal (MG), which is produced from non-enzymatic reactions with DHAP or G3P produced in glycolysis. Methylglyoxal is then converted into S-d-lactoylglutathione by enzyme GLO1 with a catalytic amount of GSH, of which is hydrolyzed into non-toxic D-lactate via GLO2, during which GSH is reformed to be consumed again by GLO1 with a new molecule of MG. [ 2 ] D-lactate ultimately goes on to be metabolized into pyruvate . [ 8 ]
There are several small molecule inducers that can induce the glyoxalase pathway by either promoting GLO1 function to increase conversion of MG into D-Lactate, which are called GLO1 activators, or by directly reducing MG levels or levels of MG substrate, which are called MG scavengers. GLO1 activators include the synthetic drug candesartan or natural compounds resveratrol , fisetin , the binary combination of trans-resveratrol and hesperetin (tRES-HESP), mangiferin , allyl isothiocyanate , phenethyl isothiocyanate , sulforaphane , and bardoxolone methyl , and MG scavengers include aminoguanidine , alagebrium , and benfotiamine . There is also the small molecule pyridoxamine , which acts as both a GLO1 activator and MG scavenger. [ 8 ]
Many inhibitors of GLO1 have been discovered since GLO1 activity tends to be promoted in cancer cells, thus GLO1 serves as a potential therapeutic target for anti-cancer drug treatment and has been the focus of many research studies regarding its regulation in tumor cells. [ 8 ]
Hyperglycemia , a side effect caused by diabetes, combines with oxidative stress to create advanced glycation end-products (AGEs) that can lead to diabetic retinopathy (RD) and cause symptoms such as blindness in adults. [ 9 ]
The manipulation of the glyoxalase system in mice retina has shown there is a potential for targeting the glyoxalase system to use as a therapeutic treatment for RD by lowering the production of AGEs. [ 9 ]
Oxidative stress can lead to worsening neurological diseases such as Alzheimer's , Parkinson's , and Autism Spectrum Disorder . Flavonoids , a type of antioxidant that combats oxidative stress in the body, has been found to help decrease the production of radical oxygen species (ROS) mostly by preventing the formation of free radicals but also partially by promoting the glyoxalase pathway via increasing transcription of GSH and GSH constituent subunits to increase intracellular levels of GSH. [ 10 ]
Although the glyoxalase pathway is the main metabolic system that reduces methylglyoxal levels in the cell, other enzymes have also been found to convert methylglyoxal into non-AGE producing species: specifically, 99% of MG is processed by glyoxalase metabolism, while less than 1% is metabolized into hydroxyacetone by aldo-keto reductases (AKRs) or into pyruvate by aldehyde dehydrogenases (ALDH). [ 8 ] Other reactions have been found to produce MG that also feeds into the glyoxalase pathway. These reactions include catabolism of threonine and acetone , peroxidation of lipids , autoxidation of glucose , and degradation of glycated proteins. [ 8 ] | https://en.wikipedia.org/wiki/Glyoxalase_system |
Glyoxylate and dicarboxylate metabolism describes a variety of reactions involving glyoxylate or dicarboxylates . Glyoxylate is the conjugate base of glyoxylic acid , and within a buffered environment of known pH such as the cell cytoplasm these terms can be used almost interchangeably, as the gain or loss of a hydrogen ion is all that distinguishes them, and this can occur in the aqueous environment at any time. Likewise dicarboxylates are the conjugate bases of dicarboxylic acids , a general class of organic compounds containing two carboxylic acid groups, such as oxalic acid or succinic acid .
A compact graphical description of major biochemical reactions involved can be found at KEGG [ 1 ] This provides information on the relevant enzymes and details the relationship with several other metabolic processes: glycine, serine, and threonine metabolism which provides hydroxypyruvate and glyoxylate , purine metabolism which provides glyoxylate, pyruvate metabolism which provides (S)- malate and formate , carbon fixation which consumes 3-phospho-D-glycerate and provides D- ribulose 1,5-P2, ascorbate and aldarate metabolism which shares tartronate-semialdehyde , nitrogen metabolism which shares formate , pyruvate metabolism and the citrate cycle which share oxaloacetate , and vitamin B 6 metabolism which consumes glycolaldehyde .
The glyoxylate cycle describes an important subset of these reactions involved in biosynthesis of carbohydrates from fatty acids or two-carbon precursors which enter the system as acetyl-coenzyme A . Its crucial enzymes are isocitrate lyase and malate synthase . However, alternate pathways have been proposed in organisms lacking isocitrate lyase. [ 2 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Glyoxylate_and_dicarboxylate_metabolism |
The glyoxylate cycle , a variation of the tricarboxylic acid cycle , is an anabolic pathway occurring in plants , bacteria , protists , and fungi . The glyoxylate cycle centers on the conversion of acetyl-CoA to succinate for the synthesis of carbohydrates . [ 1 ] In microorganisms, the glyoxylate cycle allows cells to use two carbons (C2 compounds), such as acetate, to satisfy cellular carbon requirements when simple sugars such as glucose or fructose are not available. [ 2 ] The cycle is generally assumed to be absent in animals, with the exception of nematodes at the early stages of embryogenesis. In recent years, however, the detection of malate synthase (MS) and isocitrate lyase (ICL), key enzymes involved in the glyoxylate cycle, in some animal tissue has raised questions regarding the evolutionary relationship of enzymes in bacteria and animals and suggests that animals encode alternative enzymes of the cycle that differ in function from known MS and ICL in non-metazoan species. [ 1 ] [ 3 ]
Plants as well as some algae and bacteria can use acetate as the carbon source for the production of carbon compounds. Plants and bacteria employ a modification of the TCA cycle called the glyoxylate cycle to produce four carbon dicarboxylic acid from two carbon acetate units. The glyoxylate cycle bypasses the two oxidative decarboxylation reactions of the TCA cycle and directly converts isocitrate through isocitrate lyase and malate synthase into malate and succinate.
The glyoxylate cycle was discovered in 1957 at the University of Oxford by Sir Hans Kornberg and his mentor Hans Krebs , resulting in a Nature paper Synthesis of Cell Constituents from C 2 -Units by a Modified Tricarboxylic Acid Cycle . [ 4 ]
The glyoxylate cycle uses five of the eight enzymes associated with the tricarboxylic acid cycle : citrate synthase , aconitase , succinate dehydrogenase , fumarase , and malate dehydrogenase . The two cycles differ in that in the glyoxylate cycle, isocitrate is converted into glyoxylate and succinate by isocitrate lyase (ICL) instead of into α-ketoglutarate. [ 1 ] This bypasses the decarboxylation steps that take place in the citric acid cycle (TCA cycle), allowing simple carbon compounds to be used in the later synthesis of macromolecules, including glucose. [ 2 ] Glyoxylate is subsequently combined with acetyl-CoA to produce malate , catalyzed by malate synthase. [ 1 ] Malate is also formed in parallel from succinate by the action of succinate dehydrogenase and fumarase.
Fatty acids from lipids are commonly used as an energy source by vertebrates as fatty acids are degraded through beta oxidation into acetate molecules. This acetate, bound to the active thiol group of coenzyme A , enters the citric acid cycle (TCA cycle) where it is fully oxidized to carbon dioxide . This pathway thus allows cells to obtain energy from fat. To use acetate from fat for biosynthesis of carbohydrates, the glyoxylate cycle, whose initial reactions are identical to the TCA cycle, is used.
Cell-wall containing organisms, such as plants , fungi , and bacteria , require very large amounts of carbohydrates during growth for the biosynthesis of complex structural polysaccharides , such as cellulose , glucans , and chitin . In these organisms, in the absence of available carbohydrates (for example, in certain microbial environments or during seed germination in plants), the glyoxylate cycle permits the synthesis of glucose from lipids via acetate generated in fatty acid β-oxidation.
The glyoxylate cycle bypasses the steps in the citric acid cycle where carbon is lost in the form of CO 2 . The two initial steps of the glyoxylate cycle are identical to those in the citric acid cycle: acetate → citrate → isocitrate . In the next step, catalyzed by the first glyoxylate cycle enzyme, isocitrate lyase , isocitrate undergoes cleavage into succinate and glyoxylate (the latter gives the cycle its name). Glyoxylate condenses with acetyl-CoA (a step catalyzed by malate synthase ), yielding malate . Both malate and oxaloacetate can be converted into phosphoenolpyruvate , which is the product of phosphoenolpyruvate carboxykinase , the first enzyme in gluconeogenesis . The net result of the glyoxylate cycle is therefore the production of glucose from fatty acids. Succinate generated in the first step can enter into the citric acid cycle to eventually form oxaloacetate. [ 2 ]
In plants the glyoxylate cycle occurs in special peroxisomes which are called glyoxysomes . This cycle allows seeds to use lipids as a source of energy to form the shoot during germination . The seed cannot produce biomass using photosynthesis because of lack of an organ to perform this function. The lipid stores of germinating seeds are used for the formation of the carbohydrates that fuel the growth and development of the organism.
The glyoxylate cycle can also provide plants with another aspect of metabolic diversity. This cycle allows plants to take in acetate both as a carbon source and as a source of energy. Acetate is converted to acetyl CoA (similar to the TCA cycle). This acetyl CoA can proceed through the glyoxylate cycle, and some succinate is released during the cycle. The four carbon succinate molecule can be transformed into a variety of carbohydrates through combinations of other metabolic processes; the plant can synthesize molecules using acetate as a source for carbon. The acetyl CoA can also react with glyoxylate to produce some NADPH from NADP+, which is used to drive energy synthesis in the form of ATP later in the electron transport chain . [ 5 ]
The glyoxylate cycle may serve an entirely different purpose in some species of pathogenic fungi . The levels of the main enzymes of the glyoxylate cycle, ICL and MS, are greatly increased upon contact with a human host. Mutants of a particular species of fungi that lacked ICL were also significantly less virulent in studies with mice compared to the wild type. The exact link between these two observations is still being explored, but it can be concluded that the glyoxylate cycle is a significant factor in the pathogenesis of these microbes . [ 6 ] [ 7 ]
Vertebrates were once thought to be unable to perform this cycle because there was no evidence of its two key enzymes , isocitrate lyase and malate synthase. However, some research suggests that this pathway may exist in some, if not all, vertebrates. [ 8 ] [ 9 ] Specifically, some studies show evidence of components of the glyoxylate cycle existing in significant amounts in the liver tissue of chickens. Data such as these support the idea that the cycle could theoretically occur in even the most complex vertebrates. [ 10 ] Other experiments have also provided evidence that the cycle is present among certain insect and marine invertebrate species, as well as strong evidence of the cycle's presence in nematode species. However, other experiments refute this claim. [ 11 ] Some publications conflict on the presence of the cycle in mammals : for example, one paper has stated that the glyoxylate cycle is active in hibernating bears, [ 12 ] but this report was disputed in a later paper. [ 13 ] Evidence exists for malate synthase activity in humans due to a dual functional malate/B-methylmalate synthase of mitochondrial origin called CLYBL expressed in brown fat and kidney. [ 14 ] Vitamin D may regulate this pathway in vertebrates. [ 10 ] [ 15 ]
Due to the central role of the glyoxylate cycle in the metabolism of pathogenic species including fungi and bacteria, enzymes of the glyoxylate cycle are current inhibition targets for the treatment of diseases. Most reported inhibitors of the glyoxylate cycle target the first enzyme of the cycle (ICL). Inhibitors were reported for Candida albicans for potential use as antifungal agents. [ 16 ] The mycobacterial glyoxylate cycle is also being targeted for potential treatments of tuberculosis . [ 17 ] [ 18 ]
The prospect of engineering various metabolic pathways into mammals which do not possess them is a topic of great interest for bio-engineers today. The glyoxylate cycle is one of the pathways which engineers have attempted to manipulate into mammalian cells. This is primarily of interest for engineers in order to increase the production of wool in sheep, which is limited by the access to stores of glucose. By introducing the pathway into sheep, the large stores of acetate in cells could be used in order to synthesize glucose through the cycle, allowing for increased production of wool. [ 19 ] Mammals are incapable of executing the pathway due to the lack of two enzymes, isocitrate lyase and malate synthase , which are needed in order for the cycle to take place. It is believed by some that the genes to produce these enzymes, however, are pseudogenic in mammals, meaning that the gene is not necessarily absent, rather, it is merely "turned off". [ 1 ]
In order to engineer the pathway into cells, the genes responsible for coding for the enzymes had to be isolated and sequenced, which was done using the bacteria E.coli , from which the AceA gene, responsible for encoding for isocitrate lyase , and the AceB gene, responsible for encoding for malate synthase were sequenced. [ 19 ] Engineers have been able to successfully incorporate the AceA and AceB genes into mammalian cells in culture, and the cells were successful in translating and transcribing the genes into the appropriate enzymes, proving that the genes could successfully be incorporated into the cell’s DNA without damaging the functionality or health of the cell. However, being able to engineer the pathway into transgenic mice has proven to be difficult for engineers. While the DNA has been expressed in some tissues, including the liver and small intestine in test animals, the level of expression is not high, and not found to be statistically significant. In order to successfully engineer the pathway, engineers would have to fuse the gene with promoters which could be regulated in order to increase the level of expression, and have the expression in the right cells, such as epithelial cells . [ 20 ]
Efforts to engineer the pathway into more complex animals, such as sheep, have not been effective. This illustrates that much more research needs to be done on the topic, and suggests it is possible that a high expression of the cycle in animals would not be tolerated by the chemistry of the cell. Incorporating the cycle into mammals will benefit from advances in nuclear transfer technology , which will enable engineers to examine and access the pathway for functional integration within the genome before its transfer to animals. [ 19 ]
There are possible benefits, however, to the cycle's absence in mammalian cells. The cycle is present in microorganisms that cause disease but is absent in mammals, for example humans. There is a strong plausibility of the development of antibiotics that would attack the glyoxylate cycle, which would kill the disease-causing microorganisms that depend on the cycle for their survival, yet would not harm humans where the cycle, and thus the enzymes that the antibiotic would target, are absent. [ 2 ] | https://en.wikipedia.org/wiki/Glyoxylate_cycle |
2719
14734
ENSG00000147257
ENSMUSG00000055653
P51654
Q8CFZ4
NM_004484 NM_001164617 NM_001164618 NM_001164619
NM_016697
NP_001158089 NP_001158090 NP_001158091 NP_004475 NP_004475.1
NP_057906
Glypican-3 is a protein that, in humans, is encoded by the GPC3 gene . [ 5 ] [ 6 ] [ 7 ] [ 8 ] The GPC3 gene is located on human X chromosome (Xq26) where the most common gene (Isoform 2, GenBank Accession No.: NP_004475) encodes a 70-kDa core protein with 580 amino acids. [ 9 ] Three variants have been detected that encode alternatively spliced forms termed Isoforms 1 (NP_001158089), Isoform 3 (NP_001158090) and Isoform 4 (NP_001158091). [ 9 ]
The protein core of GPC3 consists of two subunits, where the N-terminal subunit has a size of ~40 kDa and the C-terminal subunit is ~30 kDa. [ 9 ] Six glypicans (GPC1-6) have been identified in mammals. Cell surface heparan sulfate proteoglycans are composed of a membrane-associated protein core substituted with a variable number of heparan sulfate chains. Members of the glypican-related integral membrane proteoglycan family (GRIPS) contain a core protein anchored to the cytoplasmic membrane via a glycosyl phosphatidylinositol linkage. These proteins may play a role in the control of cell division and growth regulation. [ 7 ] GPC3 has been found to regulate Wnt/β-catenin and Yap signaling pathways. [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ] [ 16 ] GPC3 interacts with both Wnt and frizzled (FZD) to form a complex and triggers downstream signaling. [ 11 ] [ 17 ] The core protein of GPC3 may serve as a co-receptor or a receiver for Wnt. A cysteine-rich domain at the N-lobe of GPC3 has been identified as a hydrophobic groove that interacts with Wnt3a. [ 17 ] Blocking the Wnt binding domain on GPC3 using the HN3 single domain antibody can inhibit Wnt activation. [ 17 ] Wnt also recognizes a heparan sulfate structure on GPC3, which contains IdoA2S and GlcNS6S, and that the 3-O-sulfation in GlcNS6S3S significantly enhances the binding of Wnt to heparan sulfate. [ 10 ] GPC3 also modulates Yap signaling . [ 12 ] It interacts with FAT1 , a potential upstream cell surface receptor of YAP1 in human cells. [ 15 ] GPC3 is also found to bind Alpha-fetoprotein in liver cancer. [ 18 ]
Deletion mutations in this gene are associated with Simpson–Golabi–Behmel syndrome . [ 5 ]
Glypican 3 immunostaining has utility for differentiating hepatocellular carcinoma (HCC) [ 19 ] and dysplastic changes in cirrhotic livers ; HCC stains with glypican 3, while liver with dysplastic changes and/or cirrhotic changes does not. [ 20 ] Using the YP7 murine monoclonal antibody, GPC3 protein expression is found in HCC, not in normal liver and cholangiocarcinoma. [ 21 ] The YP7 murine antibody has been humanized and named as 'hYP7'. [ 22 ] GPC3 is also expressed to a lesser degree in melanoma, ovarian clear-cell carcinomas, yolk sac tumors, neuroblastoma, hepatoblastoma, Wilms' tumor cells, and other tumors. [ 9 ] However, the significance of GPC3 as a diagnostic tool for human tumors other than HCC is unclear. [ 9 ]
To validate GPC3 as a therapeutic target in liver cancer, the anti-GPC3 therapeutic antibodies GC33, [ 23 ] YP7, [ 21 ] HN3 [ 12 ] and HS20 [ 13 ] [ 24 ] have been made and widely tested. The laboratory of Dr. Mitchell Ho at the National Cancer Institute , NIH (Bethesda, Maryland, US) has generated YP7 murine monoclonal antibody that recognizes the C-lobe of GPC3 by hybridoma technology. [ 21 ] The antibody has been humanized (named hYP7) via antibody engineering for clinical applications. [ 22 ] The Ho lab has also identified the human single-domain antibody ('human nanobody') HN3 [ 12 ] targeting the N-lobe of GPC3 [ 17 ] and the human monoclonal antibody HS20 [ 13 ] [ 24 ] targeting the heparan sulfate chains on GPC3 by phage display technology. Both HN3 and HS20 antibodies inhibit Wnt signaling in liver cancer cells . The immunotoxins based on HN3, [ 14 ] [ 25 ] [ 26 ] the antibody-drug conjugates based on hYP7 [ 27 ] and the T-cell engaging bispecific antibodies derived from YP7 [ 28 ] [ 29 ] and GC33, [ 30 ] have been developed for treating liver cancer. The chimeric antigen receptor (CAR) T cell immunotherapies based on GC33, [ 31 ] hYP7 [ 32 ] [ 33 ] and HN3 [ 34 ] are being reported at various stages for treating liver cancer. In mice with xenograft or orthoptic liver tumors, CAR (hYP7) T cells can eliminate GPC3-positive cancer cells, by inducing perforin- and granzyme-mediated cell death and reducing Wnt signaling in tumor cells. [ 33 ] CAR (hYP7) T cells are being evaluated at a clinical trial at the NIH . [ 35 ] | https://en.wikipedia.org/wiki/Glypican_3 |
The Gmail interface makes Gmail unique amongst webmail systems for several reasons. Most evident to users are its search-oriented features and means of managing e-mail in a "conversation view" that is similar to an Internet forum .
An official redesign of the Gmail interface was rolled out on November 1, 2011 that simplified the look and feel of Gmail into a more minimalist design to provide a more consistent look throughout Google products and services as part of an overall design overhaul. [ 1 ] Another major redesign took place April 2018 which introduced new information rights management controls designed for business use cases. [ 2 ]
Gmail makes use of Ajax , employing browser features such as JavaScript , keyboard access keys and Web feed integration. [ 3 ]
Gmail allows users to conduct advanced searches using either the Advanced Search interface or through search operators in the search box. Emails can be searched by their text; by their ‘From’, ‘To’ and ‘Subject’ fields, by their location, date and size; by associated labels, categories and circles, by whether or not the message is read, and by whether or not the message has an attachment. There are also a large number of advanced search operators. [ 4 ] By default, Gmail combines search terms with an invisible "AND". Gmail allows the use of Boolean operators such as "OR" for finding messages that match at least one of the more search terms. [ 5 ]
Gmail allows users to create rules (‘ filters ’) for the automatic organization of incoming mail. Filters are created using the Advanced Search interface using the same criteria as those used for searching. Gmail can perform any combination of the following actions upon an email that meets all the specified criteria in a filter: [ 6 ]
Labels provide a flexible method of organizing emails since an email can have any number of labels (in contrast to a folder-based system in which an email can belong to only one folder). Labels are much like tags on a blog post. Labels can also do the work of folders if an email is moved to a label – this is the equivalent of applying a label to it as well as archiving it. [ 7 ] By default, labels appear on the message list and can be customized with a color. Users can also create sub-labels beneath a label to create a hierarchy or nested labels. Labels can be used as a search criterion and all emails having a particular label can be viewed together through the side menu. [ 8 ] [ 9 ] Gmail has often received praise for replacing the limitations of hierarchical folders with the flexibility of labels. [ citation needed ]
Gmail allows users to 'archive' emails. Archiving removes a conversation from the inbox and can be accessed via the 'All Mail' section. In Gmail, the 'All Mail' section displays all of a user's emails, excluding the ones in Spam and Bin. Technically, when a message is archived, the 'Inbox' label is removed from it. Archiving presents a better alternative to deleting as it helps to tidy up the inbox without deleting messages permanently. Archiving, however, is limited to message threads and individual messages cannot be archived. [ 10 ] Moreover, archiving is available only for the inbox, and messages in other places such as Sent Mail cannot be archived. However, according to About.com , this limitation can be overcome by accessing Gmail through IMAP. [ 11 ]
Marking of emails as important is more or less automatic. Users can ‘train’ Gmail in recognizing important messages by manually marking messages as important. Gmail takes into account a number of signals to determine whether a message is important or not. Messages from people who are emailed to or replied to a lot, and messages of the type that are always opened or were recently marked as important or starred, are likely to be marked as important automatically. Also, messages that are sent to a user directly and not through a mailing list, and messages containing certain keywords (password change, transaction details, shipment delivery, ticket confirmation, etc.) are marked as important. Messages of the type that were recently archived or deleted, or are rarely opened are less likely to be marked as important. [ 12 ] Important emails can be searched for using the operator “is:important”. Uninterested users have the option to turn off the entire feature. [ 12 ]
In September 2010, Google introduced the ‘priority inbox’ which makes use of important markers. Priority Inbox splits up the inbox into sections such as “Important and unread”, “Unread”, “Starred” and “Everything else” enabling a user to always see important items on the top. It is an opt-in feature. [ 13 ] [ 14 ]
In a review for Lifehacker , Adam Pash writes that Gmail is only as good at recognizing important emails as any context-ignorant computer can be. [ 15 ] However, in another review for Lifehacker , Whitson Gordon calls Priority Inbox "one of Gmail’s most unsung features". He writes that Priority Inbox can be quite helpful as long as users give it a chance to learn from their habits. [ 16 ]
Beginning June 2013, Gmail allowed for the usage of tabs in the inbox for automatically categorizing emails by five general categories: [ 17 ] [ 18 ]
Users have the choice to hide one or more of the tabs or disable the entire feature. [ 17 ] These tabs also appear in Gmail's Android and iOS apps. [ 19 ]
Even if the use of tabs is switched off, all emails are sorted into one of the five categories, which can be used as automatic labels. Like labels, categories can be used as a search criterion and be made to appear as labels on the message list. All emails with a particular category can be seen together through the side menu. [ 17 ]
Unlike other email web clients, Gmail does not permit users to see the size of an email message or to sort email (for example, alphabetically by subject). [ citation needed ]
Gmail recognizes messages related by subject and groups them into "conversations" where messages in a back-and-forth string get collected together and appear stacked one after another, with the newest messages at the top. Any duplicated text is automatically concealed. [ 20 ] The number of messages in a conversation always appears in parentheses next to the names of people in the conversation. A conversation will break off into a new thread if the subject line of a message is changed, or if the conversation reaches over 100 messages. Replied or forwarded messages from some local (like local Yahoo! Mail ) accounts also split up conversations because their subjects contain parameters in the local language, instead of "Re" or "Fwd:". [ 21 ]
User response to conversation view was mixed. Due to reduced control over individual messages, many users were vocal in expressing their dissatisfaction. [ 22 ] On September 29, 2010, Google added the option of disabling conversation view in the Gmail web app. Google software engineer Doug Che explained: "We really hoped everyone would learn to love conversation view, but we came to realize that it's just not right for some people." [ 23 ] Conversation view is still enabled automatically in mobile apps, which remains a source of user frustration. [ 22 ]
Gmail automatically saves contact details when forwarding e-mails to a previously unknown recipient. If the user changes, adds, or removes information near an e-mail such as the name while sending any e-mail, it also updates that in the contact list, unless the user is using basic HTML view, designed for people with slower internet connections or browsers that do not support AJAX. When a user starts typing in the To, CC or BCC fields it brings up a list with the relevant contacts, with their name and primary e-mail address. More information, including alternate email addresses, can be added on the Contacts page. These contacts can also be added to a group, which makes sending multiple e-mails to related contacts easier. Images can be added to contacts, which will appear whenever the mouse is over the contact's name.
Users can import contacts (in several different ways) from Microsoft Office Outlook , Mozilla Thunderbird , Eudora , Hotmail , Yahoo! Mail , orkut , and any other contact list in a CSV -format file. Gmail also allows a user to export their contacts to CSV. [ 24 ]
Gmail allowed the importation of Google+ social media contacts while it wasn't discontinued [ 25 ]
A year after Gmail was announced, Google introduced Rich Text Formatting, which allows the font size, color and text-alignment to be customized, as well as the embedding of bullet points and numbered lists. [ 26 ]
Gmail also features Autosave — a system for avoiding loss of data in case of a browser crash or other error. During the composition of an e-mail, Gmail automatically saves a draft copy of the message and of any attachments. Although messages begin to be saved once a minute, saving times vary depending on the size of the message. Draft messages that are discarded are not recoverable. [ 27 ] [ 28 ]
Gmail places the cursor above quoted text when replying, which encourages top-posting . Regardless of the formatting of received messages, Gmail's conversation view defaults to showing only unique content, in chronological order.
The 'Smart Compose' tool was introduced by Google in May 2018. It uses AI to guess what is going to be written, even before it is typed. It bases some of this on the recipient and email's subject, as well as the user's past writing habits. For example, if the subject reads, "Dinner plans", then Smart Compose will take that into account as the user begins typing and it suggests normal wording for arranging a meal. [ 29 ] Smart Compose helps save time by cutting back on repetitive writing, while reducing the chance of spelling and grammatical errors. [ 30 ]
Individual Gmail messages including attachments may be up to 25 MB in size. However, users can send files of up to 15 GB in size through Google Drive . Effectively, the files are stored on Google Drive and only links to them are sent. This means that the recipients can access the file only if it is shared with them on Google Drive. Gmail notifies the user if the file being sent is not shared with the recipient and allows the user to modify the sharing settings before sending the file. The files can either be made accessible to anyone with the link, or shared privately with the email recipients. The latter does not work if the recipients do not have a Google account or if the email address receiving the message is not associated with Google. [ 31 ] [ 32 ] [ 33 ]
Starting in December 2014, files in Google Drive can also be sent from Gmail as attachments rather than links, thus providing recipients access to the files even if they are later deleted from the sender's Drive. [ 34 ] Starting in 2019, Google+ attachments cannot be added to Gmail anymore.
In Gmail, attachments in supported formats are previewed as thumbnails within the message itself and clicking on the thumbnail opens up a full-screen view of the image or document through which users can browse through multiple attachments. [ 35 ] Attachments can be downloaded to the hard disk or to a folder on Google Drive in case of image files. [ 36 ]
The Gmail interface supports drag and drop of attachments to and from the inbox. Users can add an attachment by dragging it into the mail window. Similarly an attachment can be downloaded by dragging the attachment from the message to the desktop. [ 37 ]
Gmail supports plus-addressing of e-mails. Users can send messages to local addresses with email ID formatted username+extratext , where extratext can be any string, and will arrive in the gmail inbox of username . This allows users to sign up for different services with different aliases and then easily filter all e-mails from those services. In addition, if users receive spam messages directed to an e-mail address with the extra text, they will know what services have leaked out their e-mail address. However, some websites do not accept email addresses containing "+", even though the mail-address specification permits use of them. [ 38 ]
Additionally, Gmail does not recognize dots (periods) as characters within a username. Adding or removing dots from a Gmail address does not change the actual destination address. For instance, the account with email ID username still receives mail sent to numerous variations of that exact email IDs chaotically dotted like as user.name , u.s.e.r.n.a.m.e , etc. Likewise, the gmail account with email ID user.name receives mail sent to username email ID. This too can help in setting up filters for incoming mail. It is also not necessary to include any of dots used during the creation of the account while signing in. However, this does not work in Google Apps for Your Domain. In Apps, each username variation must be entered as a nickname by the domain administrator. [ 39 ] [ 40 ]
Gmail allows the user to add other email accounts to be used as optional sender addresses on outgoing email. The system carries out a verification process to confirm the user's ownership of each email address before it is added. "Plus-addresses" can also be added as sender addresses in a similar way. Any of the additional addresses can be set as the default address. Optionally, users can set a different "reply-to" address for each "send as" address. [ 41 ]
When using this feature, the address chosen will appear in the "From:" field of the message header. However, the SMTP envelope sender address will contain the name of the Gmail account used to send the message. Thus the underlying Gmail account address remains readily available: it will typically appear in a "Sender:" header field, or occasionally in the subject field. Some mail clients will write "From: Sender {{@}}gmail.com [mailto: Sender {{@}}gmail.com] On Behalf Of..." upon reply, making the situation very obvious.
Gmail does now allow users to specify a 3rd party SMTP server . Gmail can use this to send outgoing email for that particular account avoiding the masked account problem. [ 42 ]
The 2018 redesign introduced information rights management controls intended to give the sender the ability to "remove the option to forward, copy, download or print messages." [ 2 ] To achieve this, Google hosts the content of the message on their own servers and only includes a link to the hosted content within the main body of the email, [ 43 ] which (non-Gmail) users must click to open the message in their web browser. The feature is only effective against accidental copying, as the user can still take a screenshot [ 44 ] or override the print and copy protections entirely by using the developer tools in their web browser. [ 45 ]
The 2018 redesign introduced a "confidential mode" that builds upon the information rights management features to allow the sender to later revoke the receiver's access to a message, or to automatically revoke the receiver's access after a prespecified time period (dubbed "self-destructing emails" [ 46 ] [ 47 ] by the media).
In addition to adding extra email addresses, Gmail has a feature called "Mail Fetcher" that allows users to add up to five additional accounts to retrieve mail from via POP3 . Once accounts are added, the program asks the user if they want to create a custom sender address automatically if they have not yet done so manually. This feature does not support retrieving mail from IMAP servers. [ 48 ]
Google Talk , Google's service for instant messaging , can be accessed through a web-based interface on Gmail's site. The web-based interface is able to support voice and video calling and voice messages if the Google Talk client is running in the background. All messages are archived to the Chats mailbox in Gmail unless 'Off the Record' is enabled in Google Talk. If the fellow chatter suddenly has to go offline, any and all further messages sent will be delivered to that person via e-mail, including the entire conversation had previously. Another Google Talk integration feature is voicemail, where the message is sent to the recipient's Gmail inbox; as well as synchronizing contact pictures.
On December 4, 2007, Google announced integration with AOL Instant Messenger (AIM), allowing Gmail users to log into their AIM accounts and send instant messages to and see the online status of AIM users. [ 49 ] [ 50 ] [ 51 ]
On November 11, 2008, Google announced video chat, which Gmail integrates into its web-based client. Windows XP, Vista or Intel-based Mac is required with a supported browser (IE, Firefox, Chrome, Safari 3+). [ 52 ]
Google Calendar offered Gmail integration soon after its announcement on April 13, 2006. Events can be added while writing a message that get stored on the main Calendar interface [ clarification needed ] . Recipients who use Gmail will then receive an invitation to the event, which they can accept or decline. Furthermore, Gmail attempts to recognize event dates and locations within e-mails, and gives users the option to add the event to a calendar, similar to Microsoft 's Exchange Server .
Gmail offers further integration with some other Google products. The integration with Google Drive enables users to share large files of up to 15 GB in size stored on Drive through Gmail, and to save email attachments directly to Google Drive. Attachments in supported formats are previewed within the message. [ 35 ] Also, pictures can be sent directly from Picasa using a Gmail account.
Gmail also offered integration with its now-defunct social networking and messaging tool Google Buzz . With this feature, Gmail users could share links, photos, videos, status messages and comments organized in "conversations" and visible in the user's inbox. [ 53 ]
Gmail now has integration with Google Chat which allows you to view and send chats through gmail
Google started offering users a choice of themes on November 19, 2008 with 31 different themes, ranging from the original light blue color to designs with image backgrounds and transparencies. [ 54 ] Many of these themes are dynamic. [ 55 ] Gmail uses the location provided by the user to correctly time theme changes with the local sunrise, sunset, or weather. [ 56 ]
In June 2012, Gmail introduced custom themes, enabling users to set their own backgrounds. Users can either choose from a large number of 'featured' images, upload an image from the computer or phone, or add an image by URL. [ 57 ] [ 58 ] On April 2, 2014, Gmail added the ability to share custom themes via email or Google+, or through a public link. [ 59 ]
The conversation view groups related messages in a linear stack which a user can expand and collapse. Labelling ( tagging ) is limited to message threads. [ 60 ]
Some users can experience difficulties when submitting e-mail addresses from the Gmail address book to the addressee line on the compose e-mail window. The "Autocomplete" feature can cause problems and does not work under all browsers or operating systems. However, it is possible to open the composed message in a new window so the address book can be opened, or another instance of Gmail can be opened in another window to access the address book. Gmail's current documented help on this issue states: "While Gmail doesn't currently support the functionality to open your Contacts list while composing a message, we're testing many new features to improve our service." [ 61 ]
Although Gmail's advertisements have received praise for not obtruding, they can take up more space than Flash-based banners when up to six "sponsored links" appear next to an email. Additionally, when activated, opening emails makes the Web Clips RSS-feed bar display another sponsored link. Often the number of advertisements displayed in the Web Clips bar outnumbers the number of RSS feeds the user has requested. However, when a Gmail message is sent to another email address of a different provider, there will be no advertisements in the message unlike most other webmail providers. [ 62 ]
When a Gmail mailbox reaches capacity, users can search for emails by size in order to delete the largest ones first. [ 63 ] The web interface can help in this situation by searching for emails with attachments, but it does not indicate the sizes of those attachments. [ citation needed ] | https://en.wikipedia.org/wiki/Gmail_interface |
Gmelin's test is a chemical test used for detecting the presence of bile pigments in urine . It is named after Leopold Gmelin , who introduced the test. [ 1 ] [ 2 ] [ 3 ] Five millilitres of urine is slowly added to five millilitres of concentrated nitric acid in a test-tube. Different coloured rings between the two layers are visible if bile pigments are present as they are oxidised to various chemical products. [ 4 ] [ 5 ] Nitric acid is used as the oxidising agent . [ 6 ] Blue, green and violet rings are seen if bilirubin is present. [ 7 ] Gmelin's test is not sensitive, so a positive result always indicates the presence of bile pigments, but a negative result does not exclude the presence of small quantities of bile pigments. [ 8 ]
This article about analytical chemistry is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gmelin's_test |
The Gmelin database is a large database of organometallic and inorganic compounds updated quarterly. It is based on the German publication Gmelins Handbuch der anorganischen Chemie ("Gmelin's Handbook of Inorganic Chemistry") which was originally published by Leopold Gmelin in 1817; [ 1 ] the last print edition, the 8th, appeared in the 1990s. Although published over many decades, the printed series was not uniform in coverage or currency. Some elements are represented only by decades-old and not updated slim summary volumes. Others (Fe, B, S, F, U, etc.) have numerous supplements. Most later supplement volumes focused on an element's organic complexes. Each volume lists its literature coverage date. [ 2 ]
The database currently contains every compound/reaction discovered between 1772 and 1995, amounting to 1.5 million compounds and 1.3 million different reactions, with over 85,000 titles, keywords and abstracts. It has over 800 different data fields on subjects such as the compounds' electric, magnetic, thermal, crystal and physiological information.
The Gmelin database is maintained by Elsevier MDL . It is the sister database to the Beilstein database , which deals with organic chemicals and reactions; both are now part of the Reaxys system. The Gmelin database is less complete and less up-to-date than the handbook; the printed book is consequently kept available. [ 2 ] | https://en.wikipedia.org/wiki/Gmelin_database |
The Gnits standards are a collection of standards and recommendations for programming, maintaining, and distributing software . They are published by a group of GNU project maintainers who call themselves "Gnits", which is short for " GNU nit-pickers ". As such, they represent advice, not Free Software Foundation or GNU policy, but parts of the Gnits' standards have seen widespread adoption among free software programmers in general.
The Gnits standards are extensions to, refinements of, and annotations for the GNU Standards . However, they are in no way normative in GNU; GNU maintainers are not required to follow them. Nevertheless, maintainers and programmers often find in Gnits standards good ideas on the way to follow GNU Standards themselves, as well as tentative, non-official explanations about why some GNU standards were decided the way they are. There are very few discrepancies between Gnits and GNU standards, and they are always well noted as such.
The standards address aspects of software architecture , program behaviour, human–computer interaction , C programming, documentation , and software releases .
As of 2008, the Gnits standards carry a notice that they are moribund and no longer actively maintained, and points readers to the manuals of Gnulib , Autoconf , and Automake , which are said to cover many of the same topics. | https://en.wikipedia.org/wiki/Gnits_standards |
A gnomon ( / ˈ n oʊ ˌ m ɒ n , - m ə n / ; from Ancient Greek γνώμων ( gnṓmōn ) ' one that knows or examines ' ) [ 1 ] [ 2 ] is the part of a sundial that casts a shadow . The term is used for a variety of purposes in mathematics and other fields, typically to measure directions, position, or time.
A painted stick dating from 2300 BC that was excavated at the archeological site of Taosi is the oldest gnomon known in China. [ 4 ] The gnomon was widely used in ancient China from the second millennium BC onward in order to determine the changes in seasons, orientation, and geographical latitude. The ancient Chinese used shadow measurements for creating calendars that are mentioned in several ancient texts. [ citation needed ]
According to the collection of Zhou Chinese poetic anthologies Classic of Poetry , one of the distant ancestors of King Wen of the Zhou dynasty used to measure gnomon shadow lengths to determine the orientation around the 14th century BC. [ 5 ] [ 6 ] The ancient Greek philosopher Anaximander (610–546 BC) is credited with introducing this Babylonian instrument to the Ancient Greeks. [ 7 ]
The ancient Greek mathematician and astronomer Oenopides used the phrase drawn gnomon-wise to describe a line drawn perpendicular to another. [ 8 ] Later, the term was used for an L -shaped instrument like a steel square used to draw right angles. This shape may explain its use to describe a shape formed by cutting a smaller square from a larger one. Euclid extended the term to the plane figure formed by removing a similar parallelogram from a corner of a larger parallelogram. Indeed, the gnomon is the increment between two successive figurate numbers , including square and triangular numbers. [ citation needed ]
The ancient Greek mathematician and engineer Hero of Alexandria defined a gnomon as that which, when added or subtracted to an entity (number or shape), makes a new entity similar to the starting entity. In this sense Theon of Smyrna used it to describe a number which added to a polygonal number produces the next one of the same type. The most common use in this sense is an odd integer especially when seen as a figurate number between square numbers . [ citation needed ]
Vitruvius mentions the gnomon as " gnonomice " in the first sentence of chapter 3 in volume 1 of his book De Architectura . That Latin term " gnonomice " leaves room for interpretation. Despite its similarity to " γνωμονικός " (or its feminine form " γνωμονική "), it appears unlikely that Vitruvius refers to judgement on the one hand or to the design of sundials on the other. It appears to be more appropriate to assume that he refers to geometry, a science upon which gnomons rely heavily. In those days, calculations were carried out geometrically, in contrast to the algebraic methods in use today. Thus, it seems that he indirectly refers to mathematics and geodesy . [ citation needed ]
Perforated gnomons projecting a pinhole image of the Sun whose location can be measured to tell the time of day and year were described in the Chinese Zhoubi Suanjing , possibly dating as early as the early Zhou (11th century BC) but surviving only in forms dating to the Eastern Han (3rd century). [ 9 ]
In the Middle East and Europe, it was separately credited to the Egyptian astronomer and mathematician Ibn Yunus around AD 1000. [ 10 ] The Italian astronomer, mathematician and cosmographer Paolo Toscanelli is associated with the 1475 placement of a bronze plate with a round hole in the dome of the Cathedral of Santa Maria del Fiore in Florence to project an image of the Sun on the cathedral's floor. With markings on the floor it tells the exact time of each midday (reportedly to within half a second) as well as the date of the summer solstice. Italian mathematician, engineer, astronomer and geographer Leonardo Ximenes reconstructed the gnomon according to his new measurements in 1756. [ 11 ]
In the Northern Hemisphere , the shadow-casting edge of a sundial gnomon is normally oriented so that it points due northward and is parallel to the rotational axis of Earth . That is, it is inclined to the northern horizon at an angle that equals the latitude of the sundial's location. At present, such a gnomon should thus point almost precisely at Polaris , as this is within 1° of the north celestial pole .
On some sundials, the gnomon is vertical. These were usually used in former times for observing the altitude of the Sun , especially when on the meridian .
The style is the part of the gnomon that casts the shadow. This can change as the Sun moves. For example, the upper west edge of the gnomon might be the style in the morning and the upper east edge might be the style in the afternoon.
Gnomons have been used in space missions to the Moon and Mars. The gnomon used by the Apollo astronauts was a gimballed stadia rod mounted on a tripod. While the rod's shadow indicated the direction of the Sun, the grayscale paints of varying reflectivity and the red, green and blue patches facilitated proper photography on the surface on the Moon. [ 12 ] MarsDials have been used on Mars Exploration Rovers .
A three-dimensional gnomon is commonly used in CAD and computer graphics as an aid to positioning objects in the virtual world . By convention, the x -axis direction is colored red, the y -axis green and the z -axis blue.
The Gnomon of Saint-Sulpice inside the Parisian church, Église Saint-Sulpice , built to assist in determining the date of Easter , was fictionalized as a " Rose Line " in the novel The Da Vinci Code . [ 13 ] | https://en.wikipedia.org/wiki/Gnomon |
Gnotobiosis (from Greek roots gnostos "known" and bios "life") refers to an engineered state of an organism in which all forms of life (i.e., microorganisms ) in or on it, including its microbiota , have been identified. [ 1 ] The term gnotobiotic organism, or gnotobiote, can refer to a model organism that is colonized with a specific community of known microorganisms (isobiotic or defined flora animal) or that contains no microorganisms ( germ-free ) often for experimental purposes. [ 2 ] [ 3 ] [ 4 ] [ 5 ] The study of gnotobiosis and the generation of various types of gnotobiotic model organisms as tools for studying interactions between host organisms and microorganisms is referred to as gnotobiology. [ 2 ]
The concept and field of gnotobiology was born of a debate between Louis Pasteur and Marceli Nencki in the late 19th century, in which Pasteur argued that animal life needed bacteria to succeed while Nencki argued that animals would be healthier without bacteria, [ 2 ] but it wasn't until 1960 that the Association for Gnotobiotics was formed. [ 4 ] Early attempts in gnotobiology were limited by inadequate equipment and nutritional knowledge, however, advancements in nutritional sciences , animal anatomy and physiology , and immunology have allowed for the improvement of gnotobiotic technologies. [ 6 ]
Guinea pigs were the first germ-free animal model described in 1896 by George Nuttall and Hans Thierfelder , establishing techniques still used today in gnotobiology. [ 7 ] Early methods for maintaining sterile environments involved sterile glass jars and gloveboxes , which developed into a conversation surrounding uniformity of the methods in the field at the 1939 symposium on Micrurgical and Germ-free Methods at the University of Notre Dame. [ 4 ] Many early (1930-1950s) accomplishments in gnotobiology came from Notre Dame University , The University of Lund , and Nagoya University . [ 7 ] [ 8 ] The Laboratories of Bacteriology at the University of Notre Dame (known as LOBUND) was founded by John J. Cavanaugh and is cited for making some of the most notable achievements in the field of gnotobiotic research. [ 7 ] [ 8 ] Under the direction of James A. Reyniers, early work at LOBUND focused on obtaining gnotobiotes by sterilizing animals and maintaining the animals using high-pressure steam sterilized steel isolators; however, later work at the institute shifted the focus of the field towards establishing colonies of animals born germ-free. [ 4 ] The first germ-free rat colony was generated and maintained using a steam sterilized isolator in 1946 by Swedish scientist Bengt Gustafsson. [ 6 ] Flexible film isolators using peracetic acid vapor for sterilization began being developed in the 1950s. [ 4 ] Refined sterilization techniques and manufacturing changes from LOBUND significantly reduced the size and cost of isolators, making gnotobiotic research more universally accessible. [ 7 ] [ 8 ] After numerous advances in gnotobiotic research and technologies, the main challenges facing gnotobiotic research today are cost, space, efficiency, and operational procedure requirements. [ 7 ] In 2015, the costs of maintaining gnotobiotic mice cages was greater than 4 times the cost of maintaining those of non-gnotobiotic mice, creating a challenge for establishing and maintaining facilities using typical funding sources, such as federal grants from institutions like the NIH . [ 7 ]
The early focus of the field of gnotobiology was on proving that an organism could live in the absence of microorganisms, which ultimately resulted in the development of gnotobiotic organisms as a tool for research. [ 5 ] Between the 1950s and 1970s, germ-free models were used to study the effects of the absence of bacteria on host organism metabolism and physiology, which later evolved into intentionally infecting germ-free organisms with specific microorganisms to investigate their functions and other questions relating to the biomedical field. [ 9 ] In the early 1970s, gnotobiotes were used to study the role of microorganisms in host nutrition acquisition and immune response; however, this was limited because animals reared in a gnotobiotic colony often have poorly developed immune systems, lower cardiac output , and thin intestinal walls, which make them highly susceptible to infectious pathogens. [ 10 ] [ 11 ] After the early 1970s, gnotobiotic research decreased until the mid-1980s. [ 7 ] Within the 21st century, gnotobiotic model systems have become an important tool for investigating interactions between host organisms and their commensal microbiota, as they allow for researchers to investigate specific microbes in a highly controlled host system. [ 12 ] Historically, mouse models have been used to investigate the impacts of the microbiota composition (which microorganisms are present) on host immune system , nervous system , metabolism, and physiology; however, an increasing interest in this field has led to the incorporation of other model organisms to address a larger variety of questions relating to these topics. [ 3 ]
A gnotobiotic animal (gnotobiote) is an animal in which all microorganisms interacting with it are known and controlled. [ 13 ] Gnotobiotic animals are typically born under aseptic conditions, which may include removal from the mother by Caesarean section followed by immediate transfer of the newborn to an isolator where all incoming air, food and water is sterilized. [ 10 ] Gnotobiotes are usually raised in a sterile laboratory environment, and are only intentionally exposed to microorganisms of interest to researchers. [ 5 ] Mice and rats are common gnotobiotic animals used in research, but other examples of important gnotobiotes include Caenorhabditis elegans ( C. elegans ) , Drosophila melanogaster ( D. melanogaster ) , zebrafish , and piglets. [ 3 ] Gnotobiotes are used as a controlled environment in which to study host anatomy and physiology, the specific symbiotic interactions between a host and specific microorganisms, and the impacts of chemicals on the host and its microbiota. [ 9 ]
Rodents (primarily mice and rats) are the most common mammalian model systems used for studying gnotobiosis and are widely used to study human health relating to the gut and interactions between microorganisms and their host; however, recently there has been a rise in using gnotobiotic mice to study interactions between different microorganisms (microbe-microbe interactions) in the gut. [ 5 ] [ 14 ] Humanized gnotobiotic mice, or gnotobiotic mice introduced to human intestinal microorganisms by fecal microbiota transplant with human feces, are used in the context of studying gut microbiota and their relationship with host cancers , immune system, and nutrition. [ 15 ] Some advantages of gnotobiotic mice and rat systems include the uniformity of the organism, historical prevalence, and established system-specific methods, as well as the ability to obtain reliable gnotobiotic mice and rats commercially. [ 5 ]
Gnotobiotic fish have been used as a model organism for human health; [ 3 ] [ 7 ] however, an increased interest in aquaculture for sustainable food production has led to increasing prevalence of gnotobiotic studies focused on maximizing production and maintaining healthy captive populations. [ 16 ] The majority of research is still only conducted on a few species of fish, such as the zebra fish. [ 7 ] [ 16 ] Some of the advantages of gnotobiotic fish systems include high numbers of offspring per reproduction event coupled with fast generation times and eggs that can be sanitized. [ 7 ] [ 16 ]
Gnotobiotic plants are plants that are either grown without microorganisms present (aseptic, axenic, or sterile) or grown in the presence of one (monoxenic) or more than one (polyxenic) known microorganism. [ 17 ] To obtain gnotobiotic plants, researchers sterilize seeds using chemical agents (e.g., ethanol , sodium hypochlorite (bleach), hydrogen peroxide ) on the surface of the seed. [ 17 ] A wide variety of plants have been used to generate gnotobiotic systems such as Arabidopsis thaliana , peanuts , oats , corn , and many others. [ 17 ] Similar to animals, gnotobiotic plant systems have been used to study integral components of host physiology (e.g., nitrogen fixation ), [ 5 ] as well as pathogenic and symbiotic interactions between plants and microorganisms. [ 17 ] | https://en.wikipedia.org/wiki/Gnotobiosis |
Go-Back- N ARQ is a specific instance of the automatic repeat request (ARQ) protocol, in which the sending process continues to send a number of frames specified by a window size even without receiving an acknowledgement (ACK) packet from the receiver. It is a special case of the general sliding window protocol with the transmit window size of N and receive window size of 1. It can transmit N frames to the peer before requiring an ACK.
The receiver process keeps track of the sequence number of the next frame it expects to receive. It will discard any frame that does not have the exact sequence number it expects (either a duplicate frame it already acknowledged, or an out-of-order frame it expects to receive later) and will send an ACK for the last correct in-order frame. [ 1 ] Once the sender has sent all of the frames in its window , it will detect that all of the frames since the first lost frame are outstanding , and will go back to the sequence number of the last ACK it received from the receiver process and fill its window starting with that frame and continue the process over again.
Go-Back- N ARQ is a more efficient use of a connection than Stop-and-wait ARQ , since unlike waiting for an acknowledgement for each packet, the connection is still being utilized as packets are being sent. In other words, during the time that would otherwise be spent waiting, more packets are being sent. However, this method also results in sending frames multiple times – if any frame was lost or damaged, or the ACK acknowledging them was lost or damaged, then that frame and all following frames in the send window (even if they were received without error) will be re-sent. To avoid this, Selective Repeat ARQ can be used. [ 2 ]
These examples assume an infinite number of sequence and request numbers. [ 1 ]
There are a few things to keep in mind when choosing a value for N : | https://en.wikipedia.org/wiki/Go-Back-N_ARQ |
GoFetch is a family of cryptographic attacks on recent Apple silicon CPUs that exploits the CPU's on-chip data memory-dependent prefetcher (DMP) to investigate the contents of memory. [ 2 ] [ 1 ] CPUs affected include the M1 , M2 , M3 and A14 series system-on-a-chip processors. [ 1 ]
The DMP looks at cache memory content for possible pointer values, and prefetches the data at those locations into cache if it sees memory access patterns that suggest following those pointers would be useful. [ 3 ] [ 4 ] The GoFetch attacks use those speculative cache fetches to undermine a number of different cryptographic algorithms by using memory access timings to exfiltrate data from those algorithms using timing attacks .
The authors of GoFetch state that they were unable to make their exploit work on the Intel Raptor Lake processor they tested due to its more limited DMP functionality. [ 1 ]
This computer security article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/GoFetch |
GoPubMed was a knowledge -based search engine for biomedical texts. [ 1 ] [ 2 ] The Gene Ontology (GO) and Medical Subject Headings (MeSH) served as "Table of contents" in order to structure the millions of articles in the MEDLINE database . MeshPubMed was at one point a separate project, but the two were merged.
The technologies used in GoPubMed were generic and could in general be applied to any kind of texts and any kind of knowledge bases. The system was developed at the Technische Universität Dresden by Michael Schroeder and his team at Transinsight.
GoPubMed was recognized with the 2009 red dot: best of the best award in the category communication design – graphical user interfaces and interactive tool. Transinsight was recognized with the German Innovation Prize IT for its developments in Enterprise Semantic Intelligence at CeBIT 2011.
This article related to health informatics is a stub . You can help Wikipedia by expanding it .
This bioinformatics-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/GoPubMed |
goTenna (goTenna Inc.) is a technology company that creates mesh networking devices that pair with smartphones , allowing users to send texts and share locations on a peer-to-peer basis without needing active cell networks [ 1 ]
The idea for goTenna came about after Hurricane Sandy knocked out 25 percent of cell towers , and caused outages for 25 percent of Internet services, across 10 states on the East Coast . [ 2 ] [ 3 ] Officially incorporated in April 2013, [ 4 ]
In 2014, goTenna rolled out its first consumer product, the goTenna, a pocket-size communication tool that lets off-grid travelers talk to one another without cell service. [ 5 ]
In September 2016, goTenna launched goTenna Plus, a, subscription-based upgrade to the goTenna applications, which includes the capability to use other goTenna users as gateways to relay messages through to traditional SMS networks. [ 6 ] The company also released its software development kit , enabling developers to create new applications using goTenna hardware. [ 7 ] However, its license does not permit use with open source copyleft licenses. [ 8 ] Around the same time, goTenna unveiled a second-generation device: goTenna Mesh, the first consumer-ready mesh network of its kind, available to 49 countries. [ 9 ]
In March 2017, the company announced its goTenna Pro line, for professional mobile radio communications needs, leaving the consumer market for government markets. [ 10 ] To finance its pivot, the company raised $24M in Series C equity and debt funding in 2019 [ 11 ]
Meshtastic - an open source equivalent | https://en.wikipedia.org/wiki/GoTenna |
In computing , goal seeking is the ability to calculate backward to obtain an input that would result in a given output. This can also be called what-if analysis or backsolving . It can either be attempted through trial and improvement or more logical means. Basic goal seeking functionality is built into most modern spreadsheet packages such as Microsoft Excel .
According to O'Brien and Marakas, [ 1 ] optimization analysis is a more complex extension of goal-seeking analysis. Instead of setting a specific target value for a variable, the goal is to find the optimum value for one or more target variables, given certain constraints. Then one or more other variables are changed repeatedly, subject to the specified constraints, until you discover the best values for the target variables.
Suppose a family wanted to take out the biggest loan that they could afford to pay for. If they set aside $500 a month, the goal-seeking program would try to work out how big a loan the family could afford to take out. Even using simple trial and improvement, a computer could quickly determine that they could not afford a $50,000 loan, but could afford a $48,000 loan. It would then repeat the process until it had reached a figure such as $48,476.34, which would give them a monthly repayment as close to $500 as possible, without exceeding it.
A more efficient method, especially on more complicated calculations, would be for the program to logically work through the argument. By drawing up a simple equation, the program could come to the conclusion that the output equalled one ninety-sixth of the input, and could then multiply the output (or goal) by ninety-six to find the necessary input.
This computer-programming -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Goal_seeking |
The goat grazing problem is either of two related problems in recreational mathematics involving a tethered goat grazing a circular area: the interior grazing problem and the exterior grazing problem. The former involves grazing the interior of a circular area , and the latter, grazing an exterior of a circular area. For the exterior problem, the constraint that the rope can not enter the circular area dictates that the grazing area forms an involute . If the goat were instead tethered to a post on the edge of a circular path of pavement that did not obstruct the goat (rather than a fence or a silo), the interior and exterior problem would be complements of a simple circular area.
The original problem was the exterior grazing problem and appeared in the 1748 edition of the English annual journal The Ladies' Diary : or, the Woman's Almanack , designated as Question CCCIII attributed to Upnorensis (an unknown historical figure), stated thus:
Observing a horse tied to feed in a gentlemen's park, with one end of a rope to his fore foot, and the other end to one of the circular iron rails, enclosing a pond, the circumference of which rails being 160 yards, equal to the length of the rope, what quantity of ground at most, could the horse feed?
The related problem involving area in the interior of a circle without reference to barnyard animals first appeared in 1894 in the first edition of the renown journal American Mathematical Monthly . Attributed to Charles E. Myers, it was stated as:
A circle containing one acre is cut by another whose center is on the circumference of the given circle, and the area common to both is one-half acre. Find the radius of the cutting circle.
The solutions in both cases are non-trivial but yield to straightforward application of trigonometry, analytical geometry or integral calculus. Both problems are intrinsically transcendental – they do not have closed-form analytical solutions in the Euclidean plane. The numerical answers must be obtained by an iterative approximation procedure. The goat problems do not yield any new mathematical insights; rather they are primarily exercises in how to artfully deconstruct problems in order to facilitate solution.
Three-dimensional analogues and planar boundary/area problems on other shapes, including the obvious rectangular barn and/or field, have been proposed and solved. [ 1 ] A generalized solution for any smooth convex curve like an ellipse, and even unclosed curves, has been formulated. [ 2 ]
The question about the grazable area outside a circle is considered. This concerns a situation where the animal is tethered to a silo. The complication here is that the grazing area overlaps around the silo (i.e., in general, the tether is longer than one half the circumference of the silo): the goat can only eat the grass once, he can't eat it twice. The answer to the problem as proposed was given in the 1749 issue of the magazine by a Mr. Heath, and stated as 76,257.86 sq.yds. which was arrived at partly by "trial and a table of logarithms". The answer is not so accurate as the number of digits of precision would suggest. No analytical solution was provided.
Let tether length R = 160 yds. and silo radius r = R /(2 π ) yds. The involute in the fourth quadrant is a nearly circular arc. One can imagine a circular segment with the same perimeter (arc length) would enclose nearly the same area; the radius and therefore the area of that segment could be readily computed. The arc length of an involute is given by 1 2 r θ 2 {\displaystyle {\tfrac {1}{2}}r\theta ^{2}} so the arc length |FG| of the involute in the fourth quadrant is 1 2 r [ θ 2 ] 3 π 2 − φ 2 π {\displaystyle {\tfrac {1}{2}}r{\Big [}\theta ^{2}{\Big ]}_{{\tfrac {3\pi }{2}}-\varphi }^{2\pi }} . Let c be the length of an arc segment of the involute between the y -axis and a vertical line tangent to the silo at θ = 3 π /2; it is the arc subtended by Φ . c ≈ r {\displaystyle c\approx r} (while the arc is minutely longer than r , the difference is negligible). So | F G | = 1 2 ⋅ 25.46 ⋅ ( 6.28 2 − 4.71 2 ) + 25.46 = 245.38 {\displaystyle |FG|={\tfrac {1}{2}}\cdot 25.46\cdot (6.28^{2}-4.71^{2})+25.46=245.38} . The arc length of a circular arc is r θ {\displaystyle r\theta } and θ here is π /2 radians of the fourth quadrant, so r π 2 = 245.38 {\displaystyle r{\tfrac {\pi }{2}}=245.38} , r the radius of the circular arc is 156.21 {\displaystyle 156.21} and the area of the circular segment bounded by it is π r 2 4 = 19165 {\displaystyle {\tfrac {\pi r^{2}}{4}}=19165} . The area of the involute excludes half the area of the silo (1018.61) in the fourth quadrant, so its approximate area is 18146, and the grazable area including the half circle of radius R , ( 1 2 π R 2 {\displaystyle {\tfrac {1}{2}}\pi R^{2}} ) totals 2 ⋅ 18146 + 40212 = 76505 {\displaystyle 2\cdot 18146+40212=76505} . That is 249 sq.yds. greater than the correct area of 76256, an error of just 0.33%. This method of approximating may not be quite so good for angles < 3 π /2 of the involute.
Find the area between a circle and its involute over an angle of 2 π to −2 π excluding any overlap. In Cartesian coordinates, the equation of the involute is transcendental; doing a line integral there is hardly feasible. A more felicitous approach is to use polar coordinates ( z , θ ). Because the "sweep" of the area under the involute is bounded by a tangent line (see diagram and derivation below) which is not the boundary ( q F ¯ {\displaystyle {\overline {qF}}} ) between overlapping areas, the decomposition of the problem results in four computable areas: a half circle whose radius is the tether length ( A 1 ); the area "swept" by the tether over an angle of 2 π ( A 2 ); the portion of area A 2 from θ = 0 to the tangent line segment t F ¯ {\displaystyle {\overline {tF}}} ( A 3 ); and the wedge area qFtq ( A 4 ). So, the desired area A is A 1 + ( A 2 − A 3 + A 4 ) · 2. The area(s) required to be computed are between two quadratic curves, and will necessarily be an integral or difference of integrals.
The primary parameters of the problem are R {\displaystyle R} , the tether length defined to be 160yds, and r {\displaystyle r} , the radius of the silo. There is no necessary relationship between R {\displaystyle R} and r {\displaystyle r} , but here r = 160 2 π {\displaystyle r={\tfrac {160}{2\pi }}} is the radius of the circle whose circumference is R {\displaystyle R} . If one defines the point of tethering v {\displaystyle v} (see diagram, above) as the origin with the circle representing the circumference of the pond below the x -axis, and F {\displaystyle F} on the y -axis below the circle representing the point of intersection of the tether when wound clockwise and counterclockwise, let t {\displaystyle t} be a point on the circle such that the tangent at t {\displaystyle t} intersects F {\displaystyle F} , and | v t ⌢ | {\displaystyle |{\overset {\frown }{vt}}|} + | t F ¯ | {\displaystyle |{\overline {tF}}|} Is the length of the tether. Let q {\displaystyle q} be the point of intersection of the circumference of the pond on the y-axis (opposite to v {\displaystyle v} ) below the origin. Then let acute ∠ t F q {\displaystyle \angle tFq} be φ {\displaystyle \varphi } .
The area under the involute is a function of R 3 {\displaystyle R^{3}} because it is an integral over a quadratic curve. The area has a fixed boundary defined by the parameter r {\displaystyle r} (i.e. the circumference of the silo). In this case the area is inversely proportional to r {\displaystyle r} , i.e. the larger r {\displaystyle r} , the smaller the area of the integral, and the circumference is a linear function of r {\displaystyle r} ( 2 π r {\displaystyle 2\pi r} ). So we seek an expression for the area under the involute E = f ( R 3 / r ) {\displaystyle E=f(R^{3}/r)} .
First, the area A 1 is a half circle of radius R {\displaystyle R} so A 1 = 1 2 π ⋅ R 2 . {\displaystyle A_{1}={\tfrac {1}{2}}\pi \cdot R^{2}.}
Next compute the area between the circumference of the pond and involute. Compute the area in the tapering "tail" of the involute, i.e. the overlapped area (note, on account of the tangent tF , that this area includes the wedge section, area A 4 , which will have to be added back in during the final summation). Recall that the area of a circular sector is 1 2 r 2 θ {\displaystyle {\tfrac {1}{2}}r^{2}\theta } if the angle is in radians. Imagine an infinitely thin circular sector from o {\displaystyle o} to p {\displaystyle p} subtended by an infinitely small angle Δ θ {\displaystyle \Delta \theta } . Tangent to o {\displaystyle o} , there is a corresponding infinitely thin sector of the involute from m {\displaystyle m} to n {\displaystyle n} subtending the same infinitely small angle Δ θ {\displaystyle \Delta \theta } . The area of this sector is 1 2 z 2 Δ θ {\displaystyle {\tfrac {1}{2}}z^{2}\Delta \theta } where z {\displaystyle z} is the radius at some angle θ i {\displaystyle \theta _{i}} , which is r θ i {\displaystyle r\theta _{i}} , the arc length of the circle so far "unwrapped" at angle θ i {\displaystyle \theta _{i}} . The area under the involute is the sum of all the infinitely many infinitely thin sectors i {\displaystyle i} through some angle θ n {\displaystyle \theta _{n}} . This sum is
The bounds of the integral represent the area under the involute in the fourth quadrant between t F ¯ {\displaystyle {\overline {tF}}} and v G ¯ {\displaystyle {\overline {vG}}} . The angle is measured on the circle, not on the involute, so it is less than 3 π 2 {\displaystyle {\tfrac {3\pi }{2}}} by some angle designated φ {\displaystyle \varphi } .
Next, find the angle φ {\displaystyle \varphi } . Let x = | t F ¯ | {\displaystyle x=|{\overline {tF}}|} . φ {\displaystyle \varphi } is complementary to the opposite angle of the triangle whose right angle is at point t; and also complementary to that angle in the third quadrant of the circle. | t F ¯ | {\displaystyle |{\overline {tF}}|} is the unrolled arc v q t ⌢ {\displaystyle {\overset {\frown }{vqt}}} , so its arclength is r {\displaystyle r} times the central angle. So x = r ⋅ ( 3 π 2 − φ ) {\displaystyle x=r\cdot ({\tfrac {3\pi }{2}}-\varphi )} . x {\displaystyle x} is also a leg of the triangle vFtv so tan ( φ ) = r x {\displaystyle \tan(\varphi )={\tfrac {r}{x}}} and x = r tan ( φ ) {\displaystyle x={\tfrac {r}{\tan(\varphi )}}} . Equating the 2 expressions for x {\displaystyle x} and solving for φ {\displaystyle \varphi } , the following equation is obtained: φ = tan − 1 1 3 π 2 − φ {\displaystyle \varphi =\tan ^{-1}{\frac {1}{{\tfrac {3\pi }{2}}-\varphi }}} . That is a transcendental equation that can be solved approximately by iterative substitution of φ {\displaystyle \varphi } , polynomial expansion of tan − 1 {\displaystyle \tan ^{-1}} , or an approximation method like Newton–Raphson. A constructive way to obtain a quick and very accurate estimate of φ {\displaystyle \varphi } is: draw a diagonal from point 3 2 π {\displaystyle {\tfrac {3}{2}}\pi } on the circumference of the pond to its intersection on the y-axis. The length of the diagonal is 120yds. because it is 3 4 {\displaystyle {\tfrac {3}{4}}} of the tether. So the other leg of the triangle, the hypotenuse as drawn, is 120 2 − r 2 = 117.27 {\displaystyle {\sqrt {120^{2}-r^{2}}}=117.27} yds. So φ ≈ sin − 1 ( r 117.27 ) = .219 {\displaystyle \varphi \approx \sin ^{-1}({\tfrac {r}{117.27}})=.219} radians, rounded to three places. φ ≈ 0.21900 [ + 0 , − 0.00003 ] {\displaystyle \varphi \approx 0.21900[+0,-0.00003]} . Small inaccuracies in φ {\displaystyle \varphi } when φ ≪ 1 {\displaystyle \varphi \ll 1} don't significantly affect the final result. [ 3 ]
A 4 is the area of the peculiar wedge λ t F q t {\displaystyle \lambda ^{tFqt}} . That area is the area of a right triangle with vertex t, minus the area of a sector bounded by t q ⌢ {\displaystyle {\overset {\frown }{tq}}} . λ = r x 2 − 1 2 r 2 θ {\displaystyle \lambda ={\tfrac {rx}{2}}-{\tfrac {1}{2}}r^{2}\theta } where x is |tF| and θ is the angle opposite to Φ in the right angle triangle. So, λ = 1 2 r ( R − r ( π 2 + φ ) ) − 1 2 r 2 ( π 2 − φ ) = 1 2 ( r R − r 2 π ) {\displaystyle \lambda ={\tfrac {1}{2}}r(R-r({\tfrac {\pi }{2}}+\varphi ))-{\tfrac {1}{2}}r^{2}({\tfrac {\pi }{2}}-\varphi )={\tfrac {1}{2}}(rR-r^{2}\pi )} . If R = 2 π r {\displaystyle R=2\pi r} , then the area λ {\displaystyle \lambda } of the wedge is 1 2 π r 2 {\displaystyle {\tfrac {1}{2}}\pi r^{2}} by reduction.
Algebraic combination of the pieces does not reduce to anything useful because of the differing geometries of the pieces, and φ {\displaystyle \varphi } is not a rational fraction of π {\displaystyle \pi } so it doesn't combine with the other angle. So evaluate the pieces at once then combine them numerically. Since the total area is a bit less than the area of the great circle whose radius is R {\displaystyle R} (80,425sq.yds.), keep 6 digits of precision (5 digits plus a guard digit):
Thus A 2 − A 3 + A 4 {\displaystyle A_{2}-A_{3}+A_{4}} is the area bounded by the involute and pond in the 4th quadrant.
A = A 1 + ( A 2 − A 3 + A 4 ) ⋅ 2 ≈ 40212.4 + 18021.6 ⋅ 2 = 76255.6 {\displaystyle A=A_{1}+(A_{2}-A_{3}+A_{4})\cdot 2\approx 40212.4+18021.6\cdot 2=76255.6} ; the grazing area
The numerical answer is A = 76256 {\displaystyle A=76256} sq.yds.rounded up to the nearest square yard. [ 4 ] It is worth noting that lim φ → π 2 A = 1 2 π ⋅ R 2 + R 3 6 r {\displaystyle \lim _{\varphi \rightarrow {\frac {\pi }{2}}}A={\tfrac {1}{2}}\pi \cdot R^{2}+{\tfrac {R^{3}}{6r}}} , which is the answer given for the case where the tether length is half the circumference (or any length such that R r ≤ π {\displaystyle {\tfrac {R}{r}}\leq \pi } ) of the silo, or no overlap to account for. The goat can eat all but a bit more than 5% of the area of the great circle defined by its tether length, and almost half the area it cannot eat is within the perimeter of the pond/silo.
Just as the area below a line is proportional to the length of the line between boundaries, and the area of a circular sector is a ratio of the arc length ( L = r θ {\displaystyle L=r\theta } ) of the sector ( A = r 2 ⋅ L {\displaystyle A={\tfrac {r}{2}}\cdot L} ), the area between an involute and its bounding circle is also proportional to the involute's arc length L = 1 2 r θ 2 {\displaystyle L={\tfrac {1}{2}}r\theta ^{2}} : A = r θ 3 ⋅ L = r 2 θ 3 6 {\displaystyle A={\tfrac {r\theta }{3}}\cdot L={\tfrac {r^{2}\theta ^{3}}{6}}} for 0 < θ < θ i {\displaystyle 0<\theta <\theta _{i}} . So the total grazing area is A = A 1 + ( A 2 − A 3 + A 4 ) ⋅ 2 {\displaystyle A=A_{1}+(A_{2}-A_{3}+A_{4})\cdot 2} . A 1 = 1 2 π R 2 {\displaystyle A_{1}={\tfrac {1}{2}}\pi R^{2}} . A 2 − A 3 = [ r 2 θ 3 6 ] 3 π 2 − φ 2 π {\displaystyle A_{2}-A_{3}=\left[{\tfrac {r^{2}\theta ^{3}}{6}}\right]_{{\tfrac {3\pi }{2}}-\varphi }^{2\pi }} . A 4 = 1 2 π r 2 {\displaystyle A_{4}={\tfrac {1}{2}}\pi r^{2}} .
Let P {\displaystyle P} be the center of a unit circle. A goat/bull/horse is tethered at point Q {\displaystyle Q} on the circumference. How long does the rope r {\displaystyle r} need to be to allow the animal to graze on exactly one half of the circle's area (white area in diagram, in plane geometry, called a lens )?
The area reachable by the animal is in the form of an asymmetric lens , delimited by the two circular arcs .
The area A {\displaystyle A} of a lens with two circles of radii R , r {\displaystyle R,r} and distance between centers d {\displaystyle d} is
which simplifies in case of R = d = 1 {\displaystyle R=d=1} and one half of the circle area to
The equation can only be solved iteratively and results in r = 1.1587 … {\displaystyle r=1.1587\ldots } (sequence A133731 in the OEIS ).
By using r < 2 {\displaystyle r<{\sqrt {2}}} and integrating over the right half of the lens area with
the transcendental equation
follows, with the same solution.
In fact, using the identities arccos ( 1 − r 2 2 ) + 2 arccos ( | r | 2 ) = π {\displaystyle \arccos \left(1-{\frac {r^{2}}{2}}\right)+2\arccos \left({\frac {|r|}{2}}\right)=\pi } and arcsin ( r 2 ) = π 2 − arccos ( r 2 ) {\displaystyle \arcsin \left({\frac {r}{2}}\right)={\frac {\pi }{2}}-\arccos \left({\frac {r}{2}}\right)} , the transcendental equation derived from lens area can be obtained.
The area can be written as the sum of sector area plus segment area. [ 5 ]
Assuming the leash is tied to the bottom of the pen, define θ {\displaystyle \theta } as the angle the taut leash makes with upwards when the goat is at the circumference. Define α {\displaystyle \alpha } as the angle from downwards to the same location, but from the center of the pen instead of from the center of the larger circle. The sum of angles of a triangle equals π {\displaystyle \pi } for the resulting isosceles triangle , giving α = π − 2 θ {\displaystyle \alpha =\pi -2\theta } . Setting the pen's radius to be 1 and trigonometry such as sin ( 2 θ ) = 2 sin ( θ ) cos ( θ ) {\displaystyle \sin(2\theta )=2\sin(\theta )\cos(\theta )} then give θ = arccos ( r 2 ) {\displaystyle \theta =\arccos \left({\frac {r}{2}}\right)} .
Requiring that half the grazable area be 1/4 of the pen's area gives A s e c t o r + A s e g m e n t = π / 4 {\displaystyle A_{sector}+A_{segment}=\pi /4} . Using the circular sector and circular segment area formulae gives
which only assumes 0 < r < 2 {\displaystyle 0<r<2} .
Combining into a single equation gives
Note that solving for arccos ( r 2 ) {\displaystyle \arccos \left({\frac {r}{2}}\right)} then taking the cosine of both sides generates extra solutions even if including the obvious constraint 1 < r < 2 {\displaystyle 1<r<{\sqrt {2}}} .
Using trigonometric identities, we see that this is the same transcendental equation that lens area and integration provide.
By using complex analysis methods in 2020, Ingo Ullisch obtained a closed-form solution as the cosine of a ratio of two contour integrals : [ 6 ]
where C is the circle | z − 3 π 4 | = π 4 {\displaystyle \left|z-{\frac {3\pi }{4}}\right|={\frac {\pi }{4}}} .
A solution can also be written using Bell polynomials , which follows from the Lagrange inversion theorem :
r = 2 cos ( π 4 + 1 2 − 1 π + 1 2 ∑ n = 2 ∞ g n ( 1 − 2 π ) n n ! ) {\displaystyle r=2\cos \left({\frac {\pi }{4}}+{\frac {1}{2}}-{\frac {1}{\pi }}+{\frac {1}{2}}\sum _{n=2}^{\infty }g_{n}{\frac {\left(1-{\frac {2}{\pi }}\right)^{n}}{n!}}\right)}
where
g n = ∑ k = 1 n − 1 ( − 1 ) k ⋅ B n − 1 , k ( f ^ 1 , f ^ 2 , . . . , f ^ n − k ) ⋅ ∏ i = 0 k − 1 ( n + i ) , and {\displaystyle g_{n}=\sum _{k=1}^{n-1}\left(-1\right)^{k}\cdot B_{n-1,k}\left({\hat {f}}_{1},{\hat {f}}_{2},...,{\hat {f}}_{n-k}\right)\cdot \prod _{i=0}^{k-1}\left(n+i\right),{\text{ and}}}
f ^ k = 2 π k sin ( π 2 k ) + π 2 cos ( π 2 k ) k + 1 . {\displaystyle {\hat {f}}_{k}={\frac {2}{\pi }}{\frac {k\sin \left({\frac {\pi }{2}}k\right)+{\frac {\pi }{2}}\cos \left({\frac {\pi }{2}}k\right)}{k+1}}.}
These formulas come from exact expressions for the nth derivative of previous transcendental equations for r {\displaystyle r} .
The three-dimensional analogue to the two-dimensional goat problem is a bird tethered to the inside of a sphere, with the tether long enough to constrain the bird's flight to half the volume of the sphere. In the three-dimensional case, point Q {\displaystyle Q} lies on the surface of a unit sphere , and the problem is to find radius r {\displaystyle r} of the second sphere so that the volume of the intersection body equals exactly half the volume of the unit sphere.
The volume of the unit sphere reachable by the animal has the form of a three-dimensional lens with differently shaped sides and defined by the two spherical caps .
The volume V {\displaystyle V} of a lens with two spheres of radii R , r {\displaystyle R,r} and distance between the centers d {\displaystyle d} is
which simplifies in case of R = d = 1 {\displaystyle R=d=1} and one half of the sphere volume to
leading to a solution of r = 1.2285 … {\displaystyle r=1.2285\ldots }
It can be demonstrated that, with increasing dimensionality, the reachable area approaches one half the sphere at the critical length r = 2 {\displaystyle r={\sqrt {2}}} . If r < 2 {\displaystyle r<{\sqrt {2}}} , the area covered approaches almost none of the sphere; if r > 2 {\displaystyle r>{\sqrt {2}}} , the area covered approaches the sphere's entire area. [ 7 ] [ 8 ] | https://en.wikipedia.org/wiki/Goat_grazing_problem |
Gobby is a free software collaborative real-time editor available on Windows and Unix-like platforms. [ 3 ] (It runs on Mac OS X using Apple's X11.app .) It was initially released in June 2005 by the 0x539 dev group [ 4 ] (the hexadecimal value 0x539 is equal to 1337 in decimal ). Gobby uses GTK+ for its GUI widgets .
Gobby features a client-server architecture which supports multiple documents in one session, document synchronisation on request, password protection and an IRC -like chat for communication out of band . [ 5 ] Users can choose a colour to highlight the text they have written in a document. Gobby is fully Unicode -aware, provides syntax highlighting for most programming languages, and has basic Zeroconf support. [ 4 ]
A dedicated server called Sobby is also provided, together with a script which could format saved sessions for the web (e.g. to provide logs of meetings with a collaboratively prepared transcript). [ 6 ] The collaborative editing protocol is named Obby, and there are other implementations that use this protocol (e.g. Rudel, [ 7 ] a plugin for GNU Emacs ). Gobby 0.5 replaces Sobby with a new server called infinoted. [ 8 ] [ 9 ]
Version 0.4.0 featured fully encrypted connections and further usability enhancements. [ 4 ] Users have commented versions prior to 0.5.0 had some issues. [ 10 ]
Versions numbered 0.4.9x are preview releases for version 0.5.0. The most noticeable improvement is undo support, [ 11 ] using the adOPTed algorithm for concurrency control. [ 12 ]
While offering Unicode support it has been suggested the product is suitable for producing plaintext rather than formatted documents. [ 13 ] | https://en.wikipedia.org/wiki/Gobby |
See text .
Gobiidae or gobies is a family of bony fish in the order Gobiiformes , one of the largest fish families comprising over 2,000 species in more than 200 genera . [ 1 ] Most of gobiid fish are relatively small, typically less than 10 cm (3.9 in) in length, and the family includes some of the smallest vertebrates in the world, such as Trimmatom nanus and Pandaka pygmaea . Trimmatom nanus are under 1 cm ( 3 ⁄ 8 in) long when fully grown, while the Pandaka pygmaea standard length is 9 mm (0.35 in), with a maximum known standard length of 11 mm (0.43 in). Some large gobies can reach over 30 cm (0.98 ft) in length, but that is exceptional. Generally, they are benthic or bottom-dwellers. Although few are important as food fish for humans, they are of great significance as prey species for other commercially important fish such as cod , haddock , sea bass and flatfish . Several gobiids are also of interest as aquarium fish , such as the dartfish of the genus Ptereleotris . Phylogenetic relationships of gobiids have been studied using molecular data. [ 2 ] [ 3 ]
The most distinctive aspects of gobiid morphology are the fused pelvic fins that form a disc-shaped sucker. This sucker is functionally analogous to the dorsal fin sucker possessed by the remoras or the pelvic fin sucker of the lumpsuckers , but is anatomically distinct; these similarities are the product of convergent evolution . The species in this family can often be seen using the sucker to adhere to rocks and corals , and in aquariums they will stick to glass walls of the tank, as well.
Gobiidae are spread all over the world in tropical and temperate near shore-marine, brackish , and freshwater environments. Their range extends from the Old World coral reefs to the seas of the New World , and includes the rivers and near-shore habitats of Europe and Asia. [ 4 ] Gobies are generally bottom-dwellers. Although many live in burrows, a few species (e.g. in the genus Glossogobius ) are true cavefish . [ 5 ] On coral reefs, species of gobiids constitute 35% of the total number of fishes and 20% of the species diversity. [ 6 ]
The family Gobiidae underwent a major revision in the 5th edition of Fishes of the World . Before the revision the Gobiidae contained six subfamilies: Gobiinae , Benthophilinae , Amblyopinae , Gobionellinae , Oxudercinae , and Sicydiinae . The revision retained the first two subfamilies and removed the other four to a separate family, the Oxudercidae . In addition, species formerly placed in the families Kraemeriidae , Microdesmidae , Ptereleotridae and Schindleriidae were added to the revised Gobiidae, although no subfamilies were described. [ 7 ]
The two formerly recognised subfamilies where the species have been retained in Gobiidae in the 5th Edition of Fishes of the World : [ 7 ]
Members of Benthophilinae are endemic to the Ponto-Caspian region (including the Marmara , Black , Azov , Caspian , and Aral Seas ). [ 8 ] The representatives of the subfamily have fused pelvic fins and elongated dorsal and anal fins. [ 9 ] They are distinguished from the closely related subfamily Gobiinae by the absence of a swimbladder in adults and location of the uppermost rays of the pectoral fins within the fin membrane. [ 10 ] Its members include tadpole gobies , monkey gobies , and bighead gobies .
Members of the Gobiinae are known as true gobies . It is the most widespread and most diverse of the subfamilies formerly recognised under the Gobiidae, containing around 2000 species and 150 genera.
Gobiids are primarily fish of shallow marine habitats, including tide pools , coral reefs , and seagrass meadows ; they are also very numerous in brackish water and estuarine habitats, including the lower reaches of rivers, mangrove swamps , and salt marshes . A few gobiid species (unknown exactly, but in the low hundreds) are also fully adapted to freshwater environments. These include the round goby ( Neogobius melanostomus ), Australian desert goby ( Chlamydogobius eremius ), and the European freshwater goby Padogobius bonelli . Most gobies feed on small invertebrates, although some of the larger species eat other fish, and a few eat planktonic algae .
Most species in the Gobiidae attach their eggs to a substrate , such as vegetation, coral, or a rock surface. They lay from five to a few thousand eggs, depending on the species. After fertilizing the eggs, the male guards the eggs from predators and keep them free from detritus . The male fans the eggs, thereby providing them with oxygen. The female maintains the burrow. The eggs hatch after a few days. The larvae are born transparent, and they develop coloration after spreading to find a suitable habitat. The larvae of many freshwater gobiid species are carried downstream to the brackish waters, or even to the sea. They return to fresh water weeks or months later. [ 11 ]
Gobiids in warmer waters reach adulthood in a few months, while gobies in cooler environments reach adulthood in two years. The total lifespan of gobiid varies from one to ten years, again with the species in warmer waters generally living longer. [ 11 ]
Many species in the Gobiidae live in male-female pairs that construct and share burrows, similar to many other fish such as Mozambique tilapia . The burrows are used for shelters and spawning places. Gobiids use their mouths to dig into the sea bottom, removing dead coral-fragments, rubble, and benthic algae in order to build their burrows. [ 12 ] Gobiids maintain their burrows by fanning away sand inside the burrows. Furthermore, gobies use coral rubble to block burrow entrance. A single goby carry as many as nine pieces of coral rubble per minute. Gobiids also build a 6–13 cm high mound over the entrance of their spawning burrow. [ 12 ] The mound lets the water flow fast over the mound. The water flow created by the mound helps to provide oxygen to the eggs. While burrow building is a cooperative behavior done by both sexes, males usually put more effort in burrow maintenance than females. Females feed more instead, because the reproductive success is optimal when females put more energy in preparing for the reproduction. [ 13 ] After spawning eggs, the roles of male and female changes. Females primarily maintain the burrow, and males mainly care for the eggs by fanning them, thereby providing oxygen. When females leave the burrow, however, the mounds lose their heights. The males then give up on the eggs and eat them, preparing for future mating opportunities. Gobiid burrows vary in size depending on the size of the species. [ 13 ]
Kleptogamy refers to a "sneaking behavior" during reproduction where an unpaired male fertilises the eggs of a paired female and the paired male cares for the eggs. Females prefer male gobies with large bodies. Since not all males have large bodies, the smaller ones may cheat instead of expending energy to find mates. [ 14 ] The sneakers wait near the spawning ground of paired fish. The sneakers then release their sperm on the spawning ground as soon as the paired female releases her eggs . [ 15 ] Though sneakers’ sperm fertilizes some eggs, the paired male cannot distinguish the eggs fertilized by the sneakers from those fertilized by his own sperm. Therefore, the paired male gives parental care equally to all the eggs. [ 16 ]
Kleptogamy is a good strategy in many ways. First, the sneakers do not need their own territories, indicating that they do not need to spend energy in protecting territories, as most other males do. Most male gobies need their own territories, since females do not choose to mate with a male that does not own his own territory. [ 14 ] Secondly, the sneakers do not provide parental care to their eggs. The paired males provide parental care instead of the sneakers. Therefore, the sneakers can save energy, and they can put more effort into finding new targets for cheating. [ 14 ]
The cost of kleptogamy is that the sneakers can receive aggressive attacks from the paired males that are usually much larger and stronger than the sneakers. For small sneakers, the attacks by the paired males can be detrimental and often lead to death. [ 14 ]
The sneakers are also referred to as pseudo-females, since they are small and hardly distinguishable from females. This small body size makes cheating easier. Most of the time the paired males mistake the sneakers for females and thus do not chase the sneakers away. The paired males are called " bourgeois " males, because they are larger, stronger, and most importantly, paired. [ 14 ]
A few species of gobiid, such as blackeye goby and Lythrypnus dalli , can change their sexes. Sex change is possible in these gobies, since the external genitalia for males and females do not differ much. [ 14 ] Sex changes can take from days to weeks. Most sex changes in gobies are from female to male ( protogyny ) rather than male to female ( protandry ). Female-to-male changes are observed not only in gobiids but also in wrasses , damselfishes , and sea basses . [ 14 ] Female-to-male change usually occurs because the resident male of the group is dead. If no male is in the group, reproduction will be impossible. Therefore, the dominant female turns into male, allowing mating to happen. [ 17 ] Male-to-female change occurs when the females have preference for specific features in males. For example, females prefer large males, and a few large males mate with multiple females, whereas small males lose their chance to mate. Small males either choose to become sneakers (kleptogamy) or choose to transform into females because all females technically have high mating opportunities. By turning into females, males can ensure that they produce many offspring . [ 14 ] [ 18 ]
Some gobies have extraordinarily developed sex change ability. Gobiodon histrio from the Great Barrier Reef exhibits bidirectional sex changes. G. histrio is one of the very few species that can change sex in both ways. When two G. historio females, which used to be males, are on the same coral reef, one of them transforms back into a male goby. [ 18 ]
Sex determination in coral goby Gobiodon erythrospilus does not occur until the juveniles meet potential mates. [ 14 ] Confronting a potential mate can be difficult for Gobiodon erythrospilus juveniles, since most coral resources, crucial for attracting mates, are occupied by pre-existing paired gobies. Juveniles can only meet potential mates when one member of the pre-existing pairs dies. Juveniles’ sexes are determined according to the sexes of their potential mates. When a juvenile meets a female, it becomes a male, and vice versa . This type of sex determination is referred to as socially influenced sex determination. [ 19 ]
Some gobiids remember landmarks that are within short distances, and use them to find their ways. Small frillfin gobies ( Bathygobius soporator ) live in intertidal zones . They swim through the pools during high tides and memorize how each pool connects to the others. Then, during low tides , they can exhibit accurate jumping behaviors, as they have memorized the paths. [ 20 ] In a new environment, these fish do not show jumping behaviors or jump into wrong pools. Nevertheless, after one night, they show the same accurate jumping behaviors. [ 21 ]
A study was done to understand how gobiids react to changing habitat. The fish were given two choices: a safe habitat with less food and a dangerous habitat with more food. Results from both the full and hungry fish revealed that gobiids, when confronted with the trade-off between foraging and avoiding predation , made choices that would better their foraging. [ 22 ]
Species in the Gobiidae sometimes form symbiotic relationships with other species, [ 23 ] such as with burrowing shrimps . The shrimp maintains a burrow in the sand in which both the shrimp and the fish live. The shrimp has poor eyesight compared to the gobiid, but if it sees or feels the fish suddenly swim into the burrow, it will follow. The fish and shrimp keep in contact with each other, the shrimp using its antennae, and the fish flicking the shrimp with its tail when alarmed. These gobiids are thus sometimes known as " watchmen gobies " or "prawn gobies". Each party gains from this relationship: the shrimp gets a warning of approaching danger, and the fish gets a safe home and a place to lay its eggs . Only the alpha male and female reproduce; other fish in the colony eat sparingly to resist being eaten by the alpha male or female. This way, only the largest and fittest are able to reproduce. [ citation needed ]
Another example of symbiosis is demonstrated by the neon gobies ( Elacatinus spp.). These gobiids, known as "cleaner gobies", remove parasites from the skin, fins, mouth, and gills of a wide variety of large fish. The most remarkable aspect of this symbiosis is many of the fish that visit the cleaner gobies' cleaning stations would otherwise treat such small fish as food (for example, groupers and snapper ). Again, this is a relationship where both parties gain: the gobies get a continual supply of food as bigger fish visit their cleaning stations, and the bigger fish leave the cleaning stations healthier than they were when they arrived.
Another form of symbiosis exists between gobiids and the mushroom coral Heliofungia actiniformis ( Fungiidae ), in which representatives of the genus Eviota roam among the tentacles possibly hiding from predators. [ 24 ] [ 25 ]
Gobiids have commercial importance in Russia and Ukraine . They are fished in the Sea of Azov , northwestern Black Sea and Caspian Sea . Most important species are round goby , monkey goby , toad goby , and grass goby . The grass goby is also a commercial fish in Italy .
Several species of gobiids are kept in aquaria. [ 26 ] Most captive gobies are marine. Perhaps the most popular is the small but colorful neon goby . Most gobies stay toward the lower portion of the aquarium, hiding in the rockwork, but some species (most notably the shrimp gobies) prefer to dig themselves little burrows. Aquarists typically provide them with a fine-grained substrate to prevent damage to their delicate undersides.
Commonly kept saltwater species include Randall's shrimp goby and the watchman goby . | https://en.wikipedia.org/wiki/Gobiidae |
God is a circa 1917 sculpture by New York Dadaists Morton Livingston Schamberg and Elsa von Freytag-Loringhoven . [ 1 ] [ 2 ] [ 3 ] It is an example of readymade art, a term coined by Marcel Duchamp in 1915 to describe his found objects . God is a 10½ inch high cast iron plumbing trap turned upside down and mounted on a wooden mitre box . The work is now in the Arensberg Collection in the Philadelphia Museum of Art . [ 1 ]
It is now compared to Marcel Duchamp's famous Fountain sculpture which consists of an upended urinal . Both works were created in the same year and there is some uncertainty about who first had the idea of turning plumbing into art. Duchamp and the Baroness were friends [ 4 ] and she later made a found-object portrait of Duchamp .
God was originally solely attributed to artist Morton Livingston Schamberg. [ 2 ] The Philadelphia Museum of Art now recognizes the Baroness as a co-artist of this piece. However, according to the scholar Francis Naumann , it is reasonable to conclude, based on the works known to have been made by her, that the Baroness most likely came up with the concept of combining the two elements of the sculpture and provided the title, while Schamberg assembled and photographed the piece. [ 5 ] [ 2 ]
This article about a sculpture in the United States is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/God_(sculpture) |
In object-oriented programming , a god object (sometimes also called an omniscient or all-knowing object ) is an object that references a large number of distinct types, has too many unrelated or uncategorized methods, or some combination of both. [ 1 ] The god object is an example of an anti-pattern and a code smell . [ 2 ]
A common programming technique is to separate a large problem into several smaller problems (a divide and conquer strategy ) and create solutions for each of them. Once the smaller problems are solved, the big problem as a whole has been solved. Therefore a given object for a small problem only needs to know about itself. Likewise, there is only one set of problems an object needs to solve: its own problems. This also follows the single-responsibility principle .
In contrast, a program that employs a god object does not follow this approach. Most of such a program's overall functionality is coded into a single "all-knowing" object, which maintains most of the information about the entire program, and also provides most of the methods for manipulating this data. Because this object holds so much data and requires so many methods, its role in the program becomes god-like (all-knowing and all-encompassing). Instead of program objects communicating among themselves directly, the other objects within the program rely on the single god object for most of their information and interaction. Since this object is tightly coupled to (referenced by) so much of the other code, maintenance becomes more difficult than it would be in a more evenly divided programming design. Changes made to the object for the benefit of one routine can have a ripple effect on other unrelated functions.
A god object is the object-oriented analogue of failing to use subroutines in procedural programming languages , or of using far too many global variables to store state information.
Whereas creating a god object is typically considered bad programming practice, this technique is occasionally used for tight programming environments (such as microcontrollers ), where the performance increase and centralization of control are more important than maintainability and programming elegance. | https://en.wikipedia.org/wiki/God_object |
The Godavari River has its catchment area [ 1 ] in seven states of India : Maharashtra , Telangana , Chhattisgarh , Madhya Pradesh , Andhra Pradesh , Karnataka and Odisha . The number of dams constructed in Godavari basin is the highest among all the river basins in India. [ 2 ] Nearly 350 major and medium dams and barrages had been constructed in the river basin by the year 2012. [ 3 ] [ 4 ] [ 5 ]
This article about a location in Andhra Pradesh is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Godavari_River_Basin_Irrigation_Projects |
In rocketry , the Goddard problem is to optimize the peak altitude of a rocket, ascending vertically, and taking into account atmospheric drag and the gravitational field . This was first posed by Robert H. Goddard in his 1919 publication, "A Method of Reaching Extreme Altitudes". [ 1 ] [ 2 ]
This physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Goddard_problem |
In mathematics , and in particular in the mathematical background of string theory , the Goddard–Thorn theorem (also called the no-ghost theorem ) is a theorem describing properties of a functor that quantizes bosonic strings . It is named after Peter Goddard and Charles Thorn .
The name "no-ghost theorem" stems from the fact that in the original statement of the theorem, the natural inner product induced on the output vector space is positive definite. Thus, there were no so-called ghosts ( Pauli–Villars ghosts ), or vectors of negative norm. The name "no-ghost theorem" is also a word play on the no-go theorem of quantum mechanics.
This statement is that of Borcherds (1992).
Suppose that V {\displaystyle V} is a unitary representation of the Virasoro algebra V i r {\displaystyle \mathrm {Vir} } , so V {\displaystyle V} is equipped with a non-degenerate bilinear form ( ⋅ , ⋅ ) {\displaystyle (\cdot ,\cdot )} and there is an algebra homomorphism ρ : V i r → E n d ( V ) {\displaystyle \rho :\mathrm {Vir} \rightarrow \mathrm {End} (V)} so that ρ ( L i ) † = ρ ( L − i ) {\displaystyle \rho (L_{i})^{\dagger }=\rho (L_{-i})} where the adjoint is defined with respect to the bilinear form, and ρ ( c ) = 24 i d V . {\displaystyle \rho (c)=24\mathrm {id} _{V}.} Suppose also that V {\displaystyle V} decomposes into a direct sum of eigenspaces of L 0 {\displaystyle L_{0}} with non-negative, integer eigenvalues i ≥ 0 {\displaystyle i\geq 0} , denoted V i {\displaystyle V^{i}} , and that each V i {\displaystyle V^{i}} is finite dimensional (giving V {\displaystyle V} a Z ≥ 0 {\displaystyle \mathbb {Z} _{\geq 0}} - grading ). Assume also that V {\displaystyle V} admits an action from a group G {\displaystyle G} that preserves this grading.
For the two-dimensional even unimodular Lorentzian lattice II 1,1 , denote the corresponding lattice vertex algebra by V I I 1 , 1 {\displaystyle V_{II_{1,1}}} . This is a II 1,1 -graded algebra with a bilinear form and carries an action of the Virasoro algebra.
Let P 1 {\displaystyle P^{1}} be the subspace of the vertex algebra V ⊗ V I I 1 , 1 {\displaystyle V\otimes V_{II_{1,1}}} consisting of vectors v {\displaystyle v} such that L 0 ⋅ v = v , L n ⋅ v = 0 {\displaystyle L_{0}\cdot v=v,L_{n}\cdot v=0} for n > 0 {\displaystyle n>0} . Let P r 1 {\displaystyle P_{r}^{1}} be the subspace of P 1 {\displaystyle P^{1}} of degree r ∈ I I 1 , 1 {\displaystyle r\in II_{1,1}} . Each space inherits a G {\displaystyle G} -action which acts as prescribed on V {\displaystyle V} and trivially on V I I 1 , 1 {\displaystyle V_{II_{1,1}}} .
The quotient of P r 1 {\displaystyle P_{r}^{1}} by the nullspace of its bilinear form is naturally isomorphic as a G {\displaystyle G} -module with an invariant bilinear form, to V 1 − ( r , r ) / 2 {\displaystyle V^{1-(r,r)/2}} if r ≠ 0 {\displaystyle r\neq 0} and V 1 ⊕ R 2 {\displaystyle V^{1}\oplus \mathbb {R} ^{2}} if r = 0 {\displaystyle r=0} .
The lattice II 1,1 is the rank 2 lattice with bilinear form ( 0 − 1 − 1 0 ) . {\displaystyle {\begin{pmatrix}0&-1\\-1&0\end{pmatrix}}.} This is even, unimodular and integral with signature (+,-).
There are two naturally isomorphic functors that are typically used to quantize bosonic strings. In both cases, one starts with positive-energy representations of the Virasoro algebra of central charge 26, equipped with Virasoro-invariant bilinear forms, and ends up with vector spaces equipped with bilinear forms. Here, "Virasoro-invariant" means L n is adjoint to L − n for all integers n .
The first functor historically is "old canonical quantization", and it is given by taking the quotient of the weight 1 primary subspace by the radical of the bilinear form. Here, "primary subspace" is the set of vectors annihilated by L n for all strictly positive n , and "weight 1" means L 0 acts by identity. A second, naturally isomorphic functor, is given by degree 1 BRST cohomology. Older treatments of BRST cohomology often have a shift in the degree due to a change in choice of BRST charge, so one may see degree −1/2 cohomology in papers and texts from before 1995. A proof that the functors are naturally isomorphic can be found in Section 4.4 of Polchinski's String Theory text.
The Goddard–Thorn theorem amounts to the assertion that this quantization functor more or less cancels the addition of two free bosons, as conjectured by Lovelace in 1971. Lovelace's precise claim was that at critical dimension 26, Virasoro-type Ward identities cancel two full sets of oscillators. Mathematically, this is the following claim:
Let V be a unitarizable Virasoro representation of central charge 24 with Virasoro-invariant bilinear form, and let π 1,1 λ be the irreducible module of the R 1,1 Heisenberg Lie algebra attached to a nonzero vector λ in R 1,1 . Then the image of V ⊗ π 1,1 λ under quantization is canonically isomorphic to the subspace of V on which L 0 acts by 1-( λ , λ ).
The no-ghost property follows immediately, since the positive-definite Hermitian structure of V is transferred to the image under quantization.
The bosonic string quantization functors described here can be applied to any conformal vertex algebra of central charge 26, and the output naturally has a Lie algebra structure. The Goddard–Thorn theorem can then be applied to concretely describe the Lie algebra in terms of the input vertex algebra.
Perhaps the most spectacular case of this application is Richard Borcherds 's proof of the monstrous moonshine conjecture, where the unitarizable Virasoro representation is the monster vertex algebra (also called "moonshine module") constructed by Frenkel , Lepowsky , and Meurman . By taking a tensor product with the vertex algebra attached to a rank-2 hyperbolic lattice, and applying quantization, one obtains the monster Lie algebra , which is a generalized Kac–Moody algebra graded by the lattice. By using the Goddard–Thorn theorem, Borcherds showed that the homogeneous pieces of the Lie algebra are naturally isomorphic to graded pieces of the moonshine module, as representations of the monster simple group .
Earlier applications include Frenkel's determination of upper bounds on the root multiplicities of the Kac–Moody Lie algebra whose Dynkin diagram is the Leech lattice , and Borcherds's construction of a generalized Kac–Moody Lie algebra that contains Frenkel's Lie algebra and saturates Frenkel's 1/∆ bound. | https://en.wikipedia.org/wiki/Goddard–Thorn_theorem |
Gods in the Sky was a three-part British television series on Channel 4 , covering astronomical religion in early civilizations. [ 1 ] It is presented by the historian of science Allan Chapman . The series was filmed in Britain, Egypt , Greece , and Italy. [ 2 ]
There is a book of the same name to accompany the series. [ 3 ]
This article relating to a television programme from the UK is a stub . You can help Wikipedia by expanding it .
This astronomy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gods_in_the_Sky |
In numerical analysis and computational fluid dynamics , Godunov's scheme is a conservative numerical scheme , suggested by Sergei Godunov in 1959, [ 1 ] for solving partial differential equations . One can think of this method as a conservative finite volume method which solves exact, or approximate Riemann problems at each inter-cell boundary. In its basic form, Godunov's method is first order accurate in both space and time, yet can be used as a base scheme for developing higher-order methods.
Following the classical finite volume method framework, we seek to track a finite set of discrete unknowns, Q i n = 1 Δ x ∫ x i − 1 / 2 x i + 1 / 2 q ( t n , x ) d x {\displaystyle Q_{i}^{n}={\frac {1}{\Delta x}}\int _{x_{i-1/2}}^{x_{i+1/2}}q(t^{n},x)\,dx} where the x i − 1 / 2 = x low + ( i − 1 / 2 ) Δ x {\displaystyle x_{i-1/2}=x_{\text{low}}+\left(i-1/2\right)\Delta x} and t n = n Δ t {\displaystyle t^{n}=n\Delta t} form a discrete set of points for the hyperbolic problem: q t + ( f ( q ) ) x = 0 , {\displaystyle q_{t}+(f(q))_{x}=0,} where the indices t {\displaystyle t} and x {\displaystyle x} indicate the derivatives in time and space, respectively. If we integrate the hyperbolic problem over a control volume [ x i − 1 / 2 , x i + 1 / 2 ] , {\displaystyle [x_{i-1/2},x_{i+1/2}],} we obtain a method of lines (MOL) formulation for the spatial cell averages: ∂ ∂ t Q i ( t ) = − 1 Δ x ( f ( q ( t , x i + 1 / 2 ) ) − f ( q ( t , x i − 1 / 2 ) ) ) , {\displaystyle {\frac {\partial }{\partial t}}Q_{i}(t)=-{\frac {1}{\Delta x}}\left(f(q(t,x_{i+1/2}))-f(q(t,x_{i-1/2}))\right),} which is a classical description of the first order, upwinded finite volume method. [ 2 ]
Exact time integration of the above formula from time t = t n {\displaystyle t=t^{n}} to time t = t n + 1 {\displaystyle t=t^{n+1}} yields the exact update formula: Q i n + 1 = Q i n − 1 Δ x ∫ t n t n + 1 ( f ( q ( t , x i + 1 / 2 ) ) − f ( q ( t , x i − 1 / 2 ) ) ) d t . {\displaystyle Q_{i}^{n+1}=Q_{i}^{n}-{\frac {1}{\Delta x}}\int _{t^{n}}^{t^{n+1}}\left(f(q(t,x_{i+1/2}))-f(q(t,x_{i-1/2}))\right)\,dt.}
Godunov's method replaces the time integral of each ∫ t n t n + 1 f ( q ( t , x i − 1 / 2 ) ) d t {\displaystyle \int _{t^{n}}^{t^{n+1}}f(q(t,x_{i-1/2}))\,dt} with a forward Euler method which yields a fully discrete update formula for each of the unknowns Q i n {\displaystyle Q_{i}^{n}} . That is, we approximate the integrals with ∫ t n t n + 1 f ( q ( t , x i − 1 / 2 ) ) d t ≈ Δ t f ↓ ( Q i − 1 n , Q i n ) , {\displaystyle \int _{t^{n}}^{t^{n+1}}f(q(t,x_{i-1/2}))\,dt\approx \Delta tf^{\downarrow }\left(Q_{i-1}^{n},Q_{i}^{n}\right),} where f ↓ ( q l , q r ) {\displaystyle f^{\downarrow }\left(q_{l},q_{r}\right)} is an approximation to the exact solution of the Riemann problem. For consistency, one assumes that f ↓ ( q l , q r ) = f ( q l ) if q l = q r , {\displaystyle f^{\downarrow }(q_{l},q_{r})=f(q_{l})\quad {\text{ if }}\quad q_{l}=q_{r},} and that f ↓ {\displaystyle f^{\downarrow }} is increasing in the first argument, and decreasing in the second argument. For scalar problems where f ′ ( q ) > 0 {\displaystyle f'(q)>0} , one can use the simple Upwind scheme , which defines f ↓ ( q l , q r ) = f ( q l ) {\displaystyle f^{\downarrow }(q_{l},q_{r})=f(q_{l})} .
The full Godunov scheme requires the definition of an approximate, or an exact Riemann solver , but in its most basic form, is given by: Q i n + 1 = Q i n − λ ( f ^ i + 1 / 2 n − f ^ i − 1 / 2 n ) , λ = Δ t Δ x , f ^ i − 1 / 2 n = f ↓ ( Q i − 1 n , Q i n ) {\displaystyle Q_{i}^{n+1}=Q_{i}^{n}-\lambda \left({\hat {f}}_{i+1/2}^{n}-{\hat {f}}_{i-1/2}^{n}\right),\quad \lambda ={\frac {\Delta t}{\Delta x}},\quad {\hat {f}}_{i-1/2}^{n}=f^{\downarrow }\left(Q_{i-1}^{n},Q_{i}^{n}\right)}
In the case of a linear problem, where f ( q ) = a q {\displaystyle f(q)=aq} , and without loss of generality, we'll assume that a > 0 {\displaystyle a>0} , the upwinded Godunov method yields: Q i n + 1 = Q i n − ν ( Q i n − Q i − 1 n ) , ν = a Δ t Δ x , {\displaystyle Q_{i}^{n+1}=Q_{i}^{n}-\nu \left(Q_{i}^{n}-Q_{i-1}^{n}\right),\quad \nu =a{\frac {\Delta t}{\Delta x}},} which yields the classical first-order, upwinded Finite Volume scheme whose stability requires ν = | a Δ t Δ x | ≤ 1 {\displaystyle \nu =\left|a{\frac {\Delta t}{\Delta x}}\right|\leq 1} .
Following Hirsch, [ 3 ] the scheme involves three distinct steps to obtain the solution at t = ( n + 1 ) Δ t {\displaystyle t=(n+1)\Delta t\,} from the known solution at t = n Δ t {\displaystyle {t=n\Delta t}\,} , as follows:
The first and third steps are solely of a numerical nature and can be considered as a projection stage , independent of the second, physical step, the evolution stage . Therefore, they can be modified without influencing the physical input, for instance by replacing the piecewise constant approximation by a piecewise linear variation inside each cell, leading to the definition of second-order space-accurate schemes, such as the MUSCL scheme . | https://en.wikipedia.org/wiki/Godunov's_scheme |
In numerical analysis and computational fluid dynamics , Godunov's theorem — also known as Godunov's order barrier theorem — is a mathematical theorem important in the development of the theory of high-resolution schemes for the numerical solution of partial differential equations .
The theorem states that:
Professor Sergei Godunov originally proved the theorem as a Ph.D. student at Moscow State University . It is his most influential work in the area of applied and numerical mathematics and has had a major impact on science and engineering, particularly in the development of methods used in computational fluid dynamics (CFD) and other computational fields. One of his major contributions was to prove the theorem (Godunov, 1954; Godunov, 1959), that bears his name.
We generally follow Wesseling (2001).
Aside
Assume a continuum problem described by a PDE is to be computed using a numerical scheme based upon a uniform computational grid and a one-step, constant step-size, M grid point, integration algorithm, either implicit or explicit. Then if x j = j Δ x {\displaystyle x_{j}=j\,\Delta x} and t n = n Δ t {\displaystyle t^{n}=n\,\Delta t} , such a scheme can be described by
In other words, the solution φ j n + 1 {\displaystyle \varphi _{j}^{n+1}} at time n + 1 {\displaystyle n+1} and location j {\displaystyle j} is a linear function of the solution at the previous time step n {\displaystyle n} . We assume that β m {\displaystyle \beta _{m}} determines φ j n + 1 {\displaystyle \varphi _{j}^{n+1}} uniquely. Now, since the above equation represents a linear relationship between φ j n {\displaystyle \varphi _{j}^{n}} and φ j n + 1 {\displaystyle \varphi _{j}^{n+1}} we can perform a linear transformation to obtain the following equivalent form,
Theorem 1: Monotonicity preserving
The above scheme of equation (2) is monotonicity preserving if and only if
Proof - Godunov (1959)
Case 1: (sufficient condition)
Assume (3) applies and that φ j n {\displaystyle \varphi _{j}^{n}} is monotonically increasing with j {\displaystyle j} .
Then, because φ j n ≤ φ j + 1 n ≤ ⋯ ≤ φ j + m n {\displaystyle \varphi _{j}^{n}\leq \varphi _{j+1}^{n}\leq \cdots \leq \varphi _{j+m}^{n}} it therefore follows that φ j n + 1 ≤ φ j + 1 n + 1 ≤ ⋯ ≤ φ j + m n + 1 {\displaystyle \varphi _{j}^{n+1}\leq \varphi _{j+1}^{n+1}\leq \cdots \leq \varphi _{j+m}^{n+1}} because
This means that monotonicity is preserved for this case.
Case 2: (necessary condition)
We prove the necessary condition by contradiction. Assume that γ p < 0 {\displaystyle \gamma _{p}^{}<0} for some p {\displaystyle p} and choose the following monotonically increasing φ j n {\displaystyle \varphi _{j}^{n}\,} ,
Then from equation (2) we get
Now choose j = k − p {\displaystyle j=k-p} , to give
which implies that φ j n + 1 {\displaystyle \varphi _{j}^{n+1}} is NOT increasing, and we have a contradiction. Thus, monotonicity is NOT preserved for γ p < 0 {\displaystyle \gamma _{p}<0} , which completes the proof.
Theorem 2: Godunov’s Order Barrier Theorem
Linear one-step second-order accurate numerical schemes for the convection equation
cannot be monotonicity preserving unless
where σ {\displaystyle \sigma } is the signed Courant–Friedrichs–Lewy condition (CFL) number.
Proof - Godunov (1959)
Assume a numerical scheme of the form described by equation (2) and choose
The exact solution is
If we assume the scheme to be at least second-order accurate, it should produce the following solution exactly
Substituting into equation (2) gives:
Suppose that the scheme IS monotonicity preserving, then according to the theorem 1 above, γ m ≥ 0 {\displaystyle \gamma _{m}\geq 0} .
Now, it is clear from equation (15) that
Assume σ > 0 , σ ∉ N {\displaystyle \sigma >0,\quad \sigma \notin \mathbb {N} } and choose j {\displaystyle j} such that j > σ > ( j − 1 ) {\displaystyle j>\sigma >\left(j-1\right)} . This implies that ( j − σ ) > 0 {\displaystyle \left({j-\sigma }\right)>0} and ( j − σ − 1 ) < 0 {\displaystyle \left({j-\sigma -1}\right)<0} .
It therefore follows that,
which contradicts equation (16) and completes the proof.
The exceptional situation whereby σ = | c | Δ t Δ x ∈ N {\displaystyle \sigma =\left|c\right|{{\Delta t} \over {\Delta x}}\in \mathbb {N} } is only of theoretical interest, since this cannot be realised with variable coefficients. Also, integer CFL numbers greater than unity would not be feasible for practical problems. | https://en.wikipedia.org/wiki/Godunov's_theorem |
Goji was a location-based virtual keyboard , created for iOS 8 by The Last Guide Company . [ 1 ] [ 2 ] [ 3 ] The keyboard enabled users to output recommendations for places of interest around them by tapping on an icon. The keyboard was released in October 2014 and removed from the iOS App Store when the company was closed in August 2015. [ 4 ] [ 5 ]
Goji would display a dynamic gradient background based on the current time of day and emoji icons related to the mobile device's current location and city . For example, when on Apple Campus , Apple specific icons would be shown. [ 6 ] | https://en.wikipedia.org/wiki/Goji_(app) |
Gold(I,III) chloride is the inorganic compound with the chemical formula Au 4 Cl 8 . It is a mixed valence compound as it contains gold in two oxidation states ; square-planar gold(III) and almost linear gold(I). The compound, which is black, is photosensitive as well as air- and moisture-sensitive.
According to the procedure by Calderazzo et al., gold(I,III) chloride may be prepared by the reaction of gold(III) chloride with gold carbonyl chloride [ 1 ] or carbon monoxide [ 2 ] at room temperature in thionyl chloride .
Single crystals of gold(I,III) chloride are triclinic with a P 1 space group and consist of discrete Au 4 Cl 8 molecules with idealised C 2h symmetry . [ 1 ] Within this the Au(I) centers are linearly coordinated with a Cl-Au-Cl bond angle of 175.0° (close to the ideal value of 180°) and an average bond length of 2.30 Å . The Au(III) centers adopt a slightly irregular square-planar conformation with the Au-Cl bond lengths for bridging chlorides (2.33 Å) being slightly longer than those of terminal chlorides (2.24 Å). | https://en.wikipedia.org/wiki/Gold(I,III)_chloride |
Gold(III) bromide is a dark-red to black crystalline solid. [ 3 ] [ 4 ] [ 5 ] It has the empirical formula AuBr 3 , but exists as a dimer with the molecular formula Au 2 Br 6 in which two gold atoms are bridged by two bromine atoms. [ 4 ] [ 5 ] [ 6 ] It is commonly referred to as gold(III) bromide, gold tribromide, and rarely but traditionally auric bromide, and sometimes as digold hexabromide. The analogous copper or silver tribromides do not exist. [ 7 ]
The first mention of any research or study of the gold halides dates back to the early-to-mid-19th century, and there are three primary researchers associated with the extensive investigation of this particular area of chemistry: Thomsen, Schottländer, and Krüss. [ 8 ] [ 9 ] [ 10 ] [ 11 ]
Gold(III) bromide adopts structures seen for the other gold(III) trihalide dimeric compounds, such as the chloride . The gold centers exhibit square planar coordination with bond angles of roughly 90 degrees. [ 5 ] [ 6 ]
Calculations indicate that in the hypothetical monomeric forms of the gold trihalides, the Jahn-Teller effect causes differences to arise in the structures of the gold halide complexes. For instance, gold(III) bromide contains one long and two short gold-bromine bonds whereas gold(III) chloride and gold(III) fluoride consist of two long and one short gold-halogen bonds. [ 6 ] Moreover, gold tribromide does not exhibit the same coordination around the central gold atom as gold trichloride or gold trifluoride. In the latter complexes, the coordination exhibits a T-conformation, but in gold tribromide the coordination exists as more of a dynamic balance between a Y-conformation and a T-conformation. This coordination difference can be attributed to the Jahn-Teller effect but more so to the decrease in π-back bonding of the gold atoms with the bromine ligands compared to the π-back bonding found with fluorine and chlorine ligands. It is also this decrease in π-back bonding which explains why gold tribromide is less stable than its trifluoride and trichloride counterparts. [ 6 ]
The most common synthesis method of gold(III) bromide is heating gold and excess liquid bromine at 140 °C: [ 3 ]
Alternatively, the halide-exchange reaction of gold(III) chloride with hydrobromic acid has also been proven successful in synthesizing gold(III) bromide: [ 12 ]
Gold(III) displays square planar coordination geometry. [ 5 ]
Gold(III) trihalides form a variety of four-coordinate adducts. [ 4 ] One example is the hydrate AuBr 3 ·H 2 O . Another well known adduct is that with tetrahydrothiophene . [ 13 ] The tetrabromide is also known:
Gold(III) bromide catalyzes a variety of reactions. In one example, it catalyzes the Diels-Alder reaction of an enynal unit and carbonyl . [ 14 ]
Another catalytic use of gold tribromide is in the nucleophilic substitution reaction of propargylic alcohols. In this reaction, the gold complex serves as an alcohol-activating agent to facilitate the substitution. [ 15 ]
Gold(III) bromide can be used as a testing reagent for the presence of ketamine . [ 16 ]
0.25% AuBr 3 0.1M NaOH is prepared to give a brownish-yellow solution. Two drops of this are added to a spotting plate and a small amount of ketamine is added. The mixture gives a deep purple color within approximately one minute, which turns to a dark, blackish-purple color within approximately two minutes.
Acetaminophen , ascorbic acid , heroin , lactose , mannitol , morphine , and sucrose all cause an instant colour change to purple, as do other compounds with phenol and hydroxyl groups.
Nothing commonly found in conjunction with ketamine gave the same colour change in the same time.
"The initial purple color may be due to the formation of a complex between the gold and the ketamine. The cause for the change of color from purple to dark blackish-purple is unknown; however, it may be due to a redox reaction that produces a small amount of colloidal gold ." [ 16 ] | https://en.wikipedia.org/wiki/Gold(III)_bromide |
This page provides supplementary chemical data on gold(III) chloride
234 pm (Bridging Au-Cl)
90° (Outer Cl-Au-Cl) 86° (Bridging Cl-Au-Cl)
The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet ( MSDS ) for this chemical from a reliable source such as SIRI , and follow its directions. | https://en.wikipedia.org/wiki/Gold(III)_chloride_(data_page) |
Gold iodide is the chemical compound with the formula Au I 3 . Although Au 2 I 6 is predicted to be stable, [ 1 ] gold(III) iodide remains an example of a nonexistent or unstable compound. [ 2 ] Attempts to isolate pure samples result in the formation of gold(I) iodide and iodine:
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it .
This article about a hypothetical chemical compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gold(III)_iodide |
Gold(III) sulfide or auric sulfide is an inorganic compound with the formula Au 2 S 3 . Auric sulfide has been described as a black and amorphous solid. [ 1 ] Only the amorphous phase has been produced, and the only evidence of existence is based on thermal analysis .
Early investigations claimed to prepare auric sulfide by the reaction of lithium tetrachloroaurate with hydrogen sulfide:
Similar preparations via chloroauric acid , auric chloride , or gold(III) sulfate a claimed proceed in anhydrous solvents, but water evinces a redox decomposition into metallic gold in sulfuric acid : [ 2 ] [ 3 ] [ 1 ]
Conversely, it is claimed that cyclo -octasulfur reduces gold(III) sulfate to a mixture of gold sulfides and sulfur oxides: [ 1 ]
Auric sulfide has also been claimed as the product when auric acetate is sonicated with cyclo -octasulfur in decalin . [ 3 ]
Auric sulfide is claimed to react with nitric acid as well sodium cyanide . It is claimed to dissolve in concentrated sodium sulfide solution. [ 1 ] | https://en.wikipedia.org/wiki/Gold(III)_sulfide |
The electroscope is an early scientific instrument used to detect the presence of electric charge on a body. It detects this by the movement of a test charge due to the Coulomb electrostatic force on it. The amount of charge on an object is proportional to its voltage . The accumulation of enough charge to detect with an electroscope requires hundreds or thousands of volts, so electroscopes are used with high voltage sources such as static electricity and electrostatic machines . An electroscope can only give a rough indication of the quantity of charge; an instrument that measures electric charge quantitatively is called an electrometer .
The electroscope was the first electrical measuring instrument . The first electroscope was a pivoted needle (called the versorium ), invented by British physician William Gilbert around 1600. [ 1 ] [ 2 ] The pith-ball electroscope and the gold-leaf electroscope are two classical types of electroscope [ 2 ] that are still used in physics education to demonstrate the principles of electrostatics . A type of electroscope is also used in the quartz fiber radiation dosimeter . Electroscopes were used by the Austrian scientist Victor Hess in the discovery of cosmic rays .
In 1731, Stephen Gray used a simple hanging thread, which would be attracted to any nearby charged object. This was the first improvement on Gilbert's versorium from 1600. [ 3 ]
The pith-ball electroscope, invented by British schoolmaster and physicist John Canton in 1754, consists of one or two small balls of a lightweight nonconductive substance, originally a spongy plant material called pith , [ 4 ] suspended by silk or linen thread from the hook of an insulated stand. [ 5 ] Tiberius Cavallo made an electroscope in 1770 with pith balls at the end of silver wires. [ 3 ] Modern electroscopes usually use balls made of plastic. In order to test the presence of a charge on an object, the object is brought near to the uncharged pith ball. If the object is charged, the ball will be attracted to it and move toward it.
The attraction occurs because of induced polarization [ 6 ] of the atoms inside the pith ball. [ 7 ] [ 8 ] [ 9 ] [ 10 ] All matter consists of electrically charged particles located close together; each atom consists of a positively charged nucleus with a cloud of negatively charged electrons surrounding it. The pith is an insulator , so the electrons in the ball are bound to atoms of the pith and are not free to leave the atoms and move about in the ball, but they can move a little within the atoms. See diagram. If, for example, a positively charged object (B) is brought near the pith ball (A) , the negative electrons (blue minus signs) in each atom (yellow ovals) will be attracted and move slightly toward the side of the atom nearer the object. The positively charged nuclei (red plus signs) will be repelled and will move slightly away. Since the negative charges in the pith ball are now nearer to the object than the positive charges (C) , their attraction is greater than the repulsion of the positive charges, resulting in a net attractive force. [ 7 ] This separation of charge is microscopic, but since there are so many atoms, the tiny forces add up to a large enough force to move a light pith ball.
The pith ball can be charged by touching it to a charged object, so some of the charges on the surface of the charged object move to the surface of the ball. Then the ball can be used to distinguish the polarity of charge on other objects because it will be repelled by objects charged with the same polarity or sign it has, but attracted to charges of the opposite polarity.
Often the electroscope will have a pair of suspended pith balls. This allows one to tell at a glance whether the pith balls are charged. If one of the pith balls is touched to a charged object, charging it, the second one will be attracted and touch it, communicating some of the charge to the surface of the second ball. Now both balls have the same polarity charge, so they repel each other. They hang in an inverted 'V' shape with the balls spread apart. The distance between the balls will give a rough idea of the magnitude of the charge.
The gold-leaf electroscope was developed in 1787 by British clergyman and physicist Abraham Bennet , [ 4 ] as a more sensitive instrument than pith ball or straw blade electroscopes then in use. [ 11 ] It consists of a vertical metal rod, usually brass , from the end of which hang two parallel strips of thin flexible gold leaf . A disk or ball terminal is attached to the top of the rod, where the charge to be tested is applied. [ 11 ] To protect the gold leaves from drafts of air they are enclosed in a glass bottle, usually open at the bottom and mounted over a conductive base. Often there are grounded metal plates or foil strips in the bottle flanking the gold leaves on either side. These are a safety measure; if an excessive charge is applied to the delicate gold leaves, they will touch the grounding plates and discharge before tearing. They also capture charge leaking through the air that accumulates on the glass walls, increasing the sensitivity of the instrument. In the precision instruments the inside of the bottle was occasionally evacuated, to prevent the charge on the terminal from leaking off through the ionization of the air.
When the metal terminal is touched with a charged object, the gold leaves spread apart in an inverted 'V'. This is because some of the charge from the object is conducted through the terminal and metal rod to the leaves. [ 11 ] Since the leaves receive the same sign charge they repel each other and thus diverge. If the terminal is grounded by touching it with a finger , the charge is transferred through the human body into the earth and the gold leaves close together.
The electroscope leaves can also be charged without touching a charged object to the terminal, by electrostatic induction . As the charged object is brought near the electroscope terminal, the leaves spread apart, because the electric field from the object induces a charge in the conductive electroscope rod and leaves, and the charged leaves repel each other. The opposite-sign charge is attracted to the nearby object and collects on the terminal disk, while the same-sign charge is repelled from the object and collects on the leaves (but only as much as left the terminal), so the leaves repel each other. If the electroscope is grounded while the charged object is nearby, by touching it momentarily with a finger, the repelled same-sign charges travel through the contact to ground, leaving the electroscope with a net charge having the opposite sign as the object. The leaves initially hang down free because the net charge is concentrated at the terminal end. When the charged object is moved away, the charge at the terminal spreads into the leaves, causing them to spread apart again. | https://en.wikipedia.org/wiki/Gold-leaf_electroscope |
GoldSim is dynamic, probabilistic simulation software developed by GoldSim Technology Group.
This general-purpose simulator is a hybrid of several simulation approaches, combining an extension of system dynamics with some aspects of discrete event simulation , and embedding the dynamic simulation engine within a Monte Carlo simulation framework.
While it is a general-purpose simulator, GoldSim has been most extensively used for environmental and engineering risk analysis , with applications in the areas of water resource management
, [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] mining , [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] radioactive waste management
, [ 12 ] [ 13 ] [ 14 ] [ 15 ] geological carbon sequestration , [ 16 ] [ 17 ] aerospace mission risk analysis [ 18 ] [ 19 ] and energy. [ 20 ]
In 1990, Golder Associates , an international engineering consulting firm, was asked by the United States Department of Energy (DOE) to develop probabilistic simulation software that could be used to help with decision support and management within the Office of Civilian Radioactive Waste Management. The results of this effort were two DOS -based programs (RIP and STRIP), which were used to support radioactive waste management projects within the DOE.
In 1996, in an effort funded by Golder Associates, the US DOE, the Japan Nuclear Cycle Development Institute (currently the Japan Atomic Energy Agency ) and the Spanish National Radioactive Waste Company (ENRESA), the capabilities of RIP and STRIP were incorporated into a general purpose Windows -based simulator called GoldSim. Subsequent funding was also provided by NASA .
Initially only offered to the original funding organizations, GoldSim was released to the public in 2002. In 2004, GoldSim Technology Group LLC was spun off from Golder Associates and is now a wholly independent company. [ 21 ]
Notable applications include providing the simulation framework for: 1) the Yucca Mountain Repository Performance Assessment model developed by Sandia National Laboratories ; [ 12 ] 2) a comprehensive system-level computational model for performance assessment of geological sequestration of CO 2 developed by Los Alamos National Laboratory ; [ 16 ] 3) a flood operations model to help better understand and fine tune operations of a large dam used for water supply and flood control in Queensland, Australia; [ 4 ] and 4) models for simulating risks associated with future crewed space missions by NASA Ames Research Center . [ 18 ] [ 19 ]
GoldSim provides a visual and hierarchical modeling environment, which allows users to construct models by adding “elements” (model objects) that represent data, equations, processes or events, and linking them together into graphical representations that resemble influence diagrams . Influence arrows are automatically drawn as elements are referenced by other elements. Complex systems can be translated into hierarchical GoldSim models by creating layer of “containers” (or sub-models). Visual representations and hierarchical structures help users to build very large, complex models that can still be explained to interested stakeholders (e.g., government regulators, elected officials, and the public).
Though it is primarily a continuous simulator, GoldSim has a number of features typically associated with discrete simulators . By combining these two simulation methods, systems that are best represented using both continuous and discrete dynamics can often be more accurately simulated. Examples include tracking the quantity of water in a reservoir that is subject to both continuous inflows and outflows, as well as sudden storm events; and tracking the quantity of fuel in a space vehicle as it is subjected to random perturbations (e.g., component failures, extreme environmental conditions).
Because the software was originally developed for complex environmental applications, in which many inputs are uncertain and/or stochastic , in addition to being a dynamic simulator, GoldSim is a Monte Carlo simulator, such that inputs can be defined as distributions and the entire system simulated a large number of times to provide probabilistic outputs. [ 22 ] As such, the software incorporates a number of computational features to facilitate probabilistic simulation of complex systems, including tools for generating and correlating stochastic time series , advanced sampling capabilities (including latin hypercube sampling , nested Monte Carlo analysis, and importance sampling ), and support for distributed processing . | https://en.wikipedia.org/wiki/GoldSim |
Gold chalcogenides are compounds formed between gold and one of the chalcogens , elements from group 16 of the periodic table : oxygen , sulfur , selenium , or tellurium .
Gold telluride minerals, such as calaverite and krennerite (AuTe 2 ), petzite (Ag 3 AuTe 2 ), and sylvanite (AgAuTe 2 ), are minor ores of gold (and tellurium). See telluride minerals for more information.
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gold_chalcogenides |
Gold clusters , a part of cluster chemistry , is a term used to describe molecular clusters of gold or larger colloidal particles. Both types can described as nanoparticles , with diameters of less than one micrometer. [ 1 ] Gold nanoclusters have, despite intense efforts, as yet no commercial applications. Their optoelectronic [ 2 ] and catalytic [ 3 ] [ 4 ] properties continue to attract attention.
Bare gold clusters, i.e., clusters without stabilizing ligand shells can be synthesized and studied in vacuum using molecular beam techniques. Their structures have been experimentally studied using, e.g., anion photoelectron spectroscopy, [ 5 ] far-infrared spectroscopy, [ 6 ] as well as measurements of their ion mobility and electron diffraction studies [ 7 ] in conjunction with quantum chemical calculations. The structures of such clusters differ strongly from those of the ligand-stabilized ones, indicating an pivotal influence of the chemical environment on the cluster structure. A notable example is Au 20 which forms a perfect tetrahedron in which the Au atom packing closely resembles the atomic arrangement in the fcc bulk structure of metallic gold. [ 5 ] [ 6 ] Evidence has been presented for the existence of hollow golden cages with the partial formula Au n − with n = 16 to 18. [ 8 ] These clusters, with diameter of 550 picometres , are generated by laser vaporization and characterized by photoelectron spectroscopy .
Bulk gold exhibits a face-centered cubic (fcc) structure. As gold particle size decreases the fcc structure of gold often changes into nanoparticles with five-fold or icosahedral structures , [ 9 ] particularly in clusters of a few atoms illustrated by Au 13 . [ 1 ] It can be shown that the fcc structure can be extended by a half unit cell in order to make it look like a cuboctahedral structure. The cuboctahedral structure maintains the cubic-closed pack and symmetry of fcc. This can be thought of as redefining the unit cell into a more complicated cell. Each edge of the cuboctahedron represents a peripheral Au–Au bond. The cuboctahedron has 24 edges while the icosahedron has 30 edges; the transition from cuboctahedron to icosahedron is favored since the increase in bonds contributes to the overall stability of the icosahedron structure. [ 1 ]
The centered icosahedral cluster Au 13 is the basis of constructing large gold nanoclusters. Au 13 is the endpoint of atom-by-atom growth. In other words, starting with one gold atom up to Au 12 , each successful cluster is created by adding one additional atom. The icosahedral motif is found in many gold clusters through vertex sharing ( Au 25 and Au 36 ), face-fusion ( Au 23 and Au 29 ), and interpenetrating bi-icosahedrons ( Au 19 , Au 23 , Au 26 , and Au 29 ). [ 1 ] Larger gold nanoclusters can often be reduced to a series of icosahedrons connecting, overlapping, and/or surrounding each other. The crystallization process of gold nanoclusters with 561 atoms from the liquid involves the formation of surface segments that grow towards the center of the cluster. [ 10 ] The cluster assumes an icosahedral structure because of the associated surface energy reduction. [ 11 ] [ 12 ] Icosahedral structures and also five-fold twins are also common in nanoparticles produced by other methods. [ 13 ] [ 9 ]
Well-defined, molecular clusters are known, invariably containing organic ligands on their exteriors. Two examples are [Au 6 C(P(C 6 H 5 ) 3 ) 6 ] 2+ and [Au 9 (P(C 6 H 5 ) 3 ) 8 ] 3+ . [ 14 ] In order to generate naked gold clusters for catalytic applications, the ligands must be removed, which is typically done via a high-temperature (200 °C/392 °F or higher) calcination process, [ 15 ] but can also be achieved chemically at low temperatures (below 100 °C/212 °F), e.g. using a peroxide -assisted route. [ 16 ]
Gold clusters can be obtained in colloid form . Such colloids often occur with a surface coating of alkanethiols or proteins . Such clusters can be used in immunohistochemical staining . [ 17 ] Gold metal nanoparticles (NPs) are characterized by an intense absorption in the visible region, which enhances the utility of these species for the development of completely optical devices. The wavelength of this surface plasmon resonance (SPR) band depends on the size and shape of the nanoparticles as well as their interactions with the surrounding medium. The presence of this band enhances the potential utility of gold nanoparticle as building blocks for devices for data storage, ultrafast switching, and gas sensors. Whilst plasmonic gold nanoparticles only exhibit electric moments, clusters of such particles can exhibit magnetic moments making them of great interest for use in optical metamaterials [ 18 ]
When supported on a FeOOH surface, gold clusters catalyze oxidation of CO at ambient temperatures. [ 19 ] Similarly gold clusters supported on TiO 2 can oxidize CO at temperatures as low as 40K. [ 20 ] Catalytic activity may correlate with the size and structure of gold nanoclusters, both the energetics and electronic properties with size and structure. [ 21 ] [ 22 ] | https://en.wikipedia.org/wiki/Gold_cluster |
Gold cyanidation (also known as the cyanide process or the MacArthur–Forrest process ) is a hydrometallurgical technique for extracting gold from low-grade ore through conversion to a water-soluble coordination complex . It is the most commonly used leaching process for gold extraction . [ 1 ] Cyanidation is also widely used in silver extraction, usually after froth flotation . [ 2 ]
Production of reagents for mineral processing to recover gold represents 70% of cyanide consumption globally. While other metals, such as copper , zinc , and silver, are also recovered using cyanide, gold remains the primary driver of this technology. [ 1 ] The highly toxic nature of cyanide has led to controversy regarding its use in gold mining, with it being banned in some parts of the world. However, when used with appropriate safety measures, cyanide can be safely employed in gold extraction processes. [ 3 ] One critical factor in its safe use is maintaining an alkaline pH level above 10.5, which is typically controlled using lime in industrial-scale operations. Lime plays an essential role in gold processing, ensuring that the pH remains at the correct level to mitigate risks associated with cyanide use. [ 4 ]
In 1783, Carl Wilhelm Scheele discovered that gold dissolved in aqueous solutions of cyanide. Through the work of Bagration (1844), Elsner (1846), and Faraday (1847), it was determined that each gold atom required two cyanide ions, i.e. the stoichiometry of the soluble compound.
The expansion of gold mining in the Rand of South Africa began to slow down in the 1880s, as the new deposits found tended to contain pyritic ore . The gold could not be extracted from this compound with any of the then available chemical processes or technologies. [ 5 ] In 1887, John Stewart MacArthur , working in collaboration with brothers Robert and William Forrest for the Tennant Company in Glasgow , Scotland, developed the MacArthur–Forrest process for the extraction of gold from gold ores. Several patents were issued in the same year. [ 6 ] By suspending the crushed ore in a cyanide solution, a separation of up to 96 percent pure gold was achieved. [ 7 ] The process was first used on the Rand in 1890 and, despite operational imperfections, led to a boom of investment as larger gold mines were opened up. [ 8 ] [ 5 ]
By 1891, Nebraska pharmacist Gilbert S. Peyton had refined the process at his Mercur Mine in Utah, "the first mining plant in the United States to make a commercial success of the cyanide process on gold ores." [ 9 ] [ 10 ] In 1896, Bodländer confirmed that oxygen was necessary for the process, something that had been doubted by MacArthur, and discovered that hydrogen peroxide was formed as an intermediate. [ 8 ] Around 1900, the American metallurgist Charles Washington Merrill (1869–1956) and his engineer Thomas Bennett Crowe improved the treatment of the cyanide leachate, by using vacuum and zinc dust. Their process is the Merrill–Crowe process . [ 11 ]
The chemical reaction for the dissolution of gold, the "Elsner equation", follows:
Potassium cyanide and calcium cyanide are sometimes used in place of sodium cyanide.
Gold is one of the few metals that dissolves in the presence of cyanide ions and oxygen. The soluble gold species is dicyanoaurate . [ 13 ] from which it can be recovered by adsorption onto activated carbon. [ 14 ]
The ore is comminuted using grinding machinery. Depending on the ore, it is sometimes further concentrated by froth flotation or by centrifugal (gravity) concentration . Water is added to produce a slurry or pulp . The basic ore slurry can be combined with a solution of sodium cyanide or potassium cyanide ; many operations use calcium cyanide , which is more cost effective.
To prevent the creation of toxic hydrogen cyanide during processing, slaked lime ( calcium hydroxide ) or soda ( sodium hydroxide ) is added to the extracting solution to ensure that the acidity during cyanidation is maintained over pH 10.5 - strongly basic. Lead nitrate can improve gold leaching speed and quantity recovered, particularly in processing partially oxidized ores.
Oxygen is one of the reagents consumed during cyanidation, accepting the electrons from the gold, and a deficiency in dissolved oxygen slows leaching rate. Air or pure oxygen gas can be purged through the pulp to maximize the dissolved oxygen concentration. Intimate oxygen-pulp contactors are used to increase the partial pressure of the oxygen in contact with the solution, thus raising the dissolved oxygen concentration much higher than the saturation level at atmospheric pressure . Oxygen can also be added by dosing the pulp with hydrogen peroxide solution.
In some ores, particularly those that are partially sulfidized, aeration (prior to the introduction of cyanide) of the ore in water at high pH can render elements such as iron and sulfur less reactive to cyanide, therefore making the gold cyanidation process more efficient. Specifically, the oxidation of iron to iron (III) oxide and subsequent precipitation as iron hydroxide minimizes loss of cyanide from the formation of ferrous cyanide complexes. The oxidation of sulfur compounds to sulfate ions avoids the consumption of cyanide to thiocyanate (SCN − ) byproduct.
In order of decreasing economic efficiency, the common processes for recovery of the solubilized gold from solution are (certain processes may be precluded from use by technical factors):
The cyanide remaining in tails streams from gold plants is potentially hazardous. Therefore, some operations process the cyanide-containing waste streams in a detoxification step. This step lowers the concentrations of these cyanide compounds. The INCO-licensed process and the Caro's acid process oxidise the cyanide to cyanate , which is not as toxic as the cyanide ion, and which can then react to form carbonates and ammonia: [ 15 ]
The Inco process can typically lower cyanide concentrations to below 50 mg/L, whereas the Caro's acid process can lower cyanide levels to between 10 and 50 mg/L, with the lower concentrations achievable in solution streams rather than slurries. Caro's acid – peroxomonosulfuric acid (H 2 SO 5 ) - converts cyanide to cyanate. Cyanate then hydrolyses to ammonium and carbonate ions. The Caro's acid process is able to achieve discharge levels of Weak Acid Dissociable" (WAD) cyanide below 50 mg/L, which is generally suitable for discharge to tailings. Hydrogen peroxide and basic chlorination can also be used to oxidize cyanide, although these approaches are less common. Typically, this process blows compressed air through the tailings while adding sodium metabisulfite , which releases SO 2 . Lime is added to maintain the pH at around 8.5, and copper sulfate is added as a catalyst if there is insufficient copper in the ore extract. This procedure can reduce concentrations of WAD cyanide to below the 10 ppm mandated by the EU's Mining Waste Directive. This level compares to the 66-81 ppm free cyanide and 500-1000 ppm total cyanide in the pond at Baia Mare . [ 16 ] Remaining free cyanide degrades in the pond, while cyanate ions hydrolyse to ammonium. Studies show that residual cyanide trapped in the gold-mine tailings causes persistent release of toxic metals (e.g. mercury ) into the groundwater and surface water systems. [ 17 ] [ 18 ]
Despite being used in 90% of gold production: [ 19 ] gold cyanidation is controversial due to the toxic nature of cyanide. Although aqueous solutions of cyanide degrade rapidly in sunlight, the less-toxic products, such as cyanates and thiocyanates, may persist for some years. The famous disasters have killed few people — humans can be warned not to drink or go near polluted water, but cyanide spills can have a devastating effect on rivers, sometimes killing everything for several miles downstream. The cyanide could be washed out of river systems and, as long as organisms can migrate from unpolluted areas upstream, affected areas can soon be repopulated. Longer term impact and accumulation of cyanide in riparian or limnological benthos and environmental fate is less clear. According to Romanian authorities, in the Someș river below Baia Mare , the plankton returned to 60% of normal within 16 days of the spill; the numbers were not confirmed by Hungary or Yugoslavia. [ 16 ] Famous cyanide spills include:
Such spills have prompted fierce protests at new mines that involve use of cyanide, such as Roşia Montană in Romania, Lake Cowal in Australia, Pascua Lama in Chile, and Bukit Koman in Malaysia.
Although cyanide is cheap, effective, and biodegradable, its high toxicity & increasingly poor impact on a mine's political and social license to operate, has incentivized alternative methods for extracting gold. Other extractants have been examined including thiosulfate (S 2 O 3 2− ), thiourea (SC(NH 2 ) 2 ), iodine/iodide, ammonia, liquid mercury, and alpha- cyclodextrin . Challenges include reagent cost and the efficiency of gold recovery, although some chlorination process using sodium hypochlorite (household bleach) have shown promise in terms of reagent regeneration. These technologies are at a pre-commercialisation stage and compare favourably to equivalent cyanidation methods, including gold recovery percentage. Thiourea has been implemented commercially for ores containing stibnite. [ 22 ] Yet another alternative to cyanidation is the family of glycine-based lixiviants . [ 23 ]
The US states of Montana [ 24 ] and Wisconsin , [ 25 ] the Czech Republic , [ 26 ] Hungary , [ 27 ] have banned cyanide mining. The European Commission rejected a proposal for such a ban, noting that existing regulations (see below) provide adequate environmental and health protection. [ 28 ] Several attempts to ban gold cyanidation in Romania were rejected by the Romanian Parliament. There are currently protests in Romania calling for a ban on the use of cyanide in mining (see 2013 Romanian protests against the Roșia Montană Project ).
In the EU, industrial use of hazardous chemicals is controlled by the so-called Seveso II Directive (Directive 96/82/EC, [ 29 ] which replaced the original Seveso Directive (82/501/EEC [ 30 ] brought in after the 1976 dioxin disaster. "Free cyanide and any compound capable of releasing free cyanide in solution" are further controlled by being on List I of the Groundwater Directive (Directive 80/68/EEC) [ 31 ] which bans any discharge of a size which might cause deterioration in the quality of the groundwater at the time or in the future. The Groundwater Directive was largely replaced in 2000 by the Water Framework Directive (2000/60/EC). [ 32 ]
In response to the 2000 Baia Mare cyanide spill , the European Parliament and the Council adopted Directive 2006/21/EC on the management of waste from extractive industries. [ 33 ] Article 13(6) requires "the concentration of weak acid dissociable cyanide in the pond is reduced to the lowest possible level using best available techniques ", and at most all mines started after 1 May 2008 may not discharge waste containing over 10ppm WAD cyanide, mines built or permitted before that date are allowed no more than 50ppm initially, dropping to 25ppm in 2013 and 10ppm by 2018.
Under Article 14, companies must also put in place financial guarantees to ensure clean-up after the mine has finished. This in particular may affect smaller companies wanting to build gold mines in the EU, as they are less likely to have the financial strength to give these kinds of guarantees.
The industry has come up with a voluntary " Cyanide Code " [ 34 ] that aims to reduce environmental impacts with third party audits of a company's cyanide management. | https://en.wikipedia.org/wiki/Gold_cyanidation |
Gold extraction is the extraction of gold from dilute ores using a combination of chemical processes. Gold mining produces about 3600 tons annually, [ 1 ] and another 300 tons is produced from recycling. [ 2 ]
Since the 20th century, gold has been principally extracted in a cyanide process by leaching the ore with cyanide solution. The gold may then be further refined by gold parting , which removes other metals (principally silver ) by blowing chlorine gas through the molten metal. Historically, small particles of gold were amalgamated with mercury , and then concentrated by boiling away the mercury. The mercury method is still used in some small operations.
Gold occurs principally as a native metal , i.e., gold itself. Sometimes it is alloyed to a greater or lesser extent with silver , which is called electrum . Native gold can occur as sizeable nuggets, as fine grains or flakes in alluvial deposits , or as grains or microscopic particles (known as colour) embedded in rock minerals. Other forms of gold are the minerals calaverite (AuTe), aurostibnite (AuSb 2 ), and maldonite (Au 2 Bi). These latter three, although rarer that native gold, can be slow to react with cyanide and thus difficult to process. [ 3 ] Still other gold-containing ores include various tellurides ( sylvanite , nagyagite , petzite , and krennerite ).
Certain contaminants in ores can interfere with the extractability of gold by cyanide. These interfering agents are called "preg-robbing ores". For example, gold can bind tightly to carbon, resisting normal cyanide extraction. Gold cyanides bind also to some clays. [ 3 ]
While the romantic picture of gold mining focuses on nuggets, the reality is that gold is typically recovered from ores containing >10 ppm of the metal. Thus, the main challenge is concentrating this trace amount. [ 2 ]
The principal technology is the cyanide process , in which gold is leached from the ore by treatment with a solution of cyanide. The first step is comminution (grinding) to increase surface area and expose the gold to the extracting solution. The extraction is conducted by dump leaching or heap leaching processes. Sodium cyanide is produced on a billion-ton/year scale mainly for this purpose. "Black cyanide", a carbon-contaminated form of calcium cyanide (Ca(CN) 2 ) is often used because it is cheap. The crude ore is washed with a c. 0.3% solution of cyanide in air, often repeatedly, and the aqueous extract is collected and refined further. Recovery from solution typically involves adsorption on activated carbon, the carbon in pulp process.
Thiosulfate leaching has been proven to be effective on ores with high soluble copper values or ores which experience preg-robbing .
Leaching through bulk leach extractable gold , or BLEG, is also a process that is used to test an area for gold concentrations where gold may not be immediately visible.
Amalgamation with mercury can be used to recover very small gold particles, and mercury is still widely used in small-scale artisanal mining across the world. [ 4 ] Mercury forms a mercury-gold amalgam with smaller gold particles, and then the gold is concentrated by boiling away the mercury from the amalgam. This is effective in extracting very small gold particles, but the process is hazardous due to the toxicity of mercury vapour. Large-scale use of mercury stopped in the 1960s. However, mercury is still used in artisanal and small-scale gold mining (ASGM). [ 5 ] One mechanism by which mercury is employed in hydraulic mining is as an "undercurrent", in which the flow of smaller grains is diverted over mercury-coated copper plates. High flow velocities associated with hydraulic mining cause flouring of mercury, the wearing down of mercury particles that contributes to mercury loss into the environment. [ 6 ]
Over 10,000,000 pounds (4,500,000 kg) of mercury contaminated the environment in California as a result of placer mining in the late nineteenth and early twentieth centuries. Stamp mill mining contributed an additional 3,000,000 pounds (1,400,000 kg) of mercury contamination. [ 6 ] Mercury contamination in California waterways is a major contemporary environmental issue, [ 6 ] as is groundwater pollution , mostly by inorganic mercury. [ 7 ]
A "refractory" gold ore is an ore that has ultra-fine gold particles disseminated throughout its gold occluded minerals. These ores are naturally resistant to recovery by standard cyanidation and carbon adsorption processes. These refractory ores require pre-treatment before cyanidation can be used. A refractory ore generally contains sulphide minerals, organic carbon, or both. Sulphide minerals are impermeable minerals that occlude gold particles, making it difficult for the leach solution to form a complex with the gold. Organic carbon present in gold ore may adsorb dissolved gold-cyanide complexes in much the same way as activated carbon. This so-called "preg-robbing" carbon is washed away because it is significantly finer than the carbon recovery screens typically used to recover activated carbon. [ 3 ]
Pre-treatment options for refractory ores include:
The refractory ore treatment processes may be preceded by concentration (usually sulphide flotation). Roasting is used to oxidize both the sulphur and organic carbon at high temperatures using air and/or oxygen. Bio-oxidation involves the use of bacteria that promote oxidation reactions in an aqueous environment. Pressure oxidation is an aqueous process for sulphur removal carried out in a continuous autoclave, operating at high pressures and somewhat elevated temperatures. The Albion process utilises a combination of ultrafine grinding and atmospheric, auto-thermal, oxidative leaching.
Parting is a process by which gold is purified to a commercially-tradeable standard, typically ≥99.5%. Removal of silver is of particular interest since the two metals often co-purify. The standard procedure is based on the Miller process . The separation is achieved by passing chlorine gas into a molten alloy. The technique is practiced on a large scale (e.g. 500 kg). The principle of the method exploits the nobility of gold, such that at high temperatures, gold does not react with chlorine, but virtually all contaminating metals do. Thus, at c. 500 °C, as the chlorine gas is passed through molten mixture (again, mainly gold), a low-density slag forms on top, which can be decanted from the liquid gold. Silver chloride and other precious metals can be recovered from this slag. The slag layer is often diluted with a flux like borax to facilitate the separation. [ 2 ]
Alternative methods exist for parting gold. Silver can be dissolved selectively by boiling the mixture with 30% nitric acid, a process sometimes called inquartation. Affination is a largely obsolete process of removing silver from gold using concentrated sulfuric acid . [ 8 ] Electrolysis using the Wohlwill process is yet another approach.
The smelting of gold began sometime around 6000 – 3000 BC. [ 9 ] [ 10 ] [ 11 ] According to one source the technique began to be in use in Mesopotamia or Syria. [ 12 ] In ancient Greece, Heraclitus wrote on the subject. [ 13 ]
According to de Lecerda and Salomons (1997) mercury was first in use for extraction at about 1000 BC, [ 14 ] according to Meech and others (1998), mercury was used in obtaining gold until the latter period of the first millennia. [ 15 ] [ 16 ] [ 17 ] [ 18 ]
A technique known to Pliny the Elder was extraction by way of crushing, washing, and then applying heat, with the resultant material powdered. [ 19 ] [ 20 ] [ 21 ]
Like all metals, gold is insoluble in a water. Gold does however exhibit the distinctive properties that in the presence of cyanide ions, it dissolves in the presence of oxygen (or air). This transformation was reported in 1783 by Carl Wilhelm Scheele , but it was not until the late 19th century, that the reactions were exploited commercially. The expansion of gold mining in the Rand of South Africa began to slow down in the 1880s, as the new deposits being found tended to be pyritic ore . The gold was difficult to extract from such ores.
A process known as chlorination was once used to treat pyritic gold ore. Typically, the ore was roasted and then treated with chlorine gas. The residue was extracted to give an aqueous solution of gold chloride. It was used, notably at the Mount Morgan mine , where it remained in use until 1911. The chloride process became obsolete with the development of the cyanide process . [ 22 ] [ 23 ]
In 1887, John Stewart MacArthur , working in collaboration with brothers Dr Robert and Dr William Forrest for the Tennant Company in Glasgow , Scotland , developed the MacArthur-Forrest Process for the extraction of gold ores. By suspending the crushed ore in a cyanide solution, up to 96 percent gold was extracted. [ 24 ] [ 25 ] [ 26 ] [ 27 ] [ 28 ] [ 29 ] [ 30 ]
The process was first used on a large scale at the Witwatersrand in 1890, leading to a boom of investment as larger gold mines were opened up. In 1896, Bodländer confirmed that oxygen was necessary for the process, something that had been doubted by MacArthur, and discovered that hydrogen peroxide was formed as an intermediate. [ 31 ]
The method known as heap leaching was first proposed in 1969 by the United States Bureau of Mines , [ 32 ] and was in use by the 1970s. [ 33 ] | https://en.wikipedia.org/wiki/Gold_extraction |
Gold hexafluoride is a binary inorganic chemical compound of gold and fluorine with the chemical formula AuF 6 . [ 1 ] As of 2023, it is still a hypothetical compound that has never been prepared or observed. [ 2 ] [ 3 ] In 1999, Neil Bartlett stated, "It should exist, if made at low temperature and kept cold." [ 4 ]
Like PtF 6 , AuF 6 should be an extremely powerful oxidizer . [ 5 ] The compound is calculated to be stable. [ 6 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it .
This article about a hypothetical chemical compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gold_hexafluoride |
The extensive use of gold during early Philippine history is well-documented, both in the archeological record and in the various written accounts from precolonial and early Spanish colonial times. [ 1 ] Gold was used throughout the Philippine archipelago in various decorative and ceremonial items, as clothing, and also as currency. [ 2 ]
Gold was readily available throughout the Philippine archipelago, [ 3 ] : 309 and gold items were valued as symbols of power and markers of elite status, [ 3 ] : 299 although studies of grave artifacts suggest that these items were not as valued in precolonial Philippines as traded ornaments were. [ 3 ] : 308 Gold was plentiful enough that local elites did not feel the need to acquire large amounts of it, and only sought it as the need arose, by trading with settlements which produced it through low intensity mining. [ 3 ] : 309
Among the most prominent sites for gold mining in early Philippine history were Aringay-Tonglo-Balatok trade route covering the Cordillera Mountain Range and the Lingayen gulf towns of Agoo and Aringay; [ 4 ] the mines of Paracale on the Bicol Peninsula which were a major source of gold for the trading centers of the Visayan islands, particularly Panay and Cebu; [ 5 ] [ 6 ] and the Butuan-Surigao area, particularly along the Agusan river on the island of Mindanao, which made Butuan (historical polity) an important trading center.
Scholarly information about the use of gold in early Philippine history comes mostly from artifacts that have been discovered in various sites in the Philippines, and from historical accounts from the early Spanish colonial period. Archeological excavation sites include ones in Batangas, Mindoro, Luzon, Samar, Butuan and Surigao. [ 7 ]
Gold mined from the Cordillera Mountain Range were brought down to the coast through the Aringay-Tonglo-Balatok gold trail, [ 6 ] [ 8 ] making commercial trade centers out of Aringay and the neighboring settlement of Agoo , [ 6 ] whose coast at the time was shaped in such a way that it was a good harbor for foreign vessels coming into Lingayen Gulf . [ 9 ] [ 4 ] On the island of Mindanao , gold was mined along the Agusan River [ 8 ] : 164 in the Butuan-Surigao area [ 10 ] and extensively worked in the Butuan polity located at the mouth of the Agusan River . [ 11 ]
Many discoveries of precolonial gold artifacts go unreported because the gold is found or stolen by treasure hunters, who simply melt the gold down for profit. [ 12 ] Among the most important gold artifact discoveries are the " Surigao Treasure " found by construction worker Berto Morales in 1991, [ 12 ] the Agusan image found by Manobo woman Belay Campos in 1917, [ 13 ] the Bolinao Skull discovered by the National Museum of the Philippines at the Balingasay Archaeological Site in Bolinao , Pangasinan ,and the Oton Death Mask excavated rom San Antonio , Iloilo on Panay Island by a team from the National Museum of the Philippines and the University of the Philippines Diliman in the 1960s. [ 14 ]
Upon first arriving in the Philippine archipelago, landing specifically in the visayas, Spanish colonizers noted astonishing amounts of gold in common use, including earrings, armbands legbands, gold chains, collars of beads, wristlets, armlets, finger rings, and so on. [ 8 ] : 32 They were also integrated into clothing as sequins, [ 8 ] : 32 as clasps or buttons for cloaks [ 8 ] : 31 or as broaches. [ 8 ] : 32
Goldwork used as decorative dentistry was referred to in the Visayas as "pusad," and was noted by some of the earliest colonial era chroniclers, including Antonio Pigafetta and Fray Andres de Urdaneta . The practice is also commonly referenced in Mindanaoan epic poetry such as the Ulahingan of the Manobo people. Pegs called Bansil were inserted into holes drilled into the tooth, with the visible tip being either simple dot-shape, designed as a collection of overlapping scales, or intricate designs reminiscent of filigree. They were made more visible in light of the practice of staining teeth either black or bright red. [ 8 ] : 19
Numerous gold artifacts recovered in the Philippines are believed to have ceremonial purposes. Some of these figures indicate the Hindu and Buddhist influence which came to the Philippines through regional trade in maritime southeast asia , while others reflect nature-based religious beliefs. [ 15 ]
A notable artifact reflecting indigenous beliefs depicts what has been described as "the large, triangular face of a woman drawn in sharp lines with little shoulders and arms raised in a gesture of worship." [ 15 ]
Visayan indigenous healing beliefs are likewise reflected in a particular variant of kamagi necklaces known as "tunga," which were snake-like in shape and made of “half gold and half tumbaga ” gears strung together. These were believed to protect the wearer from the " folk illness " known as pasma . [ 16 ]
Other notable ceremonial artifacts include: the Agusan Image which depicts a female Hindu or Buddhist deity whose identity is disputed, [ 17 ] and the gold kinnari, which shows a mythical half-human half-bird figure common in hindu and buddhist parts of Maritime Southeast Asia. [ 15 ]
Aside from decorative dentistry which they wore in life and carried the grave with them, ranking datus were often buried with items of gold, either in the form of gold burial goods, or as specifically designed funerary art such as death masks. [ 3 ]
Burial goods found in graves from early Philippine history includes various beads earrings rings pendants, combs, strips, and other ornaments. [ 3 ] : 309
Another gold feature commonly discovered in elite burials from early historic Philippines are death mask artifacts, meant to cover either part or all of the deceased's face in the grave [ 18 ]
When this practice was discovered by the Spanish colonizers, they created a rule that a government representative should always be present whenever the Spanish settlers dug up a grave - so that the Spanish government could get its designated 1/5 of the dug up goods. [ 8 ]
Burial goods are among the most common surviving gold artifacts in the Philippines because gold which was not buried was typically eventually reforged into other forms as the colonial period proceeded. [ 8 ]
Accounts of early Spanish colonizers also noted the use of gold as spear decorations in the visayas. [ 8 ] : 32
Aside from use as decorative or utilitarian objects, gold was used throughout the Philippine archipelago as currency, whether in the form of gold dust, small beads, or barter rings. [ 8 ]
Modern day antique collectors have since coined the term "Piloncitos" to describe the small "bead-like" pieces of gold which were used as currency in Precolonial Philippines, [ 2 ] comparing the cone-shaped pieces to a pilon of sugar. [ 2 ] Early historical descriptions of the term include the Spanish "granitas de oro" (small grains of gold), or simply by whatever local language terms were used to mean "gold" in those times, such as "bulawan." [ 19 ] | https://en.wikipedia.org/wiki/Gold_in_early_Philippine_history |
Gold phosphides are inorganic compounds of gold and phosphorus . The only known gold phosphide is a metastable gold(I) polyphosphide with the formula Au 2 P 3 . [ 1 ] [ 2 ]
Older texts sometimes refer to a binary auric phosphide AuP ; [ 3 ] [ 4 ] this hypothetical compound has not been verified by modern methods such as X-ray crystallography .
Monoclinic Au 2 P 3 is produced by direct reaction between metallic gold and red phosphorus at high temperatures over multiple days. The reaction produced only Au 2 P 3 , with no other compounds observed across a wide variety of Au:P atom ratios. [ 2 ]
Gold(III) phosphide was purportedly prepared by the direct reaction of spongy gold and phosphorus or by passing phosphine into a solution of auric chloride in ether or alcohol: [ 5 ] [ 6 ] [ 7 ] [ better source needed ]
Au 2 P 3 is claimed to decompose in air or with H 2 O . [ 8 ] It has a monoclinic crystal structure. [ 2 ]
A mixed anion phosphide iodide , Au 7 P 10 I , is known to possess a trigonal structure. [ 2 ] | https://en.wikipedia.org/wiki/Gold_phosphide |
Gold plating is a method of depositing a thin layer of gold onto the surface of another metal, most often copper or silver (to make silver-gilt ), by a chemical or electrochemical ( electroplating ) process. Plating refers to modern coating methods, such as the ones used in the electronics industry , whereas gilding is the decorative covering of an object with gold, which typically involve more traditional methods and much larger objects.
There are five recognized classes of gold plating chemistry:
Gold plating of silver is used in the manufacture of jewellery . The thickness of gold plating on jewellery is noted in microns (or micro-meters). The microns of thickness determines how long the gold plating lasts with usage. The jewellery industry denotes different qualities of gold plating in the following terminology
Gold plated silver jewellery can still tarnish as the silver atoms diffuse into the gold layer, causing slow gradual fading of its color and eventually causing tarnishing of the surface. This process may take months and even years, depending on the thickness of the gold layer. A barrier metal layer is used to counter this effect; these can be nickel or rhodium. Copper, which also migrates into gold, does so more slowly than silver. The copper is usually further plated with nickel. A gold-plated silver article is usually a silver substrate with layers of copper, nickel, and gold deposited on top of it.
Gold, applied by evaporated methods or electroplating, has been specified by NASA to thermally control spacecraft instruments, due to its 99.4% reflectivity in infrared wavelengths. [ 1 ]
Gold plating is often used in electronics, to provide a corrosion -resistant electrically conductive layer on copper , typically in electrical connectors and printed circuit boards .
With direct gold-on-copper plating, the copper atoms tend to diffuse through the gold layer, causing tarnishing of its surface and formation of an oxide and/or sulphide layer.
A layer of a suitable barrier metal , usually nickel , is often deposited on the copper substrate before the gold plating. The layer of nickel provides mechanical backing for the gold layer, improving its wear resistance. It also reduces the impact of pores present in the gold layer.
Both the nickel and gold layers can be plated by electrolytic or electroless processes. There are many factors to consider in selection of either electrolytic or electroless plating methods. These include what the deposit will be used for, configuration of the part, materials compatibility and cost of processing. In different applications, electrolytic or electroless plating can have cost advantages.
At higher frequencies, the skin effect may cause higher losses due to higher electrical resistance of nickel; a nickel-plated trace can have its useful length shortened three times in the 1 GHz band in comparison with the non-plated one. Selective plating is used, depositing the nickel and gold layers only on areas where it is required and does not cause the detrimental side effects. [ 2 ]
Gold plating may lead to formation of gold whiskers .
Wire bonding between gold plated contacts and aluminium wires or between aluminium contacts and gold wires under certain conditions develops a brittle layer of gold-aluminium intermetallics , known as purple plague .
There are several types of gold plating used in the electronics industry: [ 3 ]
Soldering gold-plated parts can be problematic as gold is soluble in solder . Solder which contains more than 4–5% gold can become brittle. The joint surface is dull-looking.
Gold reacts with both tin and lead in their liquid state, forming brittle intermetallics . When eutectic 63% tin – 37% lead solder is used, no lead-gold compounds are formed, because gold preferentially reacts with tin, forming the AuSn 4 compound. Particles of AuSn 4 disperse in the solder matrix, forming preferential cleavage planes, significantly lowering the mechanical strength and therefore reliability of the resulting solder joints.
If the gold layer does not completely dissolve into the solder, then slow intermetallic reactions can proceed in the solid state as the tin and gold atoms cross-migrate. Intermetallics have poor electrical conductivity and low strength. The ongoing intermetallic reactions also cause Kirkendall effect , leading to mechanical failure of the joint, similar to the degradation of gold-aluminium bonds known as purple plague .
A 2–3 μm layer of gold dissolves completely within one second during typical wave soldering conditions. Layers of gold thinner than 0.5 μm (0.02 thou ) also dissolve completely into the solder, exposing the underlying metal (usually nickel) to the solder. Impurities in the nickel layer can prevent the solder from bonding to it. Electroless nickel plating contains phosphorus. Nickel with more than 8% phosphorus is not solderable. [ citation needed ] Electrodeposited nickel may contain nickel hydroxide . An acid bath is required to remove the passivation layer before applying the gold layer; improper cleaning leads to a nickel surface difficult to solder. A stronger flux can help, as it aids dissolving the oxide deposits. Carbon is another nickel contaminant that hinders solderability. | https://en.wikipedia.org/wiki/Gold_plating |
Gold working in the Bronze Age British Isles refers to the use of gold to produce ornaments and other prestige items in the British Isles during the Bronze Age , between c. 2500 and c. 800 BCE in Britain, and up to about 550 BCE in Ireland. In this period, communities in Britain and Ireland first learned how to work metal, leading to the widespread creation of not only gold but also copper and bronze items as well. Gold artefacts in particular were prestige items used to designate the high status of those individuals who wore, or were buried with them.
Around 1,500 gold objects dating to the Bronze Age survive in collections, around 1000 of them from Ireland and the other 500 from Britain; this is a much smaller number than would have been originally crafted, leading archaeologists to believe that "many thousands of gold objects were made and used" in the Bronze Age British Isles. [ 1 ]
Records indicate that Bronze Age gold artefacts had begun to be discovered by the 18th century at the least, although at the time many were melted down or lost. Only with the rise of the antiquarian and then archaeological movements were the antiquity of these items recognised, after which they were more usually preserved in collections.
The archaeologist George Eogan noted that investigation of Bronze Age gold artefacts revealed not only "the work of craftsmen and technicians" from that period but also aided our understanding of "broader aspects of society such as social stratification, trade, commerce and ritual." [ 1 ]
In prehistory gold could be found in several areas of Europe; the Carpathian region, Iberia, south-western France, Brittany, Britain and Ireland. [ 1 ] [ 2 ] The latter in particular had rich gold reserves, and as such has been labelled an "ancient El Dorado ". [ 3 ] Across the world, and in many cultures, gold has been highly valued as a precious metal , in part because of its rarity and also because of its properties; for instance, unlike bronze it is malleable , flexible and homogenous, and can be worked by hammering, rather than having to be worked through casting, annealing or soldering. Any products made from gold do not corrode, but instead have what has been described as an "intrinsic beauty", with many prehistoric peoples probably ascribing gold items a "symbolic as well as a decorative function". [ 1 ]
First developed in 1836 by Danish archaeologist Christian Jürgensen Thomsen as a part of his " Three-age system ", the term " Bronze Age " is used by archaeologists to refer to those societies which have developed bronze technology but not yet learned how to work the more complicated process involved in making iron objects. The European Bronze Age lasted from c. 3200 BCE , when the Aegean civilizations of Greece first developed bronze technology, right through to c. 600 BCE , when the Nordic Bronze Age came to an end with the development of iron among Scandinavian communities.
The period known by archaeologists as Bronze Age Britain lasted from c. 2500 BCE through to c. 800 BCE , and was defined by the adoption of copper and bronze technologies on the island. [ 4 ] Bronze Age Ireland followed a similar, yet distinct course.
The Early Bronze Age in the British Isles was marked by the adoption of what archaeologists call the " Beaker culture ", which had arrived from continental Europe. Eogan noted that the "evidence from archaeology is that Beaker-using communities were the earliest metallurgists in Britain and Ireland", with their produce including "copper artefacts such as tanged daggers but also gold objects as well as the use of gold for embellishment." [ 5 ]
Bronze Age goldwork is marked by an elegant simplicity of design and fine execution, with decoration usually restricted to relatively simple geometric patterns such as parallel lines, chevron, zig-zag and circular patterns, often extremely small and perfectly executed, especially in Ireland, as can be seen by enlarging the lunula and Irish bracelet illustrated. The objects are nearly all pieces of jewellery, and include clothes-fasteners (somewhat like large one-piece cuff-links ), torcs , bracelets , gold lunulae . A number of gold finger rings have been recorded, including the elaborately decorated Knaresborough Ring. [ 6 ] Other finds are smaller ornaments that were perhaps worn in the ear, nose or hair, or on clothing as brooches, and a range of thin disc or plaques probably sewn to clothing or worn in the hair. The ends of objects that are essentially bars bent into a round shape often thicken before ending in a flat or concave face, as for example in the Milton Keynes Hoard . The thickening is typically slight in torcs and bracelets, but extreme in clothes fasteners and ear decorations. Tightly wound spirals in pairs are popular, as they were on the continent.
Eogan (1994) noted that around 250 surviving gold objects are known to date to the Early Bronze Age, 165 of those from Ireland, and the other 83 from Britain. [ 5 ] From analysing the designs of the earliest gold artefacts in Britain, Eogan noted that they "form a homogeneous group" which, when "taken in conjunction with other metal types demonstrate that a new technology was introduced." [ 7 ] Early Bronze Age pieces are generally much smaller, with very thin decorated discs or plaques common. Two small gold cups have been found in England, the Rillaton Cup and the similar but now crushed Ringlemere Cup .
Due to its natural resources, Ireland had a "rich Early Bronze Age [metal-working] industry", producing large quantities of metal axes, halberds and daggers, and as a part of this also had a "major gold industry", seeing the production of lunulae and gold disks on a far larger scale than Britain. [ 8 ]
The transition to the Late Bronze Age brought societal change to the British Isles, and also apparently increased availability of gold, which led to a trend of much larger and more massive pieces. The largest were jewellery worn round the neck in a range of styles, the most ostentatious wide flat collars or gorgets with ribbed decoration following the shape of the piece, and round discs at the side. The Mold Cape is unique among survivals, but fits in with the trend to massive pieces emphasizing the neck and chest. It was clearly not for prolonged wear, as the wearer could not raise their arms. In Ireland, lunulae were probably replaced as neck ornaments firstly by gold torcs , found from the Irish Middle Bronze Age, and then in the Late Bronze Age by the spectacular "gorgets" of thin ribbed gold, some with round discs at the side, of which 9 examples survive, 7 in the National Museum of Ireland . [ 9 ]
Designs based on twisted bars or ribbons giving a spiral became popular, probably influenced by the Continent. "Although over 110 identifiable British [includes Ireland] ribbon torcs are known, the dating of these simple, flexible ornaments is elusive", perhaps indicating "a long-lived preference for ribbon torcs, which continued for over 1,000 years", into the Iron Age. [ 10 ]
In Bronze Age Britain, gold objects were prestigious items, and archaeologists believe that those who owned them, or were buried with them, had a high status in society. Archaeologist George Eogan noted that gold reflected "ostentation in society, a society that has divisions along rank." [ 11 ]
Archaeologist George Eogan, in his study of Bronze Age gold-working, noted that very few Bronze Age gold artefacts had been discovered through "controlled archaeological investigation", with the majority instead having been unearthed "by chance", as a result of "agricultural activities or peat-cutting". [ 12 ] In the 21st century, metal detectorists have become important, for example with the important Shropshire bulla , found in 2018.
Antiquarian interest in the gold artefacts of prehistory emerged in the British Isles during the Early Modern period . In 1696, the Ashmolean Museum in Oxford , southern England obtained the Ballyshannon Disk , the first such artefact of its type in their collection, although in ensuing centuries they would gain a number of other items to accompany it. [ 13 ] The British Museum in London would follow suit almost a century later, gaining its first Bronze Age gold artefact, a disk from Kirk Andrews on the Isle of Man, in 1782. [ 14 ]
In 1980, Joan J. Taylor published the first comprehensive study of the available evidence, entitled Bronze Age Goldwork of the British Isles . [ 15 ] In 1994, the archaeologist George Eogan published an academic monograph on the subject, entitled The Accomplished Art: Gold and Gold-Working in Britain and Ireland during the Bronze Age , which was brought out through the U.K.-based Oxbow Books. In it, Eogan noted that his study was "not a corpus or catalogue" of artefacts, instead being "an evaluation and interpretation of the material in social terms". [ 1 ] | https://en.wikipedia.org/wiki/Gold_working_in_the_Bronze_Age_British_Isles |
In number theory , Goldbach's weak conjecture , also known as the odd Goldbach conjecture , the ternary Goldbach problem , or the 3-primes problem , states that
This conjecture is called "weak" because if Goldbach's strong conjecture (concerning sums of two primes) is proven, then this would also be true. For if every even number greater than 4 is the sum of two odd primes, adding 3 to each even number greater than 4 will produce the odd numbers greater than 7 (and 7 itself is equal to 2+2+3).
In 2013, Harald Helfgott released a proof of Goldbach's weak conjecture. [ 2 ] The proof was accepted for publication in the Annals of Mathematics Studies series [ 3 ] in 2015, and has been undergoing further review and revision since; fully refereed chapters in close to final form are being made public in the process. [ 4 ]
Some state the conjecture as
This version excludes 7 = 2+2+3 because this requires the even prime 2. On odd numbers larger than 7 it is slightly stronger as it also excludes sums like 17 = 2+2+13, which are allowed in the other formulation. Helfgott's proof covers both versions of the conjecture. Like the other formulation, this one also immediately follows from Goldbach's strong conjecture.
The conjecture originated in correspondence between Christian Goldbach and Leonhard Euler . One formulation of the strong Goldbach conjecture, equivalent to the more common one in terms of sums of two primes, is
The weak conjecture is simply this statement restricted to the case where the integer is odd (and possibly with the added requirement that the three primes in the sum be odd).
In 1923, Hardy and Littlewood showed that, assuming the generalized Riemann hypothesis , the weak Goldbach conjecture is true for all sufficiently large odd numbers. In 1937, Ivan Matveevich Vinogradov eliminated the dependency on the generalised Riemann hypothesis and proved directly (see Vinogradov's theorem ) that all sufficiently large odd numbers can be expressed as the sum of three primes. Vinogradov's original proof, as it used the ineffective Siegel–Walfisz theorem , did not give a bound for "sufficiently large"; his student K. Borozdkin (1956) derived that e e 16.038 ≈ 3 3 15 {\displaystyle e^{e^{16.038}}\approx 3^{3^{15}}} is large enough. [ 6 ] The integer part of this number has 4,008,660 decimal digits, so checking every number under this figure would be completely infeasible.
In 1997, Deshouillers , Effinger, te Riele and Zinoviev published a result showing [ 7 ] that the generalized Riemann hypothesis implies Goldbach's weak conjecture for all numbers. This result combines a general statement valid for numbers greater than 10 20 with an extensive computer search of the small cases. Saouter also conducted a computer search covering the same cases at approximately the same time. [ 8 ]
Olivier Ramaré in 1995 showed that every even number n ≥ 4 is in fact the sum of at most six primes, from which it follows that every odd number n ≥ 5 is the sum of at most seven primes. Leszek Kaniecki showed every odd integer is a sum of at most five primes, under the Riemann Hypothesis . [ 9 ] In 2012, Terence Tao proved this without the Riemann Hypothesis; this improves both results. [ 10 ]
In 2002, Liu Ming-Chit ( University of Hong Kong ) and Wang Tian-Ze lowered Borozdkin's threshold to approximately n > e 3100 ≈ 2 × 10 1346 {\displaystyle n>e^{3100}\approx 2\times 10^{1346}} . The exponent is still much too large to admit checking all smaller numbers by computer. (Computer searches have only reached as far as 10 18 for the strong Goldbach conjecture, and not much further than that for the weak Goldbach conjecture.)
In 2012 and 2013, Peruvian mathematician Harald Helfgott released a pair of papers improving major and minor arc estimates sufficiently to unconditionally prove the weak Goldbach conjecture. [ 11 ] [ 12 ] [ 2 ] [ 13 ] [ 14 ] Here, the major arcs M {\displaystyle {\mathfrak {M}}} is the union of intervals ( a / q − c r 0 / q x , a / q + c r 0 / q x ) {\displaystyle \left(a/q-cr_{0}/qx,a/q+cr_{0}/qx\right)} around the rationals a / q , q < r 0 {\displaystyle a/q,q<r_{0}} where c {\displaystyle c} is a constant. Minor arcs m {\displaystyle {\mathfrak {m}}} are defined to be m = ( R / Z ) ∖ M {\displaystyle {\mathfrak {m}}=(\mathbb {R} /\mathbb {Z} )\setminus {\mathfrak {M}}} . | https://en.wikipedia.org/wiki/Goldbach's_weak_conjecture |
In mathematics , the Goldbach–Euler theorem (also known as Goldbach's theorem ), states that the sum of 1/( p − 1) over the set of perfect powers p , excluding 1 and omitting repetitions, converges to 1:
This result was first published in Euler 's 1737 paper " Variæ observationes circa series infinitas ". Euler attributed the result to a letter (now lost) from Goldbach .
Goldbach's original proof to Euler involved assigning a constant to the harmonic series : x = ∑ n = 1 ∞ 1 n {\displaystyle \textstyle x=\sum _{n=1}^{\infty }{\frac {1}{n}}} , which is divergent . Such a proof is not considered rigorous by modern standards. There is a strong resemblance between the method of sieving out powers employed in his proof and the method of factorization used to derive Euler's product formula for the Riemann zeta function .
Let x {\displaystyle x} be given by
Since the sum of the reciprocal of every power of 2 is 1 = 1 2 + 1 4 + 1 8 + 1 16 + ⋯ {\displaystyle \textstyle 1={\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+\cdots } , subtracting the terms with powers of 2 from x {\displaystyle x} gives
Repeat the process with the terms with the powers of 3: 1 2 = 1 3 + 1 9 + 1 27 + 1 81 + ⋯ {\displaystyle \textstyle {\frac {1}{2}}={\frac {1}{3}}+{\frac {1}{9}}+{\frac {1}{27}}+{\frac {1}{81}}+\cdots }
Absent from the above sum are now all terms with powers of 2 and 3. Continue by removing terms with powers of 5, 6 and so on until the right side is exhausted to the value of 1. Eventually, we obtain the equation
which we rearrange into
where the denominators consist of all positive integers that are the non-powers minus 1. By subtracting the previous equation from the definition of x {\displaystyle x} given above, we obtain
where the denominators now consist only of perfect powers minus 1.
While lacking mathematical rigor, Goldbach's proof provides a reasonably intuitive argument for the theorem's truth. Rigorous proofs require proper and more careful treatment of the divergent terms of the harmonic series. Other proofs make use of the fact that the sum of 1/( p − 1) over the set of perfect powers p , excluding 1 but including repetitions, converges to 1 by demonstrating the equivalence: | https://en.wikipedia.org/wiki/Goldbach–Euler_theorem |
The Ullmann condensation or Ullmann-type reaction is the copper-promoted conversion of aryl halides to aryl ethers, aryl thioethers, aryl nitriles, and aryl amines. These reactions are examples of cross-coupling reactions . [ 1 ]
Ullmann-type reactions are comparable to Buchwald–Hartwig reactions but usually require higher temperatures. Traditionally, these reactions require high-boiling, polar solvents such as N -methylpyrrolidone , nitrobenzene , or dimethylformamide and high temperatures (often in excess of 210 °C) with stoichiometric amounts of copper. Aryl halides are required to be activated by electron-withdrawing groups . Traditional Ullmann style reactions used "activated" copper powder, e.g. prepared in situ by the reduction of copper sulfate by zinc metal in hot water. The methodology improved with the introduction of soluble copper catalysts supported by diamines and acetylacetonate ligands. [ 1 ]
Illustrative of the traditional Ullmann ether synthesis is the preparation of p-nitrophenyl phenyl ether from 4-chloronitrobenzene and phenol . [ 2 ]
Copper is used as a catalyst, either in the form of the metal or copper salts. Modern arylations use soluble copper catalysts. [ 3 ]
A traditional Goldberg reaction involves reaction of an aniline with an aryl halide. The coupling of 2-chlorobenzoic acid and aniline is illustrative: [ 4 ]
A typical catalyst is formed from copper(I) iodide and phenanthroline . The reaction is an alternative to the Buchwald–Hartwig amination reaction.
Aryl iodides are more reactive arylating agents than are aryl chlorides, following the usual pattern. Electron-withdrawing groups on the aryl halide also accelerate the coupling. [ 5 ]
The nucleophile can also be carbon including carbanions as well as cyanide . In the traditional Hurtley reaction , the carbon nucleophiles were derived from malonic ester and other dicarbonyl compounds: [ 6 ]
More modern Cu-catalyzed C-C cross-couplings utilize soluble copper complexes containing phenanthroline ligands. [ 7 ]
The arylation of alkylthiolates proceeds by the intermediacy of cuprous thiolates. [ 8 ]
In the case of Ullmann- type reactions (aminations, etherifications, etc. of aryl halides), the conversions involve copper(I) alkoxide, copper(I) amides, copper(I) thiolates. The copper(I) reagent can be generated in situ from the aryl halide and copper metal. Even copper(II) sources are effective under some circumstances. A number of innovations have been developed with regards to copper reagents. [ 1 ]
These copper(I) compounds subsequently react with the aryl halide in a net metathesis reaction:
In the case of C-N coupling, kinetic studies implicate oxidative addition reaction followed by reductive elimination from Cu(III) intermediates ( L n = one or more spectator ligands ): [ 9 ]
The Ullmann ether synthesis is named after its inventor, Fritz Ullmann . [ 10 ] The corresponding Goldberg reaction, is named after Irma Goldberg . [ 11 ] The Hurtley reaction, which involves C-C bond formation, is similarly named after its inventor. [ 6 ] | https://en.wikipedia.org/wiki/Goldberg_reaction |
The Goldbeter–Koshland kinetics [ 1 ] [ 2 ] describe a steady-state solution for a 2-state biological system. In this system, the interconversion between these two states is performed by two enzymes with opposing effect. One example would be a protein Z that exists in a phosphorylated form Z P and in an unphosphorylated form Z ; the corresponding kinase Y and phosphatase X interconvert the two forms. In this case we would be interested in the equilibrium concentration of the protein Z (Goldbeter–Koshland kinetics only describe equilibrium properties, thus no dynamics can be modeled). It has many applications in the description of biological systems.
The Goldbeter–Koshland kinetics is described by the Goldbeter–Koshland function:
with the constants
Graphically the function takes values between 0 and 1 and has a sigmoid behavior. The smaller the parameters J 1 and J 2 the steeper the function gets and the more of a switch-like behavior is observed. Goldbeter–Koshland kinetics is an example of ultrasensitivity .
Since equilibrium properties are searched one can write
From Michaelis–Menten kinetics the rate at which Z P is dephosphorylated is known to be r 1 = k 1 [ X ] [ Z P ] K M 1 + [ Z P ] {\displaystyle r_{1}={\frac {k_{1}[X][Z_{P}]}{K_{M1}+[Z_{P}]}}} and the rate at which Z is phosphorylated is r 2 = k 2 [ Y ] [ Z ] K M 2 + [ Z ] {\displaystyle r_{2}={\frac {k_{2}[Y][Z]}{K_{M2}+[Z]}}} . Here the K M stand for the Michaelis–Menten constant which describes how well the enzymes X and Y bind and catalyze the conversion whereas the kinetic parameters k 1 and k 2 denote the rate constants for the catalyzed reactions. Assuming that the total concentration of Z is constant one can additionally write that [ Z ] 0 = [ Z P ] + [ Z ] and one thus gets:
with the constants
If we thus solve the quadratic equation (1) for z we get:
Thus (3) is a solution to the initial equilibrium problem and describes the equilibrium concentration of [ Z ] and [ Z P ] as a function of the kinetic parameters of the phosphorylation and dephosphorylation reaction and the concentrations of the kinase and phosphatase. The solution is the Goldbeter–Koshland function with the constants from (2):
The ultrasensitivity (sigmoidality) of a Goldbeter–Koshland module can be measured by its Hill Coefficient :
n H = log ( 81 ) log ( E C 90 / E C 10 ) {\displaystyle n_{H}={\frac {\log(81)}{\log(EC90/EC10)}}} .
where EC90 and EC10 are the input values needed to produce the 10% and 90% of the maximal response, respectively.
In a living cell, Goldbeter–Koshland modules are embedded in a bigger network with upstream and downstream components. This components may constrain the range of inputs that the module will receive as well as the range of the module’s outputs that network will be able to detect. Altszyler et al. (2014) [ 3 ] [ 4 ] studied how the effective ultrasensitivity of a modular system is affected by these restrictions. They found that Goldbeter–Koshland modules are highly sensitive to dynamic range limitations imposed by downstream components. However, in the case of asymmetric Goldbeter–Koshland modules, a moderate downstream constrain can produce effective sensitivities much larger than that of the original module when considered in isolation. | https://en.wikipedia.org/wiki/Goldbeter–Koshland_kinetics |
The Golden Eurydice Award is presented for an outstanding contribution, or contributions over a period, in the field of biophilosophy . It is awarded by the International Forum for Biophilosophy which was established in Belgium by royal decree in 1988. Founding members included Herman Van Den Berghe .
The award consists of a sculptured golden statue of Eurydice . Awardees must make a 20-minute presentation of their work at a special Golden Keynote evening event, which usually takes place in November/December each year. Awardees are also granted Honorary membership of the forum.
Recipients include: | https://en.wikipedia.org/wiki/Golden_Eurydice_Award |
Golden Gate Cloning or Golden Gate assembly [ 1 ] is a molecular cloning method that allows a researcher to simultaneously and directionally assemble multiple DNA fragments into a single piece using Type IIS restriction enzymes and T4 DNA ligase . [ 2 ] This assembly is performed in vitro . Most commonly used Type IIS enzymes include BsaI, BsmBI, and BbsI.
Unlike standard Type II restriction enzymes like EcoRI and BamHI , these enzymes cut DNA outside of their recognition sites and, therefore, can create non-palindromic overhangs . [ 3 ] Since 256 potential overhang sequences are possible, multiple fragments of DNA can be assembled by using combinations of overhang sequences. [ 3 ] In practice, this means that Golden Gate Cloning is typically scarless. Additionally, because the final product does not have a Type IIS restriction enzyme recognition site, the correctly-ligated product cannot be cut again by the restriction enzyme, meaning the reaction is essentially irreversible. [ 3 ] This has multiple benefits, the first is that it is possible to do digestion and ligation of the DNA fragments in a single reaction, in contrast to conventional cloning methods where these reactions are separate. The second is higher efficiency [ 1 ] because the end product cannot be cut again by the restriction enzyme.
A typical thermal cycler protocol oscillates between 37 °C (optimal for restriction enzymes) and 16 °C (optimal for ligases) many times. [ 4 ] While this technique can be used for a single insert, researchers have used Golden Gate Cloning to assemble many pieces of DNA simultaneously. [ 5 ]
Scar sequences are common in multiple segment DNA assembly. In the multisegment assembly method Gateway , segments are added into the donor with additional ATT sequences, which overlap in those added segments, and this results in the segments separated by the ATT sequences. [ 6 ] In BioBrick assembly, an eight-nucleotide scar sequence, which codes for a tyrosine and a stop codon , is left between every segment added into the plasmid. [ 6 ]
Golden Gate assembly uses Type IIS restriction enzymes cutting outside their recognition sequences. [ 6 ] Also, the same Type IIS restriction enzyme can generate copious different overhangs on the inserts and the vector; for instance, BsaI creates 256 four-basepair overhangs. [ 6 ] If the overhangs are carefully designed, the segments are ligated without scar sequences between them, and the final construct can be quasi-scarless, where the restriction enzyme sites remain on both sides of the insert. [ 6 ] As additional segments can be inserted into the vectors without scars within an open reading frame , Golden Gate is widely used in protein engineering . [ 6 ]
Although Golden Gate Cloning speeds up multisegment cloning, careful design of donor and recipient plasmids is required. [ 5 ] Scientists at New England Biolabs have successfully demonstrated the assembly of 35 fragments via a single-tube Golden Gate Assembly reaction. [ 7 ] Critical to this method of assembly, the vector backbone of the destination plasmid and all the assembly fragments are flanked by Type IIS restriction enzyme recognition sites, as this subtype of restriction enzymes cut downstream from their recognition sites . After cutting, each assembly active piece of DNA has unique overhangs that anneal to the next fragment of DNA in the planned assembly and become ligated, building the assembly. While it is also possible for an overhang to anneal back to its original complementary overhang associated with the upstream recognition site and become ligated, re-forming the original sequence, this will be susceptible to further cutting throughout the assembly reaction.
Restriction enzyme DNA assembly has cloning standards to minimize the change in cloning efficiency and the function of the plasmid, which can be caused by compatibility of the restriction sites on the insert and those on the vector. [ 8 ]
Golden Gate assembly's cloning standards have two tiers. [ 8 ] First-tier Golden Gate assembly constructs the single-gene construct by adding in genetic elements such as promoter, open reading frames , and terminators. [ 8 ] Then, second-tier Golden Gate assembly combine several constructs made in first-tier assembly to make a multigene construct. [ 8 ] To achieve second-tier assembly, modular cloning (MoClo) system and GoldenBraid2.0 standard are used. [ 8 ]
Modular Cloning, or MoClo, is an assembly method introduced in 2011 by Ernst Weber et al., whereby using Type IIS restriction sites, the user can ligate at least six DNA parts together into a backbone in a one-pot reaction. It is a method based on Golden Gate Assembly, where Type IIS restriction enzymes cleave outside of their recognition site to one side, allowing for removal of those restriction sites from the design. This helps eliminate excess base pairs, or scars, from forming between DNA Parts. However, in order to ligate together properly, MoClo utilizes a set of 4-base pair fusion sites, which remain between parts after ligation, forming 4-base pair scars between DNA parts in the final DNA sequence following ligation of two or more parts. [ 9 ]
MoClo utilizes a parallel approach, where all constructs from tier-one(level 0 modules) have restriction sites for BpiI on both sides of the inserts. The vector(also known as "destination vector"), where genes will be added, has an outward-facing BsaI restriction site with a drop-out screening cassette. [ 8 ] LacZ is a common screening cassette, where it is replaced by the multigene construct on the destination vector. [ 8 ] Each tier-one construct and the vector have different overhangs on them yet complementary to the overhang of the next segment, and this determines the layout of the final multigene construct. [ 8 ] Golden Gate Cloning usually starts with level 0 modules. [ 5 ] However, if the level 0 module is too large, cloning will start from level -1 fragments, which have to be sequenced, to help cloning the large construct. [ 5 ] If starting from level -1 fragments, the level 0 modules do not need to be sequenced again, whereas if starting from level 0 modules, the modules must be sequenced. [ 5 ]
Level 0 modules are the base for MoClo system, where they contain genetic elements like a promoter, a 5' untranslated region (UTR), a coding sequence, and a terminator. [ 5 ] For the purpose of Golden Gate Cloning, the internal sequences of level 0 modules should not contain type IIS restriction enzymes sites for BsaI, BpiI, and Esp3I while surrounded by two BsaI restriction sites in inverted orientation. [ 5 ] Level 0 modules without type IIS restriction sites flanking can add the BsaI sites during the process of Golden Gate Cloning. [ 5 ]
If the level 0 modules contains any unwanted restriction site, they can be mutated in silico by removing one nucleotide from the Type IIS restriction site. [ 5 ] In this process, one needs to make sure that the introduced mutation will not affect the genetic function encoded by the sequence of interest. [ 5 ] A silent mutation in the coding sequence is preferred, for it neither changes the protein sequence nor the function of the gene of interest. [ 5 ]
Level -1 fragments are used to help cloning large level 0 modules. [ 5 ] To clone level -1 fragments, blunt-end cloning with restriction ligation can be used. [ 5 ] The vector used in cloning level -1 fragments cannot contain Type IIS restriction site BpiI that is used for the following assembly step. [ 5 ] Moreover, the vector should also have a different selection marker from the destination vector in next assembly step, for example, if spectinomycin resistance is used in level 0 modules, level -1 fragments should have another antibiotic resistance like ampicillin. [ 5 ]
The level 1 destination vector determines the position and orientation of each gene in the final construct. [ 10 ] There are fourteen available level 1 vectors, which differ only by the sequence of the flanking fusion sites while being identical in the internal fusion sites. [ 10 ] Hence, all vectors can assemble the same level 0 parts. [ 10 ]
As all level 1 vectors are binary plasmids, they are used for Agrobacterium mediated temporary expression in plants. [ 10 ]
Level 2 vectors have two inverted BpiI sites from the insertion of level 1 modules. [ 10 ] The upstream fusion site is compatible to a gene cloned in level 1 vector while the downstream fusion site has a universal sequence. [ 10 ] Each cloning allows 2-6 genes to be inserted in the same vector. [ 10 ]
Adding more genes in one cloning step is not recommended, for this would result in incorrect constructs. [ 10 ] On one hand, this can induce more restriction sites in the construct, where this open construct allows additional genes be added. [ 10 ] On the other hand, this can also eliminate restriction sites, where this close construct stop the further addition of genes. [ 10 ]
Therefore, constructs of more than six genes need successive cloning steps, which requires end-linkers containing BsaI or BsmBI internal restriction sites and blue or purple markers. [ 10 ] Each cloning step needs to alternate the restriction site and the marker. [ 10 ] Furthermore, two restriction enzymes are needed, where BpiI is used for releasing level 1 modules from level 1 constructs and BsaI/BsmBI is for digesting and opening the recipient level 2-n plasmid. [ 10 ] When screening, the correct colonies should alternate from blue to purple every cloning step, but if a "closed" end-linker is used, the colonies will be white. [ 10 ]
Level M vectors are similar to level 2 vectors, but have a BsaI site located upstream of the two inverted BpiI sites. [ 11 ] When one or several genes are cloned in a level M vector, a second BsaI is added at the end of the construct via a Level M end-linker (ref). This allows a fragment containing all assembled genes to be excised from the vector and subcloned in a next level of cloning (Level P).
Level P vectors are similar to level M constructs except that the BpiI sites are replaced by BsaI sites and the BsaI sites are replaced by BpiI sites. Several level M constructs with compatible fusion sites can be subcloned into a level P vector in one step. Theoretically, as many as 36 genes can be assembled in one construct using 6 parallel level M reactions (each required for assembly of 6 genes per level M construct) followed by one final level P reaction. In practice, fewer genes are usually assembled as most cloning projects do not require so many genes.
The structure of level M and P vectors is designed in a such as way that genes cloned in level P constructs can be further assembled in level M vectors. Repeated cloning in level M and P vectors forms a loop that can be repeated indefinitely to assemble progressively large constructs.
In standard Golden Gate Cloning, the restriction sites from the previous tier construct cannot be reused. [ 12 ] To add more genes to the construct, restriction sites of a different Type IIS restriction enzyme need to be added to the destination vector. [ 12 ] This can be done using either level 2, or M and P. A variant version of level M and P is also provided by GoldenBraid.
GoldenBraid overcomes the problem of designing numerous destination vectors by having a double loop, which is the "braid," to allow binary assembly of multiple constructs. [ 12 ] There are two levels of destination plasmids, level α and level Ω. [ 12 ] Each level of plasmids can be used as entry plasmids for the other level of plasmids for multiple times because both levels of plasmids have different Type IIS restriction sites that are in inverted orientation. [ 12 ] For counterselection, the two levels of plasmids differ in their antibiotic resistance markers. [ 12 ]
The Golden Gate Cloning principle can also be applied to perform mutagenesis termed Golden Mutagenesis. The technology is easy to implement as a web tool is available for primer design ( https://msbi.ipb-halle.de/GoldenMutagenesisWeb/ ) and the vectors are deposited at addgene ( http://www.addgene.org/browse/article/28196591/ ). [ 13 ]
The name Golden Gate Assembly comes from a proposal of Yuri Gleba . [ 1 ] It shall refer on the one hand to the Gateway Technology , on the other hand picture the higher precision with a bridge connecting the streets of two shores seamlessly. One of the most well known bridges is the Golden Gate Bridge in San Francisco . | https://en.wikipedia.org/wiki/Golden_Gate_Cloning |
The Golden Goose Award is a United States award in recognition of scientists whose federally funded basic research has led to innovations or inventions with significant impact on humanity or society. Created by Congressman Jim Cooper of Tennessee in 2012, recipients receive the award in a ceremony during the fall each year on Capitol Hill in Washington D.C. [ 1 ]
Between 1975 and 1988, William Proxmire , a Democratic United States Senator for Wisconsin awarded the tongue-in-cheek Golden Fleece Awards to public officials for spending public money in ways he considered irresponsible or wasteful. These awards were often given to scientists working on seemingly obscure federally funded scientific studies causing ridicule and scrutiny of the usefulness of such research.
The Golden Goose Awards were established over two decades later in order to highlight the value of federally-funded basic research. With the Golden Goose Award, Cooper wanted to reverse the image created by Proxmire's award by highlighting examples of seemingly obscure studies that have led to major breakthroughs and resulted in significant societal impact. [ 2 ] [ 3 ] The award has bipartisan support in Congress, sponsored by multiple organizations and legislators.
Some of the twelve founding organizations for this award are the American Association for the Advancement of Science (AAAS), the Association of American Universities (AAU), the Association of Public and Land-grant Universities (A۰P۰L۰U), the Breakthrough Institute , the Progressive Policy Institute (PPI), and The Science Coalition (TSC) [ 3 ] | https://en.wikipedia.org/wiki/Golden_Goose_Award |
The Golden LEAF Biomanufacturing Training and Education Center (BTEC) is a multidisciplinary instructional center at North Carolina State University that provides education and training to develop skilled professionals for the biomanufacturing industry. Biomanufacturing refers to the use of living organisms or other biological material to produce commercially viable products. Examples include therapeutic proteins, monoclonal antibodies , and vaccines for medical use; amino acids and enzymes for food manufacturing; and biofuels and biochemicals for industrial applications. BTEC provides hands-on education and training in bioprocessing concepts and biomanufacturing methods that comply with cGMP (current Good Manufacturing Practice), a set regulations published by the United States Food and Drug Administration (FDA) .
BTEC reports administratively through the university's College of Engineering and is guided by an advisory board made up of representatives from the biomanufacturing industry and other organizations interested in biotechnology and biomanufacturing.
In 2003, North Carolina's Golden LEAF Foundation provided almost $39 million to build BTEC, as part of a larger grant to establish a statewide public-private partnership now called NCBioImpact . [ 1 ] [ 2 ] The state of North Carolina provided funds for process equipment and supports the operation of the facility. The NCBioImpact partnership now includes BTEC, BRITE (Biomanufacturing Research Institute and Technology Enterprise) at North Carolina Central University , North Carolina BioNetwork of the North Carolina Community College System , NCBIO (North Carolina Biosciences Organization), the North Carolina Biotechnology Center , and the Golden LEAF Foundation. It was created to provide workforce training and development for the biotechnology industry, thereby fostering the growth of this economic sector in the state. According to the North Carolina Biotechnology Center, North Carolina is home to 528 biotechnology companies that provide 57,000 jobs and $1.92 billion in taxes for state and local government. [ 3 ] Employment in the industry has grown 4.1% from 2008 to 2010, when other industries shed thousands of jobs. [ 4 ] In recent years some of the world's largest pharmaceutical companies, e.g. Novartis and Merck & Co , have located and/or expanded manufacturing operations in North Carolina. [ 5 ] [ 6 ]
BTEC opened in fall 2007 and was the first facility dedicated to biomanufacturing training. [ 7 ] BTEC is 82,500 gross square feet and contains 63,000-gross square feet of laboratories, which range from small or bench scale to large-scale suites that simulate a biomanufacturing pilot plant capable of producing biopharmaceutical products. Upstream processes utilize bacteria, yeast, animal cells , and insect cells. Equipment in these spaces includes the following:
The main BTEC facility is home to the North Carolina Community College System's BioNetwork Capstone Center, which operates an aseptic processing/filling suite and several bench-scale labs. [ 8 ] In 2012, BTEC completed construction of additional laboratories in a nearby facility for cell culture, purification, and processing of active virus.
BTEC delivers undergraduate and graduate courses to North Carolina State University students. Academic programs include the following:
Curriculum was created with extensive input from industry professionals, and most courses include substantial hands-on laboratory work. Most BTEC courses are offered in a half-semester (eight-week) format, which enables students to complete a series of courses in one academic year.
BTEC collaborates with industry partners to design, develop and deliver courses that provide professionals working for biomanufacturing companies, equipment vendors, or regulatory agencies with continuing education opportunities. Open-enrollment courses are offered throughout the year and are available to all interested parties. BTEC also regularly delivers courses customized to meet a client's specific needs for training.
BTEC provides biomanufacturing training specified in contracts of grants to provide training for government agencies. In 2007, the FDA awarded BTEC a 5-year contract to develop and deliver biomanufacturing training for FDA inspectors. [ 9 ] In 2010, BTEC received a grant for almost $900,000 from Biomedical Advanced Research and Development Authority (BARDA), part of the United States Department of Health and Human Services . [ 10 ] With funding from this grant, a team of instructors from BTEC, Duke University , and industry provide a three-week course on influenza vaccine manufacturing. Trainees were selected by institutions participating in a U.S. government-sponsored program to build vaccine production capacity among countries with developing economies. Countries represented included Egypt, India, Indonesia, Mexico, Romania, Serbia, Russia, South Korea, Thailand, and Vietnam.
When laboratories are not being used for training, BTEC uses them to perform a variety of services for scientists from industry, government, and academia. Projects involve technology development, process improvement/scale-up, analytical testing, and preparation of material for preclinical studies. These services allow scientists to advance their research projects toward commercialization. In turn, these advancements stimulate the North Carolina economy.
BTEC is located on the Centennial Campus of North Carolina State University in Raleigh, North Carolina , United States. The campus is approximately 15 miles east of Research Triangle Park and Raleigh-Durham International Airport . | https://en.wikipedia.org/wiki/Golden_LEAF_Biomanufacturing_Training_and_Education_Center |
The golden age of Spanish software ( Spanish : edad de oro del software español ) [ 1 ] [ 2 ] was a time between 1983 and 1992, when Spain became the second largest 8-bit computer entertainment software producer in Europe, [ 3 ] only behind the United Kingdom . [ citation needed ] The widespread adoption of 16-bit technology and rampant software piracy led to it abruptly stopping around 1992, [ 4 ] [ 5 ] during which many software companies based in Spain launched their career: Dinamic Software , Topo Soft , Opera Soft , Made in Spain and Zigurat among others. The name Edad de oro del soft español was coined by specialized magazines of the time and has been used to refer to these years until nowadays.
In the year 1983, the first home personal computers started arriving in Spain, all of them 8 bit machines. ZX Spectrum and Amstrad CPC were the most sold in the country, [ 6 ] followed by MSX and Commodore 64 among others. [ 7 ] These were simple machines, with lesser resources, therefore easy to manipulate, so many young programmers all over the country started experimenting with them. [ 8 ]
The Golden Era of Spanish Software officially starts with the launch of Bugaboo , by PACO & PACO, the first Spanish video game to get a massive international distribution. Shortly, Fred (Roland on the ropes for Amstrad), by others authors, this time under the company Made in Spain , was another success, and the owners of Made in Spain decided to create Zigurat , a mother company that would at first be dedicated to distribution, turning Made in Spain into a producing company for Zigurat, which also would at first distribute titles from independent companies. Years later, Made in Spain and Zigurat would completely merge into a single producer and distributor company.
Meanwhile, Dinamic Software made their first steps when they launched Yenght for ZX Spectrum, which was a text adventure. And in the field of distribution, Erbe Software, the main Spanish software distributor for more than a decade, started their activity. In their first years, Erbe tried also to produce their own titles, but in this activity they did not last for long.
In 1985, with the birth of magazines Micromanía and Microhobby , videogames gained massive popularity, and the rest of the top companies of the Era, Opera Soft in 1986 and Topo Soft in 1987 started their activity, the first one with Livingstone, I presume , and the second one with Spirits , after their authors programmed for Erbe Software Las tres luces de Glaurung ( Conquestador ).
The just born Zigurat had their biggest success as Sir Fred and El misterio del Nilo , an unofficial version of the movie The Jewel of the Nile , which caused problems internationally because one of the characters of the game was too similar to Michael Douglas , and the authors were forced to change the graphic design of this character in the international versions.
Dinamic had their first huge successes in the Johny Jones trilogy, comprising Saimazoom , Babaliba , and mainly Abu Simbel Profanation . After this, they would start another trilogy, the Moves trilogy, comprising Army Moves , Navy Moves , and much later Arctic Moves . And little by little, publishing titles starring famous sportsmen became popular. Dinamic were the first, with Basket Master starring Fernando Martín , and they were followed by other companies, with titles starring Ángel Nieto , Carlos Sainz , Poli Díaz , Emilio Butragueño and others.
Meanwhile, Opera Soft published Goody , Sol Negro , Cosa Nostra , and above all, La Abadía del Crimen , based on Umberto Eco 's The Name of the Rose '. [ 9 ] On the other hand, Topo Soft, the last of the big ones, quickly arrived on top with titles like Mad Mix Game and its continuation, and Survivor among others.
Meanwhile, Dinamic published a text adventure version of Don Quijote , and after that, a section of Dinamic dedicated only to text adventures became independent, and they named themselves Aventuras AD , publishing titles like El Jabato among others.
In 1985 the 16/32-bit Amiga and Atari ST arrived, and little by little, IBM PC compatibles , followed by consoles like SNES and Mega Drive . Although the Spanish companies did some tiny efforts to evolve, they never really switched to 16-bits and concentrated on the declining 8-bit market which, almost extinct in Europe, still had strength in Spain, mainly thanks to the rule Erbe Software, main distributor in the country, imposing a sales price of 875 pesetas (5,26 euros) for all their titles, trying to put an end to piracy.
But at this moment, Spanish companies started having serious financial problems, and one by one they launched their last titles. Topo Soft funders left the company in 1989 to establish Animagic, whose main title was Mortadelo y Filemon II ( Clever and Smart II ). Born in bad times, they did not last for long. On the other hand, Topo Soft launched Lorna , Journey to the Center of the Earth , and above all, Gremlins 2 , is the first time a Spanish video game company managed to get an exclusive license for all Europe from a Hollywood movie. In 1991, aware of the importance of 16 bit, they tried to switch, with the project of creating a desktop environment for MS-DOS, but the project did not succeed, and Topo closed on bankruptcy in 1992.
Meanwhile, Opera Soft, after publishing Gonzalezzz , Mot and Angel Nieto Pole 500 , starts decaying like the rest of the companies. In their last months, they launched titles like La Colmena and one dedicated to Barcelona 92 , to disappear shortly after. Some of their components, like Gonzalo Suárez Girard (Gonzo Suárez), would later move to Pyro Studios launching titles like Commandos: Behind Enemy Lines among others.
Aventuras AD, paradoxically, had their most successful period during this time of decline, launching the most of their titles during this time, mainly the Ci-U-Than Legends trilogy, composed of La Diosa de Cozumel , Los Templos Sagrados and Chichén Itzá , being pioneers in Spain creating a predecessor of graphic adventures with La Aventura Espacial , a text adventure controlled by menus. Nevertheless, the sales did not last for long, and Aventuras AD disappeared in 1992.
Zigurat and Dinamic were the only companies which survived from the Golden Era of Spanish Software, although they had to transform and abandon their previous activity. Zigurat, after an 8-bit market collapsed, started developing coin up arcade games, lasting for many years. Dinamic Software, on the other hand, after publishing After the War , Narco Police and Risky Woods , closed on bankruptcy and was refounded as Dinamic Multimedia in 1993, having in PC Fútbol as their biggest success during the 1990s. However, the dot-com bubble finished Dinamic Multimedia in 2001, but before this, the original founders of the company, who had left it in 1999, had already founded FX Interactive , which is still known nowadays.
The 1990s and 2000s have been described as "lost decades" for the Spanish video game industry. However, Alberto Flores de Rio wrote in the Encyclopedia of Video Games that the 2010s may be a resurgence for Spanish-based game development. Akaoni Studio and MercurySteam started off the decade with financially successful games. [ 10 ] Alejando Alcolea of Hobby Consolas called 2015 the possible start for a "second golden age of Spanish software". [ 11 ] | https://en.wikipedia.org/wiki/Golden_age_of_Spanish_software |
In geometry , the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio ; that is, into two arcs such that the ratio of the length of the smaller arc to the length of the larger arc is the same as the ratio of the length of the larger arc to the full circumference of the circle.
Algebraically, let a+b be the circumference of a circle , divided into a longer arc of length a and a smaller arc of length b such that
The golden angle is then the angle subtended by the smaller arc of length b . It measures approximately 137.507 764 050 037 854 646 3487 ...° OEIS : A096627 or in radians 2.399 963 229 728 653 32 ... OEIS : A131988 .
The name comes from the golden angle's connection to the golden ratio φ ; the exact value of the golden angle is
or
where the equivalences follow from well-known algebraic properties of the golden ratio.
As its sine and cosine are transcendental numbers , the golden angle cannot be constructed using a straightedge and compass . [ 1 ]
The golden ratio is equal to φ = a / b given the conditions above.
Let ƒ be the fraction of the circumference subtended by the golden angle, or equivalently, the golden angle divided by the angular measurement of the circle.
But since
it follows that
This is equivalent to saying that φ 2 golden angles can fit in a circle.
The fraction of a circle occupied by the golden angle is therefore
The golden angle g can therefore be numerically approximated in degrees as:
or in radians as :
The golden angle plays a significant role in the theory of phyllotaxis ; for example, the golden angle is the angle separating the florets on a sunflower . [ 2 ] Analysis of the pattern shows that it is highly sensitive to the angle separating the individual primordia , with the Fibonacci angle giving the parastichy with optimal packing density. [ 3 ]
Mathematical modelling of a plausible physical mechanism for floret development has shown the pattern arising spontaneously from the solution of a nonlinear partial differential equation on a plane. [ 4 ] [ 5 ] | https://en.wikipedia.org/wiki/Golden_angle |
A golden number (sometimes capitalized) is a number assigned to each year in sequence which is used to indicate the dates of all the calendric new moons for each year in a 19-year Metonic cycle . They are used in computus (the calculation of the date of Easter ) and also in Runic calendars . The golden number of any Julian or Gregorian calendar year can be calculated by dividing the year by 19, taking the remainder, and adding 1. (In mathematics this can be expressed as ( year number modulo 19) + 1.)
For example, 2025 divided by 19 gives 106, remainder 11. Adding 1 to the remainder gives a golden number of 12.
The golden number, as it was later called, first appears in a calendar composed by Abbo of Fleury around the year 1000. Around 1162 a certain Master William referred to this number as the golden number "because it is more precious than the other numbers." [ 1 ] The name refers to the practice of printing golden numbers in gold. [ 2 ] The term became widely known and used, in part through the computistic poem Massa Compoti written by Alexander de Villa Dei around 1200. [ 3 ] | https://en.wikipedia.org/wiki/Golden_number_(time) |
Golden rain demonstration is made by combining two colorless solutions, potassium iodide solution and Lead(II) nitrate solution at room temperature to form yellow precipitate . During the chemical reaction, golden particles gently drop from the top of Erlenmeyer flask to the bottom, similar to watching the rain through a window. The golden rain chemical reaction demonstrates the formation of a solid precipitate . The golden rain experiment involves two soluble ionic compounds, potassium iodide (KI) and lead(II) nitrate (Pb(NO 3 ) 2 ). They are initially dissolved in separate water solutions, which are each colorless. When mixed, as the lead from one solution and the iodide from the other combine to form lead(II) iodide (PbI 2 ), which is insoluble at low temperature and has a bright golden-yellow color. Although this is a reaction solely of the dissociated ions in solution, it is sometimes referred to as a double displacement reaction : [ 1 ]
At higher temperature, this substance easily re-dissolves by dissociation to its colorless ions. The actual change ( net ionic equation ) is thus: | https://en.wikipedia.org/wiki/Golden_rain_demonstration |
Golden ratio base is a non-integer positional numeral system that uses the golden ratio (the irrational number 1 + 5 2 {\textstyle {\frac {1+{\sqrt {5}}}{2}}} ≈ 1.61803399 symbolized by the Greek letter φ ) as its base . It is sometimes referred to as base-φ , golden mean base , phi-base , or, colloquially, phinary . Any non-negative real number can be represented as a base-φ numeral using only the digits 0 and 1, and avoiding the digit sequence "11" – this is called a standard form . A base-φ numeral that includes the digit sequence "11" can always be rewritten in standard form, using the algebraic properties of the base φ — most notably that φ n + φ n −1 = φ n +1 . For instance, 11 φ = 100 φ .
Despite using an irrational number base, when using standard form, all non-negative integers have a unique representation as a terminating (finite) base-φ expansion. The set of numbers which possess a finite base-φ representation is the ring Z [ 1 + 5 2 {\textstyle {\frac {1+{\sqrt {5}}}{2}}} ] ; it plays the same role in this numeral systems as dyadic rationals play in binary numbers , providing a possibility to multiply .
Other numbers have standard representations in base-φ, with rational numbers having recurring representations. These representations are unique, except that numbers with a terminating expansion also have a non-terminating expansion. For example, 1 = 0.1010101… in base-φ just as 1 = 0.99999… in decimal .
In the following example of conversion from non-standard to standard form, the notation 1 is used to represent the signed digit −1.
211.0 1 φ is not a standard base-φ numeral, since it contains a "11" and additionally a "2" and a " 1 " = −1, which are not "0" or "1".
To put a numeral in standard form, we may use the following substitutions: 0 1 _ 0 ϕ = 1 _ 01 ϕ {\displaystyle 0{\underline {1}}0_{\phi }={\underline {1}}01_{\phi }} , 1 1 _ 0 ϕ = 001 ϕ {\displaystyle 1{\underline {1}}0_{\phi }=001_{\phi }} , 200 ϕ = 1001 ϕ {\displaystyle 200_{\phi }=1001_{\phi }} , 011 ϕ = 100 ϕ {\displaystyle 011_{\phi }=100_{\phi }} . The substitutions may be applied in any order we like, as the result will be the same. Below, the substitutions applied to the number on the previous line are on the right, the resulting number on the left.
211.0 1 _ 0 ϕ = 211 . 1 _ 01 ϕ 0 1 _ 0 → 1 _ 01 = 210 .011 ϕ 1 1 _ 0 → 001 = 1011 .011 ϕ 200 → 1001 = 1100 .100 ϕ 011 → 100 = 10000 .1 ϕ 011 → 100 {\displaystyle {\begin{aligned}211.0{\underline {1}}0_{\phi }=211&.{\underline {1}}01_{\phi }&0{\underline {1}}0\rightarrow {\underline {1}}01\\=210&.011_{\phi }&1{\underline {1}}0\rightarrow 001\\=1011&.011_{\phi }&200\rightarrow 1001\\=1100&.100_{\phi }&011\rightarrow 100\\=10000&.1_{\phi }&011\rightarrow 100\\\end{aligned}}}
Any positive number with a non-standard terminating base-φ representation can be uniquely standardized in this manner. If we get to a point where all digits are "0" or "1", except for the first digit being negative , then the number is negative. (The exception to this is when the first digit is negative one and the next two digits are one, like 1 111.001=1.001.) This can be converted to the negative of a base-φ representation by negating every digit, standardizing the result, and then marking it as negative. For example, use a minus sign , or some other significance to denote negative numbers.
We can either consider our integer to be the (only) digit of a nonstandard base-φ numeral, and standardize it, or do the following:
1 × 1 = 1, φ × φ = 1 + φ and 1 / φ = −1 + φ. Therefore, we can compute
and
So, using integer values only, we can add, subtract and multiply numbers of the form ( a + b φ), and even represent positive and negative integer powers of φ.
( a + b φ) > ( c + d φ) if and only if 2( a − c ) − ( d − b ) > ( d − b ) × √ 5 . If one side is negative, the other positive, the comparison is trivial. Otherwise, square both sides, to get an integer comparison, reversing the comparison direction if both sides were negative. On squaring both sides, the 5 {\textstyle {\sqrt {5}}} is replaced with the integer 5.
So, using integer values only, we can also compare numbers of the form ( a + b φ).
The above procedure will never result in the sequence "11", since 11 φ = 100 φ , so getting a "11" would mean we missed a "1" prior to the sequence "11".
Start, e.g., with integer = 5, with the result so far being ...00000.00000... φ
Highest power of φ ≤ 5 is φ 3 = 1 + 2φ ≈ 4.236067977
Subtracting this from 5, we have 5 − (1 + 2φ) = 4 − 2φ ≈ 0.763932023..., the result so far being 1000.00000... φ
Highest power of φ ≤ 4 − 2φ ≈ 0.763932023... is φ −1 = −1 + 1φ ≈ 0.618033989...
Subtracting this from 4 − 2φ ≈ 0.763932023..., we have 4 − 2φ − (−1 + 1φ) = 5 − 3φ ≈ 0.145898034..., the result so far being 1000.10000... φ
Highest power of φ ≤ 5 − 3φ ≈ 0.145898034... is φ −4 = 5 − 3φ ≈ 0.145898034...
Subtracting this from 5 − 3φ ≈ 0.145898034..., we have 5 − 3φ − (5 − 3φ) = 0 + 0φ = 0, with the final result being 1000.1001 φ .
Just as with any base-n system, numbers with a terminating representation have an alternative recurring representation. In base-10, this relies on the observation that 0.999...=1 . In base-φ, the numeral 0.1010101... can be seen to be equal to 1 in several ways:
This non-uniqueness is a feature of the numeration system, since both 1.0000 and 0.101010... are in standard form.
In general, the final 1 of any number in base-φ can be replaced with a recurring 01 without changing the value of that number.
Every non-negative rational number can be represented as a recurring base-φ expansion, as can any non-negative element of the field Q [ √ 5 ] = Q + √ 5 Q , the field generated by the rational numbers and 5 {\textstyle {\sqrt {5}}} . Conversely any recurring (or terminating) base-φ expansion is a non-negative element of Q [ √ 5 ]. For recurring decimals, the recurring part has been overlined:
The justification that a rational gives a recurring expansion is analogous to the equivalent proof for a base- n numeration system ( n = 2,3,4,...). Essentially in base-φ long division there are only a finite number of possible remainders, and so once there must be a recurring pattern. For example, with 1 / 2 = 1 / 10.01 φ = 100 φ / 1001 φ long division looks like this (note that base-φ subtraction may be hard to follow at first):
The converse is also true, in that a number with a recurring base-φ; representation is an element of the field Q [ √ 5 ]. This follows from the observation that a recurring representation with period k involves a geometric series with ratio φ −k , which will sum to an element of Q [ √ 5 ].
The base-φ representations of some interesting numbers:
It is possible to adapt all the standard algorithms of base-10 arithmetic to base-φ arithmetic. There are two approaches to this:
For addition of two base-φ numbers, add each pair of digits, without carry, and then convert the numeral to standard form. For subtraction , subtract each pair of digits without borrow (borrow is a negative amount of carry), and then convert the numeral to standard form. For multiplication , multiply in the typical base-10 manner, without carry, then convert the numeral to standard form.
For example,
A more "native" approach is to avoid having to add digits 1+1 or to subtract 0 – 1. This is done by reorganising the operands into nonstandard form so that these combinations do not occur. For example,
The subtraction seen here uses a modified form of the standard "trading" algorithm for subtraction.
No non-integer rational number can be represented as a finite base-φ number. In other words, all finitely representable base-φ numbers are either integers or (more likely) an irrational in a quadratic field Q [ √ 5 ]. Due to long division having only a finite number of possible remainders, a division of two integers (or other numbers with finite base-φ representation) will have a recurring expansion, as demonstrated above.
Fibonacci coding is a closely related numeration system used for integers. In this system, only digits 0 and 1 are used and the place values of the digits are the Fibonacci numbers . As with base-φ, the digit sequence "11" is avoided by rearranging to a standard form, using the Fibonacci recurrence relation F k +1 = F k + F k −1 . For example,
It is possible to mix base-φ arithmetic with Fibonacci integer sequences . The sum of numbers in a General Fibonacci integer sequence that correspond with the nonzero digits in the base-φ number, is the multiplication of the base-φ number and the element at the zero-position in the sequence. For example: | https://en.wikipedia.org/wiki/Golden_ratio_base |
In geometry , a golden rectangle is a rectangle with side lengths in golden ratio 1 + 5 2 : 1 , {\displaystyle {\tfrac {1+{\sqrt {5}}}{2}}:1,} or φ : 1 , {\displaystyle \varphi :1,} with φ {\displaystyle \varphi } approximately equal to 1.618 or 89/55.
Golden rectangles exhibit a special form of self-similarity : if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well.
Owing to the Pythagorean theorem , the diagonal dividing one half of a square equals the radius of a circle whose outermost point is the corner of a golden rectangle added to the square. [ 1 ] Thus, a golden rectangle can be constructed with only a straightedge and compass in four steps:
A distinctive feature of this shape is that when a square section is added—or removed—the product is another golden rectangle, having the same aspect ratio as the first. Square addition or removal can be repeated infinitely, in which case corresponding corners of the squares form an infinite sequence of points on the golden spiral , the unique logarithmic spiral with this property. Diagonal lines drawn between the first two orders of embedded golden rectangles will define the intersection point of the diagonals of all the embedded golden rectangles; Clifford A. Pickover referred to this point as "the Eye of God". [ 2 ]
Divide a square into four congruent right triangles with legs in ratio 1 : 2 and arrange these in the shape of a golden rectangle, enclosing a similar rectangle that is scaled by factor 1 φ {\displaystyle {\tfrac {1}{\varphi }}} and rotated about the centre by arctan ( 1 2 ) . {\displaystyle \arctan({\tfrac {1}{2}}).} Repeating the construction at successively smaller scales results in four infinite sequences of adjoining right triangles, tracing a whirl of converging golden rectangles. [ 3 ]
The logarithmic spiral through the vertices of adjacent triangles has polar slope k = ln ( φ ) arctan ( 1 2 ) . {\displaystyle k={\frac {\ln(\varphi )}{\arctan({\tfrac {1}{2}})}}.} The parallelogram between the pair of upright grey triangles has perpendicular diagonals in ratio φ {\displaystyle \varphi } , hence is a golden rhombus .
If the triangle has legs of lengths 1 and 2 then each discrete spiral has length φ 2 = ∑ n = 0 ∞ φ − n . {\displaystyle \varphi ^{2}=\sum _{n=0}^{\infty }\varphi ^{-n}.} The areas of the triangles in each spiral region sum to φ = ∑ n = 0 ∞ φ − 2 n ; {\displaystyle \varphi =\sum _{n=0}^{\infty }\varphi ^{-2n};} the perimeters are equal to 5 + 5 {\displaystyle 5+{\sqrt {5}}} (grey) and 4 φ {\displaystyle 4\varphi } (yellow regions).
The proportions of the golden rectangle have been observed as early as the Babylonian Tablet of Shamash (c. 888–855 BC) , [ 4 ] though Mario Livio calls any knowledge of the golden ratio before the Ancient Greeks "doubtful". [ 5 ]
According to Livio, since the publication of Luca Pacioli 's Divina proportione in 1509, "the Golden Ratio started to become available to artists in theoretical treatises that were not overly mathematical, that they could actually use." [ 6 ]
The 1927 Villa Stein designed by Le Corbusier , some of whose architecture utilizes the golden ratio , features dimensions that closely approximate golden rectangles. [ 7 ]
Euclid gives an alternative construction of the golden rectangle using three polygons circumscribed by congruent circles: a regular decagon , hexagon , and pentagon . The respective lengths a , b , and c of the sides of these three polygons satisfy the equation a 2 + b 2 = c 2 , so line segments with these lengths form a right triangle (by the converse of the Pythagorean theorem ). The ratio of the side length of the hexagon to the decagon is the golden ratio, so this triangle forms half of a golden rectangle. [ 8 ]
The convex hull of two opposite edges of a regular icosahedron forms a golden rectangle. The twelve vertices of the icosahedron can be decomposed in this way into three mutually-perpendicular golden rectangles, whose boundaries are linked in the pattern of the Borromean rings . [ 9 ]
Assume a golden rectangle has been constructed as indicated above, with height 1 , length φ {\displaystyle \varphi } and diagonal length φ 2 + 1 {\displaystyle {\sqrt {\varphi ^{2}+1}}} . The triangles on the diagonal have altitudes 1 / 1 + φ − 2 ; {\displaystyle 1/{\sqrt {1+\varphi ^{-2}}}\,;} each perpendicular foot divides the diagonal in ratio φ 2 . {\displaystyle \varphi ^{2}.}
If a horizontal line is drawn through the intersection point of the diagonal and the internal edge of the square, the original golden rectangle and the two scaled copies along the diagonal have linear sizes in the ratios φ 2 : φ : 1 , {\displaystyle \varphi ^{2}:\varphi :1\,,} the square and rectangle opposite the diagonal both have areas equal to φ − 2 . {\displaystyle \varphi ^{-2}.} [ 10 ]
Relative to vertex A , the coordinates of feet of altitudes U and V are ( 1 5 , 1 φ 5 ) {\displaystyle \left({\tfrac {1}{\sqrt {5}}},{\tfrac {1}{\varphi {\sqrt {5}}}}\right)} and ( φ 2 5 , φ 5 ) {\displaystyle \left({\tfrac {\varphi ^{2}}{\sqrt {5}}},{\tfrac {\varphi }{\sqrt {5}}}\right)} ; the length of line segment U V ¯ {\displaystyle {\overline {UV}}} is equal to altitude h . {\displaystyle h.}
If the diagram is further subdivided by perpendicular lines through U and V , the lengths of the diagonal and its subsections can be expressed as trigonometric functions of arguments 72 and 36 degrees, the angles of the golden triangle :
Both the lengths of the diagonal sections and the trigonometric values are elements of quartic number field K = Q ( ( 5 + 5 ) / 2 ) . {\displaystyle K=\mathbb {Q} \left({\sqrt {(5+{\sqrt {5}})/2}}\right).}
The golden rhombus with edge 1 2 {\displaystyle {\tfrac {1}{2}}} has diagonal lengths equal to U V ¯ {\displaystyle {\overline {UV}}} and A U ¯ . {\displaystyle {\overline {AU}}.} The regular pentagon with side length 2 φ = sec ( 36 ) {\displaystyle {\tfrac {2}{\varphi }}=\sec(36)} has area 5 A U ¯ . {\displaystyle 5{\overline {AU}}.} Its five diagonals divide the pentagon into golden triangles and gnomons, and an upturned, scaled copy at the centre. Since the regular pentagon is defined by its side length and the angles of the golden triangle, it follows that all measures can be expressed in powers of φ {\displaystyle \varphi } and the diagonal segments of the golden rectangle, as illustrated above. [ 11 ]
Interpreting the diagonal sections as musical string lengths results in a set of ten corresponding pitches , one of which doubles at the octave . Mapping the intervals in logarithmic scale — with the 'golden octave' equal to φ 4 {\displaystyle \varphi ^{4}} — shows equally tempered semitones , minor thirds and one major second in the span of an eleventh . An analysis in musical terms is substantiated by the single exceptional pitch proportional to U S ¯ {\displaystyle {\overline {US}}} , that approximates the harmonic seventh within remarkable one cent accuracy. [ b ]
This set of ten tones can be partitioned into two modes of the pentatonic scale : the palindromic 'Egyptian' mode (red dots, Chinese rui bin diao ⓘ guqin tuning ) and the stately 'blues minor' mode (blue dots, Chinese man gong diao ⓘ tuning). | https://en.wikipedia.org/wiki/Golden_rectangle |
In geometry , a golden rhombus is a rhombus whose diagonals are in the golden ratio : [ 1 ]
Equivalently, it is the Varignon parallelogram formed from the edge midpoints of a golden rectangle . [ 1 ] Rhombi with this shape form the faces of several notable polyhedra.
The golden rhombus should be distinguished from the two rhombi of the Penrose tiling , which are both related in other ways to the golden ratio but have different shapes than the golden rhombus. [ 2 ]
(See the characterizations and the basic properties of the general rhombus for angle properties.)
The internal supplementary angles of the golden rhombus are: [ 3 ]
By using the parallelogram law (see the basic properties of the general rhombus ): [ 5 ]
The edge length of the golden rhombus in terms of the diagonal length d {\displaystyle d} is:
The diagonal lengths of the golden rhombus in terms of the edge length a {\displaystyle a} are: [ 3 ]
Note: α + β = π {\displaystyle \alpha +\beta =\pi } , hence: sin α = sin β . {\displaystyle \sin \alpha =\sin \beta ~.}
Several notable polyhedra have golden rhombi as their faces.
They include the two golden rhombohedra (with six faces each), the Bilinski dodecahedron (with 12 faces),
the rhombic icosahedron (with 20 faces),
the rhombic triacontahedron (with 30 faces), and
the nonconvex rhombic hexecontahedron (with 60 faces). The first five of these are the only convex polyhedra with golden rhomb faces, but there exist infinitely many nonconvex polyhedra having this shape for all of their faces. [ 7 ] | https://en.wikipedia.org/wiki/Golden_rhombus |
In geometry , a golden spiral is a logarithmic spiral whose growth factor is φ , the golden ratio . [ 1 ] That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.
There are several comparable spirals that approximate, but do not exactly equal, a golden spiral. [ 2 ]
For example, a golden spiral can be approximated by first starting with a rectangle for which the ratio between its length and width is the golden ratio. This rectangle can then be partitioned into a square and a similar rectangle and this rectangle can then be split in the same way. After continuing this process for an arbitrary number of steps, the result will be an almost complete partitioning of the rectangle into squares. The corners of these squares can be connected by quarter- circles . The result, though not a true logarithmic spiral , closely approximates a golden spiral. [ 2 ]
Another approximation is a Fibonacci spiral , which is constructed slightly differently. A Fibonacci spiral starts with a rectangle partitioned into 2 squares. In each step, a square the length of the rectangle's longest side is added to the rectangle. Since the ratio between consecutive Fibonacci numbers approaches the golden ratio as the Fibonacci numbers approach infinity, so too does this spiral get more similar to the previous approximation the more squares are added, as illustrated by the image.
It is sometimes erroneously stated that spiral galaxies and nautilus shells get wider in the pattern of a golden spiral, and hence are related to both φ and the Fibonacci series. [ 3 ] In truth, many mollusk shells including nautilus shells exhibit logarithmic spiral growth, but at a variety of angles usually distinctly different from that of the golden spiral. [ 4 ] [ 5 ] [ 6 ] Although spiral galaxies have often been modeled as logarithmic spirals, Archimedean spirals , or hyperbolic spirals , their pitch angles vary with distance from the galactic center, unlike logarithmic spirals (for which this angle does not vary), and also at variance with the other mathematical spirals used to model them. [ 7 ] Phyllotaxis , the pattern of plant growth, is in some case connected with the golden ratio because it involves successive leaves or petals being separated by the golden angle . Although this can sometimes be associated with spiral forms, such as in sunflower seed heads, [ 8 ] these are more closely related to Fermat spirals than logarithmic spirals. [ 9 ]
A golden spiral with initial radius 1 is the locus of points of polar coordinates ( r , θ ) {\displaystyle (r,\theta )} satisfying r = φ 2 θ / π , {\displaystyle r=\varphi ^{2\theta /\pi },} where φ {\displaystyle \varphi } is the golden ratio.
The polar equation for a golden spiral is the same as for other logarithmic spirals , but with a special value of the growth factor b : [ 10 ] r = a e b θ {\displaystyle r=ae^{b\theta }} or θ = 1 b ln ( r / a ) , {\displaystyle \theta ={\frac {1}{b}}\ln(r/a),} with e being the base of natural logarithms , a being the initial radius of the spiral, and b such that when θ is a right angle (a quarter turn in either direction): e b θ r i g h t = φ . {\displaystyle e^{b\theta _{\mathrm {right} }}=\varphi .}
Therefore, b is given by b = ln φ θ r i g h t . {\displaystyle b={\ln {\varphi } \over \theta _{\mathrm {right} }}.}
The numerical value of b depends on whether the right angle is measured as 90 degrees or as π 2 {\displaystyle \textstyle {\frac {\pi }{2}}} radians ; and since the angle can be in either direction, it is easiest to write the formula for the absolute value of b (that is, b can also be the negative of this value): | b | = ln φ 90 ≐ 0.0053468 {\displaystyle |b|={\ln {\varphi } \over 90}\doteq 0.0053468} for θ in degrees, or | b | = ln φ π / 2 ≐ 0.3063489 {\displaystyle |b|={\ln {\varphi } \over \pi /2}\doteq 0.3063489} for θ in radians. [ 11 ]
An alternate formula for a logarithmic and golden spiral is [ 12 ] r = a c θ {\displaystyle r=ac^{\theta }} where the constant c is given by c = e b {\displaystyle c=e^{b}} which for the golden spiral gives c values of c = φ 1 90 ≐ 1.0053611 {\displaystyle c=\varphi ^{\frac {1}{90}}\doteq 1.0053611} if θ is measured in degrees, and c = φ 2 π ≐ 1.358456 {\displaystyle c=\varphi ^{\frac {2}{\pi }}\doteq 1.358456} if θ is measured in radians. [ 13 ]
With respect to logarithmic spirals the golden spiral has the distinguishing property
that for four collinear spiral points A , B , C , D belonging to arguments θ , θ + π , θ + 2π , θ + 3π the point C is the projective harmonic conjugate of B with respect to A , D , i.e. the cross ratio ( A , D ; B , C ) has the singular value −1.
The golden spiral is the only logarithmic spiral with ( A , D ; B , C ) = ( A , D ; C , B ).
In the polar equation for a logarithmic spiral : r = a e b θ {\displaystyle r=ae^{b\theta }} the parameter b is related to the polar slope angle α {\displaystyle \alpha } : tan α = b . {\displaystyle \tan \alpha =b.}
In a golden spiral, b {\displaystyle b} being constant and equal to | b | = ln φ π / 2 {\displaystyle |b|={\ln {\varphi } \over \pi /2}} (for θ in radians, as defined above), the slope angle α {\displaystyle \alpha } is α = arctan ( | b | ) = arctan ( ln φ π / 2 ) , {\displaystyle \alpha =\arctan(|b|)=\arctan \left({\ln {\varphi } \over \pi /2}\right),} hence α ≐ 17.03239113 {\displaystyle \alpha \doteq 17.03239113} if measured in degrees, or α ≐ 0.2972713047 {\displaystyle \alpha \doteq 0.2972713047} if measured in radians. [ 14 ]
Its complementary angle β = π / 2 − α ≐ 1.273525022 {\displaystyle \beta =\pi /2-\alpha \doteq 1.273525022} in radians, or β = 90 − α ≐ 73 {\displaystyle \beta =90-\alpha \doteq 73} in degrees, is the angle the golden spiral arms make with a line from the center of the spiral. | https://en.wikipedia.org/wiki/Golden_spiral |
A golden triangle , also called a sublime triangle , [ 1 ] is an isosceles triangle in which the duplicated side is in the golden ratio φ {\displaystyle \varphi } to the base side:
The golden triangle is used to form some points of a logarithmic spiral . By bisecting one of the base angles, a new point is created that in turn, makes another golden triangle. [ 4 ] The bisection process can be continued indefinitely, creating an infinite number of golden triangles. A logarithmic spiral can be drawn through the vertices. This spiral is also known as an equiangular spiral, a term coined by René Descartes . "If a straight line is drawn from the pole to any point on the curve, it cuts the curve at precisely the same angle," hence equiangular . [ 5 ] This spiral is different from the golden spiral : the golden spiral grows by a factor of the golden ratio in each quarter-turn, whereas the spiral through these golden triangles takes an angle of 108° to grow by the same factor. [ 6 ]
Closely related to the golden triangle is the golden gnomon , which is the isosceles triangle in which the ratio of the equal side lengths to the base length is the reciprocal 1 φ {\displaystyle {\tfrac {1}{\varphi }}} of the golden ratio φ {\displaystyle \varphi } .
"The golden triangle has a ratio of base length to side length equal to the golden section φ, whereas the golden gnomon has the ratio of side length to base length equal to the golden section φ." [ 7 ]
(The distances AX and CX are both a ′ = a = φ , and the distance AC is b ′ = φ², as seen in the figure.) | https://en.wikipedia.org/wiki/Golden_triangle_(mathematics) |
In physics and mathematics , the Golden–Thompson inequality is a trace inequality between exponentials of symmetric and Hermitian matrices proved independently by Golden (1965) and Thompson (1965) . It has been developed in the context of statistical mechanics , where it has come to have a particular significance.
The Golden–Thompson inequality states that for (real) symmetric or (complex) Hermitian matrices A and B , the following trace inequality holds:
This inequality is well defined, since the quantities on either side are real numbers. For the expression on the right hand side of the inequality, this can be seen by rewriting it as tr ( e A / 2 e B e A / 2 ) {\displaystyle \operatorname {tr} (e^{A/2}e^{B}e^{A/2})} using the cyclic property of the trace .
Let ‖ ⋅ ‖ {\displaystyle \|\cdot \|} denote the Frobenius norm , then the Golden–Thompson inequality is equivalently stated as ‖ e A + B ‖ ≤ ‖ e A e B ‖ . {\displaystyle \|e^{A+B}\|\leq \|e^{A}e^{B}\|.}
The Golden–Thompson inequality can be viewed as a generalization of a stronger statement for real numbers. If a and b are two real numbers, then the exponential of a+b is the product of the exponential of a with the exponential of b :
If we replace a and b with commuting matrices A and B , then the same inequality e A + B = e A e B {\displaystyle e^{A+B}=e^{A}e^{B}} holds.
This relationship is not true if A and B do not commute. In fact, Petz (1994) proved that if A and B are two Hermitian matrices for which the Golden–Thompson inequality is verified as an equality, then the two matrices commute. The Golden–Thompson inequality shows that, even though e A + B {\displaystyle e^{A+B}} and e A e B {\displaystyle e^{A}e^{B}} are not equal, they are still related by an inequality.
Golden inequality ( Golden (1965) ) — If A , B {\textstyle A,B} are Hermitian and positive semidefinite, then tr ( ( A B ) 2 n ) ≤ tr ( ( A 2 1 B 2 1 ) 2 n − 1 ) ≤ tr ( ( A 2 2 B 2 2 ) 2 n − 2 ) ≤ ⋯ ≤ tr ( A 2 n B 2 n ) {\displaystyle \operatorname {tr} ((AB)^{2^{n}})\leq \operatorname {tr} ((A^{2^{1}}B^{2^{1}})^{2^{n-1}})\leq \operatorname {tr} ((A^{2^{2}}B^{2^{2}})^{2^{n-2}})\leq \dots \leq \operatorname {tr} (A^{2^{n}}B^{2^{n}})}
If tr ( ( A B ) 2 n ) ≤ tr ( ( A 2 1 B 2 1 ) 2 n − 1 ) {\textstyle \operatorname {tr} ((AB)^{2^{n}})\leq \operatorname {tr} ((A^{2^{1}}B^{2^{1}})^{2^{n-1}})} for all n {\textstyle n} , then all the other inequalities are also proven as special cases of it. So it suffices to prove that inequality.
n = 0 {\textstyle n=0} case is trivial.
n = 1 {\textstyle n=1} case. Since A , B {\textstyle A,B} are Hermitian and PSD, we can split A {\textstyle A} to ( A ) 2 {\textstyle ({\sqrt {A}})^{2}} , which allows us to write tr ( A B A B ) = ‖ A B A ‖ 2 {\textstyle \operatorname {tr} (ABAB)=\|{\sqrt {A}}B{\sqrt {A}}\|^{2}} , meaning it is a non-negative real number.
Now by Cauchy–Schwarz inequality ,
tr ( A B A B ) = ⟨ A B , B A ⟩ ≤ ‖ A B ‖ ‖ B A ‖ = ‖ A B ‖ 2 = tr ( A B B A ) = tr ( A A B B ) {\displaystyle {\begin{aligned}\operatorname {tr} (ABAB)&=\langle AB,BA\rangle \\&\leq \|AB\|\|BA\|\\&=\|AB\|^{2}\\&=\operatorname {tr} (ABBA)\\&=\operatorname {tr} (AABB)\end{aligned}}}
n ≥ 2 {\textstyle n\geq 2} case. Define two sequences of matrices a k := ( A B ) 2 n − k ( B A ) 2 n − k , b k := ( B A ) 2 n − k ( A B ) 2 n − k {\displaystyle a_{k}:=(AB)^{2^{n-k}}(BA)^{2^{n-k}},\quad b_{k}:=(BA)^{2^{n-k}}(AB)^{2^{n-k}}} which, by construction, are Hermitian and positive semidefinite.
For any N {\textstyle N} , by the cyclic property of trace, { tr ( a k N ) = tr ( ( a k + 1 b k + 1 ) N ) = tr ( b k N ) , ∀ k ∈ 0 : n − 1 tr ( a n N ) = tr ( ( A A B B ) N ) = tr ( b n N ) {\displaystyle {\begin{cases}\operatorname {tr} (a_{k}^{N})&=\operatorname {tr} ((a_{k+1}b_{k+1})^{N})=\operatorname {tr} (b_{k}^{N}),\quad \forall k\in 0:n-1\\\operatorname {tr} (a_{n}^{N})&=\operatorname {tr} ((AABB)^{N})=\operatorname {tr} (b_{n}^{N})\end{cases}}}
By the same argument as n = 1 {\textstyle n=1} case, tr ( ( A B ) 2 n ) ≤ tr ( a 1 ) {\displaystyle \operatorname {tr} ((AB)^{2^{n}})\leq \operatorname {tr} (a_{1})} . Apply Cauchy–Schwarz, and the cyclic equalities, tr ( a 1 ) = tr ( a 2 b 2 ) = ⟨ a 2 , b 2 ⟩ ≤ ‖ a 2 ‖ ‖ b 2 ‖ = ‖ a 2 ‖ 2 = tr ( a 2 a 2 ) {\displaystyle {\begin{aligned}\operatorname {tr} (a_{1})&=\operatorname {tr} (a_{2}b_{2})\\&=\langle a_{2},b_{2}\rangle \\&\leq \|a_{2}\|\|b_{2}\|\\&=\|a_{2}\|^{2}\\&=\operatorname {tr} (a_{2}a_{2})\end{aligned}}}
If n = 2 {\textstyle n=2} , then tr ( a 2 a 2 ) = tr ( ( A A B B ) 2 ) {\textstyle \operatorname {tr} (a_{2}a_{2})=\operatorname {tr} ((AABB)^{2})} .
Otherwise, by induction, tr ( a 2 a 2 ) = tr ( ( a 3 b 3 ) 2 ) ≤ tr ( a 3 a 3 b 3 b 3 ) {\displaystyle \operatorname {tr} (a_{2}a_{2})=\operatorname {tr} ((a_{3}b_{3})^{2})\leq \operatorname {tr} (a_{3}a_{3}b_{3}b_{3})} and continuing the same argument, tr ( a 3 a 3 b 3 b 3 ) ≤ tr ( a 3 4 ) {\displaystyle \operatorname {tr} (a_{3}a_{3}b_{3}b_{3})\leq \operatorname {tr} (a_{3}^{4})} . This continues until we obtain ≤ tr ( a n 2 n − 1 ) = tr ( ( A A B B ) 2 n − 1 ) {\textstyle \leq \operatorname {tr} (a_{n}^{2^{n-1}})=\operatorname {tr} ((AABB)^{2^{n-1}})} .
Golden–Thompson inequality ( Thompson (1965) ) — Given Hermitian matrices A , B {\textstyle A,B} ,
tr ( e A + B ) ≤ tr ( e A e B ) {\displaystyle \operatorname {tr} (e^{A+B})\leq \operatorname {tr} (e^{A}e^{B})}
By the Lie product formula, tr ( e A + B ) = lim n tr ( ( e A / 2 n e B / 2 n ) 2 n ) {\textstyle \operatorname {tr} (e^{A+B})=\lim _{n}\operatorname {tr} ((e^{A/2^{n}}e^{B/2^{n}})^{2^{n}})} .
By the Golden inequality, tr ( ( e A / 2 n e B / 2 n ) 2 n ) ≤ tr ( e A e B ) {\textstyle \operatorname {tr} ((e^{A/2^{n}}e^{B/2^{n}})^{2^{n}})\leq \operatorname {tr} (e^{A}e^{B})} .
In general, if A and B are Hermitian matrices and ‖ ⋅ ‖ {\displaystyle \|\cdot \|} is a unitarily invariant norm , then ( Bhatia 1997 , Theorem IX.3.7)
The standard Golden–Thompson inequality is a special case of the above inequality, where the norm is the Frobenius norm.
The general case is provable in the same way, since unitarily invariant norms also satisfy the Cauchy-Schwarz inequality. ( Bhatia 1997 , Exercise IV.2.7)
Indeed, for a slightly more general case, essentially the same proof applies. For each p ≥ 1 {\textstyle p\geq 1} , let ‖ A ‖ p p := tr ( A A ∗ ) p / 2 {\textstyle \|A\|_{p}^{p}:=\operatorname {tr} (AA^{*})^{p/2}} be the Schatten norm .
Theorem — For any integer N ≥ 1 {\textstyle N\geq 1} , ‖ e A + B ‖ 2 N ≤ ‖ e A e B ‖ 2 N {\textstyle \|e^{A+B}\|_{2^{N}}\leq \|e^{A}e^{B}\|_{2^{N}}} .
For any integer N ≥ 0 {\textstyle N\geq 0} , ‖ e A + B ‖ 2 N ≤ ‖ e A / 2 e B e A / 2 ‖ 2 N {\textstyle \|e^{A+B}\|_{2^{N}}\leq \|e^{A/2}e^{B}e^{A/2}\|_{2^{N}}} .
At N → ∞ {\textstyle N\to \infty } limit, we obtain the operator norm ‖ e A + B ‖ o p ≤ ‖ e A e B ‖ o p = ‖ e A / 2 e B e A / 2 ‖ o p {\textstyle \|e^{A+B}\|_{op}\leq \|e^{A}e^{B}\|_{op}=\|e^{A/2}e^{B}e^{A/2}\|_{op}} .
It suffices to show that tr ( ( e A + B ) 2 N ) ≤ tr ( ( e 2 A e 2 B ) 2 N − 1 ) {\textstyle \operatorname {tr} ((e^{A+B})^{2^{N}})\leq \operatorname {tr} ((e^{2A}e^{2B})^{2^{N-1}})} . tr ( ( e A + B ) 2 N ) = lim n tr ( ( e 2 N − n A e 2 N − n B ) 2 n ) ≤ lim n tr ( ( e 2 A e 2 B ) 2 N − 1 ) {\displaystyle \operatorname {tr} ((e^{A+B})^{2^{N}})=\lim _{n}\operatorname {tr} ((e^{2^{N-n}A}e^{2^{N-n}B})^{2^{n}})\leq \lim _{n}\operatorname {tr} ((e^{2A}e^{2B})^{2^{N-1}})} by the Golden inequality.
The second claim is proven similarly.
Corollary — Given Hermitian A , B {\textstyle A,B} , if e A ⪯ e B {\textstyle e^{A}\preceq e^{B}} then A ⪯ B {\textstyle A\preceq B} .
For any x {\textstyle x} , we have ⟨ e A x , x ⟩ ≤ ⟨ e B x , x ⟩ {\textstyle \langle e^{A}x,x\rangle \leq \langle e^{B}x,x\rangle } , thus ‖ e A / 2 x ‖ ≤ ‖ e B / 2 x ‖ {\textstyle \|e^{A/2}x\|\leq \|e^{B/2}x\|} .
Thus e − B / 2 e A / 2 {\textstyle e^{-B/2}e^{A/2}} is a contraction map, thus ‖ e − B / 2 e A / 2 ‖ o p ≤ 1 {\textstyle \|e^{-B/2}e^{A/2}\|_{op}\leq 1} , thus ‖ e A / 2 − B / 2 ‖ o p ≤ 1 {\textstyle \|e^{A/2-B/2}\|_{op}\leq 1} , thus all eigenvalues of ( A / 2 − B / 2 ) {\textstyle (A/2-B/2)} are nonpositive, thus A ⪯ B {\textstyle A\preceq B} .
The inequality has been generalized to three matrices by Lieb (1973) and furthermore to any arbitrary number of Hermitian matrices by Sutter, Berta & Tomamichel (2016) . A naive attempt at generalization does not work: the inequality
is false. For three matrices, the correct generalization takes the following form:
where the operator T f {\displaystyle {\mathcal {T}}_{f}} is the derivative of the matrix logarithm given by T f ( g ) = ∫ 0 ∞ d t ( f + t ) − 1 g ( f + t ) − 1 {\displaystyle {\mathcal {T}}_{f}(g)=\int _{0}^{\infty }\operatorname {d} t\,(f+t)^{-1}g(f+t)^{-1}} .
Note that, if f {\displaystyle f} and g {\displaystyle g} commute , then T f ( g ) = g f − 1 {\displaystyle {\mathcal {T}}_{f}(g)=gf^{-1}} , and the inequality for three matrices reduces to the original from Golden and Thompson.
Bertram Kostant ( 1973 ) used the Kostant convexity theorem to generalize the Golden–Thompson inequality to all compact Lie groups. | https://en.wikipedia.org/wiki/Golden–Thompson_inequality |
The Goldich dissolution series is a method of predicting the relative stability or weathering rate of common igneous minerals on the Earth's surface, with minerals that form at higher temperatures and pressures less stable on the surface than minerals that form at lower temperatures and pressures.
S. S. Goldich derived this series in 1938 after studying soil profiles and their parent rocks. [ 1 ] Based on sample analysis from a series of weathered localities, Goldich determined that the weathering rate of minerals is controlled at least in part by the order in which they crystallize from a melt. This order meant that the minerals that crystallized first from the melt were the least stable under earth surface conditions, while the minerals that crystallized last were the most stable. This is not the only control on weathering rate; this rate is dependent on both intrinsic (qualities specific to the minerals) and extrinsic (qualities specific to the environment) variables. [ 1 ] [ 2 ] Climate is a key extrinsic variable, controlling the water to rock ratio, pH , and alkalinity , all of which impact the rate of weathering. [ 1 ] The Goldich dissolution series concerns intrinsic mineral qualities, which were proven both by Goldich as well as preceding scientists to also be important for constraining weathering rates.
Earlier work by Steidtmann [ 3 ] demonstrated that the order of ionic loss of a rock as it weathers is: CO 3 2- , Mg 2+ , Na + , K + , SiO 2 − , Fe 2+/3+ , and finally Al 3+ . Goldich furthered this analysis by noting the relative mineral stability order, which is related to the relative resistance of these ions to leaching. Goldich notes that overall, mafic (rich in iron and magnesium) minerals are less stable than felsic (rich in silica) minerals. The order of stability in the series echoes Bowen's reaction series very well, leading Goldich to suggest that the relative stability at the surface is controlled by crystallization order. [ 4 ]
While Goldich’s original order of mineral weathering potential was qualitative, later work by Michal Kowalski and J. Donald Rimstidt placed in the series in quantitative terms. Kowalski and Rimstidt performed an analysis of mechanical and chemical grain weathering, and demonstrated that the average lifetime of chemically weathered detrital grains quantitatively fit the Goldich sequence extremely well. [ 5 ] This helped to supplement the real-world applicability of the dissolution series. The difference in chemical weathering time can span millions of years. For example, quickest to weather of the common igneous minerals is apatite , which reaches complete weathering in an average of 10 5.48 years, and slowest to weather is quartz, which weathers fully in 10 8.59 years. [ 5 ]
The Goldich dissolution series follows the same pattern of the Bowen's reaction series , with the minerals that are first to crystallize also the first the undergo chemical weathering . [ 4 ] The Bowen’s reaction series dictates that during fractional crystallization, olivine and Ca-plagioclase feldspars are the first to crystalize out of a melt, after which follows pyroxene , amphibole , biotite , Na-plagioglase, orthoclase feldspar, muscovite , and finally, quartz . This order is controlled by the temperature of the melt and its composition. Because earlier crystallizing minerals are more stable at higher temperatures and pressures, these weather the fastest under surface conditions.
Chemical weathering of igneous minerals leads to the formation of secondary minerals, which constitute the weathering products of the parent minerals. Secondary weathering minerals of igneous rocks can be classified mainly as iron oxides , salts , and phyllosilicates . The chemistry of the secondary minerals is controlled in part by the chemistry of the parent rock. Mafic rocks tends to contain higher proportions of magnesium and ferric and ferrous iron, which can lead to secondary minerals high in abundance of these cations, [ 6 ] including serpentine , Al-, Mg- and Ca-rich clays, [ 7 ] and iron oxides such as hematite . [ 6 ] Felsic rocks tends to have relatively higher proportions of potassium and sodium, which can lead to secondary minerals rich in these ions, including Al-, Na- and K-rich clays such as kaolinite , [ 8 ] montmorillonite [ 8 ] and illite . [ 9 ]
The Goldich dissolution series can be applied to Lithosequences , which are a way of characterizing a soil profile based on its parent material. [ 10 ] Lithosequences include soils that have undergone relatively similar weathering conditions, so variations in composition are based on the relative weathering rates of parent minerals. Therefore, the weathering rates of these soils and their compositions are primarily influenced by the relative proportion of minerals in the Goldich dissolution series. [ 10 ]
Experimental work by White and Brantley (2003) highlighted some of the limitations of the Goldich dissolution series, most notably that some variations in weathering rates of different minerals are not as pronounced as Goldich argues. [ 2 ] According to the Goldich dissolution series, anorthite, a plagioclase feldspar, should weather quickly, with a lifetime of 10 5.62 years quantified by Kowalski and Rimstidt. [ 1 ] [ 5 ] Conversely, the lifetime of K-feldspar should be much longer, at 10 8.53 years based again on Kowalski and Rimstidt’s work. However, White and Brantley’s experimental results demonstrate that the relative weathering rates of K-feldspar and plagioclase feldspar are quite similar, and mainly moderated by the extent to which the minerals had already been weathered (in an exponentially decreasing function). This demonstrates that the Goldich series may not apply across all kinds of weathering processes, and likewise does not take into account the effect of exponential decay in weathering rate of a surface. [ 2 ] | https://en.wikipedia.org/wiki/Goldich_dissolution_series |
The Goldilocks principle is named by analogy to the children's story " Goldilocks and the Three Bears ", in which a young girl named Goldilocks tastes three different bowls of porridge and finds she prefers porridge that is neither too hot nor too cold but has just the right temperature. [ 1 ] The concept of "just the right amount" is easily understood and applied to a wide range of disciplines, including developmental psychology , biology , [ 2 ] astronomy , economics [ 3 ] and engineering .
In cognitive science and developmental psychology , the Goldilocks effect or principle refers to an infant 's preference to attend events that are neither too simple nor too complex according to their current representation of the world. [ 4 ] This effect was observed in infants, who are less likely to look away from a visual sequence when the current event is moderately probable, as measured by an idealized learning model.
In astrobiology , the Goldilocks zone refers to the habitable zone around a star . As Stephen Hawking put it, "Like Goldilocks, the development of intelligent life requires that planetary temperatures be 'just right ' ". [ 5 ] The Rare Earth hypothesis uses the Goldilocks principle in the argument that a planet must be neither too far away from nor too close to a star and galactic centre to support life, while either extreme would result in a planet incapable of supporting life. [ 6 ] Such a planet is colloquially called a "Goldilocks Planet". [ 7 ] [ 8 ] Paul Davies has argued for the extension of the principle to cover the selection of our universe from a (postulated) multiverse : "Observers arise only in those universes where, like Goldilocks' porridge, things are by accident 'just right ' ". [ 9 ]
In medicine , it can refer to a drug that can hold both antagonist (inhibitory) and agonist (excitatory) properties. For example, the antipsychotic Aripiprazole causes not only antagonism of dopamine D2 receptors in areas such as the mesolimbic area of the brain (which shows increased dopamine activity in psychosis) but also agonism of dopamine receptors in areas of dopamine hypoactivity, such as the mesocortical area. [ citation needed ]
In economics, a Goldilocks economy sustains moderate economic growth and low inflation, which allows a market-friendly monetary policy . A Goldilocks market occurs when the price of commodities sits between a bear market and a bull market . Goldilocks pricing, also known as good–better–best pricing, is a marketing strategy that uses product differentiation to offer three versions of a product to corner different parts of the market: a high-end version, a middle version, and a low-end version.
In communication, the Goldilocks principle describes the amount, type, and detail of communication necessary in a system to maximise effectiveness while minimising redundancy and excessive scope on the "too much" side and avoiding incomplete or inaccurate communication on the "too little" side. [ 10 ]
In statistics , the "Goldilocks Fit" references a linear regression model that represents the perfect flexibility to reduce the error caused by bias and variance.
In the design sprint , the "Goldilocks Quality" means to create a prototype with just enough quality to evoke honest reactions from customers. [ 11 ]
In machine learning , the Goldilocks learning rate is the learning rate that results in an algorithm taking the fewest steps to achieve minimal loss . Algorithms with a learning rate that is too large often fail to converge at all, while those with too small a learning rate take too long to converge. [ 12 ] | https://en.wikipedia.org/wiki/Goldilocks_principle |
The Goldman–Hodgkin–Katz voltage equation , sometimes called the Goldman equation , is used in cell membrane physiology to determine the resting potential across a cell's membrane, taking into account all of the ions that are permeant through that membrane.
The discoverers of this are David E. Goldman of Columbia University , and the Medicine Nobel laureates Alan Lloyd Hodgkin and Bernard Katz .
The GHK voltage equation for M {\displaystyle M} monovalent positive ionic species and A {\displaystyle A} negative:
This results in the following if we consider a membrane separating two K x N a 1 − x C l {\displaystyle \mathrm {K} _{x}\mathrm {Na} _{1-x}\mathrm {Cl} } -solutions: [ 1 ] [ 2 ] [ 3 ]
It is " Nernst -like" but has a term for each permeant ion:
R T F {\displaystyle {\frac {RT}{F}}} is approximately 26.7 mV at human body temperature (37 °C); when factoring in the change-of-base formula between the natural logarithm, ln, and logarithm with base 10 ( [ log 10 exp ( 1 ) ] − 1 = ln ( 10 ) = 2.30258... ) {\displaystyle ([\log _{10}\exp(1)]^{-1}=\ln(10)=2.30258...)} , it becomes 26.7 m V ⋅ 2.303 = 61.5 m V {\displaystyle 26.7\,\mathrm {mV} \cdot 2.303=61.5\,\mathrm {mV} } , a value often used in neuroscience.
The ionic charge determines the sign of the membrane potential contribution. During an action potential, although the membrane potential changes about 100mV, the concentrations of ions inside and outside the cell do not change significantly. They are always very close to their respective concentrations when the membrane is at their resting potential.
Using R ≈ 8.3 J K ⋅ m o l {\displaystyle R\approx {\frac {8.3\ \mathrm {J} }{\mathrm {K} \cdot \mathrm {mol} }}} , F ≈ 9.6 × 10 4 J m o l ⋅ V {\displaystyle F\approx {\frac {9.6\times 10^{4}\ \mathrm {J} }{\mathrm {mol} \cdot \mathrm {V} }}} , (assuming body temperature) T = 37 ∘ C = 310 K {\displaystyle T=37\ ^{\circ }\mathrm {C} =310\ \mathrm {K} } and the fact that one volt is equal to one joule of energy per coulomb of charge, the equation
can be reduced to
which is the Nernst equation .
Goldman's equation seeks to determine the voltage E m across a membrane. [ 5 ] A Cartesian coordinate system is used to describe the system, with the z direction being perpendicular to the membrane. Assuming that the system is symmetrical in the x and y directions (around and along the axon, respectively), only the z direction need be considered; thus, the voltage E m is the integral of the z component of the electric field across the membrane.
According to Goldman's model, only two factors influence the motion of ions across a permeable membrane: the average electric field and the difference in ionic concentration from one side of the membrane to the other. The electric field is assumed to be constant across the membrane, so that it can be set equal to E m / L , where L is the thickness of the membrane. For a given ion denoted A with valence n A , its flux j A —in other words, the number of ions crossing per time and per area of the membrane—is given by the formula
The first term corresponds to Fick's law of diffusion , which gives the flux due to diffusion down the concentration gradient, i.e., from high to low concentration. The constant D A is the diffusion constant of the ion A. The second term reflects the flux due to the electric field, which increases linearly with the electric field; Formally, it is [A] multiplied by the drift velocity of the ions, with the drift velocity expressed using the Stokes–Einstein relation applied to electrophoretic mobility . The constants here are the charge valence n A of the ion A (e.g., +1 for K + , +2 for Ca 2+ and −1 for Cl − ), the temperature T (in kelvins ), the molar gas constant R , and the faraday F , which is the total charge of a mole of electrons .
This is a first-order ODE of the form y' = ay + b , with y = [A] and y' = d[A]/d z ; integrating both sides from z =0 to z = L with the boundary conditions [A](0) = [A] in and [A]( L ) = [A] out , one gets the solution
where μ is a dimensionless number
and P A is the ionic permeability, defined here as
The electric current density J A equals the charge q A of the ion multiplied by the flux j A
Current density has units of (Amperes/m 2 ). Molar flux has units of (mol/(s m 2 )). Thus, to get current density from molar flux one needs to multiply by Faraday's constant F (Coulombs/mol). F will then cancel from the equation below. Since the valence has already been accounted for above, the charge q A of each ion in the equation above, therefore, should be interpreted as +1 or −1 depending on the polarity of the ion.
There is such a current associated with every type of ion that can cross the membrane; this is because each type of ion would require a distinct membrane potential to balance diffusion, but there can only be one membrane potential. By assumption, at the Goldman voltage E m , the total current density is zero
(Although the current for each ion type considered here is nonzero, there are other pumps in the membrane, e.g. Na + /K + -ATPase , not considered here which serve to balance each individual ion's current, so that the ion concentrations on either side of the membrane do not change over time in equilibrium.) If all the ions are monovalent—that is, if all the n A equal either +1 or −1—this equation can be written
whose solution is the Goldman equation
where
If divalent ions such as calcium are considered, terms such as e 2μ appear, which is the square of e μ ; in this case, the formula for the Goldman equation can be solved using the quadratic formula . | https://en.wikipedia.org/wiki/Goldman_equation |
The Goldman–Hodgkin–Katz flux equation (or GHK flux equation or GHK current density equation) describes the ionic flux across a cell membrane as a function of the transmembrane potential and the concentrations of the ion inside and outside of the cell. Since both the voltage and the concentration gradients influence the movement of ions, this process is a simplified version of electrodiffusion . Electrodiffusion is most accurately defined by the Nernst–Planck equation and the GHK flux equation is a solution to the Nernst–Planck equation with the assumptions listed below.
The American David E. Goldman of Columbia University , and the English Nobel laureates Alan Lloyd Hodgkin and Bernard Katz derived this equation.
Several assumptions are made in deriving the GHK flux equation (Hille 2001, p. 445) :
The GHK flux equation for an ion S (Hille 2001, p. 445):
where
The reversal potential is shown to be contained in the GHK flux equation (Flax 2008). The proof is replicated from the reference (Flax 2008) here.
We wish to show that when the flux is zero, the transmembrane potential is not zero. Formally it is written lim Φ S → 0 V m ≠ 0 {\displaystyle \lim _{\Phi _{S}\rightarrow 0}V_{m}\neq 0} which is equivalent to writing lim V m → 0 Φ S ≠ 0 {\displaystyle \lim _{V_{m}\rightarrow 0}\Phi _{S}\neq 0} , which states that when the transmembrane potential is zero, the flux is not zero.
However, due to the form of the GHK flux equation when V m = 0 {\displaystyle V_{m}=0} , Φ S = 0 0 {\displaystyle \Phi _{S}={\frac {0}{0}}} . This is a problem as the value of 0 0 {\displaystyle {\frac {0}{0}}} is indeterminate .
We turn to l'Hôpital's rule to find the solution for the limit:
where [ f ] ′ {\displaystyle [f]'} represents the differential of f and the result is :
It is evident from the previous equation that when V m = 0 {\displaystyle V_{m}=0} , Φ S ≠ 0 {\displaystyle \Phi _{S}\neq 0} if ( [ S ] i − [ S ] o ) ≠ 0 {\displaystyle ([{\mbox{S}}]_{i}-[{\mbox{S}}]_{o})\neq 0} and thus
which is the definition of the reversal potential.
By setting Φ S = 0 {\displaystyle \Phi _{S}=0} we can also obtain the reversal potential :
which reduces to :
and produces the Nernst equation :
Since one of the assumptions of the GHK flux equation is that the ions move independently of each other, the total flow of ions across the membrane is simply equal to the sum of two oppositely directed fluxes. Each flux approaches an asymptotic value as the membrane potential diverges from zero. These asymptotes are
and
where subscripts 'i' and 'o' denote the intra- and extracellular compartments, respectively. Intuitively one may understand these limits as follows: if an ion is only found outside a cell, then the flux is Ohmic (proportional to voltage) when the voltage causes the ion to flow into the cell, but no voltage could cause the ion to flow out of the cell, since there are no ions inside the cell in the first place.
Keeping all terms except V m constant, the equation yields a straight line when plotting Φ {\displaystyle \Phi } S against V m . It is evident that the ratio between the two asymptotes is merely the ratio between the two concentrations of S, [S] i and [S] o . Thus, if the two concentrations are identical, the slope will be identical (and constant) throughout the voltage range (corresponding to Ohm's law scaled by the surface area). As the ratio between the two concentrations increases, so does the difference between the two slopes, meaning that the current is larger in one direction than the other, given an equal driving force of opposite signs. This is contrary to the result obtained if using Ohm's law scaled by the surface area, and the effect is called rectification .
The GHK flux equation is mostly used by electrophysiologists when the ratio between [S] i and [S] o is large and/or when one or both of the concentrations change considerably during an action potential . The most common example is probably intracellular calcium , [Ca 2+ ] i , which during a cardiac action potential cycle can change 100-fold or more, and the ratio between [Ca 2+ ] o and [Ca 2+ ] i can reach 20,000 or more. | https://en.wikipedia.org/wiki/Goldman–Hodgkin–Katz_flux_equation |
The Goldreich-Kylafis (GK) effect is a quantum mechanical effect with applications in Astrophysics . The theoretical background of the work was published by Peter Goldreich and his at the time postdoc Nick Kylafis [ 1 ] in a series of two papers in The Astrophysical Journal .
The GK effect predicts that, under special conditions, the spectral lines emitted by interstellar molecules should be linearly polarized and the linear polarization vector should reveal the magnetic field direction in the molecular cloud . Even a μG magnetic field is enough for this effect. The lines arise from rotational transitions of molecules, say J=1 to J=0, where J is the rotational quantum number. If the magnetic sublevels of the J=1 level are equally populated, as it is usually the case, then the line is unpolarized. However, if the magnetic sublevels are unequally populated, then the line is polarized. Goldreich & Kylafis (1981) [ 2 ] showed that, if the radiation field (their own plus external) in which the molecules are embedded is anisotropic , then the magnetic sublevels are unequally populated. Since isotropic radiation fields are practically non existent in Nature (e.g. only at the center of an isolated perfectly spherical molecular cloud), the effect should be easily detectable. This is however not the case as some specific conditions are required for detection. These are that the line optical depth of the molecular cloud should be of order unity and that the radiative rates should be comparable to or larger than the collisional rates .
Since the observed lines from molecular clouds are broad, due to velocity gradients in the cloud, the GK effect has the potential to reveal the magnetic field direction along the line of sight. [ 3 ] It has been reported in star forming regions, [ 4 ] in thermal-pulsating (TP-) AGB stars [ 5 ] and recently in the disk around the T Tauri star TW Hya . [ 6 ] | https://en.wikipedia.org/wiki/Goldreich-Kylafis_effect |
The Goldschmidt classification , [ 1 ] [ 2 ] developed by Victor Goldschmidt (1888–1947), is a geochemical classification which groups the chemical elements within the Earth according to their preferred host phases into lithophile ( rock -loving), siderophile ( iron -loving), chalcophile ( sulfide ore -loving or chalcogen -loving), and atmophile (gas-loving) or volatile (the element, or a compound in which it occurs, is liquid or gaseous at ambient surface conditions).
Some elements have affinities to more than one phase. The main affinity is given in the table below and a discussion of each group follows that table.
Goldschmidt classification: Lithophile Siderophile Chalcophile Atmophile Trace/Synthetic
Lithophile elements (from Ancient Greek λῐ́θος ( líthos ) ' stone ' and φίλος ( phílos ) ' dear, beloved ' ) are those that remain on or close to the surface because they combine readily with oxygen, forming compounds that did not sink into the Earth's core . The lithophile elements include Al , B , Ba , Be , Br , Ca , Cl , Cr , Cs , F , I , Hf , K , Li , Mg , Na , Nb , O , P , Rb , Sc , Si , Sr , Ta , Th , Ti , U , V , Y , Zr , W and the lanthanides or rare earth elements (REE).
Lithophile elements mainly consist of the highly reactive metals of the s- and f-blocks . They also include a small number of reactive nonmetals, and the more reactive metals of the d-block such as titanium , zirconium and vanadium .
Most lithophile elements form very stable ions with an electron configuration of a noble gas (sometimes with additional f-electrons). The few that do not, such as silicon, phosphorus and boron, form strong covalent bonds with oxygen, often involving pi bonding . Their strong affinity for oxygen causes lithophile elements to associate very strongly with silica , forming relatively low-density minerals that thus rose towards the crust during planetary differentiation . The more soluble minerals formed by the alkali metals tend to concentrate in seawater or arid regions where they can crystallise. The less soluble lithophile elements are concentrated on ancient continental shields where soluble minerals have been weathered.
Because of their strong affinity for oxygen, most lithophile elements are enriched in the Earth's crust relative to their abundance in the Solar System . The most reactive s- and f-block metals, which form either saline or metallic hydrides , are known to be extraordinarily enriched on Earth as a whole relative to their solar abundances. This is because during the earliest stages of the Earth's formation , the abundance of stable forms of each element was determined by how readily it forms volatile hydrides; these volatiles then could "escape" the proto-Earth, leaving behind those elements unreactive with hydrogen. Under these conditions, the s- and f-block metals were strongly enriched during the formation of the Earth. The most enriched elements are rubidium , strontium and barium , which between them account for over 50 percent by mass of all elements heavier than iron in the Earth's crust.
The nonmetallic lithophiles – phosphorus and the halogens – exist on Earth as ionic salts with s-block metals in pegmatites and seawater. With the exception of fluorine , whose hydride forms hydrogen bonds and is therefore of relatively low volatility, these elements have had their concentrations on Earth significantly reduced through escape of volatile hydrides during the Earth's formation. Although they are present in the Earth's crust in concentrations quite close to their solar abundances, phosphorus and the heavier halogens are probably significantly depleted on Earth as a whole relative to their solar abundances.
Several transition metals, including chromium , molybdenum , iron and manganese , show both lithophile and siderophile characteristics and can be found in both these two layers. Although these metals form strong bonds with oxygen and are never found in the Earth's crust in the free state, metallic forms of these elements are thought very likely to exist in the core of the earth as relics from when the atmosphere did not contain oxygen. Like the "pure" siderophiles, these elements (except iron) are considerably depleted in the crust relative to their solar abundances.
Owing to their strong affinity for oxygen, lithophile metals, although they form the great bulk of the metallic elements in Earth's crust, were never available as free metals before the development of electrolysis . With this development, many lithophile metals are of considerable value as structural metals ( magnesium , aluminium , titanium , vanadium ) or as reducing agents ( sodium , magnesium , calcium ).
The non-metals phosphorus and the halogens were also not known to early chemists, though production of these elements is less difficult than of metallic lithophiles since electrolysis is required only with fluorine. Elemental chlorine is particularly important as an oxidizing agent – usually being made by electrolysis of sodium chloride .
Siderophile elements (from Ancient Greek σίδηρος ( sídēros ) ' iron ' ) are the transition metals which tend to sink towards the core during planetary differentiation , because they dissolve readily in iron either as solid solutions or in the molten state. Some sources [ 3 ] include elements which are not transition metals in their list of siderophiles, such as germanium . Other sources may also differ in their list based on the temperature being discussed – niobium , vanadium , chromium , and manganese may be considered siderophiles or not, depending on the assumed temperature and pressure. [ 4 ] Also confusing the issue is that some elements, such as the aforementioned manganese , as well as molybdenum , form strong bonds with oxygen, but in the free state (as they existed on the early Earth when free oxygen did not exist ) can mix so easily with iron that they do not concentrate in the siliceous crust, as do true lithophile elements. Iron , meanwhile, is simply everywhere .
The siderophile elements include the highly siderophilic ruthenium , rhodium , palladium , rhenium , osmium , iridium , platinum , and gold , the moderately siderophilic cobalt and nickel , in addition to the "disputed" elements mentioned earlier – some sources [ 3 ] even include tungsten and silver . [ 5 ]
Most siderophile elements have practically no affinity for oxygen: indeed oxides of gold are thermodynamically unstable . They form stronger bonds with carbon or sulfur , but even these are not strong enough to separate out with the chalcophile elements. Thus, siderophile elements are bound with iron through metallic bonding in the Earth's core, where pressures may be high enough to keep the iron solid. Manganese, iron, and molybdenum do form strong bonds with oxygen, but in the free state (as on the early Earth) can mix so easily with iron that they do not concentrate in the siliceous crust, as do true lithophile elements. However, ores of manganese are found in much the same sites as are those of aluminium and titanium, owing to manganese's great reactivity towards oxygen.
Because they are so concentrated in the dense core, siderophile elements are known for their rarity in the Earth's crust. Most of them have always been known as precious metals because of this. Iridium is the rarest transition metal occurring within the Earth's crust, with an abundance by mass of less than one part per billion. Mineable deposits of precious metals usually form as a result of the erosion of ultramafic rocks , but are not highly concentrated even compared to their crustal abundances , which are typically several orders of magnitude below their solar abundances. However, because they are concentrated in the Earth's mantle and Earth's core , siderophile elements are believed to be present in the Earth as a whole (including the core) in something approaching their solar abundances.
The chalcophile elements (from Ancient Greek χαλκός ( khalkós ) ' copper, brass, bronze', also 'ore ' ) include Ag , As , Bi , Cd , Cu , Ga , Ge , Hg , In , Pb , S , Sb , Se , Sn , Te , Tl and Zn . [ 6 ]
Chalcophile elements are those that remain on or close to the surface because they combine readily with sulfur and some other chalcogens other than oxygen, forming compounds which did not sink along with iron towards the Earth's core. Chalcophile elements are those metals and heavier nonmetals that have a low affinity for oxygen and prefer to bond with sulfur as highly insoluble sulfides .
Because these sulfides are much denser than the silicate minerals formed by lithophile elements, chalcophile elements separated below the lithophiles at the time of the first crystallization of the Earth's crust. This has led to their depletion in the Earth's crust relative to their solar abundances, though because the minerals they form are nonmetallic, this depletion has not reached the levels found with siderophile elements.
However, because they formed volatile hydrides in the accreting protosolar nebula when the controlling redox reaction was the oxidation or reduction of hydrogen, the less metallic chalcophile elements are strongly depleted on Earth as a whole relative to cosmic abundances. This is most especially true of the chalcogens selenium and tellurium (which formed volatile hydrogen selenide and hydrogen telluride , respectively), which for this reason are among the rarest elements found in the Earth's crust (to illustrate, tellurium is only about as abundant as platinum ).
The most metallic chalcophile elements (of the copper, zinc and boron groups) may mix to some degree with iron in the Earth's core. They are not likely to be depleted on Earth as a whole relative to their solar abundances since they do not form volatile hydrides. Zinc and gallium are somewhat "lithophile" in nature because they often occur in silicate or related minerals and form quite strong bonds with oxygen. Gallium, notably, is sourced mainly from bauxite , an aluminum hydroxide ore in which gallium ions substitute for chemically similar aluminum.
Although no chalcophile element is of high abundance in the Earth's crust, chalcophile elements constitute the bulk of commercially important metals. This is because, whereas lithophile elements require energy-intensive electrolysis for extraction, chalcophiles can be easily extracted by reduction , and chalcophiles' geochemical concentration – which in extreme cases can exceed 100,000 times their average crustal abundance. These greatest enrichments occur in high plateaus like the Tibetan Plateau and the Bolivian Altiplano where large quantities of chalcophile elements have been uplifted through plate tectonics . A side-effect of this in modern times is that the rarest chalcophiles (like mercury ) are so completely exploited that their value as minerals has almost completely disappeared.
The atmophile elements (from Ancient Greek ἀτμός ( atmós ) ' vapor, steam, smoke ' ) are H , C , N and the noble gases . [ 7 ]
Atmophile elements (also called " volatile elements ") are defined as those that remain mostly on or above Earth's surface because they are, or occur in, liquids and/or gases at temperatures and pressures found on the surface. The noble gases do not form stable compounds and occur as monatomic gases , while nitrogen , although highly reactive as the free atom, bonds so strongly into diatomic molecular nitrogen that all oxides of nitrogen are thermodynamically unstable with respect to nitrogen and oxygen. Consequently, with the development of free oxygen in Earth's atmosphere, ammonia was oxidised to molecular nitrogen which has come to form four-fifths of the Earth's atmosphere. Carbon is also classed as an atmophile because it forms very strong multiple bonds with oxygen in carbon monoxide (slowly oxidised in the atmosphere) and carbon dioxide . The latter is the fourth-largest constituent of the Earth's atmosphere, while carbon monoxide occurs naturally from various sources ( volcanoes , combustion) and has a residence time in the atmosphere of a few months.
Hydrogen, which occurs in water, is also classed as an atmophile. Water is classified as a volatile, because most of it is liquid or gas, even though it can exist as a solid compound at Earth's surface. Water can also be incorporated into other minerals as water of crystallization (as in gypsum ) or through ionic and hydrogen bonding (as in talc ), giving hydrogen some lithophile character.
Because all atmophile elements are either gases or form volatile hydrides, atmophile elements are strongly depleted on Earth as a whole relative to their solar abundances owing to losses from the atmosphere during the formation of the Earth . The heavier noble gases ( krypton , xenon ) are the rarest stable elements on Earth. (In fact they, along with neon , were all first isolated and described by William Ramsay and Morris Travers and assistants, who gave them names with Ancient Greek derivations of 'hidden', 'stranger', and 'new', respectively.)
Argon is the exception among the noble gases: it is the third-most abundant component of Earth's present-day atmosphere after nitrogen and oxygen, comprising approx. 1%. Argon-40 is a stable daughter of radioactive potassium-40, and argon is heavy enough to be gravitationally captured by the post-accretion Earth, so while the proto-Earth's primordial argon was mostly driven off, this radiogenic argon has accumulated over geologic time. This makes Earth's argon abundance substantially different from cosmic abundance ratios for argon, being enormously enriched in 40 Ar , while 36 Ar predominates cosmically.
Synthetic elements are excluded from the classification, as they do not occur naturally.
Trace radioactive elements (namely Tc, Pm, Po, At, Rn, Fr, Ra, Ac, Pa, Np, Pu) are also treated as synthetic. Although these do occur in nature, [ 8 ] [ 9 ] [ 10 ] their occurrence is dependent on their long-lived parents Th and U, and they are not very mobile. For instance, polonium 's chemistry would predict it to be a chalcophile, but it tends to occur instead as a lithophile along with its parent uranium . Even radon , a gas at standard conditions , does not usually have time to travel very far from the original uranium source before decaying. When needed, these elements are typically produced synthetically in nuclear reactors instead of extraction from ores. | https://en.wikipedia.org/wiki/Goldschmidt_classification |
Goldschmidt's tolerance factor (from the German word Toleranzfaktor ) is an indicator for the stability and distortion of crystal structures. [ 1 ] It was originally only used to describe the perovskite ABO 3 structure , but now tolerance factors are also used for ilmenite . [ 2 ]
Alternatively the tolerance factor can be used to calculate the compatibility of an ion with a crystal structure. [ 3 ]
The first description of the tolerance factor for perovskite was made by Victor Moritz Goldschmidt in 1926. [ 4 ]
The Goldschmidt tolerance factor ( t {\displaystyle t} ) is a dimensionless number that is calculated from the ratio of the ionic radii : [ 1 ]
In an ideal cubic perovskite structure, the lattice parameter (i.e., length) of the unit cell (a) can be calculated using the following equation: [ 1 ]
The perovskite structure has the following tolerance factors (t): | https://en.wikipedia.org/wiki/Goldschmidt_tolerance_factor |
The Goldsmiths' Professorship of Materials Science is a professorship in the University of Cambridge , associated with the Department of Materials Science and Metallurgy . [ 1 ]
The professorship was established by grace of 20 November 1931 as the Goldsmiths' Professorship of Metallurgy to replace the Goldsmiths' Readership in Metallurgy. A further gift of £12,500 was received from the Goldsmiths' Company in 1933. It was retitled the Goldsmiths' Professorship of Materials Science by grace 4 of 19 June 1991. | https://en.wikipedia.org/wiki/Goldsmiths'_Professor_of_Materials_Science |
In particle and condensed matter physics , Goldstone bosons or Nambu–Goldstone bosons ( NGBs ) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries . They were discovered by Yoichiro Nambu in particle physics within the context of the BCS superconductivity mechanism, [ 1 ] and subsequently elucidated by Jeffrey Goldstone , [ 2 ] and systematically generalized in the context of quantum field theory . [ 3 ] In condensed matter physics such bosons are quasiparticles and are known as Anderson–Bogoliubov modes. [ 4 ] [ 5 ] [ 6 ]
These spinless bosons correspond to the spontaneously broken internal symmetry generators, and are characterized by the quantum numbers of these.
They transform nonlinearly (shift) under the action of these generators, and can thus be excited out of the asymmetric vacuum by these generators. Thus, they can be thought of as the excitations of the field in the broken symmetry directions in group space—and are massless if the spontaneously broken symmetry is not also broken explicitly .
If, instead, the symmetry is not exact, i.e. if it is explicitly broken as well as spontaneously broken, then the Nambu–Goldstone bosons are not massless, though they typically remain relatively light; they are then called pseudo-Goldstone bosons or pseudo–Nambu–Goldstone bosons (abbreviated PNGBs ).
Goldstone's theorem examines a generic continuous symmetry which is spontaneously broken ; i.e., its currents are conserved, but the ground state is not invariant under the action of the corresponding charges. Then, necessarily, new massless (or light, if the symmetry is not exact) scalar particles appear in the spectrum of possible excitations. There is one scalar particle—called a Nambu–Goldstone boson—for each generator of the symmetry that is broken, i.e., that does not preserve the ground state . The Nambu–Goldstone mode is a long-wavelength fluctuation of the corresponding order parameter .
By virtue of their special properties in coupling to the vacuum of the respective symmetry-broken theory, vanishing momentum ("soft") Goldstone bosons involved in field-theoretic amplitudes make such amplitudes vanish ("Adler zeros").
Consider a complex scalar field ϕ , with the constraint that ϕ ∗ ϕ = v 2 {\displaystyle \phi ^{*}\phi =v^{2}} , a constant. One way to impose a constraint of this sort is by including a potential interaction term in its Lagrangian density ,
and taking the limit as λ → ∞ . This is called the "Abelian nonlinear σ-model". [ nb 2 ]
The constraint, and the action, below, are invariant under a U (1) phase transformation, δϕ =i εϕ . The field can be redefined to give a real scalar field (i.e., a spin-zero particle) θ without any constraint by
where θ is the Nambu–Goldstone boson (actually v θ {\displaystyle v\theta } is) and the U (1) symmetry transformation effects a shift on θ , namely
but does not preserve the ground state |0〉 (i.e. the above infinitesimal transformation does not annihilate it —the hallmark of invariance), as evident in the charge of the current below.
Thus, the vacuum is degenerate and noninvariant under the action of the spontaneously broken symmetry.
The corresponding Lagrangian density is given by
and thus
Note that the constant term m 2 v 2 {\displaystyle m^{2}v^{2}} in the Lagrangian density has no physical significance, and the other term in it is simply the kinetic term for a massless scalar.
The symmetry-induced conserved U (1) current is
The charge, Q , resulting from this current shifts θ and the ground state to a new, degenerate, ground state. Thus, a vacuum with 〈 θ 〉 = 0 will shift to a different vacuum with 〈 θ 〉 = ε . The current connects the original vacuum with the Nambu–Goldstone boson state, 〈0| J 0 (0)| θ 〉≠ 0 .
In general, in a theory with several scalar fields, ϕ j , the Nambu–Goldstone mode ϕ g is massless , and parameterises the curve of possible (degenerate) vacuum states. Its hallmark under the broken symmetry transformation is nonvanishing vacuum expectation 〈 δϕ g 〉 , an order parameter , for vanishing 〈 ϕ g 〉 = 0 , at some ground state |0〉 chosen at the minimum of the potential, 〈∂ V /∂ ϕ i 〉 = 0 . In principle the vacuum should be the minimum of the effective potential which takes into account quantum effects, however it is equal to the classical potential to first approximation. Symmetry dictates that all variations of the potential with respect to the fields in all symmetry directions vanish. The vacuum value of the first order variation in any direction vanishes as just seen; while the vacuum value of the second order variation must also vanish, as follows. Vanishing vacuum values of field symmetry transformation increments add no new information.
By contrast, however, nonvanishing vacuum expectations of transformation increments , 〈 δϕ g 〉 , specify the relevant (Goldstone) null eigenvectors of the mass matrix ,
⟨ ∂ 2 V ∂ ϕ i ∂ ϕ j ⟩ ⟨ δ ϕ j ⟩ = 0 , {\displaystyle \left\langle {\partial ^{2}V \over \partial \phi _{i}\partial \phi _{j}}\right\rangle \langle \delta \phi _{j}\rangle =0~,}
and hence the corresponding zero-mass eigenvalues.
The principle behind Goldstone's argument is that the ground state is not unique. Normally, by current conservation, the charge operator for any symmetry current is time-independent,
Acting with the charge operator on the vacuum either annihilates the vacuum , if that is symmetric; else, if not , as is the case in spontaneous symmetry breaking, it produces a zero-frequency state out of it, through its shift transformation feature illustrated above. Actually, here, the charge itself is ill-defined, cf. the Fabri–Picasso argument below.
But its better behaved commutators with fields, that is, the nonvanishing transformation shifts 〈 δϕ g 〉 , are, nevertheless, time-invariant ,
thus generating a δ( k 0 ) in its Fourier transform. [ 15 ] (This ensures that, inserting a complete set of intermediate states in a nonvanishing current commutator can lead to vanishing time-evolution only when one or more of these states is massless.)
Thus, if the vacuum is not invariant under the symmetry, action of the charge operator produces a state which is different from the vacuum chosen, but which has zero frequency. This is a long-wavelength oscillation of a field which is nearly stationary: there are physical states with zero frequency, k 0 , so that the theory cannot have a mass gap .
This argument is further clarified by taking the limit carefully. If an approximate charge operator acting in a huge but finite region A is applied to the vacuum,
a state with approximately vanishing time derivative is produced,
Assuming a nonvanishing mass gap m 0 , the frequency of any state like the above, which is orthogonal to the vacuum, is at least m 0 ,
Letting A become large leads to a contradiction. Consequently m 0 = 0. However this argument fails when the symmetry is gauged, because then the symmetry generator is only performing a gauge transformation. A gauge transformed state is the same exact state, so that acting with a symmetry generator does not get one out of the vacuum (see Higgs mechanism ).
The argument [ 16 ] [ 17 ] requires both the vacuum and the charge Q to be translationally invariant, P |0〉 = 0 , [ P,Q ]= 0 .
Consider the correlation function of the charge with itself,
so the integrand in the right hand side does not depend on the position.
Thus, its value is proportional to the total space volume, ‖ Q | 0 ⟩ ‖ 2 = ∞ {\displaystyle \|Q|0\rangle \|^{2}=\infty } — unless the symmetry is unbroken, Q |0〉 = 0 . Consequently, Q does not properly exist in the Hilbert space.
There is an arguable loophole in the theorem. If one reads the theorem carefully, it only states that there exist non- vacuum states with arbitrarily small energies. Take for example a chiral N = 1 super QCD model with a nonzero squark VEV which is conformal in the IR . The chiral symmetry is a global symmetry which is (partially) spontaneously broken. Some of the "Goldstone bosons" associated with this spontaneous symmetry breaking are charged under the unbroken gauge group and hence, these composite bosons have a continuous mass spectrum with arbitrarily small masses but yet there is no Goldstone boson with exactly zero mass . In other words, the Goldstone bosons are infraparticles .
A version of Goldstone's theorem also applies to nonrelativistic theories. [ 18 ] [ 19 ] It essentially states that, for each spontaneously broken symmetry, there corresponds some quasiparticle which is typically a boson and has no energy gap . In condensed matter these goldstone bosons are also called gapless modes (i.e. states where the energy dispersion relation is like E ∝ p n {\displaystyle E\propto p^{n}} and is zero for p = 0 {\displaystyle p=0} ), the nonrelativistic version of the massless particles (i.e. photons where the dispersion relation is also E = p c {\displaystyle E=pc} and zero for p = 0 {\displaystyle p=0} ). Note that the energy in the non relativistic condensed matter case is H − μN − α → ⋅ P → and not H as it would be in a relativistic case. However, two different spontaneously broken generators may now give rise to the same Nambu–Goldstone boson.
As a first example an antiferromagnet has 2 goldstone bosons, a ferromagnet has 1 goldstone bosons, where in both cases we are breaking symmetry from SO(3) to SO(2), for the antiferromagnet the dispersion is E ∝ p {\displaystyle E\propto p} and the expectation value of the ground state is zero, for the ferromagnet instead the dispersion is E ∝ p 2 {\displaystyle E\propto p^{2}} and the expectation value of the ground state is not zero, i.e. there is a spontaneously broken symmetry for the ground state [ 20 ] [ 21 ]
As a second example, in a superfluid , both the U(1) particle number symmetry and Galilean symmetry are spontaneously broken. However, the phonon is the Goldstone boson for both. [ 22 ] [ 23 ]
Still in regards to symmetry breaking there is also a close analogy between gapless modes in condensed matter and the Higgs boson, e.g. in the paramagnet to ferromagnet phase transition [ 24 ] [ 25 ]
In contrast to the case of the breaking of internal symmetries, when spacetime symmetries such as Lorentz , conformal, rotational, or translational symmetries are broken, the order parameter need not be a scalar field, but may be a tensor field, and the number of independent massless modes may be fewer than the number of spontaneously broken generators. For a theory with an order parameter ⟨ ϕ ( r ) ⟩ {\displaystyle \langle \phi ({\boldsymbol {r}})\rangle } that spontaneously breaks a spacetime symmetry, the number of broken generators T a {\displaystyle T^{a}} minus the number non-trivial independent solutions c a ( r ) {\displaystyle c_{a}({\boldsymbol {r}})} to
is the number of Goldstone modes that arise. [ 26 ] For internal symmetries, the above equation has no non-trivial solutions, so the usual Goldstone theorem holds. When solutions do exist, this is because the Goldstone modes are linearly dependent among themselves, in that the resulting mode can be expressed as a gradients of another mode. Since the spacetime dependence of the solutions c a ( r ) {\displaystyle c_{a}({\boldsymbol {r}})} is in the direction of the unbroken generators, when all translation generators are broken, no non-trivial solutions exist and the number of Goldstone modes is once again exactly the number of broken generators.
In general, the phonon is effectively the Nambu–Goldstone boson for spontaneously broken translation [ 27 ] symmetry.
Spontaneously broken global fermionic symmetries, which occur in some supersymmetric models, lead to Nambu–Goldstone fermions , or goldstinos . [ 28 ] [ 29 ] These have spin 1 / 2 , instead of 0, and carry all quantum numbers of the respective supersymmetry generators broken spontaneously.
Spontaneous supersymmetry breaking smashes up ("reduces") supermultiplet structures into the characteristic nonlinear realizations of broken supersymmetry, so that goldstinos are superpartners of all particles in the theory, of any spin , and the only superpartners, at that. That is, to say, two non-goldstino particles are connected to only goldstinos through supersymmetry transformations, and not to each other, even if they were so connected before the breaking of supersymmetry. As a result, the masses and spin multiplicities of such particles are then arbitrary. | https://en.wikipedia.org/wiki/Goldstone_boson |
Gold–aluminium intermetallic is a type of intermetallic compound of gold and aluminium that usually forms at contacts between the two metals. Gold–aluminium intermetallic have different properties from the individual metals, such as low conductivity and high melting point depending on their composition. Due to the difference of density between the metals and intermetallics, the growth of the intermetallic layers causes reduction in volume, and therefore creates gaps in the metal near the interface between gold and aluminium. [ 1 ]
The production of gaps lowers the strength of the metal compound, which can cause mechanical failure at the joint, fostering the problems that the intermetallics causes in metal compounds. In microelectronics , these properties can cause problems in wire bonding .
The main compounds formed are usually Au 5 Al 2 (white plague) and AuAl 2 (purple plague), both of which form at high temperatures, then Au 5 Al 2 and AuAl 2 can further react with Au to form more stable compound, Au 2 Al. [ 2 ]
Au 5 Al 2 has low electrical conductivity and relatively low melting point. Au 5 Al 2 's formation at the joint causes increase of electrical resistance, which can lead to electrical failure. [ 3 ] Au 5 Al 2 typically forms at 95% of Au and 5% of Al by mass, its melting point is about 575 °C, which is the lowest among the major gold-aluminum intermetallic compounds. AuAl 2 is a brittle bright-purple compound, with a composition of about 78.5% Au and 21.5% Al by mass.
AuAl 2 is the most thermally stable species of the Au–Al intermetallic compounds, with a melting point of 1060 °C (see phase diagram), which is similar to the melting point of pure gold. AuAl 2 can react with Au, therefore is often replaced by Au 2 Al, a tan-colored substance, which forms at composition of 93% of Au and 7% of Al by mass. It is also a poor conductor and can cause electrical failure of the joint, which can further lead to mechanical failure.
At lower temperatures, about 400–450 °C, an interdiffusion process takes place at the junction, leading to formation of layers of different gold-aluminum intermetallic compounds with different growth rates. Gaps are formed as the denser and faster-growing layers consume the slower-growing layers. This process is known as the Kirkendall voiding , which leads to both increased electrical resistance and mechanical weakening of the wire bond. When the voids forms along the diffusion front, this process is aided by contaminants present in the lattice, and is known as the Horsting voiding, which is a similar process to the Kirkendall voiding. | https://en.wikipedia.org/wiki/Gold–aluminium_intermetallic |
Golgi's method is a silver staining technique that is used to visualize nervous tissue under light microscopy. The method was discovered by Camillo Golgi , an Italian physician and scientist , who published the first picture made with the technique in 1873. [ 1 ] It was initially named the black reaction ( la reazione nera ) by Golgi, but it became better known as the Golgi stain or later, Golgi method.
Golgi staining was used by Spanish neuroanatomist Santiago Ramón y Cajal (1852–1934) to discover a number of novel facts about the organization of the nervous system, inspiring the birth of the neuron doctrine . Ultimately, Ramón y Cajal improved the technique by using a method he termed "double impregnation". Ramón y Cajal's staining technique, still in use, is called Cajal's stain. [ citation needed ]
The cells in nervous tissue are densely packed, and little information on their structures and interconnections can be obtained if all the cells are stained. Furthermore, the thin filamentary extensions of neural cells, including the axon and the dendrites of neurons, are too slender and transparent to be seen with normal staining techniques. Golgi's method stains a limited number of cells at random in their entirety. The mechanism by which this happens is still largely unknown. [ 2 ] Dendrites, as well as the cell soma, are clearly stained in brown and black and can be followed in their entire length, which allowed neuroanatomists to track connections between neurons and to make visible the complex networking structure of many parts of the brain and spinal cord .
Golgi's staining is achieved by impregnating aldehyde-fixed nervous tissue with potassium dichromate and silver nitrate . Cells thus stained are filled by microcrystallization of silver chromate .
According to SynapseWeb, [ 3 ] this is the recipe for Golgi's staining technique:
This technique has since been refined to substitute the silver precipitate with gold by immersing the sample in gold chloride then oxalic acid , followed by removal of the silver by sodium thiosulphate . This preserves a greater degree of fine structure with the ultrastructural details marked by small particles of gold. [ 4 ]
Ramón y Cajal said of the Golgi method: | https://en.wikipedia.org/wiki/Golgi's_method |
The Golm Metabolome Database ( GMD ) [ 1 ] [ 2 ] [ 3 ] [ 4 ] is a gas chromatography (GC) – mass spectrometry (MS) reference library dedicated to metabolite profiling experiments and comprises mass spectral and retention index (RI) information for non-annotated mass spectral tags (MSTs, mass spectral information with retention time attached indices) together with data of a multitude of already identified metabolites and reference substances. The GMD is hosted at the Max Planck Institute of Molecular Plant Physiology in Golm district of Potsdam , Germany.
Gas chromatography (GC) coupled to mass spectrometry (MS) is one of the most widespread routine technologies applied to the large scale screening and discovery of novel biomarkers in metabolomics . However, the majority of MSTs currently measured in plant metabolomic profiling experiments remains unidentified due to the lack of authenticated pure reference substances and the expensive and time-consuming effort to maintain mass spectral RI libraries required for compound identification by GC-MS.
As the communication of analytical results and other approach-related details such as mass spectral and RI reference information within the scientific community is becoming increasingly popular, open access platforms for information exchange, such as the GMD, are obligatory.
Due to the lack of mandatory standards it remains difficult to compare individual mass spectrums.
While the different mass detector technologies, namely quadrupole , ion trap and time of flight , can be deemed irrelevant, the chromatography settings such as temperature programming, type of capillary column and choice of column manufacturer heavily affect the empirically determined RI properties. Procedures for the transfer of RI properties between chromatography variants are, therefore, highly relevant for a shared library use. The GMD assesses the accuracy of RI transfer between chromatography variants and implements means to transfer empirically determined RI properties. [ 5 ] Aiming at the classification and identification of un-identified MSTs, the GMD accesses the information on available reference compounds. These compounds serve as training set of data to apply decision trees (DT) as a supervised machine learning approach. Structural feature extraction was applied to classify the metabolite space of the GMD prior to DT training. DT-based predictions of the most frequent substructures classify low resolution GC-MS mass spectra of the linked (potentially unknown) metabolite with respect to the presence or absence of the chemical moieties. [ 6 ] The web-based frontend supports conventional mass spectral and RI comparison by ranked hit lists as well as advanced DT supported substructure prediction. Batch processing is enabled via Simple Object Access Protocol (SOAP)-based web services while web-based data access services expose particular data base entities adapting Representational State Transfer (ReST) principles and mass spectral standards such as NIST -MSP and JCAMP -DX.
The GMD visualise quantitative metabolite pool size changes data. | https://en.wikipedia.org/wiki/Golm_Metabolome_Database |
Golodirsen , sold under the brand name Vyondys 53 , is a medication used for the treatment of Duchenne muscular dystrophy . [ 2 ] It is an antisense oligonucleotide medication of phosphorodiamidate morpholino oligomer (PMO) chemistry . [ 1 ] [ 3 ]
The most common side effects include headache , fever , fall, cough , vomiting , abdominal pain , cold symptoms ( nasopharyngitis ) and nausea . [ 2 ] [ 1 ]
Golodirsen is indicated for the treatment of Duchenne muscular dystrophy in people who have a confirmed mutation of the dystrophin gene that is amenable to exon 53 skipping. [ 2 ] [ 1 ]
Golodirsen has been provisionally approved for approximately 8% of all people with Duchenne muscular dystrophy amenable to exon 53 skipping. [ 3 ] It works by inducing exon skipping in the dystrophin gene and thereby increasing the amount of dystrophin protein available to muscle fibers. [ 3 ]
The most common side effects include headache , fever , fall, cough , vomiting , abdominal pain , cold symptoms ( nasopharyngitis ) and nausea . [ 2 ] [ 1 ] In animal studies, no significant changes were seen in the male reproductive system of monkeys and mice following weekly subcutaneous administration. [ 3 ] According to the reports obtained from the clinical trials , pain at the site of intravenous administration, back pain , oropharyngeal pain , sprain in ligaments , diarrhea , dizziness , contusion , flu , ear infection , rhinitis , skin abrasion , tachycardia , and constipation occurred at an elevated frequency in the treatment group, as compared to their placebo counterparts. [ 3 ] Hypersensitivity reactions, including rash, fever, itching, hives, skin irritation (dermatitis) and skin peeling (exfoliation), have occurred in people who were treated with golodirsen. [ 2 ]
Renal toxicity was observed in animals who received golodirsen. [ 2 ] [ 4 ] Although renal toxicity was not observed in the clinical studies with golodirsen, potentially fatal glomerulonephritis , has been observed after administration of some antisense oligonucleotides . [ 2 ] Renal function should be monitored in those taking golodirsen. [ 2 ] [ 5 ] [ 6 ]
Following single or multiple intravenous infusions, the majority of drug elimination occurs within 24 hours of intravenous administration. The elimination half-life of golodirsen, in parity with eteplirsen was 3 to 6 hours. [ 3 ]
As a first-generation medication , golodirsen is far away from being curative; clinical trial outcomes have demonstrated it to have a marginal effect on ameliorating Duchenne muscular dystrophy pathology . [ 3 ] As of December 2019, golodirsen is approved for therapeutic use in the United States, as well as in the countries that automatically recognize the decisions of the US Food and Drug Administration , under the condition that its benefit will be demonstrated in a confirmatory clinical trial .
Golodirsen is one of the very few FDA-approved exon-skipping therapy for Duchenne muscular dystrophy, although the clinical benefits of the medication are yet to established. [ 1 ] [ 3 ] While the development of golodirsen needed huge financing, it is only applicable to a small subset of people with Duchenne muscular dystrophy. [ citation needed ] Sarepta Therapeutics has announced that golodirsen will cost in parity with eteplirsen , another medication of a similar kind, which may be as high as US$300,000 per year. [ citation needed ] Also, the accelerated approval of golodirsen has paved the way for people to have early access to the medication, at the same time, it is shrouded with controversy over a number of issues. [ 3 ] A double-blind placebo-controlled confirmatory trial ( NCT02500381 ) is ongoing to resolve the issues. [ citation needed ]
Golodirsen was developed by collaborative research led by Prof. Steve Wilton and Prof. Sue Fletcher in the Perron Institute and licensed to Sarepta Therapeutics by the University of Western Australia . [ 3 ]
In the clinical trial of golodirsen, dystrophin levels increased, on average, from 0.10% of normal at baseline to 1.02% of normal after 48 weeks of treatment with the drug or longer. [ 2 ] The change was a surrogate endpoint and the trial did not establish clinical benefit of the drug, including changes to the subject's motor function . [ 2 ]
The pharmacological assessment of golodirsen did not include special population groups, e.g., pregnant and lactating women , the elderly, and people with concurrent disease states. [ medical citation needed ] As DMD predominantly affects male children and young adults , and golodirsen is indicated for the treatment of children, but primarily not for adult women , the elderly, and people with comorbidity , it was not evaluated on them. [ 3 ]
The US Food and Drug Administration (FDA) approved golodirsen in December 2019, [ 2 ] [ 7 ] [ 8 ] under the accelerated approval pathway . [ 2 ] The application for golodirsen was granted fast track , priority review , and orphan drug designations, and a rare pediatric disease priority review voucher. [ 2 ] | https://en.wikipedia.org/wiki/Golodirsen |
Golomb coding is a lossless data compression method using a family of data compression codes invented by Solomon W. Golomb in the 1960s. Alphabets following a geometric distribution will have a Golomb code as an optimal prefix code , [ 1 ] making Golomb coding highly suitable for situations in which the occurrence of small values in the input stream is significantly more likely than large values.
Rice coding (invented by Robert F. Rice ) denotes using a subset of the family of Golomb codes to produce a simpler (but possibly suboptimal) prefix code. Rice used this set of codes in an adaptive coding scheme; "Rice coding" can refer either to that adaptive scheme or to using that subset of Golomb codes. Whereas a Golomb code has a tunable parameter that can be any positive integer value, Rice codes are those in which the tunable parameter is a power of two. This makes Rice codes convenient for use on a computer, since multiplication and division by 2 can be implemented more efficiently in binary arithmetic .
Rice was motivated to propose this simpler subset due to the fact that geometric distributions are often varying with time, not precisely known, or both, so selecting the seemingly optimal code might not be very advantageous.
Rice coding is used as the entropy encoding stage in a number of lossless image compression and audio data compression methods.
Golomb coding uses a tunable parameter M to divide an input value x into two parts: q , the result of a division by M , and r , the remainder. The quotient is sent in unary coding , followed by the remainder in truncated binary encoding . When M = 1 {\displaystyle M=1} , Golomb coding is equivalent to unary coding.
Golomb–Rice codes can be thought of as codes that indicate a number by the position of the bin ( q ), and the offset within the bin ( r ). The example figure shows the position q and offset r for the encoding of integer x using Golomb–Rice parameter M = 3 , with source probabilities following a geometric distribution with p (0) = 0.2 .
Formally, the two parts are given by the following expression, where x is the nonnegative integer being encoded:
and
Both q and r will be encoded using variable numbers of bits: q by a unary code, and r by b bits for Rice code, or a choice between b and b +1 bits for Golomb code (i.e. M is not a power of 2), with b = ⌊ log 2 ( M ) ⌋ {\displaystyle b=\lfloor \log _{2}(M)\rfloor } . If r < 2 b + 1 − M {\displaystyle r<2^{b+1}-M} , then use b bits to encode r ; otherwise, use b +1 bits to encode r . Clearly, b = log 2 ( M ) {\displaystyle b=\log _{2}(M)} if M is a power of 2 and we can encode all values of r with b bits.
The integer x treated by Golomb was the run length of a Bernoulli process , which has a geometric distribution starting at 0. The best choice of parameter M is a function of the corresponding Bernoulli process, which is parameterized by p = P ( x = 0 ) {\displaystyle p=P(x=0)} the probability of success in a given Bernoulli trial . M is either the median of the distribution or the median ±1. It can be determined by these inequalities:
which are solved by
For the example with p (0) = 0.2 :
The Golomb code for this distribution is equivalent to the Huffman code for the same probabilities, if it were possible to compute the Huffman code for the infinite set of source values.
Golomb's scheme was designed to encode sequences of non-negative numbers. However, it is easily extended to accept sequences containing negative numbers using an overlap and interleave scheme, in which all values are reassigned to some positive number in a unique and reversible way. The sequence begins: 0, −1, 1, −2, 2, −3, 3, −4, 4, ... The n -th negative value (i.e., − n {\displaystyle -n} ) is mapped to the n th odd number ( 2 n − 1 {\displaystyle 2n-1} ), and the m th positive value is mapped to the m -th even number ( 2 m {\displaystyle 2m} ). This may be expressed mathematically as follows: a positive value x is mapped to ( x ′ = 2 | x | = 2 x , x ≥ 0 {\displaystyle x'=2|x|=2x,\ x\geq 0} ), and a negative value y is mapped to ( y ′ = 2 | y | − 1 = − 2 y − 1 , y < 0 {\displaystyle y'=2|y|-1=-2y-1,\ y<0} ). Such a code may be used for simplicity, even if suboptimal. Truly optimal codes for two-sided geometric distributions include multiple variants of the Golomb code, depending on the distribution parameters, including this one. [ 2 ]
Below is the Rice–Golomb encoding, where the remainder code uses simple truncated binary encoding, also named "Rice coding" (other varying-length binary encodings, like arithmetic or Huffman encodings, are possible for the remainder codes, if the statistic distribution of remainder codes is not flat, and notably when not all possible remainders after the division are used). In this algorithm, if the M parameter is a power of 2, it becomes equivalent to the simpler Rice encoding:
Decoding:
Set M = 10 . Thus b = ⌊ log 2 ( 10 ) ⌋ = 3 {\displaystyle b=\lfloor \log _{2}(10)\rfloor =3} . The cutoff is 2 b + 1 − M = 16 − 10 = 6 {\displaystyle 2^{b+1}-M=16-10=6} .
For example, with a Rice–Golomb encoding using parameter M = 10 , the decimal number 42 would first be split into q = 4 and r = 2, and would be encoded as qcode( q ),rcode( r ) = qcode(4),rcode(2) = 11110,010 (you don't need to encode the separating comma in the output stream, because the 0 at the end of the q code is enough to say when q ends and r begins; both the qcode and rcode are self-delimited).
Given an alphabet of two symbols, or a set of two events, P and Q , with probabilities p and ( 1 − p ) respectively, where p ≥ 1/2 , Golomb coding can be used to encode runs of zero or more P ′s separated by single Q ′s. In this application, the best setting of the parameter M is the nearest integer to − 1 log 2 p {\displaystyle -{\frac {1}{\log _{2}p}}} . When p = 1/2, M = 1, and the Golomb code corresponds to unary ( n ≥ 0 P ′s followed by a Q is encoded as n ones followed by a zero). If a simpler code is desired, one can assign Golomb–Rice parameter b (i.e., Golomb parameter M = 2 b {\displaystyle M=2^{b}} ) to the integer nearest to − log 2 ( − log 2 p ) {\displaystyle -\log _{2}(-\log _{2}p)} ; although not always the best parameter, it is usually the best Rice parameter and its compression performance is quite close to the optimal Golomb code. (Rice himself proposed using various codes for the same data to figure out which was best. A later JPL researcher proposed various methods of optimizing or estimating the code parameter. [ 3 ] )
Consider using a Rice code with a binary portion having b bits to run-length encode sequences where P has a probability p . If P [ bit is part of k -run ] {\displaystyle \mathbb {P} [{\text{bit is part of }}k{\text{-run}}]} is the probability that a bit will be part of an k -bit run ( k − 1 {\displaystyle k-1} P s and one Q ) and ( compression ratio of k -run ) {\displaystyle ({\text{compression ratio of }}k{\text{-run}})} is the compression ratio of that run, then the expected compression ratio is
Compression is often expressed in terms of 1 − E [ compression ratio ] {\displaystyle 1-\mathbb {E} [{\text{compression ratio}}]} , the proportion compressed. For p ≈ 1 {\displaystyle p\approx 1} , the run-length coding approach results in compression ratios close to entropy . For example, using Rice code b = 6 {\displaystyle b=6} for p = 0.99 {\displaystyle p=0.99} yields 91.89% compression, while the entropy limit is 91.92% .
When a probability distribution for integers is not known, the optimal parameter for a Golomb–Rice encoder cannot be determined. Thus, in many applications, a two-pass approach is used: first, the block of data is scanned to estimate a probability density function (PDF) for the data. The Golomb–Rice parameter is then determined from that estimated PDF. A simpler variation of that approach is to assume that the PDF belongs to a parametrized family, estimate the PDF parameters from the data, and then compute the optimal Golomb–Rice parameter. That is the approach used in most of the applications discussed below.
An alternative approach to efficiently encode integer data whose PDF is not known, or is varying, is to use a backwards-adaptive encoder. The RLGR encoder [1] achieves that using a very simple algorithm that adjusts the Golomb–Rice parameter up or down, depending on the last encoded symbol. A decoder can follow the same rule to track the variation of the encoding parameters, so no side information needs to be transmitted, just the encoded data. Assuming a generalized Gaussian PDF, which covers a wide range of statistics seen in data such as prediction errors or transform coefficients in multimedia codecs, the RLGR encoding algorithm can perform very well in such applications.
Numerous signal codecs use a Rice code for prediction residues.
In predictive algorithms, such residues tend to fall into a two-sided geometric distribution , with small residues being more frequent than large residues, and the Rice code closely approximates the Huffman code for such a distribution without the overhead of having to transmit the Huffman table.
One signal that does not match a geometric distribution is a sine wave , because the differential residues create a sinusoidal signal whose values are not creating a geometric distribution (the highest and lowest residue values have similar high frequency of occurrences, only the median positive and negative residues occur less often).
Several lossless audio codecs , such as Shorten , [ 4 ] FLAC , [ 5 ] Apple Lossless , and MPEG-4 ALS , use a Rice code after the linear prediction step (called "adaptive FIR filter" in Apple Lossless).
Rice coding is also used in the FELICS lossless image codec.
The Golomb–Rice coder is used in the entropy coding stage of Rice algorithm based lossless image codecs . One such experiment yields the compression ratio graph shown.
The JPEG-LS scheme uses Rice–Golomb to encode the prediction residuals.
The adaptive version of Golomb–Rice coding mentioned above, the RLGR encoder [2] ,is used for encoding screen content in virtual machines in the RemoteFX component of the Microsoft Remote Desktop Protocol. | https://en.wikipedia.org/wiki/Golomb_coding |
In mathematics , a Golomb ruler is a set of marks at integer positions along a ruler such that no two pairs of marks are the same distance apart. The number of marks on the ruler is its order , and the largest distance between two of its marks is its length . Translation and reflection of a Golomb ruler are considered trivial, so the smallest mark is customarily put at 0 and the next mark at the smaller of its two possible values. Golomb rulers can be viewed as a one-dimensional special case of Costas arrays .
The Golomb ruler was named for Solomon W. Golomb and discovered independently by Sidon (1932) [ 1 ] and Babcock (1953) . Sophie Piccard also published early research on these sets, in 1939, stating as a theorem the claim that two Golomb rulers with the same distance set must be congruent . This turned out to be false for six-point rulers, but true otherwise. [ 2 ]
There is no requirement that a Golomb ruler be able to measure all distances up to its length, but if it does, it is called a perfect Golomb ruler. It has been proved that no perfect Golomb ruler exists for five or more marks. [ 3 ] A Golomb ruler is optimal if no shorter Golomb ruler of the same order exists. Creating Golomb rulers is easy, but proving the optimal Golomb ruler (or rulers) for a specified order is computationally very challenging.
Distributed.net has completed distributed massively parallel searches for optimal order-24 through order-28 Golomb rulers, each time confirming the suspected candidate ruler. [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ]
Currently, the complexity of finding optimal Golomb rulers (OGRs) of arbitrary order n (where n is given in unary) is unknown. [ clarification needed ] In the past there was some speculation that it is an NP-hard problem. [ 3 ] Problems related to the construction of Golomb rulers are provably shown to be NP-hard, where it is also noted that no known NP-complete problem has similar flavor to finding Golomb rulers. [ 9 ]
A set of integers A = { a 1 , a 2 , . . . , a m } {\displaystyle A=\{a_{1},a_{2},...,a_{m}\}} where a 1 < a 2 < . . . < a m {\displaystyle a_{1}<a_{2}<...<a_{m}} is a Golomb ruler if and only if
The order of such a Golomb ruler is m {\displaystyle m} and its length is a m − a 1 {\displaystyle a_{m}-a_{1}} . The canonical form has a 1 = 0 {\displaystyle a_{1}=0} and, if m > 2 {\displaystyle m>2} , a 2 − a 1 < a m − a m − 1 {\displaystyle a_{2}-a_{1}<a_{m}-a_{m-1}} . Such a form can be achieved through translation and reflection.
An injective function f : { 1 , 2 , . . . , m } → { 0 , 1 , . . . , n } {\displaystyle f:\left\{1,2,...,m\right\}\to \left\{0,1,...,n\right\}} with f ( 1 ) = 0 {\displaystyle f(1)=0} and f ( m ) = n {\displaystyle f(m)=n} is a Golomb ruler if and only if
The order of such a Golomb ruler is m {\displaystyle m} and its length is n {\displaystyle n} . The canonical form has
A Golomb ruler of order m with length n may be optimal in either of two respects: [ 11 ] : 237
The general term optimal Golomb ruler is used to refer to the second type of optimality.
Golomb rulers are used within information theory related to error correcting codes . [ 13 ]
Golomb rulers are used in the selection of radio frequencies to reduce the effects of intermodulation interference with both terrestrial [ 14 ] and extraterrestrial [ 15 ] applications.
Golomb rulers are used in the design of phased arrays of radio antennas. In radio astronomy one-dimensional synthesis arrays can have the antennas in a Golomb ruler configuration in order to obtain minimum redundancy of the Fourier component sampling. [ 16 ] [ 17 ]
Multi-ratio current transformers use Golomb rulers to place transformer tap points. [ citation needed ]
A number of construction methods produce asymptotically optimal Golomb rulers.
The following construction, due to Paul Erdős and Pál Turán , produces a Golomb ruler for every odd prime p. [ 12 ]
The following table contains all known optimal Golomb rulers, excluding those with marks in the reverse order. The first four are perfect .
^ * The optimal ruler would have been known before this date; this date represents that date when it was discovered to be optimal (because all other rulers were proved to not be smaller). For example, the ruler that turned out to be optimal for order 26 was recorded on 10 October 2007, but it was not known to be optimal until all other possibilities were exhausted on 24 February 2009. | https://en.wikipedia.org/wiki/Golomb_ruler |
In mathematics, the Golomb sequence , named after Solomon W. Golomb (but also called Silverman's sequence ), is a monotonically increasing integer sequence where a n is the number of times that n occurs in the sequence, starting with a 1 = 1, and with the property that for n > 1 each a n is the smallest positive integer which makes it possible to satisfy the condition. For example, a 1 = 1 says that 1 only occurs once in the sequence, so a 2 cannot be 1 too, but it can be 2, and therefore must be 2. The first few values are
a 1 = 1 Therefore, 1 occurs exactly one time in this sequence.
a 2 > 1 a 2 = 2
2 occurs exactly 2 times in this sequence. a 3 = 2
3 occurs exactly 2 times in this sequence.
a 4 = a 5 = 3
4 occurs exactly 3 times in this sequence. 5 occurs exactly 3 times in this sequence.
a 6 = a 7 = a 8 = 4 a 9 = a 10 = a 11 = 5
etc.
Colin Mallows has given an explicit recurrence relation a ( 1 ) = 1 ; a ( n + 1 ) = 1 + a ( n + 1 − a ( a ( n ) ) ) {\displaystyle a(1)=1;a(n+1)=1+a(n+1-a(a(n)))} . An asymptotic expression for a n is
where φ {\displaystyle \varphi } is the golden ratio (approximately equal to 1.618034). | https://en.wikipedia.org/wiki/Golomb_sequence |
In mathematics , the Golomb–Dickman constant , named after Solomon W. Golomb and Karl Dickman , is a mathematical constant , which arises in the theory of random permutations and in number theory . Its value is
It is not known whether this constant is rational or irrational. [ 1 ]
Its simple continued fraction is given by [ 0 ; 1 , 1 , 1 , 1 , 1 , 22 , 1 , 2 , 3 , 1 , . . . ] {\displaystyle [0;1,1,1,1,1,22,1,2,3,1,...]} , which appears to have an unusually large number of 1s. [ 2 ]
Let a n be the average — taken over all permutations of a set of size n — of the length of the longest cycle in each permutation. Then the Golomb–Dickman constant is
In the language of probability theory , λ n {\displaystyle \lambda n} is asymptotically the expected length of the longest cycle in a uniformly distributed random permutation of a set of size n .
In number theory, the Golomb–Dickman constant appears in connection with the average size of the largest prime factor of an integer. More precisely,
where P 1 ( k ) {\displaystyle P_{1}(k)} is the largest prime factor of k (sequence A006530 in the OEIS ) . So if k is a d digit integer, then λ d {\displaystyle \lambda d} is the asymptotic average number of digits of the largest prime factor of k .
The Golomb–Dickman constant appears in number theory in a different way. What is the
probability that second largest prime factor of n is smaller than the square root of the largest prime factor of n ? Asymptotically, this probability is λ {\displaystyle \lambda } .
More precisely,
where P 2 ( n ) {\displaystyle P_{2}(n)} is the second largest prime factor n .
The Golomb-Dickman constant also arises when we consider the average length of the largest cycle of any function from a finite set to itself. If X is a finite set, if we repeatedly apply a function f : X → X to any element x of this set, it eventually enters a cycle, meaning that for some k we have f n + k ( x ) = f n ( x ) {\displaystyle f^{n+k}(x)=f^{n}(x)} for sufficiently large n ; the smallest k with this property is the length of the cycle. Let b n be the average, taken over all functions from a set of size n to itself, of the length of the largest cycle. Then Purdom and Williams [ 3 ] proved that
There are several expressions for λ {\displaystyle \lambda } . These include: [ 4 ]
where l i ( t ) {\displaystyle \mathrm {li} (t)} is the logarithmic integral ,
where E 1 ( t ) {\displaystyle E_{1}(t)} is the exponential integral , and
and
where ρ ( t ) {\displaystyle \rho (t)} is the Dickman function . | https://en.wikipedia.org/wiki/Golomb–Dickman_constant |
The Gomberg–Bachmann reaction , named for the Russian-American chemist Moses Gomberg and the American chemist Werner Emmanuel Bachmann , is an aryl -aryl coupling reaction via a diazonium salt. [ 1 ] [ 2 ] [ 3 ]
The arene compound (here benzene ) is reacted with a diazonium salt in the presence of a base to provide the biaryl through an intermediate aryl radical . For example, p -bromo biphenyl may be prepared from 4-bromoaniline and benzene : [ 4 ]
The reaction offers a wide scope for both diazonium component and arene component but yields are generally low following the original procedure (less than 40%), given the many side-reactions of diazonium salts. Several improvements have been suggested. One possibility is to employ diazonium tetrafluoroborates in arene solvent together with a phase-transfer catalyst, [ 5 ] another is to use 1-aryl-3,3-dialkyltriazenes. [ 6 ]
One intramolecular variation which gives better results is the Pschorr cyclization : [ 7 ] [ 8 ] [ 9 ]
The group Z can be CH 2 , CH 2 CH 2 , NH and CO (to fluorenone [ 10 ] ) to name just a few. | https://en.wikipedia.org/wiki/Gomberg–Bachmann_reaction |
In mathematics , the Gompertz constant or Euler–Gompertz constant , [ 1 ] [ 2 ] denoted by δ {\displaystyle \delta } , appears in integral evaluations and as a value of special functions . It is named after Benjamin Gompertz .
It can be defined via the exponential integral as: [ 3 ]
The numerical value of δ {\displaystyle \delta } is about
When Euler studied divergent infinite series, he encountered δ {\displaystyle \delta } via, for example, the above integral representation. Le Lionnais called δ {\displaystyle \delta } the Gompertz constant because of its role in survival analysis . [ 1 ]
In 1962, A. B. Shidlovski proved that at least one of the Euler–Mascheroni constant and the Euler–Gompertz constant is irrational . [ 4 ] This result was improved in 2012 by Tanguy Rivoal where he proved that at least one of them is transcendental . [ 2 ] [ 5 ] [ 6 ] [ 7 ]
The most frequent appearance of δ {\displaystyle \delta } is in the following integrals:
which follow from the definition of δ by integration of parts and a variable substitution respectively.
Applying the Taylor expansion of Ei {\displaystyle \operatorname {Ei} } we have the series representation
Gompertz's constant is connected to the Gregory coefficients via the 2013 formula of I. Mező: [ 8 ]
The Gompertz constant also happens to be the regularized value of the summation of alternating factorials of all positive integers and summing over all factorial values of every integer leads to zero { divergent series : [ 2 ] [ dubious – discuss ] }
It is also related to several polynomial continued fractions : [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Gompertz_constant |
The Gompertz–Makeham law states that the human death rate is the sum of an age-dependent component (the Gompertz function , named after Benjamin Gompertz ), [ 1 ] which increases exponentially with age, [ 2 ] and an age-independent component (the Makeham term, named after William Makeham ). [ 3 ] In a protected environment where external causes of death are rare (laboratory conditions, low mortality countries, etc.), the age-independent mortality component is often negligible. In this case the formula simplifies to a Gompertz law of mortality. In 1825, Benjamin Gompertz proposed an exponential increase in death rates with age.
The Gompertz–Makeham law of mortality describes the age dynamics of human mortality rather accurately in the age window from about 30 to 80 years of age. At more advanced ages, some studies have found that death rates increase more slowly – a phenomenon known as the late-life mortality deceleration [ 2 ] – but more recent studies disagree. [ 4 ]
The decline in the human mortality rate before the 1950s was mostly due to a decrease in the age-independent (Makeham) mortality component, while the age-dependent (Gompertz) mortality component was surprisingly stable. [ 2 ] [ 6 ] Since the 1950s, a new mortality trend has started in the form of an unexpected decline in mortality rates at advanced ages and "rectangularization" of the survival curve. [ 7 ] [ 8 ]
The hazard function for the Gompertz-Makeham distribution is most often characterised as h ( x ) = α e β x + λ {\displaystyle h(x)=\alpha e^{\beta x}+\lambda } . The empirical magnitude of the beta-parameter is about .085, implying a doubling of mortality every .69/.085 = 8 years (Denmark, 2006).
The quantile function can be expressed in a closed-form expression using the Lambert W function : [ 9 ]
The Gompertz law is the same as a Fisher–Tippett distribution for the negative of age, restricted to negative values for the random variable (positive values for age). | https://en.wikipedia.org/wiki/Gompertz–Makeham_law_of_mortality |
Gonadarche ( / ˌ ɡ oʊ n ə ˈ d ɑːr k i / ) refers to the earliest gonadal (reproductive gland) changes of puberty . [ 1 ] In response to pituitary gonadotropins , the ovaries in females and the testes in males begin to grow and increase the production of the sex steroids , especially estradiol and testosterone . [ 2 ] The ovary and testis have receptors, follicle cells and leydig cells, respectively, where gonadotropins bind to stimulate the maturation of the gonads and secretion of estrogen and testosterone. [ 3 ] Certain disorders can result in changes to timing or nature of these processes.
Gonadarche should be contrasted with adrenarche . Gonadarche indicates that true central puberty has begun, while adrenarche is an independent maturational process only loosely associated with complete puberty. [ 5 ]
Puberty is influenced by a multitude of factors including genetic, prenatal, nutritional, and environmental status. Parental pubescent age also influences what age a person starts puberty. [ 6 ] Puberty usually begins around ages 10—11 in females and around ages 11—12 in males. [ 7 ] Body weight and nutrition status is evidenced to have an effect on puberty onset as well, due to some input from adipose tissue hormonal signaling. [ 8 ] Puberty involves both the processes of gonadarche and adrenarche. [ 6 ] Adrenarche is responsible for the maturation of the adrenal gland during puberty and stimulates the development of body odor, axillary hair, and acne. [ 6 ] [ 9 ]
Gonadarche starts off by the macroneurons of the hypothalamus which produce hormone called the gonadotropin-releasing hormone (GnRH) which is responsible for the release of the hormones follicle-stimulating hormone (FSH) and luteinizing hormone (LH) , which are produced by the anterior pituitary. [ 10 ]
Gonadarche marks the beginning of puberty and it is the process in which gonads, or the primary reproductive organs, mature, following stimulation of gonadotropin hormone-releasing hormone (GnRH) release in the hypothalamus. [ 6 ] The release of GnRH triggers a release of hormones that activate the maturation of the ovary and testis. [ 3 ] This release is mediated primarily through action of the hypothalamic-pituitary-gonadal axis, a hormonal signaling system active in gestation and fetal development, reactivated around the time of gonadarche to mediate GnRH pulsing release. This, as mentioned above, stimulates FSH and LH release. This activation is also influenced by release of the protein kisspeptin at the time of gonadarche onset. [ 11 ] The production of kisspeptin mediates the GnRH pulse release in puberty, but also GnRH activity during fetal development. [ 12 ] Prior to onset of gonadarche, stimulation of these hormones from the hypothalamus is suppressed through GABAergic-releasing inhibitory neurons in the central nervous system. [ 13 ] Some input of suppression is also linked to secretions of estrogen from immature ovaries in females. [ 8 ]
Onset of gonadarche varies between sexes. Average age of onset averages to around eleven years old in males and averages to around nine years old in females. [ 14 ]
In females, the first clinical indication of the beginning of adult breast development is thelarche . One in each five females may show signs of pubarche before thelarche. [ 15 ] The clinical development across normal puberty is better classified by the Tanner Stages of sexual development for breast and pubic hair. [ 16 ] In females, the pubertal growth spurt arise early in puberty due to the direct stimulation of sex steroids and indirectly by the growth hormone-insulin-like growth factor (GH-IGF) axis. [ 17 ] Ovulation and follicular functions are stimulated by the gonadotropins released by the hypothalamic-pituitary-gonadal axis' action. [ 11 ] Ovarian production of progesterone and estradiol come to adult levels through this process. [ 12 ]
In males, gonadarche is determined with testicular volume greater than 3 mL, genital stage greater than or equal to 2, or pubarche, which is defined as pubic hair stage greater than or equal to 2. If testicular volumes of the 2 testes are not equal, the larger testis measurement is used. Similarly in females, if a female has a larger breast stage on one side, this stage is used. [ 18 ] Gonadotropins release mediates maturation of seminiferous tubules to be ready to perform spermatogenesis primarily through stimulation of Sertoli cells, while Leydig cells are similarly stimulted to produce adult levels of testosterone. [ 11 ]
Hormonal markers of progression of maturation differ between sexes as well. Tracking of AMH and inhibin B levels can be useful in males, as well as gonadotropin and androgen levels earlier on in puberty. Females also have stable AMH levels, with gonadotropin levels being useful markers longer from between 8 and 4 times as long compared to as in males. [ 19 ]
The disorder Central Precocious Puberty (CPP) is also known as Progressive Precocious Gonadarche or GnRH-dependent precocious puberty, and it occurs when a child's body initiates puberty earlier than what is normally observed. Individuals with CPP will often experience an early growth spurt because their bones are maturing faster than usual. However, since their growth plates will often close earlier and without proper treatment, children with CPP may not reach their predicted adult height.
CPP is caused by premature activation or incompletely suppressed hypothalamic GnRH(gonadotropin-releasing hormone) pulse generator. [ 20 ] The GnRH pulse generator is a control center in the body that regulates the release of two important hormones, LH (Luteinizing hormone) and FSH (follicle stimulating hormone), hormones crucial in fertility.
Children with this condition undergo the typical stages of puberty, including the early development of reproductive organs, at younger ages than usual. This is a rare condition with an estimated incidence of about 0.02 to 1.07 cases per million each year based on data collected from 2008 to 2010 in Spain. [ 4 ]
CPP is seen more often in young females than males, possibly due to females having less suppression of this pulse generator before puberty. Around 90% of cases are considered to have no identifiable cause in females, while in males, 50% to 70% of cases can be linked to an identifiable cause. Some cases of CPP are associated with specific gene mutations related to GnRH and gonadotropin secretion. [ 4 ]
Preferred treatment for CPP is a GnRH receptor agonist. [ 21 ] These medications are modified variations of natural GnRH. They are degraded at a slower rate than native GnRH and have a stronger effect on GnRH receptors. This results in continuous GnRH stimulation in the pitutitary, which slows down the production of more GnRH, decreasing gonadotropin secretion. These GnRH receptor agonists are available in the US as daily injections or less frequent depot forms, given every 28 days. [ 4 ]
When treating children with CPP, the main goal is to preserve adult height. [ 22 ] When trying to preserve adult height it is important to keep a few precautions in mind. During treatment, there is a significant amount of variation in height gained, as it is closely related to the age at which treatment is started. This variation is especially seen in females. Additionally, height outcomes are usually calculated based on the difference between projected adult height, the height recorded at the beginning of treatment, and at the end of treatment. This approach is controversial, as there are frequent overestimations when heights are projected in children with CPP. As a result, health professionals are rarely able to accurately predict the hight outcome of people with CPP.
Psychological distress in relation to early puberty is a concern for many, and some have considered stopping puberty in children with CPP as a means to addressing this issue. Some reports have illustrated poorer psychological outcomes in children with CPP or early menarche. However, there are other studies that counter act this claim and find no difference in the psychological outcomes in gris with CPP. [ 22 ]
CDGP is a conditions characterized by an extreme variation from the normal timing of puberty. Both gonadarche and adrenarche are delayed in this case, resulting in some children developing later than others. There is a delay in the development of the reproductive organs and adrenal glands seen in children with CDGP. Individuals with CDGP usually will display decreased growth velocity during early years of life, but their growth will ultimately catch up with and follow growth patterns seen in the fifth percentile during childhood. However, growth velocity subsequently decreases during the early years of adolescents, due to a transient decrease in GH (growth hormone) secretion. Often, there is a family history of delayed puberty. Individuals with CDGP, often have slower bone maturation, and predicted height is often lower than what is predicted by their genetic potential (based on the height's of their biological parents). [ 6 ]
There are currently no reliable diagnostic tests that can be conducted to distinguish CDGP from Hypogonadism. As a result, diagnoses of CDGP are done by ruling out other possible causes. However, there have been laboratory studies done to differentiate a diagnosis of CDGP from Hypogonadotropic Hypogonadism using inhibin B and anti-Müllerian hormone concentrations. [ 23 ]
When treating children with CDGP, the goal is to improve growth as well as maintain average body proportions and peak bone mass, while ensuring that growth potential is not impaired. Emotional outcomes for children are also studied, as distress has been documented in some children due to their lack of growth. This distress has been shown to affect their school performance and social relationships. [ 1 ]
Childhood obesity has increased over the past several years particularly around 1975–2016. [ 24 ] The research supporting the link between obesity and delayed puberty in both females and males is still not concrete. Some studies have supported that obesity may have an effect of earlier puberty in females but the data is not consistent with its relation to delayed puberty in males. [ 25 ]
Assessment of the start of puberty can be harder to identify between males and females. Thelarche or breast bud development is usually the first sign of puberty in females. In children with obesity, it may be harder to identify excess adipose tissue with bread bud development, leading to potential false early puberty diagnosis. [ 25 ]
Some data suggests that obesity can lead to a later pubertal onset in males. [ 26 ] However, markers of early gonadal development is harder to identify in males because the true marker of the onset of puberty is testicular enlargement of 3 ml of larger which requires more invasive observations. [ 24 ]
In conclusion, starting treatment as early as right after diagnosis is related to significant success in maintaining final adult height in case of CPP. The outcomes are determined by different factors; such as advancement of bone change in case of CDGP, age at which a child's body begins changing in case of CPP, the timing of initiation, and duration of treatment. [ 27 ] The hypothalamic–pituitary–gonadal (HPG) axis which is essentially in charge of regulating reproductive activity and releasing estrogen and progesterone in humans returns to normal levels by the end of the treatment and the children generally have normal development of puberty after finishing the treatment same as the normal levels of typical children. [ 27 ] There is not much data on the long-term endocrine, metabolic, reproductive, and psychological outcomes. | https://en.wikipedia.org/wiki/Gonadarche |
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