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Mitochondrial ROS ( mtROS or mROS ) are reactive oxygen species (ROS) that are produced by mitochondria . [ 1 ] [ 2 ] [ 3 ] Generation of mitochondrial ROS mainly takes place at the electron transport chain located on the inner mitochondrial membrane during the process of oxidative phosphorylation . Leakage of electrons at complex I and complex III from electron transport chains leads to partial reduction of oxygen to form superoxide . Subsequently, superoxide is quickly dismutated to hydrogen peroxide by two dismutases including superoxide dismutase 2 (SOD2) in mitochondrial matrix and superoxide dismutase 1 (SOD1) in mitochondrial intermembrane space. Collectively, both superoxide and hydrogen peroxide generated in this process are considered as mitochondrial ROS. [ 1 ]
Once thought as merely the by-products of cellular metabolism, mitochondrial ROS are increasingly viewed as important signaling molecules, [ 4 ] whose levels of generation at 11 currently-identified sites vary depending on cellular energy supply and demand. [ 5 ] [ 6 ] At low levels, mitochondrial ROS are considered to be important for metabolic adaptation as seen in hypoxia. [ 1 ] Mitochondrial ROS, stimulated by danger signals such as lysophosphatidylcholine and Toll-like receptor 4 and Toll-like receptor 2 bacterial ligands lipopolysaccharide (LPS) and lipopeptides , are involved in regulating inflammatory response. [ 7 ] [ 8 ] Finally, high levels of mitochondrial ROS activate apoptosis / autophagy pathways capable of inducing cell death. [ 9 ]
Monocytes/macrophages are the most enriched immune cell types in the lungs of COVID-19 patients and appear to have a central role in the pathogenicity of the disease. These cells adapt their metabolism upon infection and become highly glycolytic, which facilitates SARS-CoV-2 replication. The infection triggers mitochondrial ROS production, which induces stabilization of hypoxia-inducible factor-1α ( HIF1A ) and consequently promotes glycolysis. HIF1A-induced changes in monocyte metabolism by SARS-CoV-2 infection directly inhibit T cell response and reduce epithelial cell survival. Targeting mitochondrial ROS may have great therapeutic potential for the development of novel drugs to treat patients with coronavirus. [ 10 ]
Mitochondrial ROS can promote cellular senescence and aging phenotypes in the skin of mice. [ 11 ] Ordinarily mitochondrial SOD2 protects against mitochondrial ROS. Epidermal cells in mutant mice with a genetic SOD2 deficiency undergo cellular senescence, nuclear DNA damage , and irreversible arrest of proliferation in a portion of their keratinocytes . [ 11 ] [ 12 ]
Mutant mice with a conditional deficiency for mitochondrial SOD2 in connective tissue have an accelerated aging phenotype . [ 13 ] This aging phenotype includes weight loss, skin atrophy , kyphosis (curvature of the spine), osteoporosis , muscle degeneration and reduced life span.
Mitochondrial ROS attack DNA readily, generating a variety of DNA damages such as oxidized bases and strand breaks. The major mechanism that cells use to repair oxidized bases such as 8-hydroxyguanine , formamidopyrimidine and 5-hydroxyuracil is base excision repair (BER). [ 14 ] BER occurs in both the cell nucleus and in mitochondria. | https://en.wikipedia.org/wiki/Mitochondrial_ROS |
Mitochondrial biogenesis is the process by which cells increase mitochondrial numbers. [ 1 ] [ 2 ] It was first described by John Holloszy in the 1960s, when it was discovered that physical endurance training induced higher mitochondrial content levels, leading to greater glucose uptake by muscles. [ 3 ] Mitochondrial biogenesis is activated by numerous different signals during times of cellular stress or in response to environmental stimuli, such as aerobic exercise . [ 1 ] [ 2 ] [ 4 ]
The ability for a mitochondrion to self-replicate is rooted in its evolutionary history. It is commonly thought that mitochondria descend from cells that formed endosymbiotic relationships with α-protobacteria ; they have their own genome for replication. [ 5 ] However, recent evidence suggests that mitochondria may have evolved without symbiosis. [ 6 ] The mitochondrion is a key regulator of the metabolic activity of the cell, and is also an important organelle in both production and degradation of free radicals. [ 7 ] It is postulated that higher mitochondrial copy number (or higher mitochondrial mass) is protective for the cell.
Mitochondria are produced from the transcription and translation of genes both in the nuclear genome and in the mitochondrial genome . The majority of mitochondrial protein comes from the nuclear genome, while the mitochondrial genome encodes parts of the electron transport chain along with mitochondrial rRNA and tRNA . Mitochondrial biogenesis increases metabolic enzymes for glycolysis, oxidative phosphorylation and ultimately a greater mitochondrial metabolic capacity. However, depending on the energy substrates available and the redox state of the cell, the cell may increase or decrease the number and size of mitochondria. [ 8 ] Critically, mitochondrial numbers and morphology vary according to cell type and context-specific demand, whereby the balance between mitochondrial fusion/fission regulates mitochondrial distribution, morphology, and function. [ 9 ] [ 8 ]
Since the majority of mitochondrial protein comes from the nuclear genome, the proteins need to be properly targeted and transported into the mitochondria to perform their functions. [ 8 ] [ 10 ] [ 11 ] First, mRNA is translated in the cell's cytosol. [ 10 ] [ 11 ] The resulting unfolded precursor proteins will then be able to reach their respective mitochondrial compartments. [ 11 ] [ 10 ] Precursor proteins will be transported to one of four areas of the mitochondria, which include the outer membrane, inner membrane, intermembrane space, and matrix. [ 10 ] [ 11 ] All proteins will enter the mitochondria by a translocase on the outer mitochondrial membrane (TOM). [ 11 ] [ 10 ] [ 5 ] Some proteins will have an N-terminal targeting signal, and these proteins will be detected and transported into the matrix, where they will then be cleaved and folded. [ 12 ] [ 11 ] [ 10 ] Other proteins may have targeting information in their sequences and will not include an N-terminal signal. [ 11 ] [ 10 ] During the past two decades, researchers have discovered over thirty proteins that participate in mitochondrial protein import. [ 11 ] As researchers learn more about these proteins and how they reach the respective mitochondrial compartments that utilize them, it becomes evident that there is a multitude of processes that work together in the cell to allow for mitochondrial biogenesis. [ 11 ] [ 8 ]
Mitochondria are highly versatile and are able to change their shape through fission and fusion events. [ 9 ] [ 8 ] Definitively, fission is the event of a single entity breaking apart, whereas fusion is the event of two or more entities joining to form a whole. [ 8 ] The processes of fission and fusion oppose each other and allow the mitochondrial network to constantly remodel itself. [ 9 ] [ 8 ] If a stimulus induces a change in the balance of fission and fusion in a cell, it could significantly alter the mitochondrial network. [ 9 ] [ 13 ] For example, an increase in mitochondrial fission would create many fragmented mitochondria, which has been shown to be useful for eliminating damaged mitochondria and for creating smaller mitochondria for efficient transporting to energy-demanding areas. [ 13 ] [ 14 ] Therefore, achieving a balance between these mechanisms allows a cell to have the proper organization of its mitochondrial network during biogenesis and may have an important role in muscle adaptation to physiological stress. [ 13 ]
In mammals, mitochondrial fusion and fission are both controlled by GTPases of the dynamin family. [ 8 ] [ 13 ] The process of mitochondrial fission is directed by Drp1 , a member of the cytosolic dynamin family. [ 8 ] [ 9 ] This protein forms a spiral around mitochondria and constricts to break apart both the outer and inner membranes of the organelle. [ 14 ] On the other hand, the process of fusion is directed by different membrane-anchored dynamin proteins at different levels of the mitochondria. [ 13 ] Fusion at the level of the outer mitochondrial membrane is mediated by Mfn1 and Mfn2 (Mitofusins 1 and 2), [ 15 ] and fusion at the level of the inner mitochondrial membrane is mediated by Opa1 . [ 8 ] [ 12 ] [ 13 ] Multiple research studies have observed correlated increases between mitochondrial respiratory capacity with Mfn1, Mnf2, and Drp1 gene expression after endurance exercises. [ 14 ] [ 15 ] Therefore, it is supported that reorganization of the mitochondrial network in muscle cells plays an important role in response to exercise. [ 4 ] [ 13 ] [ 15 ]
PGC-1α , a member of the peroxisome proliferator-activated receptor gamma (PGC) family of transcriptional coactivators , is the master regulator of mitochondrial biogenesis. [ 1 ] [ 2 ] [ 16 ] It is known to co-activate nuclear respiratory factor 2 (NRF2/GABPA) , and together with NRF-2 coactivates nuclear respiratory factor 1 ( NRF1 ). [ 15 ] [ 16 ] The NRFs, in turn, activate the mitochondrial transcription factor A (tfam) , which is directly responsible for transcribing nuclear-encoded mitochondrial proteins. [ 15 ] [ 16 ] This includes both structural mitochondrial proteins as well as those involved in mtDNA transcription, translation, and repair . [ 16 ] PGC-1β, a protein that is structurally similar to PGC-1α , is also involved in regulating mitochondrial biogenesis, but differs in that it does not get increased in response to exercise. [ 5 ] [ 17 ] [ 16 ] While there have been significant increases in mitochondria found in tissues where PGC-1α is overexpressed, as the cofactor interacts with these key transcription factors, knockout mice with disrupted PGC-1α are still viable and show normal mitochondrial abundance. [ 17 ] [ 5 ] [ 16 ] Thus, PGC-1α is not required for normal development of mitochondria in mice, but when put under physiological stress, these mice exhibit diminished tolerance compared to mice with normal levels of PGC-1α. [ 5 ] [ 16 ] [ 17 ] Similarly, in knockout mice with disrupted PGC-1β, the mice showed mostly normal levels of mitochondrial function with decreased ability to adapt to physiological stress. [ 18 ] [ 5 ] However, a double knockout experiment of PGC-1α/β created mice that died mostly within 24 hours by defects in mitochondrial maturation of cardiac tissue. [ 19 ] These findings suggest that while both PGC-1α and PGC- 1β do not each solely establish a cell's ability to perform mitochondrial biogenesis, together they are able to complement each other for optimal mitochondrial maturation and function during periods of physiological stress. [ 19 ] [ 5 ] [ 17 ]
AMP-activated kinase (AMPK) also regulates mitochondrial biogenesis by phosphorylating and activating PGC-1α upon sensing an energy deficiency in muscle. [ 5 ] [ 16 ] In mice with reduced ATP/AMP ratios that would occur during exercise, the energy depletion has been shown to correlate with AMPK activation. [ 5 ] [ 18 ] [ 16 ] AMPK activation then continued to activate PGC- 1α and NRFs in these mice, and mitochondrial biogenesis was stimulated. [ 5 ] [ 18 ] [ 16 ]
The capacity for mitochondrial biogenesis has been shown to decrease with age, and such decreased mitochondrial function has been associated with diabetes and cardiovascular disease. [ 20 ] [ 21 ] [ 22 ] Aging and disease can induce changes in the expression levels of proteins involved in the fission and fusion mechanisms of mitochondria, thus creating dysfunctional mitochondria. [ 23 ] [ 24 ] One hypothesis for the detrimental results of aging is associated with the loss of telomeres , the end segments of chromosomes that protect genetic information from degradation. [ 21 ] [ 24 ] Telomere loss has also been associated with decreased mitochondrial function. [ 24 ] [ 21 ] Deficiency of telomerase reverse transcriptase (TERT) , an enzyme that plays a role in preserving telomeres, has been correlated with activated p53, a protein that suppresses PGC-1α. [ 24 ] [ 23 ] [ 21 ] Therefore, the loss of telomeres and TERT that comes with aging has been associated with impaired mitochondrial biogenesis. [ 21 ] [ 23 ] [ 24 ] AMPK expression has also been shown to diminish with age, which may also contribute to suppressing mitochondrial biogenesis. [ 5 ] [ 24 ]
Mitochondrial biogenesis can be targeted to prevent cancer proliferation. Specifically, two biogenesis regulators—PGC1α and c-Myc —can be targeted to prevent cancer proliferation. PGC1α is a key component in mitochondrial biogenesis—as a transcriptional coactivator, it targets multiple transcription factors and the estrogen-related receptor alpha (ERRα). [ 25 ] Compounds that target the pathway between PGC1α and ERRα, such as the ERRα inverse agonist, XCT-790 , have been found to significantly decrease mitochondrial biogenesis, thus greatly reducing cancer cells’ proliferation and increasing their sensitivity to chemotherapeutic agents. [ 26 ] c-Myc, a transcription factor, can be inhibited during its dimerization with Max protein by molecules such as IIA6B17 [ 27 ] and omomyc. [ 28 ] Inhibition of the c-Myc-Max complex can block the cell cycle and induce apoptosis in cancer cells. | https://en.wikipedia.org/wiki/Mitochondrial_biogenesis |
Mitochondrial disease is a group of disorders caused by mitochondrial dysfunction . Mitochondria are the organelles that generate energy for the cell and are found in every cell of the human body except red blood cells . They convert the energy of food molecules into the ATP that powers most cell functions.
Mitochondrial diseases take on unique characteristics both because of the way the diseases are often inherited and because mitochondria are so critical to cell function. A subclass of these diseases that have neuromuscular symptoms are known as mitochondrial myopathies .
Mitochondrial disease can manifest in many different ways [ 1 ] whether in children [ 2 ] or adults. [ 3 ] Examples of mitochondrial diseases include:
Conditions such as Friedreich's ataxia can affect the mitochondria but are not associated with mitochondrial proteins.
Acquired conditions in which mitochondrial dysfunction has been involved include:
The body, and each mutation, is modulated by other genome variants; the mutation that in one individual may cause liver disease might in another person cause a brain disorder. The severity of the specific defect may also be great or small. Some defects include exercise intolerance . Defects often affect the operation of the mitochondria and multiple tissues more severely, leading to multi-system diseases. [ 14 ]
It has also been reported that drug tolerant cancer cells have an increased number and size of mitochondria, which suggested an increase in mitochondrial biogenesis. [ 15 ] A recent study in Nature Nanotechnology has reported that cancer cells can hijack the mitochondria from immune cells via physical tunneling nanotubes. [ 16 ]
As a rule, mitochondrial diseases are worse when the defective mitochondria are present in the muscles , cerebrum , or nerves , [ 17 ] because these cells use more energy than most other cells in the body.
Although mitochondrial diseases vary greatly in presentation from person to person, several major clinical categories of these conditions have been defined, based on the most common phenotypic features, symptoms, and signs associated with the particular mutations that tend to cause them. [ citation needed ]
An outstanding question and area of research is whether ATP depletion or reactive oxygen species are in fact responsible for the observed phenotypic consequences. [ citation needed ]
Cerebellar atrophy or hypoplasia has sometimes been reported to be associated. [ 18 ]
Mitochondrial disorders may be caused by mutations (acquired or inherited), in mitochondrial DNA (mtDNA), or in nuclear genes that code for mitochondrial components. They may also be the result of acquired mitochondrial dysfunction due to adverse effects of drugs , infections , or other environmental causes. [ 19 ]
Nuclear DNA has two copies per cell (except for sperm and egg cells), one copy being inherited from the father and the other from the mother. Mitochondrial DNA, however, is inherited from the mother only (with some exceptions ) and each mitochondrion typically contains between 2 and 10 mtDNA copies. During cell division the mitochondria segregate randomly between the two new cells. Those mitochondria make more copies, normally reaching 500 mitochondria per cell. As mtDNA is copied when mitochondria proliferate, they can accumulate random mutations, a phenomenon called heteroplasmy . If only a few of the mtDNA copies inherited from the mother are defective, mitochondrial division may cause most of the defective copies to end up in just one of the new mitochondria (for more detailed inheritance patterns, see human mitochondrial genetics ). Mitochondrial disease may become clinically apparent once the number of affected mitochondria reaches a certain level; this phenomenon is called " threshold expression ".
Mitochondria possess many of the same DNA repair pathways as nuclei do—but not all of them; [ 20 ] therefore, mutations occur more frequently in mitochondrial DNA than in nuclear DNA (see Mutation rate ). This means that mitochondrial DNA disorders may occur spontaneously and relatively often. Defects in enzymes that control mitochondrial DNA replication (all of which are encoded for by genes in the nuclear DNA) may also cause mitochondrial DNA mutations.
Most mitochondrial function and biogenesis is controlled by nuclear DNA . Human mitochondrial DNA encodes 13 proteins of the respiratory chain , while most of the estimated 1,500 proteins and components targeted to mitochondria are nuclear-encoded. Defects in nuclear-encoded mitochondrial genes are associated with hundreds of clinical disease phenotypes including anemia , dementia , hypertension , lymphoma , retinopathy , seizures , and neurodevelopmental disorders . [ 21 ]
A study by Yale University researchers (published in the February 12, 2004, issue of the New England Journal of Medicine ) explored the role of mitochondria in insulin resistance among the offspring of patients with type 2 diabetes. [ 22 ] Other studies have shown that the mechanism may involve the interruption of the mitochondrial signaling process in body cells ( intramyocellular lipids ). A study conducted at the Pennington Biomedical Research Center in Baton Rouge, Louisiana [ 23 ] showed that this, in turn, partially disables the genes that produce mitochondria.
The effective overall energy unit for the available body energy is referred to as the daily glycogen generation capacity, [ 24 ] [ 25 ] [ 26 ] and is used to compare the mitochondrial output of affected or chronically glycogen-depleted individuals to healthy individuals. [ 25 ]
The glycogen generation capacity is entirely dependent on, and determined by, the operating levels of the mitochondria in all of the cells of the human body ; [ 27 ] however, the relation between the energy generated by the mitochondria and the glycogen capacity is very loose and is mediated by many biochemical pathways . [ 24 ] The energy output of full healthy mitochondrial function can be predicted exactly by a complicated theoretical argument, but this argument is not straightforward, as most energy is consumed by the brain and is not easily measurable.
Mitochondrial diseases are usually detected by analysing muscle samples, where the presence of these organelles is higher. The most common tests for the detection of these diseases are:
Although research is ongoing, treatment options are currently limited; vitamins are frequently prescribed, though the evidence for their effectiveness is limited. [ 29 ] Pyruvate has been proposed in 2007 as a treatment option. [ 30 ] N-acetyl cysteine reverses many models of mitochondrial dysfunction. [ 31 ]
In the case of mood disorders, specifically bipolar disorder , it is hypothesized that N-acetyl-cysteine (NAC), acetyl-L-carnitine (ALCAR), S-adenosylmethionine (SAMe), coenzyme Q10 (CoQ10), alpha-lipoic acid (ALA), creatine monohydrate (CM), and melatonin could be potential treatment options. [ 32 ]
Mitochondrial replacement therapy (MRT), where the nuclear DNA is transferred to another healthy egg cell leaving the defective mitochondrial DNA behind, is an IVF treatment procedure. [ 33 ] Using a similar pronuclear transfer technique, researchers at Newcastle University led by Douglass Turnbull successfully transplanted healthy DNA in human eggs from women with mitochondrial disease into the eggs of women donors who were unaffected. [ 34 ] [ 35 ] In such cases, ethical questions have been raised regarding biological motherhood, since the child receives genes and gene regulatory molecules from two different women . Using genetic engineering in attempts to produce babies free of mitochondrial disease is controversial in some circles and raises important ethical issues . [ 36 ] [ 37 ] A male baby was born in Mexico in 2016 from a mother with Leigh syndrome using MRT. [ 38 ]
In September 2012 a public consultation was launched in the UK to explore the ethical issues involved. [ 39 ] Human genetic engineering was used on a small scale to allow infertile women with genetic defects in their mitochondria to have children. [ 40 ] In June 2013, the United Kingdom government agreed to develop legislation that would legalize the 'three-person IVF ' procedure as a treatment to fix or eliminate mitochondrial diseases that are passed on from mother to child. The procedure could be offered from 29 October 2015 once regulations had been established. [ 41 ] [ 42 ] [ 43 ] Embryonic mitochondrial transplant and protofection have been proposed as a possible treatment for inherited mitochondrial disease, and allotopic expression of mitochondrial proteins as a radical treatment for mtDNA mutation load.
In June 2018 Australian Senate's Senate Community Affairs References Committee recommended a move towards legalising Mitochondrial replacement therapy (MRT). Research and clinical applications of MRT were overseen by laws made by federal and state governments. State laws were, for the most part, consistent with federal law. In all states, legislation prohibited the use of MRT techniques in the clinic, and except for Western Australia, research on a limited range of MRT was permissible up to day 14 of embryo development, subject to a license being granted. In 2010, the Hon. Mark Butler MP, then Federal Minister for Mental Health and Ageing, had appointed an independent committee to review the two relevant acts: the Prohibition of Human Cloning for Reproduction Act 2002 and the Research Involving Human Embryos Act 2002 . The committee's report, released in July 2011, recommended the existing legislation remain unchanged
Currently, human clinical trials are underway at GenSight Biologics (ClinicalTrials.gov # NCT02064569) and the University of Miami (ClinicalTrials.gov # NCT02161380) to examine the safety and efficacy of mitochondrial gene therapy in Leber's hereditary optic neuropathy.
About 1 in 4,000 children in the United States will develop mitochondrial disease by the age of 10 years. Up to 4,000 children per year in the US are born with a type of mitochondrial disease. [ 44 ] Because mitochondrial disorders contain many variations and subsets, some particular mitochondrial disorders are very rare.
The average number of births per year among women at risk for transmitting mtDNA disease is estimated to approximately 150 in the United Kingdom and 800 in the United States . [ 45 ]
The first pathogenic mutation in mitochondrial DNA was identified in 1988; from that time to 2016, around 275 other disease-causing mutations were identified. [ 46 ]
Notable people with mitochondrial disease include: | https://en.wikipedia.org/wiki/Mitochondrial_disease |
Mitochondria are dynamic organelles with the ability to fuse and divide ( fission ), forming constantly changing tubular networks in most eukaryotic cells. These mitochondrial dynamics, first observed over a hundred years ago [ 1 ] are important for the health of the cell, and defects in dynamics lead to genetic disorders . Through fusion, mitochondria can overcome the dangerous consequences of genetic malfunction. [ 2 ] The process of mitochondrial fusion involves a variety of proteins that assist the cell throughout the series of events that form this process.
When cells experience metabolic or environmental stresses , mitochondrial fusion and fission work to maintain functional mitochondria. An increase in fusion activity leads to mitochondrial elongation, whereas an increase in fission activity results in mitochondrial fragmentation. [ 3 ] The components of this process can influence programmed cell death and lead to neurodegenerative disorders such as Parkinson's disease . Such cell death can be caused by disruptions in the process of either fusion or fission. [ 4 ]
The shapes of mitochondria in cells are continually changing via a combination of fission, fusion, and motility. Specifically, fusion assists in modifying stress by integrating the contents of slightly damaged mitochondria as a form of complementation. By enabling genetic complementation , fusion of the mitochondria allows for two mitochondrial genomes with different defects within the same organelle to individually encode what the other lacks. In doing so, these mitochondrial genomes generate all of the necessary components for a functional mitochondrion. [ 2 ]
The combined effects of continuous fusion and fission give rise to mitochondrial networks. The mechanisms of mitochondrial fusion and fission are regulated by proteolysis and posttranslational modifications. The actions of fission, fusion and motility cause the shapes of mitochondria to continually change.
The changes in balance between the rates of mitochondrial fission and fusion directly affect the wide range of mitochondrial lengths that can be observed in different cell types. Rapid fission and fusion of the mitochondria in cultured fibroblasts has been shown to promote the redistribution of mitochondrial green fluorescent protein (GFP) from one mitochondrion to all of the other mitochondria. This process can occur in a cell within a time period as short as an hour. [ 4 ]
The significance of mitochondrial fission and fusion is distinct for nonproliferating neurons, which are unable to survive without mitochondrial fission. Such nonproliferating neurons cause two human diseases known as dominant optic atrophy and Charcot Marie Tooth disease type 2A, which are both caused by fusion defects. Though the importance of these processes is evident, it is still unclear why mitochondrial fission and fusion are necessary for nonproliferating cells.
Many gene products that control mitochondrial fusion have been identified, and can be reduced to three core groups which also control mitochondrial fission. These groups of proteins include mitofusins, OPA1 /Mgm1, and Drp1/ Dnm1 . All of these molecules are GTP hydrolyzing proteins ( GTPases ) that belong to the dynamin family. Mitochondrial dynamics in different cells are understood by the way in which these proteins regulate and bind to each other. [ 2 ] These GTPases in control of mitochondrial fusion are well conserved between mammals, flies, and yeast. Mitochondrial fusion mediators differ between the outer and inner membranes of the mitochondria. Specific membrane-anchored dynamin family members mediate fusion between mitochondrial outer membranes known as Mfn1 and Mfn2 . These two proteins are mitofusin contained within humans that can alter the morphology of affected mitochondria in over-expressed conditions. However, a single dynamin family member known as OPA1 in mammals mediates fusion between mitochondrial inner membranes. These regulating proteins of mitochondrial fusion are organism-dependent; therefore, in Drosophila (fruit flies) and yeasts, the process is controlled by the mitochondrial transmembrane GTPase, Fzo. In Drosophila , Fzo is found in postmeiotic spermatids and the dysfunction of this protein results in male sterility. However, a deletion of Fzo1 in budding yeast results in smaller, spherical mitochondria due to the lack of mitochondrial DNA (mtDNA).
The balance between mitochondrial fusion and fission in cells is dictated by the up-and-down regulation of mitofusins, OPA1/Mgm1, and Drp1/Dnm1. Apoptosis , or programmed cell death , begins with the breakdown of mitochondria into smaller pieces. This process results from up-regulation of Drp1/Dnm1 and down-regulation of mitofusins. Later in the apoptosis cycle, an alteration of OPA1/Mgm1 activity within the inner mitochondrial membrane occurs. The role of the OPA1 protein is to protect cells against apoptosis by inhibiting the release of cytochrome c . Once this protein is altered, there is a change in the cristae structure, release of cytochrome c, and the activation of the destructive caspase enzymes. These resulting changes indicate that inner mitochondrial membrane structure is linked with regulatory pathways in influencing cell life and death. OPA1 plays both a genetic and molecular role in mitochondrial fusion and in cristae remodeling during apoptosis. [ 5 ] OPA1 exists in two forms; the first being soluble and found in the intermembrane space, and the second as an integral inner membrane form, work together to restructure and shape the cristae during and after apoptosis. OPA1 blocks intramitochondrial cytochrome c redistribution which proceeds remodeling of the cristae. OPA1 functions to protect cells with mitochondrial dysfunction due to Mfn deficiencies, doubly for those lacking Mfn1 and Mfn2, but it plays a greater role in cells with only Mfn1 deficiencies as opposed to Mfn2 deficiencies. Therefore, it is supported that OPA1 function is dependent on the amount of Mfn1 present in the cell to promote mitochondrial elongation. [ 6 ]
Both proteins, Mfn1 and Mfn2, can act either together or separately during mitochondrial fusion. Mfn1 and Mfn2 are 81% similar to each other and about 51% similar to the Drosophila protein Fzo. Results published for a study to determine the impact of fusion on mitochondrial structure revealed that Mfn-deficient cells demonstrated either elongated cells (majority) or small, spherical cells upon observation.
The Mfn protein has three different methods of action: Mfn1 homotypic oligomers , Mfn2 homotypic oligomers and Mfn1-Mfn2 heterotypic oligomers. It has been suggested that the type of cell determines the method of action but it has yet to be concluded whether or not Mfn1 and Mfn2 perform the same function in the process or if they are separate. Cells lacking this protein are subject to severe cellular defects such as poor cell growth, heterogeneity of mitochondrial membrane potential and decreased cellular respiration . [ 7 ]
Mitochondrial fusion plays an important role in the process of embryonic development , as shown through the Mfn1 and Mfn2 proteins. Using Mfn1 and Mfn2 knock-out mice, which die in utero at midgestation due to a placental deficiency, mitochondrial fusion was shown not to be essential for cell survival in vitro, but necessary for embryonic development and cell survival throughout later stages of development. Mfn1 Mfn2 double knock-out mice, which die even earlier in development, were distinguished from the "single" knock-out mice. Mouse embryo fibroblasts (MEFs) originated from the double knock-out mice, which do survive in culture even though there is a complete absence of fusion, but parts of their mitochondria show a reduced mitochondrial DNA ( mtDNA ) copy number and lose membrane potential. This series of events causes problems with adenosine triphosphate (ATP) synthesis.
The Mitochondrial Inner/Outer Membrane Fusion (MMF) Family ( TC# 9.B.25 ) is a family of proteins that play a role in mitochondrial fusion events. This family belongs to the larger Mitochondrial Carrier (MC) Superfamily . The dynamic nature of mitochondria is critical for function. Chen and Chan (2010) have discussed the molecular basis of mitochondrial fusion, its protective role in neurodegeneration, and its importance in cellular function. [ 8 ] The mammalian mitofusins Mfn1 and Mfn2, GTPases localized to the outer membrane, mediate outer-membrane fusion. OPA1, a GTPase associated with the inner membrane, mediates subsequent inner-membrane fusion. Mutations in Mfn2 or OPA1 cause neurodegenerative diseases. Mitochondrial fusion enables content mixing within a mitochondrial population, thereby preventing permanent loss of essential components. Cells with reduced mitochondrial fusion show a subpopulation of mitochondria that lack mtDNA nucleoids. Such mtDNA defects lead to respiration-deficient mitochondria, and their accumulation in neurons leads to impaired outgrowth of cellular processes and consequent neurodegeneration.
A representative list of the proteins belonging to the MMF family is available in the Transporter Classification Database .
Mfn1 and Mfn2 ( TC# 9.B.25.2.1 ; Q8IWA4 and O95140 , respectively), in mammalian cells are required for mitochondrial fusion, Mfn1 and Mfn2 possess functional distinctions. For instance, the formation of tethered structures in vitro occurs more readily when mitochondria are isolated from cells overexpressing Mfn1 than Mfn2. [ 9 ] In addition, Mfn2 specifically has been shown to associate with Bax and Bak (Bcl-2 family, TC#1.A.21 ), resulting in altered Mfn2 activity, indicating that the mitofusins possess unique functional characteristics. Lipidic holes may open on opposing bilayers as intermediates, and fusion in cardiac myocytes is coupled with outer mitochondrial membrane destabilization that is opportunistically employed during the mitochondrial permeability transition. [ 10 ]
Mutations in Mfn2 (but not Mfn1) result in the neurological disorder Charcot-Marie-Tooth syndrome. These mutations can be complemented by the formation of Mfn1–Mfn2 CMT2A hetero-oligomers but not homo-oligomers of Mfn2 + –Mfn2 CMT2A . [ 11 ] This suggests that within the Mfn1–Mfn2 hetero-oligomeric complex, each molecule is functionally distinct. This suggests that control of the expression levels of each protein likely represents the most basic form of regulation to alter mitochondrial dynamics in mammalian tissues. Indeed, the expression levels of Mfn1 and Mfn2 vary according to cell or tissue type as does the mitochondrial morphology. [ 12 ]
In yeast, three proteins are essential for mitochondrial fusion. Fzo1 ( P38297 ) and Mgm1 ( P32266 ) are conserved guanosine triphosphatases that reside in the outer and inner membranes, respectively. At each membrane, these conserved proteins are required for the distinct steps of membrane tethering and lipid mixing. The third essential component is Ugo1, an outer membrane protein with a region homologous to but distantly related to a region in the Mitochondrial Carrier (MC) family. Hoppins et al. , 2009 showed that Ugo1 is a modified member of this family, containing three transmembrane domains and existing as a dimer, a structure that is critical for the fusion function of Ugo1. [ 13 ] Their analyses of Ugo1 indicate that it is required for both outer and inner membrane fusion after membrane tethering, indicating that it operates at the lipid-mixing step of fusion. This role is distinct from the fusion dynamin-related proteins and thus demonstrates that at each membrane, a single fusion protein is not sufficient to drive the lipid-mixing step. Instead, this step requires a more complex assembly of proteins. The formation of a fusion pore has not yet been demonstrated. [ 13 ] [ 14 ] The Ugo1 protein is a member of the MC superfamily . | https://en.wikipedia.org/wiki/Mitochondrial_fusion |
The mitochondrial permeability transition pore ( mPTP or MPTP ; also referred to as PTP , mTP or MTP ) is a protein that is formed in the inner membrane of the mitochondria under certain pathological conditions such as traumatic brain injury and stroke . Opening allows increase in the permeability of the mitochondrial membranes to molecules of less than 1500 daltons in molecular weight. Induction of the permeability transition pore, mitochondrial membrane permeability transition ( mPT or MPT ), can lead to mitochondrial swelling and cell death through apoptosis or necrosis depending on the particular biological setting. [ 1 ]
The MPTP was originally discovered by Haworth and Hunter [ 2 ] in 1979 and has been found to be involved in neurodegeneration , hepatotoxicity from Reye-related agents, cardiac necrosis and nervous and muscular dystrophies among other deleterious events inducing cell damage and death. [ 1 ] [ 3 ] [ 4 ] [ 5 ]
MPT is one of the major causes of cell death in a variety of conditions. For example, it is key in neuronal cell death in excitotoxicity , in which overactivation of glutamate receptors causes excessive calcium entry into the cell . [ 6 ] [ 7 ] [ 8 ] MPT also appears to play a key role in damage caused by ischemia , as occurs in a heart attack and stroke . [ 9 ] However, research has shown that the MPT pore remains closed during ischemia, but opens once the tissues are reperfused with blood after the ischemic period, [ 10 ] playing a role in reperfusion injury .
MPT is also thought to underlie the cell death induced by Reye's syndrome , since chemicals that can cause the syndrome, like salicylate and valproate , cause MPT. [ 11 ] MPT may also play a role in mitochondrial autophagy . [ 11 ] Cells exposed to toxic amounts of Ca 2+ ionophores also undergo MPT and death by necrosis. [ 11 ]
While the MPT modulation has been widely studied, little is known about its structure. Initial experiments by Szabó and Zoratti proposed the MPT may comprise Voltage Dependent Anion Channel (VDAC) molecules. Nevertheless, this hypothesis was shown to be incorrect as VDAC −/− mitochondria were still capable to undergo MPT. [ 12 ] [ 13 ] Further hypothesis by Halestrap's group convincingly suggested the MPT was formed by the inner membrane Adenine Nucleotide Translocase (ANT), but genetic ablation of such protein still led to MPT onset. [ 14 ] [ 15 ] Thus, the only MPTP components identified so far are the TSPO (previously known as the peripheral benzodiazepine receptor) located in the mitochondrial outer membrane and cyclophilin-D in the mitochondrial matrix . [ 16 ] [ 17 ] Mice lacking the gene for cyclophilin-D develop normally, but their cells do not undergo Cyclosporin A-sensitive MPT, and they are resistant to necrotic death from ischemia or overload of Ca 2+ or free radicals. [ 18 ] However, these cells do die in response to stimuli that kill cells through apoptosis, suggesting that MPT does not control cell death by apoptosis. [ 18 ]
Agents that transiently block MPT include the immune suppressant cyclosporin A (CsA); N-methyl-Val-4-cyclosporin A (MeValCsA), a non- immunosuppressant derivative of CsA; another non-immunosuppressive agent, NIM811 , 2-aminoethoxydiphenyl borate (2-APB), [ 19 ] bongkrekic acid and alisporivir (also known as Debio-025). TRO40303 is a newly synthetitised MPT blocker developed by Trophos company and currently is in Phase I clinical trial . [ 20 ]
Various factors enhance the likelihood of MPTP opening. In some mitochondria, such as those in the central nervous system , high levels of Ca 2+ within mitochondria can cause the MPT pore to open. [ 21 ] [ 22 ] This is possibly because Ca 2+ binds to and activates Ca 2+ binding sites on the matrix side of the MPTP. [ 6 ] MPT induction is also due to the dissipation of the difference in voltage across the inner mitochondrial membrane (known as transmembrane potential, or Δψ).
In neurons and astrocytes, the contribution of membrane potential to MPT induction is complex, see. [ 23 ] The presence of free radicals , another result of excessive intracellular calcium concentrations , can also cause the MPT pore to open. [ 24 ]
Other factors that increase the likelihood that the MPTP will be induced include the presence of certain fatty acids, [ 25 ] and inorganic phosphate. [ 26 ] However, these factors cannot open the pore without Ca 2+ , though at high enough concentrations, Ca 2+ alone can induce MPT. [ 27 ]
Stress in the endoplasmic reticulum can be a factor in triggering MPT. [ 28 ]
Conditions that cause the pore to close or remain closed include acidic conditions, [ 29 ] high concentrations of ADP , [ 24 ] [ 30 ] high concentrations of ATP , [ 31 ] and high concentrations of NADH . Divalent cations like Mg 2+ also inhibit MPT, because they can compete with Ca 2+ for the Ca 2+ binding sites on the matrix and/or cytoplasmic side of the MPTP. [ 23 ]
Multiple studies have found the MPT to be a key factor in the damage to neurons caused by excitotoxicity . [ 6 ] [ 7 ] [ 8 ]
The induction of MPT, which increases mitochondrial membrane permeability, causes mitochondria to become further depolarized, meaning that Δψ is abolished. When Δψ is lost, protons and some molecules are able to flow across the outer mitochondrial membrane uninhibited. [ 7 ] [ 8 ] Loss of Δψ interferes with the production of adenosine triphosphate (ATP), the cell's main source of energy, because mitochondria must have an electrochemical gradient to provide the driving force for ATP production.
In cell damage resulting from conditions such as neurodegenerative diseases and head injury , opening of the mitochondrial permeability transition pore can greatly reduce ATP production, and can cause ATP synthase to begin hydrolysing , rather than producing, ATP. [ 32 ] This produces an energy deficit in the cell, just when it most needs ATP to fuel activity of ion pumps .
MPT also allows Ca 2+ to leave the mitochondrion, which can place further stress on nearby mitochondria, and which can activate harmful calcium-dependent proteases such as calpain .
Reactive oxygen species (ROS) are also produced as a result of opening the MPT pore. MPT can allow antioxidant molecules such as glutathione to exit mitochondria, reducing the organelles' ability to neutralize ROS. In addition, the electron transport chain (ETC) may produce more free radicals due to loss of components of the ETC, such as cytochrome c , through the MPTP. [ 33 ] Loss of ETC components can lead to escape of electrons from the chain, which can then reduce molecules and form free radicals.
MPT causes mitochondria to become permeable to molecules smaller than 1.5 kDa, which, once inside, draw water in by increasing the organelle's osmolar load . [ 34 ] This event may lead mitochondria to swell and may cause the outer membrane to rupture, releasing cytochrome c . [ 34 ] Cytochrome c can in turn cause the cell to go through apoptosis ("commit suicide") by activating pro-apoptotic factors. Other researchers contend that it is not mitochondrial membrane rupture that leads to cytochrome c release, but rather another mechanism, such as translocation of the molecule through channels in the outer membrane, which does not involve the MPTP. [ 35 ]
Much research has found that the fate of the cell after an insult depends on the extent of MPT. If MPT occurs to only a slight extent, the cell may recover, whereas if it occurs more it may undergo apoptosis. If it occurs to an even larger degree the cell is likely to undergo necrotic cell death . [ 9 ]
Although the MPTP has been studied mainly in mitochondria from mammalian sources, mitochondria from diverse species also undergo a similar transition. [ 36 ] While its occurrence can be easily detected, its purpose still remains elusive. Some have speculated that the regulated opening of the MPT pore may minimize cell injury by causing ROS-producing mitochondria to undergo selective lysosome-dependent mitophagy during nutrient starvation conditions. [ 37 ] Under severe stress/pathologic conditions, MPTP opening would trigger injured cell death mainly through necrosis. [ 38 ]
There is controversy about the question of whether the MPTP is able to exist in a harmless, "low-conductance" state. This low-conductance state would not induce MPT [ 6 ] and would allow certain molecules and ions to cross the mitochondrial membranes. The low-conductance state may allow small ions like Ca 2+ to leave mitochondria quickly, in order to aid in the cycling of Ca 2+ in healthy cells. [ 30 ] [ 39 ] If this is the case, MPT may be a harmful side effect of abnormal activity of a usually beneficial MPTP.
MPTP has been detected in mitochondria from plants, [ 40 ] yeasts, such as Saccharomyces cerevisiae , [ 41 ] birds, such as guinea fowl [ 42 ] and primitive vertebrates such as the Baltic lamprey . [ 43 ] While the permeability transition is evident in mitochondria from these sources, its sensitivity to its classic modulators may differ when compared with mammalian mitochondria. Nevertheless, CsA-insensitive MPTP can be triggered in mammalian mitochondria given appropriate experimental conditions [ 44 ] strongly suggesting this event may be a conserved characteristic throughout the eukaryotic domain. [ 45 ] | https://en.wikipedia.org/wiki/Mitochondrial_permeability_transition_pore |
Mitochondrial replacement therapy ( MRT ), sometimes called mitochondrial donation , is the replacement of mitochondria in one or more cells to prevent or ameliorate disease. MRT originated as a special form of in vitro fertilisation in which some or all of the future baby's mitochondrial DNA (mtDNA) comes from a third party. This technique is used in cases when mothers carry genes for mitochondrial diseases . The therapy is approved for use in the United Kingdom. [ 1 ] [ 2 ] A second application is to use autologous mitochondria to replace mitochondria in damaged tissue to restore the tissue to a functional state. This has been used in clinical research in the United States to treat cardiac-compromised newborns. [ 3 ]
Mitochondrial replacement therapy has been used to prevent the transmission of mitochondrial diseases from mother to child; it could only be performed in clinics licensed by the UK's Human Fertilisation and Embryology Authority (HFEA), only for people individually approved by the HFEA, for whom preimplantation genetic diagnosis is unlikely to be helpful, and only with informed consent that the risks and benefits are not well understood. [ 4 ]
Relevant mutations are found in about 0.5% of the population and disease affects around one in 5000 individuals (0.02%)—the percentage of people affected is much smaller because cells contain many mitochondria, only some of which carry mutations, and the number of mutated mitochondria need to reach a threshold in order to affect the entire cell, and many cells need to be affected for the person to show disease. [ 2 ]
The average number of births per year among women at risk for transmitting mtDNA disease is estimated to approximately 150 in the United Kingdom and 800 in the United States . [ 5 ]
Prior to the development of MRT, and in places where it is not legal or feasible, the reproductive options for women who are at risk for transmitting mtDNA disease and who want to prevent transmission were using an egg from another woman, adoption, or childlessness. [ 1 ] : 45
Autologous mitochondria extracted from healthy tissue and supplied to damaged tissue has been used to treat cardiac-compromised newborns. Alternatives to the approach include use of an extracorporeal membrane oxygenator (ECMO) or tissue or organ transplantation. [ 3 ]
In vitro fertilization involves removing eggs from a woman, collecting sperm from a man, fertilizing the egg with the sperm, allowing the fertilized egg to form a blastocyst , and then transferring the blastocyst into the uterus. MRT involves an additional egg from a third person, and manipulation of both the recipient egg and the donor egg. [ citation needed ]
As of 2016 there were three MRT techniques in use: maternal spindle transfer (MST); pronuclear transfer (PNT); and the newest technique, polar body transfer (PBT). The original technique, in which mitochondria-containing cytoplasm taken from a donor egg is simply injected into the recipient egg, is no longer used. [ 1 ] : 46–47
In maternal spindle transfer, an oocyte is removed from the recipient, and when it is in the metaphase II stage of cell division, the spindle-chromosome complex is removed; some of the cytoplasm comes with it, so some mitochondria are likely to be included. The spindle-chromosome complex is inserted into a donor oocyte from which the nucleus has already been removed. This egg is fertilized with sperm and allowed to form a blastocyst, which can then be investigated with preimplantation genetic diagnosis to check for mitochondrial mutations, prior to being implanted in the recipient's uterus. [ 1 ] : 47–48
In pronuclear transfer, an oocyte is removed from the recipient and fertilized with sperm. The donor oocyte is fertilized with sperm from the same person. The male and female pronuclei are removed from each fertilized egg prior to their fusing, and the pronuclei from the recipient's fertilized egg are inserted into the fertilized egg from the donor. As with MST, a small amount of cytoplasm from the recipient egg may be transferred, and as with MST, the fertilized egg is allowed to form a blastocyst, which can then be investigated with preimplantation genetic diagnosis to check for mitochondrial mutations before being implanted in the recipient's uterus. [ 1 ] : 50
In polar body transfer, a polar body (a small cell with very little cytoplasm that is created when an egg cell divides) from the recipient is used in its entirety, instead of using nuclear material extracted from the recipient's normal egg; this can be used in either MST or PNT. This technique was first published in 2014 and as of 2015 it had not been consistently replicated, but is considered promising as there is a greatly reduced chance for transmitting mitochondria from the recipient because polar bodies contain very few mitochondria, and it does not involve extracting material from the recipient's egg. [ 6 ]
Cytoplasmic transfer was originally developed in the 1980s in the course of basic research conducted with mice to study the role that parts of the cell outside of the nucleus played in embryonic development. [ 2 ] In this technique, cytoplasm , including proteins, messenger RNA (mRNA), mitochondria and other organelles, is taken from a donor egg and injected into the recipient egg, resulting in a mixture of mitochondrial genetic material. [ 2 ] This technique started to be used in the late 1990s to "boost" the eggs of older women who were having problems conceiving and led to the birth of about 30 babies. [ 2 ] Concerns were raised that the mixture of genetic material and proteins could cause problems with respect to epigenetic clashes, or differences in the ability of the recipient and donor materials to effect the development process, or due to the injection of the donor material. [ 2 ] After three children born through the technique were found to have developmental disorders (two cases of Turner's syndrome and one case of pervasive developmental disorder (an autism spectrum disorder), the FDA banned the procedure until a clinical trial could prove its safety. [ 2 ] As of 2015 that study had not been conducted, but the procedure was in use in other countries. [ 2 ]
A related approach uses autologous mitochondria taken from healthy tissue to replace the mitochondria in damaged tissue. Transfer techniques include direct injection into damaged tissue and injection into vessels that supply blood to the tissue. [ 3 ]
Assisted reproduction via MRT involves preimplantation genetic screening of the mother, preimplantation genetic diagnosis after the egg is fertilized, and in vitro fertilization . It has all the risks of those procedures. [ 1 ] : 60
In addition, both procedures used in MRT entail their own risks. On one level, the procedures physically disrupt two oocytes, removing nuclear genetic material from the recipient egg or fertilized egg and inserting the nuclear genetic material into the donor unfertilized or fertilized egg; the manipulations for both procedures may cause various forms of damage that were not well understood as of 2016. [ 7 ] : 23
Maternal mitochondria will be carried over to the donor egg; as of 2016 it was estimated that using techniques current in the UK, maternal mitochondria will comprise only around 2% or less of mitochondria in the resulting egg, a level that was considered safe by the HFEA and within the limits of mitochondrial variation that most people have. [ 7 ] : 23–24
Because MRT procedures involve actions at precise times during egg development and fertilization, and involves manipulating eggs, there is a risk that eggs may mature abnormally or that fertilization may happen abnormally; as of 2016 the HFEA judged that laboratory techniques in the UK had been well enough developed to manage these risks to proceed cautiously with making MRT available. [ 7 ] : 33–34
Because mitochondria in the final egg will come from a third party, different from the two parties whose DNA is in the nucleus, and because nuclear DNA encodes genes that make some of the proteins and mRNA used by mitochondria, there is a theoretical risk of adverse "mito–nuclear" interactions. While this theoretical risk could possibly be managed by attempting to match the haplotype of the donor and the recipient, as of 2016 there was no evidence that this is an actual risk. [ 7 ] : 34–37
Because MRT is a relatively new technology, there are concerns that it is not yet safe for public use as there have been limited studies that used MRT in large animal models. [ 8 ]
Finally, there is a risk of epigenetic modification to DNA in the nucleus and mitochondria, caused by the procedure itself or by mito–nuclear interactions. As of 2016 these risks appeared to be minimal but were being monitored by long-term study of children born from the procedure. [ 7 ] : 38
In the United States in 1996 embryologist Jacques Cohen and others at the Institute for Reproductive Medicine and Science , Saint Barnabas Medical Center in Livingston, New Jersey first used cytoplasmic transfer in a human assisted reproduction procedure. [ 9 ] In 1997 the first baby was born using this procedure. In 2001, Cohen and others reported that ten single babies, twins, and a quadruplet at his New Jersey clinic and a further six children in Israel had been born using his technique. Using modifications of his procedure, a baby had been born at Eastern Virginia Medical School , five children at the Lee Women's Hospital Infertility Clinic in Taichung, Taiwan . [ 10 ] twins in Naples, Italy [ 11 ] and a twins in India. [ 12 ] In total as of 2016, 30–50 children worldwide had been reported to have been born using cytoplasmic transfer. [ 13 ]
In 2002, the US Food and Drug Administration (FDA) asked a Biological Response Modifiers Advisory Committee Meeting to advise on the technique of cytoplasmic transfer to treat infertility. This committee felt that there were risks at the time of inadvertent transfer of chromosomes and enhanced survival of abnormal embryos. [ 13 ] The FDA informed clinics that they considered the cytoplasmic transfer technique as a new treatment, and, as such, it would require an Investigational New Drug (IND) application. Cohen's clinic started the pre-IND application, but the clinic then went private, funding for the application dried up, the application was abandoned, the research team disbanded, [ 14 ] and the cytoplasmic transfer procedure fell out of favor. [ 15 ] In 2016, 12 (out of the 13) parents of children born using cytoplasmic transfer at the Saint Barnabas Center participated in a limited follow-up inquiry via online questionnaire. Children whose ages then were 13–18 reported no major problems. [ 16 ]
In 2009, a team in Japan published studies of mitochondrial donation. [ 17 ] In the same year, a team led by scientists at Oregon Health & Science University published results of mitochondrial donation in monkeys; that team published an update reporting on the health of the monkeys born with the technique, as well as further work it had done on human embryos. [ 18 ]
Human trials in 2010 by a team in Newcastle University and Newcastle Fertility Centre were successful in reducing transmission of mtDNA. The results of the study found the mean mtDNA carried over was on average under 2% in the experimental embryos. This was true for both the MI-SCC and PN transfer methods of MTR. This research did not extend past the blastocyst stage because of ethical concerns, and there are still concerns about whether results retrieved from the blastocyst stage are viable representations of whole embryos. Because of these speculations and to further the viability of MTR as a safe and effective technique, further research and clinical trials would need to be initiated to test the efficacy of MTR in the long term in human patients. [ 19 ]
In the United Kingdom, following animal experiments and the recommendations of a government commissioned expert committee, [ 20 ] the Human Fertilisation and Embryology (Research Purposes) Regulations were passed in 2001 regulating and allowing research into human embryos. In 2004, Newcastle University applied for a license to develop pronuclear transfer to avoid the transmission of mitochondrial diseases, [ 21 ] and was granted the license in 2005. Following further research by Newcastle and the Wellcome Trust , [ 22 ] [ 23 ] scientific review, [ 24 ] public consultations, and debate, the UK government recommended that mitochondrial donation be legalized in 2013. [ 25 ] In 2015 parliament passed the Human Fertilisation and Embryology (Mitochondrial Donation) Regulations, which came into force on 29 October 2015, making human mitochondrial donation legal in the UK. The Human Fertilisation and Embryology Authority (HFEA) was authorized to license and regulate medical centers which wanted to use human mitochondrial donation. [ 26 ] [ 27 ] In February 2016, the US National Academy of Sciences issued a report describing technologies then current and the surrounding ethical issues. [ 1 ]
The HFEA Safety Committee issued its fourth report in November 2016 recommending procedures under which HFEA should authorize MRT, [ 7 ] the HFEA issued their regulations in December 2016 [ 27 ] [ 4 ] and granted their first license (to Newcastle Fertility Centre ; Newcastle upon Tyne Hospital NHS Foundation Trust led by Dr Jane Stewart as Person Responsible to the HFEA) in March 2017. [ 28 ] Between August 2017 and January 2019, the HFEA received 15 requests from women to undergo MRT, of which 14 were granted. [ 29 ] [ 30 ] As of 2020, if children have been born from these procedures, the details have not been published because of the wishes of the parents. [ 31 ]
Douglass Turnbull , the driving force behind mitochondrial research at Newcastle University, was awarded a knighthood in 2016. [ 32 ] [ 33 ]
In 2016, John Zhang and a mixed team of scientists from Mexico and New York used the spindle transfer technique to help a Jordanian woman to give birth to a baby boy. The mother had Leigh disease and already had four miscarriages and two children who had died of the disease. [ 34 ] Valery Zukin, director of the Nadiya clinic in Kyiv , Ukraine, reported in June 2018 that doctors there had used the pronuclear transfer method of MRT to help four women give birth (three boys and a girl) and three women to become pregnant (one from Sweden); the team had 14 failed attempts. [ 35 ] In January 2019 it was reported that seven babies had been born using MRT. [ 36 ] The doctors had first gotten approval from an ethical committee and a review board of the Ukrainian Association of Reproductive Medicine [ 37 ] [ 38 ] and the Ukrainian Postgraduate Medical Academy, under the auspices of the Ukrainian Ministry of Healthcare ; [ 35 ] there was no law in Ukraine against MRT. One of the first children, a boy, was born to a 34-year-old woman in January 2017, and genetic test results were reported as normal. [ 39 ] [ 40 ] In August and October 2017 the British HFEA authorized MRT for two women who had a genetic mutation in their mitichondria that causes myoclonic epilepsy with ragged red fibers . [ 41 ] In January 2019, Embryotools, Barcelona, Spain announced that a 32-year-old Greek woman had become pregnant using the spindle transfer technique. MRT was not legal in Spain so they had performed the trial in Greece where there was no law against MRT. They were helped by the Institute of Life in Athens, Greece and had obtained approval from the Greek National Authority of Assisted Reproduction. The pregnant Greek woman had already had four failed IVF cycles and surgery twice for endometriosis . [ 42 ]
In August 2017, in a letter to two clinics, including Zhang's, the FDA warned that the technique should not be marketed in the U.S. [ 43 ]
In June 2018 Australian Senate's Senate Community Affairs References Committee recommended a move towards legalising MRT, and in July 2018 the Australian senate endorsed it. [ 44 ] Research and clinical applications of MRT were overseen by laws made by federal and state governments. State laws were, for the most part, consistent with federal law. In all states, legislation prohibited the use of MRT techniques in the clinic, and except for Western Australia, research on a limited range of MRT was permissible up to day 14 of embryo development, subject to a license being granted. In 2010, the Hon. Mark Butler MP, then Federal Minister for Mental Health and Ageing, had appointed an independent committee to review the two relevant acts: the Prohibition of Human Cloning for Reproduction Act 2002 and the Research Involving Human Embryos Act 2002 . The committee's report, released in July 2011, recommended the existing legislation remain unchanged. [ 45 ] The Australian National Health and Medical Research Council issued two reports on legalising MRT in June 2020. [ 46 ] [ 47 ] In 2022, Maeve's Law was passed by the Australian Parliament, legalising MRT under a specified mitochondrial donation licence for research and training, and in clinical settings. [ 48 ]
Singapore was also considering whether to permit the MRT in 2018. [ 49 ]
In 2018, researchers announced the use of MRT to restore function to heart tissue in cardiac-compromised newborns. The damaged heart cells absorbed mitochondria extracted from healthy tissue and returned to useful activity. [ 3 ]
As of February 2016, the United States had no regulations governing mitochondrial donation, and Congress barred the FDA from evaluating any applications that involve implanting modified embryos into a woman. [ 50 ]
The United Kingdom became the first country to legalize the procedure: the UK's chief medical officer recommended it be legalized in 2013; [ 25 ] parliament passed The Human Fertilisation and Embryology (Mitochondrial Donation) Regulations in 2015, [ 51 ] [ 52 ] and the regulatory authority published regulations in 2016. [ 27 ]
Despite the promising outcomes of the two techniques, pronuclear transfer and spindle transfer, mitochondrial gene replacement raises ethical and social concerns. [ 53 ]
Mitochondrial donation involves modification of the germline , and hence such modifications would be passed on to subsequent generations. [ 54 ] Using human embryos for in vitro research is also controversial, as embryos are created specifically for research and egg donors are induced to undergo the procedure by financial compensation. [ 55 ]
Mitochondrial donation also has the potential for psychological and emotional impacts on an offspring through an effect on the person's sense of identity. Ethicists question whether the genetic make-up of children born as a result of mitochondrial replacement might affect their emotional well-being when they become aware that they are different from other healthy children conceived from two parents. [ 56 ]
Opponents argue that scientists are " playing God " and that children with three genetic parents may suffer both psychological and physical damage. [ 57 ]
On the other hand, New York University researcher James Grifo , a critic of the American ban, has argued that society "would never have made the advances in treating infertility that we have if these bans had been imposed 10 years" earlier. [ 58 ]
On February 3, 2016, the Institute of Medicine of the National Academies of Sciences, Engineering, and Medicine issued a report, commissioned by the U.S. Food and Drug Administration , addressing whether it is ethically permissible for clinical research into mitochondrial replacement techniques (MRT) to continue. The report, titled Mitochondrial Replacement Techniques: Ethical, Social, and Policy Considerations , analyzes multiple facets of the arguments surrounding MRT and concludes that it is 'ethically permissible' to continue clinical investigations of MRT, so long as certain conditions are met. It recommended that initially the technique should only be used for male embryos to ensure that DNA with potential mitochondrial disease would not be passed on. [ 1 ]
In 2018 Carl Zimmer compared the reaction to He Jiankui 's human gene editing experiment to the debate over MRT. [ 59 ] | https://en.wikipedia.org/wiki/Mitochondrial_replacement_therapy |
The mitochondrial shuttles are biochemical transport systems used to transport reducing agents across the inner mitochondrial membrane . NADH as well as NAD+ cannot cross the membrane, but it can reduce another molecule like FAD and [QH 2 ] that can cross the membrane, so that its electrons can reach the electron transport chain .
The two main systems in humans are the glycerol phosphate shuttle and the malate-aspartate shuttle . The malate / a-ketoglutarate antiporter functions move electrons while the aspartate / glutamate antiporter moves amino groups . This allows the mitochondria to receive the substrates that it needs for its functionality in an efficient manner. [ 1 ]
In humans, the glycerol phosphate shuttle is primarily found in brown adipose tissue , as the conversion is less efficient, thus generating heat, which is one of the main purposes of brown fat. It is primarily found in babies, though it is present in small amounts in adults around the kidneys and on the back of our necks. [ 2 ] The malate-aspartate shuttle is found in much of the rest of the body.
The shuttles contains a system of mechanisms used to transport metabolites that lack a protein transporter in the membrane, such as oxaloacetate .
The malate shuttle allows the mitochondria to move electrons from NADH without the consumption of metabolites and it uses two antiporters to transport metabolites and keep balance within the mitochondrial matrix and cytoplasm .
On the cytoplasmic side a transaminase enzyme is used to remove an amino group from aspartate which is converted into oxaloacetate , then malate dehydrogenase enzyme uses an NADH cofactor to reduce oxaloacetate to malate which can be transported across the membrane because of the presence of a transporter.
Once the malate is inside the matrix its converted back to oxaloacetate , which is converted to aspartate and can be transported back outside the mitochondria to allow the cycle to continue. The movement of oxaloacetate across the membrane transports electrons and is known as the outer ring. The inner ring primary function is not to move electrons but regenerate the metabolites .
The transamination of oxaloacetate to aspartate is achieved through the use of glutamate . Glutamate is transported with aspartate via antiporter , thus as one aspartate leaves the cell, a glutamate enters. Glutamate in the matrix is converted into an a-ketoglutarate which is transported in an antiporter with malate . In the cytoplasmic side a-ketoglutarate is converted back into glutamate when aspartate is converted back to oxaloacetate .
Most cancer cells cause mutation in the bodies' metabolic activities to increase glucose metabolism in order to rapidly proliferate. Mutations that increase the cells metabolic activity and turn a normal cell into a tumor cell are called oncogenes . Cancer cells are unlike many other cells. They have very little vulnerabilities, but experiments in which the inhibition of transamination of malate-shuttle slowed proliferation due to the fact metabolism of glucose was being slowed. [ 3 ] | https://en.wikipedia.org/wiki/Mitochondrial_shuttle |
Mitochondrial toxicity is a condition in which the mitochondria of a body's cells become damaged or decline significantly in number; it occurs as a side effect of certain antiretroviral drugs used to treat human immunodeficiency virus, or HIV . [ 1 ]
While the exact causes of mitochondrial toxicity are unknown, research has shown that a certain group of anti-viral drugs used to treat HIV, specifically nucleoside analog reverse transcriptase inhibitors (NRTIs), interfere with an enzyme needed in the production of mitochondria. [ 2 ]
The disruption of cell function that accompanies the condition can cause both mild and severe problems in people with mitochondrial toxicity. The most commonly observed symptom is muscle weakness, or myopathy . Others include peripheral neuropathy (numbness in the fingers and toes) and pancreatitis (inflammation of the pancreas), with the most severe being lactic acidosis , in which a build-up of lactic acid in the tissues of the body leads to loss of energy, organ failure, and eventually death. [ 3 ] | https://en.wikipedia.org/wiki/Mitochondrial_toxicity |
The mitochondrial unfolded protein response ( UPR mt ) is a cellular stress response related to the mitochondria . The UPR mt results from unfolded or misfolded proteins in mitochondria beyond the capacity of chaperone proteins to handle them. [ 1 ] The UPR mt can occur either in the mitochondrial matrix or in the mitochondrial inner membrane . [ 1 ] In the UPR mt , the mitochondrion will either upregulate chaperone proteins or invoke proteases to degrade proteins that fail to fold properly. [ 1 ] UPR mt causes the sirtuin SIRT3 to activate antioxidant enzymes and mitophagy . [ 2 ]
Mitochondrial electron transport chain mutations that extend the life span of Caenorhabditis elegans ( nematode worms) also activate the UPR mt . [ 3 ] Activation of the UPR mt in nematode worms by increasing NAD+ by supplementation with nicotinamide or nicotinamide riboside has been shown to extend lifespan. [ 4 ] Glial and germline mitochondria has been found to play a significant role in the signalling and regulation of UPR mt [ 5 ] [ 6 ] [ 7 ] have been shown to play a central role Nicotinamide riboside supplementation in mice has also been shown to activate the UPR mt . [ 8 ]
A majority of cellular proteins are translated and folded in the cytosol with the help of molecular chaperones. Just as proteins must be folded to function in the cytosol, proteins in organelles like the endoplasmic reticulum (ER) and mitochondria also must be folded to function. Consequently, specific cellular mechanisms exist that aim to detect cellular stress (causing misfolded/unfolded proteins to accumulate), transduce the signal to the nucleus, and mediate the restoration of protein homeostasis ( proteostasis ). In the cytosol, the heat shock response (HSR) manages the unfolded proteins through heat shock factor 1 (HSF1). HSF-1 is a transcription factor that, upon increases in unfolded cytosolic proteins, will trimerize and enter the nucleus to upregulate the expression of heat shock proteins (HSPs) that will act as protein folding chaperones . [ 9 ]
In organelles like the ER and mitochondria, the response is slightly more complex. Both UPR mechanisms are conceptually similar in that they are activated by the accumulation of misfolded/ unfolded proteins and induce the translational upregulation of molecular chaperones and proteases to process proteins and restore homeostasis. [ 10 ] Despite their names, the two pathways possess distinct initiating stimuli and signaling mechanisms that regulate the responses. The ER UPR is induced by a variety of cellular stressors that inhibit protein folding or exit of the ER. Within the ER GRP78, an ER lumen chaperone, is bound to ER membrane proteins. When unfolded proteins build up, it dissociates to from the membrane to aid in protein folding. GRP78 dissociation triggers the UPR ER that restores protein homeostasis via three pathways (IRE1, PERK, and ATF6 ). [ 11 ] The UPR ER restores proteostasis by selectively attenuation protein translation, upregulating protein folding chaperones, and degrading excess misfolded proteins via ER associated protein degradation ( ERAD ). Prolonged activation of the UPR ER can result in apoptosis . [ 9 ]
The UPR mt progresses through the bZIP transcription factor ATFS-1 (in C. elegans ; ATF5 in mammals). AFTS-1 is usually imported into the mitochondria where it is degraded by the LON protease. Mitochondrial dysfunction inhibits this process and allows ATFS-1 to accumulate in the cytosol and enter the nucleus where it can act as a transcription factor. This responses restores proteostasis by upregulating chaperones and proteases, increasing reactive oxygen species (ROS) detoxification, and increasing mitochondrial import machinery. [ 12 ] [ 9 ]
In mammals, UPR mt has mostly been studied using transfection with a truncated, dysfunctional mitochondrial enzyme (OTCΔ) that does not fold correctly after translocation into the mitochondrial matrix. [ 13 ] Using this approach, several components of the mammalian UPR mt have been identified including the mitochondrial chaperone heat shock protein 60 (Hsp60), the mitochondrial caseinolytic peptidase ClpP, the transcription factor Chop and the kinases c-Jun N-terminal kinase (JNK) and the interferon-induced, double-stranded RNA-activated protein kinase (Pkr). [ 13 ] [ 14 ] [ 15 ]
The appropriately named activating transcription factor associated with stress (ATFS-1) is one of the primary transcription factors required for UPR mt activation in worms. ATFS-1 has a nuclear localization sequence that allows it to be imported into the nucleus as well as an N-terminal mitochondrial targeting sequence (MTS) that allows for import into the mitochondria. [ 12 ] In healthy cells, ATFS-1 is preferentially targeted to the mitochondrial matrix where it is degraded by the Lon protease. The MTS on ATFS-1 is predicted by Mitofates [ 16 ] to be substantially weaker than most MTSs which would allow it to be sensitive to subtle mitochondrial dysfunction. [ 17 ] Following mitochondrial stress, ATFS-1 mitochondrial import efficiency is decreased resulting in a cytoplasmic accumulation of ATFS-1. Subsequently, ATFS-1 will enter the nucleus via its nuclear transport signal. In the nucleus, ATFS-1 has a broad transcriptional regulation as it will: attenuate OXPHOS gene expression in both the nucleus and mitochondria, upregulate chaperones and proteases to re-establish mitochondrial proteostasis, increase ROS detoxification, and increase mitochondrial import machinery. [ 10 ] [ 12 ]
Recent research has implicated the UPR mt in the transformation of cells in to cancer cells. Researchers have identified the SIRT3 axis of UPR mt as a marker to differentiate between metastatic and non-metastatic breast cancer. [ 18 ] As many cancers exhibit a metabolic shift from oxidative phosporylation-depentent energy production to aerobic glycolysis dependent energy production, also known as the Warburg effect , researchers suggest that cancer cells rely on the UPR mt to maintain the mitochondrial integrity. [ 19 ] Furthermore, multiple studies have shown that inhibition of UPR mt , specifically ATF5 , selectively kills human and rat cancer cells rather than non-cancer cells. [ 19 ] [ 20 ] [ 21 ]
Inflammatory bowel diseases (Crohn´s disease and ulcerative colitis) have been associated with mitochondrial dysfunction in the intestinal epithelium. [ 15 ] In mouse models of intestinal inflammation and in IBD patients, signs of UPR mt -activation have been demonstrated. [ 15 ] [ 22 ] In particular, mitochondrial dysfunction and UPR mt -activation have been linked to intestinal stemness and Paneth cell (dys-)function. [ 22 ] [ 23 ] | https://en.wikipedia.org/wiki/Mitochondrial_unfolded_protein_response |
A mitogen is a small bioactive protein or peptide that induces a cell to begin cell division , or enhances the rate of division ( mitosis ). Mitogenesis is the induction (triggering) of mitosis, typically via a mitogen.
Mitogens act primarily by influencing a set of proteins which are involved in the restriction of progression through the cell cycle . The G1 checkpoint is controlled most directly by mitogens: further cell cycle progression does not need mitogens to continue. The point where mitogens are no longer needed to move the cell cycle forward is called the " restriction point " and depends on cyclins to be passed. [ 1 ] One of the most important of these is TP53 , a gene which produces a family of proteins known as p53. It, combined with the Ras pathway, downregulate cyclin D1 , a cyclin-dependent kinase, if they are not stimulated by the presence of mitogens. In the presence of mitogens, sufficient cyclin D1 can be produced. This process cascades onwards, producing other cyclins which stimulate the cell sufficiently to allow cell division. While animals produce internal signals that can drive the cell cycle forward, external mitogens can cause it to progress without these signals. [ 2 ]
Mitogens can be either endogenous or exogenous factors. Endogenous mitogens function to control cell division is a normal and necessary part of the life cycle of multicellular organisms. For example, in zebrafish , an endogenous mitogen Nrg1 is produced in response to indications of heart damage. When it is expressed, it causes the outer layers of the heart to respond by increasing division rates and producing new layers of heart muscle cells to replace the damaged ones. This pathway can potentially be deleterious, however: expressing Nrg1 in the absence of heart damage causes uncontrolled growth of heart cells, creating an enlarged heart. [ 3 ] Some growth factors , such as vascular endothelial growth factor, are also capable of directly acting as mitogens, causing growth by directly inducing cell replication. This is not true for all growth factors, as some growth factors instead appear to cause mitogenic effects like growth indirectly by triggering other mitogens to be released, as evidenced by their lack of mitogenic activity in vitro, which VEGF has. [ 4 ] Other well-known mitogenic growth factors include platelet derived growth factor (PDGF) and epidermal growth factor (EGF). [ 5 ]
Mitogens are important in cancer research due to their effects on the cell cycle. Cancer is in part defined by a lack of, or failure of, control in the cell cycle. This is usually a combination of two abnormalities: first, cancer cells lose their dependence on mitogens. Second, cancer cells are resistant to anti-mitogens.
Rather than requiring endogenous or external mitogens to continue the cell cycle, cancer cells are able to grow, survive, and replicate without mitogens. Cancer cells may lose their dependence on external mitogens by a variety of pathways.
First, cancer cells can produce their own mitogens, a term called autocrine stimulation. [ 5 ] This can result in a deadly positive feedback loop - tumor cells produce their own mitogens, which stimulate more tumor cells to replicate, which can then produce even more mitogens. For example, consider one of the earliest oncogenes to be identified, p28sis from the simian sarcoma virus, which causes tumorigenesis in the host animal. Scientists found that p28sis has a nearly identical amino acid sequence as human platelet-derived growth factor (PDGF). [ 6 ] Thus, tumors formed by the simian sarcoma virus are no longer dependent on the fluctuations of PDGF that control cell growth; instead, they can produce their own mitogens in the form of p28sis. With enough p28sis activity, the cells can proliferate without restriction, resulting in cancer.
Second, cancer cells can have mutated cell-surface receptors for mitogens. The protein kinase domain found on mitogenic receptors is often hyperactivated in cancer cells, remaining turned on even in the absence of external mitogens. Additionally, some cancers are associated with an overproduction of mitogenic receptors on the cell surface. With this mutation, cells are stimulated to divide by abnormally low levels of mitogens. One such example is HER2 , a receptor tyrosine kinase that responds to the mitogen EGF. Overexpression of HER2 is common in 15-30% of breast cancers, [ 7 ] allowing the cell cycle to progress even with extremely low concentrations of EGF. The overexpression of kinase activity in these cells aids in their proliferation. These are known as hormone-dependent breast cancers, as the kinase activation in these cancers is connected to exposure to both growth factors and estradiol. [ 8 ]
Third, downstream effectors of mitogenic signaling are often mutated in cancer cells. An important mitogenic signaling pathway in humans is the Ras-Raf-MAPK pathway. Mitogenic signaling normally activates Ras, a GTPase, that then activates the rest of the MAPK pathway, ultimately expressing proteins that stimulate cell cycle progression. It is likely that most, if not all, cancers have some mutation in the Ras-Raf-MAPK pathway, most commonly in Ras. [ 5 ] These mutations allow the pathway to be constitutively activated, regardless of the presence of mitogens.
Cell proliferation is often regulated by not only external mitogens but also by anti-mitogens, which inhibit cell cycle progression past G1. In normal cells, anti-mitogenic signaling as a result of DNA damage, preventing the cells from replicating and dividing. Tumor cells that are resistant to anti-mitogens allow the cell cycle to move forward when it should be prevented by some anti-mitogenic mechanism. This resistance to anti-mitogens might simply arise from overstimulation by positive mitogens. In other cases, tumor cells possess loss-of-function mutations in some part of the anti-mitogenic pathway. For example, consider the well-known anti-mitogen, transforming growth factor (TGF-𝝱). TGF-𝝱 works by binding to cell-surface receptors and activating the Smad gene regulatory proteins. Smad proteins then trigger an increase in p15, which inhibits cyclin D1 and prevents cell cycle progression. In many cancers, there is a loss-of-function mutation in the Smad proteins, thus negating the entire anti-mitogenic pathway. [ 5 ]
Not just one but multiple mitogenic mutations are required for cancer to proliferate. Generally, multiple mutations in different subsystems (an oncogene and a tumor suppressor gene) are the most effective at causing cancer. For example, a mutation that hyperactivates the oncogene Ras and another that inactivates the tumor suppressor pRb is far more tumorigenic than either protein alone. [ 5 ] Tumor cells are also resistant to the hyperproliferation stress response. Normal cells have apoptotic proteins that will respond to an overstimulation of mitogenic signaling pathways by triggering cell death or senescence. This generally prevents the onset of cancer from a single oncogenic mutation. In tumor cells, there is generally another mutation that inhibits apoptotic proteins as well, suppressing the hyperproliferation stress response. [ 5 ]
Lymphocytes can enter mitosis when they are activated by mitogens or antigens. B cells specifically can divide when they encounter an antigen matching their immunoglobulin . T cells undergo mitosis when stimulated by mitogens to produce small lymphocytes that are then responsible for the production of lymphokines , which are substances that modify the host organism to improve its immunity. B cells, on the other hand, divide to produce plasma cells when stimulated by mitogens, which then produce immunoglobulins , or antibodies . [ 9 ] Mitogens are often used to stimulate lymphocytes and thereby assess immune function. The most commonly used mitogens in clinical laboratory medicine are:
Lipopolysaccharide toxin from gram-negative bacteria is thymus -independent. They may directly activate B cells through the PI3-kinase signalling pathway, regardless of their antigenic specificity . [ 11 ] Plasma cells are terminally differentiated and, therefore, cannot undergo mitosis. Memory B cells can proliferate to produce more memory cells or plasma B cells. This is how the mitogen works, that is, by inducing mitosis in memory B cells to cause them to divide, with some becoming plasma cells.
Mitogen-activated protein kinase (MAPK) pathways can induce enzymes such as the COX-2 enzyme . [ 12 ] MAPK pathways may also play a role in the regulation of PTGS2 . [ 13 ] | https://en.wikipedia.org/wiki/Mitogen |
A mitogen-activated protein kinase ( MAPK or MAP kinase ) is a type of serine/threonine-specific protein kinases involved in directing cellular responses to a diverse array of stimuli, such as mitogens , osmotic stress , heat shock and proinflammatory cytokines . They regulate cell functions including proliferation , gene expression , differentiation , mitosis , cell survival, and apoptosis . [ 1 ]
MAP kinases are found in eukaryotes only, but they are fairly diverse and encountered in all animals, fungi and plants, and even in an array of unicellular eukaryotes. [ citation needed ]
MAPKs belong to the CMGC (CDK/MAPK/GSK3/CLK) kinase group. The closest relatives of MAPKs are the cyclin-dependent kinases (CDKs). [ 2 ]
The first mitogen-activated protein kinase to be discovered was ERK1 ( MAPK3 ) in mammals. Since ERK1 and its close relative ERK2 ( MAPK1 ) are both involved in growth factor signaling, the family was termed "mitogen-activated". With the discovery of other members, even from distant organisms (e.g. plants), it has become increasingly clear that the name is a misnomer, since most MAPKs are actually involved in the response to potentially harmful, abiotic stress stimuli (hyperosmosis, oxidative stress, DNA damage, low osmolarity, infection, etc.). Because plants cannot "flee" from stress, terrestrial plants have the highest number of MAPK genes per organism ever found [ citation needed ] . Thus the role of mammalian ERK1/2 kinases as regulators of cell proliferation is not a generic, but a highly specialized function.
Most MAPKs have a number of shared characteristics, such as the activation dependent on two phosphorylation events, a three-tiered pathway architecture and similar substrate recognition sites. These are the "classical" MAP kinases. But there are also some ancient outliers from the group as sketched above, that do not have dual phosphorylation sites, only form two-tiered pathways, and lack the features required by other MAPKs for substrate binding. These are usually referred to as "atypical" MAPKs. [ 3 ] It is yet unclear if the atypical MAPKs form a single group as opposed to the classical ones. [ clarification needed ]
The mammalian MAPK family of kinases includes three subfamilies:
Generally, ERKs are activated by growth factors and mitogens , whereas cellular stresses and inflammatory cytokines activate JNKs and p38s. [ 4 ]
Mitogen-activated protein kinases are catalytically inactive in their base form. In order to become active, they require (potentially multiple) phosphorylation events in their activation loops. This is conducted by specialized enzymes of the STE protein kinase group. In this way protein dynamics can induce a conformational change in the structure of the protein via long-range allostery . [ citation needed ]
In the case of classical MAP kinases, the activation loop contains a characteristic TxY (threonine-x-tyrosine) motif (TEY in mammalian ERK1 and ERK2 , TDY in ERK5 , TPY in JNKs , TGY in p38 kinases ) that needs to be phosphorylated on both the threonine and the tyrosine residues in order to lock the kinase domain in a catalytically competent conformation. In vivo and in vitro , phosphorylation of tyrosine oftentimes precedes phosphorylation of threonine, although phosphorylation of either residue can occur in the absence of the other. [ citation needed ]
This tandem activation loop phosphorylation (that was proposed to be either distributive or processive, dependent on the cellular environment) is performed by members of the Ste7 protein kinase family, also known as MAP2 kinases . MAP2 kinases in turn, are also activated by phosphorylation, by a number of different upstream serine-threonine kinases ( MAP3 kinases ). Because MAP2 kinases display very little activity on substrates other than their cognate MAPK, classical MAPK pathways form multi-tiered, but relatively linear pathways. These pathways can effectively convey stimuli from the cell membrane (where many MAP3Ks are activated) to the nucleus (where only MAPKs may enter) or to many other subcellular targets. [ citation needed ]
In comparison to the three-tiered classical MAPK pathways, some atypical MAP kinases appear to have a more ancient, two-tiered system. ERK3 (MAPK6) and ERK4 (MAPK4) were recently shown to be directly phosphorylated and thus activated by PAK kinases (related to other MAP3 kinases). [ 6 ] In contrast to the classical MAP kinases, these atypical MAPKs require only a single residue in their activation loops to be phosphorylated. The details of NLK and ERK7 (MAPK15) activation remain unknown. [ citation needed ]
Inactivation of MAPKs is performed by a number of phosphatases . A very conserved family of dedicated phosphatases is the so-called MAP kinase phosphatases (MKPs), a subgroup of dual-specificity phosphatases (DUSPs). [ 7 ] As their name implies, these enzymes are capable of hydrolyzing the phosphate from both phosphotyrosine and the phosphothreonine residues. Since removal of either phosphate groups will greatly reduce MAPK activity, essentially abolishing signaling, some tyrosine phosphatases are also involved in inactivating MAP kinases (e.g. the phosphatases HePTP , STEP and PTPRR in mammals). [ citation needed ]
As mentioned above, MAPKs typically form multi-tiered pathways, receiving input several levels above the actual MAP kinase. In contrast to the relatively simple, phosphorylation-dependent activation mechanism of MAPKs and MAP2Ks , MAP3Ks have stunningly complex regulation. Many of the better-known MAP3Ks , such as c-Raf , MEKK4 or MLK3 require multiple steps for their activation. These are typically allosterically-controlled enzymes, tightly locked into an inactive state by multiple mechanisms. The first step en route to their activation consists of relieving their autoinhibition by a smaller ligand (such as Ras for c-Raf , GADD45 for MEKK4 [ 10 ] or Cdc42 for MLK3 [ 11 ] ). This commonly (but not always) happens at the cell membrane, where most of their activators are bound (note that small G-proteins are constitutively membrane-associated due to prenylation ). That step is followed by side-to-side homo- and heterodimerisation of their now accessible kinase domains. Recently determined complex structures reveal that the dimers are formed in an orientation that leaves both their substrate-binding regions free. [ 12 ] Importantly, this dimerisation event also forces the MAP3 kinase domains to adopt a partially active conformation. Full activity is only achieved once these dimers transphosphorylate each other on their activation loops. The latter step can also be achieved or aided by auxiliary protein kinases (MAP4 kinases, members of the Ste20 family). Once a MAP3 kinase is fully active, it may phosphorylate its substrate MAP2 kinases, which in turn will phosphorylate their MAP kinase substrates. [ citation needed ]
The ERK1/2 pathway of mammals is probably the best-characterized MAPK system. The most important upstream activators of this pathway are the Raf proteins ( A-Raf , B-Raf or c-Raf ), the key mediators of response to growth factors ( EGF , FGF , PDGF , etc.); but other MAP3Ks such as c-Mos and Tpl2/Cot can also play the same role. All these enzymes phosphorylate and thus activate the MKK1 and/or MKK2 kinases, that are highly specific activators for ERK1 and ERK2 . The latter phosphorylate a number of substrates important for cell proliferation , cell cycle progression , cell division and differentiation ( RSK kinases , Elk-1 transcription factor , etc.) [ citation needed ]
In contrast to the relatively well-insulated ERK1/2 pathway , mammalian p38 and JNK kinases have most of their activators shared at the MAP3K level ( MEKK1 , MEKK4 , ASK1 , TAK1 , MLK3 , TAOK1 , etc.). In addition, some MAP2K enzymes may activate both p38 and JNK ( MKK4 ), while others are more specific for either JNK ( MKK7 ) or p38 ( MKK3 and MKK6 ). Due to these interlocks, there are very few if any stimuli that can elicit JNK activation without simultaneously activating p38 or reversed. [ 13 ] Both JNK and p38 signaling pathways are responsive to stress stimuli, such as cytokines , ultraviolet irradiation , heat shock , and osmotic shock , and are involved in adaptation to stress , apoptosis or cell differentiation . JNKs have a number of dedicated substrates that only they can phosphorylate ( c-Jun , NFAT4 , etc.), while p38s also have some unique targets (e.g. the MAPKAP kinases MK2 and MK3 ), ensuring the need for both in order to respond to stressful stimuli. [ citation needed ]
ERK5 is part of a fairly well-separated pathway in mammals. Its sole specific upstream activator MKK5 is turned on in response to the MAP3 kinases MEKK2 and MEKK3 . The specificity of these interactions are provided by the unique architecture of MKK5 and MEKK2/3, both containing N-terminal PB1 domains, enabling direct heterodimerisation with each other. [ 14 ] The PB1 domain of MKK5 also contributes to the ERK5-MKK5 interaction: it provides a special interface (in addition to the D-motif found in MKK5) through which MKK5 can specifically recognize its substrate ERK5. [ 15 ] Although the molecular-level details are poorly known, MEKK2 and MEKK3 respond to certain developmental cues to direct endothel formation and cardiac morphogenesis . While also implicated in brain development, the embryonic lethality of ERK5 inactivation due to cardiac abnormalities underlines its central role in mammalian vasculogenesis . [ 16 ] It is notable, that conditional knockout of ERK5 in adult animals is also lethal, due to the widespread disruption of endothelial barriers . [ 17 ] Mutations in the upstream components of the ERK5 pathway (the CCM complex) are thought to underlie cerebral cavernous malformations in humans. [ citation needed ]
MAPK pathways of fungi are also well studied. In yeast, the Fus3 MAPK is responsible for cell cycle arrest and mating in response to pheromone stimulation. The pheromone alpha-factor is sensed by a seven transmembrane receptor . The recruitment and activation of Fus3 pathway components are strictly dependent on heterotrimeric G-protein activation. The mating MAPK pathway consist of three tiers (Ste11-Ste7-Fus3), but the MAP2 and MAP3 kinases are shared with another pathway, the Kss1 or filamentous growth pathway. While Fus3 and Kss1 are closely related ERK-type kinases, yeast cells can still activate them separately, with the help of a scaffold protein Ste5 that is selectively recruited by the G-proteins of the mating pathway. The trick is that Ste5 can associate with and "unlock" Fus3 for Ste7 as a substrate in a tertiary complex, while it does not do the same for Kss1, leaving the filamentous growth pathway to be activated only in the absence of Ste5 recruitment. [ 18 ]
Fungi also have a pathway reminiscent of mammalian JNK/p38 signaling. This is the Hog1 pathway: activated by high osmolarity (in Saccharomyces cerevisiae ) or a number of other abiotic stresses (in Schizosaccharomyces pombe ). The MAP2 kinase of this pathway is called Pbs2 (related to mammalian MKK3/4/6/7), the dedicated MAP3 kinases involved in activation are Ssk2 and SSk22. The system in S. cerevisiae is activated by a sophisticated osmosensing module consisting of the Sho1 and Sln1 proteins, but it is yet unclear how other stimuli can elicit activation of Hog1. Yeast also displays a number of other MAPK pathways without close homologs in animals, such as the cell wall integrity pathway (Mpk1/Slt2) or the sporulation pathway (Smk1). [ 19 ]
Despite the high number of MAPK genes, MAPK pathways of higher plants were studied less than animal or fungal ones. Although their signaling appears very complex, the MPK3, MPK4 and MPK6 kinases of Arabidopsis thaliana are key mediators of responses to osmotic shock , oxidative stress , response to cold and involved in anti-pathogen responses. [ 20 ] [ 21 ] [ 22 ] Asai et al. 2002's model of MAPK mediated immunity passes the effector recognition signal from FLS2 ⇨ MEKK1 ⇨ MKK4 or MKK5 ⇨ MPK3 and MPK6 ⇨ WRKY22 or WRKY29. [ 22 ] However the work of Mészáros et al. 2006 and Suarez-Rodriguez et al. 2007 give other orders for this pathway and it is possible that these are parallel pathways operating simultaneously. [ 22 ] They are also involved in morphogenesis , since MPK4 mutants display severe dwarfism . [ 23 ]
Members of the MAPK family can be found in every eukaryotic organism examined so far. In particular, both classical and atypical MAP kinases can be traced back to the root of the radiation of major eukaryotic groups. Terrestrial plants contain four groups of classical MAPKs (MAPK-A, MAPK-B, MAPK-C and MAPK-D) that are involved in response to myriads of abiotic stresses. [ 25 ] However, none of these groups can be directly equated to the clusters of classical MAPKs found in opisthokonts (fungi and animals). In the latter, the major subgroups of classical MAPKs form the ERK/Fus3-like branch (that is further sub-divided in metazoans into ERK1/2 and ERK5 subgroups), and the p38/Hog1-like kinases (that has also split into the p38 and the JNK subgroups in multicellular animals). [ 26 ] In addition, there are several MAPKs in both fungi and animals, whose origins are less clear, either due to high divergence (e.g. NLK), or due to possibly being an early offshoot to the entire MAPK family (ERK3, ERK4, ERK7). In vertebrates, due to the twin whole genome duplications after the cephalochordate/vertebrate split, [ 27 ] there are several paralogs in every group. Thus ERK1 and ERK2 both correspond to the Drosophila kinase rolled , JNK1, JNK2 and JNK3 are all orthologous to the gene basket in Drosophila . Although among the p38 group, p38 alpha and beta are clearly paralogous pairs, and so are p38 gamma and delta in vertebrates, the timing of the base split is less clear, given that many metazoans already possess multiple p38 homologs (there are three p38-type kinases in Drosophila , Mpk2 ( p38a ), p38b and p38c ). The single ERK5 protein appears to fill a very specialized role (essential for vascular development in vertebrates) wherever it is present. This lineage has been deleted in protostomes , together with its upstream pathway components (MEKK2/3, MKK5), although they are clearly present in cnidarians , sponges and even in certain unicellular organisms (e.g. the choanoflagellate Monosiga brevicollis ) closely related to the origins of multicellular animals. [ 28 ]
The split between classical and some atypical MAP kinases happened quite early. This is suggested not just by the high divergence between extant genes, but also recent discoveries of atypical MAPKs in primitive, basal eukaryotes. The genome sequencing of Giardia lamblia revealed the presence of two MAPK genes, one of them similar to the already-well-known mammalian MAPKs (ERKs, p38s, etc.), the other one showing similarities to the mammalian ERK7 protein. [ 29 ] The situation is similar in the multicellular amoeba Dictyostelium discoideum , where the ddERK1 protein appears to be a classical MAPK, while ddERK2 more closely resembles our ERK7 and ERK3/4 proteins. [ 30 ] Atypical MAPKs can also be found in higher plants, although they are poorly known. Similar to the situation in mammals, most aspects of atypical MAPKs are uncharacterized due to the lack of research focus on this area. [ citation needed ]
As typical for the CMGC kinase group, the catalytic site of MAP kinases has a very loose consensus sequence for substrates . Like all their relatives, they only require the target serine / threonine amino acids to be followed by a small amino acid, preferably proline ("proline-directed kinases"). But as SP/TP sites are extremely common in all proteins, additional substrate-recognition mechanisms have evolved to ensure signaling fidelity. [ 31 ] Unlike their closest relatives, the cyclin-dependent kinases (CDKs), where substrates are recognized by the cyclin subunit, MAPKs associate with their substrates via auxiliary binding regions on their kinase domains. The most important such region consists of the hydrophobic docking groove and the negatively charged CD-region. Together they recognize the so-called MAPK docking or D-motifs (also called kinase interaction motif / KIM). D-motifs essentially consist of one or two positively charged amino acids, followed by alternating hydrophobic residues (mostly leucines), typically upstream of the phosphorylation site by 10–50 amino acids. [ 32 ] Many of the known MAPK substrates contain such D-motifs that can not only bind to, but also provide specific recognition by certain MAPKs. D-motifs are not restricted to substrates: MAP2 kinases also contain such motifs on their N-termini that are absolutely required for MAP2K-MAPK interaction and MAPK activation. [ 33 ] Similarly, both dual-specificity MAP kinase phosphatases and MAP-specific tyrosine phosphatases bind to MAP kinases through the same docking site. [ 34 ] [ 35 ] D-motifs can even be found in certain MAPK pathway regulators and scaffolds (e.g. in the mammalian JIP proteins). [ citation needed ]
Other, less well characterised substrate-binding sites also exist. One such site (the DEF site) is formed by the activation loop (when in the active conformation) and the MAP kinase-specific insert below it. This site can accommodate peptides with an FxFP consensus sequence, typically downstream of the phosphorylation site. [ 36 ] Note that the latter site can only be found in proteins that need to selectively recognize the active MAP kinases, thus they are almost exclusively found in substrates. Different motifs may cooperate with each other, as in the Elk family of transcription factors, that possess both a D-motif and an FxFP motif. The presence of an FxFP motif in the KSR1 scaffold protein also serves to make it an ERK1/2 substrate, providing a negative feedback mechanism to set the correct strength of ERK1/2 activation. [ citation needed ]
Since the discovery of Ste5 in yeast, scientists were on the hunt to discover similar non-enzymatic scaffolding pathway elements in mammals. There are indeed a number of proteins involved in ERK signaling, that can bind to multiple elements of the pathway: MP1 binds both MKK1/2 and ERK1/2, KSR1 and KSR2 can bind B-Raf or c-Raf, MKK1/2 and ERK1/2. Analogous proteins were also discovered for the JNK pathway: the JIP1 / JIP2 and the JIP3 /JIP4 families of proteins were all shown to bind MLKs, MKK7 and any JNK kinase. Unfortunately, unlike the yeast Ste5, the mechanisms by which they regulate MAPK activation are considerably less understood. While Ste5 actually forms a ternary complex with Ste7 and Fus3 to promote phosphorylation of the latter, known mammalian scaffold proteins appear to work by very different mechanisms. For example, KSR1 and KSR2 are actually MAP3 kinases and related to the Raf proteins. [ 37 ] Although KSRs alone display negligible MAP3 kinase activity, KSR proteins can still participate in the activation of Raf kinases by forming side-to-side heterodimers with them, providing an allosteric pair to turn on each enzymes. [ 38 ] JIPs on the other hand, are apparently transport proteins, responsible for enrichment of MAPK signaling components in certain compartments of polarized cells. [ 39 ] In this context, JNK-dependent phosphorylation of JIP1 (and possibly JIP2) provides a signal for JIPs to release the JIP-bound and inactive upstream pathway components, thus driving a strong local positive feedback loop. [ 40 ] This sophisticated mechanism couples kinesin-dependent transport to local JNK activation, not only in mammals, but also in the fruitfly Drosophila melanogaster . [ 41 ]
Since the ERK signaling pathway is involved in both physiological and pathological cell proliferation, it is natural that ERK1/2 inhibitors would represent a desirable class of antineoplastic agents. Indeed, many of the proto-oncogenic "driver" mutations are tied to ERK1/2 signaling, such as constitutively active (mutant) receptor tyrosine kinases , Ras or Raf proteins. Although no MKK1/2 or ERK1/2 inhibitors were developed for clinical use, kinase inhibitors that also inhibit Raf kinases (e.g. Sorafenib ) are successful antineoplastic agents against various types of cancer. [ 42 ] [ 43 ] MEK inhibitor cobimetinib has been investigated in pre-clinical lung cancer models in combination with inhibition of the PI3K pathway , where the two drugs lead to a synergistic response. [ 44 ] [ 45 ]
JNK kinases are implicated in the development of insulin resistance in obese individuals [ 46 ] as well as neurotransmitter excitotoxicity after ischaemic conditions. Inhibition of JNK1 ameliorates insulin resistance in certain animal models. Mice that were genetically engineered to lack a functional JNK3 gene - the major isoform in brain – display enhanced ischemic tolerance and stroke recovery. [ 47 ] Although small-molecule JNK inhibitors are under development, none of them proved to be effective in human tests yet. A peptide-based JNK inhibitor (AM-111, a retro-inverse D-motif peptide from JIP1, formerly known as XG-102) is also under clinical development for sensorineural hearing loss . [ 48 ]
p38 was once believed to be a perfect target for anti-inflammatory drugs. Yet the failure of more than a dozen chemically different compounds in the clinical phase suggests that p38 kinases might be poor therapeutic targets in autoimmune diseases . Many of these compounds were found to be hepatotoxic to various degree and tolerance to the anti-inflammatory effect developed within weeks. [ 49 ] An alternative approach is to evaluate the potential for targeting upstream MAPKs, such as ASK1 . [ 50 ] Studies in animal models of inflammatory arthritis have yielded promising results, and ASK1 has recently been found to be unique amongst the MAPKs in that it is inducible by inflammatory cytokines such as TNF-α . [ 50 ] | https://en.wikipedia.org/wiki/Mitogen-activated_protein_kinase |
Hormesis is a two-phased dose-response relationship to an environmental agent whereby low-dose amounts have a beneficial effect and high-dose amounts are either inhibitory to function or toxic. [ 1 ] [ 2 ] [ 3 ] [ 4 ] Within the hormetic zone , the biological response to low-dose amounts of some stressors is generally favorable. An example is the breathing of oxygen , which is required in low amounts (in air) via respiration in living animals, but can be toxic in high amounts, even in a managed clinical setting. [ 5 ]
In toxicology , hormesis is a dose-response phenomenon to xenobiotics or other stressors.
In physiology and nutrition, hormesis has regions extending from low-dose deficiencies to homeostasis, and potential toxicity at high levels. [ 6 ] Physiological concentrations of an agent above or below homeostasis may adversely affect an organism, where the hormetic zone is a region of homeostasis of balanced nutrition. [ 7 ] In pharmacology , the hormetic zone is similar to the therapeutic window .
In the context of toxicology, the hormesis model of dose response is vigorously debated. [ 8 ] The biochemical mechanisms by which hormesis works (particularly in applied cases pertaining to behavior and toxins) remain under early laboratory research and are not well understood. [ 6 ]
The term "hormesis" derives from Greek hórmēsis for "rapid motion, eagerness", itself from ancient Greek hormáein to excite. [ 4 ] The same Greek root provides the word hormone . The term "hormetics" is used for the study of hormesis. [ 6 ] The word hormesis was first reported in English in 1943. [ 4 ]
A form of hormesis famous in antiquity was Mithridatism , the practice whereby Mithridates VI of Pontus supposedly made himself immune to a variety of toxins by regular exposure to small doses. Mithridate and theriac , polypharmaceutical electuaries claiming descent from his formula and initially including flesh from poisonous animals, were consumed for centuries by emperors, kings, and queens as protection against poison and ill health. In the Renaissance , the Swiss doctor Paracelsus said, " All things are poison, and nothing is without poison; the dosage alone makes it so a thing is not a poison. "
German pharmacologist Hugo Schulz first described such a phenomenon in 1888 following his own observations that the growth of yeast could be stimulated by small doses of poisons. This was coupled with the work of German physician Rudolph Arndt , who studied animals given low doses of drugs, eventually giving rise to the Arndt–Schulz rule . [ 8 ] Arndt's advocacy of homeopathy contributed to the rule's diminished credibility in the 1920s and 1930s. [ 8 ] The term "hormesis" was coined and used for the first time in a scientific paper by Chester M. Southam and J. Ehrlich in 1943 in the journal Phytopathology , volume 33, pp. 517–541.
In 2004, Edward Calabrese evaluated the concept of hormesis. [ 9 ] [ 10 ] Over 600 substances show a U-shaped dose–response relationship ; Calabrese and Baldwin wrote: "One percent (195 out of 20,285) of the published articles contained 668 dose-response relationships that met the entry criteria [of a U-shaped response indicative of hormesis]" [ 11 ]
Carbon monoxide is produced in small quantities across phylogenetic kingdoms, where it has essential roles as a neurotransmitter (subcategorized as a gasotransmitter ). The majority of endogenous carbon monoxide is produced by heme oxygenase ; the loss of heme oxygenase and subsequent loss of carbon monoxide signaling has catastrophic implications for an organism. [ 12 ] In addition to physiological roles, small amounts of carbon monoxide can be inhaled or administered in the form of carbon monoxide-releasing molecules as a therapeutic agent. [ 13 ]
Regarding the hormetic curve graph:
Many organisms maintain a hormesis relationship with oxygen, which follows a hormetic curve similar to carbon monoxide:
Physical exercise intensity may exhibit a hormetic curve. Individuals with low levels of physical activity are at risk for some diseases; however, individuals engaged in moderate, regular exercise may experience less disease risk. [ 15 ]
The possible effect of small amounts of oxidative stress is under laboratory research. [ 16 ] Mitochondria are sometimes described as "cellular power plants" because they generate most of the cell's supply of adenosine triphosphate (ATP), a source of chemical energy. Reactive oxygen species (ROS) have been discarded as unwanted byproducts of oxidative phosphorylation in mitochondria by the proponents of the free-radical theory of aging promoted by Denham Harman . The free-radical theory states that compounds inactivating ROS would lead to a reduction of oxidative stress and thereby produce an increase in lifespan, although this theory holds only in basic research . [ 17 ] However, in over 19 clinical trials , "nutritional and genetic interventions to boost antioxidants have generally failed to increase life span." [ 18 ]
Whether this concept applies to humans remains to be shown, although a 2007 epidemiological study supports the possibility of mitohormesis, indicating that supplementation with beta-carotene , vitamin A or vitamin E may increase disease prevalence in humans. [ 19 ] More recent studies have reported that rapamycin exhibits hormesis, where low doses can enhance cellular longevity by partially inhibiting mTOR, unlike higher doses that are toxic due to complete inhibition. This partial inhibition of mTOR (by the hormetic effect of low-dose rapamycin) modulates mTOR–mitochondria cross-talk , thereby demonstrating mitohormesis; and consequently reducing oxidative damage , metabolic dysregulation, and mitochondrial dysfunction , thus slowing cellular aging . [ 2 ] [ 3 ]
Alcohol is believed to be hormetic in preventing heart disease and stroke, [ 20 ] although the benefits of light drinking may have been exaggerated. [ 21 ] [ 22 ] The gut microbiome of a typical healthy individual naturally ferments small amounts of ethanol, and in rare cases dysbiosis leads to auto-brewery syndrome , therefore whether benefits of alcohol are derived from the behavior of consuming alcoholic drinks or as a homeostasis factor in normal physiology via metabolites from commensal microbiota remains unclear. [ 23 ] [ 24 ]
In 2012, researchers at UCLA found that tiny amounts (1 mM, or 0.005%) of ethanol doubled the lifespan of Caenorhabditis elegans , a roundworm frequently used in biological studies, that were starved of other nutrients. Higher doses of 0.4% provided no longevity benefit. [ 25 ] However, worms exposed to 0.005% did not develop normally (their development was arrested). The authors argue that the worms were using ethanol as an alternative energy source in the absence of other nutrition, or had initiated a stress response. They did not test the effect of ethanol on worms fed a normal diet.
In 2010, a paper in the journal Environmental Toxicology & Chemistry showed that low doses of methylmercury , a potent neurotoxic pollutant, improved the hatching rate of mallard eggs. [ 26 ] The author of the study, Gary Heinz, who led the study for the U.S. Geological Survey at the Patuxent Wildlife Research Center in Beltsville , stated that other explanations are possible. For instance, the flock he studied might have harbored some low, subclinical infection and that mercury, well known to be antimicrobial, might have killed the infection that otherwise hurt reproduction in the untreated birds. [ 26 ]
Hormesis has been observed in a number of cases in humans and animals exposed to chronic low doses of ionizing radiation. A-bomb survivors who received high doses exhibited shortened lifespan and increased cancer mortality, but those who received low doses had lower cancer mortality than the Japanese average. [ 27 ] [ 28 ]
In Taiwan, recycled radiocontaminated steel was inadvertently used in the construction of over 100 apartment buildings, causing the long-term exposure of 10,000 people. The average dose rate was 50 mSv/year and a subset of the population (1,000 people) received a total dose over 4,000 mSv over ten years. In the widely used linear no-threshold model used by regulatory bodies, the expected cancer deaths in this population would have been 302 with 70 caused by the extra ionizing radiation, with the remainder caused by natural background radiation. The observed cancer rate, though, was quite low at 7 cancer deaths when 232 would be predicted by the LNT model had they not been exposed to the radiation from the building materials. Ionizing radiation hormesis appears to be at work. [ 29 ]
No experiment can be performed in perfect isolation. Thick lead shielding around a chemical dose experiment to rule out the effects of ionizing radiation is built and rigorously controlled for in the laboratory, and certainly not the field. Likewise the same applies for ionizing radiation studies. Ionizing radiation is released when an unstable particle releases radiation, creating two new substances and energy in the form of an electromagnetic wave . The resulting materials are then free to interact with any environmental elements, and the energy released can also be used as a catalyst in further ionizing radiation interactions. [ 30 ]
The resulting confusion in the low-dose exposure field (radiation and chemical) arise from lack of consideration of this concept as described by Mothersill and Seymory. [ 31 ]
Veterans of the Gulf War (1991) who suffered from the persistent symptoms of Gulf War Illness (GWI) were likely exposed to stresses from toxic chemicals and/or radiation. [ 32 ] The DNA damaging ( genotoxic ) effects of such exposures can be, at least partially, overcome by the DNA nucleotide excision repair (NER) pathway. Lymphocytes from GWI veterans exhibited a significantly elevated level of NER repair. [ 32 ] It was suggested that this increased NER capability in exposed veterans was likely a hormetic response, that is, an induced protective response resulting from battlefield exposure. [ 32 ]
One of the areas where the concept of hormesis has been explored extensively with respect to its applicability is aging. [ 33 ] [ 34 ] Since the basic survival capacity of any biological system depends on its homeostatic ability, biogerontologists proposed that exposing cells and organisms to mild stress should result in the adaptive or hormetic response with various biological benefits. This idea has preliminary evidence showing that repetitive mild stress exposure may have anti-aging effects in laboratory models. [ 35 ] [ 36 ] Some mild stresses used for such studies on the application of hormesis in aging research and interventions are heat shock , irradiation, prooxidants , hypergravity , and food restriction. [ 35 ] [ 36 ] [ 37 ] The example of heat shock refers to the proteostasis network. The addition of a bit of stress on the cell can lead to activation of signaling pathways and unfolded protein response pathways that upregulate chaperones, downregulate translation, and other processes that allow the cell to respond to stress. In this way, the activation of these pathways prepares the cell for other stressors since the pathways are already activated. However, too much stress or prolonged stress can actually damage the cell and lead to cell death on occasion. [ 38 ] Such compounds that may modulate stress responses in cells have been termed "hormetins". [ 35 ]
Hormesis suggests dangerous substances have benefits. Concerns exist that the concept has been leveraged by lobbyists to weaken environmental regulations of some well-known toxic substances in the US. [ 39 ]
The hypothesis of hormesis has generated the most controversy when applied to ionizing radiation . This hypothesis is called radiation hormesis. For policy-making purposes, the commonly accepted model of dose response in radiobiology is the linear no-threshold model (LNT), which assumes a strictly linear dependence between the risk of radiation-induced adverse health effects and radiation dose, implying that there is no safe dose of radiation for humans.
Nonetheless, many countries including the Czech Republic , Germany , Austria , Poland , and the United States have radon therapy centers whose whole primary operating principle is the assumption of radiation hormesis, or beneficial impact of small doses of radiation on human health. Countries such as Germany and Austria at the same time have imposed very strict antinuclear regulations, which have been described as radiophobic inconsistency.
The United States National Research Council (part of the National Academy of Sciences ), [ 40 ] the National Council on Radiation Protection and Measurements (a body commissioned by the United States Congress ) [ 41 ] and the United Nations Scientific Committee on the Effects of Ionizing Radiation all agree that radiation hormesis is not clearly shown, nor clearly the rule for radiation doses.
A United States–based National Council on Radiation Protection and Measurements stated in 2001 that evidence for radiation hormesis is insufficient and radiation protection authorities should continue to apply the LNT model for purposes of risk estimation. [ 41 ]
A 2005 report commissioned by the French National Academy concluded that evidence for hormesis occurring at low doses is sufficient and LNT should be reconsidered as the methodology used to estimate risks from low-level sources of radiation, such as deep geological repositories for nuclear waste . [ 42 ]
Hormesis remains largely unknown to the public, requiring a policy change for a possible toxin to consider exposure risk of small doses. [ 43 ] | https://en.wikipedia.org/wiki/Mitohormesis |
Mitointeractome is a mitochondrial protein interactome database. [ 1 ]
This Biological database -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Mitointeractome |
Mitophagy is the selective degradation of mitochondria by autophagy . It often occurs to defective mitochondria following damage or stress. The process of mitophagy was first described in 1915 by Margaret Reed Lewis and Warren Harmon Lewis . [ 1 ] Ashford and Porter used electron microscopy to observe mitochondrial fragments in liver lysosomes by 1962, [ 2 ] and a 1977 report suggested that "mitochondria develop functional alterations which would activate autophagy." [ 3 ] The term "mitophagy" was coined by J.J. Lemasters et al. in 2005, [ 4 ] though earlier uses dating back to at least 1998 can be found. [ 5 ]
Mitophagy is key in keeping the cell healthy. It promotes turnover of mitochondria and prevents accumulation of dysfunctional mitochondria which can lead to cellular degeneration. It is mediated by Atg32 (in yeast) and NIX and its regulator BNIP3 in mammals. Mitophagy is regulated by PINK1 and parkin proteins. In addition to the selective removal of damaged mitochondria, mitophagy is also required to adjust mitochondrial numbers to changing cellular metabolic needs, for steady-state mitochondrial turnover, and during certain cellular developmental stages, such as during cellular differentiation of red blood cells. [ 4 ]
Organelles and bits of cytoplasm are sequestered and targeted for degradation by the lysosome for hydrolytic digestion by a process known as autophagy. Mitochondria metabolism leads to the creation of by-products that lead to DNA damage and mutations. Therefore, a healthy population of mitochondria is critical for the well-being of cells. Previously it was thought that targeted degradation of mitochondria was a stochastic event, but accumulating evidence suggest that mitophagy is a selective process. [ 6 ]
Generation of adenosine triphosphate (ATP) by oxidative phosphorylation leads to the production of various reactive oxygen species (ROS) in the mitochondria, and submitochondrial particles. Formation of ROS as a mitochondrial waste product will eventually lead to cytotoxicity and cell death. Because of their role in metabolism, mitochondria are very susceptible to ROS damage. Damaged mitochondria cause a depletion in ATP and a release of cytochrome c , which leads to activation of caspases and onset of apoptosis . Mitochondrial damage is not caused solely by oxidative stress or disease processes; normal mitochondria will eventually accumulate oxidative damage hallmarks overtime, which can be deleterious to mitochondria as well as to the cell. These faulty mitochondria can further deplete the cell of ATP, increase production of ROS, and release proapoptopic proteins such as caspases.
Because of the danger of having damaged mitochondria in the cell, the timely elimination of damaged and aged mitochondria is essential for maintaining the integrity of the cell. This turnover process consists of the sequestration and hydrolytic degradation by the lysosome, a process also known as mitophagy.
Mitochondrial depletion reduces a spectrum of senescence effectors and phenotypes while preserving ATP production via enhanced glycolysis . [ 7 ]
There are several pathways by which mitophagy is induced in mammalian cells. The PINK1 and Parkin pathway is, so far, the best characterized. This pathway starts by deciphering the difference between healthy mitochondria and damaged mitochondria. A 64-kDa protein, PTEN-induced kinase 1 (PINK1), has been implicated to detect mitochondrial quality. PINK1 contains a mitochondrial targeting sequence (MTS) and is recruited to the mitochondria. In healthy mitochondria, PINK1 is imported through the outer membrane via the TOM complex , and partially through the inner mitochondrial membrane via the TIM complex , so it then spans the inner mitochondrial membrane. The process of import into the inner membrane is associated with the cleavage of PINK1 from 64-kDa into a 60-kDa form. PINK1 is then cleaved by PARL into a 52-kDa form. This new form of PINK1 is degraded by proteases within the mitochondria. This keeps the concentration of PINK1 in check in healthy mitochondria. [ 8 ]
In unhealthy mitochondria, the inner mitochondrial membrane becomes depolarized. This membrane potential is necessary for the TIM-mediated protein import. In depolarized mitochondria, PINK1 is no longer imported into the inner membrane, is not cleaved by PARL and PINK1 concentration increases in the outer mitochondrial membrane. PINK1 can then recruit Parkin, a cytosolic E3 ubiquitin ligase . [ 9 ] It is thought that PINK1 phosphorylates Parkin ubiquitin ligase at S65 which initiates Parkin recruitment at the mitochondria. [ 10 ] [ 11 ] The phosphorylation site of Parkin, at S65, is homologous to the site where ubiquitin is phosphorylated. This phosphorylation activates Parkin by inducing dimerization, an active state. [ citation needed ] This allows for Parkin-mediated ubiquitination on other proteins. [ 10 ]
Because of its PINK1-mediated recruitment to the mitochondrial surface, Parkin can ubiquitylate proteins in the outer mitochondrial membrane. [ 12 ] Some of these proteins include Mfn1 / Mfn2 and mitoNEET . [ 11 ] The ubiquitylation of mitochondrial surface proteins brings in mitophagy initiating factors. Parkin promotes ubiquitin chain linkages on both K63 and K48. K48 ubiquitination initiates degradation of the proteins, and could allow for passive mitochondrial degradation. K63 ubiquitination is thought to recruit autophagy adaptors LC3 / GABARAP which will then lead to mitophagy. It is still unclear which proteins are necessary and sufficient for mitophagy, and how these proteins, once ubiquitylated, initiate mitophagy.
Other pathways that can induce mitophagy include mitophagy receptors on the outer mitochondrial membrane surface. These receptors include NIX1, BNIP3 and FUNDC1 . All of these receptors contain LC3 interacting regions (LIR) consensus sequences that bind LC3/GABARAP which can lead to the degradation of the mitochondria. In hypoxic conditions BNIP3 is upregulated by HIF1α . BNIP3 is then phosphorylated at its serine residues near the LIR sequence which promotes LC3 binding. FUNDC1 is also hypoxia sensitive, although it is constitutively present at the outer mitochondrial membrane during normal conditions. [ 10 ] Mitophagy can also be artificially introduced by a series of synthetic autophagy receptors [ 13 ] that are composed of antibody fragments to recognize the mitochondrial outer membrane proteins. [ 14 ]
In neurons , mitochondria are distributed unequally throughout the cell to areas where energy demand is high, like at synapses and Nodes of Ranvier . This distribution is maintained largely by motor protein-mediated mitochondrial transport along the axon . [ 15 ] While neuronal mitophagy is thought to occur primarily in the cell body , it also occurs locally in the axon at sites distant from the cell body; in both the cell body and the axon, neuronal mitophagy occurs via the PINK1-Parkin pathway. [ 16 ] Mitophagy in the nervous system may also occur transcellularly, where damaged mitochondria in retinal ganglion cell axons can be passed to neighboring astrocytes for degradation. [ 17 ] This process is known as transmitophagy.
Mitophagy in yeast was first presumed after the discovery of Yeast Mitochondrial Escape genes (yme), specifically yme1. Yme1 like other genes in the family showed increase escape of mtDNA, but was the only one that showed an increase in mitochondrial degradation. Through work on this gene which mediates the escape of mtDNA, researchers discovered that mitochondrial turnover is triggered by proteins. [ 18 ]
More was discovered about genetic control of mitophagy after studies on the protein UTH1. After performing a screen for genes that regulate longevity, it was found in ΔUTH1 strains that there was an inhibition of mitophagy, which occurred without affecting autophagy mechanisms. This study also showed that the Uth1p protein is necessary to move mitochondria to the vacuole. This suggested there is a specialized system for mitophagy. Other studies looked at AUP1, a mitochondrial phosphatase, and found Aup1 marks mitochondria for elimination. [ 18 ]
Another yeast protein associated with mitophagy is a mitochondrial inner membrane protein, Mdm38p/Mkh1p. This protein is part of the complex that exchanges K+/H+ ions across the inner membrane. Deletions in this protein causes swelling, a loss of membrane potential, and mitochondrial fragmentation. [ 18 ]
Recently, it has been shown that ATG32 (autophagy related gene 32) plays a crucial role in yeast mitophagy. It is localized to the mitochondria. Once mitophagy is initiated, Atg32 binds to Atg11 and the Atg32-associated mitochondria are transported to the vacuole. Atg32 silencing stops recruitment of autophagy machinery and mitochondrial degradation. Atg32 is not necessary for other forms of autophagy. [ 19 ] [ 20 ]
All of these proteins likely play a role in maintaining healthy mitochondria, but mutations have shown that dysregulation can lead to a selective degradation of mitochondria. Whether these proteins work in concert, are main players in mitophagy, or members in a larger network to control autophagy still remains to be elucidated.
Mitochondria play an important role in the functioning of the immune system. Mitochondrial damage-associated molecular patterns ( DAMPs ) such as parts of damaged organelles or mtDNA are secreted by cells following sterile inflammation, dysregulations in cell metabolism, or infection. There is evidence that these DAMPs act as one of the key triggers of the innate immune response. Mitophagy provides the elimination of non-functioning mitochondria and maintains mitochondrial homeostasis. Due to that, it can be seen as an immunomodulatory tool to keep the immune response in check. [ 21 ]
In addition to immunomodulatory functions, mitophagy can regulate the fate of hematopoietic stem cells ( HSC ). Mitophagy impaired due to the deletion of autophagy-related genes led to a loss of HSC function, more likely as a result of mitochondrial damage that stimulated excessive ROS production. On the contrary, mitophagy induction appeared to be protective for HSC and directed stem cell differentiation to the myeloid lineage. [ 22 ]
Immune cell activation and the change in phenotype are followed by metabolic reprogramming. Activated cells, including macrophages , favor glycolysis , which is also accompanied by mitochondrial clearance through mitophagy. On the contrary, macrophage regulatory phenotypes (M2) are associated with the induction of oxidative phosphorylation , which is dependent on mitochondrial biogenesis. [ 23 ] This highlights the important role of mitophagy in the determination of the macrophage phenotype.
It is also important to mention that mitophagy impairment in macrophages is quite common in the early stages of different pathological states. Macrophages play an important role in the innate immune response. However, conditions leading to immune paralysis, e.g. sepsis , make them incapable of efficient bactericidal clearance. Hence, some studies highlighted the role of mitophagy as a biomarker of different stages of sepsis, as it is inhibited in the early stage and induced later. [ 24 ] Other reports showed compromised mitophagy in experimental and human kidney fibrosis . Some mitophagy-associated molecules such as Mfn2 and Parkin are negatively regulated in this pathological state. Consequently, the frequency of regulatory profibrotic M2 macrophages was higher, confirming the role of mitophagy in the induction of the pro-inflammatory M1 phenotype . [ 24 ] [ 25 ]
Many studies demonstrate that the release of mtROS and mtDNA as DAMPs plays a crucial role in the activation of the inflammasome and following inflammation mediated by IL-1β . NF-κB , a protein complex that is important for immune cell signaling, but also plays an important role in mitophagy induction, has been reported to control the activation of the inflammasome by adopting the p62-mitophagy pathway. [ 26 ]
The importance of mitophagy was demonstrated by the deletion of Beclin 1 and LC3b autophagy-associated genes in bone marrow-derived macrophages (BMDM). Defective mitophagy and accumulation of damaged mitochondria led to enhanced mtROS production and the release of cytosolic mtDNA. As a result, activation of the NLRP3 inflammasome increased. [ 26 ] Recently, it was shown that Parkin deficiency also triggered NLRP3 activation in a mtROS-dependent manner and as a result promoted viral clearance. [ 21 ] [ 27 ] Furthermore, Pink1 and Parkin deficiency in a model of polymicrobial sepsis induced inflammasome activation and appeared to be critical in host protection. [ 28 ] Consistent with these reports, there are also studies describing the loss of the autophagy protein Atg16L1 which induced the cleavage of IL-1β by caspases associated with NLRP3. [ 21 ] Many other proteins are known to modulate mitophagy. Some are cell-specific, for example, macrophages produce stress-induced proteins that are known to induce mitophagy followed by inhibition of NLRP3 inflammasome assembly. [ 21 ] [ 29 ] In general, it can be said that many pathological inflammatory responses are the result of an imbalance in the crosstalk between the inflammasome and the mitophagy.
It is known that some viruses can modulate mitophagy (directly or indirectly) using different mechanisms and, as a result, cause a disbalance in the innate immune response. [ 21 ] mtDNA that exits damaged mitochondria acts as one of the triggers of type I interferon (IFN I) production. Some viruses can induce mitophagy and therefore inhibit the production of these crucial antiviral cytokines. There are reports of viral proteins directly or indirectly interacting with autophagy and mitophagy-associated proteins such as LC3 or Pink1-Parkin and usurping them to trigger mitophagy and subsequently inhibit IFN I responses. [ 21 ] [ 30 ]
Mitochondria is a dynamic structure regulating its morphology by context-dependent constant fission and fusion. Fission is crucial for mitophagy, as it cuts off a small mitochondrial part that can be further engulfed by the autophagosome . [ 31 ] The viruses Hepatitis B (HBV) and hepatitis C (HCV) take advantage of this mechanism by inducing mitochondrial fission and following mitophagy. HBV stimulates the phosphorylation of Drp1 , a fission-promoting GTPase molecule, and the expression and recruitment of Parkin. HCV is known to promote mitophagy by inducing ROS production. Other viruses such as Human Parainfluenza (HPIV3) regulate host immune responses by clearing mitochondrial antiviral-signaling protein (MAVS) located in the outer mitochondrial membrane. There are specific proteins produced by HPIV3 that induce mitophagy in the infected cell, thus promoting MAVS degradation and the corresponding inhibition of IFN I production. The same strategy is used by the SARS-CoV -encoded protein ORF-9b , which triggers the degradation of several mitochondrial proteins, including MAVS. [ 32 ] [ 33 ]
As of 2020, the role of mitophagy in cancer is not fully understood. Some models of mitophagy, such as PINK1 or BNIP3 -mediated mitophagy, have been associated with tumor suppression in humans and mice. Mitophagy associated with NIX , in contrast, is associated with tumor promotion. [ 34 ] In 1920 Otto Warburg observed that certain cancerous tumors display a metabolic shift towards glycolysis . This is referred to as the " Warburg effect ", in which cancer cells produce energy via the conversion of glucose into lactate, even in the presence of oxygen (aerobic glycolysis). Despite nearly a century since it was first described, a lot of questions remained unanswered regarding the Warburg effect. Initially, Warburg attributed this metabolic shift to mitochondrial dysfunction in cancer cells. Further studies in tumor biology have shown that the increased growth rate in cancer cells is due to an overdrive in glycolysis (glycolytic shift), which leads to a decrease in oxidative phosphorylation and mitochondrial density. As a consequence of the Warburg effect, cancer cells would produce large amounts of lactate. The excess lactate is then released to the extracellular environment which results in a decrease in extracellular pH. This micro-environment acidification can lead to cellular stress, which would lead to autophagy. Autophagy is activated in response to a range of stimuli, including nutrient depletion, hypoxia, and activated oncogenes. However, it appears that autophagy can help in cancer cell survival under conditions of metabolic stress and it may confer resistance to anti-cancer therapies such as radiation and chemotherapy. Additionally, in the microenvironment of cancer cells, there is an increase in hypoxia-inducible transcription factor 1-alpha ( HIF1A ), which promotes expression of BNIP3 , an essential factor for mitophagy. [ 35 ]
Parkinson's disease is a neurodegenerative disorder pathologically characterized by death of the dopamine-producing neurons in the substantia nigra . There are several genetic mutations implicated in Parkinson's disease, including loss of function PINK1 [ 36 ] and Parkin. [ 9 ] Loss of function in either of these genes results in the accumulation of damaged mitochondria, and aggregation of proteins or inclusion bodies – eventually leading to neuronal death.
Mitochondria dysfunction is thought to be involved in Parkinson's disease pathogenesis. In spontaneous, usually aging related Parkinson's disease (non-genetically linked), the disease is commonly caused by dysfunctional mitochondria, cellular oxidative stress, autophagic alterations and the aggregation of proteins. These can lead to mitochondrial swelling and depolarization. It is important to keep the dysfunctional mitochondria regulated, because all of these traits could be induced by mitochondrial dysfunction and can induce cell death. [ 37 ] Disorders in energy creation by mitochondria can cause cellular degeneration, like those seen in the substantia nigra. [ 31 ]
Tuberculosis is a contagious disease caused by infection with the airborne pathogen Mycobacterium tuberculosis . Recent investigation has shown that chronic infection by Mycobacterium tuberculosis in the lungs or ex-vivo infection by non-pathogenic mycobacteria ( M.bovis ) elicits activation of the receptor-mediated pathway for mitophagy. Here the receptor mediated mitophagy pathways are elicited through NIX that gets upregulated during M. tuberculosis infection. Elicited NIX/BNIP3L receptor recruitment of LC3 molecules mediating formation of phagophore that engulf defective mitochondria directly. [ 38 ] | https://en.wikipedia.org/wiki/Mitophagy |
Mitotic cell rounding is a shape change that occurs in most animal cells that undergo mitosis . Cells abandon the spread or elongated shape characteristic of interphase and contract into a spherical morphology during mitosis. The phenomenon is seen both in artificial cultures in vitro and naturally forming tissue in vivo .
In 1935, one of the first published accounts of mitotic rounding in live tissue described cell rounding in the pseudostratified epithelium of the mammalian neural tube . [ 1 ] Sauer noticed that cells in mitosis rounded up to the apical , or luminal, surface of the columnar epithelium before dividing and returning to their elongated morphology .
For a long time it was not clear why cells became round in mitosis. Recent studies in the epithelia and epidermis of various organisms, however, show that mitotic cell rounding might serve several important functions. [ 2 ]
Thus, mitotic cell rounding is involved in tissue organization and homeostasis.
To understand the physical mechanisms of how cells round up in mitosis, researchers have conducted mechanical measurements with cultured cells in vitro . The forces that drive cell rounding have recently been characterized by researchers from the groups of Professors Tony Hyman and Daniel Muller , who used flat atomic force microscopy cantilevers to constrain mitotic cells and measure the response force. [ 10 ] [ 11 ] More than 90% of the forces are generated by the collective activity of myosin II molecular motors in the actin cortex. [ 10 ] [ 11 ] As a result, the surface tension and effective stiffness of the actin cortex increase as has been consistently observed in mitotic cells. [ 12 ] [ 13 ] [ 14 ] This in turn yields an increase in intracellular hydrostatic pressure due to the Law of Laplace , which relates surface tension of a fluid interface to the differential pressure sustained across that interface. [ 15 ] The increase in hydrostatic pressure is important because it produces the outward force necessary to push and rounds up against external objects or impediments, such as flexible cantilever , [ 10 ] [ 11 ] soft gel [ 8 ] or micropillar [ 16 ] ( in vitro examples), or surrounding extracellular matrix and neighboring cells [ 7 ] ( in vivo examples). In HeLa cells in vitro , the force generated by a half-deformed mitotic cell is on the order of 50 to 100 nano newtons . [ 10 ] [ 11 ] Internal hydrostatic pressure has been measured to increase from below 100 pascals in interphase to 3 to 10 fold that in mitosis. [ 10 ] [ 11 ] [ 15 ]
In similar in vitro experiments, it was found that the threshold forces required to prevent mitosis are in excess of 100 nN. [ 9 ] At threshold forces the cell suffers a loss of cortical F-actin uniformity, which further amplifies the susceptibility to applied force. These effects potentiate distortion of cell dimensions and subsequent perturbation of mitotic progression via spindle defects. [ 8 ] [ 9 ]
Release of stable focal adhesions is another important aspect of mitotic rounding. Cells that are genetically perturbed to manifest constitutively active adhesion regulators are unable to properly remodel their focal adhesions and facilitate the generation of a uniform actomyosin cortex. [ 8 ] [ 17 ] Overall, the biochemical events governing the morphological and mechanical changes in mitotic cells are orchestrated by the mitotic master regulator Cdk1 . [ 11 ] [ 18 ] [ 19 ]
Apart from actomyosin-related genes, several disease genes have recently been implicated in mitotic cell rounding. These include Parkinson’s disease associated DJ-1 / Park7 and FAM134A/RETREG2. [ 20 ] | https://en.wikipedia.org/wiki/Mitotic_cell_rounding |
Mitotic recombination is a type of genetic recombination that may occur in somatic cells during their preparation for mitosis in both sexual and asexual organisms. In asexual organisms, the study of mitotic recombination is one way to understand genetic linkage because it is the only source of recombination within an individual. [ 1 ] Additionally, mitotic recombination can result in the expression of recessive alleles in an otherwise heterozygous individual. This expression has important implications for the study of tumorigenesis and lethal recessive alleles. [ 1 ] [ 2 ] Mitotic homologous recombination occurs mainly between sister chromatids subsequent to replication (but prior to cell division). Inter-sister homologous recombination is ordinarily genetically silent. During mitosis the incidence of recombination between non-sister homologous chromatids is only about 1% of that between sister chromatids. [ 3 ]
The discovery of mitotic recombination came from the observation of twin spotting in Drosophila melanogaster . This twin spotting, or mosaic spotting, was observed in D. melanogaster as early as 1925, but it was only in 1936 that Curt Stern explained it as a result of mitotic recombination. Prior to Stern's work, it was hypothesized that twin spotting happened because certain genes had the ability to eliminate the chromosome on which they were located. [ 4 ] Later experiments uncovered when mitotic recombination occurs in the cell cycle and the mechanisms behind recombination.
Mitotic recombination can happen at any locus but is observable in individuals that are heterozygous at a given locus. If a crossover event between non-sister chromatids affects that locus, then both homologous chromosomes will have one chromatid containing each genotype. The resulting phenotype of the daughter cells depends on how the chromosomes line up on the metaphase plate . If the chromatids containing different alleles line up on the same side of the plate, then the resulting daughter cells will appear heterozygous and be undetectable, despite the crossover event. However, if chromatids containing the same alleles line up on the same side, the daughter cells will be homozygous at that locus. This results in twin spotting , where one cell presents the homozygous recessive phenotype and the other cell has the homozygous wild type phenotype. If those daughter cells go on to replicate and divide, the twin spots will continue to grow and reflect the differential phenotype.
Mitotic recombination takes place during interphase . It has been suggested that recombination takes place during G1, when the DNA is in its 2-strand phase, and replicated during DNA synthesis. [ 5 ] It is also possible to have the DNA break leading to mitotic recombination happen during G1, but for the repair to happen after replication. [ 6 ] [ 7 ]
In the budding yeast Saccharomyces cerevisiae , mutations in several genes needed for mitotic (and meiotic) recombination cause increased sensitivity to inactivation by radiation and/or genotoxic chemicals . [ 8 ] For example, gene rad52 is required for mitotic recombination [ 9 ] as well as meiotic recombination. [ 10 ] Rad52 mutant yeast cells have increased sensitivity to killing by X-rays , methyl methanesulfonate and the DNA crosslinking agent 8-methoxypsoralen -plus-UV light, suggesting that mitotic recombinational repair is required for removal of the different DNA damages caused by these agents.
The mechanisms behind mitotic recombination are similar to those behind meiotic recombination. These include sister chromatid exchange and mechanisms related to DNA double strand break repair by homologous recombination such as single-strand annealing , synthesis-dependent strand annealing ( SDSA ), and gene conversion through a double-Holliday Junction intermediate or SDSA. In addition, non-homologous mitotic recombination is a possibility and can often be attributed to non-homologous end joining . [ 6 ] [ 7 ] [ 11 ] [ 12 ]
There are several theories on how mitotic crossover occurs. In the simple crossover model, the two homologous chromosomes overlap on or near a common Chromosomal fragile site (CFS). This leads to a double-strand break , [ 13 ] which is then repaired using one of the two strands. This can lead to the two chromatids switching places. In another model, two overlapping sister chromatids form a double Holliday junction at a common repeat site and are later sheared in such a way that they switch places. In either model, the chromosomes are not guaranteed to trade evenly, or even to rejoin on opposite sides thus most patterns of cleavage do not result in any crossover event. Uneven trading introduces many of the deleterious effects of mitotic crossover.
Alternatively, a crossover can occur during DNA repair [ 14 ] if, due to extensive damage, the homologous chromosome is chosen to be the template over the sister chromatid. This leads to gene synthesis since one copy of the allele is copied across from the homologous chromosome and then synthesized into the breach on the damaged chromosome. The net effect of this would be one heterozygous chromosome and one homozygous chromosome.
Mitotic crossover is known to occur in D. melanogaster , some asexually reproducing fungi and in normal human cells, where the event may allow normally recessive cancer-causing alleles to be expressed and thus predispose the cell in which it occurs to the development of cancer . Alternately, a cell may become a homozygous mutant for a tumor-suppressing gene, leading to the same result. [ 2 ] For example, Bloom's syndrome is caused by a mutation in RecQ helicase , which plays a role in DNA replication and repair. This mutation leads to high rates of mitotic recombination in mice, and this recombination rate is in turn responsible for causing tumor susceptibility in those mice. [ 15 ] At the same time, mitotic recombination may be beneficial: it may play an important role in repairing double stranded breaks, and it may be beneficial to the organism if having homozygous dominant alleles is more functional than the heterozygous state. [ 2 ] For use in experimentation with genomes in model organisms such as Drosophila melanogaster , mitotic recombination can be induced via X-ray and the FLP-FRT recombination system. [ 16 ] | https://en.wikipedia.org/wiki/Mitotic_recombination |
A mitotoxin is a cytotoxic molecule targeted to specific cells by a mitogen . Generally found in snake venom . Mitotoxins are responsible for mediating cell death [ 1 ] by interfering with protein or DNA synthesis. [ 2 ] Some mechanisms by which mitotoxins can interfere with DNA or protein synthesis include the inactivation of ribosomes [ 1 ] or the inhibition of complexes in the mitochondrial electron transport chain . [ 3 ] These toxins have a very high affinity and level of specificity for the receptors that they bind to. Mitotoxins bind to receptors on cell surfaces and are then internalized into cells via receptor-mediated endocytosis . Once in the endosome , the receptor releases its ligand and a mitotoxin can mediate cell death. [ 1 ]
There are different classes of mitotoxins, each acting on a different type of cell or system. The mitotoxin classes that have been identified thus far include: interleukin -based, transferrin based, epidermal growth factor -based, nerve growth factor -based, insulin-like growth factor -I-based, and fibroblast growth factor -based mitotoxins. [ 1 ] Because of the high affinity and specificity of mitotoxin binding, they present the possibility of creating precise therapeutic agents. [ 1 ] A major one of these possibilities is the potential usage of growth factor-based mitotoxins as anti-neoplastic [ 4 ] agents that can modulate the growth of melanomas . [ 5 ] | https://en.wikipedia.org/wiki/Mitotoxin |
Mitrofan Cioban (5 January 1942 – 2 February 2021) was a Moldovan mathematician specializing in topology , a member of the Academy of Sciences of Moldova .
Cioban was born in Copceac (then in Tighina County , Romania , now in Ștefan Vodă District , Moldova ), the forth child out of seven of farmers Mihail and Tecla Cioban. [ 1 ] At age 17 he enrolled in the Faculty of Mathematics and Physics of Tiraspol State University . [ 2 ] After one year Cioban transferred to Moscow State University , where he started attending the Topology seminar of Pavel Alexandrov . He obtained his PhD in 1969 with thesis Properties of Quotient Mappings and Classification of Spaces written under the direction of Alexander Arhangelskii . [ 3 ] Despite initially not knowing Russian , German , or English , he became well-versed in mathematical literature in these languages. [ 4 ]
Upon graduation, Cioban returned in 1970 to Tiraspol State University as a faculty member, where he directed 17 PhD theses and served as prorector and then rector . [ 2 ]
He published over 200 papers in academic journals from 1966 to 2020, mostly under the names of Choban or Čoban, and occasionally Cioban, Ciobanu, or Coban. Starting from 1999, he served as president of the Mathematical Society of the Republic of Moldova , with headquarters in Chișinău . [ 2 ] [ 5 ] Cioban supervised 22 PhD students and 4 doctors for their habilitation in mathematics. [ 4 ]
Cioban helped found the Moldovan school of general topology and made substantial contributions to the areas of topology and topological algebra , descriptive set theory , functional analysis , optimization theory , and measure theory . [ 4 ] He published his first major result in 1966 in Proceedings of the USSR Academy of Sciences , in which he generalized a theorem of Arthur Harold Stone on the metrizability of quotient spaces. [ 4 ]
Cioban died from COVID-19 on 2 February 2021 in Chișinău during the COVID-19 pandemic in Moldova . [ 6 ] | https://en.wikipedia.org/wiki/Mitrofan_Cioban |
Mitsubishi MCA stands for M itsubishi C lean A ir, a moniker used in Japan to identify vehicles built with emission control technology. The term was first introduced in Japan, with later introductions internationally. The technology first appeared in January 1973 on the Mitsubishi 4G32A gasoline-powered inline four cylinder engine installed in all Mitsubishi vehicles using the 4G32 engine, and the Saturn-6 6G34 six-cylinder gasoline-powered engine installed in the Mitsubishi Debonair . [ 1 ] [ 2 ] The technology was installed so that their vehicles would be in compliance with Japanese Government emission regulations passed in 1968.
Emission reducing technology began with the installation of a positive crankcase ventilation (PCV) valve (MCA-I), followed by the addition of a thermo reactor air pump and catalytic converter in addition to an exhaust gas recirculation (EGR) valve (MCA-II) and a solenoid controlled automatic choke installed on the carburetor.
The MCA-Jet system has a small third valve separate from the intake and exhaust valves. Separate passages in the intake manifold feed each MCA-Jet valve. Since these passages are smaller than the main intake manifold passages, the air/fuel mixture must move faster. When the faster moving air/fuel mixture from the MCA-Jet valve hits the slower moving air/fuel mixture from the intake valve, a strong air swirling effect occurs that promotes more complete combustion. With MCA-Jet it was found that stable combustion could be obtained even with large amounts of exhaust gas recirculation (EGR), NOx could be reduced, and combustion improved. [ 3 ] [ 4 ] Honda's CVCC Stratified charge engine approach also used a small third valve, but sent a richer air/fuel mixture to a small pre-combustion chamber near the spark plug, to help ignite a leaner air/fuel mixture in the main combustion chamber. MCA-Jet was a simpler system that sent the same air/fuel mixture to all intake and MCA-Jet valves. Each MCA-Jet valve is quite small and may be prone to carbon build-up, causing the MCA-Jet valve(s) to stick open. If a Mitsubishi-designed engine has low compression, the MCA-Jet valve(s) could be the cause. Each MCA-Jet valve and valve seat are a self-contained cylinder-shaped unit that screws into the cylinder head for easy replacement. Aftermarket MCA-Jet valves are available. With the advent of 4-valve-per-cylinder engines, manufacturers typically design the camshaft(s) to open one intake valve slightly before the other to create a swirling effect. This has made the MCA-Jet system obsolete. The MCA-Jet system was used in certain Mitsubishi-designed engines installed in both Mitsubishi-branded and Chrysler/Dodge/Plymouth-branded vehicles during the late 1970s to late 1980s. | https://en.wikipedia.org/wiki/Mitsubishi_MCA |
Mitsubishi Tanabe Pharma Corporation is a Japanese pharmaceuticals company from Osaka, [ 1 ] a subsidiary of Mitsubishi Chemical Holdings Corporation . Mitsubishi Pharma Corporation ( 三菱ウェルファーマ株式会社 , Mitsubishi Werufāma Kabushiki-gaisha ) was formed in 2001 from the merger of Mitsubishi-Tokyo Pharmaceuticals and Welfide Corporation. On October 1, 2007, Tanabe Seiyaku Co., Ltd. merged with Mitsubishi Pharma to form Mitsubishi Tanabe Pharma. [ 2 ]
Originally founded in 1678, Mitsubishi Tanabe considers itself as one of the oldest pharmaceutical companies in the world. [ 1 ] Mitsubishi Tanabe Pharma is a member of the Mitsubishi UFJ Financial Group (MUFJ) keiretsu .
Mitsubishi-Tanabe Pharmaceuticals developed the first BET inhibitor molecules. [ 3 ] [ 4 ]
In August 2014, the company announced three-year research collaboration agreement with AstraZeneca on diabetic nephropathy , to replace dialysis or kidney transplantation. [ 5 ]
An intravenous treatment of Mitsubishi Tanabe is Radicava (edaravone) which has the goal to slow the decline of physical function in patients with amyotrophic lateral sclerosis (ALS) and was approved by the U.S. Food and Drug Administration in 2017. The U.S. American branch of Mitsubishi Tanabe created a locator for healthcare and infusion centers. [ 6 ]
Mitsubishe Tanabe has also an orally disintegrating tablet for ALS with Exservan ( riluzole ). [ 1 ]
In 1604, Tanabeya Matazaemon is granted a license by Tokugawa Ieyasu for trade in herbal medicines with Luzon and Siam . [ 7 ]
In 1901, Motosaburo Tanabe, the Twelfth established a pharmacy in Tokyo , which incorporated in 1921 as Motosaburo Tanabe Shoten.
In 1921, Nippon Tar Industries was established.
In 1940, Takeda Kasei Co., Ltd. was established by Chobei Takeda & Co., Ltd. (present-day Takeda Pharmaceutical Company ) and Nippon Kasei Chemical Co. Ltd. (present-day Mitsubishi Chemical Corporation ) and built its first plant in Higashi-Yoshitomi-mura, Fukuoka Prefecture .
In 1943, Motosaburo Tanabe Shoten, changed its name to Tokyo Tanabe Pharmaceuticals Co., Ltd.
In 1946, Takeda Kasei Co., Ltd. changed its name to Yoshitomi Pharmaceutical Co., Ltd.
In 1949, Yoshitomi Pharmaceutical Co., Ltd. listed on Tokyo and Osaka stock exchanges.
In 1950, The Blood Plasma Corporation of Japan was established with head office and plant in Osaka . The founders included war criminals such as Kitano Masaji who performed torture and experimentations on humans in the Japanese military's notorious Unit 731 during World War II. These crimes were recognized by the UN as extreme "crimes against humanity".
In 1952, Nippon Tar Industries became Mitsubishi Chemical Industries, Ltd.
In 1964, Blood Plasma Corporation changed its name to Green Cross Corporation .
In 1998, Green Cross Corporation was acquired by Yoshitomi Pharmaceutical.
In 2000, Green Cross Corporation changing its name to Welfide Corporation.
In 1981, Mitsubishi Chemical Industries, Ltd. established a business alliance with Tokyo Tanabe Pharmaceuticals Co.
In 1984, Mitsubishi Chemical Industries, Ltd. changed its name to Mitsubishi Chemical Corporation following the merger with Mitsubishi Petrochemical Co., Ltd.
In 1999, Mitsubishi Chemical Corporation and Tokyo Tanabe Pharmaceuticals Co. merged formally and formed Mitsubishi-Tokyo Pharmaceuticals, Inc., to take over the combined pharmaceutical operations of the two companies.
In 2001, Mitsubishi-Tokyo Pharmaceuticals and Welfide Corporation merged to establish Mitsubishi Pharma Corporation, and Mitsubishi Tanabe Pharma. [ 8 ]
In October 2005, Mitsubishi Pharma Corporation joined again with Mitsubishi Chemical Corporation to create Mitsubishi Chemical Holdings Corporation .
In July, 2017, Mitsubishi Tanabe Pharma acquired Neuroderm for $1.1 billion. [ 9 ]
On 27 February 2020, Mitsubishi Tanabe Pharma was delisted from the Tokyo Stock Exchange, and is now described as a member of the Mitsubishi Chemical Holdings Group [ 10 ]
In February 2025, American private equity firm Bain Capital agreed to acquire Mitsubishi Tanabe Pharma for ¥ 510 billion (US$3.4 billion). [ 11 ] | https://en.wikipedia.org/wiki/Mitsubishi_Tanabe_Pharma |
Tomoe ( 巴 , also written 鞆絵 ) , [ a ] commonly translated as " comma ", [ 2 ] [ 3 ] is a comma-like swirl symbol used in Japanese mon (roughly equivalent to a heraldic badge or charge in European heraldry). It closely resembles the usual form of a magatama .
The tomoe appears in many designs with various uses. The simplest, most common patterns of the device contain from one to four tomoe , and are reminiscent of similar designs that have been found in wide distribution around the world. When circumscribed in a circle, it often appears in a set of three, with this design known as the mitsudomoe ( 三ツ巴 ) . [ 4 ]
Originally, the Chinese character 巴, a hieroglyphic character that represents a person lying on their stomach was applied, because of the similarity in shape. But it is likely not directly related to the Japanese word "Tomoe" itself. The character 巴 (Chinese pronunciation bā ) has several meanings, ranging from a Sichuan toponym to a crust formed by dryness, parts of the body such as hands or cheeks, and, as a verb, bearing the sense of "to hope", "expect" or "be anxious over". The Chinese character used to depict, according to Bernhard Karlgren 's interpretation of the small seal script graph, a python . [ 5 ]
The most common view is that the word refers to a picture e ( 絵 ) of a tomo ( 鞆 ) , or drawings on the latter, the tomo in question, in archaic Japanese tömö , [ b ] being a round leather arm protector, like the bracer or gauntlet tab of European archery. [ 8 ] Roy Andrew Miller describes it as "a small hollow sack or bulb of sewn leather with leather tie straps, sometimes embossed with a comma like decorative device ( tomoe ) of continental origin". [ 6 ] It was worn on the left elbow or wrist of an archer either to prevent chafing from the bowstring ( tsuru : 弦) twanging back to position on the release of an arrow, or to strike fear into the enemy from the sharp sound caused by the bowstring hitting the wrist guard. [ 9 ] [ 10 ] [ 6 ] The 'tomo picture' ( tomoe ) can therefore be interpreted either as a visual pun on the tomo represented, or, otherwise, as taking its name from that object. Several such examples are conserved in Nara at the Shōsōin . [ 6 ]
Another view is The Japanese word itself may be of Mongolic origin , since it bears comparison with Middle Mongol tomuüa "twisted horse headdress", from the verb tomu (plait, twist), and Ordos Mongolian t'omok ('a little bag hung on a horse's head'). In this latter connection Tang ceramic figures of horses show small sacks tethered to the lower neck, perhaps to stop the horse from throwing its head back. [ 11 ]
The origin of the tomoe design is uncertain. The most common view is that tomoe patterns originated in magatama jewelry from late Jōmon period approximately 1,000 BCE of Japan which was used for the shinto rituals. A pattern resembling the two-comma tomoe ( futatsudomoe ) has been found in ancient cultures on all inhabited continents. [ 12 ] A stylized design on a Yangshao bowl dates back to 2,000 BCE. [ 13 ] The motif of two encircling dolphins biting each other's tails has been found on Cretan ceramics dating from the Minoan period (1700–1400 BCE), and the two fish biting each other in circular fashion recurs in both Chinese and Central Mexican ware. [ 14 ] It is frequently seen on prehistoric Celtic remains, and one mirror from Balmaclellan is almost identical to the mitsudomoe . [ 15 ] In China, the double comma form came to be assimilated to the Yin-Yang philosophy of opposing male/female principles, formalized in the Tàijítú design of the late Song dynasty period . [ c ] This in turn recurs in the seventh century in Unified Silla (now Korea), where it was known as taegeuk . [ 17 ] and also in the Japanese futatsudomoe and mitsudomoe patterns, the former in association with divinatory rites, the latter frequently linked to temple drums with apotropaic functions. [ 3 ] According to Jean Herbert in these contexts, the mitsudomoe embodied three spirits, the yin-yang dyad being represented by an aramitama (rough kami ) and a nigimitama (gentle kami), while the third comma denoted the sakimitama , or lucky spirit. [ d ] However, there is no clear evidence tomoe, taijitu and yin-yang is directly related.
Neil Gordon Munro argued that the basis for the mitsudomoe pattern, a motif found also among the Ainu , was the eastern European and western Asian figure of the triskelion , which he believed lay behind the Chinese three-legged crow design, and, in his view, its reflex in the mythical Japanese crow, the Yatagarasu (八咫烏). [ 18 ] [ 19 ]
As a leather [ e ] wrist protector tomo appear to have been employed at least as early as the Kofun period , where they are frequently attested on haniwa terracotta figurines depicting archers, [ 21 ] and may even have had, aside from their military function, a ritual or fetish value, perhaps related to their phallic shape. [ 11 ] The pattern was also interpreted as water swirling, and because it is a water-related pattern, the Tomoe pattern was applied to roof tiles on buildings at the end of the Heian period as a fire protection.
The tomoe emblem established itself as a common emblem during the Fujiwara ascendency of the late Heian period , around the 10th–11th centuries, and proliferated through to Kamakura times. It is thought that a resemblance between the tomoe and the Emperor Ōjin found in the Nihongi may also account for its rising popularity among samurai, since Ōjin was apotheosized as a god in Hachiman shrines. [ 9 ] [ 22 ]
In the Nihongi account, when Ōjin was born, inspection of his body revealed a fleshy growth on his arm similar to a warrior's wrist or elbow pad, and for this reason he was called homuta (誉田: lit.(Lord) Armguard) [ 23 ] ( OJ : pomuda ), [ f ] an old word for a tomo . [ g ]
Fragmentary sources suggest that the First Shō dynasty , who founded the Ryukyu Kingdom , used the symbol if not as their family crest. American historian George H. Kerr claims that King Shō Toku adopted the mitsudomoe as the crest of the royal house after his successful invasion of Kikai Island in 1465.( Kerr 2011 , p. 101) The Second Shō dynasty , who ruled the Ryukyu Kingdom from 1470 to 1879, adopted the mitsudomoe as its family crest. Since it was the royal family crest, its usage was once severely restricted. Okinawans who visited Japan shortly after the kingdom's annexation in 1879 were surprised that mitsudomoe banners were flown everywhere. [ 27 ] During the American military occupation of Okinawa Prefecture , the United States Civil Administration of the Ryukyu Islands (USCAR) made a failed attempt to recreate a Ryukyuan national flag with a mitsudomoe, only to find that Okinawans were apathetic towards, or did not recognize, the former royal family's symbol. Today the symbol is still regarded as a symbol for Ryukyu and, to a lesser extent, Okinawa.
The mitsudomoe is closely associated with Shinto shrines , in particular those dedicated to Hachiman , the god of war and archery. Hachiman in Shinto cosmology and ritual, as for example at Hakozaki Shrine , is repeatedly connected with the number three. [ 28 ] In Shintoist thinking, this number is taken to represent the three aspects of the four mitama or 'souls' (the other, the kushimitama being considered far rarer). [ 29 ]
It is also commonly displayed on banners and lanterns used in festivals and rituals related to Amaterasu-ōmikami , [ 30 ] who in the Kojiki confronts her brother Susanoo when he usurps her terrain on earth by dressing as an archer, adorned with magatama beads and 'an awesome high arm-guard' ( itu nö takatömö ). [ h ]
A third element of its symbolic panorama concerns water, an association engendered by its swirling pattern. For this reason, it is said to be located on roofs and gables as a charm against fire. [ 32 ]
Since Hachiman was worshipped as the guardian of warriors, it was adopted as a common design element in Japanese family emblems ( 家紋 , kamon ) by various samurai clans [ 33 ] such as the Nagao , Kobayakawa and Utsunomiya . Among aristocrats, the Saionji family used it as its family emblem. The Koyasan Shingon sect of Buddhism uses the mitsudomoe as a visual representation of the cycle of life.
Tomoe also is a personal name, dating at least back to Tomoe Gozen (巴御前), a famous female warrior celebrated in The Tale of the Heike account of the Genpei War . In Kyoto's Jidai Matsuri festival, she appears in the Heian period section of the procession in samurai costume, and parades as a symbol of feminine gallantry. [ 34 ]
The tomoe has also been adopted as a corporate logo in Japan. [ 35 ]
The mitsudomoe is also the logo of the OBS Studio application since it released in 2012. [ 36 ]
The two-fold tomoe is almost identical in its design elements to the Chinese symbol known as a taijitu , while the three-fold tomoe is similar to the Korean tricolored taegeuk which is originated in taijitsu. However, there is no clear evidence tomoe and taijitu is directly related. Also note that the negative space in between the swirls of a fourfold tomoe forms a swastika -like shape, which is fairly prominent in many Indian religions such as Hinduism and Jainism and Buddhism . A similar design can also be found in the some forms of the Celtic spiral triskele as well as with the Basque lauburu and the Sicilian Trinacria . | https://en.wikipedia.org/wiki/Mitsudomoe |
The Mitsunobu reaction is an organic reaction that converts an alcohol into a variety of functional groups, such as an ester , using triphenylphosphine and an azodicarboxylate such as diethyl azodicarboxylate (DEAD) or diisopropyl azodicarboxylate (DIAD). [ 1 ] Although DEAD and DIAD are most commonly used, there are a variety of other azodicarboxylates available which facilitate an easier workup and/or purification and in some cases, facilitate the use of more basic nucleophiles. It was discovered by Oyo Mitsunobu (1934–2003). In a typical protocol, one dissolves the alcohol, the carboxylic acid, and triphenylphosphine in tetrahydrofuran or other suitable solvent (e.g. diethyl ether ), cool to 0 °C using an ice-bath, slowly add the DEAD dissolved in THF, then stir at room temperature for several hours. [ 2 ] The alcohol reacts with the phosphine to create a good leaving group then undergoes an inversion of stereochemistry in classic S N 2 fashion as the nucleophile displaces it. A common side-product is produced when the azodicarboxylate displaces the leaving group instead of the desired nucleophile. This happens if the nucleophile is not acidic enough ( pK a larger than 13) or is not nucleophilic enough due to steric or electronic constraints. A variation of this reaction utilizing a nitrogen nucleophile is known as a Fukuyama–Mitsunobu.
Several reviews have been published. [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ]
The reaction mechanism of the Mitsunobu reaction is fairly complex. The identity of intermediates and the roles they play has been the subject of debate.
Initially, the triphenyl phosphine ( 2 ) makes a nucleophilic attack upon diethyl azodicarboxylate ( 1 ) producing a betaine intermediate 3 , which deprotonates the carboxylic acid ( 4 ) to form the ion pair 5 . The formation of the ion pair 5 is very fast.
The second phase of the mechanism is proposed to be phosphorus-centered, the DEAD having been converted to the hydrazine. The ratio and interconversion of intermediates 8 – 11 depend on the carboxylic acid pK a and the solvent polarity. [ 8 ] [ 9 ] [ 10 ] Although several phosphorus intermediates are present, the attack of the carboxylate anion upon intermediate 8 is the only productive pathway forming the desired product 12 and triphenylphosphine oxide ( 13 ).
The formation of the oxyphosphonium intermediate 8 is slow and facilitated by the alkoxide. Therefore, the overall rate of reaction is controlled by carboxylate basicity and solvation. [ 11 ]
The order of addition of the reagents of the Mitsunobu reaction can be important. Typically, one dissolves the alcohol, the carboxylic acid, and triphenylphosphine in tetrahydrofuran or other suitable solvent (e.g. diethyl ether ), cool to 0 °C using an ice-bath, slowly add the DEAD dissolved in THF, then stir at room temperature for several hours. If this is unsuccessful, then preforming the betaine may give better results. To preform the betaine, add DEAD to triphenylphosphine in tetrahydrofuran at 0 °C, followed by the addition of the alcohol and finally the acid. [ 12 ]
Many other functional groups can serve as nucleophiles besides carboxylic acids . For the reaction to be successful, the nucleophile must have a p K a less than 15.
Several modifications to the original reagent combination have been developed in order to simplify the separation of the product and avoid production of so much chemical waste. One variation of the Mitsunobu reaction uses resin-bound triphenylphosphine and uses di- tert -butylazodicarboxylate instead of DEAD. The oxidized triphenylphosphine resin can be removed by filtration, and the di- tert -butylazodicarboxylate byproduct is removed by treatment with trifluoroacetic acid . [ 18 ] Bruce H. Lipshutz has developed an alternative to DEAD, di-(4-chlorobenzyl)azodicarboxylate (DCAD) where the hydrazine by-product can be easily removed by filtration and recycled back to DCAD. [ 19 ]
A modification has also been reported in which DEAD can be used in catalytic versus stoichiometric quantities, however this procedure requires the use of stoichiometric (diacetoxyiodo)benzene to oxidise the hydrazine by-product back to DEAD. [ 20 ]
Denton and co-workers have reported a redox-neutral variant of the Mitsunobu reaction which employs a phosphorus(III) catalyst to activate the substrate, ensuring inversion in the nucleophilic attack, and uses a Dean-Stark trap to remove the water by-product. [ 21 ]
Tsunoda et al. have shown that one can combine the triphenylphosphine and the diethyl azodicarboxylate into one reagent: a phosphorane ylide . Both (cyanomethylene)trimethylphosphorane (CMMP, R = Me) and (cyanomethylene)tributylphosphorane (CMBP, R = Bu) have proven particularly effective. [ 22 ]
The ylide acts as both the reducing agent and the base. The byproducts are acetonitrile ( 6 ) and the trialkylphosphine oxide ( 8 ).
The Mitsunobu reaction has been applied in the synthesis of aryl ethers : [ 23 ]
With these particular reactants the conversion with DEAD fails because the hydroxyl group is only weakly acidic. Instead the related 1,1'-(azodicarbonyl)dipiperidine (ADDP) is used of which the betaine intermediate is a stronger base. The phosphine is a polymer-supported triphenylphosphine (PS-PPh 3 ).
The reaction has been used to synthesize quinine , colchicine , sarain, morphine , stigmatellin , eudistomin , oseltamivir , strychnine , and nupharamine . [ 24 ] | https://en.wikipedia.org/wiki/Mitsunobu_reaction |
Mitsuo Tasumi (January 23, 1937 – November 24, 2021) was a Japanese physical chemist known for his vibrational spectroscopic works on synthetic and biological macromolecules. [ 1 ] He was Professor Emeritus of the University of Tokyo , and a former president of Saitama University , having trained
a number of physical chemists active in academia and industry. [ 2 ] Moto-o Tasumi , a zoologist at Kyoto University , was his brother.
Tasumi earned his B.Sc. (1959), M.Sc. (1961) and Ph.D. (1964) from the University of Tokyo in the laboratories of San-Ichiro Mizushima and of Takehiko Shimanouchi , where he reported the first phonon dispersion
of polyethylene. [ 4 ] He spent the subsequent 33 years (1964–97) as a faculty member initially in
the Department of Biochemistry and then in the Department of Chemistry of the University of Tokyo. During this period,
he spent a year (1965–66) at University of Michigan as a Fulbright scholar in the laboratory of Samuel Krimm and another year (1966–67)
at Polytechnic University of Milan as a postdoctoral scholar in the laboratory of Giuseppe Zerbi under Giulio Natta , a Nobel laureate. [ 5 ]
At the University of Tokyo, Tasumi led a large group of spectroscopists, developing new
experimental and computational techniques of infrared spectroscopy and Raman scattering spectroscopy. [ 1 ] He is known
for establishing the theoretical basis for interpreting the spectra of synthetic
polymers (including electrical conductive polymers),
proteins, and photosynthetic systems to elucidate their relationship with the structural,
thermal, mechanical, transport, and response properties. He published several papers [ 6 ] with Hideki Shirakawa , who was awarded a Nobel Prize jointly with Alan MacDiarmid and Alan Heeger .
He was among the earliest spectroscopists
who saw the great utility of ab initio electronic structure calculations in
understanding vibrational spectra. In particular, he established a steady-state spectroscopic method
that can determine the structures and dynamics of electronic excited states by resonance Raman excitation
profile, and applied it to polyenes including carotenoids . At the same time, he made important contributions
to the development and applications of time-resolved vibrational spectroscopies.
He is a co-author of the Protein Data Bank [ 7 ] and the editor/author of "Introduction to Experimental Infrared Spectroscopy: Fundamentals and Practical Methods." [ 8 ]
In 2004–08, Tasumi was the President of Saitama University after serving as Professor of Chemistry (1996-2002) of Saitama University and as Visiting Professor (2002–03) at University of California, Berkeley (stayed at the laboratory of Herbert Strauss ).
In 1987–89, Tasumi was a member of the Board of Directors of the Chemical Society of Japan . [ 9 ] In 1994–2000, he was an Executive Committee Member of CODATA . [ 10 ] In 1997–99, he was the president of the Spectroscopical Society of Japan . [ 11 ] | https://en.wikipedia.org/wiki/Mitsuo_Tasumi |
In mathematics, the Mittag-Leffler polynomials are the polynomials g n ( x ) or M n ( x ) studied by Mittag-Leffler ( 1891 ).
M n ( x ) is a special case of the Meixner polynomial M n ( x;b,c ) at b = 0, c = -1 .
The Mittag-Leffler polynomials are defined respectively by the generating functions
They also have the bivariate generating function [ 1 ]
The first few polynomials are given in the following table. The coefficients of the numerators of the g n ( x ) {\displaystyle g_{n}(x)} can be found in the OEIS, [ 2 ] though without any references, and the coefficients of the M n ( x ) {\displaystyle M_{n}(x)} are in the OEIS [ 3 ] as well.
The polynomials are related by M n ( x ) = 2 ⋅ n ! g n ( x ) {\displaystyle M_{n}(x)=2\cdot {n!}\,g_{n}(x)} and we have g n ( 1 ) = 1 {\displaystyle g_{n}(1)=1} for n ⩾ 1 {\displaystyle n\geqslant 1} . Also g 2 k ( 1 2 ) = g 2 k + 1 ( 1 2 ) = 1 2 ( 2 k − 1 ) ! ! ( 2 k ) ! ! = 1 2 ⋅ 1 ⋅ 3 ⋯ ( 2 k − 1 ) 2 ⋅ 4 ⋯ ( 2 k ) {\displaystyle g_{2k}({\frac {1}{2}})=g_{2k+1}({\frac {1}{2}})={\frac {1}{2}}{\frac {(2k-1)!!}{(2k)!!}}={\frac {1}{2}}\cdot {\frac {1\cdot 3\cdots (2k-1)}{2\cdot 4\cdots (2k)}}} .
Explicit formulas are
(the last one immediately shows n g n ( m ) = m g m ( n ) {\displaystyle ng_{n}(m)=mg_{m}(n)} , a kind of reflection formula), and
In terms of the Gaussian hypergeometric function , we have [ 4 ]
As stated above, for m , n ∈ N {\displaystyle m,n\in \mathbb {N} } , we have the reflection formula n g n ( m ) = m g m ( n ) {\displaystyle ng_{n}(m)=mg_{m}(n)} .
The polynomials M n ( x ) {\displaystyle M_{n}(x)} can be defined recursively by
Another recursion formula, which produces an odd one from the preceding even ones and vice versa, is
As for the g n ( x ) {\displaystyle g_{n}(x)} , we have several different recursion formulas:
Concerning recursion formula (3), the polynomial g n ( x ) {\displaystyle g_{n}(x)} is the unique polynomial solution of the difference equation x ( f ( x + 1 ) − f ( x − 1 ) ) = 2 n f ( x ) {\displaystyle x(f(x+1)-f(x-1))=2nf(x)} , normalized so that f ( 1 ) = 1 {\displaystyle f(1)=1} . [ 5 ] Further note that (2) and (3) are dual to each other in the sense that for x ∈ N {\displaystyle x\in \mathbb {N} } , we can apply the reflection formula to one of the identities and then swap x {\displaystyle x} and n {\displaystyle n} to obtain the other one. (As the g n ( x ) {\displaystyle g_{n}(x)} are polynomials, the validity extends from natural to all real values of x {\displaystyle x} .)
The table of the initial values of g n ( m ) {\displaystyle g_{n}(m)} (these values are also called the "figurate numbers for the n-dimensional cross polytopes" in the OEIS [ 6 ] ) may illustrate the recursion formula (1), which can be taken to mean that each entry is the sum of the three neighboring entries: to its left, above and above left, e.g. g 5 ( 3 ) = 51 = 33 + 8 + 10 {\displaystyle g_{5}(3)=51=33+8+10} . It also illustrates the reflection formula n g n ( m ) = m g m ( n ) {\displaystyle ng_{n}(m)=mg_{m}(n)} with respect to the main diagonal, e.g. 3 ⋅ 44 = 4 ⋅ 33 {\displaystyle 3\cdot 44=4\cdot 33} .
For m , n ∈ N {\displaystyle m,n\in \mathbb {N} } the following orthogonality relation holds: [ 7 ]
(Note that this is not a complex integral. As each g n {\displaystyle g_{n}} is an even or an odd polynomial, the imaginary arguments just produce alternating signs for their coefficients. Moreover, if m {\displaystyle m} and n {\displaystyle n} have different parity, the integral vanishes trivially.)
Being a Sheffer sequence of binomial type , the Mittag-Leffler polynomials M n ( x ) {\displaystyle M_{n}(x)} also satisfy the binomial identity [ 8 ]
Based on the representation as a hypergeometric function, there are several ways of representing g n ( z ) {\displaystyle g_{n}(z)} for | z | < 1 {\displaystyle |z|<1} directly as integrals, [ 9 ] some of them being even valid for complex z {\displaystyle z} , e.g.
There are several families of integrals with closed-form expressions in terms of zeta values where the coefficients of the Mittag-Leffler polynomials occur as coefficients. All those integrals can be written in a form containing either a factor tan ± n {\displaystyle \tan ^{\pm n}} or tanh ± n {\displaystyle \tanh ^{\pm n}} , and the degree of the Mittag-Leffler polynomial varies with n {\displaystyle n} . One way to work out those integrals is to obtain for them the corresponding recursion formulas as for the Mittag-Leffler polynomials using integration by parts.
1. For instance, [ 10 ] define for n ⩾ m ⩾ 2 {\displaystyle n\geqslant m\geqslant 2}
These integrals have the closed form
in umbral notation, meaning that after expanding the polynomial in ζ {\displaystyle \zeta } , each power ζ k {\displaystyle \zeta ^{k}} has to be replaced by the zeta value ζ ( k ) {\displaystyle \zeta (k)} . E.g. from g 6 ( x ) = 1 45 ( 23 x 2 + 20 x 4 + 2 x 6 ) {\displaystyle g_{6}(x)={\frac {1}{45}}(23x^{2}+20x^{4}+2x^{6})\ } we get I ( n , 7 ) = n ! 2 n − 1 23 ζ ( n − 1 ) + 20 ζ ( n − 3 ) + 2 ζ ( n − 5 ) 45 {\displaystyle \ I(n,7)={\frac {n!}{2^{n-1}}}{\frac {23~\zeta (n-1)+20~\zeta (n-3)+2~\zeta (n-5)}{45}}\ } for n ⩾ 7 {\displaystyle n\geqslant 7} .
2. Likewise take for n ⩾ m ⩾ 2 {\displaystyle n\geqslant m\geqslant 2}
In umbral notation, where after expanding, η k {\displaystyle \eta ^{k}} has to be replaced by the Dirichlet eta function η ( k ) := ( 1 − 2 1 − k ) ζ ( k ) {\displaystyle \eta (k):=\left(1-2^{1-k}\right)\zeta (k)} , those have the closed form
3. The following [ 11 ] holds for n ⩾ m {\displaystyle n\geqslant m} with the same umbral notation for ζ {\displaystyle \zeta } and η {\displaystyle \eta } , and completing by continuity η ( 1 ) := ln 2 {\displaystyle \eta (1):=\ln 2} .
Note that for n ⩾ m ⩾ 2 {\displaystyle n\geqslant m\geqslant 2} , this also yields a closed form for the integrals
4. For n ⩾ m ⩾ 2 {\displaystyle n\geqslant m\geqslant 2} , define [ 12 ] K ( n , m ) := ∫ 0 ∞ tanh n ( x ) x m d x {\displaystyle \quad K(n,m):=\int \limits _{0}^{\infty }{\dfrac {\tanh ^{n}(x)}{x^{m}}}dx} .
If n + m {\displaystyle n+m} is even and we define h k := ( − 1 ) k − 1 2 ( k − 1 ) ! ( 2 k − 1 ) ζ ( k ) 2 k − 1 π k − 1 {\displaystyle h_{k}:=(-1)^{\frac {k-1}{2}}{\frac {(k-1)!(2^{k}-1)\zeta (k)}{2^{k-1}\pi ^{k-1}}}} , we have in umbral notation, i.e. replacing h k {\displaystyle h^{k}} by h k {\displaystyle h_{k}} ,
Note that only odd zeta values (odd k {\displaystyle k} ) occur here (unless the denominators are cast as even zeta values), e.g.
5. If n + m {\displaystyle n+m} is odd, the same integral is much more involved to evaluate, including the initial one ∫ 0 ∞ tanh 3 ( x ) x 2 d x {\displaystyle \int \limits _{0}^{\infty }{\dfrac {\tanh ^{3}(x)}{x^{2}}}dx} . Yet it turns out that the pattern subsists if we define [ 13 ] s k := η ′ ( − k ) = 2 k + 1 ζ ( − k ) ln 2 − ( 2 k + 1 − 1 ) ζ ′ ( − k ) {\displaystyle s_{k}:=\eta '(-k)=2^{k+1}\zeta (-k)\ln 2-(2^{k+1}-1)\zeta '(-k)} , equivalently s k = ζ ( − k ) ζ ′ ( − k ) η ( − k ) + ζ ( − k ) η ( 1 ) − η ( − k ) η ( 1 ) {\displaystyle s_{k}={\frac {\zeta (-k)}{\zeta '(-k)}}\eta (-k)+\zeta (-k)\eta (1)-\eta (-k)\eta (1)} . Then K ( n , m ) {\displaystyle K(n,m)} has the following closed form in umbral notation, replacing s k {\displaystyle s^{k}} by s k {\displaystyle s_{k}} :
Note that by virtue of the logarithmic derivative ζ ′ ζ ( s ) + ζ ′ ζ ( 1 − s ) = log π − 1 2 Γ ′ Γ ( s 2 ) − 1 2 Γ ′ Γ ( 1 − s 2 ) {\displaystyle {\frac {\zeta '}{\zeta }}(s)+{\frac {\zeta '}{\zeta }}(1-s)=\log \pi -{\frac {1}{2}}{\frac {\Gamma '}{\Gamma }}\left({\frac {s}{2}}\right)-{\frac {1}{2}}{\frac {\Gamma '}{\Gamma }}\left({\frac {1-s}{2}}\right)} of Riemann's functional equation , taken after applying Euler's reflection formula , [ 14 ] these expressions in terms of the s k {\displaystyle s_{k}} can be written in terms of ζ ′ ( 2 j ) ζ ( 2 j ) {\displaystyle {\frac {\zeta '(2j)}{\zeta (2j)}}} , e.g.
6. For n < m {\displaystyle n<m} , the same integral K ( n , m ) {\displaystyle K(n,m)} diverges because the integrand behaves like x n − m {\displaystyle x^{n-m}} for x ↘ 0 {\displaystyle x\searrow 0} . But the difference of two such integrals with corresponding degree differences is well-defined and exhibits very similar patterns, e.g. | https://en.wikipedia.org/wiki/Mittag-Leffler_polynomials |
The Mivar-based approach is a mathematical tool for designing artificial intelligence (AI) systems. Mivar ( Multidimensional Informational Variable Adaptive Reality ) was developed by combining production and Petri nets . The Mivar-based approach was developed for semantic analysis and adequate representation of humanitarian epistemological and axiological principles in the process of developing artificial intelligence. The Mivar-based approach incorporates computer science , informatics and discrete mathematics , databases , [ 1 ] expert systems , [ 2 ] graph theory , matrices and inference systems. The Mivar-based approach involves two technologies: [ 3 ]
Mivar networks allow us to develop cause-effect dependencies (“If-then”) and create an automated, trained, logical reasoning system.
Representatives of Russian association for artificial intelligence (RAAI) – for example, V. I. Gorodecki , doctor of technical science, professor at SPIIRAS and V. N. Vagin, doctor of technical science, professor at MPEI declared that the term is incorrect and suggested that the author should use standard terminology.
While working in the Russian Ministry of Defense , O. O. Varlamov started developing the theory of “rapid logical inference” in 1985. [ 6 ] [ 7 ] He was analyzing Petri nets and productions to construct algorithms. Generally, mivar-based theory represents an attempt to combine entity-relationship models and their problem instance – semantic networks and Petri networks.
The abbreviation MIVAR was introduced as a technical term by O. O. Varlamov, Doctor of Technical Science, professor at Bauman MSTU in 1993 to designate a “semantic unit” in the process of mathematical modeling. [ 6 ] [ 8 ] The term has been established and used in all of his further works.
The first experimental systems operating according to mivar-based principles were developed in 2000. Applied mivar systems were introduced in 2015.
Mivar is the smallest structural element of discrete information space.
Object-Property-Relation (VSO) is a graph, the nodes of which are concepts and arcs are connections between concepts.
Mivar space represents a set of axes, a set of elements, a set of points of space and a set of values of points.
A = { a n } , n = 1 , … , N , {\displaystyle A=\{a_{n}\},n=1,\ldots ,N,}
where:
Then: ∀ a n ∃ F n = { f n i n } , n = 1 , … , N , i n = 1 , … , I n , {\displaystyle \forall a_{n}\exists F_{n}=\{f_{{ni}_{n}}\},n=1,\ldots ,N,i_{n}=1,\ldots ,I_{n},}
where:
F n {\displaystyle F_{n}} sets form multidimensional space: M = F 1 × F 2 × ⋯ × F n . {\displaystyle M=F_{1}\times F_{2}\times \cdots \times F_{n}.} m = ( i 1 , i 2 , … , i N ) , {\displaystyle m=(i_{1},i_{2},\ldots ,i_{N}),}
where:
There is a set of values of multidimensional space points of M {\displaystyle M} :
where:
For every point of space M {\displaystyle M} there is a single value from C M {\displaystyle C_{M}} set or there is no such value. Thus, C M {\displaystyle C_{M}} is a set of data model state changes represented in multidimensional space. To implement a transition between multidimensional space and set of points values the relation μ {\displaystyle \mu } has been introduced: C x = μ ( M x ) , {\displaystyle C_{x}=\mu (M_{x}),}
where:
To describe a data model in mivar information space it is necessary to identify three axes:
These sets are independent. The mivar space can be represented by the following tuple:
Thus, mivar is described by « V S O {\displaystyle VSO} » formula, in which « V {\displaystyle V} » denotes an object or a thing, « S {\displaystyle S} » denotes properties, « O {\displaystyle O} » variety of relations between other objects of a particular subject domain. [ 9 ] The category “Relations” can describe dependencies of any complexity level: formulae, logical transitions, text expressions, functions, services, computational procedures and even neural networks . A wide range of capabilities complicates description of modeling interconnections, but can take into consideration all the factors. Mivar computations use mathematical logic. In a simplified form they can be represented as implication in the form of an "if…, then …” [ 10 ] formula. The result of mivar modeling can be represented in the form of a bipartite graph binding two sets of objects: source objects and resultant objects.
Mivar network is a method for representing objects of the subject domain and their processing rules in the form of a bipartite directed graph consisting of objects and rules. [ 11 ]
A Mivar network is a bipartite graph that can be described in the form of a two-dimensional matrix, in that records information about the subject domain of the current task. [ 12 ] [ 13 ]
Generally, mivar networks provide formalization and representation of human knowledge in the form of a connected multidimensional space. That is, a mivar network is a method of representing a piece of mivar space information in the form of a bipartite, directed graph . The mivar space information is formed by objects and connections, which in total represent the data model of the subject domain. Connections include rules for objects processing. Thus, a mivar network of a subject domain is a part of the mivar space knowledge for that domain.
The graph can consist of objects-variables and rules-procedures. First, two lists are made that form two nonintersecting partitions: the list of objects and the list of rules. Objects are denoted by circles. Each rule in a mivar network is an extension of productions, hyper-rules with multi-activators or computational procedures. It is proved that from the perspective of further processing, these formalisms are identical and in fact are nodes of the bipartite graph, denoted by rectangles. [ 13 ]
Mivar networks can be implemented on single computing systems or service-oriented architectures . Certain constraints restrict their application, in particular, the dimension of matrix of linear matrix method for determining logical inference path on the adaptive rule networks. The matrix dimension constraint is due to the fact that implementation requires sending a general matrix to multiple processors. Since every matrix value is initially represented in symbol form, the amount of sent data is crucial when obtaining, for example, 10000 rules/variables. Classical mivar-based method requires storing three values in each matrix cell:
The analysis of possibility of firing a rule is separated from determining output variables according to stages after firing the rule. Consequently, it is possible to use different matrices for “search for fired rules” and “setting values for output variables”. This allowsthe use of multidimensional binary matrices. Binary matrix fragments occupy much less space and improve possibilities of applying mivar networks.
To implement logical-and-computational data processing the following should be done. First, a formalized subject domain description is developed. The main objects-variables and rules-procedures are specified on the basis of mivar-based approach and then corresponding lists of “objects” and “rules” are formed. This formalized representation is analogous to the bipartite logical network graph.
The main stages of mivar-based information processing are:
The first stage is the stage of synthesis of conceptual subject domain model and its formalization in the form of production rules with a transition to mivar rules. “Input objects – rules/procedures – output objects”. Currently, this stage is the most complex and requires involvement of a human expert to develop a mivar model of the subject domain.
Automated solution algorithm construction or logical inference is implemented at the second stage. Input data for algorithm construction are: mivar matrix of subject domain description and a set input of object-variables and required object-variables.
The solution is implemented at the third stage. [ 14 ]
Firstly, the matrix is constructed. Matrix analysis determines whether a successful inference path exists. Then possible logical inference paths are defined and at the last stage the shortest path is selected according to the set optimality criteria.
Let m {\displaystyle m} rules and n {\displaystyle n} variables be included in the rules as input variables activating them or as output variables. Then, matrix V ( m ⋅ n ) {\displaystyle V(m\cdot n)} , each row of which corresponds to one of the rules and contains the information about variables used in the rule, can represent all the interconnections between rules and variables .
One row and one column are added in the matrix V {\displaystyle V} to store service information.
So, the matrix V {\displaystyle V} of dimension ( m + n ) × ( n + 1 ) {\displaystyle (m+n)\times (n+1)} , is obtained, which shows the whole structure of the source rule network. The structure of this logical network can change, that is, this is a network of rules with evolutionary dynamics.
To search for a logical inference path the following actions are implemented: | https://en.wikipedia.org/wiki/Mivar-based_approach |
In audio engineering , a mix-minus or clean feed is a particular setup of a mixing console or matrix mixer , such that an output of the mixer contains everything except a designated input. Mix-minus is often used to prevent echoes or feedback in broadcast or sound reinforcement systems .
A common situation in which a mix-minus is used is when a telephone hybrid is connected to a console, usually at a radio station . The person on the telephone hears all relevant feeds, usually an identical mix to that of the master bus, including the DJ 's mic feed, except that the caller does not hear their own voice. [ 1 ]
Mix-minus is also often used together with IFB systems in electronic news gathering (ENG) for television news reporters and interview subjects speaking to a host from a remote outside broadcast (OB) location. Because of the delay that is introduced in most means of transmission (including satellite feeds and audio over IP connections), the remote subject's voice has to be removed from their earpiece . Otherwise, the subject would hear themselves with a slight (but very distracting) delay. [ 1 ]
Another common example is in the field of sound reinforcement, when people need to hear a full mix except their own microphone. Legislative bodies of government may use a large mix-minus system, for instance houses of parliament or congressional groups that have a small loudspeaker and a microphone at each seat. From the desktop loudspeaker, each person hears every microphone except their own. This enables all participants to hear each other clearly but minimizes problems with acoustic feedback . In 1994, the first digital audio implementation of such a system was installed at the United States Senate building, with more than 100 mix-minus outputs, one for each senator and also guest seats. [ 2 ]
Mix-minus is also used with VoIP communication when recording for podcasts : mix-minus removes the caller's voice from the VoIP call, but allows them to hear all other channels available at the mixing console (mixer).
Some broadcast mixing desks, notably those designed in house by the BBC , maintain a separate mix bus for clean feeds . | https://en.wikipedia.org/wiki/Mix-minus |
In music recording , mix automation allows the mixing console to remember the audio engineer's adjustment of faders during the post-production editing process. A timecode is necessary for the synchronization of automation. Modern mixing consoles and digital audio workstations use comprehensive mix automation.
The need for mix automation originates from the 1970s and the changeover from studios mostly using eight-track tape machines to multiple, synchronized 24-track recorders. Mixing could be laborious and require up to four people, and the results could be almost impossible to reproduce. Manufacturers such as Solid State Logic and AMS Neve developed systems that enabled one engineer to oversee every detail of a complex mix, although the computers required to power these desks remained a rarity into the late 1970s. [ 1 ]
According to record producer Roy Thomas Baker , Queen 's 1975 single " Bohemian Rhapsody " was one of the first mixes to be done with automation. [ 2 ]
All of these include the mute button. If mute is pressed during writing of automation, the audio track will be muted during playback of that automation.
Depending on software, other parameters such as panning , sends , and plug-in controls can be automated as well. In some cases, automation can be written using a digital potentiometer instead of a fader.
Free open source Mix automation software | https://en.wikipedia.org/wiki/Mix_automation |
Mixed-anion compounds , heteroanionic materials or mixed-anion materials are chemical compounds containing cations and more than one kind of anion . The compounds contain a single phase, rather than just a mixture. [ 1 ] [ 2 ]
By having more than one anion, many more compounds can be made, and properties tuned to desirable values. [ 3 ] In terms of optics, properties include phosphorescence , photocatalysis , [ 4 ] laser damage threshold, refractive index , birefringence , absorption particularly in the ultraviolet or near infrared , non-linearity . [ 5 ] Mechanical properties can include ability to grow a large crystal, ability to form a thin layer, strength, or brittleness.
Thermal properties can include melting point , thermal stability , phase transition temperatures, thermal expansion coefficient .
For electrical properties, electric conductivity, band gap , superconducting transition temperature piezoelectricity , pyroelectricity , ferromagnetism , dielectric constant , charge-density wave transition can be adjusted.
Many of the non-metals that could make mixed-anion compounds may have greatly varying volatilities. This makes it more difficult to combine the elements together. Compounds may be produced in a solid state reaction, by heating solids together, either in a vacuum or a gas. Common gases used include, oxygen, hydrogen, ammonia, chlorine, fluorine, hydrogen sulfide , or carbon disulfide. Soft chemical approaches to manufacture include solvothermal synthesis , or substituting atoms in a structure by others, including by water, oxygen, fluorine, or nitrogen. Teflon pouches can be used to separate different formulations. Thin film deposits can yield strained layers. High pressures can be used to prevent evaporation of volatiles. High pressure can result in different crystal forms, perhaps with higher coordination number . [ 1 ]
Some elements can form several kinds of anions, and compounds may exist with more than one. Examples include the iodate periodates, [ 10 ] sulfite sulfates , selenate selenites , tellurite tellurates , nitrate nitrites , phosphate phosphites , and arsenate arsenites .
These kinds also include different oligomeric forms such as phosphates or fluorotitanates, such as [Ti 4 F 20 ] 4- and [TiF 5 ] − . [ 11 ] | https://en.wikipedia.org/wiki/Mixed-anion_compounds |
Mixed-function oxidase is the name of a family of oxidase enzymes that catalyze a reaction in which each of the two atoms of oxygen in O 2 is used for a different function in the reaction. [ 1 ]
Oxidase is a general name for enzymes that catalyze oxidations in which molecular oxygen is the electron acceptor but oxygen atoms do not appear in the oxidized product. Often, oxygen is reduced to either water ( cytochrome oxidase of the mitochondrial electron transfer chain ) or hydrogen peroxide ( dehydrogenation of fatty acyl-CoA in peroxisomes ). Most of the oxidases are flavoproteins .
The name "mixed-function oxidase" indicates that the enzyme oxidizes two different substrates simultaneously. Desaturation of fatty acyl-CoA in vertebrates is an example of the mixed-function oxidase reaction. In the process, saturated fatty acyl-CoA and NADPH are oxidized by molecular oxygen (O 2 ) to produce monounsaturated fatty acyl-CoA, NADP + and 2 molecules of water.
The mixed-function oxidase reaction proceeds as follows:
AH + BH 2 + O 2 --> AOH + B + H 2 O (H 2 O as catalyst.)
High levels of mixed-function oxidase activity have been studied for their activation effects in human colon carcinoma cell lines, [ 2 ] to study the susceptibility to certain cancers. The research has been successful in mice but remains inconclusive in humans. [ 3 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Mixed-function_oxidase |
Mixed-mode chromatography (MMC) , or multimodal chromatography , refers to chromatographic methods that utilize more than one form of interaction between the stationary phase and analytes in order to achieve their separation. [ 1 ] [ 2 ] [ 3 ] What is distinct from conventional single-mode chromatography is that the secondary interactions in MMC cannot be too weak, and thus they also contribute to the retention of the solutes.
Before MMC was considered as a chromatographic approach, secondary interactions were generally believed to be the main cause of peak tailing. [ 4 ] [ 5 ] [ 6 ] [ 7 ] However, it was discovered afterwards that secondary interactions can be applied for improving separation power. In 1986, Regnier’s group synthesized a stationary phase that had characteristics of anion exchange chromatography (AEX) and hydrophobic interaction chromatography (HIC) on protein separation. [ 8 ] In 1998, a new form of MMC, hydrophobic charge induction chromatography (HCIC), was proposed by Burton and Harding. [ 9 ] In the same year, conjoint liquid chromatography (CLC), which combines different types of monolithic convective interaction media (CIM) disks in the same housing, was introduced by Štrancar et al. [ 10 ] In 1999, Yates’ group [11] loaded strong-cation exchange (SCX) and reversed phase liquid chromatography (RPLC) stationary phases sequentially into a capillary column coupled with tandem mass spectrometry (MS/MS) in the analysis of peptides, which became one of the most efficient technique in proteomics afterwards. [ 11 ] In 2009, Geng’s group first achieved online two-dimensional (2D) separation of intact proteins using a single column possessing separation features of weak-cation exchange chromatography (WCX) and HIC (termed as two-dimensional liquid chromatography using a single column, (2D-LC-1C). [ 12 ]
Higher selectivity: for example, positive, negative and neutral substances could be separated by a reversed phase (RP)/anion-cation exchange (ACE) column in a single run. [ 13 ] Higher loading capacity, [ 14 ] [ 15 ] [ 16 ] for example, loading capacity of ACE/ hydrophilic interaction chromatography (HILIC) increased 10-100 times when compared with RPLC, [ 15 ] which offered a new selection and idea for developing semi-preparative and preparative chromatography. [ 17 ] [ 18 ]
One mixed-mode column can replace two or even more single mode columns, which is economic and eco-friendly for employing the stationary phase more sufficiently and reducing the consuming and ‘waste’ of raw materials.
Single mixed-mode column can be applied for on-line two-dimensional (2D) analysis in a sealed system via establishing corresponding chromatographic system or off-line 2D analysis as two columns.
MMC can be classified into physical MMC and chemical MMC. In the former method, the stationary phase is constructed of two or more types of packing materials. In the chemical method, just one type of packing material containing two or more functionalities is used.
The simplest approach is to connect two commercial columns in series, which is termed a “tandem column”. Another approach is “biphasic column”, by packing two stationary phases separately in two ends of the same column. The third approach is to homogenize two or more different types of stationary phases in a single column, which is termed a “hybrid column” or “mixed-bed column”.
Since IEC and HIC conditions are the closest ones to physiological conditions which are fit for maintaining biological activity, the combinations of them are widely used in the separation of biological products. IEC/HIC MMC has improved separation power and selectivity on the grounds that it applies both electrostatic and hydrophobic interactions.
IEC/RP MMC combines the advantages of RPLC and IEC. For example, WAX/RP has increased separation power and degree of freedom in adjusting the separation selectivity when compared with single WAX or RPLC. [ 19 ]
Liu et al. synthesized a HILIC/RP stationary phase which could show RPLC or HILIC retention by adjusting the organic phase in mobile phase. [ 20 ]
Mant et al. reported that HILIC/CEX offered unique selectivity, stronger separation power and wider range of applications compared to RPLC for peptide separations. [ 21 ]
Hydrophobic interactions in protein SEC are relatively weak at low ionic strength, electrostatic effects may contribute significantly to retention, and this allows us to use an SEC column as a weak ion exchanger. | https://en.wikipedia.org/wiki/Mixed-mode_chromatography |
Mixed-precision arithmetic is a form of floating-point arithmetic that uses numbers with varying widths in a single operation.
A common usage of mixed-precision arithmetic is for operating on inaccurate numbers with a small width and expanding them to a larger, more accurate representation. For example, two half-precision or bfloat16 (16-bit) floating-point numbers may be multiplied together to result in a more accurate single-precision (32-bit) float. [ 1 ] In this way, mixed-precision arithmetic approximates arbitrary-precision arithmetic , albeit with a low number of possible precisions.
Iterative algorithms (like gradient descent ) are good candidates for mixed-precision arithmetic. In an iterative algorithm like square root , a coarse integral guess can be made and refined over many iterations until the error in precision makes it such that the smallest addition or subtraction to the guess is still too coarse to be an acceptable answer. When this happens, the precision can be increased to something more precise, which allows for smaller increments to be used for the approximation.
Supercomputers such as Summit utilize mixed-precision arithmetic to be more efficient with regards to memory and processing time, as well as power consumption. [ 1 ] [ 2 ] [ 3 ]
A floating-point number is typically packed into a single bit-string, as the sign bit, the exponent field, and the significand or mantissa, from left to right. As an example, a IEEE 754 standard 32-bit float ("FP32", "float32", or "binary32") is packed as follows:
The IEEE 754 binary floats are:
bias
precision
decimal digits
Mixed-precision arithmetic is used in the field of machine learning , since gradient descent algorithms can use coarse and efficient half-precision floats for certain tasks, but can be more accurate if they use more precise but slower single-precision floats. Some platforms, including Nvidia , Intel , and AMD CPUs and GPUs, provide mixed-precision arithmetic for this purpose, using coarse floats when possible, but expanding them to higher precision when necessary. [ 1 ] [ 2 ] [ 4 ] [ 5 ]
PyTorch implements automatic mixed-precision (AMP), which performs autocasting, gradient scaling, and loss scaling. [ 6 ] [ 7 ]
PyTorch AMP uses exponential backoff to automatically adjust the scale factor for loss scaling. That is, it periodically increase the scale factor. Whenever the gradients contain a NaN (indicating overflow), the weight update is skipped, and the scale factor is decreased. | https://en.wikipedia.org/wiki/Mixed-precision_arithmetic |
A mixed-species feeding flock , also termed a mixed-species foraging flock , mixed hunting party or informally bird wave , is a flock of usually insectivorous birds of different species that join each other and move together while foraging. [ 1 ] These are different from feeding aggregations, which are congregations of several species of bird at areas of high food availability.
While it is currently unknown how mixed-species foraging flocks originate, researchers have proposed a few mechanisms for their initiation. Many believe that nuclear species play a vital role in mixed-species flock initiation. [ 2 ] Additionally, the forest structure is hypothesized to play a vital role in these flocks' formation. [ 3 ] In Sri Lanka , for example, vocal mimicry by the greater racket-tailed drongo might have a key role in the initiation of mixed-species foraging flocks, [ 4 ] while in parts of the American tropics packs of foraging golden-crowned warblers might play the same role. [ 5 ]
Mixed-species foraging flocks tend to form around a "nuclear" species. Researchers believe nuclear species both stimulate the formation of a mixed-species flock and maintain the cohesion between bird species. [ 2 ] They tend to have a disproportionately large influence on the flock. [ 6 ] Nuclear species have a few universal qualities. Typically, they are both generalists [ 7 ] that employ a gleaning foraging strategy [ 8 ] and intraspecifically social birds. [ 9 ] "Associate" or "attendant" species are birds that trail the flock only after it has entered their territory. [ 10 ] Researchers have shown that these species tend to have a higher fitness following mixed-species foraging flocks. [ 11 ] The third class of birds found in mixed-species flocks have been termed "sentinel" species. Unlike nuclear species, sentinels are fly-catching birds that are rarely gregarious . [ 12 ] Their role is to alert the other birds in the mixed-species flock to the arrival of potential predators. [ 13 ]
Ecologists generally assume that species in the same ecological niche compete for resources. The formation of mixed-species flocks demonstrates a possible exception to this universal ecological assumption. Instead of competing with one another for limited resources, some bird species who share the same food source can co-exist in mixed-species flocks. In fact, the more similar body size, taxonomy , and foraging style two bird species are, the more likely they are to be found cooperating in mixed-species flocks. [ 14 ] Researchers have proposed two primary evolutionary mechanisms to explain the formation of mixed-species flocks. The first mechanistic explanation is that these different bird species cooperate to gain access to more food. Studies have shown that birds in mixed-species flocks are more likely to spot potential food sources, [ 15 ] avoid already exploited locations, [ 16 ] and drive insects out of hiding. [ 17 ] The second mechanistic explanation is that birds join mixed-species flocks to avoid predation. A bird reduces its risk of being eaten when it is surrounded by other birds who can be potential food for the predator instead. [ 18 ] Other studies have hypothesized that multi-species flocks form because large groups reduce a predator's ability to single out one prey, [ 19 ] while others have hypothesized that multi-species flocks are more likely to spot predators. [ 20 ]
Mixed-species feeding flocks are not purely beneficial for their member species. Some bird species suffer a higher cost when joining mixed-species flocks. Studies have shown that some bird species will leave their standard optimal feeding area to travel to a worse foraging location in order to follow the path of a mixed-species flock. [ 21 ] Birds may also be forced to change their foraging strategy in order to conform with the flock. [ 22 ] Another third proposed cost of mixed-species flocks is an increased risk of kleptoparasitism . [ 23 ]
In the North Temperate Zone , they are typically led by Paridae (tits and chickadees), [ 24 ] often joined by nuthatches , [ 25 ] treecreepers , woodpeckers (such as the downy woodpecker and lesser spotted woodpecker ), [ 26 ] kinglets , and in North America Parulidae (New World "warblers") [ 27 ] – all insect-eating birds. This behavior is particularly common outside the breeding season. [ 24 ]
The advantages of this behavior are not certain, but evidence suggests that it confers some safety from predators, especially for the less watchful birds such as vireos and woodpeckers, and also improves feeding efficiency, perhaps because arthropod prey that flee one bird may be caught by another. [ 24 ]
Insectivorous feeding flocks reach their fullest development in tropical forests , where they are a typical feature of bird life. In the Neotropics the leaders or "core" members may be black-throated shrike-tanagers in southern Mexico , or three-striped warblers elsewhere in Central America . In South America , core species may include antbirds such as Thamnomanes , antshrikes , Furnariidae (ovenbirds and woodcreepers) like the buff-fronted foliage-gleaner or the olivaceous woodcreeper , or Parulidae (New World "warblers") like the golden-crowned warblers . [ 5 ] In open cerrado habitat, it may be white-rumped or white-banded tanagers . [ 28 ] Core species often have striking plumage and calls that attract other birds; they are often also known to be very active sentinels, providing warning of would-be predators . [ 28 ] [ 29 ]
But while such easy-to-locate bird species serve as a focal point for flock members, they do not necessarily initiate the flock. In one Neotropic mixed flock feeding on swarming termites, it was observed that buff-throated warbling finches were most conspicuous. [ 30 ] As this species is not an aerial insectivore, it is unlikely to have actually initiated the flock rather than happening across it and joining in. And while Basileuterus species are initiators as well as core species, mixed flocks of Tangara species – in particular red-necked , brassy-breasted , and green-headed tanagers – often initiate formation of a larger and more diverse feeding flock, of which they are then only a less significant component. [ 5 ]
Nine-primaried oscines make up much of almost every Neotropical mixed-species feeding flock. Namely, these birds are from families such as the cardinals , Parulidae (New World "warblers"), and in particular Passerellidae (American "sparrows") and Thraupidae (tanagers). Other members of a Neotropic mixed feeding flock may come from most of the local families of smaller diurnal insectivorous birds, and can also include woodpecker, toucans , and trogons . Most Furnariidae do not participate in mixed flocks, though there are exceptions such as Synallaxis spinetails and some species of the woodcreeper subfamily – e.g. those mentioned above or the lesser woodcreeper – are common or even "core" members. Among the tyrant flycatchers there are also some species joining mixed flocks on a somewhat regular basis, including the sepia-capped flycatcher , eared pygmy tyrant , white-throated spadebill , and Oustalet's tyrannulet . [ 5 ] [ 28 ] [ 30 ]
However, even of commonly participating families not all species join mixed flocks. There are genera such as Vireo in which some species do not join mixed flocks, while others (e.g., the red-eyed vireo ) will even do so in their winter quarters. [ 5 ] Of the three subspecies groups of the yellow-rumped warbler , only one ( Audubon's warbler ) typically does. And while the importance of certain Thraupidae in initiating and keeping together mixed flocks has been mentioned already, for example the black-goggled tanager is an opportunistic feeder that will appear at but keep its distance from any disturbance—be it a mixed feeding flock, an army ant column or a group of monkeys – and pick off prey trying to flee. [ 5 ]
Gnateaters are notable for their absence from these flocks, [ 31 ] while swifts and swallows rarely join them, but will if there is for example an ant or termite swarm. [ 30 ] [ 32 ] [ 33 ] [ 32 ] Cotingidae (cotingas) are mainly opportunistic associates which rarely join flocks for long if they do so at all; the same holds true for most Muscicapoidea (mockingbirds and relatives), though some thrushes may participate on more often. [ 5 ] And though most Tityridae rarely join mixed flocks, becards do so regularly. [ 5 ] Tapaculos are rarely seen with mixed flocks, though the collared crescentchest , doubtfully assigned to that family, may be a regular member. [ 28 ] Icteridae (grackles and relatives) are also not too often seen to take part in these assemblages, though caciques like the golden-winged or red-rumped cacique join mixed flocks on a somewhat more regular basis. [ 5 ] Cuculiformes ( cuckoos and allies) are usually absent from mixed feeding flocks, but some – for example, the squirrel cuckoo – can be encountered not infrequently. [ 5 ]
Some species appear to prefer when certain others are present: Cyanolyca jays like to flock with unicolored jays and the emerald toucanets species complex . Many Icteridae associate only with related species, but the western subspecies of the yellow-backed oriole associates with jays and the band-backed wren . [ 34 ]
Other species participate to varying extents depending on location or altitude – presumably, the different species composition of mixed flocks at varying locations allows these irregular members more or less opportunity to get food. Such species include the grey-hooded flycatcher , or the plain antvireo and the red-crowned ant tanager which are often recorded in lowland flocks but rarely join them at least in some more montane regions. [ 5 ]
A typical Neotropic mixed feeding flock moves through the forest at about 0.3 kilometers per hour (0.19 mph), with different species foraging in their preferred niches (on the ground, on trunks, in high or low foliage, etc.). Some species follow the flock all day, while others – such as the long-billed gnatwren [ 31 ] – join it only as long as it crosses their own territories. [ 29 ]
The flocks in the Old World are often much more loosely bonded than in the Neotropics, many being only casual associations lasting the time the flock of core species spends in the attendants' territory. The more stable flocks are observed in tropical Asia, and especially Sri Lanka. Flocks there may number several hundred birds spending the entire day together, and an observer in the rain forest may see virtually no birds except when encountering a flock. For example, as a flock approaches in the Sinharaja Forest Reserve in Sri Lanka, the typical daytime quiet of the jungle is broken by the noisy calls of the orange-billed babbler and greater racket-tailed drongo , joined by species such as the ashy-headed laughingthrush , Kashmir flycatcher , and velvet-fronted nuthatch .
A mixed flock in the Cordillera Central of Luzon in the Philippines was mainly composed of bar-bellied cuckooshrikes , Philippine fairy-bluebirds , and violaceous crows . Luzon hornbills were also recorded as present. With the crows only joining later and the large hornbills probably only opportunistic attendants rather than core species, it is likely that this flock was started by one of the former species – probably the bold and vocal cuckoo-shrikes rather than the more retiring fairy-bluebirds, which are known to seek out such opportunities to forage. [ 35 ]
African rainforests also hold mixed-species flocks, the core species including bulbuls and sunbirds , and attendants being as diverse as the red-billed dwarf hornbill and the tit-hylia , the smallest bird of Africa. Drongos and paradise-flycatchers are sometimes described as the sentinels of the flock, but they are also known to steal prey from other flock members. Acanthizidae are typical core members in New Guinea and Australia; in Australia, fairy-wrens are also significant. The core species are joined by birds of other families such as minivets . [ 36 ] | https://en.wikipedia.org/wiki/Mixed-species_foraging_flock |
Mixed valence complexes contain an element which is present in more than one oxidation state . [ 2 ] Well-known mixed valence compounds include the Creutz–Taube complex , Prussian blue , and molybdenum blue . Many solids are mixed-valency including indium chalcogenides .
Mixed-valence compounds are subdivided into three groups, according to the Robin–Day classification : [ 3 ]
The Creutz–Taube complex is a robust, readily analyzed, mixed-valence complex consisting of otherwise equivalent Ru(II) and Ru(III) centers bridged by the pyrazine . This complex serves as a model for the bridged intermediate invoked in inner-sphere electron transfer . [ 8 ]
Organic mixed valence compounds are also known. [ 11 ] Mixed valency in fact seems to be required for organic compounds to exhibit electrical conductivity. | https://en.wikipedia.org/wiki/Mixed-valence_complex |
Mixed Groups of Reconstruction Machines ( Greek : Μικτές Ομάδες Μηχανημάτων Ανασυγκροτήσεως ), commonly known by the acronym MOMA , was a Greek military construction organization which was active from 1957 to 1992.
It was established in 1957, with sections based in Athens , Thessaloniki , Heraklion , Patras , Lamia , Larissa , and Ioannina , and comprised both permanent and conscript personnel from the Engineers arm of the Hellenic Army , as well as contracted civilian engineers, drivers, workers, and other personnel. [ 1 ] Its main purpose was the construction of infrastructure (bridges, airports, roads etc) in the country following the extensive devastation of World War II , the Axis occupation of Greece , and the Greek Civil War . [ 1 ] It was abolished in 1992, but in 2015, a similar service, under the name "MOMKA" (Μονάδα Μελετών και Κατασκευών) was established. [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Mixed_Groups_of_Reconstruction_Machines |
In biochemistry , mixed acid fermentation is the metabolic process by which a six-carbon sugar (e.g. glucose , C 6 H 12 O 6 ) is converted into a complex and variable mixture of acids . It is an anaerobic (non-oxygen-requiring) fermentation reaction that is common in bacteria . It is characteristic for members of the Enterobacteriaceae , a large family of Gram-negative bacteria that includes E. coli . [ 3 ]
The mixture of end products produced by mixed acid fermentation includes lactate , acetate , succinate , formate , ethanol and the gases H 2 and CO 2 . The formation of these end products depends on the presence of certain key enzymes in the bacterium. The proportion in which they are formed varies between different bacterial species. [ 4 ] The mixed acid fermentation pathway differs from other fermentation pathways, which produce fewer end products in fixed amounts. The end products of mixed acid fermentation can have many useful applications in biotechnology and industry . For instance, ethanol is widely used as a biofuel . [ 5 ] Therefore, multiple bacterial strains have been metabolically engineered in the laboratory to increase the individual yields of certain end products. [ 2 ] This research has been carried out primarily in E. coli and is ongoing. Variations of mixed acid fermentation occur in a number of bacterial species, including bacterial pathogens such as Haemophilus influenzae where mostly acetate and succinate are produced and lactate can serve as a growth substrate. [ 6 ]
E. coli use fermentation pathways as a final option for energy metabolism, as they produce very little energy in comparison to respiration. [ 7 ] Mixed acid fermentation in E. coli occurs in two stages. These stages are outlined by the biological database for E. coli , EcoCyc . [ 1 ]
The first of these two stages is a glycolysis reaction . Under anaerobic conditions, a glycolysis reaction takes place where glucose is converted into pyruvate :
glucose → 2 pyruvate
There is a net production of 2 ATP and 2 NADH molecules per molecule of glucose converted. ATP is generated by substrate-level phosphorylation . NADH is formed from the reduction of NAD.
In the second stage, pyruvate produced by glycolysis is converted to one or more end products via the following reactions. In each case, both of the NADH molecules generated by glycolysis are reoxidized to NAD + . Each alternative pathway requires a different key enzyme in E. coli . After the variable amounts of different end products are formed by these pathways, they are secreted from the cell. [ 1 ]
Pyruvate produced by glycolysis is converted to lactate . This reaction is catalysed by the enzyme lactate dehydrogenase (LDHA). [ 1 ]
pyruvate + NADH + H + → lactate + NAD +
Pyruvate is converted into acetyl-coenzyme A (acetyl-CoA) by the enzyme pyruvate dehydrogenase . This acetyl-CoA is then converted into acetate in E. coli , whilst producing ATP by substrate-level phosphorylation . Acetate formation requires two enzymes: phosphate acetyltransferase and acetate kinase. [ 1 ]
acetyl-CoA + phosphate → acetyl-phosphate + CoA
acetyl-phosphate + ADP → acetate + ATP
Ethanol is formed in E. coli by the reduction of acetyl coenzyme A using NADH. This two-step reaction requires the enzyme alcohol dehydrogenase (ADHE). [ 1 ]
acetyl-CoA + NADH + H + → acetaldehyde + NAD + + CoA
acetaldehyde + NADH + H + → ethanol + NAD +
Formate is produced by the cleavage of pyruvate. This reaction is catalysed by the enzyme pyruvate-formate lyase (PFL), which plays an important role in regulating anaerobic fermentation in E. coli . [ 8 ]
pyruvate + CoA → acetyl-CoA + formate
Succinate is formed in E. coli in several steps.
Phosphoenolpyruvate (PEP), a glycolysis pathway intermediate , is carboxylated by the enzyme PEP carboxylase to form oxaloacetate . [ 9 ] This is followed by the conversion of oxaloacetate to malate by the enzyme malate dehydrogenase . Fumarate hydratase then catalyses the dehydration of malate to produce fumarate . [ 10 ]
phosphoenolpyruvate + HCO 3 → oxaloacetate + phosphate
oxaloacetate + NADH + H + → malate + NAD +
malate → fumarate + H 2 O
The final reaction in the formation of succinate is the reduction of fumarate. It is catalysed by the enzyme fumarate reductase .
fumarate + NADH + H + → succinate + NAD +
This reduction is an anaerobic respiration reaction in E. coli , as it uses electrons associated with NADH dehydrogenase and the electron transport chain . ATP is generated by using an electrochemical gradient and ATP synthase . This is the only case in the mixed acid fermentation pathway where ATP is not produced via substrate-level phosphorylation. [ 1 ] [ 2 ]
Vitamin K 2 , also known as menaquinone, is very important for electron transport to fumarate in E. coli . [ 11 ]
Formate can be converted to hydrogen gas and carbon dioxide in E. coli . This reaction requires the enzyme formate-hydrogen lyase . It can be used to prevent the conditions inside the cell becoming too acidic. [ 1 ]
formate → H 2 and CO 2
The methyl red (MR) test can detect whether the mixed acid fermentation pathway occurs in microbes when given glucose. A pH indicator is used that turns the test solution red if the pH drops below 4.4. [ 12 ] If the fermentation pathway has taken place, the mixture of acids it has produced will make the solution very acidic and cause a red colour change.
The methyl red test belongs to a group known as the IMViC tests.
Multiple bacterial strains have been metabolically engineered to increase the individual yields of end products formed by mixed acid fermentation. For instance, strains for the increased production of ethanol, lactate, succinate and acetate have been developed due to the usefulness of these products in biotechnology . [ 2 ] The major limiting factor for this engineering is the need to maintain a redox balance in the mixture of acids produced by the fermentation pathway. [ 13 ]
Ethanol is the most commonly used biofuel and can be produced on large scale via fermentation. The maximum theoretical yield for the production of ethanol was achieved around 20 years. [ 14 ] [ 15 ] A plasmid that carried the pyruvate decarboxylase and alcohol dehydrogenase genes from the bacteria Z. mobilis was used by scientists. This was inserted into E. coli and resulted in an increased yield of ethanol. The genome of this E. coli strain, KO11, has more recently been sequenced and mapped. [ 16 ]
The E. coli strain W3110 was genetically engineered to generate 2 moles of acetate for every 1 mole of glucose that undergoes fermentation. This is known as a homoacetate pathway. [ 17 ]
Lactate can be used to produce a bioplastic called polylactic acid (PLA). The properties of PLA depend on the ratio of the two optical isomers of lactate (D-lactate and L-lactate). D-lactate is produced by mixed acid fermentation in E. coli . [ 18 ] Early experiments engineered the E. coli strain RR1 to produce either one of the two optical isomers of lactate. [ 19 ]
Later experiments modified the E. coli strain KO11, originally developed to enhance ethanol production. Scientists were able to increase the yield of D-lactate from fermentation by performing several deletions . [ 20 ]
Increasing the yield of succinate from mixed acid fermentation was first done by overexpressing the enzyme PEP carboxylase . [ 21 ] This produced a succinate yield that was approximately 3 times greater than normal. Several experiments using a similar approach have followed.
Alternative approaches have altered the redox and ATP balance to optimize the succinate yield. [ 22 ]
There are a number of other fermentation pathways that occur in microbes. [ 4 ] All these pathways begin by converting pyruvate, but their end products and the key enzymes they require are different.
These pathways include: | https://en.wikipedia.org/wiki/Mixed_acid_fermentation |
In Euclidean geometry , an angle or plane angle is the figure formed by two rays , called the sides of the angle, sharing a common endpoint, called the vertex of the angle. [ 1 ] Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection. Angles are also formed by the intersection of two planes; these are called dihedral angles .
In any case, the resulting angle lies in a plane (spanned by the two rays or perpendicular to the line of plane-plane intersection ).
The magnitude of an angle is called an angular measure or simply "angle". This measure, for an ordinary angle, is often visualized or defined using the arc of a circle centered at the vertex and lying between the sides. Two different angles may have the same measure, as in an isosceles triangle . "Angle" also denotes the angular sector , the infinite region of the plane bounded by the sides of an angle. [ 2 ] [ 3 ] [ a ]
Angle of rotation is a measure conventionally defined as the ratio of a circular arc length to its radius , and may be a negative number ; the arc is centered at the center of the rotation and delimited by any other point and its image after the rotation.
The word angle comes from the Latin word angulus , meaning "corner". Cognate words include the Greek ἀγκύλος ( ankylοs ) meaning "crooked, curved" and the English word " ankle ". Both are connected with the Proto-Indo-European root *ank- , meaning "to bend" or "bow". [ 7 ]
Euclid defines a plane angle as the inclination to each other, in a plane, of two lines that meet each other and do not lie straight with respect to each other. According to the Neoplatonic metaphysician Proclus , an angle must be either a quality, a quantity, or a relationship. The first concept, angle as quality, was used by Eudemus of Rhodes , who regarded an angle as a deviation from a straight line ; the second, angle as quantity, by Carpus of Antioch , who regarded it as the interval or space between the intersecting lines; Euclid adopted the third: angle as a relationship. [ 8 ]
In mathematical expressions , it is common to use Greek letters ( α , β , γ , θ , φ , . . . ) as variables denoting the size of some angle [ 9 ] (the symbol π is typically not used for this purpose to avoid confusion with the constant denoted by that symbol ). Lower case Roman letters ( a , b , c , . . . ) are also used. In contexts where this is not confusing, an angle may be denoted by the upper case Roman letter denoting its vertex. See the figures in this article for examples.
The three defining points may also identify angles in geometric figures. For example, the angle with vertex A formed by the rays AB and AC (that is, the half-lines from point A through points B and C) is denoted ∠BAC or B A C ^ {\displaystyle {\widehat {\rm {BAC}}}} . Where there is no risk of confusion, the angle may sometimes be referred to by a single vertex alone (in this case, "angle A").
In other ways, an angle denoted as, say, ∠BAC might refer to any of four angles: the clockwise angle from B to C about A, the anticlockwise angle from B to C about A, the clockwise angle from C to B about A, or the anticlockwise angle from C to B about A, where the direction in which the angle is measured determines its sign (see § Signed angles ). However, in many geometrical situations, it is evident from the context that the positive angle less than or equal to 180 degrees is meant, and in these cases, no ambiguity arises. Otherwise, to avoid ambiguity, specific conventions may be adopted so that, for instance, ∠BAC always refers to the anticlockwise (positive) angle from B to C about A and ∠CAB the anticlockwise (positive) angle from C to B about A.
There is some common terminology for angles, whose measure is always non-negative (see § Signed angles ):
The names, intervals, and measuring units are shown in the table below:
When two straight lines intersect at a point, four angles are formed. Pairwise, these angles are named according to their location relative to each other.
The equality of vertically opposite angles is called the vertical angle theorem . Eudemus of Rhodes attributed the proof to Thales of Miletus . [ 14 ] [ 15 ] The proposition showed that since both of a pair of vertical angles are supplementary to both of the adjacent angles, the vertical angles are equal in measure. According to a historical note, [ 15 ] when Thales visited Egypt, he observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as:
When two adjacent angles form a straight line, they are supplementary. Therefore, if we assume that the measure of angle A equals x , the measure of angle C would be 180° − x . Similarly, the measure of angle D would be 180° − x . Both angle C and angle D have measures equal to 180° − x and are congruent. Since angle B is supplementary to both angles C and D , either of these angle measures may be used to determine the measure of Angle B . Using the measure of either angle C or angle D , we find the measure of angle B to be 180° − (180° − x ) = 180° − 180° + x = x . Therefore, both angle A and angle B have measures equal to x and are equal in measure.
A transversal is a line that intersects a pair of (often parallel) lines and is associated with exterior angles , interior angles , alternate exterior angles , alternate interior angles , corresponding angles , and consecutive interior angles . [ 16 ]
The angle addition postulate states that if B is in the interior of angle AOC, then
m ∠ A O C = m ∠ A O B + m ∠ B O C {\displaystyle m\angle \mathrm {AOC} =m\angle \mathrm {AOB} +m\angle \mathrm {BOC} }
I.e., the measure of the angle AOC is the sum of the measure of angle AOB and the measure of angle BOC.
Three special angle pairs involve the summation of angles:
The adjective complementary is from the Latin complementum , associated with the verb complere , "to fill up". An acute angle is "filled up" by its complement to form a right angle.
The difference between an angle and a right angle is termed the complement of the angle. [ 18 ]
If angles A and B are complementary, the following relationships hold: sin 2 A + sin 2 B = 1 cos 2 A + cos 2 B = 1 tan A = cot B sec A = csc B {\displaystyle {\begin{aligned}&\sin ^{2}A+\sin ^{2}B=1&&\cos ^{2}A+\cos ^{2}B=1\\[3pt]&\tan A=\cot B&&\sec A=\csc B\end{aligned}}}
(The tangent of an angle equals the cotangent of its complement, and its secant equals the cosecant of its complement.)
The prefix " co- " in the names of some trigonometric ratios refers to the word "complementary".
If the two supplementary angles are adjacent (i.e., have a common vertex and share just one side), their non-shared sides form a straight line . Such angles are called a linear pair of angles . [ 20 ] However, supplementary angles do not have to be on the same line and can be separated in space. For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary.
If a point P is exterior to a circle with center O, and if the tangent lines from P touch the circle at points T and Q, then ∠TPQ and ∠TOQ are supplementary.
The sines of supplementary angles are equal. Their cosines and tangents (unless undefined) are equal in magnitude but have opposite signs.
In Euclidean geometry, any sum of two angles in a triangle is supplementary to the third because the sum of the internal angles of a triangle is a straight angle.
The difference between an angle and a complete angle is termed the explement of the angle or conjugate of an angle.
Measurement of angles is intrinsically linked with circles and rotation. The angle is first considered as within a circle of given size, centred at the vertex, and from that arrangement a ratio of certain lengths can be used quantify the angle size. As there are a number of valid measurement approaches, some have argued it useful to consider angle size as being proportional to these ratios, rather than defined by or equal to them. [ 25 ]
The usual characterization is to consider the smallest rotation of one of the rays about the vertex that maps it onto the other. The length of the arc , s , traced along the circle as the ray is rotated is said to be the arc length that is subtended by (or equivalently, subtends) the angle. However as s is dependent on the arbitrary choice of circle size, the ratio of length s to either the radius or circumference of the circle gives a general measure of angle size.
The ratio of the length s by the radius r is the number of radians in the angle, while the ratio of length s by the circumference C is the number of turns : [ 26 ] θ = s r r a d . {\displaystyle \theta ={\frac {s}{r}}\,\mathrm {rad} .} θ = s C = s 2 π r t u r n s . {\displaystyle \theta ={\frac {s}{C}}\ ={\frac {s}{2\pi r}}\,\mathrm {turns} .}
The value of θ thus defined is independent of the size of the circle: if the length of the radius is changed, then the arc length changes in the same proportion, so the ratio s / r is unaltered. [ nb 1 ]
Conventionally, in mathematics and the SI , the radian is treated as being equal to the dimensionless unit 1, thus being normally omitted.
Other angular units are typically based on subdivisions of the turn and may then be obtained by multiplying the angle by a suitable conversion constant of the form k / 2 π , where k is the measure of a complete turn expressed in the chosen unit (for example, k = 360° for degrees or 400 grad for gradians ):
θ = k 2 π ⋅ s r . {\displaystyle \theta ={\frac {k}{2\pi }}\cdot {\frac {s}{r}}.} Angles of the same size are said to be equal congruent or equal in measure .
In some contexts, such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts, such as identifying a point on a spiral curve or describing an object's cumulative rotation in two dimensions relative to a reference orientation, angles that differ by a non-zero multiple of a full turn are not equivalent.
Throughout history, angles have been measured in various units . These are known as angular units , with the most contemporary units being the degree ( ° ), the radian (rad), and the gradian (grad), though many others have been used throughout history . [ 28 ]
In the International System of Quantities , an angle is defined as a dimensionless quantity, and in particular, the radian unit is dimensionless. This convention impacts how angles are treated in dimensional analysis .
The following table lists some units used to represent angles.
[ 30 ] It is 1 / 256 of a turn. [ 29 ]
Plane angle may be defined as θ = s / r , where θ is the magnitude in radians of the subtended angle, s is circular arc length, and r is radius. One radian corresponds to the angle for which s = r , hence 1 radian = 1 m/m = 1. [ 34 ] However, rad is only to be used to express angles, not to express ratios of lengths in general. [ 35 ] A similar calculation using the area of a circular sector θ = 2 A / r 2 gives 1 radian as 1 m 2 /m 2 = 1. [ 36 ] The key fact is that the radian is a dimensionless unit equal to 1 . In SI 2019, the SI radian is defined accordingly as 1 rad = 1 . [ 37 ] It is a long-established practice in mathematics and across all areas of science to make use of rad = 1 . [ 38 ] [ 39 ]
Giacomo Prando writes "the current state of affairs leads inevitably to ghostly appearances and disappearances of the radian in the dimensional analysis of physical equations". [ 40 ] For example, an object hanging by a string from a pulley will rise or drop by y = rθ centimetres, where r is the magnitude of the radius of the pulley in centimetres and θ is the magnitude of the angle through which the pulley turns in radians. When multiplying r by θ , the unit radian does not appear in the product, nor does the unit centimetre—because both factors are magnitudes (numbers). Similarly in the formula for the angular velocity of a rolling wheel, ω = v / r , radians appear in the units of ω but not on the right hand side. [ 41 ] Anthony French calls this phenomenon "a perennial problem in the teaching of mechanics". [ 42 ] Oberhofer says that the typical advice of ignoring radians during dimensional analysis and adding or removing radians in units according to convention and contextual knowledge is "pedagogically unsatisfying". [ 43 ]
In 1993 the American Association of Physics Teachers Metric Committee specified that the radian should explicitly appear in quantities only when different numerical values would be obtained when other angle measures were used, such as in the quantities of angle measure (rad), angular speed (rad/s), angular acceleration (rad/s 2 ), and torsional stiffness (N⋅m/rad), and not in the quantities of torque (N⋅m) and angular momentum (kg⋅m 2 /s). [ 44 ]
At least a dozen scientists between 1936 and 2022 have made proposals to treat the radian as a base unit of measurement for a base quantity (and dimension) of "plane angle". [ 45 ] [ 46 ] [ 47 ] Quincey's review of proposals outlines two classes of proposal. The first option changes the unit of a radius to meters per radian, but this is incompatible with dimensional analysis for the area of a circle , π r 2 . The other option is to introduce a dimensional constant. According to Quincey this approach is "logically rigorous" compared to SI, but requires "the modification of many familiar mathematical and physical equations". [ 48 ] A dimensional constant for angle is "rather strange" and the difficulty of modifying equations to add the dimensional constant is likely to preclude widespread use. [ 47 ]
In particular, Quincey identifies Torrens' proposal to introduce a constant η equal to 1 inverse radian (1 rad −1 ) in a fashion similar to the introduction of the constant ε 0 . [ 48 ] [ b ] With this change the formula for the angle subtended at the center of a circle, s = rθ , is modified to become s = ηrθ , and the Taylor series for the sine of an angle θ becomes: [ 47 ] [ 49 ] Sin θ = sin x = x − x 3 3 ! + x 5 5 ! − x 7 7 ! + ⋯ = η θ − ( η θ ) 3 3 ! + ( η θ ) 5 5 ! − ( η θ ) 7 7 ! + ⋯ , {\displaystyle \operatorname {Sin} \theta =\sin \ x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots =\eta \theta -{\frac {(\eta \theta )^{3}}{3!}}+{\frac {(\eta \theta )^{5}}{5!}}-{\frac {(\eta \theta )^{7}}{7!}}+\cdots ,} where x = η θ = θ / rad {\displaystyle x=\eta \theta =\theta /{\text{rad}}} is the angle in radians.
The capitalized function Sin is the "complete" function that takes an argument with a dimension of angle and is independent of the units expressed, [ 49 ] while sin is the traditional function on pure numbers which assumes its argument is a dimensionless number in radians. [ 50 ] The capitalised symbol Sin {\displaystyle \operatorname {Sin} } can be denoted sin {\displaystyle \sin } if it is clear that the complete form is meant. [ 47 ] [ 51 ]
Current SI can be considered relative to this framework as a natural unit system where the equation η = 1 is assumed to hold, or similarly, 1 rad = 1 . This radian convention allows the omission of η in mathematical formulas. [ 52 ]
It is frequently helpful to impose a convention that allows positive and negative angular values to represent orientations and/or rotations in opposite directions or "sense" relative to some reference.
In a two-dimensional Cartesian coordinate system , an angle is typically defined by its two sides, with its vertex at the origin. The initial side is on the positive x-axis , while the other side or terminal side is defined by the measure from the initial side in radians, degrees, or turns, with positive angles representing rotations toward the positive y-axis and negative angles representing rotations toward the negative y -axis. When Cartesian coordinates are represented by standard position , defined by the x -axis rightward and the y -axis upward, positive rotations are anticlockwise , and negative cycles are clockwise .
In many contexts, an angle of − θ is effectively equivalent to an angle of "one full turn minus θ ". For example, an orientation represented as −45° is effectively equal to an orientation defined as 360° − 45° or 315°. Although the final position is the same, a physical rotation (movement) of −45° is not the same as a rotation of 315° (for example, the rotation of a person holding a broom resting on a dusty floor would leave visually different traces of swept regions on the floor).
In three-dimensional geometry, "clockwise" and "anticlockwise" have no absolute meaning, so the direction of positive and negative angles must be defined in terms of an orientation , which is typically determined by a normal vector passing through the angle's vertex and perpendicular to the plane in which the rays of the angle lie.
In navigation , bearings or azimuth are measured relative to north. By convention, viewed from above, bearing angles are positive clockwise, so a bearing of 45° corresponds to a north-east orientation. Negative bearings are not used in navigation, so a north-west orientation corresponds to a bearing of 315°.
For an angular unit, it is definitional that the angle addition postulate holds. Some quantities related to angles where the angle addition postulate does not hold include:
The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection. Various names (now rarely, if ever, used) have been given to particular cases:— amphicyrtic (Gr. ἀμφί , on both sides, κυρτός, convex) or cissoidal (Gr. κισσός, ivy), biconvex; xystroidal or sistroidal (Gr. ξυστρίς, a tool for scraping), concavo-convex; amphicoelic (Gr. κοίλη, a hollow) or angulus lunularis , biconcave. [ 59 ]
The ancient Greek mathematicians knew how to bisect an angle (divide it into two angles of equal measure) using only a compass and straightedge but could only trisect certain angles. In 1837, Pierre Wantzel showed that this construction could not be performed for most angles.
In the Euclidean space , the angle θ between two Euclidean vectors u and v is related to their dot product and their lengths by the formula
u ⋅ v = cos ( θ ) ‖ u ‖ ‖ v ‖ . {\displaystyle \mathbf {u} \cdot \mathbf {v} =\cos(\theta )\left\|\mathbf {u} \right\|\left\|\mathbf {v} \right\|.}
This formula supplies an easy method to find the angle between two planes (or curved surfaces) from their normal vectors and between skew lines from their vector equations.
To define angles in an abstract real inner product space , we replace the Euclidean dot product ( · ) by the inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } , i.e.
⟨ u , v ⟩ = cos ( θ ) ‖ u ‖ ‖ v ‖ . {\displaystyle \langle \mathbf {u} ,\mathbf {v} \rangle =\cos(\theta )\ \left\|\mathbf {u} \right\|\left\|\mathbf {v} \right\|.}
In a complex inner product space , the expression for the cosine above may give non-real values, so it is replaced with
Re ( ⟨ u , v ⟩ ) = cos ( θ ) ‖ u ‖ ‖ v ‖ . {\displaystyle \operatorname {Re} \left(\langle \mathbf {u} ,\mathbf {v} \rangle \right)=\cos(\theta )\left\|\mathbf {u} \right\|\left\|\mathbf {v} \right\|.}
or, more commonly, using the absolute value, with
| ⟨ u , v ⟩ | = | cos ( θ ) | ‖ u ‖ ‖ v ‖ . {\displaystyle \left|\langle \mathbf {u} ,\mathbf {v} \rangle \right|=\left|\cos(\theta )\right|\left\|\mathbf {u} \right\|\left\|\mathbf {v} \right\|.}
The latter definition ignores the direction of the vectors. It thus describes the angle between one-dimensional subspaces span ( u ) {\displaystyle \operatorname {span} (\mathbf {u} )} and span ( v ) {\displaystyle \operatorname {span} (\mathbf {v} )} spanned by the vectors u {\displaystyle \mathbf {u} } and v {\displaystyle \mathbf {v} } correspondingly.
The definition of the angle between one-dimensional subspaces span ( u ) {\displaystyle \operatorname {span} (\mathbf {u} )} and span ( v ) {\displaystyle \operatorname {span} (\mathbf {v} )} given by
| ⟨ u , v ⟩ | = | cos ( θ ) | ‖ u ‖ ‖ v ‖ {\displaystyle \left|\langle \mathbf {u} ,\mathbf {v} \rangle \right|=\left|\cos(\theta )\right|\left\|\mathbf {u} \right\|\left\|\mathbf {v} \right\|}
in a Hilbert space can be extended to subspaces of finite dimensions. Given two subspaces U {\displaystyle {\mathcal {U}}} , W {\displaystyle {\mathcal {W}}} with dim ( U ) := k ≤ dim ( W ) := l {\displaystyle \dim({\mathcal {U}}):=k\leq \dim({\mathcal {W}}):=l} , this leads to a definition of k {\displaystyle k} angles called canonical or principal angles between subspaces.
In Riemannian geometry , the metric tensor is used to define the angle between two tangents . Where U and V are tangent vectors and g ij are the components of the metric tensor G ,
cos θ = g i j U i V j | g i j U i U j | | g i j V i V j | . {\displaystyle \cos \theta ={\frac {g_{ij}U^{i}V^{j}}{\sqrt {\left|g_{ij}U^{i}U^{j}\right|\left|g_{ij}V^{i}V^{j}\right|}}}.}
A hyperbolic angle is an argument of a hyperbolic function just as the circular angle is the argument of a circular function . The comparison can be visualized as the size of the openings of a hyperbolic sector and a circular sector since the areas of these sectors correspond to the angle magnitudes in each case. [ 60 ] Unlike the circular angle, the hyperbolic angle is unbounded. When the circular and hyperbolic functions are viewed as infinite series in their angle argument, the circular ones are just alternating series forms of the hyperbolic functions. This comparison of the two series corresponding to functions of angles was described by Leonhard Euler in Introduction to the Analysis of the Infinite (1748).
In geography , the location of any point on the Earth can be identified using a geographic coordinate system . This system specifies the latitude and longitude of any location in terms of angles subtended at the center of the Earth, using the equator and (usually) the Greenwich meridian as references.
In astronomy , a given point on the celestial sphere (that is, the apparent position of an astronomical object) can be identified using any of several astronomical coordinate systems , where the references vary according to the particular system. Astronomers measure the angular separation of two stars by imagining two lines through the center of the Earth , each intersecting one of the stars. The angle between those lines and the angular separation between the two stars can be measured.
In both geography and astronomy, a sighting direction can be specified in terms of a vertical angle such as altitude / elevation with respect to the horizon as well as the azimuth with respect to north .
Astronomers also measure objects' apparent size as an angular diameter . For example, the full moon has an angular diameter of approximately 0.5° when viewed from Earth. One could say, "The Moon's diameter subtends an angle of half a degree." The small-angle formula can convert such an angular measurement into a distance/size ratio.
Other astronomical approximations include:
These measurements depend on the individual subject, and the above should be treated as rough rule of thumb approximations only.
In astronomy, right ascension and declination are usually measured in angular units, expressed in terms of time, based on a 24-hour day.
This article incorporates text from a publication now in the public domain : Chisholm, Hugh , ed. (1911), " Angle ", Encyclopædia Britannica , vol. 2 (11th ed.), Cambridge University Press, p. 14 | https://en.wikipedia.org/wiki/Mixed_angle |
Mixed conductors , also known as mixed ion-electron conductors (MIEC), are a single-phase material that has significant conduction ionically and electronically . [ 1 ] [ 2 ] [ 3 ] Due to the mixed conduction, a formally neutral species can transport in a solid and therefore mass storage and redistribution are enabled. Mixed conductors are well known in conjugation with high-temperature superconductivity and are able to capacitate rapid solid-state reactions .
They are used as catalysts (for oxidation), permeation membranes , sensors , and electrodes in batteries and fuel cells , because they allow for rapidly transducing chemical signals and permeating chemical components. [ 3 ]
Strontium titanate ( SrTiO 3 ), titanium dioxide ( TiO 2 ), (La,Ba,Sr)(Mn,Fe,Co)O 3−d ,La2CuO 4+d , cerium(IV) oxide ( CeO 2 ), lithium iron phosphate ( LiFePO 4 ), and LiMnPO 4 are examples of mixed conductors. [ 1 ]
MIEC materials tend to be nonstoichiometric oxides , many of which have perovskite structures with rare earth metals on the A-site and transition metals on the B-site. [ 4 ] Substituting various ions into the lattice of such an oxide can result in increased electronic conductivity through the formation of holes and introduce ionic conductivity by developing oxygen vacancies. [ 4 ] This mechanism is known as defect theory, which states that defects like these offer additional pathways that favor fast diffusion. [ 5 ] Other promising materials include those with pyrochlore , brownmillerite , Ruddlesden-Popper , and orthorhombic K 2 NiF 4 -type structures. [ 5 ]
However, true (single-phase) MIECs that are compatible with other design parameters can be difficult to find, so many researchers have turned to heterogeneous MIEC materials (H-MIECs). An H-MIEC is a composite mixture of two phases: one for conducting ions, and another conducting electrons or holes. [ 6 ] These materials are desirable for the ability to tune their properties for specific applications by adjusting concentration levels to achieve optimal electron and ion transport. [ 7 ] Porous H-MIECs also incorporate a third phase in the form of pores, which allow the formation of triple phase boundaries (TPBs) between the three phases that provide high catalytic activity. [ 7 ]
Current state-of-the-art solid oxide fuel cells (SOFCs) and electrolysis cells (SOECs) frequently incorporate electrodes made of MIEC materials. SOFCs are unique among fuel cells in that negatively charged ions (O 2- ) are transported from the cathode to the anode across the electrolyte , making MIEC cathode materials critical to achieving high performance. These fuel cells operate with the following oxidation-reduction reaction:
MIECs like lanthanum strontium cobalt ferrite (LSCF) are frequently the subject of modern fuel cell research, as they enable the reduction reaction to occur over the entire cathode surface area instead of only at the cathode/electrolyte interface. [ 8 ]
One of the most commonly used oxygen electrode (cathode) materials is the H-MIEC LSM-YSZ, consisting of lanthanum strontium manganite (LSM) infiltrated onto a Y 2 O 3 -doped ZrO 2 scaffold. [ 9 ] The LSM nanoparticles are deposited on the walls of the porous YSZ scaffold to provide an electronically conductive pathway and a high density of TPBs for the reduction reaction to occur. [ 9 ] | https://en.wikipedia.org/wiki/Mixed_conductor |
A mixed criticality system is a system containing computer hardware and software that can execute several applications of different criticality, such as safety-critical and non-safety critical, or of different safety integrity level (SIL). Different criticality applications are engineered to different levels of assurance, with high criticality applications being the most costly to design and verify. These kinds of systems are typically embedded in a machine such as an aircraft whose safety must be ensured.
Traditional safety-critical systems had to be tested and certified in their entirety to show that they were safe to use. However, many such systems are composed of a mixture of safety-critical and non-critical parts, as for example when an aircraft contains a passenger entertainment system that is isolated from the safety-critical flight systems. Some issues to address in mixed criticality systems include real-time behaviour , memory isolation, data and control coupling.
Computer scientists have developed techniques for handling systems which thus have mixed criticality, but there are many challenges remaining especially for multi-core hardware. [ 1 ] [ 2 ] [ 3 ] [ 4 ]
Basically, most errors are currently committed when making confusion between priority attribution and criticality management. As priority defines an order between different tasks or messages to be transmitted inside a system, criticality defines classes of messages which can have different parameters depending on the current use case. For example, in case of car crash avoidance or obstacle anticipation, camera sensors can suddenly emit messages more often, and so create an overload in the system. That is when we need to make Mixed-Criticality operate : to select messages to absolutely guarantee on the system in these overload cases.
EU funded research projects on mixed criticality include:
UK EPSRC funded research projects on mixed criticality include:
Several research projects have decided to present their research results at the EU-funded Mixed-Criticality Forum
Workshops and seminars on Mixed Criticality Systems include: | https://en.wikipedia.org/wiki/Mixed_criticality |
In mathematical optimization theory , the mixed linear complementarity problem , often abbreviated as MLCP or LMCP , is a generalization of the linear complementarity problem to include free variables .
This linear algebra -related article is a stub . You can help Wikipedia by expanding it .
This mathematical analysis –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Mixed_linear_complementarity_problem |
Mixed liquor suspended solids ( MLSS ) is the concentration of suspended solids, in an aeration tank during the activated sludge process , which occurs during the treatment of waste water . The units MLSS is primarily measured in milligram per litre (mg/L), but for activated sludge its mostly measured in gram per litre [g/L] which is equal to kilogram per cubic metre [kg/m3]. Mixed liquor is a combination of raw or unsettled wastewater or pre-settled wastewater and activated sludge within an aeration tank. MLSS consists mostly of microorganisms and non-biodegradable suspended matter. MLSS is an important part of the activated sludge process to ensure that there is a sufficient quantity of active biomass available to consume the applied quantity of organic pollutant at any time. This is known as the food to microorganism ratio, more commonly notated as the F/M ratio. By maintaining this ratio at the appropriate level the biomass will consume high percentages of the food. This minimizes the loss of residual food in the treated effluent. In simple terms, the more the biomass consumes the lower the biochemical oxygen demand ( BOD ) will be in the discharge. It is important that MLSS removes COD and BOD in order to purify water for clean surface waters, and subsequently clean drinking water and hygiene. Raw sewage enters in the water treatment process with a concentration of sometimes several hundred mg/L of BOD. Upon being treated by screening, pre-settling, activated sludge processes or other methods of treatment, the concentration of BOD in water can be lowered to less than 2 mg/L, which is considered to be clean, safe to discharge to surface waters or to reuse water.
The total weight of MLSS within an aeration tank can be calculated by multiplying the concentration of MLSS (kg/m3) in the aeration tank by the tank volume (m3).
MLSS is responsible for removing the biochemical oxygen demand make-up of a large portion of the solids that are retained in the activated sludge process within the water treatment process. They are the "active" part of the activated sludge process. Mixed liquor suspended solids are the solids under aeration . MLSS is measured by filtering a known volume of the mixed liquor sample, which is the same way that suspended solids are measured in wastewater. Some of the MLSS may be an inorganic material. Sometimes this may represent a large percentage of the solids present in the wastewater.
Environmental engineering focuses on the particles suspended in water and the suitable operation of water treatment plants. Therefore, it is important to measure the total mass of suspended solids, which is the MLSS, as well as the mass of organic matter suspended in the activated sludge unit. These measurements allow engineers to adjust the flow rate of return sludge from the secondary clarifier into the secondary treatment reactor. This ensures that influent organic matter will be treated with a correct concentration of microorganisms.
The portion of the MLSS that is actually eating the incoming food(in terms of COD & BOD) is referred to as the Mixed Liquor Volatile Suspended Solids (MLVSS). The volatile solids concentration in a sample of mixed liquor will consist mostly of microorganisms and organic matter. As a result, the volatile solids concentration of mixed liquor is approximately equal to the amount of microorganisms in the water and can be used to determine whether there are enough microorganisms present to purify the water
MLSS is separated from the treated or purified water by settling in a settling tank in the activated sludge process. The excess sludge has to be removed from the system.
it will create thick foam on upper surface layer.
The typical control band for the concentration of MLSS is 2 to 4 g/L for conventional activated sludge, or up to 15 g/L for membrane bioreactors .
One of the easiest control procedures for activated sludge systems is the Constant Mixed Liquor Suspended Solids method. In this method, the operator selects a certain MLSS concentration or range of mix liquor concentrations that produces the best effluent and the highest removal efficiencies. This specific value or range must be calculated depending on COD or BOD load [kg/d]. When the operator finds the optimum MLSS concentration for each plant, they attempt to maintain this value by adjusting the sludge wasting or sludge excess rate. One rule of thumb for activated sludge systems is that for every pound of BOD removed in the secondary system a half a pound of new solids is generated through reproduction of the organisms and addition of new organisms from the influent wastes. So, the operator tries to waste the proper amount of solids to keep their selected optimum mix liquor concentration constant. If the MLSS concentration is above the desired concentration, the wasting of the excess solids will have to be started or increased. If the MLSS concentration is below the desired concentration level, wasting should be decreased or stopped.
MLSS (g/L) = SV [mL/L]/SVI [mL/g] or SVI [mL/g] = SV30 [mL/L]/MLSS (g/L)
Where: SVI = sludge volume index (mL/g) SV30 = Volume of settled solids per 1 litre after 30 minutes
In fact SVI is a calculation from two analyses : SV30 and MLSS.
0=(Q+Q r )(X')-(Q r X' r +Q s X' r )
Where: Q = wastewater flow rate (m 3 /d) Q r = return sludge flow rate (m 3 /d) X' = MLSS (kg/m 3 ) X' r = return sludge concentration (kg/m 3 ) Q s = sludge surplus (or excess) flow rate (m 3 /d)
This equilibrium formula for settling tanks is mostly calculated for the initial flows in m3/h.
This formula describes that the incoming amount of MLSS in a settler should be equivalent to the outcoming amount of MLSS via the return sludge flow. This equilibrium is only valid if the effluent water contains a low concentration in suspended solids. In normal conditions the excess amount is very low in comparison to the return amount, and for that reason many times the excess amount is neglected.
In that case the formula will be : (Q+Q r )(X') = (Q r X' r ) | https://en.wikipedia.org/wiki/Mixed_liquor_suspended_solids |
Mixed lymphocyte reaction (MLR) is a test used by pharmaceutical and biotech organizations to show the safety of a drug or implantable material. It is commonly used as part of the FDA clearance process. [ 1 ] Put simply, it is mixing populations of T-lymphocytes (category of white blood cells) together, and measuring the reaction that occurs. Technically, it is an ex-vivo cellular immune assay that occurs between two allogeneic lymphocyte populations (same species but genetically distinct). [ 2 ] In a one-way MLR, only one lymphocyte population can respond or proliferate. In a two-way MLR, both populations can proliferate. MLR’s are performed to assess how T-cells react to external stimuli. T cells are a type of white blood cell that scans for cellular abnormalities and infections. They are essential to human immunity. [ 3 ]
The MLR was first recognized when researchers mixed leukocytes from two unrelated donors in culture. [ 4 ] [ 5 ] After several days, lymphocytes underwent blast transformation, DNA synthesis and cellular proliferation in response to the major histocompatibility antigen ( MHC Class I and II) differences between the two cell populations designated as Responder and Stimulator cells. Responder cells proliferated without previous exposure to Stimulator MHC antigens. This response became quantifiable when incorporating radioactive [3H] labelled thymidine or 5-bromo-2’-deoxyuridine (BrdU) , into the mixed cell suspension. This cellular response to the histocompatibility antigens that occurs in the MLR is also involved in cell-mediated immune responses within an individual and offered an in vitro correlate of cellular immune function. [ 6 ] [ 7 ] Standard MLR assays were performed in humans and most other animal species. [ citation needed ]
The leukocyte subpopulations involved in the MLR were first characterized by using cells from neonatally thymectomized and bursectomized chickens. No MLR occurred when the Responder cells came from thymectomized animals, whereas bursectomized chicken leukocytes reacted in culture demonstrating that T-cells were the major cell type in Responder cell populations. [ 8 ]
Originally, this assay was used to study possible donor — recipient incompatibilities for graft transplants to help predict better outcomes. [ 9 ] However, the standard for graft matching now depends on a series of HLA -matching done with molecular typing methods. [ 10 ]
The assay set-up consists of purifying responder lymphocytes from peripheral blood, thymus, lymph nodes or spleen and co-culturing with stimulator cells. Stimulator cell populations that also contain T-cells (Two way mixed lymphocyte reaction) will replicate in the presence of the Responder cells, therefore for a One way mixed lymphocyte reaction, stimulator cells are prevented from replicating by irradiation or treatment with mitomycin C , a DNA crosslinker to prevent cell replication. Maximum measurable cellular proliferation occurs around 5–7 days. [ citation needed ]
For research purposes, the MLR cell-based assay continues to provide an in vitro correlate of T cell function. Further characterization of the lymphocytes, accessory cells (dendritic cells, macrophage ) and cytokines that participate in the MLR have been done as this assay continues to be used to define mechanisms for understanding cellular immune function in vitro. [ 11 ] | https://en.wikipedia.org/wiki/Mixed_lymphocyte_reaction |
Mixed oxides of nitrogen (MON) are solutions of dinitrogen trioxide (N 2 O 3 ) in dinitrogen tetroxide / nitrogen dioxide (N 2 O 4 and NO 2 ). It may be used as an oxidizing agent in rocket propulsion systems. [ 1 ]
Mixed oxides of nitrogen are produced by dissolving nitric oxide (NO) gas in liquid dinitrogen tetroxide. Nitric oxide reacts with nitrogen dioxide, present in dinitrogen tetroxide, to from dinitrogen trioxide. Resulting mixture is greenish blue, while dinitrogen tetroxide is colorless or brownish yellow. Liquid phase of MON contains no nitric oxide. [ 2 ]
N 2 O 4 ⇌ 2NO 2
NO 2 + NO ⇌ N 2 O 3
A broad range of compositions is available, and can be denoted as MON i , where i represents the percentage of nitric oxide in the mixture (e.g. MON3 contains 3% nitric oxide, MON25 25% nitric oxide). An upper limit is MON40 (40% by weight). In Europe MON 1.3 is mostly used for rocket propulsion systems, while NASA seems to prefer MON 3. A higher percentage of NO decreases the corrosiveness of the liquid, but decreases oxidation potential and increases costs.
The addition of nitric oxide also reduces the freezing point to a more desirable temperature. The freezing point of pure nitrogen tetroxide is −9 °C (16 °F), while MON3 is −15 °C (5 °F) and MON25 is −55 °C (−67 °F). [ 3 ] | https://en.wikipedia.org/wiki/Mixed_oxides_of_nitrogen |
Mixed potential theory is a theory used in electrochemistry that relates the potentials and currents from differing constituents into a 'weighted' potential at zero net current. In other words, it is an electrode potential resulting from a simultaneous action of more than a single redox couple , while the net electrode current is zero.
According to the IUPAC definition, [ 1 ] mixed potential is the potential of an electrode (against a suitable
reference electrode, often the standard hydrogen electrode ) when an appreciable fraction of the anodic or cathodic current arises from two or more different redox couples, but when the total current on the electrode remains at zero.
This electrochemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Mixed_potential_theory |
Mixed quantum-classical ( MQC ) dynamics is a class of computational theoretical chemistry methods tailored to simulate non- adiabatic (NA) processes in molecular and supramolecular chemistry . [ 1 ] Such methods are characterized by:
In the Born-Oppenheimer approximation , the ensemble of electrons of a molecule or supramolecular system can have several discrete states. The potential energy of each of these electronic states depends on the position of the nuclei, forming multidimensional surfaces .
Under usual conditions (room temperature, for instance), the molecular system is in the ground electronic state (the electronic state of lowest energy). In this stationary situation, nuclei and electrons are in equilibrium, and the molecule naturally vibrates near harmonically due to the zero-point energy .
Particle collisions and photons with wavelengths in the range from visible to X-ray can promote the electrons to electronically excited states. Such events create a non-equilibrium between nuclei and electrons, which leads to an ultrafast response (picosecond scale) of the molecular system. During the ultrafast evolution, the nuclei may reach geometric configurations where the electronic states mix , allowing the system to transfer to another state spontaneously. These state transfers are nonadiabatic phenomena.
Nonadiabatic dynamics is the field of computational chemistry that simulates such ultrafast nonadiabatic response.
In principle, the problem can be exactly addressed by solving the time-dependent Schrödinger equation (TDSE) for all particles (nuclei and electrons). Methods like the multiconfigurational self-consistent Hartree (MCTDH) have been developed to do such task. [ 2 ] Nevertheless, they are limited to small systems with two dozen degrees of freedom due to the enormous difficulties of developing multidimensional potential energy surfaces and the costs of the numerical integration of the quantum equations.
NA-MQC dynamics methods have been developed to reduce the burden of these simulations by profiting from the fact that the nuclear dynamics is near classical. [ 3 ] Treating the nuclei classically allows simulating the molecular system in full dimensionality. The impact of the underlying assumptions depends on each particular NA-MQC method.
Most of NA-MQC dynamics methods have been developed to simulate internal conversion (IC), the nonadiabatic transfer between states of the same spin multiplicity . The methods have been extended, however, to deal with other types of processes like intersystem crossing (ISC; transfer between states of different multiplicities) [ 4 ] and field-induced transfers. [ 5 ]
NA-MQC dynamics has been often used in theoretical investigations of photochemistry and femtochemistry , especially when time-resolved processes are relevant. [ 6 ] [ 7 ]
NA-MQC dynamics is a general class of methods developed since the 1970s. It encompasses:
The classical trajectories can be integrated with conventional methods, as the Verlet algorithm . Such integration requires the forces acting on the nuclei. They are proportional to the gradient of the potential energy of the electronic states and can be efficiently computed with diverse electronic structure methods for excited states, like the multireference configuration interaction (MRCI) or the linear-response time-dependent density functional theory (TDDFT).
In NA-MQC methods like FSSH or MFE, the trajectories are independent of each other. In such a case, they can be separately integrated and only grouped afterward for the statistical analysis of the results. In methods like CT-MQC or diverse TSH variants, [ 18 ] the trajectories are coupled and must be integrated simultaneously.
In NA-MQC dynamics, the electrons are usually treated by a local approximation of the TDSE, i.e., they depend only on the electronic forces and couplings at the instantaneous position of the nuclei.
There are three basic algorithms to recover nonadiabatic information in NA-MQC methods: [ 1 ]
NA-MQC dynamics are approximated methods to solve the time-dependent Schrödinger equation for a molecular system. Methods like TSH, in particular in the fewest switches surface hopping (FSSH) formulation, do not have an exact limit. [ 19 ] Other methods like MS or CT-MQC can in principle deliver the exact non-relativistic solution. [ 10 ] [ 11 ]
In the case of multiple spawning, it is hierarchically connected to MCTDH , [ 2 ] while CT-MQC is connected to the exact factorization method. [ 11 ]
The most common approach in NA-MQC dynamics is to compute the electronic properties on-the-fly, i.e., at each timestep of the trajectory integration. Such an approach has the advantage of not requiring pre-computed multidimensional potential energy surfaces. Nevertheless, the costs associated with the on-the-fly approach are significantly high, leading to a systematic level downgrade of the simulations. This downgrade has been shown to lead to qualitatively wrong results. [ 20 ]
The local approximation implied by the classical trajectories in NA-MQC dynamics also leads to failing in the description of non-local quantum effects, as tunneling and quantum interference. Some methods like MFE and FSSH are also affected by decoherence errors. [ 21 ] New algorithms have been developed to include tunneling [ 22 ] and decoherence effects. [ 23 ] [ 24 ] Global quantum effects can also be considered by applying quantum forces between trajectories. [ 11 ]
Survey of NA-MQC dynamics implementations in public software.
FSSH
a Development version. | https://en.wikipedia.org/wiki/Mixed_quantum-classical_dynamics |
In tensor analysis , a mixed tensor is a tensor which is neither strictly covariant nor strictly contravariant ; at least one of the indices of a mixed tensor will be a subscript (covariant) and at least one of the indices will be a superscript (contravariant).
A mixed tensor of type or valence ( M N ) {\textstyle {\binom {M}{N}}} , also written "type ( M , N )", with both M > 0 and N > 0, is a tensor which has M contravariant indices and N covariant indices. Such a tensor can be defined as a linear function which maps an ( M + N )-tuple of M one-forms and N vectors to a scalar .
Consider the following octet of related tensors: T α β γ , T α β γ , T α β γ , T α β γ , T α β γ , T α β γ , T α β γ , T α β γ . {\displaystyle T_{\alpha \beta \gamma },\ T_{\alpha \beta }{}^{\gamma },\ T_{\alpha }{}^{\beta }{}_{\gamma },\ T_{\alpha }{}^{\beta \gamma },\ T^{\alpha }{}_{\beta \gamma },\ T^{\alpha }{}_{\beta }{}^{\gamma },\ T^{\alpha \beta }{}_{\gamma },\ T^{\alpha \beta \gamma }.} The first one is covariant, the last one contravariant, and the remaining ones mixed. Notationally, these tensors differ from each other by the covariance/contravariance of their indices. A given contravariant index of a tensor can be lowered using the metric tensor g μν , and a given covariant index can be raised using the inverse metric tensor g μν . Thus, g μν could be called the index lowering operator and g μν the index raising operator .
Generally, the covariant metric tensor, contracted with a tensor of type ( M , N ), yields a tensor of type ( M − 1, N + 1), whereas its contravariant inverse, contracted with a tensor of type ( M , N ), yields a tensor of type ( M + 1, N − 1).
As an example, a mixed tensor of type (1, 2) can be obtained by raising an index of a covariant tensor of type (0, 3), T α β λ = T α β γ g γ λ , {\displaystyle T_{\alpha \beta }{}^{\lambda }=T_{\alpha \beta \gamma }\,g^{\gamma \lambda },} where T α β λ {\displaystyle T_{\alpha \beta }{}^{\lambda }} is the same tensor as T α β γ {\displaystyle T_{\alpha \beta }{}^{\gamma }} , because T α β λ δ λ γ = T α β γ , {\displaystyle T_{\alpha \beta }{}^{\lambda }\,\delta _{\lambda }{}^{\gamma }=T_{\alpha \beta }{}^{\gamma },} with Kronecker δ acting here like an identity matrix.
Likewise, T α λ γ = T α β γ g β λ , {\displaystyle T_{\alpha }{}^{\lambda }{}_{\gamma }=T_{\alpha \beta \gamma }\,g^{\beta \lambda },} T α λ ϵ = T α β γ g β λ g γ ϵ , {\displaystyle T_{\alpha }{}^{\lambda \epsilon }=T_{\alpha \beta \gamma }\,g^{\beta \lambda }\,g^{\gamma \epsilon },} T α β γ = g γ λ T α β λ , {\displaystyle T^{\alpha \beta }{}_{\gamma }=g_{\gamma \lambda }\,T^{\alpha \beta \lambda },} T α λ ϵ = g λ β g ϵ γ T α β γ . {\displaystyle T^{\alpha }{}_{\lambda \epsilon }=g_{\lambda \beta }\,g_{\epsilon \gamma }\,T^{\alpha \beta \gamma }.}
Raising an index of the metric tensor is equivalent to contracting it with its inverse, yielding the Kronecker delta , g μ λ g λ ν = g μ ν = δ μ ν , {\displaystyle g^{\mu \lambda }\,g_{\lambda \nu }=g^{\mu }{}_{\nu }=\delta ^{\mu }{}_{\nu },} so any mixed version of the metric tensor will be equal to the Kronecker delta, which will also be mixed. | https://en.wikipedia.org/wiki/Mixed_tensor |
According to the United States Environmental Protection Agency , mixed waste ( MW ) is a waste type defined as follows; "MW contains both hazardous waste (as defined by RCRA and its amendments) and radioactive waste (as defined by AEA and its amendments). It is jointly regulated by NRC or NRC's Agreement States and EPA or EPA's RCRA Authorized States. The fundamental and most comprehensive statutory definition is found in the Federal Facilities Compliance Act (FFCA) where Section 1004(41) was added to RCRA: "The term 'mixed waste' means waste that contains both hazardous waste and source, special nuclear , or byproduct material subject to the Atomic Energy Act of 1954 ."
Mixed waste is much more expensive to manage and dispose of than waste that is solely radioactive. Waste generators can avoid higher charge back costs by eliminating or minimizing the volume of mixed waste generated.
The EPA defines hazardous waste as the following: [ 1 ] A subset of solid wastes that pose substantial or potential threats to public health or the environment and meet any of the following criteria identified 40 CFR 260 and 261:
This radioactivity –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Mixed_waste_(radioactive/hazardous) |
Mixer settlers are a class of mineral process equipment used in the solvent extraction process. A mixer settler consists of a first stage that mixes the phases together followed by a quiescent settling stage that allows the phases to separate by gravity.
A mixing chamber where a mechanical agitator brings in intimate contact the feed solution and the solvent to carry out the transfer of solute(s). The mechanical agitator is equipped with a motor which drives a mixing and pumping turbine. This turbine draws the two phases from the settlers of the adjacent stages, mixes them, and transfers this emulsion to the associated settler.
The mixer may consists of one or multiple stages of mixing tanks. Common laboratory mixers consist of a single mixing stage, whereas industrial scale copper mixers may consist of up to three mixer stages where each stage performs a combined pumping and mixing action. Use of multiple stages allows a longer reaction time and also minimizes the short circuiting of unreacted material through the mixers. [ 1 ]
A settling chamber where the two phases separate by static decantation. Coalescence plates facilitate the separation of the emulsion into two phases (heavy and light). The two phases then pass to continuous stages by overflowing the light phase and heavy phase weirs. The height of the heavy phase weir can be adjusted in order to position the heavy/light interphase in the settling chamber based on the density of each one of the phases.
The settler is a calm pool downstream of the mixer where the liquids are allowed to separate by gravity. The liquids are then removed separately from the end of the mixer.
Industrial mixer settlers are commonly used in the copper , nickel , uranium , lanthanide , and cobalt hydrometallurgy industries, when solvent extraction processes are applied.
They are also used in the Nuclear reprocessing field to separate and purify primarily Uranium and Plutonium, removing the fission product impurities.
In the multiple countercurrent process, multiple mixer settlers are installed with mixing and settling chambers located at alternating ends for each stage (since the outlet of the settling sections feed the inlets of the adjacent stage's mixing sections). Mixer-settlers are used when a process requires longer residence times and when the solutions are easily separated by gravity. They require a large facility footprint, but do not require much headspace, and need limited remote maintenance capability for occasional replacement of mixing motors. (Colven, 1956; Davidson, 1957) [ 2 ]
The equipment units can be arrayed as:
In the case of oxide copper ore , a heap leaching pad will dissolve a dilute copper sulfate solution in a weak sulfuric acid solution. This pregnant leach solution (PLS) is pumped to an extraction mixer settler where it is mixed with the organic phase (a kerosene hosted extractant). The copper transfers to the organic phase, and the aqueous phase (now called raffinate) is pumped back to the heap to recover more copper.
In a high-chloride environment typical of Chilean copper mines, a wash stage will rinse any residual pregnant solution entrained in the organic with clean water.
The copper is then stripped from organic phase in the strip stage into a strong sulfuric acid solution suitable for electrowinning . This strong acid solution is called barren electrolyte when it enters the cell, and strong electrolyte when it is copper bearing after reacting in the cell. | https://en.wikipedia.org/wiki/Mixer-settler |
In mathematics , mixing is an abstract concept originating from physics : the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: e.g. mixing paint, mixing drinks, industrial mixing .
The concept appears in ergodic theory —the study of stochastic processes and measure-preserving dynamical systems . Several different definitions for mixing exist, including strong mixing , weak mixing and topological mixing , with the last not requiring a measure to be defined. Some of the different definitions of mixing can be arranged in a hierarchical order; thus, strong mixing implies weak mixing. Furthermore, weak mixing (and thus also strong mixing) implies ergodicity : that is, every system that is weakly mixing is also ergodic (and so one says that mixing is a "stronger" condition than ergodicity).
The mathematical definition of mixing aims to capture the ordinary every-day process of mixing, such as mixing paints, drinks, cooking ingredients, industrial process mixing , smoke in a smoke-filled room, and so on. To provide the mathematical rigor, such descriptions begin with the definition of a measure-preserving dynamical system , written as ( X , A , μ , T ) {\displaystyle (X,{\mathcal {A}},\mu ,T)} .
The set X {\displaystyle X} is understood to be the total space to be filled: the mixing bowl, the smoke-filled room, etc. The measure μ {\displaystyle \mu } is understood to define the natural volume of the space X {\displaystyle X} and of its subspaces. The collection of subspaces is denoted by A {\displaystyle {\mathcal {A}}} , and the size of any given subset A ⊂ X {\displaystyle A\subset X} is μ ( A ) {\displaystyle \mu (A)} ; the size is its volume. Naively, one could imagine A {\displaystyle {\mathcal {A}}} to be the power set of X {\displaystyle X} ; this doesn't quite work, as not all subsets of a space have a volume (famously, the Banach–Tarski paradox ). Thus, conventionally, A {\displaystyle {\mathcal {A}}} consists of the measurable subsets—the subsets that do have a volume. It is always taken to be a Borel set —the collection of subsets that can be constructed by taking intersections , unions and set complements ; these can always be taken to be measurable.
The time evolution of the system is described by a map T : X → X {\displaystyle T:X\to X} . Given some subset A ⊂ X {\displaystyle A\subset X} , its map T ( A ) {\displaystyle T(A)} will in general be a deformed version of A {\displaystyle A} – it is squashed or stretched, folded or cut into pieces. Mathematical examples include the baker's map and the horseshoe map , both inspired by bread -making. The set T ( A ) {\displaystyle T(A)} must have the same volume as A {\displaystyle A} ; the squashing/stretching does not alter the volume of the space, only its distribution. Such a system is "measure-preserving" (area-preserving, volume-preserving).
A formal difficulty arises when one tries to reconcile the volume of sets with the need to preserve their size under a map. The problem arises because, in general, several different points in the domain of a function can map to the same point in its range; that is, there may be x ≠ y {\displaystyle x\neq y} with T ( x ) = T ( y ) {\displaystyle T(x)=T(y)} . Worse, a single point x ∈ X {\displaystyle x\in X} has no size. These difficulties can be avoided by working with the inverse map T − 1 : A → A {\displaystyle T^{-1}:{\mathcal {A}}\to {\mathcal {A}}} ; it will map any given subset A ⊂ X {\displaystyle A\subset X} to the parts that were assembled to make it: these parts are T − 1 ( A ) ∈ A {\displaystyle T^{-1}(A)\in {\mathcal {A}}} . It has the important property of not "losing track" of where things came from. More strongly, it has the important property that any (measure-preserving) map A → A {\displaystyle {\mathcal {A}}\to {\mathcal {A}}} is the inverse of some map X → X {\displaystyle X\to X} . The proper definition of a volume-preserving map is one for which μ ( A ) = μ ( T − 1 ( A ) ) {\displaystyle \mu (A)=\mu (T^{-1}(A))} because T − 1 ( A ) {\displaystyle T^{-1}(A)} describes all the pieces-parts that A {\displaystyle A} came from.
One is now interested in studying the time evolution of the system. If a set A ∈ A {\displaystyle A\in {\mathcal {A}}} eventually visits all of X {\displaystyle X} over a long period of time (that is, if ∪ k = 1 n T k ( A ) {\displaystyle \cup _{k=1}^{n}T^{k}(A)} approaches all of X {\displaystyle X} for large n {\displaystyle n} ), the system is said to be ergodic . If every set A {\displaystyle A} behaves in this way, the system is a conservative system , placed in contrast to a dissipative system , where some subsets A {\displaystyle A} wander away , never to be returned to. An example would be water running downhill—once it's run down, it will never come back up again. The lake that forms at the bottom of this river can, however, become well-mixed. The ergodic decomposition theorem states that every ergodic system can be split into two parts: the conservative part, and the dissipative part.
Mixing is a stronger statement than ergodicity. Mixing asks for this ergodic property to hold between any two sets A , B {\displaystyle A,B} , and not just between some set A {\displaystyle A} and X {\displaystyle X} . That is, given any two sets A , B ∈ A {\displaystyle A,B\in {\mathcal {A}}} , a system is said to be (topologically) mixing if there is an integer N {\displaystyle N} such that, for all A , B {\displaystyle A,B} and n > N {\displaystyle n>N} , one has that T n ( A ) ∩ B ≠ ∅ {\displaystyle T^{n}(A)\cap B\neq \varnothing } . Here, ∩ {\displaystyle \cap } denotes set intersection and ∅ {\displaystyle \varnothing } is the empty set .
The above definition of topological mixing should be enough to provide an informal idea of mixing (it is equivalent to the formal definition, given below). However, it made no mention of the volume of A {\displaystyle A} and B {\displaystyle B} , and, indeed, there is another definition that explicitly works with the volume. Several, actually; one has both strong mixing and weak mixing; they are inequivalent, although a strong mixing system is always weakly mixing. The measure-based definitions are not compatible with the definition of topological mixing: there are systems which are one, but not the other. The general situation remains cloudy: for example, given three sets A , B , C ∈ A {\displaystyle A,B,C\in {\mathcal {A}}} , one can define 3-mixing. As of 2020, it is not known if 2-mixing implies 3-mixing. (If one thinks of ergodicity as "1-mixing", then it is clear that 1-mixing does not imply 2-mixing; there are systems that are ergodic but not mixing.)
The concept of strong mixing is made in reference to the volume of a pair of sets. Consider, for example, a set A {\displaystyle A} of colored dye that is being mixed into a cup of some sort of sticky liquid, say, corn syrup, or shampoo, or the like. Practical experience shows that mixing sticky fluids can be quite hard: there is usually some corner of the container where it is hard to get the dye mixed into. Pick as set B {\displaystyle B} that hard-to-reach corner. The question of mixing is then, can A {\displaystyle A} , after a long enough period of time, not only penetrate into B {\displaystyle B} but also fill B {\displaystyle B} with the same proportion as it does elsewhere?
One phrases the definition of strong mixing as the requirement that
The time parameter n {\displaystyle n} serves to separate A {\displaystyle A} and B {\displaystyle B} in time, so that one is mixing A {\displaystyle A} while holding the test volume B {\displaystyle B} fixed. The product μ ( A ) μ ( B ) {\displaystyle \mu (A)\mu (B)} is a bit more subtle. Imagine that the volume B {\displaystyle B} is 10% of the total volume, and that the volume of dye A {\displaystyle A} will also be 10% of the grand total. If A {\displaystyle A} is uniformly distributed, then it is occupying 10% of B {\displaystyle B} , which itself is 10% of the total, and so, in the end, after mixing, the part of A {\displaystyle A} that is in B {\displaystyle B} is 1% of the total volume. That is, μ ( after-mixing ( A ) ∩ B ) = μ ( A ) μ ( B ) . {\displaystyle \mu \left({\mbox{after-mixing}}(A)\cap B\right)=\mu (A)\mu (B).} This product-of-volumes has more than passing resemblance to Bayes' theorem in probabilities; this is not an accident, but rather a consequence that measure theory and probability theory are the same theory: they share the same axioms (the Kolmogorov axioms ), even as they use different notation.
The reason for using T − n A {\displaystyle T^{-n}A} instead of T n A {\displaystyle T^{n}A} in the definition is a bit subtle, but it follows from the same reasons why T − 1 A {\displaystyle T^{-1}A} was used to define the concept of a measure-preserving map. When looking at how much dye got mixed into the corner B {\displaystyle B} , one wants to look at where that dye "came from" (presumably, it was poured in at the top, at some time in the past). One must be sure that every place it might have "come from" eventually gets mixed into B {\displaystyle B} .
Let ( X , A , μ , T ) {\displaystyle (X,{\mathcal {A}},\mu ,T)} be a measure-preserving dynamical system , with T being the time-evolution or shift operator . The system is said to be strong mixing if, for any A , B ∈ A {\displaystyle A,B\in {\mathcal {A}}} , one has
For shifts parametrized by a continuous variable instead of a discrete integer n , the same definition applies, with T − n {\displaystyle T^{-n}} replaced by T g {\displaystyle T_{g}} with g being the continuous-time parameter.
A dynamical system is said to be weak mixing if one has
In other words, T {\displaystyle T} is strong mixing if μ ( A ∩ T − n B ) − μ ( A ) μ ( B ) → 0 {\displaystyle \mu (A\cap T^{-n}B)-\mu (A)\mu (B)\to 0} in the usual sense, weak mixing if
in the Cesàro sense, and ergodic if μ ( A ∩ T − n B ) → μ ( A ) μ ( B ) {\displaystyle \mu \left(A\cap T^{-n}B\right)\to \mu (A)\mu (B)} in the Cesàro sense. Hence, strong mixing implies weak mixing, which implies ergodicity. However, the converses are not true: There exist ergodic dynamical systems which are not weakly mixing, and weakly mixing dynamical systems which are not strongly mixing. The Chacon system was historically the first example given of a system that is weak mixing but not strong mixing. [ 1 ]
Theorem. Weak mixing implies ergodicity.
Proof. If the action of the map decomposes into two components A , B {\displaystyle A,B} , then we have μ ( T − n ( A ) ∩ B ) = μ ( A ∩ B ) = μ ( ∅ ) = 0 {\displaystyle \mu (T^{-n}(A)\cap B)=\mu (A\cap B)=\mu (\emptyset )=0} , so weak mixing implies | μ ( A ∩ B ) − μ ( A ) μ ( B ) | = 0 {\displaystyle \vert \mu (A\cap B)-\mu (A)\mu (B)\vert =0} , so one of A , B {\displaystyle A,B} has zero measure, and the other one has full measure.
Given a topological space, such as the unit interval (whether it has its end points or not), we can construct a measure on it by taking the open sets, then take their unions, complements, unions, complements, and so on to infinity , to obtain all the Borel sets . Next, we define a measure μ {\displaystyle \mu } on the Borel sets, then add in all the subsets of measure-zero ("negligible sets"). This is how we obtain the Lebesgue measure and the Lebesgue measurable sets.
In most applications of ergodic theory, the underlying space is almost-everywhere isomorphic to an open subset of some R n {\displaystyle \mathbb {R} ^{n}} , and so it is a Lebesgue measure space. Verifying strong-mixing can be simplified if we only need to check a smaller set of measurable sets.
A covering family C {\displaystyle {\mathcal {C}}} is a set of measurable sets, such that any open set is a disjoint union of sets in it. Compare this with base in topology , which is less restrictive as it allows non-disjoint unions.
Theorem. For Lebesgue measure spaces, if T {\displaystyle T} is measure-preserving, and lim n μ ( T − n ( A ) ∩ B ) = μ ( A ) μ ( B ) {\displaystyle \lim _{n}\mu (T^{-n}(A)\cap B)=\mu (A)\mu (B)} for all A , B {\displaystyle A,B} in a covering family, then T {\displaystyle T} is strong mixing.
Proof. Extend the mixing equation from all A , B {\displaystyle A,B} in the covering family, to all open sets by disjoint union, to all closed sets by taking the complement, to all measurable sets by using the regularity of Lebesgue measure to approximate any set with open and closed sets. Thus, lim n μ ( T − n ( A ) ∩ B ) = μ ( A ) μ ( B ) {\displaystyle \lim _{n}\mu (T^{-n}(A)\cap B)=\mu (A)\mu (B)} for all measurable A , B {\displaystyle A,B} .
The properties of ergodicity, weak mixing and strong mixing of a measure-preserving dynamical system can also be characterized by the average of observables. By von Neumann's ergodic theorem, ergodicity of a dynamical system ( X , A , μ , T ) {\displaystyle (X,{\mathcal {A}},\mu ,T)} is equivalent to the property that, for any function f ∈ L 2 ( X , μ ) {\displaystyle f\in L^{2}(X,\mu )} , the sequence ( f ∘ T n ) n ≥ 0 {\displaystyle (f\circ T^{n})_{n\geq 0}} converges strongly and in the sense of Cesàro to ∫ X f d μ {\displaystyle \int _{X}f\,d\mu } , i.e.,
A dynamical system ( X , A , μ , T ) {\displaystyle (X,{\mathcal {A}},\mu ,T)} is weakly mixing if, for any functions f {\displaystyle f} and g ∈ L 2 ( X , μ ) , {\displaystyle g\in L^{2}(X,\mu ),}
A dynamical system ( X , A , μ , T ) {\displaystyle (X,{\mathcal {A}},\mu ,T)} is strongly mixing if, for any function f ∈ L 2 ( X , μ ) {\displaystyle f\in L^{2}(X,\mu )} , the sequence ( f ∘ T n ) n ≥ 0 {\displaystyle (f\circ T^{n})_{n\geq 0}} converges weakly to ∫ X f d μ {\displaystyle \int _{X}f\,d\mu } , i.e., for any function g ∈ L 2 ( X , μ ) , {\displaystyle g\in L^{2}(X,\mu ),}
Since the system is assumed to be measure preserving, this last line is equivalent to saying that the covariance lim n → ∞ Cov ( f ∘ T n , g ) = 0 {\displaystyle \lim _{n\to \infty }\operatorname {Cov} (f\circ T^{n},g)=0} , so that the random variables f ∘ T n {\displaystyle f\circ T^{n}} and g {\displaystyle g} become orthogonal as n {\displaystyle n} grows. Actually, since this works for any function g {\displaystyle g} , one can informally see mixing as the property that the random variables f ∘ T n {\displaystyle f\circ T^{n}} and g {\displaystyle g} become independent as n {\displaystyle n} grows.
Given two measured dynamical systems ( X , μ , T ) {\displaystyle (X,\mu ,T)} and ( Y , ν , S ) , {\displaystyle (Y,\nu ,S),} one can construct a dynamical system ( X × Y , μ ⊗ ν , T × S ) {\displaystyle (X\times Y,\mu \otimes \nu ,T\times S)} on the Cartesian product by defining ( T × S ) ( x , y ) = ( T ( x ) , S ( y ) ) . {\displaystyle (T\times S)(x,y)=(T(x),S(y)).} We then have the following characterizations of weak mixing: [ 2 ]
The definition given above is sometimes called strong 2-mixing , to distinguish it from higher orders of mixing. A strong 3-mixing system may be defined as a system for which
holds for all measurable sets A , B , C . We can define strong k-mixing similarly. A system which is strong k - mixing for all k = 2,3,4,... is called mixing of all orders .
It is unknown whether strong 2-mixing implies strong 3-mixing. It is known that strong m -mixing implies ergodicity .
Irrational rotations of the circle, and more generally irreducible translations on a torus, are ergodic but neither strongly nor weakly mixing with respect to the Lebesgue measure.
Many maps considered as chaotic are strongly mixing for some well-chosen invariant measure, including: the dyadic map , Arnold's cat map , horseshoe maps , Kolmogorov automorphisms , and the Anosov flow (the geodesic flow on the unit tangent bundle of compact manifolds of negative curvature .)
The dyadic map is "shift to left in binary". In general, for any n ∈ { 2 , 3 , … } {\displaystyle n\in \{2,3,\dots \}} , the "shift to left in base n {\displaystyle n} " map T ( x ) = n x mod 1 {\displaystyle T(x)=nx{\bmod {1}}} is strongly mixing on the covering family { ( k n s , k + 1 n s ) ∖ Q : s ≥ 0 , ≤ k < n s } {\displaystyle \left\{\left({\tfrac {k}{n^{s}}},{\tfrac {k+1}{n^{s}}}\right)\smallsetminus \mathbb {Q} :s\geq 0,\leq k<n^{s}\right\}} , therefore it is strongly mixing on ( 0 , 1 ) ∖ Q {\displaystyle (0,1)\smallsetminus \mathbb {Q} } , and therefore it is strongly mixing on [ 0 , 1 ] {\displaystyle [0,1]} .
Similarly, for any finite or countable alphabet Σ {\displaystyle \Sigma } , we can impose a discrete probability distribution on it, then consider the probability distribution on the "coin flip" space, where each "coin flip" can take results from Σ {\displaystyle \Sigma } . We can either construct the singly-infinite space Σ N {\displaystyle \Sigma ^{\mathbb {N} }} or the doubly-infinite space Σ Z {\displaystyle \Sigma ^{\mathbb {Z} }} . In both cases, the shift map (one letter to the left) is strongly mixing, since it is strongly mixing on the covering family of cylinder sets. The Baker's map is isomorphic to a shift map, so it is strongly mixing.
A form of mixing may be defined without appeal to a measure , using only the topology of the system. A continuous map f : X → X {\displaystyle f:X\to X} is said to be topologically transitive if, for every pair of non-empty open sets A , B ⊂ X {\displaystyle A,B\subset X} , there exists an integer n such that
where f n {\displaystyle f^{n}} is the n th iterate of f . In the operator theory , a topologically transitive bounded linear operator (a continuous linear map on a topological vector space ) is usually called hypercyclic operator . A related idea is expressed by the wandering set .
Lemma: If X is a complete metric space with no isolated point , then f is topologically transitive if and only if there exists a hypercyclic point x ∈ X {\displaystyle x\in X} , that is, a point x such that its orbit { f n ( x ) : n ∈ N } {\displaystyle \{f^{n}(x):n\in \mathbb {N} \}} is dense in X .
A system is said to be topologically mixing if, given open sets A {\displaystyle A} and B {\displaystyle B} , there exists an integer N , such that, for all n > N {\displaystyle n>N} , one has
For a continuous-time system, f n {\displaystyle f^{n}} is replaced by the flow φ g {\displaystyle \varphi _{g}} , with g being the continuous parameter, with the requirement that a non-empty intersection hold for all ‖ g ‖ > N {\displaystyle \Vert g\Vert >N} .
A weak topological mixing is one that has no non-constant continuous (with respect to the topology) eigenfunctions of the shift operator.
Topological mixing neither implies, nor is implied by either weak or strong mixing: there are examples of systems that are weak mixing but not topologically mixing, and examples that are topologically mixing but not strong mixing.
Let ( X t ) − ∞ < t < ∞ {\displaystyle (X_{t})_{-\infty <t<\infty }} be a stochastic process on a probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P} )} . The sequence space into which the process maps can be endowed with a topology, the product topology . The open sets of this topology are called cylinder sets . These cylinder sets generate a σ-algebra , the Borel σ-algebra ; this is the smallest σ-algebra that contains the topology.
Define a function α {\displaystyle \alpha } , called the strong mixing coefficient , as
for all − ∞ < s < ∞ {\displaystyle -\infty <s<\infty } . The symbol X a b {\displaystyle X_{a}^{b}} , with − ∞ ≤ a ≤ b ≤ ∞ {\displaystyle -\infty \leq a\leq b\leq \infty } denotes a sub-σ-algebra of the σ-algebra; it is the set of cylinder sets that are specified between times a and b , i.e. the σ-algebra generated by { X a , X a + 1 , … , X b } {\displaystyle \{X_{a},X_{a+1},\ldots ,X_{b}\}} .
The process ( X t ) − ∞ < t < ∞ {\displaystyle (X_{t})_{-\infty <t<\infty }} is said to be strongly mixing if α ( s ) → 0 {\displaystyle \alpha (s)\to 0} as s → ∞ {\displaystyle s\to \infty } . That is to say, a strongly mixing process is such that, in a way that is uniform over all times t {\displaystyle t} and all events, the events before time t {\displaystyle t} and the events after time t + s {\displaystyle t+s} tend towards being independent as s → ∞ {\displaystyle s\to \infty } ; more colloquially, the process, in a strong sense, forgets its history.
Suppose ( X t ) {\displaystyle (X_{t})} were a stationary Markov process with stationary distribution Q {\displaystyle \mathbb {Q} } and let L 2 ( Q ) {\displaystyle L^{2}(\mathbb {Q} )} denote the space of Borel-measurable functions that are square-integrable with respect to the measure Q {\displaystyle \mathbb {Q} } . Also let
denote the conditional expectation operator on L 2 ( Q ) . {\displaystyle L^{2}(\mathbb {Q} ).} Finally, let
denote the space of square-integrable functions with mean zero.
The ρ -mixing coefficients of the process { x t } are
The process is called ρ -mixing if these coefficients converge to zero as t → ∞ , and “ ρ -mixing with exponential decay rate” if ρ t < e − δt for some δ > 0 . For a stationary Markov process, the coefficients ρ t may either decay at an exponential rate, or be always equal to one. [ 3 ]
The α -mixing coefficients of the process { x t } are
The process is called α -mixing if these coefficients converge to zero as t → ∞ , it is " α -mixing with exponential decay rate" if α t < γe − δt for some δ > 0 , and it is α -mixing with a sub-exponential decay rate if α t < ξ ( t ) for some non-increasing function ξ {\displaystyle \xi } satisfying
as t → ∞ {\displaystyle t\to \infty } . [ 3 ]
The α -mixing coefficients are always smaller than the ρ -mixing ones: α t ≤ ρ t , therefore if the process is ρ -mixing, it will necessarily be α -mixing too. However, when ρ t = 1 , the process may still be α -mixing, with sub-exponential decay rate.
The β -mixing coefficients are given by
The process is called β -mixing if these coefficients converge to zero as t → ∞ , it is β -mixing with an exponential decay rate if β t < γe − δt for some δ > 0 , and it is β -mixing with a sub-exponential decay rate if β t ξ ( t ) → 0 as t → ∞ for some non-increasing function ξ {\displaystyle \xi } satisfying
as t → ∞ {\displaystyle t\to \infty } . [ 3 ]
A strictly stationary Markov process is β -mixing if and only if it is an aperiodic recurrent Harris chain . The β -mixing coefficients are always bigger than the α -mixing ones, so if a process is β -mixing it will also be α -mixing. There is no direct relationship between β -mixing and ρ -mixing: neither of them implies the other. | https://en.wikipedia.org/wiki/Mixing_(physics) |
In industrial process engineering , mixing is a unit operation that involves manipulation of a heterogeneous physical system with the intent to make it more homogeneous . Familiar examples include pumping of the water in a swimming pool to homogenize the water temperature, and the stirring of pancake batter to eliminate lumps (deagglomeration).
Mixing is performed to allow heat and/or mass transfer to occur between one or more streams, components or phases. Modern industrial processing almost always involves some form of mixing. [ 1 ] Some classes of chemical reactors are also mixers.
With the right equipment, it is possible to mix a solid, liquid or gas into another solid, liquid or gas. A biofuel fermenter may require the mixing of microbes, gases and liquid medium for optimal yield; organic nitration requires concentrated (liquid) nitric and sulfuric acids to be mixed with a hydrophobic organic phase; production of pharmaceutical tablets requires blending of solid powders.
The opposite of mixing is segregation . A classical example of segregation is the brazil nut effect .
The mathematics of mixing is highly abstract, and is a part of ergodic theory , itself a part of chaos theory .
The type of operation and equipment used during mixing depends on the state of materials being mixed (liquid, semi-solid, or solid) and the miscibility of the materials being processed. In this context, the act of mixing may be synonymous with stirring-, or kneading -processes. [ 1 ]
Mixing of liquids occurs frequently in process engineering. The nature of liquids to blend determines the equipment used. Single-phase blending tends to involve low-shear, high-flow mixers to cause liquid engulfment, while multi-phase mixing generally requires the use of high-shear, low-flow mixers to create droplets of one liquid in laminar , turbulent or transitional flow regimes, depending on the Reynolds number of the flow. Turbulent or transitional mixing is frequently conducted with turbines or impellers ; laminar mixing is conducted with helical ribbon or anchor mixers. [ 2 ]
Mixing of liquids that are miscible or at least soluble in each other occurs frequently in engineering (and in everyday life). An everyday example would be the addition of milk or cream to tea or coffee. Since both liquids are water-based, they dissolve easily in one another. The momentum of the liquid being added is sometimes enough to cause enough turbulence to mix the two, since the viscosity of both liquids is relatively low. If necessary, a spoon or paddle could be used to complete the mixing process. Blending in a more viscous liquid, such as honey , requires more mixing power per unit volume to achieve the same homogeneity in the same amount of time. [ citation needed ]
Dry blenders are a type of industrial mixer which are typically used to blend multiple dry components until they are homogeneous . Often minor liquid additions are made to the dry blend to modify the product formulation. Blending times using dry ingredients are often short (15–30 minutes) but are somewhat dependent upon the varying percentages of each component, and the difference in the bulk densities of each. Ribbon, paddle, tumble and vertical blenders are available. Many products including pharmaceuticals , foods , chemicals , fertilizers , plastics , pigments , and cosmetics are manufactured in these designs. Dry blenders range in capacity from half-cubic-foot laboratory models to 500-cubic-foot production units. A wide variety of horsepower -and-speed combinations and optional features such as sanitary finishes, vacuum construction, special valves and cover openings are offered by most manufacturers.
Blending powders is one of the oldest unit-operations in the solids handling industries. For many decades powder blending has been used just to homogenize bulk materials. Many different machines have been designed to handle materials with various bulk solids properties. On the basis of the practical experience gained with these different machines, engineering knowledge has been developed to construct reliable equipment and to predict scale-up and mixing behavior. Nowadays the same mixing technologies are used for many more applications: to improve product quality, to coat particles, to fuse materials, to wet, to disperse in liquid, to agglomerate, to alter functional material properties, etc.
This wide range of applications of mixing equipment requires a high level of knowledge, long time experience and extended test facilities to come to the optimal selection of equipment and processes.
Solid-solid mixing can be performed either in batch mixers, which is the simpler form of mixing, or in certain cases in continuous dry-mix, more complex but which provide interesting advantages in terms of segregation, capacity and validation. [ 3 ] One example of a solid–solid mixing process is mulling foundry molding sand, where sand, bentonite clay , fine coal dust and water are mixed to a plastic , moldable and reusable mass, applied for molding and pouring molten metal to obtain sand castings that are metallic parts for automobile, machine building, construction or other industries.
In powder two different dimensions in the mixing process can be determined: convective mixing and intensive mixing. [ 4 ] In the case of convective mixing material in the mixer is transported from one location to another. This type of mixing leads to a less ordered state inside the mixer, the components that must be mixed are distributed over the other components. With progressing time the mixture becomes more randomly ordered. After a certain mixing time the ultimate random state is reached. Usually this type of mixing is applied for free-flowing and coarse materials.
Possible threats during macro mixing is the de-mixing of the components, since differences in size, shape or density of the different particles can lead to segregation.
When materials are cohesive, which is the case with e.g. fine particles and also with wet material, convective mixing is no longer sufficient to obtain a randomly ordered mixture. The relative strong inter-particle forces form lumps, which are not broken up by the mild transportation forces in the convective mixer. To decrease the lump size additional forces are necessary; i.e. more energy intensive mixing is required. These additional forces can either be impact forces or shear forces.
Liquid–solid mixing is typically done to suspend coarse free-flowing solids, or to break up lumps of fine agglomerated solids. An example of the former is the mixing granulated sugar into water; an example of the latter is the mixing of flour or powdered milk into water. In the first case, the particles can be lifted into suspension (and separated from one another) by bulk motion of the fluid; in the second, the mixer itself (or the high shear field near it) must destabilize the lumps and cause them to disintegrate. [ citation needed ]
One example of a solid–liquid mixing process in industry is concrete mixing, where cement, sand, small stones or gravel and water are commingled to a homogeneous self-hardening mass , used in the construction industry. [ citation needed ]
Suspension of solids into a liquid is done to improve the rate of mass transfer between the solid and the liquid. Examples include dissolving a solid reactant into a solvent, or suspending catalyst particles in liquid to improve the flow of reactants and products to and from the particles. The associated eddy diffusion increases the rate of mass transfer within the bulk of the fluid, and the convection of material away from the particles decreases the size of the boundary layer , where most of the resistance to mass transfer occurs. Axial-flow impellers are preferred for solid suspension because solid suspension needs momentum rather than shear, although radial-flow impellers can be used in a tank with baffles, which converts some of the rotational motion into vertical motion. When the solid is denser than the liquid (and therefore collects at the bottom of the tank), the impeller is rotated so that the fluid is pushed downwards; when the solid is less dense than the liquid (and therefore floats on top), the impeller is rotated so that the fluid is pushed upwards (though this is relatively rare). The equipment preferred for solid suspension produces large volumetric flows but not necessarily high shear; high flow-number turbine impellers, such as hydrofoils, are typically used. Multiple turbines mounted on the same shaft can reduce power draw. [ 5 ]
The degree of homogeneity of a solid-liquid suspension can be described by the RSD ( Relative Standard Deviation of the solid volume fraction field in the mixing tank). A perfect suspension would have a RSD of 0% but in practice, a RSD inferior or equal to 20% can be sufficient for the suspension to be considered homogeneous, [ 7 ] although this is case-dependent. The RSD can be obtained by experimental measurements or by calculations.
Measurements can be performed at full scale but this is generally unpractical, so it is common to perform measurements at small scale and use a "scale-up" criterion to extrapolate the RSD from small to full scale.
Calculations can be performed using a computational fluid dynamics software or by using correlations built on theoretical developments, experimental measurements and/or computational fluid dynamics data.
Computational fluid dynamics calculations are quite accurate and can accommodate virtually any tank and agitator designs, but they require expertise and long computation time. Correlations are easy to use but are less accurate and don't cover any possible designs. The most popular correlation is the ‘just suspended speed’ correlation published by Zwietering (1958). [ 8 ] It's an easy to use correlation but it is not meant for homogeneous suspension. It only provides a crude estimate of the stirring speed for ‘bad’ quality suspensions (partial suspensions) where no particle remains at the bottom for more than 1 or 2 seconds. Another equivalent correlation is the correlation from Mersmann (1998). [ 9 ] For ‘good’ quality suspensions, some examples of useful correlations can be found in the publications of Barresi (1987), [ 10 ] Magelli (1991), [ 11 ] Cekinski (2010) [ 12 ] or Macqueron (2017). [ 6 ] Machine learning can also be used to build models way more accurate than "classical" correlations. [ 6 ] [ 13 ]
Very fine powders, such as titanium dioxide pigments, and materials that have been spray dried may agglomerate or form lumps during transportation and storage. Starchy materials or those that form gels when exposed to solvent can form lumps that are wetted on the outside but dry on the inside. These types of materials are not easily mixed into liquid with the types of mixers preferred for solid suspension because the agglomerate particles must be subjected to intense shear to be broken up. In some ways, deagglomeration of solids is similar to the blending of immiscible liquids, except for the fact that coalescence is usually not a problem. An everyday example of this type of mixing is the production of milkshakes from liquid milk and solid ice cream. [ citation needed ]
Liquids and gases are typically mixed to allow mass transfer to occur. For instance, in the case of air stripping , gas is used to remove volatiles from a liquid. Typically, a packed column is used for this purpose, with the packing acting as a motionless mixer and the air pump providing the driving force. When a tank and impeller are used, the objective is typically to ensure that the gas bubbles remain in contact with the liquid for as long as possible. This is especially important if the gas is expensive, such as pure oxygen , or diffuses slowly into the liquid. Mixing in a tank is also useful when a (relatively) slow chemical reaction is occurring in the liquid phase, and so the concentration difference in the thin layer near the bubble is close to that of the bulk. This reduces the driving force for mass transfer. If there is a (relatively) fast chemical reaction in the liquid phase, it is sometimes advantageous to disperse but not recirculate the gas bubbles, ensuring that they are in plug flow and can transfer mass more efficiently. [ citation needed ]
Rushton turbines have been traditionally used to disperse gases into liquids, but newer options, such as the Smith turbine and Bakker turbine are becoming more prevalent. [ 14 ] One of the issues is that as the gas flow increases, more and more of the gas accumulates in the low pressure zones behind the impeller blades, which reduces the power drawn by the mixer (and therefore its effectiveness). Newer designs, such as the GDX impeller, have nearly eliminated this problem. [ citation needed ]
Gas–solid mixing may be conducted to transport powders or small particulate solids from one place to another, or to mix gaseous reactants with solid catalyst particles. In either case, the turbulent eddies of the gas must provide enough force to suspend the solid particles, which otherwise sink under the force of gravity . The size and shape of the particles is an important consideration, since different particles have different drag coefficients , and particles made of different materials have different densities .
A common unit operation the process industry uses to separate gases and solids is the cyclone , which slows the gas and causes the particles to settle out. [ citation needed ]
Multiphase mixing occurs when solids, liquids and gases are combined in one step. This may occur as part of a catalytic chemical process, in which liquid and gaseous reagents must be combined with a solid catalyst (such as hydrogenation ); or in fermentation, where solid microbes and the gases they require must be well-distributed in a liquid medium. The type of mixer used depends upon the properties of the phases. In some cases, the mixing power is provided by the gas itself as it moves up through the liquid, entraining liquid with the bubble plume. This draws liquid upwards inside the plume, and causes liquid to fall outside the plume. If the viscosity of the liquid is too high to allow for this (or if the solid particles are too heavy), an impeller may be needed to keep the solid particles suspended. [ citation needed ]
For liquid mixing, the nomenclature is rather standardized:
Many of the equations used for determining the output of mixers are empirically derived, or contain empirically derived constants. Since mixers operate in the turbulent regime, many of the equations are approximations that are considered acceptable for most engineering purposes.
When a mixing impeller rotates in the fluid, it generates a combination of flow and shear. The impeller generated flow can be calculated with the following equation:
Q = F l ∗ N ∗ D 3 {\displaystyle Q=Fl*N*D^{3}}
Flow numbers for impellers have been published in the North American Mixing Forum sponsored Handbook of Industrial Mixing. [ 15 ]
The power required to rotate an impeller can be calculated using the following equations:
P = P o ρ N 3 D 5 {\displaystyle P=P_{o}\rho N^{3}D^{5}} (Turbulent regime) [ 16 ]
P = K p μ N 2 D 3 {\displaystyle P=K_{p}\mu N^{2}D^{3}} (Laminar regime)
P o {\displaystyle P_{o}} is the (dimensionless) power number, which is a function of impeller geometry; ρ {\displaystyle \rho } is the density of the fluid; N {\displaystyle N} is the rotational speed, typically rotations per second; D {\displaystyle D} is the diameter of the impeller; K p {\displaystyle K_{p}} is the laminar power constant; and μ {\displaystyle \mu } is the viscosity of the fluid. Note that the mixer power is strongly dependent upon the rotational speed and impeller diameter, and linearly dependent upon either the density or viscosity of the fluid, depending on which flow regime is present. In the transitional regime, flow near the impeller is turbulent and so the turbulent power equation is used.
The time required to blend a fluid to within 5% of the final concentration, θ 95 {\displaystyle {\theta _{95}}} , can be calculated with the following correlations:
θ 95 = 5.40 P o 1 3 N ( T D ) 2 {\displaystyle {\theta _{95}}={\frac {5.40}{P_{o}^{1 \over 3}N}}({\frac {T}{D}})^{2}} (Turbulent regime)
θ 95 = 34596 P o 1 3 N 2 D 2 ( μ ρ ) ( T D ) 2 {\displaystyle {\theta _{95}}={\frac {34596}{P_{o}{1 \over 3}N^{2}D^{2}}}({\frac {\mu }{\rho }})({\frac {T}{D}})^{2}} (Transitional region)
θ 95 = 896 ∗ 10 3 K p − 1.69 N {\displaystyle {\theta _{95}}={\frac {896*10^{3}K_{p}^{-1.69}}{N}}} (Laminar regime)
The Transitional/Turbulent boundary occurs at P o 1 3 R e = 6404 {\displaystyle P_{o}^{1 \over 3}Re=6404}
The Laminar/Transitional boundary occurs at P o 1 3 R e = 186 {\displaystyle P_{o}^{1 \over 3}Re=186}
At a laboratory scale, mixing is achieved by magnetic stirrers or by simple hand-shaking. Sometimes mixing in laboratory vessels is more thorough and occurs faster than is possible industrially. Magnetic stir bars are radial-flow mixers that induce solid body rotation in the fluid being mixed. This is acceptable on a small scale, since the vessels are small and mixing therefore occurs rapidly (short blend time). A variety of stir bar configurations exist, but because of the small size and (typically) low viscosity of the fluid, it is possible to use one configuration for nearly all mixing tasks. The cylindrical stir bar can be used for suspension of solids, as seen in iodometry , deagglomeration (useful for preparation of microbiology growth medium from powders), and liquid–liquid blending. Another peculiarity of laboratory mixing is that the mixer rests on the bottom of the vessel instead of being suspended near the center. Furthermore, the vessels used for laboratory mixing are typically more widely varied than those used for industrial mixing; for instance, Erlenmeyer flasks , or Florence flasks may be used in addition to the more cylindrical beaker . [ citation needed ]
When scaled down to the microscale, fluid mixing behaves radically different. [ 17 ] [ 18 ] This is typically at sizes from a couple (2 or 3) millimeters down to the nanometer range. At this size range normal advection does not happen unless it is forced by a hydraulic pressure gradient. Diffusion is the dominant mechanism whereby two different fluids come together. Diffusion is a relatively slow process. Hence a number of researchers had to devise ways to get the two fluids to mix. This involved Y junctions, T junctions, three-way intersections and designs where the interfacial area between the two fluids is maximized. Beyond just interfacing the two liquids people also made twisting channels to force the two fluids to mix. These included multilayered devices where the fluids would corkscrew, looped devices where the fluids would flow around obstructions and wavy devices where the channel would constrict and flare out. Additionally channels with features on the walls like notches or groves were tried. [ citation needed ]
One way to know if mixing is happening due to advection or diffusion is by finding the Peclet number . It is the ratio of advection to diffusion . At high Peclet numbers (> 1), advection dominates. At low Peclet numbers (< 1), diffusion dominates. [ citation needed ]
At an industrial scale, efficient mixing can be difficult to achieve. A great deal of engineering effort goes into designing and improving mixing processes. Mixing at industrial scale is done in batches (dynamic mixing), inline or with help of static mixers . Moving mixers are powered with electric motors that operate at standard speeds of 1800 or 1500 RPM, which is typically much faster than necessary. Gearboxes are used to reduce speed and increase torque. Some applications require the use of multi-shaft mixers, in which a combination of mixer types are used to completely blend the product. [ 19 ]
In addition to performing typical batch mixing operations, some mixing can be done continuously. Using a machine like the Continuous Processor, one or more dry ingredients and one or more liquid ingredients can be accurately and consistently metered into the machine and see a continuous, homogeneous mixture come out the discharge of the machine. [ 20 ] Many industries have converted to continuous mixing for many reasons. Some of those are ease of cleaning, lower energy consumption, smaller footprint, versatility, control, and many others. Continuous mixers, such as the twin-screw Continuous Processor, also have the ability to handle very high viscosities. [ citation needed ]
A selection of turbine geometries and power numbers are shown below.
Different types of impellers are used for different tasks; for instance, Rushton turbines are useful for dispersing gases into liquids, but are not very helpful for dispersing settled solids into liquid. Newer turbines have largely supplanted the Rushton turbine for gas–liquid mixing, such as the Smith turbine and Bakker turbine. [ 21 ] The power number is an empirical measure of the amount of torque needed to drive different impellers in the same fluid at constant power per unit volume; impellers with higher power numbers require more torque but operate at lower speed than impellers with lower power numbers, which operate at lower torque but higher speeds. [ citation needed ]
A planetary mixer is a device used to mix round products including adhesives , pharmaceuticals , foods (including dough ), chemicals , solid rocket propellants , electronics , plastics and pigments . Planetary mixers are ideal for mixing and kneading viscous pastes (up to 6 million centipoise ) under atmospheric or vacuum conditions. Capacities range from 0.5 US pints (0.24 L; 0.42 imp pt) through 750 US gallons (2,800 L; 620 imp gal). Many options including jacketing for heating or cooling, vacuum or pressure, vari speed drives, etc. are available. Planetary blades each rotate on their own axes , and at the same time on a common axis, thereby providing complete mixing in a very short timeframe. [ 22 ]
Large industrial scale planetary mixers are used in the production of solid rocket fuel for long-range ballistic missiles . They are used to blend and homgenize the components of solid rocket propellant, ensuring a consistent and stable mixture of fuel & oxidizer. [ 23 ] [ 24 ]
ResonantAcoustic mixing (RAM) is able to mix, coat, mill, and sieve materials without impellers or blades touching the materials, yet typically 10X [ 25 ] -100X [ 26 ] faster than alternative technologies by generating a high level of energy (up to 100 g) through seeking and operating at the resonant condition of the mechanical system - at all times.
ResonantAcoustic mixers from lab scale to industrial production to continuous mixing are used for energetic materials like explosives , propellants , and pyrotechnic compositions , as well as pharmaceuticals , powder metallurgy , 3D printing , rechargeable battery materials, and battery recycling . [ 27 ] [ 28 ] [ 29 ]
There are two main types of close-clearance mixers: anchors and helical ribbons. Anchor mixers induce solid-body rotation and do not promote vertical mixing, but helical ribbons do. Close clearance mixers are used in the laminar regime, because the viscosity of the fluid overwhelms the inertial forces of the flow and prevents the fluid leaving the impeller from entraining the fluid next to it. Helical ribbon mixers are typically rotated to push material at the wall downwards, which helps circulate the fluid and refresh the surface at the wall. [ 30 ]
High shear dispersers create intense shear near the impeller but relatively little flow in the bulk of the vessel. Such devices typically resemble circular saw blades and are rotated at high speed. Because of their shape, they have a relatively low drag coefficient and therefore require comparatively little torque to spin at high speed. High shear dispersers are used for forming emulsions (or suspensions) of immiscible liquids and solid deagglomeration. [ 31 ]
Static mixers are used when a mixing tank would be too large, too slow, or too expensive to use in a given process.
Liquid whistles are a kind of static mixer which pass fluid at high pressure through an orifice and subsequently over a blade. [ 32 ] This subjects the fluid to high turbulent stresses and may result in mixing , emulsification , [ 33 ] [ 34 ] deagglomeration and disinfection. | https://en.wikipedia.org/wiki/Mixing_(process_engineering) |
In particle physics and quantum mechanics , mixing angles are the angles between two sets of ( complex -valued) orthogonal basis vectors, or states , usually the eigenbases of two quantum mechanical operators . The choice of angles (parameterization) is not unique but based on convention.
The relation between two eigenbases is described completely by a unitary matrix , the analogue of a rotation matrix in a complex vector space . The number of degrees of freedom in this matrix is usually reduced by removing any excess complex phase from the transformation, since in most cases that is not a measurable quantity.
For two-dimensional vector space this reduces the matrix to a rotation matrix, which can be described completely by one mixing angle. In a three dimensional space there are three mixing angles and one additional complex phase parameter . Different conventions exist for how the three angles are defined, such as Euler angles .
Some notable mixing angles in particle physics are:
This particle physics –related article is a stub . You can help Wikipedia by expanding it .
This quantum mechanics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Mixing_angle |
In chemistry and physics , the dimensionless mixing ratio is the abundance of one component of a mixture relative to that of all other components. The term can refer either to mole ratio (see concentration ) or mass ratio (see stoichiometry ). [ 1 ]
In atmospheric chemistry , mixing ratio usually refers to the mole ratio r i , which is defined as the amount of a constituent n i divided by the total amount of all other constituents in a mixture:
The mole ratio is also called amount ratio . [ 2 ] If n i is much smaller than n tot (which is the case for atmospheric trace constituents), the mole ratio is almost identical to the mole fraction .
In meteorology , mixing ratio usually refers to the mass ratio of water ζ {\displaystyle \zeta } , which is defined as the mass of water m H 2 O {\displaystyle m_{\mathrm {H2O} }} divided by the mass of dry air ( m a i r − m H 2 O {\displaystyle m_{\mathrm {air} }-m_{\mathrm {H2O} }} ) in a given air parcel: [ 3 ]
The unit is typically given in g k g − 1 {\displaystyle \mathrm {g} \,\mathrm {kg} ^{-1}} . The definition is similar to that of specific humidity .
Two binary solutions of different compositions or even two pure components can be mixed with various mixing ratios by masses, moles, or volumes.
The mass fraction of the resulting solution from mixing solutions with masses m 1 and m 2 and mass fractions w 1 and w 2 is given by:
where m 1 can be simplified from numerator and denominator
and
is the mass mixing ratio of the two solutions.
By substituting the densities ρ i ( w i ) and considering equal volumes of different concentrations one gets:
Considering a volume mixing ratio r V (21)
The formula can be extended to more than two solutions with mass mixing ratios
to be mixed giving:
The condition to get a partially ideal solution on mixing is that the volume of the resulting mixture V to equal double the volume V s of each solution mixed in equal volumes due to the additivity of volumes. The resulting volume can be found from the mass balance equation involving densities of the mixed and resulting solutions and equalising it to 2:
implies
Of course for real solutions inequalities appear instead of the last equality.
Mixtures of different solvents can have interesting features like anomalous conductivity (electrolytic) of particular lyonium ions and lyate ions generated by molecular autoionization of protic and aprotic solvents due to Grotthuss mechanism of ion hopping depending on the mixing ratios. Examples may include hydronium and hydroxide ions in water and water alcohol mixtures, alkoxonium and alkoxide ions in the same mixtures, ammonium and amide ions in liquid and supercritical ammonia, alkylammonium and alkylamide ions in ammines mixtures, etc.... | https://en.wikipedia.org/wiki/Mixing_ratio |
Mixlink (Mixlink II) is a computer used with Agfa scales. [ 1 ] It was developed to facilitate calculation of color mixes.
Mixlink contains the Intel 80386 processor with the clock rate which may be set to either 9.2 or 33 MHz. The RAM size is 640 kB. The HDD function is served by the built-in flash memory that has the size of approximately 800 kB. Mixlink has the monochrome display .
Mixlink is also staffed with CD drive and floppy drive .
Mixlink was intended to be used with the supplied floppy and CD disk , which provided the system environment ("operating system") and the application to be used for calculating color mixes. However, it is possible to install and run MS-DOS on Mixlink.
Currently, Mixlink computers are not used; their functions may solely be performed by personal computers (PCs) . | https://en.wikipedia.org/wiki/Mixlink |
The Mixmaster universe (named after Sunbeam Mixmaster, a brand of Sunbeam Products electric kitchen mixer) [ 1 ] is a solution to Einstein field equations of general relativity studied by Charles Misner in 1969 in an effort to better understand the dynamics of the early universe . [ 2 ] He hoped to solve the horizon problem in a natural way by showing that the early universe underwent an oscillatory, chaotic epoch.
The model is similar to the closed Friedmann–Lemaître–Robertson–Walker universe, in that spatial slices are positively curved and are topologically three- spheres S 3 {\displaystyle S^{3}} . However, in the FRW universe, the S 3 {\displaystyle S^{3}} can only expand or contract: the only dynamical parameter is overall size of the S 3 {\displaystyle S^{3}} , parameterized by the scale factor a ( t ) {\displaystyle a(t)} . In the Mixmaster universe, the S 3 {\displaystyle S^{3}} can expand or contract, but also distort anisotropically. Its evolution is described by a scale factor a ( t ) {\displaystyle a(t)} as well as by two shape parameters β ± ( t ) {\displaystyle \beta _{\pm }(t)} . Values of the shape parameters describe distortions of the S 3 {\displaystyle S^{3}} that preserve its volume and also maintain a constant Ricci curvature scalar. Therefore, as the three parameters a , β ± {\displaystyle a,\beta _{\pm }} assume different values, homogeneity but not isotropy is preserved.
The model has a rich dynamical structure. Misner showed that the shape parameters β ± ( t ) {\displaystyle \beta _{\pm }(t)} act like the coordinates of a point mass moving in a triangular potential with steeply rising walls with friction. By studying the motion of this point, Misner showed that the physical universe would expand in some directions and contract in others, with the directions of expansion and contraction changing repeatedly. Because the potential is roughly triangular, Misner suggested that the evolution is chaotic.
The metric studied by Misner (very slightly modified from his notation) is given by,
where
and the σ k {\displaystyle \sigma _{k}} , considered as differential forms , are defined by
In terms of the coordinates ( θ , ψ , ϕ ) {\displaystyle (\theta ,\psi ,\phi )} . These satisfy
where d {\displaystyle {\text{d}}} is the exterior derivative and ∧ {\displaystyle \wedge } the wedge product of differential forms. The 1-forms σ i {\displaystyle \sigma _{i}} form a left-invariant co-frame on the Lie group SU(2) , which is diffeomorphic to the 3- sphere S 3 {\displaystyle S^{3}} , so the spatial metric in Misner's model can concisely be described as just a left-invariant metric on the 3-sphere; indeed, up to the adjoint action of SU(2) , this is actually the general left-invariant metric. As the metric evolves via Einstein's equation, the geometry of this S 3 {\displaystyle S^{3}} typically distorts anisotropically. Misner defines parameters Ω ( t ) {\displaystyle \Omega (t)} and R ( t ) {\displaystyle R(t)} which measure the volume of spatial slices, as well as "shape parameters" β k {\displaystyle \beta _{k}} , by
Since there is one condition on the three β k {\displaystyle \beta _{k}} , there should only be two free functions, which Misner chooses to be β ± {\displaystyle \beta _{\pm }} , defined as
The evolution of the universe is then described by finding β ± {\displaystyle \beta _{\pm }} as functions of Ω {\displaystyle \Omega } .
Misner hoped that the chaos would churn up and smooth out the early universe. Also, during periods in which one direction was static (e.g., going from expansion to contraction) formally the Hubble horizon H − 1 {\displaystyle H^{-1}} in that direction is infinite, which he suggested meant that the horizon problem could be solved. Since the directions of expansion and contraction varied, presumably given enough time the horizon problem would get solved in every direction.
While an interesting example of gravitational chaos, it is widely recognized that the cosmological problems the Mixmaster universe attempts to solve are more elegantly tackled by cosmic inflation . The metric Misner studied is also known as the Bianchi type IX metric. | https://en.wikipedia.org/wiki/Mixmaster_universe |
Mixotricha paradoxa is a species of protozoan that lives inside the gut of the Australian termite species Mastotermes darwiniensis .
It is composed of five different organisms: three bacterial ectosymbionts live on its surface for locomotion and at least one endosymbiont lives inside to help digest cellulose in wood to produce acetate for its host(s).
Mixotricha mitochondria degenerated in hydrogenosomes and mitosomes and lost the ability to produce energy aerobically by oxidative phosphorylation . [ 1 ] [ 2 ] The mitochondria-derived nuclear genes were however conserved. [ 2 ]
The name was given by the Australian biologist J.L. Sutherland, who first described Mixotricha in 1933. [ 3 ] [ 4 ] The name means "the paradoxical being with mixed-up hairs" because this protist has both cilia and flagella , which was not thought to be possible for protists . [ 5 ] [ 2 ]
Mixotricha is a species of protozoan that lives inside the gut of the Australian termite species Mastotermes darwiniensis and has multiple bacterial symbionts . [ 6 ] [ 7 ]
Mixotricha is a large protozoan .5 millimetres (0.020 in) long and contains hundreds of thousands of bacteria. [ 5 ] It is an endosymbiont and digests cellulose for the termite. [ 5 ]
Trichomonads like Mixotricha reproduce by a special form of longitudinal fission , leading to large numbers of trophozoites in a relatively short time. Cysts never form, so transmission from one host to another is always based on direct contact between the sites they occupy. [ 8 ]
Species of the order Trichomonadida typically have four to six flagella at the cell's apical pole , one of which is recurrent - that is, it runs along a surface wave, giving the aspect of an undulating membrane. Mixotricha paradoxa have four weak flagella that serve as rudders. [ 9 ] It has four large flagella at the front end, three pointing forwards and one backward. [ 5 ]
The basal bodies are also bacteria, not spirochaetes but oval, pill-shaped bacteria. There is a one-to-one relationship between a bracket, a spirochaete, and a basal bacterium. Each bracket has one spirochaete running through it and one pill bacterium at its base as the basal body. [ 5 ] It has not been shown definitely, but the basal bodies could also be making cellulases that digest wood. [ 5 ]
At least one endosymbiont lives inside the protist to help digest cellulose and lignin , a major component of the wood the termites eat. The cellulose gets converted to glucose then to acetate, and the lignin is digested directly to acetate. [ 2 ] The acetate probably crosses the termite gut membrane to be digested later. [ 2 ]
Mixotricha forms a mutualistic relationship with bacteria living inside the termite. There are a total of four species of bacterial symbionts. It has spherical bacteria inside the cell, which function as mitochondria , which Mixotricha lacks. Mixotricha mitochondria degenerated and lost the ability to produce energy aerobically by oxidative phosphorylation . [ 1 ] [ 2 ] Mitochondrial relics include hydrogenosomes which produce hydrogen and small structures called mitosomes . [ 2 ]
Three surface colonising bacteria are anchored on the surface. [ 10 ]
The flagella and cilia are actually two different single celled organisms. The ciliate belongs to an archaic group that used to be called archezoa but this term is no longer in fashion. [ 11 ] It has four weak flagella, which serve as a rudder. [ 12 ] [ 11 ]
While Mixotricha has four anterior flagella, it does not use them for locomotion, but more for steering. [ 5 ] For locomotion, about 250,000 hairlike Treponema spirochaetes , a species of helical bacteria, are attached to the cell surface and provide the cell with cilia -like movements. [ 2 ]
The wavelength of the cilia is about .1 millimetres (0.0039 in) and suggests that the spirochaetes are somehow in touch with each other. [ 5 ]
Mixotricha also has rod-shaped bacteria arranged in an ordered pattern on the surface of the cell. [ 13 ]
Each spirochaete has its own little emplacement, called a 'bracket'. [ 14 ] Spirochetes move continuously forwards or backwards but when they are attached they move in one direction. [ 2 ]
Sperm tails might have their origin in spirochaetes. [ 2 ] The evidence that cilia (undulipodia) are symbiotic bacteria is found unpersuasive. [ 5 ]
Mixotricha have five genomes , as they form very close symbiotic relationships with four types of bacteria. [ 15 ] It is a good example organism for symbiogenesis and nestedness. [ 2 ]
There are two spirochete and one-rod bacteria on its surface, one endosymbiotic bacteria inside to digest cellulose and the host nucleus. [ 2 ] | https://en.wikipedia.org/wiki/Mixotricha_paradoxa |
A mixotroph is an organism that uses a mix of different sources of energy and carbon , instead of having a single trophic mode, on the continuum from complete autotrophy to complete heterotrophy . It is estimated that mixotrophs comprise more than half of all microscopic plankton . [ 1 ] There are two types of eukaryotic mixotrophs. There are those with their own chloroplasts – including those with endosymbionts providing the chloroplasts. And there are those that acquire them through kleptoplasty , or through symbiotic associations with prey, or through 'enslavement' of the prey's organelles. [ 2 ]
Possible combinations are photo- and chemotrophy , litho- and organotrophy ( osmotrophy , phagotrophy and myzocytosis ), auto- and heterotrophy or other combinations of these. Mixotrophs can be either eukaryotic or prokaryotic . [ 3 ] They can take advantage of different environmental conditions. [ 4 ]
If a trophic mode is obligate, it is always necessary to sustain growth and maintenance; if facultative, it can be used as a supplemental source. [ 3 ] Some organisms have incomplete Calvin cycles , so they are incapable of fixing carbon dioxide and must use organic carbon sources.
Organisms may employ mixotrophy obligately or facultatively .
Amongst plants, mixotrophy classically applies to carnivorous , hemi-parasitic and myco-heterotrophic species. However, this characterisation as mixotrophic could be extended to a higher number of clades as research demonstrates that organic forms of nitrogen and phosphorus—such as DNA, proteins, amino-acids or carbohydrates—are also part of the nutrient supplies of a number of plant species. [ 6 ]
Mycoheterotrophic plants form symbiotic relationships with mycorrhizal fungi , which provide them with organic carbon and nutrients from nearby photosynthetic plants or soil. They often lack chlorophyll or have reduced photosynthetic capacity. An example is Indian pipe , a white, non-photosynthetic plant that relies heavily on fungal networks for nutrients. Pinesap also taps into fungal networks for sustenance, similar to Indian pipe. Certain orchids, such as Corallorhiza , depend on fungi for carbon and nutrients while developing photosynthetic capabilities (especially in their early stages).
Carnivorous plants are plants that derive some or most of their nutrients from trapping and consuming animals [ 7 ] or protozoans , typically insects and other arthropods , and occasionally small mammals and birds . They have adapted to grow in waterlogged sunny places where the soil is thin or poor in nutrients , especially nitrogen , such as acidic bogs . [ 8 ]
Hemiparasitic plants are partially parasitic, attaching to the roots or stems of host plants to extract water, nutrients, or organic compounds while still performing photosynthesis. Examples are mistletoe (absorbs water and nutrients from host trees but also photosynthesizes), Indian paintbrush (connects to the roots of other plants for nutrients while maintaining photosynthetic leaves), and Yellow rattle (a root parasite that supplements its nutrition by tapping into host plants).
Some epiphytic plants, which are plants that grow on other plants, absorb organic matter, such as decaying debris or animal waste, through specialized structures while still photosynthesizing. For example, some bromeliads have tank-like leaf structures that collect water and organic debris, absorbing nutrients through their leaves. Also, some epiphytic orchids absorb nutrients from organic matter caught in their aerial roots.
Some plants incorporate algae or cyanobacteria , which provide photosynthetically derived carbon, while the plant also absorbs external nutrients. For example, Azolla filiculoides , is a floating fern that hosts the nitrogen-fixing cyanobacteria Anabaena in its leaves, supplementing nutrient intake while photosynthesizing. This has led to the plant being dubbed a "super-plant", as it can readily colonise areas of freshwater, and grow at great speed - doubling its biomass in as little as 1.9 days. [ 9 ]
Mixotrophy is less common among animals than among plants and microbes, but there are many examples of mixotrophic invertebrates and at least one example of a mixotrophic vertebrate .
Several very similar categorization schemes have been suggested to characterize the sub-domains within mixotrophy. Consider the example of a marine protist with heterotrophic and photosynthetic capabilities:
In the breakdown put forward by Jones, [ 22 ] there are four mixotrophic groups based on relative roles of phagotrophy and phototrophy.
An alternative scheme by Stoeker [ 21 ] also takes into account the role of nutrients and growth factors, and includes mixotrophs that have a photosynthetic symbiont or who retain chloroplasts from their prey. This scheme characterizes mixotrophs by their efficiency.
Another scheme, proposed by Mitra et al. , specifically classifies marine planktonic mixotrophs so that mixotrophy can be included in ecosystem modeling. [ 23 ] This scheme classified organisms as:
Mixotrophs are especially common in marine environments, where the levels of energy from the sun and nutrients in the water can vary greatly. For example, in nutrient-poor ( oligotrophic ) waters, mixotrophic phytoplankton supplement their diet by consuming bacteria. [ 25 ] [ 26 ]
The effects of mixotrophy on organic and inorganic carbon pools introduce a metabolic plasticity which blurs the lines between producers and consumers . [ 27 ] Prior to the discovery of mixotrophs, it was thought that only organisms with chloroplasts were capable of photosynthesis and vice versa. This additional functional group of plankton, capable of both phototrophy and phagotrophy , provides a further boost in the biomass and energy transfer to higher trophic levels . [ 28 ] | https://en.wikipedia.org/wiki/Mixotroph |
In chemistry , a mixture is a material made up of two or more different chemical substances which can be separated by physical method. It is an impure substance made up of 2 or more elements or compounds mechanically mixed together in any proportion. [ 1 ] A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the form of solutions , suspensions or colloids . [ 2 ] [ 3 ]
Mixtures are one product of mechanically blending or mixing chemical substances such as elements and compounds , without chemical bonding or other chemical change, so that each ingredient substance retains its own chemical properties and makeup. [ 4 ] Despite the fact that there are no chemical changes to its constituents, the physical properties of a mixture, such as its melting point , may differ from those of the components. Some mixtures can be separated into their components by using physical (mechanical or thermal) means. Azeotropes are one kind of mixture that usually poses considerable difficulties regarding the separation processes required to obtain their constituents (physical or chemical processes or, even a blend of them). [ 5 ] [ 6 ] [ 7 ]
All mixtures can be characterized as being separable by mechanical means (e.g. purification , distillation , electrolysis , chromatography , heat , filtration , gravitational sorting, centrifugation ). [ 8 ] [ 9 ] Mixtures differ from chemical compounds in the following ways:
In the example of sand and water, neither one of the two substances changed in any way when they are mixed. Although the sand is in the water it still keeps the same properties that it had when it was outside the water.
The following table shows the main properties and examples for all possible phase combinations of the three "families" of mixtures :
Mixtures can be either homogeneous or heterogeneous : a mixture of uniform composition and in which all components are in the same phase, such as salt in water, is called homogeneous, whereas a mixture of non-uniform composition and of which the components can be easily identified, such as sand in water, it is called heterogeneous.
In addition, " uniform mixture " is another term for homogeneous mixture and " non-uniform mixture " is another term for heterogeneous mixture . These terms are derived from the idea that a homogeneous mixture has a uniform appearance , or only one phase , because the particles are evenly distributed. However, a heterogeneous mixture has constituent substances that are in different phases and easily distinguishable from one another. In addition, a heterogeneous mixture may have a uniform (e.g. a colloid) or non-uniform (e.g. a pencil) composition.
Several solid substances, such as salt and sugar , dissolve in water to form homogeneous mixtures or " solutions ", in which there are both a solute (dissolved substance) and a solvent (dissolving medium) present. Air is an example of a solution as well: a homogeneous mixture of gaseous nitrogen solvent, in which oxygen and smaller amounts of other gaseous solutes are dissolved. Mixtures are not limited in either their number of substances or the amounts of those substances, though in most solutions, the solute-to-solvent proportion can only reach a certain point before the mixture separates and becomes heterogeneous.
A homogeneous mixture is characterized by uniform dispersion of its constituent substances throughout; the substances exist in equal proportion everywhere within the mixture. Differently put, a homogeneous mixture will be the same no matter from where in the mixture it is sampled. For example, if a solid-liquid solution is divided into two halves of equal volume , the halves will contain equal amounts of both the liquid medium and dissolved solid (solvent and solute)
A solution is equivalent to a "homogeneous mixture". In solutions, solutes will not settle out after any period of time and they cannot be removed by physical methods, such as a filter or centrifuge . [ 12 ] As a homogeneous mixture, a solution has one phase (solid, liquid, or gas), although the phase of the solute and solvent may initially have been different (e.g., salt water).
Gases exhibit by far the greatest space (and, consequently, the weakest intermolecular forces) between their atoms or molecules; since intermolecular interactions are minuscule in comparison to those in liquids and solids, dilute gases very easily form solutions with one another. Air is one such example: it can be more specifically described as a gaseous solution of oxygen and other gases dissolved in nitrogen (its major component).
Examples of heterogeneous mixtures are emulsions and foams . In most cases, the mixture consists of two main constituents. For an emulsion, these are immiscible fluids such as water and oil. For a foam, these are a solid and a fluid, or a liquid and a gas. On larger scales both constituents are present in any region of the mixture, and in a well-mixed mixture in the same or only slightly varying concentrations. On a microscopic scale, however, one of the constituents is absent in almost any sufficiently small region. (If such absence is common on macroscopic scales, the combination of the constituents is a dispersed medium , not a mixture.) One can distinguish different characteristics of heterogeneous mixtures by the presence or absence of continuum percolation of their constituents. For a foam, a distinction is made between reticulated foam in which one constituent forms a connected network through which the other can freely percolate, or a closed-cell foam in which one constituent is present as trapped in small cells whose walls are formed by the other constituents. A similar distinction is possible for emulsions. In many emulsions, one constituent is present in the form of isolated regions of typically a globular shape, dispersed throughout the other constituent. However, it is also possible each constituent forms a large, connected network. Such a mixture is then called bicontinuous . [ 13 ]
Making a distinction between homogeneous and heterogeneous mixtures is a matter of the scale of sampling. On a coarse enough scale, any mixture can be said to be homogeneous, if the entire article is allowed to count as a "sample" of it. On a fine enough scale, any mixture can be said to be heterogeneous, because a sample could be as small as a single molecule. In practical terms, if the property of interest of the mixture is the same regardless of which sample of it is taken for the examination used, the mixture is homogeneous.
Gy's sampling theory quantitatively defines the heterogeneity of a particle as: [ 14 ]
where h i {\displaystyle h_{i}} , c i {\displaystyle c_{i}} , c batch {\displaystyle c_{\text{batch}}} , m i {\displaystyle m_{i}} , and m aver {\displaystyle m_{\text{aver}}} are respectively: the heterogeneity of the i {\displaystyle i} th particle of the population, the mass concentration of the property of interest in the i {\displaystyle i} th particle of the population, the mass concentration of the property of interest in the population, the mass of the i {\displaystyle i} th particle in the population, and the average mass of a particle in the population.
During sampling of heterogeneous mixtures of particles, the variance of the sampling error is generally non-zero.
Pierre Gy derived, from the Poisson sampling model, the following formula for the variance of the sampling error in the mass concentration in a sample:
in which V is the variance of the sampling error, N is the number of particles in the population (before the sample was taken), q i is the probability of including the i th particle of the population in the sample (i.e. the first-order inclusion probability of the i th particle), m i is the mass of the i th particle of the population and a i is the mass concentration of the property of interest in the i th particle of the population.
The above equation for the variance of the sampling error is an approximation based on a linearization of the mass concentration in a sample.
In the theory of Gy, correct sampling is defined as a sampling scenario in which all particles have the same probability of being included in the sample. This implies that q i no longer depends on i , and can therefore be replaced by the symbol q . Gy's equation for the variance of the sampling error becomes:
where a batch is that concentration of the property of interest in the population from which the sample is to be drawn and M batch is the mass of the population from which the sample is to be drawn.
Air pollution research [ 15 ] [ 16 ] show biological and health effects after exposure to mixtures are more potent than effects from exposures of individual components. [ 17 ] | https://en.wikipedia.org/wiki/Mixture |
Mixture fraction ( Z {\displaystyle Z} ) is a quantity used in combustion studies that measures the mass fraction of one stream of a mixture formed by two feed streams, one the fuel stream and the other the oxidizer stream. [ 1 ] [ 2 ] Both the feed streams are allowed to have inert gases. [ 3 ] The mixture fraction definition is usually normalized such that it approaches unity in the fuel stream and zero in the oxidizer stream. [ 4 ] The mixture-fraction variable is commonly used as a replacement for the physical coordinate normal to the flame surface, in nonpremixed combustion.
Assume a two-stream problem having one portion of the boundary the fuel stream with fuel mass fraction Y F = Y F , F {\displaystyle Y_{F}=Y_{F,F}} and another portion of the boundary the oxidizer stream with oxidizer mass fraction Y O = Y O , O {\displaystyle Y_{O}=Y_{O,O}} . For example, if the oxidizer stream is air and the fuel stream contains only the fuel, then Y O , O = 0.232 {\displaystyle Y_{O,O}=0.232} and Y F , F = 1 {\displaystyle Y_{F,F}=1} . In addition, assume there is no oxygen in the fuel stream and there is no fuel in the oxidizer stream. Let s {\displaystyle s} be the mass of oxygen required to burn unit mass of fuel (for hydrogen gas, s = 8 {\displaystyle s=8} and for C m H n {\displaystyle \mathrm {C} _{m}\mathrm {H} _{n}} alkanes , s = 32 ( m + n / 4 ) / ( 12 m + n ) {\displaystyle s=32(m+n/4)/(12m+n)} [ 5 ] ). Introduce the scaled mass fractions as y F = Y F / Y F , F {\displaystyle y_{F}=Y_{F}/Y_{F,F}} and y O = Y O / Y O , O {\displaystyle y_{O}=Y_{O}/Y_{O,O}} . Then the mixture fraction is defined as
where
is the stoichiometry parameter, also known as the overall equivalence ratio . On the fuel-stream boundary, y F = 1 {\displaystyle y_{F}=1} and y O = 0 {\displaystyle y_{O}=0} since there is no oxygen in the fuel stream, and hence Z = 1 {\displaystyle Z=1} . Similarly, on the oxidizer-stream boundary, y F = 0 {\displaystyle y_{F}=0} and y O = 1 {\displaystyle y_{O}=1} so that Z = 0 {\displaystyle Z=0} . Anywhere else in the mixing domain, 0 < Z < 1 {\displaystyle 0<Z<1} . The mixture fraction is a function of both the spatial coordinates x {\displaystyle \mathbf {x} } and the time t {\displaystyle t} , i.e., Z = Z ( x , t ) . {\displaystyle Z=Z(\mathbf {x} ,t).}
Within the mixing domain, there are level surfaces where fuel and oxygen are found to be mixed in stoichiometric proportion. This surface is special in combustion because this is where a diffusion flame resides. Constant level of this surface is identified from the equation Z ( x , t ) = Z s {\displaystyle Z(\mathbf {x} ,t)=Z_{s}} , where Z s {\displaystyle Z_{s}} is called as the stoichiometric mixture fraction which is obtained by setting Y F = Y O = 0 {\displaystyle Y_{F}=Y_{O}=0} (since if they were react to consume fuel and oxygen, only on the stoichiometric locations both fuel and oxygen will be consumed completely) in the definition of Z {\displaystyle Z} to obtain
When there is no chemical reaction, or considering the unburnt side of the flame, the mass fraction of fuel and oxidizer are y F , u = Z {\displaystyle y_{F,u}=Z} and y O , u = 1 − Z {\displaystyle y_{O,u}=1-Z} (the subscript u {\displaystyle u} denotes unburnt mixture). This allows to define a local fuel-air equivalence ratio ϕ {\displaystyle \phi }
The local equivalence ratio is an important quantity for partially premixed combustion. The relation between local equivalence ratio and mixture fraction is given by
The stoichiometric mixture fraction Z s {\displaystyle Z_{s}} defined earlier is the location where the local equivalence ratio ϕ = 1 {\displaystyle \phi =1} .
In turbulent combustion, a quantity called the scalar dissipation rate χ {\displaystyle \chi } with dimensional units of that of an inverse time is used to define a characteristic diffusion time. Its definition is given by
where D {\displaystyle D} is the diffusion coefficient of the scalar. Its stoichiometric value is χ s = 2 D s | ∇ Z | s 2 {\displaystyle \chi _{s}=2D_{s}|\nabla Z|_{s}^{2}} .
Amable Liñán introduced a modified mixture fraction in 1991 [ 6 ] [ 7 ] that is appropriate for systems where the fuel and oxidizer have different Lewis numbers . If L e F {\displaystyle Le_{F}} and L e O 2 {\displaystyle Le_{O_{2}}} are the Lewis number of the fuel and oxidizer, respectively, then Liñán's mixture fraction is defined as
where
The stoichiometric mixture fraction Z ~ s {\displaystyle {\tilde {Z}}_{s}} is given by | https://en.wikipedia.org/wiki/Mixture_fraction |
A Miyake event is an observed sharp enhancement of the production of cosmogenic isotopes by cosmic rays . It can be marked by a spike in the concentration of radioactive carbon isotope 14 C in tree rings, as well as 10 Be and 36 Cl in ice cores, which are all independently dated. At present, five significant events are known (7176 BCE, 5259 BCE, 664-663 BCE [ 1 ] (historically referred to as 660 BCE), 774 CE , 993 CE ) for which the spike in 14 C is quite remarkable, i.e. above 1% rise over a period of two years, and four more events (12,350 BCE, [ 2 ] 5410 BCE, 1052 CE, 1279 CE) need independent confirmation. It is not known how often Miyake events occur, but from the available data it is estimated to be every 400 to 2,400 years. [ 3 ]
There is strong evidence that Miyake events are caused by extreme solar particle events [ 4 ] [ 5 ] and they are likely related to super-flares discovered on solar-like stars. [ 5 ] [ 6 ] Although Miyake events are based on extreme year-to-year rises of 14 C concentration, the duration of the periods over which the 14 C levels increase or stay at high levels is longer than one year. [ 7 ] [ 8 ] However, a universal cause and origin of all the events is not yet established, and some of the events may be caused by other phenomena coming from beyond the Solar System, such as a gamma-ray burst . [ 9 ]
In 2023, the largest known Miyake event was reported between 12,350 and 12,349 BCE. It was identified by a study conducted by an international team of researchers who measured radiocarbon levels in ancient trees recovered from the eroded banks of the Drouzet River, near Gap in the Southern French Alps. [ 10 ] [ 11 ] [ 12 ] Although the 14 C increase was nearly double that for the next strongest spike in 774 CE, the strength of the corresponding solar event was only 18 % higher, because of the combined effect of the lower atmospheric CO2 level and weaker geomagnetic field [ 13 ] However, the event has not yet been independently confirmed in wood from other regions, nor it is reliably supported by a clear corresponding spike in other isotopes, such as beryllium-10 , that are needed to reconstruct the spectrum of solar energetic particles. [ 8 ]
A Miyake event occurring in modern conditions might have significant impacts on global technological infrastructure such as satellites, telecommunications, and power grids. [ 8 ] [ 14 ] [ 15 ]
The events are named after the Japanese physicist Fusa Miyake who, as a doctoral student, was the first one to identify these radiocarbon spikes and published the results with co-authors in 2012 in the journal Nature . [ 16 ] The investigation at that time found a strong 14 C increase in the annual rings of Japanese cedars for the years 774/775 . The event of 775 was independently discovered, using the low-resolution IntCal data. [ 17 ]
In 2013, Miyake and co-authors published the discovery of another similar radiocarbon spike in the years 993/994 . [ 18 ] In December 2013, Miyake received her Doctor of Science degree from Nagoya University . [ 19 ]
After a Miyake event is well-studied and confirmed, it can serve as a reference time benchmark, a "year-stamp", enabling more precise dating of historical buildings, objects, and events. Six diverse historical occurrences, from archaeological sites to natural disasters, have thus been dated to a specific year, using Miyake events as benchmarks and counting tree rings . [ 20 ] For example, wooden construction elements from the Viking archaeological site at L'Anse aux Meadows in Newfoundland were dated by identifying the 14 C spike of 993 CE in a sequence of tree-rings , which showed that the wood is from a tree felled in 1021 CE, thus definitely confirming Viking presence in the Americas at least before 1021 CE. [ 21 ] Another study performed on the tree-rings of wooden building remains from the Neolithic waterlogged site of Dispilio in north-western Greece , identified the Miyake event of 5259 BC, thus for a first time absolutely dating a Neolithic site in Europe from the 6th millennium BC to a single calendar year. [ 22 ] | https://en.wikipedia.org/wiki/Miyake_event |
Miyaura borylation , also known as the Miyaura borylation reaction , is a named reaction in organic chemistry that allows for the generation of boronates from vinyl or aryl halides with the cross-coupling of bis(pinacolato)diboron in basic conditions with a catalyst such as PdCl 2 (dppf) . The resulting borylated products can be used as coupling partners for the Suzuki reaction . [ 1 ]
The Miyaura borylation has shown to work for:
Alkyl halides, [ 2 ] aryl halides, [ 1 ] [ 3 ] [ 4 ] aryl halides using tetrahydroxydiboron , [ 5 ] aryl halides using bis-boronic acid, [ 6 ] aryl triflates , [ 7 ] aryl mesylates , [ 8 ] vinyl halides, [ 9 ] vinyl halides of α,β-unsaturated carbonyl compounds, [ 10 ] and vinyl triflates. [ 11 ] | https://en.wikipedia.org/wiki/Miyaura_borylation |
The Mizar system consists of a formal language for writing mathematical definitions and proofs, a proof assistant , which is able to mechanically check proofs written in this language, and a library of formalized mathematics , which can be used in the proof of new theorems. [ 1 ] The system is maintained and developed by the Mizar Project, formerly under the direction of its founder Andrzej Trybulec .
In 2009 the Mizar Mathematical Library was the largest coherent body of strictly formalized mathematics in existence. [ 2 ]
The Mizar Project was started around 1973 by Andrzej Trybulec as an attempt to reconstruct mathematical vernacular so it can be checked by a computer. [ 3 ] Its current goal, apart from the continual development of the Mizar System, is the collaborative creation of a large library of formally verified proofs, covering most of the core of modern mathematics. This is in line with the influential QED manifesto . [ 4 ]
Currently the project is developed and maintained by research groups at Białystok University , Poland, the University of Alberta , Canada, and Shinshu University , Japan. While the Mizar proof checker remains proprietary, [ 5 ] the Mizar Mathematical Library—the sizable body of formalized mathematics that it verified—is licensed open-source. [ 6 ]
Papers related to the Mizar system regularly appear in the peer-reviewed journals of the mathematic formalization academic community. These include Studies in Logic, Grammar and Rhetoric , Intelligent Computer Mathematics , Interactive Theorem Proving , Journal of Automated Reasoning and the Journal of Formalized Reasoning .
The distinctive feature of the Mizar language is its readability. As is common in mathematical text, it relies on classical logic and a declarative style . [ 7 ] Mizar articles are written in ordinary ASCII , but the language was designed to be close enough to the mathematical vernacular that most mathematicians could read and understand Mizar articles without special training. [ 1 ] Yet, the language enables the increased level of formality necessary for automated proof checking .
For a proof to be admitted, all steps have to be justified either by elementary logical arguments or by citing previously verified proofs. [ 8 ] This results in a higher level of rigor and detail than is customary in mathematical textbooks and publications. Thus, a typical Mizar article is about four times as long as an equivalent paper written in ordinary style. [ 9 ]
Formalization is relatively labor-intensive, but not impossibly difficult. Once one is versed in the system, it takes about one week of full-time work to have a textbook page formally verified. This suggests that its benefits are now within the reach of applied fields such as probability theory and economics . [ 2 ]
The Mizar Mathematical Library (MML) includes all theorems to which authors can refer in newly written articles. Once approved by the proof checker they are further evaluated in a process of peer-review for appropriate contribution and style. If accepted they are published in the associated Journal of Formalized Mathematics [ 10 ] and added to the MML.
As of July 2012, the MML included 1150 articles written by 241 authors. [ 11 ] In aggregate, these contain more than 10,000 formal definitions of mathematical objects and about 52,000 theorems proved on these objects. More than 180 named mathematical facts have been given formal codification in this manner. [ 12 ] Some examples are the Hahn–Banach theorem , Kőnig's lemma , the Brouwer fixed point theorem , Gödel's completeness theorem , and the Jordan curve theorem .
This breadth of coverage has led some [ 13 ] to suggest Mizar as one of the leading approximations to the QED utopia of encoding all core mathematics in computer verifiable form.
All MML articles are available in PDF form as the papers of the Journal of Formalized Mathematics . [ 10 ] The full text of the MML is distributed with the Mizar checker and can be freely downloaded from the Mizar website. In an ongoing recent project [ 14 ] the library was also made available in an experimental wiki form [ 15 ] that only admits edits when they are approved by the Mizar checker. [ 16 ]
The MML Query website [ 11 ] implements a powerful search engine for the contents of the MML. Among other abilities, it can retrieve all MML theorems proved about any particular type or operator. [ 17 ] [ 18 ]
The MML is built on the axioms of the Tarski–Grothendieck set theory . Even though semantically all objects are sets , the language allows one to define and use syntactical weak types . For example, a set may be declared to be of type Nat only when its internal structure conforms with a particular list of requirements. In turn, this list serves as the definition of the natural numbers and the set of all the sets that conform to this list is denoted as NAT . [ 19 ] This implementation of types seeks to reflect the way most mathematicians formally think of symbols [ 20 ] and so streamline codification.
Distributions of the Mizar Proof Checker for all major operating systems are freely available for download at the Mizar Project website. Use of the proof checker is free for all non-commercial purposes. It is written in Free Pascal and the source code is available on GitHub. [ 21 ] | https://en.wikipedia.org/wiki/Mizar_system |
Mizrah (also spelled Mizrach , Mizrakh ) ( Hebrew : מִזְרָח , romanized : mīzrāḥ ) is the "east" and the direction that Jews in the Diaspora west of Israel face during prayer . Practically speaking, Jews face the city of Jerusalem when praying, and those north, east, or south of Jerusalem face south, west, and north respectively. [ 1 ]
In European and Mediterranean communities west of the Holy Land, mizrah also refers to the wall of the synagogue that faces east, where seats are reserved for the rabbi and other dignitaries. In addition, mizrah refers to an ornamental wall plaque used to indicate the direction of prayer in Jewish homes.
The Talmud states that a Jew praying in the Diaspora shall direct themself toward the Land of Israel ; in Israel, toward Jerusalem ; in Jerusalem, toward the Temple ; and in the Temple, toward the Holy of Holies . The same rule is found in the Mishnah but prescribed for individual prayers rather than congregational ones (i.e., in a synagogue). Thus, if one is east of the Temple, one should turn westward; if in the west, eastward; in the south, northward; and if in the north, southward.
The custom is based on the prayer of Solomon ( I Kings 8:33, 44, 48 ; II Chronicles 6:34 ). Another passage supporting this rule is found in the Book of Daniel , which relates that in the upper chamber of the house in which Daniel prayed three times daily, the windows were opened toward Jerusalem ( Daniel 9:3, 6:10 ).
The Tosefta demands that the entrance to the synagogue should be on the eastern side, with the congregation facing west during prayer. The requirement is probably based on the orientation of the Tent of Meeting , which had its gates on the eastern side ( 2:2–3; 3:38 , or Solomon's Temple —the portals of which were to the east ( Ezekiel 43:1–4 ). Maimonides attempted to reconcile the Tosefta's provision with the requirement to pray toward Jerusalem by stating that the doors of the synagogue should face east and the Ark should be placed "in the direction in which people pray in that city" (i.e., toward Jerusalem). The Shulkhan Arukh records the same rule but also recommends that one turn toward the southeast instead of the east to avoid the semblance of worshiping the sun .
If one cannot ascertain the cardinal points , one should direct the heart toward Jerusalem.
Excavations of ancient synagogues show that their design generally conformed with the Talmudic and traditional rule on prayer direction. The synagogues excavated west of Eretz Israel in Miletus , Priene , and Aegina all show an eastern orientation. Josephus , in his work Against Apion , recorded that the same was the case for Egyptian synagogues. Synagogues north of Jerusalem and west of the Jordan River , as in Bet Alfa , Capernaum , Hammath, and Khorazin, all face southward, whereas houses of worship east of the Jordan all face west. In the south, the synagogue excavated at Masada faces northwest to Jerusalem. The Tosefta's regulation that the entrance to the synagogue should be on the eastern side, while the orientation of the building should be toward the west was followed only in the synagogue in Irbid .
Initially, the mizrah wall in synagogues was on the side of the entrance. However, the remains of the Dura-Europos synagogue on the Euphrates reveal that by the 3rd century C.E. the doors were on the eastern side and the opposite wall, in which a special niche had been made to place the scrolls during worship, faced Jerusalem. In Eretz Israel, the wall facing the Temple site was changed from the side of the entrance to the side of the Ark in the 5th or 6th century. This change is found in synagogues at Naaran , near Jericho , and Beit Alfa . Worshipers came through the portals and immediately faced both the scrolls and Jerusalem.
It is customary in traditional Jewish homes to mark the wall in the direction of mizrah to facilitate proper prayer. For this purpose, people use artistic wall plaques inscribed with the word mizrah and scriptural passages like "From the rising ( mi-mizrah ) of the sun unto the going down thereof, the Lord's name is to be praised" ( Psalm 113:3 , Septuagint Ps. 112:3), kabbalistic inscriptions, or pictures of holy places. These plaques are generally placed in rooms in which people pray, such as the living room or bedrooms.
There are also papercuts described as "mizrah- shiviti ", because they served a dual purpose: as mizrah (decoration for the eastern wall, marking the direction of prayer), and as shiviti , meaning "I have set [before me]" ( Psalm 16:8 , LXX Ps. 15:8) and intended to inspire worshippers to adopt a proper attitude toward prayer. [ 2 ]
Like the Jews, Muslims used Jerusalem as their qiblah ( Arabic : قِـبْـلَـة , direction of prayer), before it was permanently changed in the second Hijri year (624 CE) to Mecca . [ 1 ] [ 3 ] [ 4 ] | https://en.wikipedia.org/wiki/Mizrah |
Mizuna ( ミズナ（水菜） , "water greens") , kyouna (京菜) , [ 1 ] Japanese mustard greens , [ 2 ] [ 3 ] or spider mustard , [ 2 ] is a cultivar of Brassica rapa var. niposinica .
Possessing dark green, serrated leaves, mizuna is described as having, when raw, a "piquant, mild peppery flavor...slightly spicy, but less so than arugula ." [ 4 ] It is also used in stir-fries , soups , and nabemono (Japanese hot pots ).
In addition to the term mizuna (and its alternates) being applied to at least two different species of Brassica , horticulturalists have defined and named a number of varieties. For example, a resource provided by Cornell University and the United States Department of Agriculture lists sixteen varieties including "Early Mizuna", "Kyona Mizuna", " Komatsuna Mizuna", "Vitamin Green Mizuna", "Kyoto Mizuna", "Happy Rich Mizuna", "Summer Fest Mizuna", "Tokyo Early Mizuna", "Mibuna Mizuna", "Red Komatsuna Mizuna", "Waido Mizuna" and "Purple Mizuna". [ 5 ] There is also a variety known as pink mizuna. [ 6 ]
Mizuna has been cultivated in Japan since ancient times. Mizuna was successfully grown in the International Space Station in 2019. [ 7 ] It grows in hardiness zones 4 to 9, prefers full sun or partial shade, well-drained soil and a pH of 6.5–7.0. [ 8 ] It can be grown as a microgreen , sowing every 3 cm, or for its leaves with a 20 cm spacing. [ 9 ] It is produced by more than 30 countries around the world, but China, Japan, South Korea, India and the United States account for 70% of global production. [ 10 ] | https://en.wikipedia.org/wiki/Mizuna |
Manganese(II) acetate are chemical compounds with the formula Mn(CH 3 CO 2 ) 2 ·(H 2 O)n where n = 0, 2, 4. These materials are white or pale pink solids. Some of these compounds are used as a catalyst and as fertilizer . [ 3 ]
Manganese(II) acetate can be formed by treating either manganese(II,III) oxide or manganese(II) carbonate with acetic acid: [ 4 ]
The anhydrous material and dihydrate Mn(CH 3 CO 2 ) 2 ·2H 2 O are coordination polymers . The dihydrate has been characterized by X-ray crystallography. Each Mn(II) center is surrounded by six oxygen centers provided by aquo ligands and acetates. | https://en.wikipedia.org/wiki/Mn(CH3COO)2 |
Manganese(II) nitrate refers to the inorganic compounds with formula Mn ( NO 3 ) 2 ·(H 2 O) n . These compounds are nitrate salts containing varying amounts of water. A common derivative is the tetrahydrate, Mn(NO 3 ) 2 ·4H 2 O, but mono- and hexahydrates are also known as well as the anhydrous compound. Some of these compounds are useful precursors to the oxides of manganese. [ 1 ] Typical of a manganese(II) compound, it is a paramagnetic pale pink solid.
Manganese(II) compounds, especially with oxygenated ligands, are typically octahedral. Following this trend, the tetrahydrate features four aquo ligands bound to Mn as well as two mutually cis, unidentate nitrate ligands . [ 2 ] The hexaaquo salt features octahedral [Mn(H 2 O) 6 ] 2+ . [ 3 ]
Manganese(II) nitrate is prepared from manganese dioxide and nitrogen dioxide : [ 1 ]
In this redox reaction, two moles of the reductant NO 2 (gas) donate each one electron to MnO 2 (black solid), the oxidant , which is reduced from its oxidation state (+4) to its lower state (+2). Simultaneously, NO 2 (+4) is oxidized to form nitrate ( NO − 3 ) (+5).
Heating the tetrahydrate to 110 °C gives the pale yellow monohydrate. [ 4 ] The reaction is reversible in the sense that heating the Mn(II) dinitrate to 450 °C gives a slightly nonstoichiometric Mn(IV) dioxide. [ 5 ]
Manganese(II) nitrate is the precursor to manganese(II) carbonate ( MnCO 3 ), which is used in fertilizers and as a colourant . The advantage of this method, based on the use of ammonia ( NH 3 ) and carbon dioxide (CO 2 ) as reaction intermediates, being that the side product ammonium nitrate ( NH 4 NO 3 ) is also useful as a fertilizer. [ 1 ] | https://en.wikipedia.org/wiki/Mn(NO3)2 |
Dimanganese decacarbonyl , [ 3 ] which has the chemical formula Mn 2 (CO) 10 , is a binary bimetallic carbonyl complex centered around the first row transition metal manganese . The first reported synthesis of Mn 2 (CO) 10 was in 1954 at Linde Air Products Company and was performed by Brimm, Lynch, and Sesny. [ 4 ] Their hypothesis about, and synthesis of, dimanganese decacarbonyl was fundamentally guided by the previously known dirhenium decacarbonyl (Re 2 (CO) 10 ), the heavy atom analogue of Mn 2 (CO) 10 . Since its first synthesis, Mn 2 (CO) 10 has been use sparingly as a reagent in the synthesis of other chemical species, but has found the most use as a simple system on which to study fundamental chemical and physical phenomena, most notably, the metal-metal bond . Dimanganese decacarbonyl is also used as a classic example to reinforce fundamental topics in organometallic chemistry like d-electron count , the 18-electron rule , oxidation state , valency , [ 5 ] and the isolobal analogy .
Many procedures have been reported for the synthesis of Mn 2 (CO) 10 since 1954. Some of these methods serendipitously produce Mn 2 (CO) 10 .
The carbonylation route involves treatment of Mn(II) salt under high pressure of CO and in the presence of a reductant. This is the method reported in 1954 by Brimm, Lynch, and Sesny, albeit in yields of ~1%. They used manganese(II) iodide with magnesium(0) as the reductant under 3000 psi (~200 atm) of carbon monoxide (CO): [ 4 ]
A more efficient preparation was developed in 1958 and entails reduction of anhydrous manganese(II) chloride with sodium benzophenone ketyl radical under similarly high pressures (200 atm) of CO. [ 6 ] The yield is ~32%.
An ambient pressure synthesis of Mn 2 (CO) 10 was reported from the commercially available and inexpensive methylcyclopentadienyl manganese tricarbonyl (MMT) and sodium(0) as the reductant. [ 7 ] The balanced equation being:
The efficiency of the method ranged from 16 to 20% yield, lower than what was previously reported, however, it could be performed more conveniently and on mole scale .
pentacarbonylhydridomanganese(-I) Mn source, oxidized by Se(PF 2 ) 2 : [ 8 ] Other terminal oxidants achieve the same effect, [ 9 ] [ 10 ] [ 11 ] and stable pentacarbonylmanganate (Mn(CO) − 5 ) salts can substitute for the hydride. [ 12 ] [ 13 ] [ 14 ] Thus for example triphenylcyclopropenium tetrafluoroborate reacts with sodium pentacarbonyl manganate to produce the dimer of each: [ 15 ]
Similar methods exist for Mn(CO) 5 X compounds where X = Cl , Br , or I ; and, more rarely, for Mn(CO) + 6 bound with a weakly coordinating anion . [ 16 ] [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] One additional interesting synthesis of Mn 2 (CO) 10 occurs by combination of a hexacarbonylmanganese(I) tetrafluoroborate salt with a sodium pentacarbonyl manganate salt. In this instance, manganese is both the oxidant and reductant, producing two formal Mn(0) atoms: [ 22 ] [ Mn ( CO ) 6 ] ( BF 4 ) + Na [ Mn ( CO ) 5 ] ⟶ Mn 2 ( CO ) 10 + Na [ BF 4 ] + CO {\displaystyle {\ce {[Mn(CO)6](BF4) + Na[Mn(CO)5] -> Mn2(CO)10 + Na[BF4] + CO}}}
This hypothesized structure was confirmed explicitly through x-ray diffraction studies , first in two dimensions in 1957, [ 23 ] followed by its single crystal three-dimensional analysis in 1963. [ 24 ] The crystal structure of Mn 2 (CO) 10 was redetermined at high precision at room temperature in 1981 and bond lengths mentioned herein refer to results from that study. [ 25 ] Mn 2 (CO) 10 has no bridging CO ligands: it can be described as containing two axially-linked (CO) 5 Mn- subunits. These Mn subunits are spaced at a distance of 290.38(6) pm, a bonding distance that is longer than that predicted. [ 26 ] Two CO ligands are linked to each Mn atom that is coaxial with the Mn-Mn bond and four “equatorial” carbonyls bonded to each Mn atom that are nearly perpendicular to the Mn-Mn bond (Mn’-Mn-CO(equatorial) angles range from 84.61(7) to 89.16(7) degrees). The axial carbonyl distance of (181.1 pm ) is 4.5 pm shorter than the average equatorial manganese-carbonyl distance of 185.6 pm . In the stable rotamer , the two Mn(CO) 5 subunits are staggered . Thus, the overall molecule has approximate point group D 4d symmetry, which is an uncommon symmetry shared with S 2 F 10 . The Mn 2 (CO) 10 molecule is isomorphous with the other group 7 binary metal carbonyls Tc 2 (CO) 10 and Re 2 (CO) 10 .
Initial fundamental experimental and theoretical studies on the electronic structure of Mn 2 (CO) 10 were performed used a mixture of photoelectron spectroscopy , infrared spectroscopy , and an iterative extended-Hückel-type molecular orbital calculation. [ 27 ] [ 28 ] The electronic structure of Mn 2 (CO) 10 was most reported in 2017 using the BP86D functional with TZP basis set . [ 29 ] The electronic structure described herein, along with relevant orbital plots, are reproduced from the methods used in that study using Orca (5.0.3) [ 30 ] and visualized using IBOView (v20150427). [ 31 ] The two main interactions of interest in the system are the metal-to-ligand pi-backbonding interactions and the metal-metal sigma bonding orbital. The pi-backbonding interactions illustrated below occur between the t 2g d-orbital set and the CO π* antibonding orbitals . The degenerate d xz and d yz backbonding interactions with both axial and equatorial CO ligands is the HOMO-15 . More total delocalization occurs onto the axial CO antibonding orbital than does the equatorial, which is thought to rationalize the shorter Mn-C bond length. The primary Mn-Mn σ-bonding orbital is composed of two d z2 orbitals, represented by the HOMO-9.
Other large contributions made in this area were by Ahmed Zewail using ultrafast, femtosecond spectroscopy en route to his 1999 Nobel Prize . [ 32 ] His discoveries elucidated much about the time scales and energies associated with the molecular motions of Mn 2 (CO) 10 , as well as the Mn-Mn and Mn-C bond cleavage events. [ 33 ]
Mn 2 (CO) 10 is air stable as a crystalline solid, but solutions require Schlenk techniques. Mn 2 (CO) 10 is chemically active at both the Mn-Mn and Mn-CO bonds due to low, and similar, bond dissociation energies of ~36 kcal/mol (151 kJ/mol) [ 34 ] and ~38 kcal/mol (160 kJ/mol), [ 35 ] respectively. For this reason, reactivity can happen at either site of the molecule, sometimes selectively.
The Mn-Mn bond is sensitive to both oxidation and reduction, producing two equivalents of the corresponding Mn(I) and Mn(-I) species, respectively. Both of the potential resultant species can be derived further. Redox neutral cleavage is possible both thermally and photochemically , producing two equivalents of the Mn(0) radical.
Selective mono-oxidation of the Mn-Mn bond is most often done via addition of classical metal oxidants (e.g. Ce IV , Pb IV , etc) or weak homonuclear single covalent bonds of the form X-X (X is group 16 or 17 element). [ 36 ] [ 37 ] [ 38 ] [ 39 ] [ 40 ] These reactions yield the [Mn(CO) 5 ] + cation with a bound weakly coordinating anion, or the Mn(CO) 5 X complex. The general reaction schemes for each are seen as balanced equations below: Mn 2 ( CO ) 10 + 2 M n X n ⟶ 2 Mn ( CO ) 5 X + 2 M ( n − 1 ) X ( n − 1 ) {\displaystyle {\ce {Mn2(CO)10 + 2 M^{n}X_{n}-> 2Mn(CO)5X + 2M^{(n-1)}X_{(n-1)}}}} or for two-electron oxidants Mn 2 ( CO ) 10 + M n X n ⟶ 2 Mn ( CO ) 5 X + M ( n − 2 ) X ( n − 2 ) {\displaystyle {\ce {Mn2(CO)10 + M^{n}X_{n}-> 2Mn(CO)5X + M^{(n-2)}X_{(n-2)}}}} and Mn 2 ( CO ) 10 + RE − ER ⟶ 2 Mn ( CO ) 5 ( ER ) {\displaystyle {\ce {Mn2(CO)10 + RE-ER -> 2Mn(CO)5(ER)}}} for E = O , S , Se , Te Mn 2 ( CO ) 10 + X − X ⟶ 2 Mn ( CO ) 5 X {\displaystyle {\ce {Mn2(CO)10 + X-X -> 2Mn(CO)5X}}} for X = F , Cl, Br, I
Reductive cleavage is almost always done with sodium metal, [ 41 ] [ 42 ] yielding the [Mn(CO) 5 ] − anion with the sodium counterion . The balanced general reactions are given below: Mn 2 ( CO ) 10 + 2 Na 0 ⟶ 2 Na [ Mn ( CO ) 5 ] {\displaystyle {\ce {Mn2(CO)10 + 2 Na^{0}-> 2Na[Mn(CO)5]}}} The resultant manganate anion is a potent nucleophile , which can be protonated to give the manganese hydride, [ 43 ] [ 44 ] or alkylated with organic halides [ 45 ] [ 46 ] [ 43 ] to give a large swath of organomanganese(I) complexes.
Homolytic cleavage , usually via light, [ 47 ] but sometimes heat, [ 48 ] gives the Mn(0) metalloradical, which can react with itself to reform Mn 2 (CO) 10 , or combine with other radical species that usually result in formal oxidation to Mn(I). This reactivity is comparable to that of organic, carbon-based radicals via the isolobal analogy. The homolytic cleavage is given by: Mn 2 ( CO ) 10 + h ν ⟶ 2 [ Mn ( CO ) 5 ] ⋅ {\displaystyle {\ce {Mn2(CO)10 + h\nu -> 2[Mn(CO)5]^{.}}}} The use of the produced radical species, [Mn(CO) 5 ]*, has found several applications as a radical initiator for various organic methodologies [ 49 ] [ 50 ] [ 51 ] and polymerization reactions. [ 52 ] [ 53 ] [ 54 ]
Ligand substitution reactions that do not disrupt the Mn-Mn bonding is done by using strongly sigma donating L-type ligands that can outcompete CO without participating in redox reactivity. [ 55 ] This requirement usually necessitates phosphines [ 56 ] [ 57 ] or N-heterocyclic carbenes (NHCs), [ 58 ] with substitution occurring at the axial position according to the reactions below:
Mn 2 (CO) 10 is a volatile source of a metal and a source of CO. | https://en.wikipedia.org/wiki/Mn2(CO)10 |
Manganese(III) oxide is a chemical compound with the formula Mn 2 O 3 . It occurs in nature as the mineral bixbyite (recently changed to bixbyite-(Mn) [ 3 ] [ 4 ] ) and is used in the production of ferrites and thermistors .
Heating MnO 2 in air at below 800 °C produces α-Mn 2 O 3 (higher temperatures produce Mn 3 O 4 ). [ 5 ] γ-Mn 2 O 3 can be produced by oxidation followed by dehydration of manganese(II) hydroxide . [ 5 ] Many preparations of nano-crystalline Mn 2 O 3 have been reported, for example syntheses involving oxidation of Mn II salts or reduction of MnO 2 . [ 6 ] [ 7 ] [ 8 ]
Manganese(III) oxide is formed by the redox reaction in an alkaline cell:
Manganese(III) oxide Mn 2 O 3 must not be confused with MnOOH manganese(III) oxyhydroxide. Contrary to Mn 2 O 3 , MnOOH is a compound that decomposes at about 300 °C to form MnO 2 . [ 9 ]
Mn 2 O 3 is unlike many other transition metal oxides in that it does not adopt the corundum ( Al 2 O 3 ) structure. [ 5 ] Two forms are generally recognized, α-Mn 2 O 3 and γ-Mn 2 O 3 , [ 10 ] although a high pressure form with the CaIrO 3 structure has been reported too. [ 11 ]
α-Mn 2 O 3 has the cubic bixbyite structure, which is an example of a C-type rare earth sesquioxide ( Pearson symbol cI80, space group Ia 3 , #206). The bixbyite structure has been found to be stabilised by the presence of
small amounts of Fe 3+ , pure Mn 2 O 3 has an orthorhombic structure ( Pearson symbol oP24, space group Pbca, #61). [ 12 ] α-Mn 2 O 3 undergoes antiferromagnetic transition at 80 K. [ 13 ]
γ-Mn 2 O 3 has a structure related to the spinel structure of Mn 3 O 4 where the oxide ions are cubic close packed. This is similar to the relationship between γ-Fe 2 O 3 and Fe 3 O 4 . [ 10 ] γ-Mn 2 O 3 is ferrimagnetic with a Néel temperature of 39 K. [ 14 ]
ε-Mn 2 O 3 takes on a rhombohedral ilmenite structure (the first binary compound known to do so), wherein the manganese cations divided equally into oxidation states 2+ and 4+. ε-Mn 2 O 3 is antiferromagnetic with a Néel temperature of 210 K. [ 15 ] | https://en.wikipedia.org/wiki/Mn2O3 |
Manganese(VII) oxide (manganese heptoxide) is an inorganic compound with the formula Mn 2 O 7 . Manganese heptoxide is a volatile liquid with an oily consistency. It is a highly reactive and powerful oxidizer that reacts explosively with nearly any organic compound . It was first described in 1860. [ 1 ] It is the acid anhydride of permanganic acid .
The crystalline form of this chemical compound is dark green. The liquid is green by reflected light and red by transmitted light. [ 2 ] It is soluble in carbon tetrachloride , and decomposes when in contact with water.
Its solubility properties indicate a nonpolar molecular species, which is confirmed by its structure. The molecules consist of a pair of tetrahedra that share a common vertex. The vertices are occupied by oxygen atoms and at the centers of the tetrahedra are the Mn(VII) centers. The connectivity is indicated by the formula O 3 Mn−O−MnO 3 . The terminal Mn−O distances are 1.585 Å and the bridging oxygen is 1.77 Å distant from the two Mn atoms. The Mn−O−Mn angle is 120.7°. [ 3 ]
Pyrosulfate , pyrophosphate , and dichromate adopt structures similar to that of Mn 2 O 7 . Probably the most similar main group species is Cl 2 O 7 . Focusing on comparisons within the transition metal series, Tc 2 O 7 and Mn 2 O 7 are structurally similar but the Tc−O−Tc angle is 180°. Solid Re 2 O 7 is not molecular but consists of crosslinked Re centers with both tetrahedral and octahedral sites; [ 4 ] in the vapour phase it is molecular with a similar structure to Tc 2 O 7 . [ 5 ]
Mn 2 O 7 arises as a dark green oil by the addition of cold concentrated H 2 SO 4 to solid KMnO 4 . [ 2 ] The reaction initially produces permanganic acid , HMnO 4 (structurally, HOMnO 3 ), which is dehydrated by cold sulfuric acid to form its anhydride , Mn 2 O 7 :
Mn 2 O 7 can react further with sulfuric acid to give the remarkable manganyl(VII) cation MnO + 3 , which is isoelectronic with CrO 3 :
Mn 2 O 7 decomposes near room temperature, explosively so above 55 °C (131 °F). The explosion can be initiated by striking the sample or by its exposure to oxidizable organic compounds. The products are MnO 2 and O 2 . [ 6 ] Ozone is also produced, giving a strong smell to the substance. The ozone can spontaneously ignite a piece of paper impregnated with an alcohol solution. [ citation needed ]
Manganese heptoxide reacts with hydrogen peroxide in presence of sulfuric acid , liberating oxygen and ozone :
Demonstration of manganese heptoxide's properties on YouTube | https://en.wikipedia.org/wiki/Mn2O7 |
MnO·Mn 2 O 3
Manganese(II,III) oxide is the manganese oxide with the chemical compound with formula Mn 3 O 4 . Manganese is present in two oxidation states , +2 and +3, and the formula is sometimes written as MnO · Mn 2 O 3 . Mn 3 O 4 is found in nature as the mineral hausmannite .
Mn 3 O 4 formed when any manganese oxide is heated in air above 1000 °C. [ 3 ] Considerable research has centred on producing nanocrystalline Mn 3 O 4 and various syntheses that involve oxidation of Mn II or reduction of Mn VI . [ 4 ] [ 5 ] [ 6 ]
Mn 3 O 4 has been found to act as a catalyst for a range of reactions e.g. the oxidation of methane and carbon monoxide; [ 7 ] [ 8 ] the decomposition of NO, [ 9 ] the reduction of nitrobenzene [ 10 ] and the catalytic combustion of organic compounds. [ 11 ]
Mn 3 O 4 has the spinel structure, where the oxide ions are cubic close packed and the Mn II occupy tetrahedral sites and the Mn III octahedral sites. [ 3 ] The structure is distorted due to the Jahn–Teller effect . [ 3 ] At room temperature Mn 3 O 4 is paramagnetic , below 41-43 K, it is ferrimagnetic [ 12 ] although this has been reported as reducing in nanocrystalline samples to around 39 K. [ 13 ]
Mn 3 O 4 is sometimes used as a starting material in the production of soft ferrites e.g. manganese zinc ferrite, [ 14 ] and lithium manganese oxide, used in lithium batteries. [ 15 ]
Manganese tetroxide can also be used as a weighting agent while drilling reservoir sections in oil and gas wells. [ citation needed ] | https://en.wikipedia.org/wiki/Mn3O4 |
Geigerite is a mineral, a complex hydrous manganese arsenate with formula: Mn 5 (AsO 3 OH) 2 (AsO 4 ) 2 ·10H 2 O. It forms triclinic pinacoidal, vitreous, colorless to red to brown crystals. It has a Mohs hardness of 3 and a specific gravity of 3.05. [ 2 ] [ 3 ]
It was discovered in Grischun , Switzerland in 1989. It was named
in honor of Thomas Geiger (1886–1976), Wiesendangen, Switzerland, who studied the Falotta manganese ores. [ 5 ] [ 6 ]
The chemical composition of geigerite is hydrous manganese arsenate (Mn 5 (AsO 3 OH) 2 (AsO 4 ) 2 ·10H 2 O). [ 4 ] The chemical composition was found by using an electron microprobe in the Falotta mines in Switzerland. [ 4 ]
Geigerite can be found in the abandoned manganese mine in Oberhalbstein, Switzerland. It is mainly found in cavities in adiolarites, which are a form of igneous rock that have either a
radial or fanlike texture of crystals. Geigerite is then formed by metamorphism of manganese
oxide ores. [ 4 ] Recently, geigerite has been found in Fukushima Prefecture , Japan. [ 7 ] Geigerite has also been found in Mt. Nero Mine, Borghetto Di Vara , La Spieza, Italy. [ 8 ]
Geigerite’s crystal system is triclinic with perfect cleavage on the {010}. The Herman Mauguin symbol for geigerite is 1 and its space group is P 1 . [ 2 ] Geigerite contains two arsenate ions which are independent of one another. The first is the AsO 3 OH group, and the second is the AsO 4 . In the acidic AsO 3 OH group, the As-O bonds are much shorter than the As-OH bonds. Similarly, in the AsO 4 group, As-O bonds are also shorter than the As-O bonds. The remaining bonds within both arsenate groups have nearly equal distances. In the ions there are three manganese atoms, these three links to six oxygen atoms to form a normal octahedral formation. [ 4 ]
One interesting structural feature of geigerite is the presence of a complicated network of
hydrogen bonds, which exceed the number of the hydrogen atoms. [ 4 ] Geigerite
is classified under a group of metal copper (II) arsenates called the Lindackerite group. Minerals
within this group have a formula where M equals either copper, calcium, manganese, zinc, or
cobalt. [ 9 ] | https://en.wikipedia.org/wiki/Mn5(AsO3OH)2(AsO4)2·10H2O |
Arsenoclasite (originally arsenoklasite ) is a red or dark orange brown mineral with formula Mn 5 (AsO 4 ) 2 (OH) 4 . The name comes from the Greek words αρσενικόν (for arsenic ) and κλάσις (for cleavage ), as arsenoclasite contains arsenic and has perfect cleavage. [ 1 ] The mineral was discovered in 1931 in Långban , Sweden.
Arsenoclasite is red or dark orange brown in color. The mineral rarely occurs as crystals; rather it has either a massive or granular habit . When crystals are present, they are no larger than 5 millimetres (0.20 in). Arsenoclasite has been found in association with adelite , allactite , barite , calcite , dolomite , gatehouseite , hausmannite , hematite , manganoan ferroan calcite, sarkinite , and shigaite . The mineral occurs in fissures of metamorphosed Fe - Mn ore bodies and sedimentary Fe-Mn deposits. [ 3 ]
A 1971 study identified the mineral's structure as an array of oxygen atoms in a double hexagonal close packed pattern. However, a 1977 study discovered that all the manganese ions in arsenoclasite are six-coordinated , a constraint this structure cannot permit without severe distortion. [ 6 ] The 1977 study identified arsenoclasite as isostructural to Co 5 (PO 4 ) 2 (OH) 4 and Mn 5 (PO 4 ) 2 (OH) 4 . [ 7 ]
Arsenoclasite was noted from specimens at Långban , Värmland , Sweden, by Gust Flink in 1924 as a mineral that appeared similar to sarkinite , but with one perfect cleavage. [ 8 ] Arsenoclasite was discovered in Långban and officially identified by G. Aminoff in 1931 under the name arsenoklasite. [ 8 ] [ 9 ] The samples observed by Aminoff did not occur as crystals. [ 10 ]
As of 2012 [update] , arsenoclasite is known from Långban, Sweden, the Valgraveglia Mine in Liguria , Italy, and the Iron Monarch open cut in South Australia . [ 1 ] The type material is held at the Swedish Museum of Natural History in Stockholm and the Natural History Museum, London . [ 3 ] | https://en.wikipedia.org/wiki/Mn5(AsO4)2(OH)4 |
Hureaulite is a manganese phosphate with the formula Mn 2+ 5 (PO 3 OH) 2 (PO 4 ) 2 ·4H 2 O . It was discovered in 1825 and named in 1826 for the type locality, Les Hureaux, Saint-Sylvestre, Haute-Vienne , Limousin , France . It is sometimes written as huréaulite, but the IMA does not recommend this for English language text. [ 7 ]
A complete series exists from lithiophilite , LiMn 2+ PO 4 to triphylite , LiFe 2+ PO 4 , including hureaulite, strengite, FePO 4 ·2H 2 O , stewartite, Mn 2+ Fe 3+ 2 (OH,PO 4 ) 2 ·8H 2 O , and sicklerite, (LiMn 2+ ,Fe 3+ )PO 4 . [ 8 ]
Hureaulite is a secondary mineral occurring in granite pegmatites . [ 6 ] At the type locality it occurs in a zone of altered triphylite , LiMn 2+ PO 4 , in pegmatite. Typically occurs very late in the sequence of formation of secondary phosphate minerals. [ 9 ] Associated at the type locality with vivianite , Fe 2+ 3 (PO 4 ) 2 ·8H 2 O ; rockbridgeite , Fe 2+ Fe 3+ 4 (PO 4 ) 3 (OH) 5 ; heterosite , (Fe 3+ ,Mn 3+ )PO 4 and cacoxenite , Fe 3+ 24 AlO 6 (PO 4 ) 17 (OH) 12 ·17H 2 O . It can be synthesised; [ 10 ] most natural hureaulites are Mn-rich compounds but extensive ( Mn,Fe ) solution is known for synthetic material. [ 9 ]
The type locality is Les Hureaux, Saint-Sylvestre, Haute-Vienne, Limousin , France . Hureaulite is also found in a granite pegmatite known for its phosphates in the Aimorés pegmatite district, at the Cigana claim in Galiléia , Doce valley, Minas Gerais , Brazil , formerly known as the Jocão Mine. [ 4 ] | https://en.wikipedia.org/wiki/Mn5(PO3OH)2(PO4)2·4H2O |
Gatehouseite is a manganese hydroxy phosphate mineral with formula Mn 5 (PO 4 ) 2 (OH) 4 . [ 5 ] First discovered in 1987, it was identified as a new mineral species in 1992 and named for Bryan M. K. C. Gatehouse (born 1932). As of 2012 [update] , it is known from only one mine in South Australia .
Gatehouseite occurs as radiating or divergent groups of bladelike crystals up to 100 μm by 20 μm by 5 μm in size and as overgrowths on arsenoclasite that are up to 5 mm long. [ 6 ] The transparent mineral can be brownish-orange or yellow in color. [ 3 ] Gatehouseite is the phosphorus analogue of arsenoclasite. [ 6 ]
The mineral occurs in cavities in sedimentary iron and manganese deposits in association with arsenoclasite , shigaite , hematite , hausmannite , triploidite , barite , and manganoan ferroan calcite . [ 3 ] Based on a 1977 experiment that produced triploidite, it is likely that gatehouseite formed by a reaction between hausmannite and basic phosphorus-rich fluids at low temperature and variable pH conditions. [ 3 ] [ 6 ]
In May 1987, Glyn Francis, an employee at the Iron Monarch mine in South Australia, submitted for identification some mineral specimens from the mine to A. Pring. Very small, unidentified pale brownish orange crystals were seen in one specimen; study showed they had a formula of the type M 5 ( X O 4 ) 2 (OH) 4 and contained manganese , phosphorus , and a minor quantity of arsenic . The powder X-ray diffraction pattern could not be recorded as insufficient material was available. Another specimen in the same group consisted of arsenoclasite crystals overgrown by what appeared to be its as yet undescribed phosphorus analogue. [ 5 ] Francis later discovered more of the brownish orange crystals in sufficient quantity to obtain an X-ray diffraction pattern . This proved that the crystals and the overgrowths were the same, new mineral species. [ 6 ]
Gathehouseite was named for Bryan Michael Kenneth Cummings Gatehouse for his contributions to the study of oxides and oxysalts . The Commission on New Minerals and Mineral Names recognized the mineral and approved its name in 1992 (IMA 1992-016). [ 1 ] [ 6 ]
Due to the small size and intergrowth of the crystals, single-crystal X-ray crystallography is difficult to perform on gatehouseite. In 2011, this technique was successfully used to determine the crystal structure of the mineral. [ 4 ]
The type material is housed at the South Australian Museum in Adelaide and the Museum of Victoria in Melbourne. [ 6 ] As of 2012 [update] , the Iron Monarch open cut remains the only site from which gatehouseite is known. [ 1 ]
Gatehouseite has the space group P2 1 2 1 2 1 . The crystal structure consists of Mn(O, OH) 6 octahedra and PO 4 tetrahedra . The five manganese sites are occupied by manganese and small amounts of magnesium. The two phosphorus sites are occupied by phosphorus and small amounts of silicon and arsenic. [ 4 ] | https://en.wikipedia.org/wiki/Mn5(PO4)2(OH)4 |
Alleghanyite is a moderately rare humite mineral with formula Mn 5 (SiO 4 ) 2 (OH) 2 , belonging to the nesosilicates class. In general its occurrences are related with metamorphic (metamorphosed) manganese deposits. The mineral is named after Alleghany County , North Carolina , US. [ 2 ]
This article about a specific silicate mineral is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Mn5(SiO4)2(OH)2 |
Waterhouseite , Mn 7 (PO 4 ) 2 (OH) 8 , is a hydroxy manganese phosphate mineral. It is a medium-soft, brittle mineral occurring in pseudo-orthorhombic monoclinic bladed crystals and orange-brown to dark brown in color. Waterhouseite is on the softer side with a Mohs hardness of 4, has a specific gravity of 3.5 and a yellowish-brown streak . It is named after Frederick George Waterhouse , first director of the South Australian Museum, as well as recognizes the work Waterhouse Club has done in support of the South Australian Museum. [ 4 ]
Waterhouseite occurs in divergent sprays of bladed crystals up to 1mm in length and 20 micrometers in thickness. [ 4 ]
It is found in South Australia , specifically in the Iron Monarch mine, Iron Knob , Middleback Range , Eyre Peninsula , South Australia.
Waterhouseite is generally found in a carbonate rich cavities with other minerals such as gatehouseite , seamanite , rhodochrosite , shigaite , baryte , hausmannite and hematite .
Waterhouseite has a unique asymmetrical structure consisting of a dense, complex framework of Mn(O, OH) 6 octahedra and PO 4 tetrahedra which are linked by both edges and corners. [ 4 ] It is highly unusual for the PO 4 tetrahedron to share two of its edges with the Mn(O, OH) 6 octahedral. There are only two other known arsenates that have the same edge sharing as waterhouseite. | https://en.wikipedia.org/wiki/Mn7(PO4)2(OH)8 |
Manganese arsenide ( MnAs ) is an intermetallic compound , an arsenide of manganese . It forms ferromagnetic crystals with hexagonal (NiAs-type) crystal structure, which convert to the paramagnetic orthorhombic β-phase upon heating to 45 °C (113 °F). MnAs has potential applications in spintronics , for electrical spin injection into GaAs and Si based devices. [ 2 ] | https://en.wikipedia.org/wiki/MnAs |
Manganese(II) bromide is the chemical compound composed of manganese and bromine with the formula MnBr 2 .
It can be used in place of palladium in the Stille reaction , which couples two carbon atoms using an organotin compound . [ 2 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/MnBr2 |
Manganese carbonate is a compound with the chemical formula Mn CO 3 . Manganese carbonate occurs naturally as the mineral rhodochrosite but it is typically produced industrially. It is a pale pink, water-insoluble solid. Approximately 20,000 metric tonnes were produced in 2005. [ 3 ]
MnCO 3 adopts a structure like calcite , consisting of manganese(II) ions in an octahedral coordination geometry . [ 4 ]
Treatment of aqueous solutions of manganese(II) nitrate with ammonia and carbon dioxide leads to precipitation of this faintly pink solid. The side product, ammonium nitrate is used as fertilizer.
The carbonate is insoluble in water but, like most carbonates, hydrolyses upon treatment with acids to give water-soluble salts.
Manganese carbonate decomposes with release of carbon dioxide , i.e. calcining , at 200 °C to give MnO 1.88 :
This method is sometimes employed in the production of manganese dioxide , which is used in dry-cell batteries and for ferrites . [ 3 ]
Manganese carbonate is widely used as an additive within plant fertilizers. It is also used in multivitamins , in ceramics as a glaze colorant and flux, and in concrete stains . [ 5 ]
Manganese poisoning, also known as manganism , may be caused by long-term exposure to manganese dust or fumes. | https://en.wikipedia.org/wiki/MnCO3 |
Manganese(II) chloride is the di chloride salt of manganese , MnCl 2 . This inorganic chemical exists in the anhydrous form, as well as the di hydrate (MnCl 2 ·2H 2 O) and tetrahydrate (MnCl 2 ·4H 2 O), with the tetrahydrate being the most common form. Like many Mn(II) species, these salts are pink, with the paleness of the color being characteristic of transition metal complexes with high spin d 5 configurations. [ 2 ]
Manganese chloride is produced by treating manganese(IV) oxide with concentrated hydrochloric acid.
In the 19th century this reaction was used for the manufacture of chlorine . By carefully neutralizing the resulting solution with MnCO 3 , one can selectively precipitate iron salts, which are common impurities in manganese dioxide. [ 3 ] In the laboratory, manganese chloride can be prepared by treating manganese metal or manganese(II) carbonate with hydrochloric acid :
Anhydrous MnCl 2 adopts a layered cadmium chloride -like structure. The tetrahydrate consists of octahedral cis -Mn(H 2 O) 4 Cl 2 molecules. The trans isomer, which is metastable, is also known. [ 4 ] [ 5 ] The dihydrate MnCl 2 (H 2 O) 2 is a coordination polymer . Each Mn center is coordinated to four doubly bridging chloride ligands . The octahedron is completed by a pair of mutually trans aquo ligands . [ 6 ]
The hydrates dissolve in water to give mildly acidic solutions with a pH of around 4. These solutions consist of the metal aquo complex [Mn(H 2 O) 6 ] 2+ .
It is a weak Lewis acid , reacting with chloride ions to produce a series of salts containing the following ions [MnCl 3 ] − , [MnCl 4 ] 2− , and [MnCl 6 ] 4− .
Upon treatment with typical organic ligands, manganese(II) undergoes oxidation by air to give Mn(III) complexes . Examples include [Mn( EDTA )] − , [Mn( CN ) 6 ] 3− , and [Mn( acetylacetonate ) 3 ]. Triphenylphosphine forms a labile 2:1 adduct :
Anhydrous manganese(II) chloride serves as a starting point for the synthesis of a variety of organomanganese compounds . For example, manganocene is prepared by reaction of MnCl 2 with a solution of sodium cyclopentadienide in tetrahydrofuran (THF).
Similar reactions are used in the preparation of the antiknock compound methylcyclopentadienyl manganese tricarbonyl . [ 3 ]
Manganese chloride is a precursor to organomanganese reagents in organic chemistry. [ 7 ] [ 8 ]
Manganese chloride is mainly used in the production of dry cell batteries.
Manganese(II) salts are paramagnetic. As such the presence of such salts profoundly affect NMR spectra . [ 9 ]
Scacchite is the natural, anhydrous form of manganese(II) chloride. [ 10 ]
Manganism , or manganese poisoning, can be caused by long-term exposure to manganese dust or fumes. | https://en.wikipedia.org/wiki/MnCl2 |
Manganese(III) chloride is the hypothetical inorganic compound with the formula MnCl 3 .
The existence of this binary halide has not been demonstrated. [ 1 ] [ 2 ] Nonetheless, many derivatives of MnCl 3 are known, such as MnCl 3 (THF) 3 and the bench-stable MnCl 3 (OPPh 3 ) 2 . Contrasting with the elusive nature of MnCl 3 , trichlorides of the adjacent metals on the periodic table — iron(III) chloride , chromium(III) chloride , and technetium(III) chloride —are all isolable compounds.
MnCl 3 was claimed to be a dark solid and produced by the reaction of "anhydrous manganese(III) acetate " and liquid hydrogen chloride at −100 °C and decomposes above -40 °C. [ 3 ] Other claims involved reaction of manganese(III) oxide , manganese(III) oxide-hydroxide, and basic manganese acetate with hydrochloric acid . Given recent investigations however, such claims have been disproved or called into serious doubt. [ 4 ] Specifically, all known compounds containing MnCl 3 are known to be solvent or ligand-stabilized adducts .
MnCl 3 can be stabilized by complexation to diverse Lewis bases , as has been established over the course of many years of study. [ 4 ] Meta stable acetonitrile -solvated Mn(III)Cl 3 can be prepared at room temperature by treating [Mn 12 O 12 (OAc) 16 (H 2 O) 4 ] with trimethylsilyl chloride . [ 5 ] The treatment of permanganate salts with trimethylsilylchloride generates solutions containing Mn(III)–Cl species for alkene dichlorination reactions; [ 6 ] [ 7 ] [ 8 ] electrocatalytic methods that use Mn(III)–Cl intermediates have been developed for the same purpose. [ 9 ] [ 10 ]
The reaction of manganese dioxide with hydrochloric acid in tetrahydrofuran gives MnCl 3 (H 2 O)(THF) 2 . [ 4 ] Manganese(III) fluoride suspended in THF reacts with boron trichloride , giving MnCl 3 (THF) 3 which has the appearance of dark purple prisms. [ 4 ] This compound has a monoclinic crystal structure, reacts with water, and decomposes at room temperature. [ 4 ]
The most readily handled of this series of adducts is MnCl 3 (OPPh 3 ) 2 . [ 11 ]
Another common manganese(III) chloride compound is the pentachloromanganate(III) dianion. It is usually charge balanced with counterion (s) like tetraethylammonium . [ 12 ] The pentachloromanganates are typically green in color, light sensitive, maintain pentacoordination in solution, and have S = 2 ground states at room temperature. [ 12 ] [ 13 ] Crystal structures of pentachloromanganate indicate the anion is square pyramidal . [ 14 ] [ 15 ] Tetraethylammonium pentachloromanganate(III), [Et 4 N] 2 [MnCl 5 ], can be prepared and isolated by treating suspension of [Mn 12 O 12 (OAc) 16 (H 2 O) 4 ] in diethyl ether with trimethylsilylchloride , collecting the resulting purple solid in the dark, and then treating this solid with 0.6 M solution of tetraethylammonium chloride . [ 5 ] The green product is air stable but should be kept in the dark.
Some manganese compounds with macrocyclic tetradentate coordination can stabilize the manganese(III) monochloride, Mn(III)–Cl, moiety. Jacobson's catalyst is an example of a coordination compound containing the Mn(III)–Cl moiety and is stabilized by N,N,O,O coordination from a salen ligand . Jacobson's catalyst and related Mn(III)–Cl complexes react with O-atom transfer reagents to form high-valent Mn(V)O that are reactive in alkene epoxidation . Tetraphenylporphyrin Mn(III)Cl is a related commercially available compound. | https://en.wikipedia.org/wiki/MnCl3 |
Manganese(II) fluoride is the chemical compound composed of manganese and fluoride with the formula MnF 2 . It is a light pink solid, the light pink color being characteristic for manganese(II) compounds. It is made by treating manganese and diverse compounds of manganese(II) in hydrofluoric acid . Like some other metal difluorides, MnF 2 crystallizes in the rutile structure, which features octahedral Mn centers. [ 3 ]
MnF 2 is used in the manufacture of special kinds of glass and lasers . [ 4 ] It is a canonical example of uniaxial antiferromagnet (with Neel temperature of 68 K) [ 5 ] which has been experimentally studied since early on. [ 6 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/MnF2 |
Manganese(III) fluoride (also known as Manganese trifluoride ) is the inorganic compound with the formula MnF 3 . This red/purplish solid is useful for converting hydrocarbons into fluorocarbons , i.e., it is a fluorination agent. [ 2 ] It forms a hydrate and many derivatives.
MnF 3 can be prepared by treating a solution of MnF 2 in hydrogen fluoride with fluorine : [ 3 ]
It can also be prepared by the reaction of elemental fluorine with a manganese(II) halide at ~250 °C. [ 4 ]
Like vanadium(III) fluoride , MnF 3 features octahedral metal centers with the same average M-F bond distances. In the Mn compound, however, is distorted (and hence a monoclinic unit cell vs. a higher symmetry one) due to the Jahn-Teller effect , with pairs of Mn-F distances of 1.79, 1.91, 2.09 Å. [ 5 ] [ 6 ] [ 7 ]
The hydrate MnF 3 . 3H 2 O is obtained by crystallisation of MnF 3 from hydrofluoric acid. The hydrate exists as two polymorphs, with space groups P2 1 /c and P2 1 /a. Each consists of the salt [Mn(H 2 O) 4 F 2 ] + [Mn(H 2 O) 2 F 4 ] − ). [ 8 ]
MnF 3 is Lewis acidic and forms a variety of derivatives. One example is K 2 MnF 3 (SO 4 ). [ 9 ] MnF 3 reacts with sodium fluoride to give the octahedral hexafluoride: [ 4 ]
Related reactions salts of the anions MnF 5 2− or MnF 4 − . These anions adopt chain and layer structures respectively, with bridging fluoride. Manganese remains 6 coordinate, octahedral, and trivalent in all of these materials. [ 4 ]
Manganese(III) fluoride fluorinates organic compounds including aromatic hydrocarbons, [ 10 ] cyclobutenes, [ 11 ] and fullerenes . [ 12 ]
On heating, MnF 3 decomposes to manganese(II) fluoride . [ 13 ] [ 14 ]
MnF 3 is a source of MnCl 3 complexes by reaction with bismuth trichloride. [ 15 ] | https://en.wikipedia.org/wiki/MnF3 |
Manganese tetrafluoride , MnF 4 , is the highest fluoride of manganese . It is a powerful oxidizing agent and is used as a means of purifying elemental fluorine . [ 3 ] [ 5 ]
Manganese tetrafluoride was first unequivocally prepared in 1961 [ Note 2 ] by the reaction of manganese(II) fluoride (or other Mn II compounds) with a stream of fluorine gas at 550 °C: the MnF 4 sublimes into the gas stream and condenses onto a cold finger . [ 2 ] [ 7 ] This is still the commonest method of preparation, although the sublimation can be avoided by operating at increased fluorine pressure (4.5–6 bar at 180–320 °C) and mechanically agitating the powder to avoid sintering of the grains. [ 3 ] [ 8 ] The reaction can also be carried out starting from manganese powder in a fluidized bed . [ 9 ] [ 10 ]
Other preparations of MnF 4 include the fluorination of MnF 2 with krypton difluoride , [ 11 ] or with F 2 in liquid hydrogen fluoride solution under ultraviolet light . [ 12 ] Manganese tetrafluoride has also been prepared (but not isolated) in an acid–base reaction between antimony pentafluoride and K 2 MnF 6 as part of a chemical synthesis of elemental fluorine. [ 13 ]
Manganese tetrafluoride is in equilibrium with manganese(III) fluoride and elemental fluorine :
Decomposition is favoured by increasing temperature, and disfavoured by the presence of fluorine gas, but the exact parameters of the equilibrium are unclear, with some sources saying that MnF 4 will decompose slowly at room temperature, [ 14 ] [ 15 ] others placing a practical lower temperature limit of 70 °C, [ 3 ] [ 16 ] and another claiming that MnF 4 is essentially stable up to 320 °C. [ 17 ] The equilibrium pressure of fluorine above MnF 4 at room temperature has been estimated at 10 −4 Pa (10 −9 bar), and the enthalpy change of reaction at +44(8) kJ mol −1 . [ 18 ] [ Note 3 ]
Manganese tetrafluoride reacts violently with water and even with sodium-dried petroleum ether . It immediately decomposes on contact with moist air. [ 2 ]
Reaction with alkali metal fluorides or concentrated hydrofluoric acid gives the yellow hexafluoromanganate(IV) anion [MnF 6 ] 2− . [ 17 ]
The main application of manganese tetrafluoride is in the purification of elemental fluorine . Fluorine gas is produced by electrolysis of anhydrous hydrogen fluoride (with a small amount of potassium fluoride added as a support electrolyte) in a Moissan cell . The technical product is contaminated with HF, much of which can be removed by passing the gas over solid KF, but also with oxygen (from traces of water) and possibly heavy-metal fluorides such as arsenic pentafluoride (from contamination of the HF). These contaminants are particularly problematic for the semiconductor industry, which uses high-purity fluorine for etching silicon wafers. Further impurities, such as iron , nickel , gallium and tungsten compounds, can be introduced if unreacted fluorine is recycled. [ 5 ]
The technical-grade fluorine is purified by reacting it with MnF 3 to form manganese tetrafluoride. As this stage, any heavy metals present will form involatile complex fluorides, while the HF and O 2 are unreactive. Once the MnF 3 has been converted, the excess gas is vented for recycling, carrying the remaining gaseous impurities with it. The MnF 4 is then heated to 380 °C to release fluorine at purities of up to 99.95%, reforming MnF 3 , which can be reused. [ 3 ] [ 5 ] By placing two reactors in parallel, the purification process can be made continuous, with one reactor taking in technical fluorine while the other delivers high-grade fluorine. [ 5 ] Alternatively, the manganese tetrafluoride can be isolated and transported to where the fluorine is needed, at lower cost and greater safety than pressurized fluorine gas. [ 3 ] [ 8 ]
The yellow hexafluoromanganate(2−) of alkali metal and alkaline earth metal cations have been known since 1899, and can be prepared by the fluorination of MnF 2 in the presence of the fluoride of the appropriate cation. [ 12 ] [ 20 ] [ 21 ] [ 22 ] They are much more stable than manganese tetrafluoride. [ 13 ] Potassium hexafluoromanganate(IV), K 2 MnF 6 , can also be prepared by the controlled reduction of potassium permanganate in 50% aqueous hydrofluoric acid . [ 23 ] [ 24 ]
The pentafluoromanganate(1−) salts of potassium , rubidium and caesium , MMnF 5 , can be prepared by fluorination of MMnF 3 or by the reaction of [MnF 4 (py)(H 2 O)] with MF. [ 22 ] [ 24 ] The lemon-yellow heptafluoromanganate(3−) salts of the same metals, M 3 MnF 7 , have also been prepared. [ 25 ]
When potassium hexafluoromanganate is doped into potassium fluorosilicate it forms a narrow band red phosphor. [ 26 ] | https://en.wikipedia.org/wiki/MnF4 |
Manganese germanide ( MnGe ) is an intermetallic compound , a germanide of manganese . Its crystals have a cubic symmetry with no inversion center , they are therefore helical, with right-hand and left-handed chiralities . [ 1 ]
At low temperatures, MnGe and its relative MnSi exhibit unusual spatial arrangements of electron spin, which were named magnetic skyrmion , tetrahedral and cubic hedgehog lattices. Their structure can be controlled not only by the Si/Ge ratio, but also by temperature and magnetic field. This property has potential application in ultrahigh-density magnetic storage devices. [ 2 ]
MnGe crystals can be produced by processing a mixture of Mn and Ge powders at a pressure of 4–5 GPa and a temperature of 600–1000 °C for 1–3 hours. They are metastable and decompose into Mn 11 Ge 8 and Ge upon subsequent heating to 600 °C at ambient pressure. [ 1 ]
Manganese germanide is a non-stoichiometric compound where the Ge:Mn ratio often deviates from 1. The Mn 3 Ge 5 compound is a Nowotny phase exhibiting a chimney ladder structure. It is either a semimetal or a narrow-gap semiconductor . [ 3 ] | https://en.wikipedia.org/wiki/MnGe |
Manganese(II) iodide is the chemical compound composed of manganese and iodide with the formula MnI 2 (H2O) n . The tetrahydrate is a pink solid while the anhydrous derivative is beige. [ 2 ] Both forms feature octahedral Mn centers. Unlike MnCl 2 (H 2 O) 4 and MnBr 2 (H 2 O) 4 which are cis, MnI 2 (H 2 O) 4 is trans. [ 3 ]
Anhydrous MnI 2 is prepared from the elements: [ 4 ]
The tetrahydrate can be prepared by treating manganese(II) carbonate with hydriodic acid . The anhydrous form can be produced from it by dehydration in a vacuum. [ 2 ]
Samples turn brown in air under the influence of light as a result of the oxidation of the iodide ion to iodine. [ 5 ] It has a trigonal crystal structure of the cadmium iodide type (polytype 2H) [ 6 ] [ 7 ] with the space group P 3 m1 (space group no. 164). It dissolves in water and decomposes. [ 5 ] The tetrahydrate has a monoclinic crystal structure with the space group P2 1 /c (No. 14). [ 3 ]
It is often used in the lighting industry. [ 8 ] | https://en.wikipedia.org/wiki/MnI2 |
Manganese(II) molybdate is an inorganic compound with the chemical formula MnMoO 4 . α-MnMoO 4 has a monoclinic crystal structure. [ 2 ] It is also antiferromagnetic at low temperatures. [ 3 ]
Manganese(II) molybdate can be prepared through a double displacement reaction between sodium molybdate and manganese sulphate : [ 1 ]
Manganese(II) molybdate has minimal solubility in water and will form a white-yellow precipitate which turns beige upon being refluxed. [ 1 ] The precipitate can then be filtered from solution, which gives the monohydrate (MnMoO 4 ·H 2 O); heating to 360 °C then provides the anhydrous salt. [ 1 ]
Manganese(II) molybdate may also be prepared by heating various manganese oxides and molybdenum trioxide to 700 °C. [ 4 ]
MnMoO 4 serves as the active material in electrodes for aqueous supercapacitors [ 2 ] [ 5 ] due to fast pseudocapacitive redox reactions . It has been evaluated as catalyst for hydrogen evolution . [ 5 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/MnMoO4 |
Manganese dioxide is the inorganic compound with the formula MnO 2 . This blackish or brown solid occurs naturally as the mineral pyrolusite , which is the main ore of manganese and a component of manganese nodules . The principal use for MnO 2 is for dry-cell batteries , such as the alkaline battery and the zinc–carbon battery , although it is also used for other battery chemistries such as aqueous zinc-ion batteries. [ 4 ] [ 5 ] MnO 2 is also used as a pigment and as a precursor to other manganese compounds, such as KMnO 4 . It is used as a reagent in organic synthesis , for example, for the oxidation of allylic alcohols . MnO 2 has an α- polymorph that can incorporate a variety of atoms (as well as water molecules) in the "tunnels" or "channels" between the manganese oxide octahedra. There is considerable interest in α-MnO 2 as a possible cathode for lithium-ion batteries . [ 6 ] [ 7 ]
Several polymorphs of MnO 2 are claimed, as well as a hydrated form. Like many other dioxides, MnO 2 crystallizes in the rutile crystal structure (this polymorph is called pyrolusite or β-MnO 2 ), with three-coordinate oxide anions and octahedral metal centres. [ 4 ] MnO 2 is characteristically nonstoichiometric , being deficient in oxygen. The complicated solid-state chemistry of this material is relevant to the lore of "freshly prepared" MnO 2 in organic synthesis . [ 8 ] The α-polymorph of MnO 2 has a very open structure with "channels", which can accommodate metal ions such as silver or barium. α-MnO 2 is often called hollandite , after a closely related mineral. Two other polymorphs, Todorokite and Romanechite MnO 2 , have a similar structure to α-MnO 2 but with larger channels. δ-MnO 2 exhibits a layered structure more akin to that of graphite . [ 5 ]
Naturally occurring manganese dioxide contains impurities and a considerable amount of manganese(III) oxide . Production of batteries and ferrite (two of the primary uses of manganese dioxide) requires high purity manganese dioxide. Batteries require "electrolytic manganese dioxide" while ferrites require "chemical manganese dioxide". [ 9 ]
One method starts with natural manganese dioxide and converts it using dinitrogen tetroxide and water to a manganese(II) nitrate solution. Evaporation of the water leaves the crystalline nitrate salt. At temperatures of 400 °C, the salt decomposes, releasing N 2 O 4 and leaving a residue of purified manganese dioxide. [ 9 ] These two steps can be summarized as:
In another process, manganese dioxide is carbothermically reduced to manganese(II) oxide which is dissolved in sulfuric acid . The filtered solution is treated with ammonium carbonate to precipitate MnCO 3 . The carbonate is calcined in air to give a mixture of manganese(II) and manganese(IV) oxides. To complete the process, a suspension of this material in sulfuric acid is treated with sodium chlorate . Chloric acid , which forms in situ, converts any Mn(III) and Mn(II) oxides to the dioxide, releasing chlorine as a by-product. [ 9 ]
Lastly, the action of potassium permanganate over manganese sulfate crystals produces the desired oxide. [ 10 ]
Electrolytic manganese dioxide (EMD) is used in zinc–carbon batteries together with zinc chloride and ammonium chloride . EMD is commonly used in zinc manganese dioxide rechargeable alkaline (Zn RAM) cells also. For these applications, purity is extremely important. EMD is produced in a similar fashion as electrolytic tough pitch (ETP) copper : The manganese dioxide is dissolved in sulfuric acid (sometimes mixed with manganese sulfate ) and subjected to a current between two electrodes. The MnO 2 dissolves, enters solution as the sulfate, and is deposited on the anode . [ 11 ]
The important reactions of MnO 2 are associated with its redox , both oxidation and reduction.
MnO 2 is the principal precursor to ferromanganese and related alloys, which are widely used in the steel industry. The conversions involve carbothermal reduction using coke : [ 12 ]
The key redox reactions of MnO 2 in batteries is the one-electron reduction:
MnO 2 catalyses several reactions that form O 2 . In a classical laboratory demonstration, heating a mixture of potassium chlorate and manganese dioxide produces oxygen gas. Manganese dioxide also catalyses the decomposition of hydrogen peroxide to oxygen and water :
Manganese dioxide decomposes above about 530 °C to manganese(III) oxide and oxygen. At temperatures close to 1000 °C, the mixed-valence compound Mn 3 O 4 forms. Higher temperatures give MnO, which is reduced only with difficulty. [ 12 ]
Hot concentrated sulfuric acid reduces MnO 2 to manganese(II) sulfate : [ 4 ]
The reaction of hydrogen chloride with MnO 2 was used by Carl Wilhelm Scheele in the original isolation of chlorine gas in 1774:
As a source of hydrogen chloride, Scheele treated sodium chloride with concentrated sulfuric acid. [ 4 ]
The reaction would not be expected to proceed, based on the standard electrode potentials , but is favoured by the extremely high acidity and the evolution (and removal) of gaseous chlorine.
This reaction is also a convenient way to remove the manganese dioxide precipitate from the ground glass joints after running a reaction (for example, an oxidation with potassium permanganate ).
Heating a mixture of KOH and MnO 2 in air gives green potassium manganate :
Potassium manganate is the precursor to potassium permanganate , a common oxidant.
Excavations at the Pech-de-l'Azé cave site in southwestern France have yielded blocks of manganese dioxide writing tools, which date back 50,000 years and have been attributed to Neanderthals . Scientists have conjectured that Neanderthals used this mineral for body decoration, but there are many other readily available minerals that are more suitable for that purpose. Heyes et al. (in 2016) determined that the manganese dioxide lowers the combustion temperatures for wood from above 350°C (662°F) to 250°C (482°F), making fire making much easier and this is likely to be the purpose of the blocks. [ 13 ]
The predominant application of MnO 2 is as a component of dry cell batteries: alkaline batteries and so called Leclanché cell , or zinc–carbon batteries . Approximately 500,000 tonnes are consumed for this application annually. [ 14 ]
δ- MnO 2 has also been researched as the primary cathode material for aqueous zinc-ion battery systems. Such cathodes often contain additives to address structural, kinetic , and conductivity -based issues. These carbon additives can include reduced graphene oxide (rGO) and carbon nanotubes , among others. [ 15 ]
A specialized use of manganese dioxide is as oxidant in organic synthesis . [ 8 ] The effectiveness of the reagent depends on the method of preparation, a problem that is typical for other heterogeneous reagents where surface area, among other variables, is a significant factor. [ 16 ] The mineral pyrolusite makes a poor reagent. Usually, however, the reagent is generated in situ by treatment of an aqueous solution KMnO 4 with a Mn(II) salt, typically the sulfate. MnO 2 oxidizes allylic alcohols to the corresponding aldehydes or ketones : [ 17 ]
The configuration of the double bond is conserved in the reaction. The corresponding acetylenic alcohols are also suitable substrates, although the resulting propargylic aldehydes can be quite reactive. Benzylic and even unactivated alcohols are also good substrates. 1,2- Diols are cleaved by MnO 2 to dialdehydes or diketones . Otherwise, the applications of MnO 2 are numerous, being applicable to many kinds of reactions including amine oxidation, aromatization, oxidative coupling , and thiol oxidation.
In Geobacteraceae sp., MnO 2 functions as an electron acceptor coupled to the oxidation of organic compounds. This theme has possible implications for bioremediation within the field of microbiology. [ 18 ]
MnO 2 is used as an inorganic pigment in ceramics and in glassmaking . | https://en.wikipedia.org/wiki/MnO2 |
Manganese trioxide fluoride is an inorganic compound with the formula MnO 3 F . A green diamagnetic liquid, the compound has no applications, but it is of some academic interest as a rare example of a metal trioxide fluoride.
The compound was detected in the 1880s but was only purified and crystallized much more recently. [ 1 ] It can be prepared by fluorosulfuric acid and potassium permanganate :
MnO 3 F crystallizes as a monomer, as confirmed by X-ray crystallography . The molecules are tetrahedral with Mn-O and Mn-F distances of 1.59 and 1.72 Å, respectively.
In contrast with MnO 3 F , TcO 3 F and ReO 3 F have more complex structures as solids. The Re compound crystallizes as chains or rings consisting of fluoride-bridge octahedra. TcO 3 F crystallizes as dimers with fluoride bridges . [ 2 ] The rhenium compound also forms stable adducts with Lewis bases , [ 3 ] whereas the MnO 3 F is unstable in the presence of Lewis bases. | https://en.wikipedia.org/wiki/MnO3F |
A permanganate ( / p ər ˈ m æ ŋ ɡ ə n eɪ t , p ɜːr -/ ) [ 1 ] is a chemical compound with the manganate(VII) ion , MnO − 4 , the conjugate base of permanganic acid . Because the manganese atom has a +7 oxidation state , the permanganate(VII) ion is a strong oxidising agent . The ion is a transition metal ion with a tetrahedral structure . [ 2 ] Permanganate solutions are purple in colour and are stable in neutral or slightly alkaline media.
Permanganates can be produced by oxidation of manganese compounds such as manganese chloride or manganese sulfate by strong oxidizing agents, for instance, sodium hypochlorite or lead dioxide :
It may also be produced by the disproportionation of manganates , with manganese dioxide as a side-product:
They are produced commercially by electrolysis or air oxidation of alkaline solutions of manganate salts ( MnO 2− 4 ). [ 3 ]
Permanganate compounds are common and strong disinfectants, used regularly to sanitize baths, toilets, and wash basins. [ citation needed ] It is a cheap and extremely effective compound for the task.
Potassium permanganate is used as a disinfectant and water treatment additive in aquaculture. [ 4 ]
Permanganate compounds are useful reagents , but not very selective with organic compounds when used in organic synthesis .
Permanganates are salts of permanganic acid. They have a deep purple colour, due to a charge transfer transition from oxo ligand p orbitals to empty orbitals derived from manganese(VII) d orbitals. [ 5 ] Permanganate(VII) is a strong oxidizer , and similar to perchlorate . It is therefore in common use in qualitative analysis that involves redox reactions ( permanganometry ). According to theory, permanganate is strong enough to oxidize water, but this does not actually happen to any extent. Besides this, it is stable.
Permanganates are not very stable thermally. For instance, potassium permanganate decomposes at 230 °C to potassium manganate and manganese dioxide , releasing oxygen gas:
In an acidic solution, permanganate(VII) is reduced to the pale pink manganese(II) (Mn 2+ ) with an oxidation state of +2.
In a strongly basic or alkaline solution, permanganate(VII) is reduced to the green manganate ion, MnO 2− 4 with an oxidation state of +6.
In a neutral solution, however, it gets reduced to the brown manganese dioxide MnO 2 with an oxidation state of +4.
When used to oxidize organic compounds, the exact chemical reaction depends on the organic reactant present. For example, trichloroethane (C 2 H 3 Cl 3 ) is oxidised by permanganate ions to form carbon dioxide (CO 2 ), manganese dioxide (MnO 2 ), hydrogen ions (H + ), and chloride ions (Cl − ). [ 6 ]
A permanganate can oxidize an amine to a nitro compound , [ 7 ] [ 8 ] a secondary alcohol to a ketone , [ 9 ] a primary alcohol or aldehyde to a carboxylic acid , [ 10 ] [ 11 ] a terminal alkene to a carboxylic acid , [ 12 ] oxalic acid to carbon dioxide , [ 13 ] and an alkene to a diol . [ 14 ] This list is not exhaustive.
In alkene oxidations one intermediate is a cyclic Mn(V) species: [ 15 ]
The fatal dose of permanganate is about 10 g, and several fatal intoxications have occurred. The strong oxidative effect leads to necrosis of the mucous membrane . For example, the esophagus is affected if the permanganate is swallowed. Only a limited amount is absorbed by the intestines, but this small amount shows severe effects on the kidneys and on the liver. [ 16 ] [ 17 ] | https://en.wikipedia.org/wiki/MnO4 |
Manganese(III) phosphate is an inorganic chemical compound of manganese with the formula MnPO 4 . It is a hygroscopic purple solid that absorbs moisture to form the pale-green monohydrate, [ 1 ] though the anhydrous and monohydrate forms are typically each synthesized by separate methods.
Manganese phosphate monohydrate is produced by the reaction of an Mn(II) salt, such as manganese(II) sulfate , and phosphoric acid , followed by oxidation by nitric acid . Another method of producing the monohydrate is by the comproportionation of permanganate and Mn(II) in phosphoric acid: [ 2 ] [ 3 ] [ 4 ]
The diphosphomanganate(III) ion slowly converts to the monohydrate. Heating of the monohydrate does not yield the anhydrous form, instead, it decomposes to manganese(II) pyrophosphate (Mn 2 P 2 O 7 ) at 420 °C: [ 3 ]
To produce the anhydrous form, lithium manganese(II) phosphate is oxidized with nitronium tetrafluoroborate under inert conditions. [ 1 ]
The anhydrous form is sensitive to moisture. In the absence of moisture, it decomposes at 400 °C, but when moisture is present, it slowly transitions to an amorphous phase and decomposes at 250 °C. [ 1 ]
The anhydrous form has an olivine structure and naturally occurs as the mineral purpurite . The monohydrate has a monoclinic structure, similar to that of magnesium sulfate monohydrate , but has distortions at the octahederal manganese center due to the Jahn-Teller effect . It naturally occurs as the mineral serrabrancaite . [ 5 ] [ 6 ] [ 7 ]
The monohydrate form has cell parameters of a = 6.912 Å, b = 7.470 Å, β = 112.3°, and Z = 4. It consists of interconnected distorted trans -[Mn(PO 4 ) 4 (H 2 O) 2 ] octahederons. [ 5 ] | https://en.wikipedia.org/wiki/MnPO4 |
Manganese(II) sulfide is a chemical compound of manganese and sulfur . It occurs in nature as the mineral alabandite (isometric), rambergite (hexagonal), and recently found browneite (isometric, with sphalerite-type structure, extremely rare, known only from a meteorite). [ 4 ]
Manganese(II) sulfide can be prepared by reacting a manganese(II) salt (such as manganese(II) chloride ) with ammonium sulfide :
The crystal structure of manganese(II) sulfide is similar to that of sodium chloride .
The pink color of MnS likely results from poor coupling between the lowest energy unoccupied Mn orbitals, resulting in discrete states rather than a delocalized band. Thus the lowest energy band-to-band electronic transition requires very high energy (ultraviolet) photons. | https://en.wikipedia.org/wiki/MnS |
Manganese(II) sulfate usually refers to the inorganic compound with the formula MnSO 4 ·H 2 O. This pale pink deliquescent solid is a commercially significant manganese(II) salt. Approximately 260,000 tonnes of manganese(II) sulfate were produced worldwide in 2005. It is the precursor to manganese metal and many other chemical compounds . Manganese-deficient soil is remediated with this salt . [ 1 ]
Like many metal sulfates , manganese sulfate forms a variety of hydrates : monohydrate, tetrahydrate, pentahydrate, and heptahydrate. All of these salts dissolve in water to give faintly pink solutions of the aquo complex [Mn(H 2 O) 6 ] 2+ . The structure of MnSO 4 ·H 2 O has been determined by X-ray crystallography (see figure). The tetrahydrate also features Mn(II) in an O 6 coordination sphere provided by bridging two sulfate anions and four aquo ligands . [ 3 ]
Typically, manganese ores are purified by their conversion to manganese(II) sulfate. Treatment of aqueous solutions of the sulfate with sodium carbonate leads to precipitation of manganese carbonate , which can be calcined to give the oxides MnO x . In the laboratory, manganese sulfate can be made by treating manganese dioxide with sulfur dioxide : [ 4 ]
It can also be made by mixing potassium permanganate with sodium hydrogen sulfate and hydrogen peroxide .
Manganese sulfate is a by-product of various industrially significant oxidations that use manganese dioxide, including the manufacture of hydroquinone and anisaldehyde . [ 1 ]
Electrolysis of manganese sulfate reverses the above reaction yielding manganese dioxide , which is called EMD for electrolytic manganese dioxide. Alternatively oxidation of manganese sulfate with potassium permanganate yields the so-called chemical manganese dioxide (CMD). These materials, especially EMD, are used in dry-cell batteries . [ 1 ]
Manganese(II) sulfate minerals are very rare in nature and always occur as hydrates. The monohydrate is called szmikite; the tetrahydrate is called ilesite; the pentahydrate is called jōkokuite; the hexahydrate, the most rare, is called chvaleticeite ; and the heptahydrate is called mallardite. [ 5 ] | https://en.wikipedia.org/wiki/MnSO4 |
Managnese(II) selenide is an inorganic compound with the chemical formula MnSe. It is a dense gray solid that dissolves only by reaction.
Manganese(II) selenide can be synthesized by the reaction of selenium powder and manganese(II) acetate in an alkaline solution with a reducing agent such as hydrazine at 180°C. [ 1 ]
Manganese selenide exists in three polymorphs. Most common is the stable α-phase ( NaCl type ). [ 2 ] There is also a metastable γ-phase ( wurtzite type ) and an unstable β phase ( zincblende type ). [ 1 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/MnSe |
Manganese monosilicide ( MnSi ) is an intermetallic compound , a silicide of manganese . It occurs in cosmic dust as the mineral brownleeite . MnSi has a cubic crystal lattice with no inversion center ; therefore its crystal structure is helical, with right-hand and left-hand chiralities .
MnSi is a paramagnetic metal that turns into a ferromagnet at cryogenic temperatures below 29 K. In the ferromagnetic state, the spatial arrangement of electron spins in MnSi changes with magnetic field, forming helical , conical, skyrmion , and regular ferromagnetic phases.
Manganese monosilicide is a non-stoichiometric compound , meaning that the 1:1 Mn:Si composition, lattice constant and many other properties vary depending on the synthesis and processing history of the crystal. [ 3 ]
MnSi has a cubic crystal lattice with no inversion center ; therefore its crystal structure is helical, with right-hand and left-hand chiralities .
At low temperatures and magnetic fields, the magnetic structure of MnSi can be described as a stack of ferromagnetically ordered layers lying parallel to the (111) crystallographic planes. The direction of magnetic moment varies from layer to layer by a small angle due to the antisymmetric exchange . [ 3 ]
Upon cooling to temperatures below T c = 29 K, MnSi changes from a paramagnetic into a ferromagnetic state; the transition temperature T c decreases with increasing pressure, vanishing at 1.4 GPa. [ 3 ]
Electron spins in MnSi show dissimilar, yet regular spatial arrangements at different values of applied magnetic field. Those arrangements are named helical, skyrmion , conical, and regular ferromagnetic. They can be controlled not only by temperature and magnetic field, but also by electric current , and the current density required for manipulating skyrmions (~10 6 A/m 2 ) is approximately one million times smaller than that needed for moving magnetic domains in traditional ferromagnets. As a result, skyrmions in MnSi have potential application in ultrahigh-density magnetic storage devices. [ 4 ]
Centimeter-scale single crystals of MnSi can be prepared by direct crystallization from the melt using the Bridgman , zone melting or Czochralski methods . [ 3 ] | https://en.wikipedia.org/wiki/MnSi |
Manganese disilicide ( MnSi 2 ) is an intermetallic compound , a silicide of manganese . It is a non-stoichiometric compound , with a silicon deficiency expressed as MnSi 2–x . Crystal structures of many MnSi 2–x compounds resemble a chimney ladder and are called Nowotny phases . They include
MnSi 2 (x=0), Mn 4 Si 7 (x=0.250), Mn 11 Si 19 (x=0.273), Mn 15 Si 26 (x=0.267) and Mn 27 Si 47 (x=0.259). These phases have very similar unit cells whose length varies from 1.75 nm for MnSi 2 or Mn 4 Si 7 , which have almost the same structures, to 11.8 nm for Mn 27 Si 47 . [ 5 ]
MnSi 2–x Nowotny phases have a Mn sublattice with a β- tin structure overlaid with a face-centered cubic Si sublattice. They resemble chimneys of transition metal atoms containing spiraling ladders of Si. These phases are semiconductors with a band gap of 0.4 to 0.9 eV. They exhibit a reasonably high thermoelectric figure of merit ZT ~ 0.8 and have potential applications in thermoelectric generators . [ 5 ] | https://en.wikipedia.org/wiki/MnSi2 |
Manganese(II) telluride is an inorganic compound with the chemical formula MnTe. It is a gray solid obtained by the reaction of the elements.
Manganese telluride crystallizes in the NaCl structure motif . [ 2 ] [ 3 ]
Long thought to be antiferromagnetic , manganese telluride has been determined to be altermagnetic . [ 4 ] It has a Néel temperature of 307 K. [ 5 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/MnTe |
Managnese(II) titanate is an inorganic compound with the chemical formula MnTiO 3 . [ 1 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/MnTiO3 |
Potassium octachlorodimolybdate (systematically named potassium bis(tetrachloromolybdate)( Mo – Mo )(4−) ) is an inorganic compound with the chemical formula K 4 [Mo 2 Cl 8 ] . It is known as a red-coloured, microcrystalline solid. The anion is of historic interest as one of the earliest illustrations of a quadruple bonding . The salt is usually obtained as the pink-coloured dihydrate .
The compound is prepared in two steps from molybdenum hexacarbonyl : [ 1 ] [ 2 ]
The reaction of the acetate with HCl was first described as providing trimolybdenum compounds, [ 3 ] but subsequent crystallographic analysis confirmed that the salt contains the [Cl 4 Mo≣MoCl 4 ] 4− anion , with D 4h symmetry, in which the two Mo atoms are linked by a quadruple bond. Each Mo atom is bounded with four Cl − ligands by a single bond . Each MoCl 4 group is a regular square pyramid , with an Mo atom at the apex , and four Cl atoms at the vertices of the square base of the pyramid . The Mo–Mo distance is 214 pm. [ 4 ] | https://en.wikipedia.org/wiki/Mo2Cl8 |
Molybdenum dichloride describes chemical compounds with the empirical formula MoCl 2 . At least two forms are known, and both have attracted much attention from academic researchers because of the unexpected structures seen for these compounds and the fact that they give rise to hundreds of derivatives. The form discussed here is Mo 6 Cl 12 . The other molybdenum(II) chloride is potassium octachlorodimolybdate .
Rather than adopting a close-packed structure typical of metal dihalides, e.g., cadmium chloride , molybdenum(II) chloride forms a structure based on clusters. Molybdenum(II), which is a rather large ion , prefers to form compounds with metal-metal bonds, i.e. metal clusters . In fact all "lower halides" (i.e. where halide/M ratio is <4) in the "early transition metal series (Ti, V, Cr, Mn triads) do. The species Mo 6 Cl 12 is polymeric, consisting of cubic Mo 6 Cl 8 4+ clusters interconnected by chloride ligands that bridge from cluster to cluster. This material converts readily to salts of the dianion [Mo 6 Cl 14 ] 2− . In this anion, each Mo bears one terminal chloride but is otherwise part of an Mo 6 octahedron embedded inside a cube defined by eight chloride centers. Thus, the coordination environment of each Mo is four triply bridging chloride ligands, four Mo neighbors, and one terminal Cl. The cluster has 24e − , four being provided by each Mo 2+ . [ 1 ]
Mo 6 Cl 12 is prepared by the reaction of molybdenum(V) chloride with molybdenum metal:
This reaction proceeds via the intermediacy of MoCl 3 and MoCl 4 , which also are reduced by the presence of excess Mo metal. The reaction is conducted in a tube furnace at 600–650 °C. [ 2 ]
Once isolated, Mo 6 Cl 12 undergoes many reactions with retention of the Mo 6 12+ core. Heating in concentrated HCl gives (H 3 O) 2 [Mo 6 Cl 14 ]. The terminal chloride ligands, labeled "ausser" are readily exchanged:
Under more forcing conditions, all 14 ligands can be exchanged, to giving salts of [Mo 6 Br 14 ] 2− and [Mo 6 I 14 ] 2− .
A variety of clusters are structurally related to [Mo 6 Cl 14 ] 2− . The tungsten analogue is known. Ta and Nb form related clusters where halides are bridge edges of the Ta 6 octahedron vs faces. The resulting formula is [Ta 6 Cl 18 ] 4− .
Sulfido and selenido derivatives are also well studied. [Re 6 Se 8 Cl 6 ] 4− has the same number of valence electrons as does [Mo 6 Cl 14 ] 2− . [ 3 ]
The Mo-S clusters Mo 6 S 8 L 6 , analogues of the "Chevrel phases", have been prepared by the reaction of sulfide sources with Mo 6 Cl 12 in the presence of donor ligands L. [ 4 ] | https://en.wikipedia.org/wiki/Mo6Cl12 |
Molybdenum(II) bromide is an inorganic compound with the formula MoBr 2 . It forms yellow-red crystals. [ 1 ]
Molybdenum(II) bromide is created by the reaction of elemental molybdenum(II) chloride with lithium bromide .
Alternatively, it can be prepared by the disproportionation of molybdenum(III) bromide in a vacuum at 600 °C (1,112 °F).
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/MoBr2 |
Molybdenum(III) bromide is the inorganic compound with the formula MoBr 3 . It is a black solid that is insoluble in most solvents but dissolves in donor solvents such as pyridine .
Molybdenum(III) bromide is produced by the reaction of elemental molybdenum and bromine at 350 °C (662 °F). [ 1 ]
It can also be prepared from the reduction of molybdenum(IV) bromide with molybdenum metal, hydrogen gas, or a hydrocarbon . [ 2 ]
It has a structure consisting of infinite chains of face-sharing octahedra with alternatingly short and long Mo-Mo contacts. The same structure is adopted by the tribromides of ruthenium and technetium. [ 3 ] [ 4 ] In contrast, in the high temperature phase of titanium(III) iodide , the Ti---Ti separation is invariant. | https://en.wikipedia.org/wiki/MoBr3 |
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