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myo -Inositol trispyrophosphate ( ITPP ) is an inositol phosphate , a pyrophosphate , a drug candidate , and a putative performance-enhancing substance , which exerts its biological effects by increasing tissue oxygenation. [ 1 ]
ITPP is a pyrophosphate derivative of phytic acid with the molecular formula C 6 H 12 O 21 P 6 . [ 1 ]
ITPP is a membrane-permeant allosteric regulator of hemoglobin that mildly reduces its oxygen-binding affinity , which shifts the oxygen-hemoglobin dissociation curve to the right and thereby increases oxygen release from the blood into tissue. [ 1 ] Phytic acid , in contrast, is not membrane-permeant due to its charge distribution . [ 1 ]
Rodent studies in vivo demonstrated increased tissue oxygenation and dose-dependent increases in endurance during physical exercise, in both healthy mice and transgenic mice expressing a heart failure phenotype. [ 1 ]
The substance is believed to have a high potential for use in athletic doping , and liquid chromatography–mass spectrometry tests have been developed to detect ITPP in urine tests . [ 2 ] Its use as a performance-enhancing substance in horse racing has also been suspected and similar tests have been developed for horses [ 3 ]
ITPP has been studied for potential adjuvant use in the treatment of cancer in conjunction with chemotherapy , due to its effects in reducing tissue hypoxia . [ 4 ] Human clinical trials were registered in 2014 under the compound number OXY111A. [ 5 ] The substance has also been examined in the context of other illnesses involving hypoxia, such as cardiovascular disease and dementia [ 2 ] | https://en.wikipedia.org/wiki/Myo-Inositol_trispyrophosphate |
Myocarditis-myositis-myasthenia gravis overlap syndrome ( IM3OS ) is a rare immune-related adverse event primarily associated with the use of immune checkpoint inhibitors (ICIs). These ICIs, which have been incorporated into the treatment of various malignancies , function by activating the immune system to detect and attack cancer cells . However, a side effect can involve the immune system inadvertently attacking normal tissues and organs. [ 1 ]
The most commonly reported symptoms in patients with IM3OS include fatigue and muscle weakness . Other symptoms can be specific to the organs affected, such as cardiac arrhythmias and depressed ejection fraction in cases where the heart is involved. [ 2 ]
A high index of clinical suspicion is necessary for diagnosis. Prompt comprehensive investigations are required to ascertain the presence of IM3OS, especially in patients who have recently received ICIs. The median number of ICI doses before the onset of IM3OS symptoms has been reported to be one. [ 2 ] Immediate initiation of immunosuppressive therapy and supportive therapies , such as high-dose steroids , is paramount upon suspicion or diagnosis of IM3OS. Early multidisciplinary team involvement is also essential. [ 1 ] [ 2 ]
IM3OS is associated with significant mortality and morbidity. In a systematic review, 60% of patients diagnosed with IM3OS succumbed to acute complications in the hospital. [ 2 ] | https://en.wikipedia.org/wiki/Myocarditis-myositis-myasthenia_gravis_overlap_syndrome |
Myoepithelial cells (sometimes referred to as myoepithelium ) are cells usually found in glandular epithelium as a thin layer above the basement membrane but generally beneath the luminal cells. These may be positive for alpha smooth muscle actin and can contract and expel the secretions of exocrine glands . They are found in the sweat glands , mammary glands , lacrimal glands , and salivary glands . Myoepithelial cells in these cases constitute the basal cell layer of an epithelium that harbors the epithelial progenitor . In the case of wound healing, myoepithelial cells reactively proliferate . Presence of myoepithelial cells in a hyperplastic tissue proves the benignity of the gland and, when absent, indicates cancer . Only rare cancers like adenoid cystic carcinomas contains myoepithelial cells as one of the malignant components.
It can be found in endoderm or ectoderm . [ 1 ]
Myoepithelial cells are true epithelial cells positive for keratins , not to be confused with myofibroblasts which are true mesenchymal cells positive for vimentin . These cells are generally positive for alpha smooth muscle actin (αSMA), cytokeratin 5/6 and other high molecular weight cytokeratins, p63 and caldesmon .
Myoepithelial cells are stellate in shape and are also known as basket cells.
They lie between the basement membrane and glandular epithelium.
Each cell consists of a cell body from which 4-8 processes radiate and embrace the secretory unit. Myoepithelial cells have contractile functions. They help in expelling secretions from the lumen of secretory units and facilitate the movement of saliva in salivary ducts.
List of distinct cell types in the adult human body
This anatomy article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Myoepithelial_cell |
Myogenic tone is a state of muscle tone in living creatures that originates from the muscle itself rather than from the autonomic nervous system or from hormone processes. It may be contrasted with neurogenic tone , which is created by actions of the autonomic nervous system. [ 1 ]
This human musculoskeletal system article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Myogenic_tone |
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Myogenin , is a transcriptional activator encoded by the MYOG gene . [ 5 ] Myogenin is a muscle-specific basic-helix-loop-helix (bHLH) transcription factor involved in the coordination of skeletal muscle development or myogenesis and repair. Myogenin is a member of the MyoD family of transcription factors , which also includes MyoD , Myf5 , and MRF4 .
In mice, myogenin is essential for the development of functional skeletal muscle. Myogenin is required for the proper differentiation of most myogenic precursor cells during the process of myogenesis . When the DNA coding for myogenin was knocked out of the mouse genome , severe skeletal muscle defects were observed. Mice lacking both copies of myogenin ( homozygous -null) suffer from perinatal lethality due to the lack of mature secondary skeletal muscle fibers throughout the body. [ 6 ] [ 7 ]
In cell culture, myogenin can induce myogenesis in a variety of non-muscle cell types.
Myogenin has been shown to interact with: | https://en.wikipedia.org/wiki/Myogenin |
A myokine is one of several hundred cytokines or other small proteins (~5–20 kDa) and proteoglycan peptides that are produced and released by skeletal muscle cells (muscle fibers) in response to muscular contractions . [ 1 ] They have autocrine , paracrine and/or endocrine effects; [ 2 ] their systemic effects occur at picomolar concentrations. [ 3 ] [ 4 ]
Receptors for myokines are found on muscle, fat, liver, pancreas, bone, heart, immune, and brain cells. [ 2 ] The location of these receptors reflects the fact that myokines have multiple functions. Foremost, they are involved in exercise-associated metabolic changes, as well as in the metabolic changes following training adaptation. [ 1 ] They also participate in tissue regeneration and repair, maintenance of healthy bodily functioning, immunomodulation ; and cell signaling, expression and differentiation. [ 1 ]
The definition and use of the term myokine first occurred in 2003. [ 5 ] In 2008, the first myokine, myostatin , was identified. [ 4 ] [ 6 ] The gp130 receptor cytokine IL-6 ( Interleukin 6 ) was the first myokine found to be secreted into the blood stream in response to muscle contractions. [ 7 ] [ 8 ]
There is an emerging understanding of skeletal muscle as a secretory organ, and of myokines as mediators of physical fitness through the practice of regular physical exercise ( aerobic exercise and strength training ), as well as new awareness of the anti-inflammatory and thus disease prevention aspects of exercise. Different muscle fiber types – slow twitch muscle fibers , oxidative muscle fibers , intermediate twitch muscle fibers , and fast twitch muscle fibers – release different clusters of myokines during contraction. [ 9 ] This implies that variation of exercise types, particularly aerobic training / endurance training and muscle contraction against resistance ( strength training ) may offer differing myokine-induced benefits. [ 10 ]
"Some myokines exert their effects within the muscle itself. Thus, myostatin , LIF , IL-6 and IL-7 are involved in muscle hypertrophy and myogenesis , whereas BDNF and IL-6 are involved in AMPK-mediated fat oxidation. IL-6 also appears to have systemic effects on the liver, adipose tissue and the immune system, and mediates crosstalk between intestinal L cells and pancreatic islets . Other myokines include the osteogenic factors IGF-1 and FGF-2 ; FSTL-1 , which improves the endothelial function of the vascular system; and the PGC-1alpha -dependent myokine irisin , which drives brown fat -like development. Studies in the past few years suggest the existence of yet unidentified factors, secreted from muscle cells, which may influence cancer cell growth and pancreas function. Many proteins produced by skeletal muscle are dependent upon contraction; therefore, physical inactivity probably leads to an altered myokine response, which could provide a potential mechanism for the association between sedentary behaviour and many chronic diseases." [ 3 ]
Physical exercise rapidly triggers substantial changes at the organismal level, including the secretion of myokines and metabolites by muscle cells. [ 2 ] For instance, aerobic exercise in humans leads to significant structural alterations in the brain, while wheel-running in rodents promotes neurogenesis and improves synaptic transmission in particular in the hippocampus. Moreover, physical exercise triggers histone modifications and protein synthesis which ultimately positively influence mood and cognitive abilities. [ 11 ] Notably, regular exercise is somewhat associated with a better sleep quality, [ 12 ] which could be mediated by the muscle secretome. [ 13 ]
Heart muscle is subject to two kinds of stress: physiologic stress, i.e. exercise; and pathologic stress, i.e. disease related. Likewise, the heart has two potential responses to either stress: cardiac hypertrophy , which is a normal, physiologic, adaptive growth; or cardiac remodeling , which is an abnormal, pathologic, maladaptive growth. Upon being subjected to either stress, the heart "chooses" to turn on one of the responses and turn off the other. If it has chosen the abnormal path, i.e. remodeling, exercise can reverse this choice by turning off remodeling and turning on hypertrophy. The mechanism for reversing this choice is the microRNA miR-222 in cardiac muscle cells, which exercise up-regulates via unknown myokines. miR-222 represses genes involved in fibrosis and cell-cycle control. [ 14 ]
Immunomodulation and immunoregulation were a particular focus of early myokine research, as, according to Dr. Bente Klarlund Pedersen and her colleagues, "the interactions between exercise and the immune system provided a unique opportunity to evaluate the role of underlying endocrine and cytokine mechanisms." [ 1 ]
Muscle has an impact on the trafficking and inflammation of lymphocytes and neutrophils. During exercise, both neutrophils and NK cells and other lymphocytes enter the blood. Long-duration, high-intensity exercise leads to a decrease in the number of lymphocytes, while the concentration of neutrophils increases through mechanisms including adrenaline and cortisol .Interleukin-6 has been shown to mediate the increase in Cortisol : IL-6 stimulates the production of cortisol and therefore induces leukocytosis and lymphocytopenia . [ 15 ]
Both aerobic exercise and strength training (resistance exercise) attenuate myostatin expression, and myostatin inactivation potentiates the beneficial effects of endurance exercise on metabolism. [ 16 ]
Aerobic exercise provokes a systemic cytokine response, including, for example, IL-6, IL-1 receptor antagonist (IL-1ra), and IL-10 ( Interleukin 10 ) and the concentrations of chemokines, IL-8, macrophage inflammatory protein α (MIP-1α), MIP-1β, and MCP-1 rise after vigorous exercise. IL-6 was identified as a myokine based on the observation that it increased in an exponential fashion proportional to the length of exercise and the amount of muscle mass engaged in the exercise. This increase is followed by the appearance of IL-1ra and the anti-inflammatory cytokine IL-10. In general, the cytokine response to exercise and sepsis differs with regard to TNF-α . Thus, the cytokine response to exercise is not preceded by an increase in plasma-TNF-α. Following exercise, the basal plasma IL-6 concentration may increase up to 100-fold, but less dramatic increases are more frequent. The exercise-induced increase of plasma IL-6 occurs in an exponential manner and the peak IL-6 level is reached at the end of the exercise or shortly thereafter. It is the combination of mode, intensity, and duration of the exercise that determines the magnitude of the exercise-induced increase of plasma IL-6. [ 7 ]
As studies have demonstrated IL-6 has pro-inflammatory functions when evaluated in regard to sepsis and obesity, it was initially hypothesized that the exercise-induced IL-6 response was related to muscle damage. [ 17 ] However, a recent study suggests that eccentric exercise is not associated with a larger increase in plasma IL-6 than exercise involving concentric “nondamaging” muscle contractions. This finding supports the hypothesis that muscle damage is not required to provoke an increase in plasma IL-6 during exercise. [ 4 ]
IL-6, among an increasing number of other recently identified myokines, remains an important topic of myokine research. It appears in muscle tissue and in the circulation during exercise at levels up to one hundred times basal rates, as noted, and may have a beneficial impact on health and bodily functioning with transient increases as P. Munoz-Canoves et al. write: "It appears consistently in the literature that IL-6, produced locally by different cell types, has a positive impact on the proliferative capacity of muscle stem cells. This physiological mechanism functions to provide enough muscle progenitors in situations that require a high number of these cells, such as during the processes of muscle regeneration and hypertrophic growth after an acute stimulus. IL-6 is also the founding member of the myokine family of muscle-produced cytokines. Indeed, muscle-produced IL-6 after repeated contractions also has important autocrine and paracrine benefits, acting as a myokine, in regulating energy metabolism, controlling, for example, metabolic functions and stimulating glucose production. It is important to note that these positive effects of IL-6 and other myokines are normally associated with its transient production and short-term action." [ 18 ]
Interleukin-15 stimulates fat oxidation, glucose uptake, mitochondrial biogenesis and myogenesis in skeletal muscle and adipose tissue. In humans, basal concentrations of IL-15 and its alpha receptor (IL-15Rα) in blood have been inversely associated with physical inactivity and fat mass, [ 19 ] particularly trunk fat mass. [ 20 ] Moreover, in response to a single session of resistance exercise the IL-15/IL-15Rα complex has been related to myofibrillar protein synthesis ( hypertrophy ). [ 21 ]
Brain-derived neurotrophic factor ( BDNF ) is also a myokine, though BDNF produced by contracting muscle is not released into circulation. Rather, BDNF produced in skeletal muscle appears to enhance the oxidation of fat. Skeletal muscle activation through exercise also contributes to an increase in BDNF secretion in the brain. A beneficial effect of BDNF on neuronal function has been noted in multiple studies. [ 20 ] [ 22 ] Dr. Pedersen writes, " Neurotrophins are a family of structurally related growth factors, including brain-derived neurotrophic factor (BDNF), which exert many of their effects on neurons primarily through Trk receptor tyrosine kinases. Of these, BDNF and its receptor TrkB are most widely and abundantly expressed in the brain. However, recent studies show that BDNF is also expressed in non-neurogenic tissues, including skeletal muscle. BDNF has been shown to regulate neuronal development and to modulate synaptic plasticity. BDNF plays a key role in regulating survival, growth and maintenance of neurons, and BDNF has a bearing on learning and memory. However, BDNF has also been identified as a key component of the hypothalamic pathway that controls body mass and energy homeostasis.
"Most recently, we have shown that BDNF appears to be a major player not only in central metabolic pathways but also as a regulator of metabolism in skeletal muscle. Hippocampal samples from Alzheimer’s disease donors show decreased BDNF expression and individuals with Alzheimer’s disease have low plasma levels of BDNF. Also, patients with major depression have lower levels of serum BDNF than normal control subjects. Other studies suggest that plasma BDNF is a biomarker of impaired memory and general cognitive function in ageing women and a low circulating BDNF level was recently shown to be an independent and robust biomarker of mortality risk in old women. Low levels of circulating BDNF are also found in obese individuals and those with type 2 diabetes. In addition, we have demonstrated that there is a cerebral output of BDNF and that this is inhibited during hyperglycaemic clamp conditions in humans. This last finding may explain the concomitant finding of low circulating levels of BDNF in individuals with type 2 diabetes, and the association between low plasma BDNF and the severity of insulin resistance.
BDNF appears to play a role in both neurobiology and metabolism. Studies have demonstrated that physical exercise may increase circulating BDNF levels in humans. To identify whether the brain is a source of BDNF during exercise, eight volunteers rowed for 4 h while simultaneous blood samples were obtained from the radial artery and the internal jugular vein. To further identify the putative cerebral region(s) responsible for BDNF release, mouse brains were dissected and analysed for BDNF mRNA expression following treadmill exercise. In humans, a BDNF release from the brain was observed at rest and increased 2- to 3-fold during exercise. Both at rest and during exercise, the brain contributed 70–80% of the circulating BDNF, while this contribution decreased following 1 h of recovery. In mice, exercise induced a 3- to 5-fold increase in BDNF mRNA expression in the hippocampus and cortex, peaking 2 h after the termination of exercise. These results suggest that the brain is a major but not the sole contributor to circulating BDNF. Moreover, the importance of the cortex and hippocampus as sources of plasma BDNF becomes even more prominent in the response to exercise.” [ 20 ]
With respect to studies of exercise and brain function, a 2010 report is of particular interest. Erickson et al. have shown that the volume of the anterior hippocampus increased by 2% in response to aerobic training in a randomized controlled trial with 120 older adults. The authors also summarize several previously-established research findings relating to exercise and brain function: (1) Aerobic exercise training increases grey and white matter volume in the prefrontal cortex of older adults and increases the functioning of key nodes in the executive control network. (2) Greater amounts of physical activity have been associated with sparing of prefrontal and temporal brain regions over a 9-y period, which reduces the risk for cognitive impairment. (3) Hippocampal and medial temporal lobe volumes are larger in higher-fit older adults (larger hippocampal volumes have been demonstrated to mediate improvements in spatial memory). (4) Exercise training increases cerebral blood volume and perfusion of the hippocampus. [ 22 ]
Regarding the 2010 study, the authors conclude: "We also demonstrate that increased hippocampal volume is associated with greater serum levels of BDNF, a mediator of neurogenesis in the dentate gyrus . Hippocampal volume declined in the control group, but higher preintervention fitness partially attenuated the decline, suggesting that fitness protects against volume loss. Caudate nucleus and thalamus volumes were unaffected by the intervention. These theoretically important findings indicate that aerobic exercise training is effective at reversing hippocampal volume loss in late adulthood, which is accompanied by improved memory function." [ 22 ] [ 23 ]
Decorin is an example of a proteoglycan which functions as a myokine. Kanzleiter et al have established that this myokine is secreted during muscular contraction against resistance, and plays a role in muscle growth. They reported on July 1, 2014: "The small leucine-rich proteoglycan decorin has been described as a myokine for some time. However, its regulation and impact on skeletal muscle (had) not been investigated in detail. In (our recent) study, we report decorin to be differentially expressed and released in response to muscle contraction using different approaches. Decorin is released from contracting human myotubes, and circulating decorin levels are increased in response to acute resistance exercise in humans. Moreover, decorin expression in skeletal muscle is increased in humans and mice after chronic training. Because decorin directly binds myostatin, a potent inhibitor of muscle growth, we investigated a potential function of decorin in the regulation of skeletal muscle growth. In vivo overexpression of decorin in murine skeletal muscle promoted expression of the pro-myogenic factor Mighty, which is negatively regulated by myostatin. We also found Myod1 and follistatin to be increased in response to decorin overexpression. Moreover, muscle-specific ubiquitin ligases atrogin1 and MuRF1, which are involved in atrophic pathways, were reduced by decorin overexpression. In summary, our findings suggest that decorin secreted from myotubes in response to exercise is involved in the regulation of muscle hypertrophy and hence could play a role in exercise-related restructuring processes of skeletal muscle." [ 10 ]
Irisin is a cleaved version of FNDC5 . Boström and coworkers named the cleaved product irisin, after the Greek messenger goddess Iris . [ 24 ] FNDC5 was initially discovered in 2002 by two independent groups of researchers. [ 25 ] [ 26 ] [ 27 ]
Irisin (fibronectin type III domain-containing protein 5 or FNDC5), a recently described myokine hormone produced and secreted by acutely exercising skeletal muscles, is thought to bind white adipose tissue cells via undetermined receptors. Irisin has been reported to promote a brown adipose tissue -like phenotype upon white adipose tissue by increasing cellular mitochondrial density and expression of uncoupling protein-1, thereby increasing adipose tissue energy expenditure via thermogenesis . This is considered important, because excess visceral adipose tissue in particular distorts the whole body energy homeostasis, increases the risk of cardiovascular disease and raises exposure to a milieu of adipose tissue-secreted hormones (adipokines) that promote inflammation and cellular aging. The authors enquired whether the favorable impact of irisin on white adipose tissue might be associated with maintenance of telomere length, a well-established genetic marker in the aging process. They conclude that these data support the view that irisin may have a role in the modulation not only of energy balance but also the aging process. [ 28 ]
However, exogenous irisin may aid in heightening energy expenditure, and thus in reducing obesity. Boström et al. reported on December 14, 2012: "Since the conservation of calories would likely provide an overall survival advantage for mammals, it appears paradoxical that exercise would stimulate the secretion of a polypeptide hormone that increases thermogenesis and energy expenditure. One explanation for the increased irisin expression with exercise in mouse and man may have evolved as a consequence of muscle contraction during shivering. Muscle secretion of a hormone that activates adipose thermogenesis during this process might provide a broader, more robust defense against hypothermia. The therapeutic potential of irisin is obvious. Exogenously administered irisin induces the browning of subcutaneous fat and thermogenesis, and it presumably could be prepared and delivered as an injectable polypeptide. Increased formation of brown or beige/brite fat has been shown to have anti-obesity, anti-diabetic effects in multiple murine models, and adult humans have significant deposits of UCP1 -positive brown fat. (Our data show) that even relatively short treatments of obese mice with irisin improves glucose homeostasis and causes a small weight loss. Whether longer treatments with irisin and/or higher doses would cause more weight loss remains to be determined. The worldwide, explosive increase in obesity and diabetes strongly suggests exploring the clinical utility of irisin in these and related disorders. Another potentially important aspect of this work relates to other beneficial effects of exercise, especially in some diseases for which no effective treatments exist. The clinical data linking exercise with health benefits in many other diseases suggests that irisin could also have significant effects in these disorders." [ 24 ]
While the murine findings reported by Boström et al. appear encouraging, other researchers have questioned whether irisin operates in a similar manner in humans. For example, Timmons et al. noted that over 1,000 genes are upregulated by exercise and examined how expression of FNDC5 was affected by exercise in ~200 humans. They found that it was upregulated only in highly active elderly humans, casting doubt on the conclusions of Boström et al. [ 29 ] Further discussion of this issue can be found in Irisin § Function .
A novel myokine osteonectin , or SPARC (secreted protein acidic and rich in cysteine), plays a vital role in bone mineralization, cell-matrix interactions, and collagen binding. Osteonectin inhibits tumorigenesis in mice. Osteonectin can be classed as a myokine, as it was found that even a single bout of exercise increased its expression and secretion in skeletal muscle in both mice and humans. [ 30 ]
Peroxisome proliferator activated receptor gamma 1-alpha coactivator ( PGC-1 alpha ) is a specific myokine since it stimulates satellite cells, but stimulates M1 and M2 macrophages ; M1 macrophages release interleukin 6 (IL-6), Insulin growth factor type 1 ( IGF-1 ) and vascular endothelial growth factor (VEGF), while M2 macrophages mainly secrete IGF-1, VEGF and monocyte chemoattractant protein 1 (MCP-1)) and all this process the muscle becomes muscle hypertrophy. [ 31 ]
Macrophages M2 stimulate satellite cells for proliferation and growth but M1 stimulates blood vessels and produces pro-inflammatory cytokines only M2 produces anti-inflammatory in muscles.
The myokine oncostatin M has been shown to inhibit the proliferation of breast cancer cells, IL-6, IL-15, epinephrine and norepinephrine for the recruitment of NK cells and replacement of old neutrophils into new and more functional ones and limit induced inflammation by Macrophages M1 and increase in Macrophages M2 (anti-inflammatory). [ 15 ] [ 32 ] | https://en.wikipedia.org/wiki/Myokine |
Myology is the study of the muscular system , including the study of the structure, function and diseases of muscle . [ 1 ] The muscular system consists of skeletal muscle , which contracts to move or position parts of the body (e.g., the bones that articulate at joints), smooth and cardiac muscle that propels, expels or controls the flow of fluids and contained substance.
This muscle article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Myology |
Myomeres are blocks of skeletal muscle tissue arranged in sequence, commonly found in aquatic chordates . Myomeres are separated from adjacent myomeres by fascia consisting of connective tissue , known as myosepta . Myomere counts are sometimes used for identifying specimens using meristics , since their number corresponds to the number of vertebrae in the adults. Myomere location varies, with some species containing these only near the tails, while some have them located near the scapular or pelvic girdles . Depending on the species, myomeres could be arranged in an epaxial or hypaxial manner; hypaxial refers to ventral muscles (those of the " stomach " region) and related structures, while epaxial refers to more dorsal muscles (those of the " back "). The horizontal septum divides these two regions in vertebrates from cyclostomes (jawless lamprey and hagfish) to gnathostomes (jawed fish). In terrestrial chordates , which are gnathostomes themselves, the myomeres become fused as well as indistinct, due to the disappearance of myosepta.
Myomeres are overlapping " cones " of muscle fibers bound by connective tissue . The shape of myomeres varies by species. Myomeres are commonly zig-zaged, being muscle fibers shaped like "V" (lancelets), "W" (fishes), or straight (tetrapods). Generally, cyclostome myomeres are arranged in vertical strips while those of jawed fishes are folded in a complex manner due to their evolution of advanced swimming capability. Specifically, myomeres of elasmobranchs and eels are W-shaped, while the myomeres of tetrapods, such as mudpuppies , run vertically and do not display complex folding. Myomeres overlap each other in succession, meaning myomere activation also allows neighboring myomeres to activate. [ 1 ] They are innervated by spinal nerves, which pass into each myomere. [ 2 ]
Myomeres are made up of myoglobin -rich dark muscle as well as white muscle . Dark muscles generally function as slow-twitch muscle fibers while white muscle is composed of fast-twitch fibers. [ citation needed ]
There are three types of myomeres observed in fish-like chordates: amphioxine (lancelet), cyclostomine (jawless fish), and gnathostomine (jawed fish). All myomeres flex the body laterally into concavity to provide force for locomotion. [ 1 ] Since myomeres are composed of multinucleated myofibers (contractile cells), force can be generated via muscle contraction that gets transmitted by the intricate connective tissue (myosepta) network.
Myomeres compose most of the lateral musculature and provide propulsive force to travel along the line of travel. In this sense, they cause flexion to either side in order to produce locomotor force (the forward swimming motion). Myomeres attach to centra of vertebrae , and neural and haemal spines . The folded shape of each myomere as V- or W-shaped extends over various axial segments, allowing fibers control over a large amount of the body. [ citation needed ]
There are different variations of myomere activation depending on the type of swimming or movement. For example, high loading situations such as fast-starts and turning require almost maximal myomere activation in teleost fish. Further, if swim speeds are lower and movement is in one plane, there is less activation of myomeres. Research has discovered that fish are able to spatially restrict axial myomeres during different swimming behaviors. [ 3 ] [ 4 ]
Some research theorizes that myomeres play additional roles for fish beyond force generation in swimming; microdissection and polarized light microscopy research suggests that anterior myomeres have elongated and reinforced dorsal posterior cones that allow epaxial muscle force to be transmitted to the neurocranium for its elevation, which is a crucial part of suction feeding . [ citation needed ]
Published information on Pikaia gracilens (a well-known Cambrian fossil ) explains evolution of swimming ability in chordates related to myomere shape and function. Specifically, myomeres in this species possessed minimal overlap between successive ones and myosepta dividing them were gently curved. In a biomechanical evaluation, it is presumed that Pikaia were not capable of rapid swimming like in living chordates. Several theories for this idea include lacking fast-twitch muscle fibers, ancestral muscle fiber types more like modern slow-twitch fibers, and less tension on myosepta due to less overlap between successive myomeres. [ 5 ]
Larval fish and amphioxus myomeres are V-shaped. They are involved in the specialized notochord of amphioxus. There are muscle cells within myomeres that send, and synapse cytoplasmic extensions of muscle cells with contractile fibrils to the nerve cord surface.
In amphioxus, myomeres run longitudinally along the length of the body in a "V"-shape. As sequential contraction for swimming occurs, force from the myomeres is transmitted via connective tissues to the notochord.
Being model organisms , zebrafish myomeres have been extensively studied. The tail-bending maneuver generated by myomeres in zebrafish requires innervation from motor neurons for both the hypaxial and epaxial muscle regions. It has been found that timing/intensity of neurons firing in these two regions varies, respectively. This process is mediated by a circuit that controls motor neuron activation during swimming behaviors, which, in turn, affects force generation. Similar to this idea, one study found that hypaxial and epaxial myomere activation did not always correlate with myomeric fibers closer to the horizontal septum itself. [ 6 ] [ better source needed ]
Eel myomeres are W-shaped and cover the entire body. Within these is a mucosal-like matrix that is a-cellular. Superficial to these myomeres is an epithelial layer. Leptocephalus myomeres are also W-shaped and extend from head all the way to the tail. Distinguishing eels can be done through evaluation of the number of myomeres (European has 112-119 while American has 103–11).
The myomeres of some Chondrichthyes , specifically sharks , are W-shaped. Thus, function in Chondrichthyes is similar to that of bony fish, where myomeres contribute to propulsive force for locomotion. [ citation needed ]
The myomeres of tetrapods run vertically and do not undergo folding like in bony fishes. Further, in higher order vertebrates, myomeres are fused and run longitudinally. Myosepta are not present in amniotes . [ citation needed ]
In salamanders , hypaxial muscles, myomeres, and myosepta run in a straight line mid-laterally to mid-ventrally. Specifically, the orientation of collagen fibers within these myomeres runs mediolateral. It is also theorized that, in salamanders, myosepta increase the amplification of strain of angled muscle fibers. This controls how myomeres bulge during contraction in what is called the 'bulge control hypothesis'. [ 7 ] Salamanders in the genus Necturus (mudpuppies) are a salamander species with simply-lain myomeres, unlike the complex nature of bony fishes. [ 8 ]
Myomeres also play a role in swimming in adult newts . Specifically, epaxial myomeres located opposite to each other at the same longitudinal site alternate rhythmic contraction. During stepping on the ground, the myomeres of the mid-trunk undergo bursts of contraction that are synchronized in contrast to double bursting patterns (in opposite directions) expressed in the anterior and posterior trunks. [ 9 ] | https://en.wikipedia.org/wiki/Myomere |
A myoneme (or spasmoneme ) is a contractile structure found in some eukaryotic single-celled organisms, particularly Vorticella . [ 1 ] It consists of a series of protein filaments that shorten rapidly upon exposure to calcium . Although the shortening can be up to 100 lengths per second, faster than any muscle, the relaxation time is several seconds (compared to approximately one tenth of a second for muscle). The myonemes of Acantharea also display slow contraction and undulation movements. [ 2 ] | https://en.wikipedia.org/wiki/Myoneme |
In the context of numeric naming systems for powers of ten , myriad is the quantity ten thousand ( 10,000 ). Idiomatically, in English , myriad is an adjective used to mean that a group of things has indefinitely large quantity . [ 1 ]
Myriad derives from the ancient Greek for ten thousand ( μυριάς , myrias ) and is used with this meaning in literal translations from Greek , Latin or Sinospheric languages ( Chinese , Japanese , Korean , and Vietnamese ), and in reference to ancient Greek numerals .
The term myriad is also used in the form "a myriad" for a 100 km × 100 km square (10,000 km²) the grid size of the British Ordnance Survey National Grid and the US Military Grid Reference System . It contains 100 hectads . [ citation needed ]
The Aegean numerals of the Minoan and Mycenaean civilizations included a symbol composed of a circle with four dashes 𐄫 to denote tens of thousands. [ 2 ]
In classical Greek numerals , myriad was written as a capital mu : Μ . To distinguish this numeral from letters, it was sometimes given an overbar : M . Multiples were written above this sign. For example M δ ϕ π β {\displaystyle {\stackrel {\delta \phi \pi \beta }{\mathrm {M} }}} is 4,582×10,000 or 45,820,000.
The etymology of myriad is uncertain. It has been variously connected to PIE *meu- ("damp") in reference to the waves of the sea and to Greek myrmex ( μύρμηξ , "ant") in reference to their swarms. [ 3 ]
In his Sand Reckoner , Archimedes used "myriad myriad" ( MM , one hundred million) as the basis for a numeration system of large powers of ten, which he used to count grains of sand. [ 4 ]
Myriad may be used either as an adjective (there are myriad people outside) or as a noun (there is a myriad of people outside), [ 5 ] but there are small differences. The former might imply that it is a diverse group of people whereas the latter usually does not.
Despite its usually meaning (a large, unspecified quantity), myriad is sometimes used in English to mean ten thousand although usually restricted to translation from other languages like ancient Greek and Chinese where quantities are grouped by 10,000. Such use permits the translator to remain closer to the original text and avoid unwieldy mentions of "tens of thousands". For example, "the original number of the crews supplied by the several nations I find to have been twenty-four myriads" [ 6 ] and "What is the distance between one bridge and another? Twelve myriads of parasangs ". [ 7 ]
Most European languages include a variation of myriad with a similar meaning to the English word.
Additionally, the prefix myria- indicating multiplication times ten thousand (×10 4 ), was part of the original metric system adopted by France in 1795. [ 8 ] Although it was not retained after the 11th CGPM conference in 1960, myriameter is sometimes still encountered as a translation of the Scandinavian mile ( Swedish & Norwegian : mil ) of 10 kilometers (6.21 mi), or in some classifications of wavelengths as the adjective myriametric . The myriagramme (10 kg) was a French approximation of the avoirdupois quartier of 25 pounds (11 kg) and the myriaton appears in Isaac Asimov 's Foundation novel trilogy.
In modern Greek , the word "myriad" is rarely used to denote 10,000, but a million is ekatommyrio ( εκατομμύριο , lit. 'hundred myriad') and a thousand million is disekatommyrio ( δισεκατομμύριο , lit. 'twice hundred myriad').
In East Asia , the traditional numeral systems of China , Korea , and Japan are all decimal -based but grouped into ten thousands rather than thousands. The character for myriad is 萬 in traditional script and 万 in simplified form in both mainland China and Japanese ; its pronunciation varies between languages ( Mandarin : wàn , Hakka : wan 5 , Minnan : bān , Cantonese : maan 6 , Japanese and Korean : man , Vietnamese : vạn , Thai : หมื่น muen and Khmer : ម៉ឺន meun ). [ citation needed ]
Because of this grouping into fours, higher orders of numbers are provided by the powers of 10,000 rather than 1,000: In China, 10,000 2 was 萬萬 in ancient texts but is now called 億 and sometimes written as 1,0000,0000; 10,000 3 is 1,0000,0000,0000 or 兆 ; 10,000 4 is 1,0000,0000,0000,0000 or 京 ; and so on. Conversely, Chinese, Japanese, and Korean generally do not have native words for powers of one thousand: what is called "one million" in English is "100 萬 " (100 myriad) in the Sinosphere , and "one billion" in English is " 十億 " (ten myllion ) or " 十萬萬 " (ten myriad myriad) in the Sinosphere. Unusually, Vietnam employs its former translation of 兆 , một triệu , to mean 1,000,000 rather than the Chinese figure. Similarly, the Chinese government has adapted the word 兆 to mean the scientific prefix mega- , but transliterations are used instead for giga- , tera- , and other larger prefixes. This has caused confusion in areas closely related to China such as Hong Kong and Macau , where 兆 is still largely used to mean 10,000 3 . [ citation needed ]
萬 and 万 are also frequently employed colloquially in expressions, clichés , and chengyu (idioms) in the senses of "vast", "numerous", "numberless", and "infinite". A skeleton key is a 万 能 钥 匙 ("myriad-use key"), [ 9 ] the emperor was the "lord of myriad chariots " ( 萬乘之主 ), [ 10 ] the Great Wall is called 万 里 长 城 ("Myriad- mile Long Wall"), Zhu Xi 's statement 月 映 万 川 ("the moon reflects in myriad rivers") had the sense of supporting greater empiricism in Chinese philosophy , [ 11 ] and Ha Qiongwen's popular 1959 propaganda poster 毛 主席 万岁 , meaning "Long live Chairman Mao ", literally reads as "[May] Chairman Mao [live to be] 10,000 years old ". [ 12 ] Its literary use may thus mean something huge and plentiful. [ 13 ] : 60
A similar term is the Old Turkic word tümän , [ 14 ] whose variant forms remain in use for "ten thousand" among modern Mongolian , Turkish . [ 15 ] [ 16 ] According to Sir Gerard Clauson (1891–1974), it was likely borrowed from Tokharian tmān , which may have been borrowed in turn from Old Chinese tman 萬 > wan . [ 17 ]
In Hebrew the word רבבה (pronounced "revava") means 10,000, and is the highest number represented in Hebrew. Its sources go back to biblical times. [ 18 ] Its usage became very rare after the 19th century. The term 60 ריבוא ("60 ribo"), which literally stands for 600,000 is used several times in the bible to denote "a very large undefinitive number". [ citation needed ]
The dictionary definition of myriad at Wiktionary | https://en.wikipedia.org/wiki/Myriad |
Myrinet , ANSI/VITA 26-1998, is a high-speed local area networking system designed by the company Myricom to be used as an interconnect between multiple machines to form computer clusters .
Myrinet was promoted as having lower protocol overhead than standards such as Ethernet , and therefore better throughput , less interference, and lower latency while using the host CPU. Although it can be used as a traditional networking system, Myrinet is often used directly by programs that "know" about it, thereby bypassing a call into the operating system .
Earlier versions of Myrinet used a variety of media and connectors: [ 1 ]
The later versions of Myrinet physically consist of two fibre optic cables, upstream and downstream, connected to the host computers with a single connector. Machines are connected via low-overhead routers and switches , as opposed to connecting one machine directly to another. Myrinet includes a number of fault-tolerance features, mostly backed by the switches. These include flow control, error control, and "heartbeat" monitoring on every link. The "fourth-generation" Myrinet, called Myri-10G, supported a 10 Gbit/s data rate and can use 10 Gigabit Ethernet on PHY , the physical layer (cables, connectors, distances, signaling). Myri-10G started shipping at the end of 2005.
Myrinet was approved in 1998 by the American National Standards Institute for use on the VMEbus as ANSI/VITA 26-1998. [ 2 ] One of the earliest publications on Myrinet is a 1995 IEEE article. [ 3 ]
Myrinet is a lightweight protocol with little overhead that allows it to operate with throughput close to the basic signaling speed of the physical layer. For supercomputing, the low latency of Myrinet is even more important than its throughput performance, since, according to Amdahl's law , a high-performance parallel system tends to be bottlenecked by its slowest sequential process, which in all but the most embarrassingly parallel supercomputer workloads is often the latency of message transmission across the network.
According to Myricom, 141 (28.2%) of the June 2005 TOP500 supercomputers used Myrinet technology. In the November 2005 TOP500, the number of supercomputers using Myrinet was down to 101 computers, or 20.2%, in November 2006, 79 (15.8%), and by November 2007, 18 (3.6%), a long way behind gigabit Ethernet at 54% and InfiniBand at 24.2%.
In the June 2014 TOP500 list, the number of supercomputers using Myrinet interconnect was 1 (0.2%). [ 7 ] [ 8 ]
In November, 2013, the assets of Myricom (including the Myrinet technology) were acquired by CSP Inc. [ 9 ] In 2016, it was reported that Google had also offered to buy the company. [ 10 ] | https://en.wikipedia.org/wiki/Myrinet |
Myristoylation is a lipidation modification where a myristoyl group , derived from myristic acid , is covalently attached by an amide bond to the alpha-amino group of an N -terminal glycine residue. [ 1 ] Myristic acid is a 14-carbon saturated fatty acid (14:0) with the systematic name of n -tetradecanoic acid. This modification can be added either co-translationally or post-translationally . N -myristoyltransferase (NMT) catalyzes the myristic acid addition reaction in the cytoplasm of cells. [ 2 ] This lipidation event is the most common type of fatty acylation [ 3 ] and is present in many organisms, including animals , plants , fungi , protozoans [ 4 ] and viruses . [ 5 ] [ 6 ] Myristoylation allows for weak protein–protein and protein–lipid interactions [ 7 ] and plays an essential role in membrane targeting, protein–protein interactions and functions widely in a variety of signal transduction pathways.
In 1982, Koiti Titani's lab identified an " N -terminal blocking group" on the catalytic subunit of cyclic AMP-dependent protein kinase in cows as n -tetradecanoyl. [ 8 ] Almost simultaneously in Claude B. Klee's lab, this same N -terminal blocking group was further characterized as myristic acid. [ 9 ] Both labs made this discovery utilizing similar techniques: mass spectrometry and gas chromatography . [ 8 ] [ 9 ]
The enzyme N -myristoyltransferase (NMT) or glycylpeptide N -tetradecanoyltransferase is responsible for the irreversible addition of a myristoyl group to N -terminal or internal glycine residues of proteins. This modification can occur co-translationally or post-translationally . In vertebrates, this modification is carried about by two NMTs, NMT1 and NMT2 , both of which are members of the GCN5 acetyltransferase superfamily. [ 10 ]
The crystal structure of NMT reveals two identical subunits, each with its own myristoyl CoA binding site. Each subunit consists of a large saddle-shaped β-sheet surrounded by α-helices . The symmetry of the fold is pseudo twofold. [ clarification needed ] Myristoyl CoA binds at the N -terminal portion, while the C -terminal end binds the protein. [ 11 ]
The addition of the myristoyl group proceeds via a nucleophilic addition-elimination reaction . First, myristoyl coenzyme A (CoA) is positioned in its binding pocket of NMT so that the carbonyl faces two amino acid residues, phenylalanine 170 and leucine 171. [ 11 ] This polarizes the carbonyl so that there is a net positive charge on the carbon, making it susceptible to nucleophilic attack by the glycine residue of the protein to be modified. When myristoyl CoA binds, NMT reorients to allow binding of the peptide. The C -terminus of NMT then acts as a general base to deprotonate the NH 3 + , activating the amino group to attack at the carbonyl group of myristoyl-CoA. The resulting tetrahedral intermediate is stabilized by the interaction between a positively charged oxyanion hole and the negatively charged alkoxide anion. Free CoA is then released, causing a conformational change in the enzyme that allows the release of the myristoylated peptide. [ 2 ]
Co-translational and post-translational covalent modifications enable proteins to develop higher levels of complexity in cellular function, further adding diversity to the proteome . [ 12 ] The addition of myristoyl-CoA to a protein can occur during protein translation or after. During co-translational addition of the myristoyl group, the N -terminal glycine is modified following cleavage of the N -terminal methionine residue in the newly forming, growing polypeptide . [ 1 ] Post-translational myristoylation typically occurs following a caspase cleavage event, resulting in the exposure of an internal glycine residue, which is then available for myristic acid addition. [ 10 ]
Myristoylation not only diversifies the function of a protein, but also adds layers of regulation to it. One of the most common functions of the myristoyl group is in membrane association and cellular localization of the modified protein. Though the myristoyl group is added onto the end of the protein, in some cases it is sequestered within hydrophobic regions of the protein rather than solvent exposed. [ 7 ] By regulating the orientation of the myristoyl group, these processes can be highly coordinated and closely controlled. Myristoylation is thus a form of " molecular switch ." [ 15 ]
Both hydrophobic myristoyl groups and "basic patches" (highly positive regions on the protein) characterize myristoyl-electrostatic switches. The basic patch allows for favorable electrostatic interactions to occur between the negatively charged phospholipid heads of the membrane and the positive surface of the associating protein. This allows tighter association and directed localization of proteins. [ 7 ]
Myristoyl-conformational switches can come in several forms. Ligand binding to a myristoylated protein with its myristoyl group sequestered can cause a conformational change in the protein, resulting in exposure of the myristoyl group. Similarly, some myristoylated proteins are activated not by a designated ligand, but by the exchange of GDP for GTP by guanine nucleotide exchange factors in the cell. Once GTP is bound to the myristoylated protein, it becomes activated, exposing the myristoyl group. These conformational switches can be utilized as a signal for cellular localization, membrane-protein, and protein–protein interactions . [ 7 ] [ 15 ] [ 16 ]
Further modifications on N -myristoylated proteins can add another level of regulation for myristoylated protein. Dual acylation can facilitate more tightly regulated protein localization, specifically targeting proteins to lipid rafts at membranes [ 17 ] or allowing dissociation of myristoylated proteins from membranes.
Myristoylation and palmitoylation are commonly coupled modifications. Myristoylation alone can promote transient membrane interactions [ 7 ] that enable proteins to anchor to membranes but dissociate easily. Further palmitoylation allows for tighter anchoring and slower dissociation from membranes when required by the cell. This specific dual modification is important for G protein-coupled receptor pathways and is referred to as the dual fatty acylation switch. [ 7 ] [ 10 ]
Myristoylation is often followed by phosphorylation of nearby residues. Additional phosphorylation of the same protein can decrease the electrostatic affinity of the myristoylated protein for the membrane, causing translocation of that protein to the cytoplasm following dissociation from the membrane. [ 7 ]
Myristoylation plays a vital role in membrane targeting and signal transduction [ 18 ] in plant responses to environmental stress. In addition, in signal transduction via G protein, palmitoylation of the α subunit, prenylation of the γ subunit, and myristoylation is involved in tethering the G protein to the inner surface of the plasma membrane so that the G protein can interact with its receptor. [ 19 ]
Myristoylation is an integral part of apoptosis , or programmed cell death. Apoptosis is necessary for cell homeostasis and occurs when cells are under stress such as hypoxia or DNA damage . Apoptosis can proceed by either mitochondrial or receptor mediated activation. In receptor mediated apoptosis, apoptotic pathways are triggered when the cell binds a death receptor. In one such case, death receptor binding initiates the formation of the death-inducing signaling complex , a complex composed of numerous proteins including several caspases, including caspase 3 . Caspase 3 cleaves a number of proteins that are subsequently myristoylated by NMT. The pro-apoptotic BH3-interacting domain death agonist (Bid) is one such protein that once myristoylated, translocates to the mitochondria where it prompts the release of cytochrome c leading to cell death. [ 10 ] Actin , gelsolin and p21-activated kinase 2 PAK2 are three other proteins that are myristoylated following cleavage by caspase 3 , which leads to either the up-regulation or down-regulation of apoptosis. [ 10 ]
c-Src is a gene that codes for proto-oncogene tyrosine-protein kinase Src, a protein important for normal mitotic cycling . It is phosphorylated and dephosphorylated to turn signaling on and off. Proto-oncogene tyrosine-protein kinase Src must be localized to the plasma membrane in order to phosphorylate other downstream targets; myristoylation is responsible for this membrane targeting event. Increased myristoylation of c-Src can lead to enhanced cell proliferation and be responsible for transforming normal cells into cancer cells . [ 7 ] [ 16 ] [ 20 ] Activation of c-Src can lead to the so-called " hallmarks of cancer ", among them upregulation of angiogenesis , proliferation, and invasion . [ 21 ]
HIV-1 is a retrovirus that relies on myristoylation of one of its structural proteins in order to successfully package its genome, assemble and mature into a new infectious particle. Viral matrix protein , the N -terminal–most domain of the gag polyprotein , is myristoylated. [ 22 ] This myristoylation modification targets gag to the membrane of the host cell. Utilizing the myristoyl-electrostatic switch, [ 15 ] including a basic patch on the matrix protein, gag can assemble at lipid rafts at the plasma membrane for viral assembly, budding and further maturation. [ 20 ] In order to prevent viral infectivity, myristoylation of the matrix protein could become a good drug target.
Certain NMTs are therapeutic targets for development of drugs against bacterial infections . Myristoylation has been shown to be necessary for the survival of a number of disease-causing fungi , among them C. albicans and C. neoformans . In addition to prokaryotic bacteria, the NMTs of numerous disease-causing eukaryotic organisms have been identified as drug targets as well. Proper NMT functioning in the protozoa Leishmania major and Leishmania donovani ( leishmaniasis ), Trypanosoma brucei ( African sleeping sickness ), and P. falciparum ( malaria ) is necessary for survival of the parasites. Inhibitors of these organisms are under current investigation. A pyrazole sulfonamide inhibitor has been identified that selectively binds T. brucei , competing for the peptide binding site, thus inhibiting enzymatic activity and eliminating the parasite from the bloodstream of mice with African sleeping sickness . [ 10 ]
Inhibition of myristoylated proteins that are essential for the viral life cycle would inhibit viral propagation. Indeed, this has been shown with mammarenaviruses , including the hemorrhagic fever viruses such as lassa and junin , where the affected myristoylated proteins are Z matrix protein, which aids in viral assembly and budding, and the glycoprotein 1 (GP1), specifically the signal peptide of GP1. Inhibition of myristoylation in cells infected with mammarenaviruses, signaled Z protein and signal peptide of GP1 for degradation, which limits viral assembly, budding and propagation. [ 5 ] Both vaccinia and monkeypox viruses have four myristoylated proteins that can be targeted which would interrupt viral lifecycle, inhibition of myristoylation has been shown to completely inhibit viral propagation in combination therapies, L1R is an essential protein, for the life cycle, in both vaccinia and monkeypox viruses, and myristoylation inhibition in montherapy and combination resulted in complete inhibition. [ 23 ] | https://en.wikipedia.org/wiki/Myristoylation |
Myrmecochory ( / m ɜːr m ɪ ˈ k ɒ k ɔː r i / (sometimes myrmechory ); [ 1 ] from Ancient Greek : μύρμηξ , romanized : mýrmēks ("ant") and χορεία khoreíā ("circular dance") is seed dispersal by ants , an ecologically significant ant–plant interaction with worldwide distribution. Most myrmecochorous plants produce seeds with elaiosomes , a term encompassing various external appendages or "food bodies" rich in lipids , amino acids , or other nutrients that are attractive to ants. The seed with its attached elaiosome is collectively known as a diaspore . Seed dispersal by ants is typically accomplished when foraging workers carry diaspores back to the ant colony , after which the elaiosome is removed or fed directly to ant larvae . [ 2 ] Once the elaiosome is consumed, the seed is usually discarded in an underground midden or ejected from the nest. Although diaspores are seldom distributed far from the parent plant, myrmecochores also benefit from this predominantly mutualistic interaction through dispersal to favourable locations for germination , as well as escape from seed predation . [ 2 ]
Myrmecochory is exhibited by more than 3,000 plant species worldwide [ 3 ] and is present in every major biome on all continents except Antarctica. [ 4 ] Seed dispersal by ants is particularly common in the dry heath and sclerophyll woodlands of Australia (1,500 species) and the South African fynbos (1,000 species). Both regions have a Mediterranean climate and largely infertile soils (characterized by low phosphorus availability), two factors that are often cited to explain the distribution of myrmecochory. [ 5 ] Myrmecochory is also present in mesic forests in temperate regions of the Northern Hemisphere ( i.e. in Europe and in eastern North America ), as well as in tropical forests and dry deserts , though to a lesser degree. [ 2 ] [ 6 ] Estimates for the true biodiversity of myrmecochorous plants range from 11,000 to as high as 23,000 species worldwide, or about 5% of all flowering plant species. [ 4 ] [ 7 ]
Myrmecochory has evolved independently many times in a large number of plant families . A recent phylogenetic study identified more than 100 separate origins of myrmecochory in 55 families of flowering plants. [ 4 ] [ 7 ] With many independent evolutionary origins, elaiosomes have evolved from a wide variety of parent tissues. [ 6 ] Strong selective pressure or the relative ease with which elaiosomes can develop from parent tissues may explain the multiple origins of myrmecochory. [ 7 ] These findings identify myrmecochory as a prime example of convergent evolution . In addition, phylogenetic comparison of myrmecochorous plant groups reveals that more than half of the lineages in which myrmecochory evolved are more species-rich than their nonmyrmecochorous sister groups. Not only is myrmecochory a convergent trait, but it also promotes diversification in multiple flowering plant lineages. [ 4 ]
Myrmecochory is usually classified as a mutualism , but this is contingent on the degree to which participating species benefit from the interaction . Several different factors likely combine to create mutualistic conditions. Myrmecochorous plants may derive benefit from increased dispersal distance, directed dispersal to nutrient -enriched or protected microsites , and/or seed predator avoidance. [ 2 ] Costs incurred by myrmecochorous plants include the energy required to provision diaspores, particularly when a disproportionate investment is made of growth-limiting mineral nutrients. For instance, some Australian Acacia species invest a significant portion of their yearly phosphorus uptake in producing diaspores. [ 8 ] Diaspores must also be protected from outright predation by ants. This is typically accomplished by the production of a hard, smooth testa, or seed coat .
Few studies have examined the costs and benefits to ants participating in myrmecochory. Much remains to be understood about the selective advantages conferred upon myrmecochorous ants. [ 9 ]
No single hypothesis explains the evolution and persistence of myrmecochory. Instead, a combination of beneficial effects working at different spatiotemporal scales likely contribute to the viability of this predominantly mutualistic interaction. Three commonly cited advantages to myrmecochorous plants are increased dispersal distance, directed dispersal, and seed predator avoidance.
Increasing dispersal distance from the parent plant is likely to reduce seed mortality resulting from density-dependent effects . [ 10 ] Ants can transport seeds as far as 180 m [ 11 ] but the average is less than 2 m, and values between 0.5 and 1.5 m are most common. [ 6 ] Perhaps due to the relatively limited distance that ants disperse seeds, many myrmecochores exhibit diplochory , a two-staged dispersal mechanism, often with ballistic projection as the initial mechanism, that can increase dispersal distance by as much as 50%. [ 2 ] [ 6 ] In some cases, ballistic dispersal distance regularly exceeds that of transport by ants. [ 12 ] The dispersal distance achieved through myrmecochory is likely to provide an advantage proportionate to the spatial scale of density-dependent effects acting on individual plants. As such, the relatively modest distances ants transport seeds are likely to be more advantageous for myrmecochorous shrubs , forbs , and other plants of small stature. [ 9 ]
Myrmecochorous plants may benefit when ants disperse seeds to nutrient-rich or protected microsites that enhance germination and establishment of seedlings . Ants disperse seeds in fairly predictable ways, either by disposing of them in underground middens or by ejecting them from the nest. [ 2 ] These patterns of ant dispersal are predictable enough to permit plants to manipulate animal behaviour and influence seed fate, [ 13 ] effectively directing the dispersal of seeds to desirable sites. For example, myrmecochores can influence seed fate by producing rounder, smoother diaspores that inhibit ants from redispersing seeds after elaiosome removal. This increases the likelihood that seeds will remain underground instead of being ejected from the nest. [ 14 ]
Nest chemistry is ideally suited for seed germination given that ant colonies are typically enriched with plant nutrients such as phosphorus and nitrate . [ 2 ] This is likely to be advantageous in areas with infertile soils and less important in areas with more favourable soil chemistry, as in fertile forests. [ 9 ] In fire-prone areas , depth of burial is an important factor for successful post-burn germination. This, in turn, is influenced by the nesting habits of the myrmecochorous ants. [ 15 ] As such, the value of directed dispersal is largely context-dependent.
Myrmecochorous plants escape or avoid seed predation by granivores when ants remove and sequester diaspores. [ 2 ] This benefit is particularly pronounced in areas where myrmecochorous plants are subject to heavy seed predation, which may be common. In mesic forest habitats, seed predators remove around 60% of all dispersed seeds within a few days, and eventually remove all seeds not removed by ants. [ 12 ] [ 16 ] In addition to attracting ants, elaiosomes also appeal to granivores, and their presence can increase seed predation rates. [ 9 ]
Myrmecochory is traditionally thought to be a diffuse or facultative mutualism with low specificity between myrmecochores and individual ant species. [ 9 ] [ 16 ] This assertion has been challenged in a study of Iberian myrmecochores, demonstrating the disproportionate importance of specific ant species in dispersing seeds. [ 17 ] Ant-plant interactions with a single species of myrmecochore were recorded for 37 species of ants, but only two of these were found to disperse diaspores to any significant degree; the rest were seed predators or “cheaters” opportunistically feeding on elaiosomes in situ without dispersing seeds. Larger diaspores are hypothesized to increase the degree of specialization, since ant mutualists need to be larger to successfully carry the diaspore back to the nest. [ 17 ]
Ants, however, do not appear to form obligate relationships with myrmecochorous plants. Since no known ant species relies entirely on elaiosomes for their nutritional needs, ants remain generalist foragers even when entering into relationships with a more specialized myrmecochore. [ 16 ]
As with many other facultative mutualisms, cheating is present on both sides of the interaction. Ants cheat by consuming elaiosomes without transporting seeds or through outright seed predation. Myrmecochorous plants can also cheat, either by producing diaspores with nonremovable elaiosomes or by simulating the presence of a nonexistent reward with chemical cues . Ants are sometimes capable of discriminating between cheaters and mutualists as shown by studies demonstrating preference for the diaspores of noncheating myrmecochores. [ 18 ] Cheating is also inhibited by ecological interactions external to the myrmecochorous interaction; simple models suggest that predation exerts a stabilizing influence on a mutualism such as myrmecochory. [ 16 ]
Myrmecochores are threatened by invasive species in some ecosystems. For instance, the Argentine ant is an aggressive invader capable of displacing native ant populations. Since Argentine ants do not disperse seeds, invasions may lead to a breakdown in the myrmecochory mutualism, inhibiting the dispersal ability of myrmecochores and causing long-term alterations in plant community dynamics. [ 19 ] [ 20 ] Invasive ant species can also maintain seed dispersal in their introduced range, as is the case with the red fire ant in the Southeastern United States. [ 21 ] Some invasive ants are also seed-disperses in their native range, such as the European fire ant , and can act as a high-quality disperser in their introduced range [ 22 ]
In South Africa, the Argentine ant has in some cases displaced native ants that disperse the seeds of Fynbos plants like Mimetes cucullatus . The Argentine ants don't take the seeds underground and leave them on the surface, resulting in ungerminated plants and the dwindling of Fynbos seed reserves after veld fires . [ 23 ]
Myrmecochorous plants are also capable of invading ecosystems. These invaders may gain an advantage in areas where native ants disperse invasive seeds. Similarly, the spread of myrmecochorous invaders may be inhibited by limitations in the ranges of native ant populations. [ 24 ] | https://en.wikipedia.org/wiki/Myrmecochory |
Myrmecophily ( / m ɜːr m ə ˈ k ɒ f ə l i / mur-mə- KOF -ə-lee , lit. ' love of ants ' ) consists of positive, mutualistic , interspecies associations between ants and a variety of other organisms, such as plants, other arthropods, and fungi. It may also include commensal or even parasitic interactions.
A "myrmecophile" is an animal that associates with ants. An estimated 10,000 species of ants (Formicidae) are known, with a higher diversity in the tropics. [ 1 ] In most terrestrial ecosystems, ants are ecologically and numerically dominant, being the main invertebrate predators. As a result, ants play a key role in controlling arthropod richness, abundance, and community structure. [ 2 ] Some evidence shows that the evolution of myrmecophilous interactions has contributed to the abundance and ecological success of ants, [ 1 ] [ 3 ] by ensuring a dependable and energy-rich food supply, thus providing a competitive advantage for ants over other invertebrate predators. [ 4 ] Most myrmecophilous associations are opportunistic, unspecialized, and facultative (meaning both species are capable of surviving without the interaction), though obligate mutualisms (those in which one or both species are dependent on the interaction for survival) have also been observed for many species. [ 5 ]
As ant nests grow, they are more likely to house more and greater varieties of myrmecophiles. This is partly because larger colonies have greater specializations, so more diversity of ecology within the nests, allowing for more diversity and population sizes among the myrmecophiles. [ 6 ] [ 7 ]
A "myrmecophile" is an organism that lives in association with ants .
Myrmecophiles may have various roles in their host ant colony. Many consume waste materials in the nests, such as dead ants, dead larvae, or fungi growing in the nest. Some myrmecophiles, however, feed on the stored food supplies of ants, and a few are predatory on ant eggs, larvae, or pupae. Others benefit the ants by providing a food source for them. Most associations are facultative, benefiting one or both participants, but not being necessary to their survival, although many myrmecophilous relationships are obligate, meaning one or the other participant requires the relationship for survival.
Myrmecophilous associations are best known in butterflies of the family Lycaenidae . Many lycaenid caterpillars produce nectar by specialized organs, and communicate with the ants through sound and vibrations. [ 8 ] The association with ants is believed to reduce the parasitisation of the butterfly caterpillars. [ 9 ]
Some myrmecophilous beetles are in the families Coccinellidae (e.g. the ladybird Thalassa saginata ), Aphodiidae , Scarabaeidae , Lucanidae , Cholevidae , Pselaphidae , Staphylinidae , Histeridae , and Ptiliidae (some treated here as subfamilies). In ant-beetle associations, the myrmecophilous staphylinids are the most diverse of the beetle families. [ 10 ] [ better source needed ] Myrmecophilous associations are also seen in various other insects, such as aphids and treehoppers , as well as the hoverfly genus Microdon and several other groups of flies. [ 11 ]
Ant nests provide environmentally stable environments that are well organized and protected by the host colony. The benefit of ant colonies has resulted in infiltration from a variety of myrmecophiles. [ 12 ] The ant guests can have a positive, neutral, or negative effect on the colony. If the infiltrating species' impact is too negative on the colony, they risk discovery; this usually results in relatively small populations of myrmecophiles. Some spider species will use traits such as myrmecomorphy – ant mimicry - and chemical mimicry to infiltrate ant nests, usually to prey on food supplies or the ants themselves. [ 13 ] Aribates javensis , a species of oribatid mites, is an obligate myrmecophile that lives in ant nests. These mites are cared for by their ant hosts in exchange for eating litter and bacteria in the nest. [ 14 ]
Other myrmecophile groups include:
Ant-plant interactions are geographically widespread, [ 16 ] with hundreds of species of myrmecophytic plants in several families, including the Leguminosae , Euphorbiaceae , and Orchidaceae . [ 3 ] In general, myrmecophytes (or ant plants) usually provide some form of shelter and food in exchange for ant "tending", which may include protection, seed dispersal (see myrmecochory ), reduced competition from other plants, hygienic services, and/or nutrient supplementation. [ 1 ] [ 17 ]
Three of the most common and important structural adaptations of ant plants are extrafloral nectaries , domatia , and (least commonly) Beltian bodies . Plant domatia are formed nesting sites provided by the plant in the form of hollow stems, petioles, thorns, or curled leaves. [ 17 ] The production of ant-specialized domatia has been documented in over 100 genera of tropical plants. [ 17 ] Beltian bodies provide a high-energy food source to ants in the form of nutritive corpuscles produced on leaflet tips, [ 1 ] and they have been described in at least 20 plant families. [ 17 ] Extrafloral nectaries (EFNs) are known to occur in at least 66 families of angiosperm plants in both temperate and tropical regions, as well as some ferns, but are absent in all gymnosperms and are most abundant in the tropics. [ 17 ] EFNs being outside of the plant flowers are not employed in pollination; their primary purpose is to attract and sustain tending ants. Many plants can control the flow of nectar from the EFNs so that the availability of nectar varies according to daily and seasonal cycles. Because ants can respond quickly to changes in flow rate from EFNs, this may be possible mechanism by which plants can induce greater ant activity during times of peak herbivory, and minimize overall costs of nectar production. [ 17 ] The combined nutritional output of EFNs and Beltian bodies can be a significant food source for tending ants, and in some cases can provide the total nutritive needs for an ant colony.
In exchange for nesting sites and food resources, ants protect plants from herbivores . One of the best-known examples of ant-plant mutualism is in bullhorn acacias ( Acacia cornigera ) and their tending Pseudomyrmex ants in Central America. [ 3 ] [ 16 ] This system was studied by Daniel Janzen in the late 1960s, who provided some of the first experimental evidence that ants significantly reduce herbivory rates of myrmecophytes. [ 18 ] [ 19 ] Since then many other studies have demonstrated similar results in other systems. [ 3 ] [ 17 ] In the bullhorn acacia system, in exchange for protection, the acacias provide domatia, Beltian bodies, and EFNs, and evidence indicates that the Pseudomyrmex ants can survive exclusively on these food resources without having to forage elsewhere. [ 1 ] For many plants, including the bullhorn acacias, ants can significantly reduce herbivory from both phytophagous insects and larger organisms, such as large grazing mammals. [ 20 ] Obligately associated ant species are some of most aggressive ants in the world, and can defend a plant against herbivory by large mammals by repeatedly biting their attacker and spraying formic acid into the wound. [ 3 ]
Myrmecophily is considered a form of indirect plant defense against herbivory, though ants often provide other services in addition to protection. Some ants provide hygienic services to keep leaf surfaces clean and deter disease, and defense against fungal pathogens has also been demonstrated. [ 17 ] Ants commonly prune epiphytes , vines, and parasitic plants from their host plant, and they sometimes thin the shoots of neighboring plants, as well. In doing so, ants reduce plant-plant competition for space, light, nutrients, and water. [ 1 ] Finally, current work focusing on ants' role in nutrient supplementation for plants has shown that in many ant-plant relationships, nutrient flow is bidirectional. One study has estimated that while 80% of the carbon in the bodies of Azteca spp. workers is supplied by the host tree ( Cecropia spp.), 90% of the Cecropia tree's nitrogen was supplied by ant debris carried to the tree as a result of external foraging. [ 21 ] In light of these services, myrmecophily has been considered advantageous in ensuring a plant's survival and ecological success, [ 17 ] although the costs to the plant of providing for the ants can be sufficiently high to offsets benefits. [ 20 ]
Many species of arthropods are dependent on ant species and live amongst them in their nests. Mites are particularly adept at being myrmecophiles, being that they are small enough to enter nests easily and to not be evicted from the homes and bodies of ants. [ 6 ] In fact,
multiple studies show mites exhibit extreme myrmecophily to numbers far above other myrmecophiles. [ 22 ] [ 6 ]
Ants tend a wide variety of insect species, most notably lycaenid butterfly caterpillars and hemipterans. [ 5 ] About 41% of all ant genera include species that associate with insects. [ 23 ] These types of ant-insect interactions involve the ant providing some service in exchange for nutrients in the form of honeydew, a sugary fluid excreted by many phytophagous insects. . [ 5 ] Interactions between honeydew-producing insects and ants is often called trophobiosis , a term which merges notions of trophic relationships with symbioses between ants and insects. This term has been criticized, however, on the basis that myrmecophilous interactions are often more complex than simple trophic interactions, and the use of symbiosis is inappropriate for describing interactions among free-living organisms. [ 5 ]
Insects may also form adaptations to contend with ant aggression, resulting in either mutualistic or parasitic bonds with ant colonies. Some beetles from the family Coccinellidae have developed behaviors, body shapes, and chemical mimicry to prey on ant-tended aphids. [ 24 ]
Some of the best-studied myrmecophilous interactions involve ants and hemipterans, especially aphids . Around 4000 species of aphids are described, and they are the most abundant myrmecophilous organisms in the northern temperate zones. [ 3 ] [ 5 ] Aphids feed on the phloem sap of plants, and as they feed, they excrete honeydew droplets from their anuses. The tending ants ingest these honeydew droplets, then return to their nest to regurgitate the fluid for their nestmates (see trophallaxis ). [ 1 ] Between 90 and 95% of the dry weight of aphid honeydew is various sugars, while the remaining matter includes vitamins, minerals, and amino acids. [ 3 ] Aphid honeydew can provide an abundant food source for ants (aphids in the genus Tuberolachnus can secrete more honeydew droplets per hour than their body weight) and for some ants, aphids may be their only source of food. In these circumstances, ants may supplement their honeydew intake by preying on the aphids once the aphid populations have reached certain densities. In this way, ants can gain extra protein and ensure efficient resource extraction by maintaining honeydew flow rates that do not exceed the ants' collection capabilities. [ 3 ] Even with some predation by ants, aphid colonies can reach larger densities with tending ants than colonies without. Ants have been observed to tend large "herds" of aphids, protecting them from predators and parasitoids . Aphid species that are associated with ants often have reduced structural and behavioral defense mechanisms, and are less able to defend themselves from attack than aphid species that are not associated with ants. [ 3 ]
Ants engage in associations with other honeydew-producing hemipterans, such as scale insects ( Coccidae ), mealybugs ( Pseudococcidae ), and treehoppers ( Membracidae ), and most of these interaction are facultative and opportunistic with some cases of obligate associations, such as hemipterans that are inquiline , meaning they can only survive inside ant nests. [ 5 ] In addition to protection, ants may provide other services in exchange for hemipteran honeydew. Some ants bring hemipteran larvae into the ant nests and rear them along with their own ant brood. [ 3 ] Additionally, ants may actively aid in hemipteran dispersal; queen ants have been observed transporting aphids during their dispersive flights to establish a new colony, and worker ants often carry aphids to a new nesting site if the previous ant nest has been disturbed. Ants may also carry hemipterans to different parts of a plant or to different plants to ensure a fresh food source and/or adequate protection for the herd.
Myrmecophily among lycaenid caterpillars differs from the associations of hemipterans because caterpillars feed on plant tissues, not phloem sap, and therefore do not continually excrete honeydew. Caterpillars of lycaenid butterflies have therefore evolved specialized organs that secrete chemicals to feed and appease ants. [ 3 ] The secretions are a mixture of sugar and amino acids, which in synergy is more attractive to the ants than either component in its own. [ 25 ] The secretions of Narathura japonica caterpillars are thought to be more than merely providing nutrition, with components that cause behavior alteration in the ants, with a reduction in the locomotory activity of caterpillar attendants, increased aggression and protectiveness by Pristomyrmex punctatus ants, suggesting that the association are better treated as parasitic than mutualistic. [ 26 ] Because caterpillars do not automatically pass honeydew, they must be stimulated to secrete droplets, and do so in response to ant antennation, which is the drumming or stroking of the caterpillar's body by the ants' antennae. [ 2 ] Some caterpillars possess specialized receptors that allow them to distinguish between ant antennation and contact from predators and parasites, and others produce acoustic signals that agitate ants, making them more active and likely better defenders of the larvae. [ 27 ] [ 28 ] As with hemipteran myrmecophiles, ants protect lycaenid larvae from predatory insects (including other ants) and parasitoid wasps, which lay their eggs in the bodies of many species of Lepidoptera larvae. For example, one study conducted by Pierce and colleagues in Colorado experimentally found that for the larvae of Glaucopsyche lygdamus that were tended by a certain ant species ( Formica podzolica ), compared to untended larvae, the percentage of larvae disappearing from plants before late final instar decreased (not statistically significantly, though) and the percentage of larvae infected by parasitoids significantly decreased (from 33% to 9%–12%). [ 29 ] These interactions do not come without an energetic cost to the butterfly, however, and ant-tended individuals reach smaller adult sizes than untended individuals due to the costs of appeasing ants during the larval stage. [ 30 ] Interactions with ants are not limited to the butterfly's larval stage, and in fact ants can be important partners for butterflies at all stages of their lifecycles. [ 2 ] For example, adult females of many lycaenid butterflies, such as J. evagoras , [ 31 ] preferentially oviposit on plants where ant partners are present, possibly by using ants' own chemical cues to locate sites where juvenile butterflies will likely be tended by ants. [ 28 ] While ant attendance has been widely documented in lycaenid butterflies and to some extent in riodinid butterflies such as Eurybia elvina , [ 32 ] many other lepidopteran species are known to associate with ants, including many moths. [ 28 ]
Many trophobiotic ants can simultaneously maintain associations with multiple species. [ 23 ] Ants that interact with myrmecophilous insects and myrmecophytes are highly associated; species that are adapted to interact with one of these myrmecophiles may switch among them depending on resource availability and quality. Of the ant genera that include species that associate with ant plants, 94% also include species that associate with trophobionts. In contrast, ants that are adapted to cultivate fungus (leaf cutter ants, tribe Attini ) do not possess the morphological or behavioral adaptations to switch to trophobiotic partners. [ 23 ] Many ant mutualists can exploit these multispecies interactions to maximize the benefits of myrmecophily. For example, some plants host aphids instead of investing in EFNs, which may be more energetically costly depending on local food availability. [ 5 ] The presence of multiple interactors can strongly influence the outcomes of myrmecophily, often in unexpected ways. [ 33 ]
Mutualisms are geographically ubiquitous, found in all organismic kingdoms, and play a major role in all ecosystems. [ 33 ] [ 34 ] Combined with the fact that ants are one of the most dominant lifeforms on earth, [ 16 ] myrmecophily clearly plays a significant role in the evolution and ecology of diverse organisms, and in the community structure of many terrestrial ecosystems.
Questions of how and why species coevolve are of great interest and significance. In many myrmecophilous organisms, ant associations have been influential in the ecological success, diversity, and persistence of species. Analyses of phylogenetic information for myrmecophilous organisms, as well as ant lineages, have demonstrated that myrmecophily has arisen independently in most groups several times. Because multiple gains (and perhaps losses) of myrmecophilous adaptations have happened, the evolutionary sequence of events in most lineages is unknown. [ 30 ] Exactly how these associations evolve also remains unclear.
In studying the coevolution of myrmecophilous organisms, many researchers have addressed the relative costs and benefits of mutualistic interactions, which can vary drastically according to local species composition and abundance, variation in nutrient requirements and availability, host plant quality, presence of alternative food sources, abundance and composition of predator and parasitoid species, and abiotic conditions. [ 23 ] Because of the large amounts of variation in some of these factors, the mechanisms that support the stable persistence of myrmecophily are still unknown. [ 33 ] In many cases, variation in external factors can result in interactions that shift along a continuum of mutualism, commensalism, and even parasitism. In almost all mutualisms, the relative costs and benefits of interactions are asymmetrical; that is, one partner experiences greater benefits and/or fewer costs than the other partner. This asymmetry leads to "cheating", in which one partner evolves strategies to receive benefits without providing services in return. As with many other mutualisms, cheating has evolved in interactions between ants and their partners. For example, some lycaenid larvae are taken into ant nests, where they prey on ant brood and offer no services to the ants. [ 3 ] Other lycaenids may parasitize ant-plant relationships by feeding on plants that are tended by ants, apparently immune to ant attack because of their own appeasing secretions. Hemipterophagous lycaenids engage in a similar form of parasitism in ant-hemipteran associations. [ 17 ] In light of the variability in outcomes of mutualistic interactions, and also the evolution of cheating in many systems, much remains to be learned about the mechanisms that maintain mutualism as an evolutionarily stable interaction. [ 34 ]
In addition to leading to coevolution, mutualisms also play an important role in structuring communities. [ 33 ] One of the most obvious ways in which myrmecophily influences community structure is by allowing for the coexistence of species that might otherwise be antagonists or competitors. For many myrmecophiles, engaging in ant associations is first and foremost a method of avoiding predation by ants. For example, the caterpillars of lycaenid butterflies are an ideal source of food for ants: they are slow-moving, soft-bodied, and highly nutritious, yet they have evolved complex structures to not only appease ant aggression, but also to elicit protective services from the ants. [ 2 ] To explain why ants cooperate with other species as opposed to preying on them, two related hypotheses have been proposed; cooperation either provides ants with resources that are otherwise difficult to find, or it ensures the long-term availability of those resources. [ 5 ]
At both small and large spatiotemporal scales, mutualistic interactions influence patterns of species richness, distribution, and abundance. [ 35 ] Myrmecophilous interactions play an important role in determining community structure by influencing inter- and intraspecific competition; regulating population densities of arthropods, fungi, and plants; determining arthropod species assemblages; and influencing trophic dynamics. [ 5 ] Recent work in tropical forests has shown that ant mutualisms may play key roles in structuring food webs, as ants can control entire communities of arthropods in forest canopies. [ 17 ] Myrmecophily has also been key in the ecological success of ants. Ant biomass and abundance in many ecosystems exceeds that of their potential prey, suggesting a strong role of myrmecophily in supporting larger populations of ants than would otherwise be possible. [ 17 ] Furthermore, by providing associational refugia and habitat amelioration for many species, ants are considered dominant ecosystem engineers. [ 3 ] [ 35 ]
Myrmecophilous interactions provide an important model system for exploring ecological and evolutionary questions regarding coevolution, plant defense theory, food web structure, species coexistence, and evolutionarily stable strategies. Because many myrmecophilous relationships are easily manipulated and tractable, they allow for testing and experimentation that may not be possible in other interactions. Therefore, they provide ideal model systems in which to explore the magnitude, dynamics, and frequency of mutualism in nature. [ 17 ] | https://en.wikipedia.org/wiki/Myrmecophily |
Many species of Staphylinidae (commonly known as "rove beetles") have developed complex interspecies relationships with ants, known as myrmecophily . Rove beetles are among the most rich and diverse families of myrmecophilous beetles, with a wide variety of relationships with ants. Ant associations range from near free-living species which prey only on ants, to obligate inquilines of ants, which exhibit extreme morphological and chemical adaptations to the harsh environments of ant nests. Some species are fully integrated into the host colony, and are cleaned and fed by ants. Many of these, including species in tribe Clavigerini, are myrmecophagous , placating their hosts with glandular secretions while eating the brood. [ 1 ]
Staphylinidae is currently considered to be the largest family of beetles, with over 58,000 species described. As such, many myrmecophilous species are unknown. The majority of studied myrmecophilous rove beetles belong to the subfamily Aleocharinae , including the commonly studied genera Pella , Dinarda , Tetradonia , Ecitomorpha , Ecitophya , Atemeles , and Lomechusa , and to the subfamily Pselaphinae , which includes Claviger and Adranes . There are also representatives of Scydmaenidae , which includes 117 myrmecophilous species in 20 genera [ 2 ] The Aleocharinae possess defensive glands on their abdomens, which are used in myrmecophilous species to prevent attacks by their host ant and in more extreme cases to integrate completely into the colony. Many Pselephinae species have trichomes , tufts of hairs which hold placating pheromones. Pselephines have evolved trichomes independently at least four times, most notably in all members of Clavigerini, but also in Attapsenius and Songius genera. [ 3 ]
Due to their large number and diversity, myrmecophilous rove beetles occupy an array of behaviors. Myrmecophilous interactions can be generalized into categories, in three of which staphylinids can be found. The synecthrans, or “persecuted guests,” the synoeketes, or “tolerated guests,” and the symphiles , or “true guests.” [ 4 ]
Synecthran staphylinids live on the periphery of the host colony and are not accepted into the colony. The majority are in the subfamily Aleocharinae, having defensive glands on their terminal abdominal segments. Species in this group, such as those in the genus Pella , commonly lay their eggs in the refuse heaps of their host ant, where the larvae feed on the discarded carcasses of ants. If detected by the host ant, the larvae enters a typical defense position, facing the ant with its abdomen tip raised. Usually this behavior results in the ant palpating the beetle's abdomen and stopping the attack. [ 5 ] At least two members of Pella, P. funestus and P. humeralis , produce several of their host ant's alarm pheromones to avoid aggression. [ 6 ] Other species, like members of Myrmechusa, Aenictonia , and Anommatochara , prey on raiding columns or on the nests of driver ants ( Dorylus ). [ 7 ] Myrmechusa species attack the ants from the rear before pulling them from the main column. If pursued, they rapidly wave their abdomens through the air, releasing a noticeable scent. Ants encountering this scent seem disoriented and take almost 20 minutes to recover. [ 8 ]
Synoeketetic staphylinids live in close contact with their host ants but are not integrated into the colony. These species may be further categorized as neutral, mimetic, loricate, and symphiloid synoeketes. Neutral synoeketes ignore and are ignored by their host, but feed on refuse. There are few staphylinid neutral synoeketes, but some are found in the genus Athetini , which live in the debris and fungal chambers of leaf cutter ants ( Atta ). [ 7 ] Mimetic synoeketes are myrmecoid, resembling their host ant morphologically. Many mimetic species are guests of driver ants, which are blind. Driver ants have strong senses of touch, suggesting mimics fool their hosts tactilely. It is also possible that mimicry may reduce predation from more visual animals, such as birds. Loricate, or “tear-drop shaped”, synoeketes are “defensive forms”. They typically exhibit long tapering bodies with broad thoraxes and smooth bodies, which prevent aggressing ants from gripping them. Symphiloids strongly resemble “true guests,” but are not fully integrated into the colony. They are often mimics, and in some species have developed trichomes . [ 9 ] Syneoketes generally live on or inside of ant nests, where they feed on refuse and may steal food from their hosts. There is some overlap between synoeketes and other categories, especially in loricate species and synecthrans, and symphiloids and symphiles, where the behavior of “true guests” may be difficult to determine.
Symphilic staphylinids have been fully integrated into the host ant's society. Symphilic species have undergone complex morphological adaptations, many becoming myrmecoid. Most have developed trichomes, which secrete appeasement pheromones. The most extreme adaptations, found in members of tribe Clavigerini, include the reduction of mouthparts for trophallaxis and the fusing of many body and antennal segments. While most symphiles use antennal contact to stimulate food giving from their host, at least one member of Clavigerini, Claviger testaceus , secretes a chemical to induce regurgitation from its host ant Lasius flavus . [ 10 ] Symphiles typically take on many roles in the colony, raising young, feeding and grooming adults, and helping transport food and larvae. Many staphylinids are capable of following ant pheromone trails, although they are not limited to following trails laid by their host ant. This allows symphiles of army ants to migrate with the colony. [ 11 ] Most species are kleptoparasites fed by members of the ant colony, often through trophallaxis . [ 12 ] Almost all species have also been observed feeding on the brood. Some of these species die if kept away from the appropriate ant colonies, and others lay their own eggs in ant brood galleries, effectively making them obligate parasites . [ 12 ]
Chemical mimicry refers to the production of one species’ chemical signals by another species. Many myrmecophilous staphylinids have evolved chemical mimicry to deter or placate ants. Synecthrans, as non-tolerated guests, primarily produce defensive secretions. Pella species produce two compounds found in their host ant Lasius fuliginosus , undecane and sulcatone, which elicit aggressive and panic reactions respectively. Although it seems counterintuitive to release an aggressive alarm pheromone as a defense, the presence of sulcatone stops the aggression response to undecane. Ants exposed to the defensive secretion act less aggressively and avoid the odor.
For staphylinids accepted into the host colony, chemical mimicry is used more for camouflage. The majority of the chemical signals used are cuticular hydrocarbons, which are produced in the cuticle of the host ant at certain concentrations and are palpated to determine the identity of an ant. Species in close contact with their host ants are able to pick up the host's hydrocarbons and imitate the ant's hydrocarbon pattern, thus appearing in scent at least to be the same species as the host ant. As hydrocarbon patterns are specific to an individual colony, the rove beetles are generally restricted to one nest. The production of a new hydrocarbon pattern takes time, during which the beetle is vulnerable to detection and attack. [ 6 ] Some species, such as Zyras comes , produce volatile pheromones as well as cuticular hydrocarbons, which may provide it more protection than contact based pheromones while traveling with its host in foraging trails. [ 13 ] | https://en.wikipedia.org/wiki/Myrmecophily_in_Staphylinidae |
Myrtenol is a chemical compound isolated from plants in the genus Taxus . [ 1 ]
This organic chemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Myrtenol |
Mysterium Cosmographicum (lit. The Cosmographic Mystery , [ note 1 ] alternately translated as Cosmic Mystery , The Secret of the World , or some variation) is an astronomy book by the German astronomer Johannes Kepler , published at Tübingen in late 1596 [ 1 ] [ note 2 ] and in a second edition in 1621. Kepler proposed that the distance relationships between the six planets known at that time could be understood in terms of the five Platonic solids , enclosed within a sphere that represented the orbit of Saturn .
This book explains Kepler's cosmological theory, based on the Copernican system , in which the five Platonic solids dictate the structure of the universe and reflect God's plan through geometry . This was virtually the first attempt since Copernicus to say that the theory of heliocentrism is physically true. [ 2 ] Thomas Digges had published a defense of Copernicus in an appendix in 1576. According to Kepler's account, he discovered the basis of the model while demonstrating the geometrical relationship between two circles. From this he realized that he had stumbled on a similar ratio to the one between the orbits of Saturn and Jupiter. He wrote, "I believe it was by divine ordinance that I obtained by chance that which previously I could not reach by any pains." [ 3 ] But after doing further calculations he realized he could not use two-dimensional polygons to represent all the planets, and instead had to use the five Platonic solids .
Johannes Kepler's first major astronomical work, Mysterium Cosmographicum ( The Cosmographic Mystery ), was a defence of the Copernican system . Kepler claimed to have had an epiphany on July 19, 1595, while teaching in Graz , demonstrating the periodic conjunction of Saturn and Jupiter in the zodiac : he realized that regular polygons bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe. After failing to find a unique arrangement of polygons that fit known astronomical observations (even with extra planets added to the system), Kepler began experimenting with 3-dimensional polyhedra . He found that each of the five Platonic solids could be uniquely inscribed and circumscribed by spherical orbs ; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets— Mercury , Venus , Earth , Mars , Jupiter , and Saturn . By ordering the solids correctly— octahedron , icosahedron , dodecahedron , tetrahedron , and cube —Kepler found that the spheres correspond to the relative sizes of each planet's path around the Sun, generally varying from astronomical observations by less than 10%. He attributed most of the variances to inaccuracies in measurement. [ 4 ]
Kepler also found a formula relating the size of each planet's orbit to the length of its orbital period : from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius. However, Kepler later rejected this formula because it was not precise enough. [ 5 ]
As he indicated in the title, Kepler thought he had revealed God ’s geometrical plan for the universe. Much of Kepler's enthusiasm for the Copernican system stemmed from his theological convictions about the connection between the physical and the spiritual ; the universe itself was an image of the Trinity , with the Sun corresponding to the Father , the stellar sphere to the Son , and the intervening space between to the Holy Spirit . His first manuscript of Mysterium contained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism . [ 6 ]
With the support of his mentor Michael Maestlin , Kepler received permission from the Tübingen university senate to publish his manuscript, pending removal of the Bible exegesis and the addition of a simpler, more understandable description of the Copernican system (the Narratio prima by Rheticus ) as an appendix. Mysterium was published late in 1596, and Kepler received his copies and began sending them to prominent astronomers and patrons early in 1597; it was not widely read, but it established Kepler's reputation as a highly skilled astronomer. The effusive dedication, to powerful patrons as well as to the men who controlled his position in Graz, also provided a crucial doorway into the patronage system . [ 7 ]
Though the details would be modified in light of his later work, Kepler never relinquished the Platonist polyhedral-spherical cosmology of Mysterium Cosmographicum . His subsequent main astronomical works were in some sense only further developments of it, concerned with finding more precise inner and outer dimensions for the spheres by calculating the eccentricities of the planetary orbits within it. In 1621, Kepler published an expanded second edition of Mysterium , half as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication. [ 8 ]
Many of Kepler's thoughts about epistemology can be found in his Defense of Tycho against Ursus or Contra Ursum (CU), a work which emerged from a polemical framework, the plagiarism conflict between Nicolaus Raimarus Ursus (1551–1600) and Tycho Brahe: causality and physicalization of astronomical theories, the concept and status of astronomical hypotheses, the polemic “realism-instrumentalism”, his criticism of scepticism in general, the epistemological role of history, etc. Jardine has pointed out that it would be sounder to read Kepler's CU more as a work against scepticism than in the context of the modern realism/instrumentalism debate. [ 9 ]
On the one hand, "causality" is a notion implying the most general idea of "actual scientific knowledge" which guides and stimulates each investigation. In this sense, Kepler already embarked in his MC on a causal investigation by asking for the cause of the number, the sizes and the "motions" (the speeds) of the heavenly spheres. On the other hand, "causality" implies in Kepler, according to the Aristotelian conception of physical science, the concrete "physical cause", the efficient cause which produces a motion or is responsible for keeping the body in motion. Original to Kepler, however, and typical of his approach is the resoluteness with which he was convinced that the problem of equipollence of the astronomical hypotheses can be resolved and the consequent introduction of the concept of causality into astronomy—traditionally a mathematical science. This approach is already present in his MC, where he, for instance, relates for the first time the distances of the planets to a power which emerges from the Sun and decreases in proportion to the distance of each planet, up to the sphere of the fixed stars. [ 10 ]
Kepler corresponded with and provided courtesy book copies to a number of astronomers around the time of publication, including Galileo Galilei , Tycho Brahe , Reimarus Ursus , and Georg Limnaeus . [ 11 ] In response to Mysterium Cosmographicum , the Danish astronomer Tycho Brahe (whom Kepler had sent a copy) [ 12 ] said that the ideas were intriguing but could only be verified through the observations Brahe himself had been making over the past 30 years. Because he was promised use of these observations by Brahe, Kepler sought him out in the beginning of 1600. Brahe only gave him the data on Mars, [ 13 ] but this meeting helped Kepler formulate his laws of planetary motion . [ 12 ]
The Mysterium Cosmographicum was featured on the Austrian 10 euro Johannes Kepler silver commemorative coin minted in 2002. [ 14 ] | https://en.wikipedia.org/wiki/Mysterium_Cosmographicum |
Mystic Mountain is a photograph and a term for a region in the Carina Nebula imaged by the Hubble Space Telescope . The view was captured by the then-new Wide Field Camera 3 , though the region was also viewed by the previous generation instrument. The new view celebrated the telescope's 20th anniversary of being in space in 2010. [ 1 ] Mystic Mountain contains multiple Herbig–Haro objects where nascent stars are firing off jets of gas which interact with surrounding clouds of gas and dust. [ 2 ] [ 3 ] This region is about 7,500 light-years (2,300 parsecs ) away from Earth. The pillar measures around three light-years in height (190,000 astronomical units ). [ 1 ] The name was influenced by the works of H. P. Lovecraft . [ 4 ]
Media related to Mystic Mountain at Wikimedia Commons | https://en.wikipedia.org/wiki/Mystic_Mountain |
A mythical number is a number used and accepted as deriving from scientific investigation and/or careful selection, but whose origin is unknown and whose basis is unsubstantiated. An example is the number 48 billion, which has often been accepted as the number of dollars per year of identity theft. This number "has appeared in hundreds of news stories, including a New York Times piece" [ 1 ] despite the fact that it has been shown repeatedly to be highly inaccurate. The term was coined in 1971 by Max Singer , one of the founders of the Hudson Institute .
The origins of such numbers are akin to those of urban legends and may include (among others):
This article about a number is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Mythical_number |
Myzocytosis (from Greek : myzein , ( μυζεῖν ) meaning "to suck" and kytos ( κύτος ) meaning "container", hence referring to "cell") is a method of feeding found in some heterotrophic organisms . It is also called "cellular vampirism" as the predatory cell pierces the cell wall and/or cell membrane of the prey cell with a feeding tube, the conoid , sucks out the cellular content and digests it.
Myzocytosis is found in Myzozoa [ 1 ] and also in some species of Ciliophora (both comprise the alveolates ). A classic example of myzocytosis is the feeding method of the infamous predatory ciliate, Didinium , where it is often depicted devouring a hapless Paramecium . [ 2 ] The suctorian ciliates were originally thought to have fed exclusively through myzocytosis, sucking out the cytoplasm of prey via superficially drinking straw -like pseudopodia. It is now understood that suctorians do not feed through myzocytosis, but actually, instead, manipulate and envenomate captured prey with their tentacle-like pseudopodia. [ 3 ]
This ecology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Myzocytosis |
Mónica Morales Masis (born 1982) is a Costa Rican physicist and materials scientist who works in The Netherlands as a professor at the University of Twente . Her research focuses on optoelectronics , transparent electronics , and solar cells . [ 1 ] [ 2 ] [ 3 ]
Morales is originally from Cartago, Costa Rica , [ 4 ] where she was born in 1982. [ 5 ] A childhood idol was Costa Rican astronaut Franklin Chang-Díaz . [ 4 ] After a 2004 bachelor's degree in physics from the University of Costa Rica , she traveled to the US for a master's degree at Wright State University , in 2007, and then to The Netherlands for a doctorate at Leiden University , [ 4 ] focusing on condensed-matter physics . [ 5 ] [ 6 ] Her 2012 doctoral thesis concerned the memristive properties of silver sulfide , [ 7 ] [ 5 ] and was promoted by Jan van Ruitenbeek; it also included work done at the National Institute for Materials Science in Japan with Tsuyoshi Hasegawa. [ 5 ]
Next, she went to Switzerland for postdoctoral research at the École Polytechnique Fédérale de Lausanne (EPFL). Her interest in photovoltaics developed at that time, and she continued at EPFL as a research group leader in the subject. She took a tenure-track faculty position at the University of Twente in 2018, and became a full professor there. [ 6 ] At Twente, she is affiliated with the faculty of science and technology, in the inorganic materials science group, [ 7 ] and with the MESA+ Institute for Nanotechnology. [ 8 ]
Morales joined the Young Academy of Europe in 2022. [ 8 ] | https://en.wikipedia.org/wiki/Mónica_Morales_Masis |
In organic chemistry , Möbius aromaticity is a special type of aromaticity believed to exist in a number of organic molecules . [ 1 ] [ 2 ] In terms of molecular orbital theory these compounds have in common a monocyclic array of molecular orbitals in which there is an odd number of out-of-phase overlaps, the opposite pattern compared to the aromatic character in Hückel systems . The nodal plane of the orbitals, viewed as a ribbon, is a Möbius strip , rather than a cylinder, hence the name. The pattern of orbital energies is given by a rotated Frost circle (with the edge of the polygon on the bottom instead of a vertex), so systems with 4 n electrons are aromatic, while those with 4 n + 2 electrons are anti-aromatic/non-aromatic. Due to the incrementally twisted nature of the orbitals of a Möbius aromatic system, stable Möbius aromatic molecules need to contain at least 8 electrons, although 4-electron Möbius aromatic transition states are well known in the context of the Dewar-Zimmerman framework for pericyclic reactions . Möbius molecular systems were considered in 1964 by Edgar Heilbronner by application of the Hückel method , [ 3 ] but the first such isolable compound was not synthesized until 2003 by the group of Rainer Herges . [ 4 ] However, the fleeting trans- C 9 H 9 + cation, one conformation of which is shown on the right, was proposed to be a Möbius aromatic reactive intermediate in 1998 based on computational and experimental evidence.
The Herges compound ( 6 in the image below) was synthesized in several photochemical cycloaddition reactions from tetradehydrodianthracene 1 and the ladderane syn-tricyclooctadiene 2 as a substitute for cyclooctatetraene . [ note 1 ]
Intermediate 5 was a mixture of 2 isomers and the final product 6 a mixture of 5 isomers with different cis and trans configurations . One of them was found to have a C 2 molecular symmetry corresponding to a Möbius aromatic and another Hückel isomer was found with C s symmetry. Despite having 16 electrons in its pi system (making it a 4n antiaromatic compound) the Heilbronner prediction was borne out because according to Herges the Möbius compound was found to have aromatic properties. With bond lengths deduced from X-ray crystallography a HOMA value was obtained of 0.50 (for the polyene part alone) and 0.35 for the whole compound which qualifies it as a moderate aromat.
Henry Rzepa pointed out that the conversion of intermediate 5 to 6 can proceed by either a Hückel or a Möbius transition state . [ 5 ]
The difference was demonstrated in a hypothetical pericyclic ring opening reaction to cyclododecahexaene . The Hückel TS (left) involves 6 electrons (arrow pushing in red) with C s molecular symmetry conserved throughout the reaction. The ring opening is disrotatory and suprafacial and both bond length alternation and NICS values indicate that the 6 membered ring is aromatic. The Möbius TS with 8 electrons on the other hand has lower computed activation energy and is characterized by C 2 symmetry, a conrotatory and antarafacial ring opening and 8-membered ring aromaticity.
Another interesting system is the cyclononatetraenyl cation explored for over 30 years by Paul v. R. Schleyer et al. This reactive intermediate is implied in the solvolysis of the bicyclic chloride 9-deutero-9'-chlorobicyclo[6.1.0]-nonatriene 1 to the indene dihydroindenol 4 . [ 6 ] [ 7 ] The starting chloride is deuterated in only one position but in the final product deuterium is distributed at every available position. This observation is explained by invoking a twisted 8-electron cyclononatetraenyl cation 2 for which a NICS value of -13.4 (outsmarting benzene ) is calculated. [ 8 ] A more recent study, however, suggests that the stability of trans -C 9 H 9 + is not much different in energy compared to a Hückel topology isomer. The same study suggested that for [13]annulenyl cation, the Möbius topology penta- trans -C 13 H 13 + is a global energy minimum and predicts that it may be directly observable. [ 9 ]
In 2005 the same P. v. R. Schleyer [ 10 ] questioned the 2003 Herges claim: he analyzed the same crystallographic data and concluded that there was indeed a large degree of bond length alternation resulting in a HOMA value of -0.02, a computed NICS value of -3.4 ppm also did not point towards aromaticity and (also inferred from a computer model) steric strain would prevent effective pi-orbital overlap.
A Hückel-Möbius aromaticity switch (2007) has been described based on a 28 pi-electron porphyrin system: [ 11 ] [ note 2 ]
The phenylene rings in this molecule are free to rotate forming a set of conformers : one with a Möbius half-twist and another with a Hückel double-twist (a figure-eight configuration) of roughly equal energy.
In 2014, Zhu and Xia (with the help of Schleyer) synthesized a planar Möbius system that consisted of two pentene rings connected with an osmium atom. [ 12 ] They formed derivatives where osmium had 16 and 18 electrons and determined that Craig–Möbius aromaticity is more important for the stabilization of the molecule than the metal's electron count.
In contrast to the rarity of Möbius aromatic ground state molecular systems, there are many examples of pericyclic transition states that exhibit Möbius aromaticity. The classification of a pericyclic transition state as either Möbius or Hückel topology determines whether 4 N or 4 N + 2 electrons are required to make the transition state aromatic or antiaromatic, and therefore, allowed or forbidden, respectively. Based on the energy level diagrams derived from Hückel MO theory , (4 N + 2)-electron Hückel and (4 N )-electron Möbius transition states are aromatic and allowed, while (4 N + 2)-electron Möbius and (4 N )-electron Hückel transition states are antiaromatic and forbidden. This is the basic premise of the Möbius-Hückel concept . [ 13 ] [ 14 ]
From the figure above, it can also be seen that the interaction between two consecutive p z {\displaystyle p_{z}} AOs is attenuated by the incremental twisting between orbitals by cos ω {\displaystyle \cos \omega } , where ω = π / N {\displaystyle \omega =\pi /N} is the angle of twisting between consecutive orbitals, compared to the usual Hückel system. For this reason resonance integral β ′ {\displaystyle \beta ^{\prime }} is given by
where β {\displaystyle \beta } is the standard Hückel resonance integral value (with completely parallel orbitals).
Nevertheless, after going all the way around, the N th and 1st orbitals are almost completely out of phase. (If the twisting were to continue after the N {\displaystyle N} th orbital, the ( N + 1 ) {\displaystyle (N+1)} st orbital would be exactly phase-inverted compared to the 1st orbital). For this reason, in the Hückel matrix the resonance integral between carbon 1 {\displaystyle 1} and N {\displaystyle N} is − β ′ {\displaystyle -\beta ^{\prime }} . For the generic N {\displaystyle N} carbon Möbius system, the Hamiltonian matrix H {\displaystyle \mathbf {H} } is:
Eigenvalues for this matrix can now be found, which correspond to the energy levels of the Möbius system. Since H {\displaystyle \mathbf {H} } is a N × N {\displaystyle N\times N} matrix, we will have N {\displaystyle N} eigenvalues E k {\displaystyle E_{k}} and N {\displaystyle N} MOs. Defining the variable
we have:
To find nontrivial solutions to this equation, we set the determinant of this matrix to zero to obtain
Hence, we find the energy levels for a cyclic system with Möbius topology,
In contrast, recall the energy levels for a cyclic system with Hückel topology, | https://en.wikipedia.org/wiki/Möbius_aromaticity |
In mathematics , the classic Möbius inversion formula is a relation between pairs of arithmetic functions , each defined from the other by sums over divisors . It was introduced into number theory in 1832 by August Ferdinand Möbius . [ 1 ]
A large generalization of this formula applies to summation over an arbitrary locally finite partially ordered set , with Möbius' classical formula applying to the set of the natural numbers ordered by divisibility: see incidence algebra .
The classic version states that if g and f are arithmetic functions satisfying
then
where μ is the Möbius function and the sums extend over all positive divisors d of n (indicated by d ∣ n {\displaystyle d\mid n} in the above formulae). In effect, the original f ( n ) can be determined given g ( n ) by using the inversion formula. The two sequences are said to be Möbius transforms of each other.
The formula is also correct if f and g are functions from the positive integers into some abelian group (viewed as a Z - module ).
In the language of Dirichlet convolutions , the first formula may be written as
where ∗ denotes the Dirichlet convolution, and 1 is the constant function 1 ( n ) = 1 . The second formula is then written as
Many specific examples are given in the article on multiplicative functions .
The theorem follows because ∗ is (commutative and) associative, and 1 ∗ μ = ε , where ε is the identity function for the Dirichlet convolution, taking values ε (1) = 1 , ε ( n ) = 0 for all n > 1 . Thus
Replacing f , g {\displaystyle f,g} by ln f , ln g {\displaystyle \ln f,\ln g} , we obtain the product version of the Möbius inversion formula:
Let
so that
is its transform. The transforms are related by means of series: the Lambert series
and the Dirichlet series :
where ζ ( s ) is the Riemann zeta function .
Given an arithmetic function, one can generate a bi-infinite sequence of other arithmetic functions by repeatedly applying the first summation.
For example, if one starts with Euler's totient function φ , and repeatedly applies the transformation process, one obtains:
If the starting function is the Möbius function itself, the list of functions is:
Both of these lists of functions extend infinitely in both directions. The Möbius inversion formula enables these lists to be traversed backwards.
As an example the sequence starting with φ is:
The generated sequences can perhaps be more easily understood by considering the corresponding Dirichlet series : each repeated application of the transform corresponds to multiplication by the Riemann zeta function .
A related inversion formula more useful in combinatorics is as follows: suppose F ( x ) and G ( x ) are complex -valued functions defined on the interval [1, ∞) such that
then
Here the sums extend over all positive integers n which are less than or equal to x .
This in turn is a special case of a more general form. If α ( n ) is an arithmetic function possessing a Dirichlet inverse α −1 ( n ) , then if one defines
then
The previous formula arises in the special case of the constant function α ( n ) = 1 , whose Dirichlet inverse is α −1 ( n ) = μ ( n ) .
A particular application of the first of these extensions arises if we have (complex-valued) functions f ( n ) and g ( n ) defined on the positive integers, with
By defining F ( x ) = f (⌊ x ⌋) and G ( x ) = g (⌊ x ⌋) , we deduce that
A simple example of the use of this formula is counting the number of reduced fractions 0 < a / b < 1 , where a and b are coprime and b ≤ n . If we let f ( n ) be this number, then g ( n ) is the total number of fractions 0 < a / b < 1 with b ≤ n , where a and b are not necessarily coprime. (This is because every fraction a / b with gcd( a , b ) = d and b ≤ n can be reduced to the fraction a / d / b / d with b / d ≤ n / d , and vice versa.) Here it is straightforward to determine g ( n ) = n ( n − 1) / 2 , but f ( n ) is harder to compute.
Another inversion formula is (where we assume that the series involved are absolutely convergent):
As above, this generalises to the case where α ( n ) is an arithmetic function possessing a Dirichlet inverse α −1 ( n ) :
For example, there is a well known proof relating the Riemann zeta function to the prime zeta function that uses the series-based form of
Möbius inversion in the previous equation when s = 1 {\displaystyle s=1} . Namely, by the Euler product representation of ζ ( s ) {\displaystyle \zeta (s)} for ℜ ( s ) > 1 {\displaystyle \Re (s)>1}
These identities for alternate forms of Möbius inversion are found in. [ 2 ] A more general theory of Möbius inversion formulas partially cited in the next section on incidence algebras is constructed by Rota in. [ 3 ]
As Möbius inversion applies to any abelian group, it makes no difference whether the group operation is written as addition or as multiplication. This gives rise to the following notational variant of the inversion formula:
The first generalization can be proved as follows. We use Iverson's convention that [condition] is the indicator function of the condition, being 1 if the condition is true and 0 if false. We use the result that
that is, 1 ∗ μ = ε {\displaystyle 1*\mu =\varepsilon } , where ε {\displaystyle \varepsilon } is the unit function .
We have the following:
The proof in the more general case where α ( n ) replaces 1 is essentially identical, as is the second generalisation.
For a poset P , a set endowed with a partial order relation ≤ {\displaystyle \leq } , define the Möbius function μ {\displaystyle \mu } of P recursively by
(Here one assumes the summations are finite.) Then for f , g : P → K {\displaystyle f,g:P\to K} , where K is a commutative ring, we have
if and only if
(See Stanley's Enumerative Combinatorics , Vol 1, Section 3.7.) The classical arithmetic Mobius function is the special case of the poset P of positive integers ordered by divisibility : that is, for positive integers s, t, we define the partial order s ≼ t {\displaystyle s\preccurlyeq t} to mean that s is a divisor of t .
The statement of the general Möbius inversion formula [for partially ordered sets] was first given independently by Weisner (1935) and Philip Hall (1936); both authors were motivated by group theory problems. Neither author seems to have been aware of the combinatorial implications of his work and neither developed the theory of Möbius functions. In a fundamental paper on Möbius functions, Rota showed the importance of this theory in combinatorial mathematics and gave a deep treatment of it. He noted the relation between such topics as inclusion-exclusion, classical number theoretic Möbius inversion, coloring problems and flows in networks. Since then, under the strong influence of Rota, the theory of Möbius inversion and related topics has become an active area of combinatorics. [ 4 ] | https://en.wikipedia.org/wiki/Möbius_inversion_formula |
In mathematics, the classical Möbius plane (named after August Ferdinand Möbius ) is the Euclidean plane supplemented by a single point at infinity . It is also called the inversive plane because it is closed under inversion with respect to any generalized circle , and thus a natural setting for planar inversive geometry .
An inversion of the Möbius plane with respect to any circle is an involution which fixes the points on the circle and exchanges the points in the interior and exterior, the center of the circle exchanged with the point at infinity. In inversive geometry a straight line is considered to be a generalized circle containing the point at infinity; inversion of the plane with respect to a line is a Euclidean reflection .
More generally, a Möbius plane is an incidence structure with the same incidence relationships as the classical Möbius plane. It is one of the Benz planes : Möbius plane, Laguerre plane and Minkowski plane .
Affine planes are systems of points and lines that satisfy, amongst others, the property that two points determine exactly one line. This concept can be generalized to systems of points and circles, with each circle being determined by three non-collinear points. However, three collinear points determine a line, not a circle. This drawback can be removed by adding a point at infinity to every line. If we call both circles and such completed lines cycles , we get an incidence structure in which every three points determine exactly one cycle.
In an affine plane the parallel relation between lines is essential. In the geometry of cycles, this relation is generalized to the touching relation. Two cycles touch each other if they have just one point in common. This is true for two tangent circles or a line that is tangent to a circle . Two completed lines touch if they have only the point at infinity in common, so they are parallel. The touching relation has the property
These properties essentially define an axiomatic Möbius plane . But the classical Möbius plane is not the only geometrical structure that satisfies the properties of an axiomatic Möbius plane. A simple further example of a Möbius plane can be achieved if one replaces the real numbers by rational numbers . The usage of complex numbers (instead of the real numbers) does not lead to a Möbius plane, because in the complex affine plane the curve x 2 + y 2 = 1 {\displaystyle x^{2}+y^{2}=1} is not a circle-like curve, but a hyperbola-like one. Fortunately there are a lot of fields (numbers) together with suitable quadratic forms that lead to Möbius planes (see below). Such examples are called miquelian , because they fulfill Miquel's theorem . All these miquelian Möbius planes can be described by space models. The classical real Möbius plane can be considered as the geometry of circles on the unit sphere. The essential advantage of the space model is that any cycle is just a circle (on the sphere).
We start from the real affine plane A ( R ) {\displaystyle {\mathfrak {A}}(\mathbb {R} )} with the quadratic form ρ ( x , y ) = x 2 + y 2 {\displaystyle \rho (x,y)=x^{2}+y^{2}} and get the real Euclidean plane : R 2 {\displaystyle \mathbb {R} ^{2}} is the point set, the lines are described by equations y = m x + b {\displaystyle y=mx+b} or x = c {\displaystyle x=c} and a circle is a set of points that fulfills an equation
The geometry of lines and circles of the euclidean plane can be homogenized (similarly to the projective completion of an affine plane) by embedding it into the incidence structure
with
Then ( P , Z , ∈ ) {\displaystyle ({\mathcal {P}},{\mathcal {Z}},\in )} is called the classical real Möbius plane .
Within the new structure the completed lines play no special role anymore. Obviously ( P , Z , ∈ ) {\displaystyle ({\mathcal {P}},{\mathcal {Z}},\in )} has the following properties.
( P , Z , ∈ ) {\displaystyle ({\mathcal {P}},{\mathcal {Z}},\in )} can be described using the
complex numbers. z = x + i y {\displaystyle z=x+iy} represents point ( x , y ) ∈ R 2 {\displaystyle (x,y)\in \mathbb {R} ^{2}} and z ¯ = x − i y {\displaystyle {\overline {z}}=x-iy} is the complex conjugate of z {\displaystyle z} .
The advantage of this description is, that one checks easily that the following permutations of P {\displaystyle {\mathcal {P}}} map cycles onto cycles.
Considering C ∪ { ∞ } {\displaystyle \mathbb {C} \cup \{\infty \}} as projective line over C {\displaystyle \mathbb {C} } one recognizes
that the mappings (1)-(3) generate the group PGL ( 2 , C ) {\displaystyle \operatorname {PGL} (2,\mathbb {C} )} (see PGL(2,C) , Möbius transformation ). The geometry ( P , Z , ∈ ) {\displaystyle ({\mathcal {P}},{\mathcal {Z}},\in )} is a homogeneous structure, i.e. , its automorphism group is transitive . Hence from (4) we get: For any cycle there exists an inversion . For example: z → 1 z ¯ {\displaystyle z\rightarrow {\tfrac {1}{\overline {z}}}} is the inversion which fixes the unit circle z z ¯ = 1 {\displaystyle z{\overline {z}}=1} . This property gives rise to the alternate name inversive plane .
Similarly to the space model of a desarguesian projective plane there exists a
space model for the geometry ( P , Z , ∈ ) {\displaystyle ({\mathcal {P}},{\mathcal {Z}},\in )} which omits the formal difference between cycles defined by lines and cycles defined by circles: The geometry ( P , Z , ∈ ) {\displaystyle ({\mathcal {P}},{\mathcal {Z}},\in )} is isomorphic to the geometry of circles on a sphere. The isomorphism can be performed by a suitable stereographic projection . For example: [ 1 ]
Φ {\displaystyle \Phi } is a projection with center ( 0 , 0 , 1 ) {\displaystyle (0,0,1)} and maps
The incidence behavior of the classical real Möbius plane gives rise to the following definition of an axiomatic Möbius plane.
An incidence structure M = ( P , Z , ∈ ) {\displaystyle {\mathfrak {M}}=({\mathcal {P}},{\mathcal {Z}},\in )} with point set P {\displaystyle {\mathcal {P}}} and set of cycles Z {\displaystyle {\mathcal {Z}}} is called a Möbius plane if the following axioms hold:
Four points A , B , C , D {\displaystyle A,B,C,D} are concyclic if there is a cycle z {\displaystyle z} with A , B , C , D ∈ z {\displaystyle A,B,C,D\in z} .
One should not expect that the axioms above define the classical real Möbius plane. There are many axiomatic Möbius planes which are different from the classical one (see below). Similar to the minimal model of an affine plane is the "minimal model" of a Möbius plane. It consists of 5 {\displaystyle 5} points:
P := { A , B , C , D , ∞ } , Z := { z ∣ z ⊂ P , | z | = 3 } . {\displaystyle {\mathcal {P}}:=\{A,B,C,D,\infty \},\quad {\mathcal {Z}}:=\{z\mid z\subset {\mathcal {P}},|z|=3\}.} Hence: | Z | = ( 5 3 ) = 10. {\displaystyle |{\mathcal {Z}}|={5 \choose 3}=10.}
The connection between the classical Möbius plane and the real affine plane is similar to that between the minimal model of a Möbius plane and the minimal model of an affine plane. This strong connection is typical for Möbius planes and affine planes (see below).
For a Möbius plane M = ( P , Z , ∈ ) {\displaystyle {\mathfrak {M}}=({\mathcal {P}},{\mathcal {Z}},\in )} and P ∈ P {\displaystyle P\in {\mathcal {P}}} we define structure A P := ( P ∖ { P } , { z ∖ { P } ∣ P ∈ z ∈ Z } , ∈ ) {\displaystyle {\mathfrak {A}}_{P}:=({\mathcal {P}}\setminus \{P\},\{z\setminus \{P\}\mid P\in z\in {\mathcal {Z}}\},\in )} and call it the residue at point P .
For the classical model the residue A ∞ {\displaystyle {\mathfrak {A}}_{\infty }} at point ∞ {\displaystyle \infty } is the underlying real affine plane. The essential meaning of the residue shows the following theorem.
Theorem: Any residue of a Möbius plane is an affine plane.
This theorem allows to use the many results on affine planes for investigations on Möbius planes and gives rise to an equivalent definition of a Möbius plane:
Theorem: An incidence structure ( P , Z , ∈ ) {\displaystyle ({\mathcal {P}},{\mathcal {Z}},\in )} is a Möbius plane if and only if the following
property is fulfilled:
For finite Möbius planes, i.e. | P | < ∞ {\displaystyle |{\mathcal {P}}|<\infty } , we have (as with affine planes):
This justifies the following definition:
From combinatorics we get:
Looking for further examples of Möbius planes it seems promising to generalize the classical construction starting with a quadratic form ρ {\displaystyle \rho } on an affine plane over a field K {\displaystyle K} for defining circles. But, just to replace the real numbers R {\displaystyle \mathbb {R} } by any field K {\displaystyle K} and to keep the classical quadratic form x 2 + y 2 {\displaystyle x^{2}+y^{2}} for describing the circles does not work in general. For details one should look into the lecture note below. So, only for suitable pairs of fields and quadratic forms one gets Möbius planes M ( K , ρ ) {\displaystyle {\mathfrak {M}}(K,\rho )} . They are (as the classical model) characterized by huge homogeneity and the following theorem of Miquel.
Theorem (Miquel): For the Möbius plane M ( K , ρ ) {\displaystyle {\mathfrak {M}}(K,\rho )} the following is true: If for any 8 points P 1 , . . . , P 8 {\displaystyle P_{1},...,P_{8}} which can be assigned to the vertices
of a cube such that the points in 5 faces correspond to concyclical
quadruples, then the sixth quadruple of points is concyclical, too.
The converse is true, too.
Theorem (Chen): Only a Möbius plane M ( K , ρ ) {\displaystyle {\mathfrak {M}}(K,\rho )} satisfies the Theorem of Miquel.
Because of the last Theorem a Möbius plane M ( K , ρ ) {\displaystyle {\mathfrak {M}}(K,\rho )} is called a miquelian Möbius plane .
Remark: The minimal model of a Möbius plane is miquelian. It is isomorphic to the Möbius plane
Remark: If we choose K = C {\displaystyle K=\mathbb {C} } the field of complex numbers, there is no suitable quadratic form at all.
Remark: A stereographic projection shows: M ( K , ρ ) {\displaystyle {\mathfrak {M}}(K,\rho )} is isomorphic
to the geometry of the plane
Remark: A proof of Miquel's theorem for the classical (real) case can be found here . It is elementary and based on the theorem of an inscribed angle .
Remark: There are many Möbius planes which are not miquelian (see weblink below). The class which is most similar to miquelian Möbius planes are the ovoidal Möbius planes . An ovoidal Möbius plane is the geometry of the plane sections of an ovoid . An ovoid is a quadratic set and bears the same geometric properties as a sphere in a projective 3-space: 1) a line intersects an ovoid in none, one or two points and 2) at any point of the ovoid the set of the tangent lines form a plane, the tangent plane . A simple ovoid in real 3-space can be constructed by glueing together two suitable halves of different ellipsoids, such that the result is not a quadric. Even in the finite case there exist ovoids (see quadratic set ). Ovoidal Möbius planes are characterized by the bundle theorem .
A block design with the parameters of the one-point extension of a finite affine plane of order n {\displaystyle n} , i.e. a 3 {\displaystyle 3} - ( n 2 + 1 , n + 1 , 1 ) {\displaystyle (n^{2}+1,n+1,1)} -design, is a Möbius plane of order n {\displaystyle n} .
These finite block designs satisfy the axioms defining a Möbius plane, when a circle is interpreted as a block of the design.
The only known finite values for the order of a Möbius plane are prime or prime powers. The only known finite Möbius planes are constructed within finite projective geometries. | https://en.wikipedia.org/wiki/Möbius_plane |
In chemistry , the Möbius–Hückel treatment is a methodology used to predict whether a reaction is allowed or forbidden. It is often used along with the Woodward–Hoffmann approach. The description in this article uses the plus and minus sign notation for parity as shorthand while proceeding around a cycle of orbitals in a molecule or system, while the Woodward–Hoffmann methodology uses a large number of rules with the same consequences.
One year following the Woodward–Hoffmann [ 1 ] and Longuet-Higgins –Abrahmson [ 2 ] publications, it was noted by Zimmerman that both transition states and stable molecules sometimes involved a Möbius array of basis orbitals . [ 3 ] [ 4 ] The Möbius–Hückel treatment provides an alternative to the Woodward–Hoffmann one. In contrast to the Woodward–Hoffmann approach the Möbius–Hückel treatment is not dependent on symmetry and only requires counting the number of plus-sign ↔ minus-sign inversions in proceeding around the cyclic array of orbitals. Where one has zero or an even number of sign inversions there is a Hückel array. Where an odd-number of sign inversions is found a Möbius array is determined to be present. Thus the approach goes beyond the geometric consideration of Edgar Heilbronner. In any case, symmetry may be present or may not.
Edgar Heilbronner had described twisted annulenes which had Möbius topology, but in including the twist of these systems, he concluded that Möbius systems could never be lower in energy than the Hückel counterparts. [ 5 ] In contrast, the Möbius–Hückel concept considers systems with an equal twist for Hückel and Möbius systems.
For Möbius systems there is an odd number of plus–minus sign inversions in the basis set in proceeding around the cycle. A circle mnemonic [ 3 ] was advanced which provides the MO energies of the system; this was the counterpart of the Frost–Musulin mnemonic [ 6 ] for ordinary Hückel systems. It was concluded that 4 n electrons is the preferred number for Möbius moieties in contrast to the common 4 n + 2 electrons for Hückel systems.
To determine the energy levels, the polygon corresponding to the cyclic annulene is desired is inscribed in the circle of radius 2 β and centered at α (the energy of an isolated p orbital). The y- coordinate of the vertices of the polygon are the simple Hückel theory orbital energies. For systems with Hückel topology, the vertex is positioned at the circle bottom as suggested by Frost; for systems with Möbius topology, a polygon side is positioned at the circle bottom. In other words, for an N carbon system, the Möbius Frost circle is rotated by π/ N radians compared to the Hückel system. It is seen that with one MO at the bottom and then groups of degenerate pairs, the Hückel systems will accommodate 4 n + 2 electrons, following the ordinary Hückel rule. However, in contrast, the Möbius Systems have degenerate pairs of molecular orbitals starting at the circle bottom and thus will accommodate 4 n electrons. For cyclic annulenes one then predicts which species will be favored. The method applies equally to cyclic reaction intermediates and transition states for pericyclic processes.
Thus it was noted that along the reaction coordinate of pericyclic processes one could have either a Möbius or a Hückel array of basis orbitals. With 4 n or 4 n + 2 electrons, one is then led to a prediction of allowedness or forbiddenness. Additionally, the M–H mnemonics give the MOs at part reaction. At each degeneracy there is a crossing of MOs. Thus one can determine if the highest occupied MO becomes antibonding with a forbidden reaction resulting. Finally, the M–H parity of sign inversions was utilized in the 1970 W–H treatment of allowedness and forbiddenness. The parity of sign inversions between bonds and atoms was used in place of the M–H use of atoms; the two approaches are equivalent. [ 7 ]
The table in Figure 2 summarizes the Möbius–Hückel concept. The columns specify whether one has a Möbius or a Hückel structure and the rows specify whether 4 n + 2 electrons or 4 n electrons are present. Depending on which is present, a Möbius or a Hückel system, one selects the first or the second column. Then depending on the number of electrons present, 4 n + 2 or 4 n , one selects the first or the second row. [ 7 ]
The two orbital arrays in Figure 3 are just examples and do not correspond to real systems. In inspecting the Möbius one on the left, plus–minus overlaps are seen between orbital pairs 2-3, 3-4, 4-5, 5-6, and 6-1, corresponding to an odd number (5), as required by a Möbius system. Inspection of the Hückel one on the right, plus–minus overlaps are seen between orbital pairs 2-3, 3-4, 4-5, and 6-1, corresponding to an even number (4), as required by a Hückel system.
The plus–minus orientation of each orbital is arbitrary since these are just basis set orbitals and do not correspond to any molecular orbital. If any orbital were to change signs, two plus–minus overlaps are either removed or added and the parity (evenness or oddness) is not changed. One choice of signs leads to zero plus–minus overlaps for the Hückel array on the right.
Figure 4 shows the orbital array involved in the butadiene to cyclobutene interconversion. It is seen that there are four orbitals in this cyclic array. Thus in the interconversion reactions orbitals 1 and 4 overlap either in a conrotatory or a disrotatory fashion. Also, it is seen that the conrotation involves one plus–minus overlap as drawn while the disrotation involves zero plus–minus overlaps as drawn. Thus the conrotation uses a Möbius array while the disrotation uses a Hückel array. [ 3 ]
But it is important to note, as described for the generalized orbital array in Figure 3, that the assignment of the basis-set p-orbitals is arbitrary. Were one p-orbital in either reaction mode to be written upside-down, this would change the number of sign inversions by two and not change the evenness or oddness of the orbital array.
With a conrotation giving a Möbius system, with butadiene's four electrons, we find an "allowed" reaction model. With disrotation giving a Hückel system, with the four electrons, we find a "forbidden" reaction model.
Although in these two examples symmetry is present, symmetry is not required or involved in determination of reaction allowedness versus forbiddenness. Hence a very large number of organic reactions can be understood. Even where symmetry is present, the Möbius–Hückel analysis proves simple to employ.
It has been noted that for every degeneracy along a reaction coordinate there is a molecular orbital crossing. [ 4 ] Thus for the butadiene to cyclobutene conversion, the two Möbius (here conrotatory) and Hückel (here disrotatory) modes are shown in Figure 5. The starting MOs are depicted in the center of the correlation diagram with blue correlation lines connecting MOs. It is seen that for the Möbius mode the four electrons in MOs 1 and 2 end in the bonding MOs (i.e. σ and π) of cyclobutene. In contrast, for the Hückel mode, there is a degeneracy and thus an MO crossing leading to two electrons (drawn in red) are headed for an antibonding MO. Thus the Hückel mode is forbidden while the Möbius mode is allowed.
One further relevant point is that the first organic correlation diagrams were in a 1961 publication on carbanion rearrangements. [ 8 ] It had been noted that when an occupied molecular orbital becomes antibonding the reaction is inhibited and this phenomenon was correlated with a series of rearrangements.
Until 1969 there was no obvious relationship except that the two methods lead to the same predictions. As noted earlier, the Woodward–Hoffmann method requires symmetry. But in 1969 and 1970 a general formulation was published, [ 9 ] [ 10 ] namely, A ground-state pericyclic change is symmetry-allowed when the total number of (4 q + 2) s and (4 r ) a components is odd. The 1969–1970 Woodward–Hoffmann general formulation is seen to be equivalent to the Zimmerman Möbius–Hückel concept. Thus each (4 r ) a component provides one plus–minus overlap in the cyclic array (i.e. an odd number) for 4 n electrons. The (4 q + 2) s component just makes certain that the number of electrons in symmetric bonds is 4 n + 2.
The equivalency of the more recent formulation of the Woodward–Hoffmann rules has been discussed. [ 11 ] | https://en.wikipedia.org/wiki/Möbius–Hückel_concept |
The Mössbauer effect , or recoilless nuclear resonance fluorescence , is a physical phenomenon discovered by Rudolf Mössbauer in 1958. It involves the resonant and recoil -free emission and absorption of gamma radiation by atomic nuclei bound in a solid. Its main application is in Mössbauer spectroscopy .
In the Mössbauer effect, a narrow resonance for nuclear gamma emission and absorption results from the momentum of recoil being delivered to a surrounding crystal lattice rather than to the emitting or absorbing nucleus alone. When this occurs, no gamma energy is lost to the kinetic energy of recoiling nuclei at either the emitting or absorbing end of a gamma transition: emission and absorption occur at the same energy, resulting in strong, resonant absorption.
The emission and absorption of X-rays by gases had been observed previously. It was expected that a similar phenomenon would be found for gamma rays , which are created by nuclear transitions (as opposed to X-rays, which are typically produced by electronic transitions ). However, attempts to observe nuclear resonance produced by gamma rays in gases failed due to energy being lost to recoil, preventing resonance (the Doppler effect also broadens the gamma-ray spectrum). Mössbauer observed resonance in nuclei of solid iridium , which raised the question of why gamma-ray resonance was possible in solids but not in gases. Mössbauer proposed that, for the case of atoms bound into a solid, a fraction of the nuclear events could occur essentially without recoil under certain circumstances. He attributed the observed resonance to this recoil-free fraction of nuclear events.
The Mössbauer effect was one of the last major discoveries in physics to be originally reported in the German language. The first reports in English were a pair of letters describing independent repetitions of the experiment. [ 1 ] [ 2 ]
The discovery was rewarded with the Nobel Prize in Physics in 1961, together with Robert Hofstadter 's research of electron scattering in atomic nuclei.
In general, gamma rays are produced by nuclear transitions from an unstable high-energy state to a stable low-energy state. The energy of the emitted gamma ray corresponds to the energy of the nuclear transition, minus an amount of energy that is lost as recoil to the emitting atom. If the lost recoil energy is small compared with the energy linewidth of the nuclear transition, then the gamma-ray energy still corresponds to the energy of the nuclear transition and the gamma ray can be absorbed by a second atom of the same type as the first. This emission and subsequent absorption is called resonant fluorescence . Additional recoil energy is also lost during absorption, so in order for resonance to occur, the recoil energy must actually be less than half the linewidth for the corresponding nuclear transition.
The amount of energy in the recoiling body ( E R ) can be found from momentum conservation:
where P R is the momentum of the recoiling matter, and P γ the momentum of the gamma ray. Substituting energy into the equation gives:
where E R ( 0.002 eV for 57 Fe ) is the energy lost as recoil, E γ is the energy of the gamma ray ( 14.4 keV for 57 Fe ), M ( 56.9354 u for 57 Fe ) is the mass of the emitting or absorbing body, and c is the speed of light . [ 3 ] In the case of a gas, the emitting and absorbing bodies are atoms, so the mass is relatively small, resulting in a large recoil energy, which prevents resonance. (The same equation applies for recoil energy losses in X-rays, but the photon energy is much less, resulting in a lower energy loss, which is why gas-phase resonance could be observed with X-rays.)
In a solid, the nuclei are bound to the lattice and do not recoil as in a gas. The lattice as a whole recoils, but the recoil energy is negligible because the M in the above equation is the mass of the entire lattice. However, the energy in a decay can be taken up or supplied by lattice vibrations. The energy of these vibrations is quantised in units known as phonons . The Mössbauer effect occurs because there is a finite probability of a decay involving no phonons. Thus in a fraction of the nuclear events (the recoil-free fraction , given by the Lamb–Mössbauer factor ), the entire crystal acts as the recoiling body, and these events are essentially recoil-free. In these cases, since the recoil energy is negligible, the emitted gamma rays have the appropriate energy and resonance can occur.
In general (depending on the half-life of the decay), gamma rays have very narrow line widths. This means they are very sensitive to small changes in the energies of nuclear transitions. In fact, gamma rays can be used as a probe to observe the effects of interactions between a nucleus and its electrons and those of its neighbors. This is the basis for Mössbauer spectroscopy, which combines the Mössbauer effect with the Doppler effect to monitor such interactions.
Zero-phonon optical transitions , a process closely analogous to the Mössbauer effect, can be observed in lattice-bound chromophores at low temperatures. | https://en.wikipedia.org/wiki/Mössbauer_effect |
Møller–Plesset perturbation theory ( MP ) is one of several quantum chemistry post-Hartree–Fock ab initio methods in the field of computational chemistry . It improves on the Hartree–Fock method by adding electron correlation effects by means of Rayleigh–Schrödinger perturbation theory (RS-PT), usually to second (MP2), third (MP3) or fourth (MP4) order. Its main idea was published as early as 1934 by Christian Møller and Milton S. Plesset . [ 1 ]
The MP perturbation theory is a special case of RS perturbation theory. In RS theory one considers an unperturbed Hamiltonian operator H ^ 0 {\displaystyle {\hat {H}}_{0}} , to which a small (often external) perturbation V ^ {\displaystyle {\hat {V}}} is added:
Here, λ is an arbitrary real parameter that controls the size of the perturbation. In MP theory the zeroth-order wave function is an exact eigenfunction of the Fock operator , which thus serves as the unperturbed operator. The perturbation is the correlation potential.
In RS-PT the perturbed wave function and perturbed energy are expressed as a power series in λ:
Substitution of these series into the time-independent Schrödinger equation gives a new equation as m → ∞ {\displaystyle m\to \infty } :
Equating the factors of λ k {\displaystyle \lambda ^{k}} in this equation gives a k th-order perturbation equation, where k = 0, 1, 2, ..., m . See perturbation theory for more details.
The MP-energy corrections are obtained from Rayleigh–Schrödinger (RS) perturbation theory with the unperturbed Hamiltonian defined as the shifted Fock operator ,
and the perturbation defined as the correlation potential ,
where the normalized Slater determinant Φ 0 is the lowest eigenstate of the Fock operator:
Here N is the number of electrons in the molecule under consideration (a factor of 2 in the energy arises from the fact that each orbital is occupied by a pair of electrons with opposite spin), H ^ {\displaystyle {\hat {H}}} is the usual electronic Hamiltonian , f ^ ( k ) {\displaystyle {\hat {f}}(k)} is the one-electron Fock operator, and ε i is the orbital energy belonging to the doubly occupied spatial orbital φ i .
Since the Slater determinant Φ 0 is an eigenstate of F ^ {\displaystyle {\hat {F}}} , it follows readily that
i.e. the zeroth-order energy is the expectation value of H ^ {\displaystyle {\hat {H}}} with respect to Φ 0 , the Hartree-Fock energy. Similarly, it can be seen that in this formulation the MP1 energy
Hence, the first meaningful correction appears at MP2 energy.
In order to obtain the MP2 formula for a closed-shell molecule, the second order RS-PT formula is written in a basis of doubly excited Slater determinants. (Singly excited Slater determinants do not contribute because of the Brillouin theorem ). After application of the Slater–Condon rules for the simplification of N -electron matrix elements with Slater determinants in bra and ket and integrating out spin, it becomes
where 𝜑 i and 𝜑 j are canonical occupied orbitals and 𝜑 a and 𝜑 b are virtual (or unoccupied) orbitals. The quantities ε i , ε j , ε a , and ε b are the corresponding orbital energies. Clearly, through second-order in the correlation potential, the total electronic energy is given by the Hartree–Fock energy plus second-order MP correction: E ≈ E HF + E MP2 . The solution of the zeroth-order MP equation (which by definition is the Hartree–Fock equation) gives the Hartree–Fock energy. The first non-vanishing perturbation correction beyond the Hartree–Fock treatment is the second-order energy.
Equivalent expressions are obtained by a slightly different partitioning of the Hamiltonian, which results in a different division of energy terms over zeroth- and first-order contributions, while for second- and higher-order energy corrections the two partitionings give identical results. The formulation is commonly used by chemists, who are now large users of these methods. [ 2 ] This difference is due to the fact, well known in Hartree–Fock theory, that
(The Hartree–Fock energy is not equal to the sum of occupied-orbital energies). In the alternative partitioning, one defines
Clearly, in this partitioning,
Obviously, with this alternative formulation, the Møller–Plesset theorem does not hold in the literal sense that E MP1 ≠ 0. The solution of the zeroth-order MP equation is the sum of orbital energies. The zeroth plus first-order correction yields the Hartree–Fock energy. As with the original formulation, the first non-vanishing perturbation correction beyond the Hartree–Fock treatment is the second-order energy. To reiterate, the second- and higher-order corrections are the same in both formulations.
Second (MP2), [ 3 ] third (MP3), [ 4 ] [ 5 ] and fourth (MP4) [ 6 ] order Møller–Plesset calculations are standard levels used in calculating small systems and are implemented in many computational chemistry codes. Higher level MP calculations, generally only MP5, [ 7 ] are possible in some codes. However, they are rarely used because of their cost.
Systematic studies of MP perturbation theory have shown that it is not necessarily a convergent theory at high orders. Convergence can be slow, rapid, oscillatory, regular, highly erratic or simply non-existent, depending on the precise chemical system or basis set. [ 8 ] The density matrix for the first-order and higher MP2 wavefunction is of the
type known as response density , which differs from the
more usual expectation value density . [ 9 ] [ 10 ] The eigenvalues of
the response density matrix (which are the occupation numbers of the MP2 natural orbitals) can therefore be greater than 2 or negative. Unphysical numbers are a sign of a divergent perturbation expansion. [ 11 ]
Additionally, various important molecular properties calculated at MP3 and MP4 level are no better than their MP2 counterparts, even for small molecules. [ 12 ]
For open shell molecules, MPn-theory can directly be applied only to unrestricted Hartree–Fock reference functions (since UHF states are not in general eigenvectors of the Fock operator). However, the resulting energies often suffer from severe spin contamination , leading to large errors. A possible better alternative is to use one of the MP2-like methods based on restricted open-shell Hartree–Fock (ROHF). There are many ROHF based MP2-like methods because of arbitrariness in the ROHF wavefunction [ 13 ] [ 14 ] (for example HCPT, [ 15 ] ROMP, [ 16 ] RMP [ 17 ] (also called ROHF-MBPT2 [ 18 ] ), OPT1 and OPT2, [ 19 ] ZAPT, [ 20 ] IOPT, [ 21 ] etc. [ 22 ] [ 23 ] ). Some of the ROHF based MP2-like theories suffer from spin-contamination in their perturbed density and energies beyond second-order. [ 24 ]
These methods, Hartree–Fock, unrestricted Hartree–Fock and restricted Hartree–Fock use a single determinant wave function. Multi-configurational self-consistent field (MCSCF) methods use several determinants and can be used for the unperturbed operator, although not uniquely, so many methods, such as complete active space perturbation theory (CASPT2), [ 25 ] and Multi-Configuration Quasi-Degenerate Perturbation
Theory (MCQDPT), [ 26 ] [ 27 ] have been developed. [ 28 ] MCSCF based methods are not without perturbation series divergences. [ 29 ]
The analogue to what MP pertubation theory is in HF theory is Görling-Levy (GL) pertubation theory in Kohn-Sham (KS) density functional theory (DFT) . | https://en.wikipedia.org/wiki/Møller–Plesset_perturbation_theory |
In quantum computing , Mølmer–Sørensen gate scheme (or MS gate ) refers to an implementation procedure for various multi- qubit quantum logic gates used mostly in trapped ion quantum computing . This procedure is based on the original proposition by Klaus Mølmer and Anders Sørensen in 1999–2000. [ 1 ] [ 2 ] [ 3 ]
This proposal was an alternative to the 1995 Cirac–Zoller controlled-NOT gate implementation for trapped ions, which requires that the system be restricted to the joint motional ground state of the ions. [ 4 ]
In an MS gate, entangled states are prepared by illuminating ions with a bichromatic light field. Mølmer and Sørensen identified two regimes in which this is possible:
In both regimes, a red and blue sideband interaction are applied simultaneously to each ion, with the red and blue tones symmetrically detuned by δ ′ {\displaystyle \delta '} from the sidebands. This results in laser detunings ± ( ω k + δ ′ ) {\displaystyle \pm (\omega _{k}+\delta ')} , where ω k {\displaystyle \omega _{k}} is the motional mode frequency.
When an MS gate is applied globally to all ions in a chain, multipartite entanglement is created, with the form of the gate being a sum of local XX (or YY, or XY depending on experimental parameters) interactions applied to all qubit pairs. When the gate is performed on a single pair of ions, it reduces to the R XX gate . Thus, the CNOT gate can be decomposed into an MS gate and combination of single particle rotations.
Trapped ions were identified by Ignacio Cirac and Peter Zoller at the University of Innsbruck , Austria in 1995, as the first realistic system with which to implement a quantum computer, in a proposal which included a procedure for implementing a CNOT gate by coupling ions through their collective motion. [ 4 ] A major drawback of Cirac and Zoller's scheme was that it required the trapped ion system to be restricted to its joint motional ground state, which is difficult to achieve experimentally. The Cirac-Zoller CNOT gate was not experimentally demonstrated with two ions until 8 years later, in 2003, with a fidelity of 70-80%. [ 5 ] Around 1998, there was a collective effort to develop two-qubit gates independent of the motional state of individual ions, [ 6 ] [ 1 ] [ 7 ] one of which was the scheme proposed by Klaus Mølmer and Anders Sørensen in Aarhus University , Denmark.
In 1999, Mølmer and Sørensen proposed a native multi-qubit trapped ion gate as an alternative to Cirac and Zoller's scheme, insensitive to the vibrational state of the system and robust against changes in the vibrational number during gate operation. [ 1 ] [ 2 ] Mølmer and Sørensen's scheme requires only that the ions be in the Lamb-Dicke regime , and it produces an Ising-like interaction Hamiltonian using a bichromatic laser field.
Following Mølmer and Sørensen's 1999 papers, Gerard J. Milburn proposed a 2-qubit gate that makes use of a stroboscopic Hamiltonian in order to couple internal state operators to different quadrature components. [ 8 ] Soon after, in 2000, Mølmer and Sørensen published a third article [ 3 ] illustrating that their 1999 scheme was already a realization of Milburn's, just with a harmonic rather than stroboscopic application of the Hamiltonian coupling terms.
Mølmer and Sørensen's 2000 article also takes a more general approach to the gate scheme compared to the 1999 proposal. In the 1999 papers, only the "slow gate" regime is considered, in which a large detuning from resonance is required to avoid off-resonant coupling to unwanted phonon modes. In 2000, Mølmer and Sørensen remove this restriction and show how to remove phonon number dependence in the "fast gate" regime, where lasers are tuned close to the sidebands.
The first experimental demonstration of the MS gate was performed in 2000 by David J. Wineland 's group at the National Institute of Standards and Technology (NIST), with fidelities of F = .83 for 2 ions and F =.57 for 4 ions. [ 9 ] In 2003, Wineland's group produced better results by using a geometric phase gate, [ 10 ] which is a specific case of the more general formalism put forward by Mølmer, Sørensen, Milburn, and Xiaoguang Wang. Today, the MS gate is widely used and accepted as the standard by trapped ion groups (and companies), [ 11 ] [ 12 ] and optimizing and generalizing MS gates is currently an active field in the trapped ion community. [ 13 ] [ 14 ] [ 15 ] [ 16 ] MS-like gates have also been developed for other quantum computing platforms. [ 17 ]
To implement the scheme, two ions are irradiated with a bichromatic laser field with frequencies ω e g ± δ {\displaystyle \omega _{eg}\pm \delta } , where ℏ ω e g {\displaystyle \hbar \omega _{eg}} is the energy splitting of the qubit states and δ = ω k + δ ′ {\displaystyle \delta =\omega _{k}+\delta '} is a detuning close to the motional frequency ω k {\displaystyle \omega _{k}} of the ions. Depending on the interaction time, this produces the states [ 18 ]
∣ e e ⟩ → ( | e e ⟩ + i | g g ⟩ ) / 2 ∣ e g ⟩ → ( | e g ⟩ − i | g e ⟩ ) / 2 ∣ g e ⟩ → ( | g e ⟩ − i | e g ⟩ ) / 2 ∣ g g ⟩ → ( | g g ⟩ + i | e e ⟩ ) / 2 {\displaystyle {\begin{aligned}\mid ee\rangle \rightarrow (|ee\rangle +i|gg\rangle )/{\sqrt {2}}\\\mid eg\rangle \rightarrow (|eg\rangle -i|ge\rangle )/{\sqrt {2}}\\\mid ge\rangle \rightarrow (|ge\rangle -i|eg\rangle )/{\sqrt {2}}\\\mid gg\rangle \rightarrow (|gg\rangle +i|ee\rangle )/{\sqrt {2}}\end{aligned}}}
The above is equivalent to the Ising coupling gate R yy (π/2) ; It can then be shown that this gate (along with arbitrary single-qubit rotation) produces a universal set of gates.
An alternative definition of MS gate equates it to R xx (π/2) , and is adopted as IonQ 's native gate for two-qubit entanglement. [ 19 ] In this definition, CNOT gate can be decomposed as
The Mølmer–Sørensen gate implementation has the advantage that it does not fail if the ions were not cooled completely to the ground state , and it does not require the ions to be individually addressed. [ 20 ] However, this thermal insensitivity is only valid in the Lamb–Dicke regime , so most implementations first cool the ions to the motional ground state. [ 21 ] An experiment was done by P.C. Haljan, K. A. Brickman, L. Deslauriers, P.J. Lee, and C. Monroe where this gate was used to produce all four Bell states and to implement Grover's algorithm successfully. [ 22 ]
The relevant Hamiltonian for a single trapped ion consists of the interaction between a spin-1/2 system, a harmonic oscillator trapping potential, and an external laser radiation field: [ 23 ]
H = H 0 + H I = ( H s p i n + H H O ) + H f i e l d = − ℏ ω g e 2 σ z + ℏ ω 0 ( a † a + 1 2 ) − μ e → ⋅ E → . {\displaystyle {\begin{aligned}H&=H_{0}+H_{I}\\&=(H_{\rm {spin}}+H_{\rm {HO}})+H_{\rm {field}}\\&=-\hbar {\frac {\omega _{ge}}{2}}\sigma _{z}+\hbar \omega _{0}(a^{\dagger }a+{\frac {1}{2}})-{\vec {\mu _{e}}}\cdot {\vec {E}}.\end{aligned}}}
Here, ω g e {\displaystyle \omega _{ge}} is the energy splitting between qubit states | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } , a † {\displaystyle a^{\dagger }} and a {\displaystyle a} are the creation and annihilation operators of phonons in the ions' collective motional mode, ℏ ω 0 {\displaystyle \hbar \omega _{0}} is the energy of those phonons, and σ z {\displaystyle \sigma _{z}} is the Pauli Z matrix .
The third term, the interaction Hamiltonian, can be written
H I = − μ E → ⋅ E → = Ω σ x cos ( k z − ω L t + ϕ ) = Ω 2 ( σ + + σ − ) ( e i ( η ( a + a † ) − ω L t + ϕ ) + e − i ( η ( a + a † ) − ω L t + ϕ ) ) {\displaystyle {\begin{aligned}H_{I}&=-{\vec {\mu _{E}}}\cdot {\vec {E}}\\&=\Omega \sigma _{x}\cos(kz-\omega _{L}t+\phi )\\&={\frac {\Omega }{2}}(\sigma _{+}+\sigma _{-})(e^{i(\eta (a+a^{\dagger })-\omega _{L}t+\phi )}+e^{-i(\eta (a+a^{\dagger })-\omega _{L}t+\phi )})\\\end{aligned}}}
for an x − {\displaystyle x-} polarized laser propagating along z {\displaystyle z} . Here, we have defined the Rabi frequency Ω = − μ E E {\displaystyle \Omega =-\mu _{E}E} (dimensions of energy), as well as the operator for center-of-mass motion in the z {\displaystyle z} -direction z = z 0 ( a + a † ) {\displaystyle z=z_{0}(a+a^{\dagger })} . Here, z 0 = ( ℏ / 2 m ω z ) 1 / 2 {\displaystyle z_{0}=(\hbar /2m\omega _{z})^{1/2}} is the spread of the zero-point wavefunction, m {\displaystyle m} is the ion mass, and the Lamb-Dicke parameter η = k z 0 {\displaystyle \eta =kz_{0}} parameterizes the size of the ground state wavepacket compared to radiation wavelength λ = 2 π k {\displaystyle \lambda =2\pi k} .
Now we will move into the interaction picture with respect to H H O {\displaystyle H_{\rm {HO}}} and H s p i n {\displaystyle H_{\rm {spin}}} and make a rotating wave approximation to get
H I = Ω 2 σ − e − i ( η ( a e − i ω 0 t + a † e i ω 0 t ) − δ t ) + h . c . {\displaystyle H_{I}={\frac {\Omega }{2}}\sigma _{-}e^{-i(\eta (ae^{-i\omega _{0}t}+a^{\dagger }e^{i\omega _{0}t})-\delta t)}+h.c.}
where we have detuned the laser by δ {\displaystyle \delta } from the qubit frequency ω g e {\displaystyle \omega _{ge}} and absorbed the phase into the Rabi frequency Ω → Ω e i Δ ϕ {\displaystyle \Omega \rightarrow \Omega e^{i\Delta \phi }} .
Within the Lamb-Dicke regime, we can make the approximation
e − i η ( e i ω 0 t a † + e − i ω 0 t a ) ≈ 1 − i η ( e i ω 0 t a † + e − i ω 0 t a ) {\displaystyle e^{-i\eta (e^{i\omega _{0}t}a^{\dagger }+e^{-i\omega _{0}t}a)}\approx 1-i\eta (e^{i\omega _{0}t}a^{\dagger }+e^{-i\omega _{0}t}a)}
which splits the Hamiltonian into three parts corresponding to a carrier transition, red sideband (RSB) transition, and blue sideband (BSB) transition:
H I = Ω 2 σ − ( e i δ t − i η e i ( δ + ω 0 ) t a † − i η e i ( δ − ω 0 ) t a ) + h . c . {\displaystyle H_{I}={\frac {\Omega }{2}}\sigma _{-}(e^{i\delta t}-i\eta e^{i(\delta +\omega _{0})t}a^{\dagger }-i\eta e^{i(\delta -\omega _{0})t}a)+h.c.}
By making a second rotating wave approximation to neglect oscillation terms, each piece can be examined independently. For δ = 0 {\displaystyle \delta =0} , only the first term is kept, and the Hamiltonian becomes H c a r r i e r = Ω 2 ( σ − + σ + ) , {\displaystyle H_{\rm {carrier}}={\frac {\Omega }{2}}(\sigma _{-}+\sigma _{+}),} which alters the spin state of the ion without affecting its motional state. For δ = − ω 0 {\displaystyle \delta =-\omega _{0}} , only the second term is kept since | δ + ω 0 | ≪ | δ | , | δ − ω 0 | {\displaystyle |\delta +\omega _{0}|\ll |\delta |,|\delta -\omega _{0}|} . Then the red sideband (RSB) Hamiltonian is
H R S B = − i η Ω 2 ( a † σ − ) e i ( δ + ω 0 ) t + h . c . {\displaystyle H_{\rm {RSB}}=-i\eta {\frac {\Omega }{2}}(a^{\dagger }\sigma _{-})e^{i(\delta +\omega _{0})t}+h.c.}
The RSB transition can be thought of as an `exchange' of motion for spin. For an ion with phonon occupation number n {\displaystyle n} , an RSB π {\displaystyle \pi } -pulse will take | g , n ⟩ → | e , n − 1 ⟩ {\displaystyle |g,n\rangle \rightarrow |e,n-1\rangle } with oscillation frequency Ω R S B = η Ω n {\displaystyle \Omega _{\rm {RSB}}=\eta \Omega {\sqrt {n}}} .
For δ = ω 0 {\displaystyle \delta =\omega _{0}} , only the third term is kept since | δ − ω 0 | ≪ | δ | , | δ + ω 0 | {\displaystyle |\delta -\omega _{0}|\ll |\delta |,|\delta +\omega _{0}|} . Then the blue sideband (BSB) Hamiltonian is
H B S B = − i η Ω 2 ( a σ − ) e i ( δ − ω 0 ) t + h . c . {\displaystyle H_{\rm {BSB}}=-i\eta {\frac {\Omega }{2}}(a\sigma _{-})e^{i(\delta -\omega _{0})t}+h.c.}
which is also a spin-motion exchange. For an ion with phonon occupation number n {\displaystyle n} , a BSB π {\displaystyle \pi } -pulse will take | g , n ⟩ → | e , n + 1 ⟩ {\displaystyle |g,n\rangle \rightarrow |e,n+1\rangle } with oscillation frequency Ω B S B = η Ω n + 1 {\displaystyle \Omega _{\rm {BSB}}=\eta \Omega {\sqrt {n+1}}} .
The MS Hamiltonian is the application of simultaneous, symmetrically detuned red and blue sideband tones over j {\displaystyle j} ions. Written in the interaction picture with respect to H s p i n {\displaystyle H_{\rm {spin}}} ,
H M S = ∑ j H H O + H c a r r i e r + H R S B + H B S B {\displaystyle H_{\rm {MS}}=\sum _{j}H_{\rm {HO}}+H_{\rm {carrier}}+H_{\rm {RSB}}+H_{\rm {BSB}}}
where the single-ion Hamiltonians (in the rotating-wave approximation with respect to H H O {\displaystyle H_{\rm {HO}}} and counter-rotating terms) are given by
H c a r r i e r = ( Ω R 2 e i δ R t + Ω B 2 e i δ B t ) σ − + h . c . H R S B = i η Ω R 2 σ − a † e i δ R t + h . c . H B S B = i η Ω B 2 σ − a e i δ B t + h . c . {\displaystyle {\begin{aligned}H_{\rm {carrier}}&=\left({\frac {\Omega _{R}}{2}}e^{i\delta _{R}t}+{\frac {\Omega _{B}}{2}}e^{i\delta _{B}t}\right)\sigma _{-}+h.c.\\H_{\rm {RSB}}&=i\eta {\frac {\Omega _{R}}{2}}\sigma _{-}a^{\dagger }e^{i\delta _{R}t}+h.c.\\H_{\rm {BSB}}&=i\eta {\frac {\Omega _{B}}{2}}\sigma _{-}ae^{i\delta _{B}t}+h.c.\end{aligned}}}
The red and blue tones have the effective Rabi frequencies Ω R = Ω e i ϕ R {\displaystyle \Omega _{R}=\Omega e^{i\phi _{R}}} and Ω B = Ω e i ϕ B {\displaystyle \Omega _{B}=\Omega e^{i\phi _{B}}} , respectively.
To be thorough, we will also sum over all k {\displaystyle k} motional modes ( N {\displaystyle N} ions × {\displaystyle \times } d {\displaystyle d} motional dimensions), each with eigenvector b k {\displaystyle b^{k}} and eigenfrequency ω k {\displaystyle \omega _{k}} . The red and blue tones are symmetrically detuned by δ ′ {\displaystyle \delta '} from the sidebands, results in laser detunings ± ( ω k + δ ′ ) {\displaystyle \pm (\omega _{k}+\delta ')} . We also assume that the tones are detuned near a motional mode which is far from the carrier such that the RWA is invoked to drop H c a r r i e r {\displaystyle H_{\rm {carrier}}} .
We define μ ≡ δ B = − δ R {\displaystyle \mu \equiv \delta _{B}=-\delta _{R}} and write the detuning from each motional mode as μ k = μ − δ ′ {\displaystyle \mu _{k}=\mu -\delta '} .
Under the preceding assumptions, the MS interaction Hamiltonian (with respect to H H O {\displaystyle H_{\rm {HO}}} ) becomes
H i n t = i ∑ j , k η j , k Ω j 2 σ − , j [ a k e − i ( μ k t − ϕ R ) + a k † e i ( μ k t + ϕ B ) ] + h . c . {\displaystyle H_{\rm {int}}=i\sum _{j,k}\eta _{j,k}{\frac {\Omega _{j}}{2}}\sigma _{-,j}[a_{k}e^{-i(\mu _{k}t-\phi _{R})}+a_{k}^{\dagger }e^{i(\mu _{k}t+\phi _{B})}]+h.c.}
where η j , k = Δ k ℏ / ( 2 M ω k ) b j k {\displaystyle \eta _{j,k}=\Delta k{\sqrt {\hbar /(2M\omega _{k})}}b_{j}^{k}} . Now we define spin and motional phases
ϕ s ≡ ϕ B + ϕ R 2 , ϕ m ≡ ϕ B − ϕ R 2 {\displaystyle \phi _{s}\equiv {\frac {\phi _{B}+\phi _{R}}{2}}{\text{ }},{\text{ }}\phi _{m}\equiv {\frac {\phi _{B}-\phi _{R}}{2}}}
such that the Hamiltonian can be separated into its spin and motional components:
H i n t = i ∑ j , k η j , k Ω j 2 [ e i ( μ k t + ϕ B ) σ − , j a k − e − ( μ k t + ϕ B ) σ + , j a k † + e − i ( μ k t + ϕ R ) σ − , j a k † − e i ( μ k t − ϕ R ) σ + , j a k ] = i ∑ j , k η j , k Ω j 2 [ ( σ − , j e i ϕ s − σ + , j e − i ϕ s ) ( a k e i μ k t e i ϕ m + a k † e − i μ k t e − i ϕ m ) ] ≡ i ∑ j , k η j , k Ω j 2 [ σ ^ j ⊗ A ^ k ( t ) ] {\displaystyle {\begin{aligned}H_{\rm {int}}&=i\sum _{j,k}\eta _{j,k}{\frac {\Omega _{j}}{2}}[e^{i(\mu _{k}t+\phi _{B})}\sigma _{-,j}a_{k}-e^{-(\mu _{k}t+\phi _{B})}\sigma _{+,j}a_{k}^{\dagger }+e^{-i(\mu _{k}t+\phi _{R})}\sigma _{-,j}a_{k}^{\dagger }-e^{i(\mu _{k}t-\phi _{R})}\sigma _{+,j}a_{k}]\\&=i\sum _{j,k}\eta _{j,k}{\frac {\Omega _{j}}{2}}[(\sigma _{-,j}e^{i\phi _{s}}-\sigma _{+,j}e^{-i\phi _{s}})(a_{k}e^{i\mu _{k}t}e^{i\phi _{m}}+a_{k}^{\dagger }e^{-i\mu _{k}t}e^{-i\phi _{m}})]\\&\equiv i\sum _{j,k}\eta _{j,k}{\frac {\Omega _{j}}{2}}[{\hat {\sigma }}_{j}\otimes {\hat {A}}_{k}(t)]\end{aligned}}}
where we have now defined the spin operator σ ^ j {\displaystyle {\hat {\sigma }}_{j}} and displacement operator A ^ k ( t ) {\displaystyle {\hat {A}}_{k}(t)} .
The time evolution operator is obtained through the Magnus expansion
U ( t ) = e ∑ l = 1 ∞ M l ( t ) {\displaystyle U(t)=e^{\sum _{l=1}^{\infty }M_{l}(t)}}
where the first two M l ( t ) {\displaystyle M_{l}(t)} are
M 1 ( t ) = − i ℏ ∫ 0 t H i n t ( t 1 ) d t 1 M 2 ( t ) = 1 2 ( − i ℏ ) 2 ∫ 0 t ∫ 0 t 1 [ H i n t ( t 1 ) , H i n t ( t 2 ) ] d t 2 d t 1 {\displaystyle {\begin{aligned}M_{1}(t)&=-{\frac {i}{\hbar }}\int _{0}^{t}H_{\rm {int}}(t_{1})dt_{1}\\M_{2}(t)&={\frac {1}{2}}(-{\frac {i}{\hbar }})^{2}\int _{0}^{t}\int _{0}^{t_{1}}[H_{\rm {int}}(t_{1}),H_{\rm {int}}(t_{2})]dt_{2}dt_{1}\end{aligned}}}
and higher order terms vanish for the MS Hamiltonian since [ M 2 ( t 1 ) , H i n t ( t 2 ) ] = 0. {\displaystyle [M_{2}(t_{1}),H_{\rm {int}}(t_{2})]=0.}
The first order term is
M 1 ( t ) = ∑ j , k σ j ^ [ α j , k ( t ) a k + α j , k ∗ ( t ) a k † ] {\displaystyle M_{1}(t)=\sum _{j,k}{\hat {\sigma _{j}}}[\alpha _{j,k}(t)a_{k}+\alpha _{j,k}^{*}(t)a_{k}^{\dagger }]}
where α k ( t ) = η j , k ( Ω j / 2 μ k ) e i μ k t / 2 sin ( μ k t / 2 ) e i ϕ m {\displaystyle \alpha _{k}(t)=\eta _{j,k}(\Omega _{j}/2\mu _{k})e^{i\mu _{k}t/2}\sin(\mu _{k}t/2)e^{i\phi _{m}}} describes the displacement of the k t h {\displaystyle k^{th}} motional mode through phase space.
In the weak field regime, where η Ω ≪ μ {\displaystyle \eta \Omega \ll \mu } , this term can be neglected, as the phase space trajectory consists of very small, fast loops about the origin.
The second order term is
M 2 ( t ) = i ∑ i < j , k σ i ^ σ j ^ η i , k η j , k Ω i Ω j 2 μ k ( μ k t − sin ( μ k t ) ) {\displaystyle M_{2}(t)=i\sum _{i<j,k}{\hat {\sigma _{i}}}{\hat {\sigma _{j}}}{\frac {\eta _{i,k}\eta _{j,k}\Omega _{i}\Omega _{j}}{2\mu _{k}}}(\mu _{k}t-\sin(\mu _{k}t))}
over ion pairs { i , j } {\displaystyle \{i,j\}} .
If we set the phases such that ϕ R = 0 {\displaystyle \phi _{R}=0} and ϕ B = π {\displaystyle \phi _{B}=\pi } then σ ^ → − σ x {\displaystyle {\hat {\sigma }}\rightarrow -\sigma _{x}} .
In the strong field regime, ions are coherently excited and the motional state is highly entangled with the internal state until all undesirable excitations are deterministically removed toward the end of the interaction. Care must be taken to end the gate at a time when all motional modes have returned to the origin in phase space, and so the gate time is defined by α = 0 ⟶ μ k t g a t e = 2 π {\displaystyle \alpha =0\longrightarrow \mu _{k}t_{\rm {gate}}=2\pi } for each mode k {\displaystyle k} .
For μ k t = 2 π {\displaystyle \mu _{k}t=2\pi } , the second term of M 2 ( t ) {\displaystyle M_{2}(t)} also vanishes, and so the time evolution operator becomes
U f a s t ( t g a t e ) = exp [ i π 2 ∑ i < j . k η i , k η j , k Ω i Ω j μ k 2 σ ^ i σ ^ j ] . {\displaystyle U_{\rm {fast}}(t_{\rm {gate}})=\exp[i{\frac {\pi }{2}}\sum _{i<j.k}{\frac {\eta _{i,k}\eta _{j,k}\Omega _{i}\Omega _{j}}{\mu _{k}^{2}}}{\hat {\sigma }}_{i}{\hat {\sigma }}_{j}].}
Mølmer and Sørensen's original proposition considers operations in the limit η Ω ≪ ω k − δ {\displaystyle \eta \Omega \ll \omega _{k}-\delta } . In this 'weak-field regime', there is insensitivity to vibrational state and robustness against changes in vibrational motion throughout the entire gate operation, due to exploiting two important effects of quantum mechanics:
If we consider two ions, each illuminated by lasers with detunings δ = ± ( ω k + δ ′ ) {\displaystyle \delta =\pm (\omega _{k}+\delta ')} from ω e g {\displaystyle \omega _{eg}} , the only energy-conserving transitions are | g g ⟩ ↔ | e e ⟩ {\displaystyle |gg\rangle \leftrightarrow |ee\rangle } and | g e ⟩ ↔ | e g ⟩ {\displaystyle |ge\rangle \leftrightarrow |eg\rangle } . Under the Lamb-Dicke approximation e − i η ( a † + a ) ≈ 1 − i η ( a † + a ) {\displaystyle e^{-i\eta (a^{\dagger }+a)}\approx 1-i\eta (a^{\dagger }+a)} , we determine the effective Rabi frequency for the | g g , n ⟩ ↔ | e e , n ⟩ {\displaystyle |gg,n\rangle \leftrightarrow |ee,n\rangle } transition via intermediate states m {\displaystyle m} using second order perturbation theory:
Ω ~ = 2 ∑ m ⟨ e e , n | H i n t | m ⟩ ⟨ m | H i n t | g g , n ⟩ E g g , n + ℏ ω i − E m {\displaystyle {\tilde {\Omega }}=2\sum _{m}{\frac {\langle ee,n|H_{\rm {int}}|m\rangle \langle m|H_{\rm {int}}|gg,n\rangle }{E_{gg,n}+\hbar \omega _{i}-E_{m}}}}
There are four possible transition paths between | g g , n ⟩ {\displaystyle |gg,n\rangle } and | e e , n ⟩ {\displaystyle |ee,n\rangle } :
| g g , n ⟩ ↔ | e g , n + 1 ⟩ {\displaystyle |gg,n\rangle \leftrightarrow |eg,n+1\rangle } , | e g , n + 1 ⟩ ↔ | e e , n ⟩ {\displaystyle |eg,n+1\rangle \leftrightarrow |ee,n\rangle }
| g g , n ⟩ ↔ | e g , n − 1 ⟩ {\displaystyle |gg,n\rangle \leftrightarrow |eg,n-1\rangle } , | e g , n − 1 ⟩ ↔ | e e , n ⟩ {\displaystyle |eg,n-1\rangle \leftrightarrow |ee,n\rangle }
| g g , n ⟩ ↔ | g e , n + 1 ⟩ {\displaystyle |gg,n\rangle \leftrightarrow |ge,n+1\rangle } , | g e , n + 1 ⟩ ↔ | e e , n ⟩ {\displaystyle |ge,n+1\rangle \leftrightarrow |ee,n\rangle }
| g g , n ⟩ ↔ | g e , n − 1 ⟩ {\displaystyle |gg,n\rangle \leftrightarrow |ge,n-1\rangle } , | g e , n − 1 ⟩ ↔ | e e , n ⟩ {\displaystyle |ge,n-1\rangle \leftrightarrow |ee,n\rangle }
and so the summation can be restricted to these four intermediate terms.
The pathways involving intermediate states with n + 1 {\displaystyle n+1} quanta yield n + 1 Ω 2 η 2 / ( δ − ω k ) {\displaystyle {\sqrt {n+1}}\Omega ^{2}\eta ^{2}/(\delta -\omega _{k})} , while the n − 1 {\displaystyle n-1} pathways yield − n Ω 2 η 2 / ( δ − ω k ) {\displaystyle -n\Omega ^{2}\eta ^{2}/(\delta -\omega _{k})} . Summing terms, we obtain the effective Rabi frequency Ω ~ = ( Ω η ) 2 δ ′ {\displaystyle {\tilde {\Omega }}={\frac {(\Omega \eta )^{2}}{\delta '}}} , which is independent of phonon number n {\displaystyle n} due to destructive interference between pathways.
Four similar transition pathways can be identified between | g e , n ⟩ ↔ | e g , n ⟩ {\displaystyle |ge,n\rangle \leftrightarrow |eg,n\rangle } , resulting in the state evolution:
| g g ⟩ → cos ( Ω ~ t 2 ) | g g ⟩ + i sin ( Ω ~ t 2 ) | e e ⟩ {\displaystyle |gg\rangle \rightarrow \cos({\frac {{\tilde {\Omega }}t}{2}})|gg\rangle +i\sin({\frac {{\tilde {\Omega }}t}{2}})|ee\rangle }
| e e ⟩ → cos ( Ω ~ t 2 ) | e e ⟩ + i sin ( Ω ~ t 2 ) | g g ⟩ {\displaystyle |ee\rangle \rightarrow \cos({\frac {{\tilde {\Omega }}t}{2}})|ee\rangle +i\sin({\frac {{\tilde {\Omega }}t}{2}})|gg\rangle }
| g e ⟩ → cos ( Ω ~ t 2 ) | g e ⟩ − i sin ( Ω ~ t 2 ) | e g ⟩ {\displaystyle |ge\rangle \rightarrow \cos({\frac {{\tilde {\Omega }}t}{2}})|ge\rangle -i\sin({\frac {{\tilde {\Omega }}t}{2}})|eg\rangle }
| e g ⟩ → cos ( Ω ~ t 2 ) | e g ⟩ − i sin ( Ω ~ t 2 ) | g e ⟩ {\displaystyle |eg\rangle \rightarrow \cos({\frac {{\tilde {\Omega }}t}{2}})|eg\rangle -i\sin({\frac {{\tilde {\Omega }}t}{2}})|ge\rangle } .
Maximally entangled states are created at time t = π / ( 2 | Ω ~ | ) {\displaystyle t=\pi /(2|{\tilde {\Omega }}|)} .
In the weak field regime, M 1 ( t ) {\displaystyle M_{1}(t)} can be neglected, as the phase space trajectory consists of very small, fast loops about the origin. To find M 2 ( t ) {\displaystyle M_{2}(t)} , counter-rotating terms neglected in the rotating wave approximation must be re-introduced as a linear term appears that dominates at long times.
Doing so, the effective time evolution operator becomes
U s l o w ( t ) ≈ exp [ i ∑ i < j , k ( σ ^ i σ ^ j ) η i , k η j , k Ω i Ω j μ 2 − ω k 2 ω k t ] {\displaystyle U_{\rm {slow}}(t)\approx \exp[i\sum _{i<j,k}({\hat {\sigma }}_{i}{\hat {\sigma }}_{j}){\frac {\eta _{i,k}\eta _{j,k}\Omega _{i}\Omega _{j}}{\mu ^{2}-\omega _{k}^{2}}}\omega _{k}t]}
which is equivalent to that of an Ising Hamiltonian
H e f f ≈ ∑ i < j J i j σ ^ i σ ^ j , {\displaystyle H_{\rm {eff}}\approx \sum _{i<j}J_{ij}{\hat {\sigma }}_{i}{\hat {\sigma }}_{j},}
with coupling between i {\displaystyle i} and j {\displaystyle j} given by
J i j ≈ Ω i Ω j ∑ k η i , k η j , k μ 2 − ω k 2 ω k {\displaystyle J_{ij}\approx \Omega _{i}\Omega _{j}\sum _{k}{\frac {\eta _{i,k}\eta _{j,k}}{\mu ^{2}-\omega _{k}^{2}}}\omega _{k}} . | https://en.wikipedia.org/wiki/Mølmer–Sørensen_gate |
The M–sigma (or M – σ ) relation is an empirical correlation between the stellar velocity dispersion σ of a galaxy bulge and the mass M of the supermassive black hole at its center.
The M – σ relation was first presented in 1999 during a conference at the Institut d'Astrophysique de Paris in France . The proposed form by David Merritt of the relation, which was called the "Faber–Jackson law for black holes", was [ 1 ]
where M ⊙ {\displaystyle M_{\odot }} is the solar mass . Publication of the relation in a refereed journal, by two groups, took place the following year . [ 2 ] [ 3 ] One of many recent studies, [ 4 ] [ 5 ] based on the growing sample of published black hole masses in nearby galaxies, gives [ 6 ]
Earlier work demonstrated a relationship between galaxy luminosity and black hole mass, [ 7 ] which nowadays has a comparable level of scatter. [ 8 ] [ 9 ] The M – σ relation is generally interpreted as implying some source of mechanical feedback between the growth of supermassive black holes and the growth of galaxy bulges, although the source of this feedback is still uncertain.
Discovery of the M – σ relation was taken by many astronomers to imply that supermassive black holes are fundamental components of galaxies. Prior to about 2000, the main concern had been the simple detection of black holes, while afterward the interest changed to understanding the role of supermassive black holes as a critical component of galaxies. This led to the main uses of the relation to estimate black hole masses in galaxies that are too distant for direct mass measurements to be made, and to assay the overall black hole content of the Universe.
The tightness of the M – σ relation suggests that some kind of feedback acts to maintain the connection between black hole mass and stellar velocity dispersion, in spite of processes like galaxy mergers and gas accretion that might be expected to increase the scatter over time.
One such mechanism was suggested by Joseph Silk and Martin Rees in 1998. [ 10 ] These authors proposed a model in which supermassive black holes first form via collapse of giant
gas clouds before most of the bulge mass has turned into stars. The black holes created in this way would then accrete and radiate, driving a wind which acts back on the accretion flow.
The flow would stall if the rate of deposition of mechanical energy into the infalling gas was large enough to unbind the protogalaxy in one crossing time . The Silk and Rees model predicts
a slope for the M – σ relation of α = 5 , which is approximately correct. However, the predicted normalization of the relation is too small by about a factor of one thousand. [ citation needed ] The reason is that there is far more energy released in the formation of a supermassive black hole than is needed to completely unbind the stellar bulge. [ citation needed ]
A more successful feedback model was first presented by Andrew King at the University of Leicester in 2003. [ 11 ] In King's model, feedback occurs through momentum transfer, rather than energy transfer as in the case of Silk & Rees's model. A "momentum-driven flow" is one in which the gas cooling time is so short that essentially all the energy in the flow is in the form of bulk motion. In such a flow, most of the energy released by the black hole is lost to radiation, and only a few percent is left to affect the gas mechanically. King's model predicts a slope of α = 4 for the M – σ relation, and the normalization is exactly correct; it is roughly a factor c / σ ≈ 10 3 times larger than in Silk & Rees's relation.
Before the M – σ relation was discovered in 2000, a large discrepancy existed between black hole masses derived using three techniques. [ 12 ] Direct, or dynamical, measurements based on the motion of stars or gas near the black hole seemed to give masses that averaged ≈1% of the bulge mass (the "Magorrian relation"). Two other techniques— reverberation mapping in active galactic nuclei , and the Sołtan argument , which computes the cosmological density in black holes needed to explain the quasar light—both gave a mean value of M / M bulge that was a factor ≈10 smaller than implied by the Magorrian relation. The M – σ relation resolved this discrepancy by showing that most of the direct black hole masses published prior to 2000 were significantly in error, presumably because the data on which they were based were of insufficient quality to resolve the black hole's dynamical sphere of influence . [ 13 ] The mean ratio of black hole mass to bulge mass in big early-type galaxies is now believed to be approximately 1 : 200 , and increasingly smaller as one moves to less massive galaxies.
A common use of the M – σ relation is to estimate black hole masses in distant galaxies using the easily measured quantity σ. Black hole masses in thousands of galaxies have been estimated in this way. The M – σ relation is also used to calibrate so-called secondary and tertiary mass estimators, which relate the black hole mass to the strength of emission lines from hot gas in the nucleus or to the velocity dispersion of gas in the bulge. [ 14 ]
The tightness of the M – σ relation has led to suggestions that every bulge must contain a supermassive black hole. However, the number of galaxies in which the effect of the black hole's gravity on the motion of stars or gas is unambiguously seen is still quite small. [ 15 ] It is unclear whether the lack of black hole detections in many galaxies implies that these galaxies do not contain black holes; or that their masses are significantly below the value implied by the M – σ relation; or that the data are simply too poor to reveal the presence of the black hole. [ 16 ]
The smallest supermassive black hole with a well-determined mass has M bh ≈ 10 6 M ☉ . [ 13 ] [ needs update ] The existence of black holes in the mass range 10 2 –10 5 M ☉ (" intermediate-mass black holes ") is predicted by the M – σ relation in low-mass galaxies, and the existence of intermediate-mass black holes has been reasonably well established in a number of galaxies that contain active galactic nuclei , although the values of M bh in these galaxies are very uncertain. [ 17 ] No clear evidence has been found for ultra-massive black holes with masses above 10 10 M ☉ , although this may be an expected consequence of the observed upper limit to σ . [ 18 ] | https://en.wikipedia.org/wiki/M–sigma_relation |
In mathematics , the n ! conjecture is the conjecture that the dimension of a certain bi-graded module of diagonal harmonics is n !. It was made by A. M. Garsia and M. Haiman and later proved by M. Haiman . It implies Macdonald 's positivity conjecture about the Macdonald polynomials .
The Macdonald polynomials P λ {\displaystyle P_{\lambda }} are a two-parameter family of orthogonal polynomials indexed by a positive weight λ of a root system , introduced by Ian G. Macdonald (1987). They generalize several other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials . They are known to have deep relationships with affine Hecke algebras and Hilbert schemes , which were used to prove several conjectures made by Macdonald about them.
Macdonald (1988) introduced a new basis for the space of symmetric functions , which specializes to many of the well-known bases for the symmetric functions, by suitable substitutions for the parameters q and t .
In fact, we can obtain in this manner the Schur functions , the Hall–Littlewood symmetric functions, the Jack symmetric functions, the zonal symmetric functions , the zonal spherical functions , and the elementary and monomial symmetric functions.
The so-called q , t - Kostka polynomials are the coefficients of a resulting transition matrix . Macdonald conjectured that they are polynomials in q and t , with non-negative integer coefficients.
It was Adriano Garsia 's idea to construct an appropriate module in order to prove positivity (as was done in his previous joint work with Procesi on Schur positivity of Kostka–Foulkes polynomials ).
In an attempt to prove Macdonald's conjecture, Garsia & Haiman (1993) introduced the bi-graded module H μ {\displaystyle H_{\mu }} of diagonal harmonics and conjectured that the (modified) Macdonald polynomials are the Frobenius image of the character generating function of H μ , under the diagonal action of the symmetric group .
The proof of Macdonald's conjecture was then reduced to the n ! conjecture; i.e., to prove that the dimension of H μ is n !. In 2001, Haiman proved that the dimension is indeed n ! (see [4]).
This breakthrough led to the discovery of many hidden connections and new aspects of symmetric group representation theory , as well as combinatorial objects (e.g., insertion tableaux, Haglund's inversion numbers, and the role of parking functions in representation theory ). | https://en.wikipedia.org/wiki/N!_conjecture |
N ′ -Formylkynurenine is an intermediate in the catabolism of tryptophan . It is a formylated derivative of kynurenine . The formation of N ′ -formylkynurenine is catalyzed by heme dioxygenases . [ 1 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N'-Formylkynurenine |
N (6)-Carboxymethyllysine (CML), also known as N ε -(carboxymethyl)lysine, is an advanced glycation endproduct (AGE). CML has been the most used marker for AGEs in food analysis. [ 1 ]
Recently, it has been demonstrated that gut microbiota mediates an aging-associated decline in gut barrier function, allowing AGEs to leak into the bloodstream from the gut and impairing microglial function in the brain. It is suggested that the amount of CML in human blood samples may correlated with age. [ 2 ]
A humanized monoclonal antibody which binds to N6 – carboxymethyl lysine shows considerable promise as a possible therapeutic agent for treating pancreatic cancer. [ 3 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N(6)-Carboxymethyllysine |
Trimethylamine ( TMA ) is an organic compound with the formula N(CH 3 ) 3 . It is a trimethylated derivative of ammonia . TMA is widely used in industry. [ 5 ] [ 6 ] At higher concentrations it has an ammonia -like odor, and can cause necrosis of mucous membranes on contact. [ 7 ] At lower concentrations, it has a "fishy" odor, the odor associated with rotting fish .
TMA is a colorless, hygroscopic , and flammable tertiary amine . It is a gas at room temperature but is usually sold as a 40% solution in water . It is also sold in pressurized gas cylinders .
TMA protonates to give the trimethylammonium cation. Trimethylamine is a good nucleophile , and this reactivity underpins most of its applications. Trimethylamine is a Lewis base that forms adducts with a variety of Lewis acids . [ 8 ]
Trimethylamine is prepared by the reaction of ammonia and methanol employing a catalyst: [ 5 ]
This reaction coproduces the other methylamines, dimethylamine (CH 3 ) 2 NH and methylamine CH 3 NH 2 .
Trimethylammonium chloride has been prepared by a reaction of ammonium chloride and paraformaldehyde : [ 9 ]
Trimethylamine is produced by several routes in nature. Well studied are the degradation of choline and carnitine . [ 10 ]
Trimethylamine is used in the synthesis of choline , tetramethylammonium hydroxide , plant growth regulators , herbicides , strongly basic anion exchange resins , dye leveling agents and a number of basic dyes. [ 5 ] [ 6 ] Gas sensors to test for fish freshness detect trimethylamine.
In humans, ingestion of certain plant and animal (e.g., red meat, egg yolk) food containing lecithin , choline , and L-carnitine provides certain gut microbiota with the substrate to synthesize TMA, which is then absorbed into the bloodstream. [ 11 ] [ 12 ] High levels of trimethylamine in the body are associated with the development of trimethylaminuria, or fish odor syndrome , caused by a genetic defect in the enzyme which degrades TMA; or by taking large doses of supplements containing choline or L-carnitine . [ 11 ] [ 12 ] TMA is metabolized by the liver to trimethylamine N-oxide (TMAO); TMAO is being investigated as a possible pro atherogenic substance which may accelerate atherosclerosis in those eating foods with a high content of TMA precursors. [ 12 ] TMA also causes the odor of some human infections , bad breath , and bacterial vaginosis .
Trimethylamine is a full agonist of human TAAR5 , [ 13 ] [ 14 ] [ 15 ] a trace amine-associated receptor that is expressed in the olfactory epithelium and functions as an olfactory receptor for tertiary amines . [ 15 ] [ 16 ] One or more additional odorant receptors appear to be involved in trimethylamine olfaction in humans as well. [ 16 ]
Acute and chronic toxic effects of TMA were suggested in medical literature as early as the 19th century. TMA causes eye and skin irritation, and it is suggested to be a uremic toxin . [ 17 ] In patients, trimethylamine caused stomach ache, vomiting, diarrhoea, lacrimation, greying of the skin and agitation. [ 18 ] Apart from that, reproductive / developmental toxicity has been reported. [ 7 ] Some experimental studies suggested that TMA may be involved in etiology of cardiovascular diseases . [ 19 ] [ 20 ]
Guidelines with exposure limit for workers are available e.g. the Recommendation from the Scientific Committee on Occupational Exposure Limits by the European Union Commission. [ 21 ]
Trimethylaminuria is an autosomal recessive genetic disorder involving a defect in the function or expression of flavin-containing monooxygenase 3 (FMO3) which results in poor trimethylamine metabolism . Individuals with trimethylaminuria develop a characteristic fish odor—the smell of trimethylamine—in their sweat , urine , and breath after the consumption of choline -rich foods. A condition similar to trimethylaminuria has also been observed in a certain breed of Rhode Island Red chicken that produces eggs with a fishy smell, especially after eating food containing a high proportion of rapeseed . [ 22 ] [ 23 ]
The first dream of his own which Sigmund Freud tried to analyse in detail, when he was developing his theories about the interpretation of dreams, involved a patient of Freud's who had to have an injection of trimethylamine, and the chemical formula of the substance, written in bold letters on the bottle, jumping out at Freud. [ 24 ] | https://en.wikipedia.org/wiki/N(CH3)3 |
Tetramethylammonium pentafluoroxenate is a chemical compound with the chemical formula [N(CH 3 ) 4 ] + [XeF 5 ] − . This salt consists of tetramethylammonium cations [N(CH 3 ) 4 ] + and pentafluoroxenate(IV) anions [XeF 5 ] − . The [XeF 5 ] − ion was the first example of a pentagonal planar molecular geometry AX 5 E 2 species. [ 1 ] It was prepared by the reaction of [N(CH 3 ) 4 ]F with xenon tetrafluoride , [N(CH 3 ) 4 ]F being chosen because it can be prepared in anhydrous form and is readily soluble in organic solvents. [ 1 ] The anion is planar, with the fluorine atoms in a slightly distorted pentagonal coordination (Xe–F bond lengths 197.9–203.4 pm, and F–X–F bond angles 71.5°–72.3°). [ 1 ] Other salts have been prepared with sodium, caesium and rubidium, and vibrational spectra show that these contain the same planar ion. [ 1 ] The isolated anion has the point group of D 5h . [ 1 ] | https://en.wikipedia.org/wiki/N(CH3)4XeF5 |
Trinitramide is a compound of nitrogen and oxygen with the molecular formula N (N O 2 ) 3 . The compound was detected and described in 2010 by researchers at the Royal Institute of Technology (KTH) in Sweden . [ 1 ] It is made of a nitrogen atom bonded to three nitro groups ( −NO 2 ).
Earlier, there had been speculation [ by whom? ] whether trinitramide could exist. [ need quotation to verify ] Theoretical calculations by Montgomery and Michels in 1993 showed that the compound was likely to be stable. [ 2 ]
Trinitramide is prepared by the nitration reaction of either potassium dinitramide or ammonium dinitramide with nitronium tetrafluoroborate in acetonitrile at low temperatures. [ 1 ]
Trinitramide has a potential use as one of the most efficient and least polluting of rocket propellant oxidizers , as it is chlorine -free. [ 3 ] This is potentially an important development, because the Tsiolkovsky rocket equation implies that even small improvements in specific impulse yields a similar change in delta-v , which can make large improvements in the size of practical rocket launch payloads.
The density impulse (impulse per volume) of a trinitramide based propellant could be 20 to 30 percent better than most existing formulations, [ 4 ] however the specific impulse (impulse per mass) of formulations with liquid oxygen is higher. [ 1 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N(NO2)3 |
Redundancy is a form of resilience that ensures system availability in the event of component failure. Components ( N ) have at least one independent backup component (+1). The level of resilience is referred to as active/passive or standby as backup components do not actively participate within the system during normal operation. The level of transparency (disruption to system availability) during failover is dependent on a specific solution, though degradation to system resilience will occur during failover. [ 1 ]
It is also possible to have N +1 redundancy with active-active components, in such cases the backup component will remain active in the operation even if all other components are fully functional, however the system will be able to perform in the event that one component is faulted and recover from a single component failure.
1+1 redundancy typically offers the advantage of additional failover transparency in the event of component failure. The level of resilience is referred to as active/active or hot as backup components actively participate with the system during normal operation. Failover is generally transparent (no disruption to system availability) as failover does not actually occur (just degradation to system resilience ) as the backup components were already active within the system. [ 1 ]
2+1 redundancy or 3+1 redundancy is common on power systems for blade servers where a relatively small number of highly rated Uninterruptible Power Supplies (UPS) efficiently power a greater number of blades. An example is a server chassis that has three power supplies ; the system may be set to 2+1 redundancy so that the blades can enjoy the power of two PSUs and have one available to give redundancy if one fails. It is also common to mix live (hot) redundancy where UPSes are online, and cold standby redundancy where they are offline until needed. The reason for this, in the case of UPSes, is that a common failure mode is component's end-of-life failure, and if UPSes are equally used, then they are highly likely to fail within a short space of time of each other when toward the end of service life.
Redundant systems are often used in data centers to maximise uptime or availability of computer systems. Other common implementations include aerospace , where redundant systems are used to improve safety and integrity of spacecraft , electric power systems and automobiles , where the emergency brake is available in a car as a redundant component in case of failure of the main brake systems. The German power system, which has N+1 redundancy and is known as "(n-1) Sicherheit" in German, is one example of its application. [ 2 ] | https://en.wikipedia.org/wiki/N+1_redundancy |
N , N ′-Dicyclohexylcarbodiimide ( DCC or DCCD ) [ 1 ] is an organic compound with the chemical formula (C 6 H 11 N) 2 C. It is a waxy white solid with a sweet odor. Its primary use is to couple amino acids during artificial peptide synthesis . The low melting point of this material allows it to be melted for easy handling. It is highly soluble in dichloromethane , tetrahydrofuran , acetonitrile and dimethylformamide , but insoluble in water .
The C−N=C=N−C core of carbodiimides (N=C=N) is linear, being related to the structure of allene . The molecule has idealized C 2 symmetry .
The N=C=N moiety gives characteristic IR spectroscopic signature at 2117 cm −1 . [ 2 ] The 15 N NMR spectrum shows a characteristic shift of 275 ppm upfield of nitric acid and the 13 C NMR spectrum features a peak at about 139 ppm downfield from TMS . [ 3 ]
DCC is produced by the decarboxylation of cyclohexyl isocyanate using phosphine oxides as a catalyst: [ 4 ]
Alternative catalysts for this conversion include the highly nucleophilic OP(MeNCH 2 CH 2 ) 3 N. [ 2 ]
Of academic interest, palladium acetate , iodine, and oxygen can be used to couple cyclohexyl amine and cyclohexyl isocyanide . [ 5 ] Yields of up to 67% have been achieved using this route:
DCC has also been prepared from dicyclohexylurea using a phase transfer catalyst . The disubstituted urea, arenesulfonyl chloride, and potassium carbonate react in toluene in the presence of benzyl triethylammonium chloride to give DCC in 50% yield. [ 6 ]
DCC is a dehydrating agent for the preparation of amides , ketones , and nitriles . [ 1 ] In these reactions, DCC hydrates to form dicyclohexylurea (DCU), a compound that is nearly insoluble in most organic solvents and insoluble in water. The majority of the DCU is thus readily removed by filtration, although the last traces can be difficult to eliminate from non-polar products. DCC can also be used to invert secondary alcohols . In the Steglich esterification , alcohols, including even some tertiary alcohols, can be esterified using a carboxylic acid in the presence of DCC and a catalytic amount of DMAP . [ 7 ]
In protein synthesis (such as Fmoc solid-state synthesizers ), the N-terminus is often used as the attachment site on which the amino acid monomers are added. To enhance the electrophilicity of carboxylate group, the negatively charged oxygen must first be "activated" into a better leaving group . DCC is used for this purpose. The negatively charged oxygen will act as a nucleophile , attacking the central carbon in DCC. DCC is temporarily attached to the former carboxylate group forming a highly electrophilic intermediate, making nucleophilic attack by the terminal amino group on the growing peptide more efficient.
In combination with dimethyl sulfoxide (DMSO), DCC affects the Pfitzner–Moffatt oxidation . [ 8 ] This procedure is used for the oxidation of alcohols to aldehydes and ketones. Unlike metal-mediated oxidations , such as the Jones oxidation , the reaction conditions are sufficiently mild to avoid over-oxidation of aldehydes to carboxylic acids. Generally, three equivalents of DCC and 0.5 equivalents of proton source in DMSO are allowed to react overnight at room temperature. The reaction is quenched with acid.
DCC is a classical inhibitor of ATP synthase . [ 10 ] DCC inhibits ATP synthase by binding to one of the c subunits and causing steric hindrance of the rotation of the F O subunit. [ 11 ]
DCC often causes rashes. [ 1 ] In vivo dermal sensitization studies according to OECD 429 [ 12 ] confirmed DCC is a strong skin sensitizer , showing a response at 0.03 wt% in the Local Lymph Node Assay (LLNA) placing it in Globally Harmonized System of Classification and Labelling of Chemicals (GHS) Dermal Sensitization Category 1A. [ 13 ] Thermal hazard analysis by differential scanning calorimetry (DSC) shows DCC poses minimal explosion risks. [ 14 ] | https://en.wikipedia.org/wiki/N,N'-Dicyclohexylcarbodiimide |
N , N ′ -Diisopropylcarbodiimide is a carbodiimide used in peptide synthesis . [ 1 ] [ 2 ] As a liquid, it is easier to handle than the commonly used N , N ′ -dicyclohexylcarbodiimide , a waxy solid. In addition, N , N ′ -diisopropylurea, its byproduct in many chemical reactions, is soluble in most organic solvents , a property that facilitates work-up .
In vivo dermal sensitization studies according to OECD 429 [ 3 ] confirmed DIC is a strong skin sensitizer , showing a response at 0.20 wt% in the Local Lymph Node Assay (LLNA) placing it in Globally Harmonized System of Classification and Labelling of Chemicals (GHS) Dermal Sensitization Category 1A. [ 4 ] Thermal hazard analysis by differential scanning calorimetry (DSC) shows DIC poses minimal explosion risks. [ 5 ]
This article about an organic compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N,N'-Diisopropylcarbodiimide |
N -Acetyl-γ-aminobutyric acid ( N -acetyl-GABA ), also known as N -acetyl-4-aminobutyric acid , is a metabolic intermediate in the biosynthesis of γ-aminobutyric acid (GABA) from putrescine . [ 1 ] [ 2 ] [ 3 ] [ 4 ] Other intermediates in this pathway include N -acetylputrescine and N -acetyl-γ-aminobutyraldehyde ( N -acetyl-GABAL or N -acetyl-GABA aldehyde). [ 2 ] [ 3 ] [ 4 ] Enzymes mediating the transformations in this pathway include putrescine acetyltransferase (PAT), monoamine oxidase B (MAO-B), aldehyde dehydrogenase (ALDH), and an unknown deacetylase enzyme . [ 2 ] [ 3 ] [ 4 ] The pathway is a minor pathway in GABA synthesis compared to the main pathway in which GABA is synthesized from glutamate . [ 2 ] [ 3 ] [ 4 ] However, the pathway has been found to have an important physiological role in the brain, for instance in the production of GABA in the striatum and resultant inhibition of dopaminergic neurons in this brain area. [ 1 ] [ 4 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N-Acetyl-γ-aminobutyric_acid |
The N -Acetylglucosamine receptor is a receptor which binds N -Acetylglucosamine .
The N-Acetylglucosamine (GlcNAc) receptor has been recently found to interact and bind with vimentins at the cell surface. Research indicates that the GlcNAc receptor can therefore be used to target vimentin-expressing cells for gene delivery via receptor-mediated endocytosis . [ 1 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N-Acetylglucosamine_receptor |
N -Acetylputrescine ( NacPut ), also known as monoacetylputrescine , is an endogenous metabolite of putrescine and a precursor and metabolic intermediate in the biosynthesis of γ-aminobutyric acid (GABA) from putrescine. [ 1 ] [ 2 ] [ 3 ]
The metabolic pathway is specifically putrescine into N -acetylputrescine by putrescine acetyltransferase (PAT), N -acetylputrescine into N -acetyl-γ-aminobutyraldehyde ( N -acetyl-GABAL or N -acetyl-GABA aldehyde) by monoamine oxidase B (MAO-B), N -acetyl-GABAL into N -acetyl-γ-aminobutyric acid ( N -acetyl-GABA) by aldehyde dehydrogenase (ALDH), and N -acetyl-GABA into GABA by an unknown deacetylase enzyme . [ 1 ] [ 2 ] [ 3 ] This pathway is a minor alternative pathway to the major and primary pathway in which GABA is synthesized from glutamate . [ 1 ] There is also another alternative pathway in which putrescine is converted into GABA with γ-aminobutyraldehyde (GABAL or GABA aldehyde) as an intermediate instead. [ 1 ] It has been estimated that about 2 to 3% of GABA is synthesized from putrescine in the mouse brain, whereas in the case of the rat brain, the amount was negligible. [ 1 ]
In 2021, it was discovered that MAO-B does not mediate dopamine catabolism in the rodent striatum but instead participates in striatal GABA synthesis and that synthesized GABA in turn inhibits dopaminergic neurons in this brain area. [ 4 ] [ 3 ] It has been found that MAO-B, via the putrescine pathway, importantly mediates GABA synthesis in astrocytes in various brain areas, including in the hippocampus , cerebellum , striatum, cerebral cortex , and substantia nigra pars compacta (SNpc). [ 4 ] [ 3 ] These findings may warrant a rethinking of the actions of MAO-B inhibitors in the treatment of Parkinson's disease . [ 4 ] [ 3 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N-Acetylputrescine |
N -Bromosuccinimide or NBS is a chemical reagent used in radical substitution , electrophilic addition , and electrophilic substitution reactions in organic chemistry . NBS can be a convenient source of Br • , the bromine radical. [ 1 ]
NBS is commercially available. It can also be synthesized in the laboratory. To do so, sodium hydroxide and bromine are added to an ice-water solution of succinimide . The NBS product precipitates and can be collected by filtration. [ 2 ]
Crude NBS gives better yield in the Wohl–Ziegler reaction . In other cases, impure NBS (slightly yellow in color) may give unreliable results. It can be purified by recrystallization from preheated (90 to 95 °C) water (10 g of NBS for 100 mL of water). [ 1 ]
NBS reacts with alkenes in aqueous solvents to give bromohydrins . The preferred conditions are the portionwise addition of NBS to a solution of the alkene in 50% aqueous DMSO , DME , THF , or tert -butanol at 0 °C. [ 3 ] Formation of a bromonium ion and immediate attack by water gives strong Markovnikov addition and anti stereochemical selectivities. [ 4 ]
Side reactions include the formation of α-bromoketones and dibromo compounds. These can be minimized by the use of freshly recrystallized NBS.
With the addition of nucleophiles , instead of water , various bifunctional alkanes can be synthesized. [ 5 ]
Standard conditions for using NBS in allylic and/or benzylic bromination involves refluxing a solution of NBS in anhydrous CCl 4 with a radical initiator—usually azobisisobutyronitrile ( AIBN ) or benzoyl peroxide , irradiation, or both to effect radical initiation . [ 1 ] [ 6 ] The allylic and benzylic radical intermediates formed during this reaction are more stable than other carbon radicals and the major products are allylic and benzylic bromides. This is also called the Wohl–Ziegler reaction . [ 7 ] [ 8 ]
The carbon tetrachloride must be maintained anhydrous throughout the reaction, as the presence of water may likely hydrolyze the desired product. [ 9 ] Barium carbonate is often added to maintain anhydrous and acid-free conditions.
In the above reaction, while a mixture of isomeric allylic bromide products are possible, only one is created due to the greater stability of the 4-position radical over the methyl-centered radical.
NBS can α-brominate carbonyl derivatives via either a radical pathway (as above) or via acid-catalysis. For example, hexanoyl chloride 1 can be brominated in the alpha-position by NBS using acid catalysis. [ 10 ]
The reaction of enolates , enol ethers, or enol acetates with NBS is the preferred method of α-bromination as it is high-yielding with few side-products. [ 11 ] [ 12 ]
Electron-rich aromatic compounds, such as phenols , anilines , and various aromatic heterocycles , [ 13 ] can be brominated using NBS. [ 14 ] [ 15 ] Using DMF as the solvent gives high levels of para-selectivity. [ 16 ]
NBS, in the presence of a strong base, such as DBU , reacts with primary amides to produce a carbamate via the Hofmann rearrangement . [ 17 ]
It is uncommon, but possible for NBS to oxidize alcohols. E. J. Corey et al. found that one can selectively oxidize secondary alcohols in the presence of primary alcohols using NBS in aqueous dimethoxyethane (DME). [ 18 ]
NBS electrophilically brominates the amine, which is followed by decarboxylation and release of an imine. Further hydrolysis will yield an aldehyde and ammonia. [ 19 ] [ 20 ] (cf. non-oxidative PLP dependent decarboxylation)
NBS is a weaker equivalent to bromine in its dangers. NBS is typically stored in a refrigerator. Pure NBS is white, but it is often found to be off-white or brown colored by bromine.
Some reactions involving NBS are exothermic, requiring suitable precautions. | https://en.wikipedia.org/wiki/N-Bromosuccinimide |
n -Butyllithium C 4 H 9 Li (abbreviated n -BuLi ) is an organolithium reagent . It is widely used as a polymerization initiator in the production of elastomers such as polybutadiene or styrene-butadiene-styrene (SBS) . Also, it is broadly employed as a strong base ( superbase ) in the synthesis of organic compounds as in the pharmaceutical industry.
Butyllithium is commercially available as solutions (15%, 25%, 1.5 M , 2 M, 2.5 M, 10 M, etc.) in alkanes such as pentane , hexanes , and heptanes . Solutions in diethyl ether and THF can be prepared, but are not stable enough for storage. Annual worldwide production and consumption of butyllithium and other organolithium compounds is estimated at 2000 to 3000 tonnes. [ 2 ]
Although butyllithium is colorless, n -butyllithium is usually encountered as a pale yellow solution in alkanes. Such solutions are stable indefinitely if properly stored, [ 3 ] but in practice, they degrade upon aging, where a fine white precipitate ( lithium hydride ) is deposited and the color changes to orange. [ 3 ] [ 4 ]
n -BuLi exists as a cluster both in the solid state and in a solution. The tendency to aggregate is common for organolithium compounds. The aggregates are held together by delocalized covalent bonds between lithium and the terminal carbon of the butyl chain. [ 5 ] In the case of n -BuLi, the clusters are tetrameric (in ether) or hexameric (in cyclohexane ). The cluster is a distorted cubane-type cluster with Li and C H 2 R groups at alternating vertices. An equivalent description describes the tetramer as a Li 4 tetrahedron interpenetrated with a tetrahedron [ C H 2 R] 4 . Bonding within the cluster is related to that used to describe diborane, but more complex since eight atoms are involved. Reflecting its electron-rich character, n -butyllithium is highly reactive toward Lewis acids .
Due to the large difference between the electronegativities of carbon (2.55) and lithium (0.98), the C−Li bond is highly polarized. The charge separation has been estimated to be 55–95%. For practical purposes, n -BuLi can often be considered to react as the butyl anion , n -Bu − , and a lithium cation , Li + .
The standard preparation for n -BuLi is reaction of 1-bromobutane or 1-chlorobutane with Li metal: [ 3 ]
If the lithium used for this reaction contains 1–3% sodium , the reaction proceeds more quickly than if pure lithium is used. Solvents used for this preparation include benzene , cyclohexane, and diethyl ether. When BuBr is the precursor, the product is a homogeneous solution, consisting of a mixed cluster containing both LiBr and BuLi, together with a small amount of octane . BuLi forms a weaker complex with LiCl, so that the reaction of BuCl with Li produces a precipitate of LiCl .
Solutions of butyllithium, which are susceptible to degradation by air, are standardized by titration . A popular weak acid is biphenyl -4-methanol, which gives a deeply colored dilithio derivative at the end point. [ 6 ]
Butyllithium is principally valued as an initiator for the anionic polymerization of dienes , such as butadiene . [ 7 ] The reaction is called "carbolithiation":
Isoprene can be polymerized stereospecifically in this way. Also of commercial importance is the use of butyllithium for the production of styrene-butadiene polymers. Even ethylene will insert into BuLi. [ 8 ]
Butyllithium is a strong base (p K b ≈ −36), but it is also a powerful nucleophile and reductant , depending on the other reactants. Furthermore, in addition to being a strong nucleophile, n -BuLi binds to aprotic Lewis bases, such as ethers and tertiary amines , which partially disaggregate the clusters by binding to the lithium centers. Its use as a strong base is referred to as metalation . Reactions are typically conducted in tetrahydrofuran and diethyl ether , which are good solvents for the resulting organolithium derivatives (see below).
One of the most useful chemical properties of n -BuLi is its ability to deprotonate a wide range of weak Brønsted acids . t -Butyllithium and s -butyllithium are more basic. n -BuLi can deprotonate (that is, metalate) many types of C−H bonds, especially where the conjugate base is stabilized by electron delocalization or one or more heteroatoms (non-carbon atoms). Examples include acetylenes ( H− CC−R), methyl sulfides ( H −CH 2 SR), thioacetals ( H −CH(SR) 2 , e.g. dithiane ), methylphosphines ( H −CH 2 PR 2 ), furans , thiophenes and ferrocene (Fe( H −C 5 H 4 )(C 5 H 5 )). [ 9 ] In addition to these, it will also deprotonate all more acidic compounds such as alcohols, amines, enolizable carbonyl compounds, and any overtly acidic compounds, to produce alkoxides, amides, enolates and other salts of lithium, respectively. The stability and volatility of the butane resulting from such deprotonation reactions is convenient, but can also be a problem for large-scale reactions because of the volume of a flammable gas produced.
The kinetic basicity of n -BuLi is affected by the solvent or cosolvent. Ligands that complex Li + such as tetrahydrofuran (THF), tetramethylethylenediamine (TMEDA), hexamethylphosphoramide (HMPA), and 1,4-diazabicyclo[2.2.2]octane ( DABCO ) further polarize the Li−C bond and accelerate the metalation. Such additives can also aid in the isolation of the lithiated product, a famous example of which is dilithioferrocene.
Schlosser's base is a superbase produced by treating butyllithium with potassium t -butoxide . It is kinetically more reactive than butyllithium and is often used to accomplish difficult metalations . While some n -butylpotassium is present and is a stronger base than n -BuLi, the reactivity of the mixture is not exactly the same as isolated n -butylpotassium. [ 10 ]
An example of the use of n -butyllithium as a base is the addition of an amine to methyl carbonate to form a methyl carbamate , where n -butyllithium serves to deprotonate the amine:
Butyllithium reacts with some organic bromides and iodides in an exchange reaction to form the corresponding organolithium derivative. The reaction usually fails with organic chlorides and fluorides:
This lithium–halogen exchange reaction is useful for preparation of several types of RLi compounds, particularly aryl lithium and some vinyl lithium reagents. The utility of this method is significantly limited, however, by the presence in the reaction mixture of n -BuBr or n -BuI, which can react with the RLi reagent formed, and by competing dehydrohalogenation reactions, in which n -BuLi serves as a base:
These side reaction are significantly less important for RI than for RBr, since the iodine–lithium exchange is several orders of magnitude faster than the bromine–lithium exchange. For these reasons, aryl, vinyl and primary alkyl iodides are the preferred substrates, and t -BuLi rather than n -BuLi is usually used, since the formed t -BuI is immediately destroyed by the t -BuLi in a dehydrohalogenation reaction (thus requiring two equivalents of t -BuLi). Alternatively, vinyl lithium reagents can be generated by direct reaction of the vinyl halide (e.g. cyclohexenyl chloride) with lithium or by tin–lithium exchange (see next section). [ 3 ]
A related family of reactions are the transmetalations , wherein two organometallic compounds exchange their metals. Many examples of such reactions involve lithium exchange with tin :
The tin–lithium exchange reactions have one major advantage over the halogen–lithium exchanges for the preparation of organolithium reagents, in that the product tin compounds (C 4 H 9 SnMe 3 in the example above) are much less reactive towards lithium reagents than are the halide products of the corresponding halogen–lithium exchanges (C 4 H 9 Br or C 4 H 9 Cl). Other metals and metalloids which undergo such exchange reactions are organic compounds of mercury , selenium , and tellurium .
Organolithium reagents, including n -BuLi are used in synthesis of specific aldehydes and ketones . One such synthetic pathway is the reaction of an organolithium reagent with disubstituted amides :
THF is deprotonated by butyllithium, especially in the presence of TMEDA , by loss of one of four protons adjacent to oxygen. This process, which consumes butyllithium to generate butane, induces a ring opening to give enolate of acetaldehyde and ethylene . [ 11 ] Therefore, reactions of BuLi in THF are typically conducted at low temperatures, such as −78 °C, as is conveniently produced by a freezing bath of dry ice and acetone. Higher temperatures (−25 °C or even −15 °C) are also used.
When heated, n -BuLi, analogously to other alkyllithium reagents with "β-hydrogens", undergoes β-hydride elimination to produce 1-butene and lithium hydride (LiH):
Alkyl-lithium compounds are stored under inert gas to prevent loss of activity and for reasons of safety. n -BuLi reacts violently with water:
This is an exergonic and highly exothermic reaction. If oxygen is present the butane produced may ignite.
BuLi also reacts with CO 2 to give lithium pentanoate: | https://en.wikipedia.org/wiki/N-Butyllithium |
N -Chlorosuccinimide ( NCS ) is the organic compound with the formula C 2 H 4 (CO) 2 NCl. This white solid is used for chlorinations. [ 2 ] It is also used as a mild oxidant . [ 3 ] NCS is related to succinimide, but with N-Cl in place of N-H. The N–Cl bond is highly reactive, and NCS functions as a source of "Cl + ".
NCS is produced from succinimide by treatment with Cl + sources, such as sodium hypochlorite (bleach), and t-butylhypochlorite , and even chlorine . [ 2 ]
Electron-rich arenes are readily monochlorinated by NCS. Aniline and mesitylene are converted to the respective chlorinated derivatives. [ 2 ] | https://en.wikipedia.org/wiki/N-Chlorosuccinimide |
N -Ethylmaleimide ( NEM ) is an organic compound that is derived from maleic acid . It contains the amide functional group , but more importantly it is an alkene that is reactive toward thiols and is commonly used to modify cysteine residues in proteins and peptides . [ 2 ]
NEM is a Michael acceptor in the Michael reaction , which means that it adds nucleophiles such as thiols. The resulting thioether features a strong C–S bond and the reaction is virtually irreversible. Reaction with thiols occur in the pH range 6.5–7.5, NEM may react with amines or undergo hydrolysis at a more alkaline pH. NEM has been widely used to probe the functional role of thiol groups in enzymology . NEM is an irreversible inhibitor of all cysteine peptidases , with alkylation occurring at the active site thiol group (see schematic). [ 3 ] [ 4 ]
NEM blocks vesicular transport . In lysis buffers, 20 to 25 mM of NEM is used to inhibit de- sumoylation of proteins for Western Blot analysis. NEM has also been used as an inhibitor of deubiquitinases.
N -Ethylmaleimide was used by Arthur Kornberg and colleagues to knock out DNA polymerase III in order to compare its activity to that of DNA polymerase I (pol III and I, respectively). Kornberg had been awarded the Nobel Prize for discovering pol I, then believed to be the mechanism of bacterial DNA replication , although in this experiment he showed that pol III was the actual replicative machinery.
NEM activates ouabain -insensitive Cl-dependent K efflux in low-K sheep and goat red blood cells. [ 5 ] This discovery contributed to the molecular identification of K–Cl cotransport (KCC) in human embryonic cells transfected by KCC1 isoform cDNA, 16 years later. [ 6 ] Since then, NEM has been widely used as a diagnostic tool to uncover or manipulate the membrane presence of K–Cl cotransport in cells of many species in the animal kingdom. [ 7 ] Despite repeated unsuccessful attempts to identify chemically the target thiol group, [ 8 ] at physiological pH, NEM may form adducts with thiols within protein kinases that phosphorylate KCC at specific serine and threonine residues primarily within the C-terminal domain of the transporter. [ 9 ] The ensuing dephosphorylation of KCC by protein phosphatases leads to activation of KCC. [ 10 ] | https://en.wikipedia.org/wiki/N-Ethylmaleimide |
N -Fluoropyridinium triflate is an organofluorine compound with the formula [C 5 H 5 NF]O 3 SCF 3 . It is a white solid with low solubility in polar organic solvents. The compound is used as an electrophilic fluorinating agent . It is a salt, consisting of the N -fluoropyridinium cation ([C 5 H 5 NF] + ) and the triflate anion. [ 1 ] Related reagents include Selectfluor , which is also an N-fluorinated salt.
N -Fluoropyridinium cations are not only electrophilic fluorinating agents (i.e., sources of "F + "), they are also one-electron oxidants. [ 2 ] | https://en.wikipedia.org/wiki/N-Fluoropyridinium_triflate |
N -Iodosuccinimide ( NIS ) is a reagent used in organic chemistry for the iodination of alkenes and as a mild oxidant. [ 2 ]
NIS is the iodine analog of N -chlorosuccinimide (NCS) and N -bromosuccinimide (NBS) which are used for similar applications. | https://en.wikipedia.org/wiki/N-Iodosuccinimide |
N -Methylmorpholine is the organic compound with the formula O(CH 2 CH 2 ) 2 NCH 3 . It is a colorless liquid. It is a cyclic tertiary amine . It is used as a base catalyst for generation of polyurethanes and other reactions. It is produced by the reaction of methylamine and diethylene glycol as well as by the hydrogenolysis of N-formylmorpholine. [ 2 ] It is the precursor to N -methylmorpholine N -oxide , a commercially important oxidant. | https://en.wikipedia.org/wiki/N-Methylmorpholine |
N -Methylmorpholine N -oxide (more correctly 4-methylmorpholine 4-oxide), NMO or NMMO is an organic compound . This heterocyclic amine oxide and morpholine derivative is used in organic chemistry as a co-oxidant and sacrificial catalyst in oxidation reactions for instance in osmium tetroxide oxidations and the Sharpless asymmetric dihydroxylation or oxidations with TPAP . [ 1 ] NMO is commercially supplied both as a monohydrate C 5 H 11 NO 2 ·H 2 O and as the anhydrous compound. The monohydrate is used as a solvent for cellulose in the lyocell process to produce cellulose fibers .
NMMO monohydrate is used as a solvent in the lyocell process to produce lyocell fiber. [ 2 ] [ 3 ] It dissolves cellulose to form a solution called dope, and the cellulose is reprecipitated in a water bath to produce a fiber. The process is similar but not analogous to the viscose process. In the viscose process, cellulose is made soluble by conversion to its xanthate derivatives. With NMMO, cellulose is not derivatized but dissolves to give a homogeneous polymer solution. The resulting fiber is similar to viscose ; this was observed, for example, for Valonia cellulose microfibrils. Dilution with water causes the cellulose to reprecipitate, i.e. the solvation of cellulose with NMMO is a water sensitive process. [ 4 ]
Cellulose remains insoluble in most solvents because it has a strong and highly structured intermolecular hydrogen bonding network, which resists common solvents. NMMO breaks the hydrogen bonding network that keeps cellulose insoluble in water and other solvents. Similar solubility has been obtained in a few solvents, particularly a mix of lithium chloride in dimethyl acetamide and some hydrophilic ionic liquids .
Another use of NMMO is in the dissolution of scleroprotein (found in animal tissue). This dissolution occurs in the crystal areas which are more homogeneous and contain glycine and alanine residues with a small number of other residues. How NMMO dissolves these proteins is scarcely studied. Other studies, however, have been done in similar amide systems (i.e. hexapeptide ). The hydrogen bonds of the amides can be broken by NMMO. [ 5 ]
NMO, as an N-oxide , is an oxidant in the Upjohn dihydroxylation . It is generally used in stoichiometric amounts as a secondary oxidant (a cooxidant) to regenerate a primary (catalytic) oxidant after the latter has been reduced by the substrate. Vicinal syn-dihydroxylation reactions for example, would, in theory, require stoichiometric amounts of toxic, volatile and expensive osmium tetroxide , but if continuously regenerated with NMO, the amount required can be reduced to catalytic quantities. | https://en.wikipedia.org/wiki/N-Methylmorpholine_N-oxide |
N -Nitroso- N -methylurea ( NMU ) is a highly reliable carcinogen , mutagen , and teratogen . NMU is an alkylating agent , and exhibits its toxicity by transferring its methyl group to nucleobases in nucleic acids , which can lead to AT:GC transition mutations. [ citation needed ]
NMU is the traditional precursor in the synthesis of diazomethane . [ 2 ] [ 3 ] It has the potentially advantageous property that the stoichiometric byproducts formed are water, carbon dioxide, and ammonia, which are innocuous or easily removed. However, because it is unstable at temperatures beyond 20 °C and somewhat shock-sensitive, it has become obsolete for this purpose and replaced by other N-nitroso compounds: ( N -methyl)nitrosamides and nitrosamines . Most chemical supply houses have stopped carrying it. [ citation needed ]
Acute exposure to NMU in humans can result in skin and eye irritation, headache, nausea, and vomiting. [ 4 ] NMU is reasonably anticipated to be a human carcinogen based on sufficient evidence of carcinogenicity in experimental animals ( IARC 1972, 1978, 1987). [ 5 ] Various cancers induced in animal models include: squamous cell carcinomas of the forestomach, sarcomas and gliomas of the brain, adenocarcinomas of the pancreas, mammary carcinomas, leukemia , and lymphomas . [ 5 ] However, the actual potential for human exposure is quite limited, as the chemical is not produced or used in large quantities [ 5 ]
NMU is teratogenic and embryotoxic, resulting in craniofacial ( cleft palate ) and skeletal defects, fetal growth retardation, and increased fetal resorption . [ 6 ] [ 7 ] [ 8 ] Exposure to NMU during pre-implantation, post-implantation, organogenesis, or by paternal exposure can result in these effects. [ citation needed ] | https://en.wikipedia.org/wiki/N-Nitroso-N-methylurea |
N -Nitrosomorpholine (NNM, NMOR) is an organic compound which is known to be a carcinogen and mutagen .
NMOR is a pale yellow sand-like powder below 84°F. [ 1 ] [ 2 ] NMOR is most commonly produced from morpholine, but can also be made by the reaction of dimorpholinomethane in fuming nitric acid . [ 3 ] Few reactions using NMOR as a starting material are reported in the organic synthesis literature, but it can be used as a precursor to a nitrogen-centered radical. [ 4 ]
NMOR is generally not used intentionally, but is instead created by the nitrosation of morpholine or morpholine derivatives which are used for several industrial purposes.
2-(Morpholinothio)benzothiazole is used as an accelerator/stabilizer for vulcanization, or the manufacture of rubber products. It is the precursor to NMOR in the vulcanization process, as it is nitrosated by ambient sources of the nitro group present in the manufacturing process. As such, workers and others exposed to the rubber industry or its byproducts are exposed to higher levels of NMOR than the general population, raising their risk of cancer. [ 5 ]
NMOR is a component of tobacco products. As of 2014, detectable levels of NMOR are present in tobacco products in the United States and China. [ 6 ] [ 7 ] The presence of NMOR and other n-nitrosoamines is not limited to cigarettes, but is found in smokeless tobacco products (snuff tobacco, Snus, etc.) as well. [ 8 ] Volatile nitrosamines, including NMOR, are detectable in the urine of tobacco smokers. [ 9 ]
Morpholine oleate is used in glazing wax which covers fruit. NMOR can be generated by the nitration of morpholine, causing its presence in waxed fruits. [ 10 ] [ 11 ] Health Canada , the Canadian governmental department of public health, has stated in 2002 that this does not pose a risk to human health. [ 12 ]
Consumption of nitrate-rich diets is correlated with levels of salivary and urinary NMOR. [ 13 ] The presence of NMOR can also be observed in gastric juices. [ 14 ]
NMOR has been found in several cosmetic products. [ 15 ] [ 16 ]
The mechanisms of carcinogenesis are not completely clear in humans. NMOR and its metabolites may induce DNA damage by directly forming reactive oxygen species or compounds which crosslink DNA. In a rat model in 2013, it was observed that NMOR is hydroxylated, probably by a P450 enzyme, alpha to the N-nitroso moiety. [ 17 ] This then decomposes into a diazonium-containing aldehyde which is capable of crosslinking DNA. [ 18 ]
Endogenous synthesis from morpholine in the digestive system is observed. NMOR can be generated from N-nitrosating species formed by salivary nitrite and stomach acid, potentially leading to more damage in individuals with acid reflux . [ 19 ] H. pylori does not induce NMOR formation in vitro, though this has yet to be confirmed in vivo. [ 20 ]
NMOR is in fact used to generate liver cancer models in rats. Along with N -diethylnitrosamine, it is the gold standard for producing hepatocarcinoma with 100% lung metastasis. [ 21 ] | https://en.wikipedia.org/wiki/N-Nitrosomorpholine |
N -Oxoammonium salts are a class of organic compounds with the formula [R 1 R 2 + N =O]X − . The cation [R 1 R 2 + N =O] is of interest for the dehydrogenation of alcohols. Oxoammonium salts are diamagnetic, whereas the nitroxide has a doublet ground state. A prominent N -oxoammonium salt is prepared by oxidation of (2,2,6,6-tetramethylpiperidin-1-yl)oxyl , commonly referred to as [TEMPO] + . A less expensive analogue is Bobbitt's salt .
Oxoammonium cations are isoelectronic with carbonyls and structurally related to aldoximes (hydroxylamines), and aminoxyl (nitroxide) radicals, with which they can interconvert via a series of redox steps. According to X-ray crystallography , the N–O distance in [TEMPO]BF 4 is 1.184 Å, 0.1 Å shorter than the N–O distance of 1.284 Å in the charge-neutral TEMPO. Similarly, the N in [TEMPO] + is nearly planar, but the O moves 0.1765 Å out of the plane in the neutral TEMPO. [ 1 ]
The N -oxoammonium salts are used for oxidation of alcohols to carbonyl groups, [ 2 ] as well as other forms of oxoammonium-catalyzed oxidations . The nitroxyl TEMPO reacts via its N -oxoammonium salt. [ 3 ]
This organic chemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N-Oxoammonium_salt |
N -Sulfinyl imines ( N -sulfinylimines , sulfinimines , thiooxime S -oxides ) are a class of imines bearing a sulfinyl group attached to nitrogen. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] These imines display useful stereoselectivity reactivity and due to the presence of the chiral electron withdrawing N -sulfinyl group. They allow 1,2-addition of organometallic reagents to imines. The N -sulfinyl group exerts powerful and predictable stereodirecting effects resulting in high levels of asymmetric induction . Racemization of the newly created carbon-nitrogen stereo center is prevented because anions are stabilized at nitrogen (i.e., the sulfinyl group is a versatile amine protection group). The sulfinyl chiral auxiliary is readily removed by simple acid hydrolysis . The addition of organometallic reagents to N -sulfinyl imines is the most reliable and versatile method for the asymmetric synthesis of amine derivatives. These building blocks have been employed in the asymmetric synthesis of numerous biologically active compounds. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ]
The first N -sulfinyl imines in racemic form were formed by oxidation of p -toluene-sulfenyl imines with m-CPBA . [ 9 ] Enantiopure p -toluene-sulfinyl imines arise by the reaction of the commercially available Andersen reagent (menthyl p -toluenesulfinate) [ 10 ] with metallo-ketimines but is limited to ketone derived N -sulfinyl imines. [ 11 ] A more general method for the preparation of N -sulfinyl imines is the asymmetric oxidation of achiral sulfenyl imines with a chiral oxaziridine . [ 12 ] The utility of this method is limited by the availability of the N -sulfonyloxaziridine, which is difficult to prepare. [ 13 ] More practical is the one-pot procedure from the Andersen reagent making a variety of p -toluene-sulfinyl imines available from both aromatic and aliphatic aldehydes. [ 14 ]
A widely used method for the asymmetric synthesis of N -sulfinyl imines is the condensation of enantiopure primary sulfinamides with aldehyde or ketones. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] A mild Lewis acid dehydrating reagents such as titanium ethoxide facilitate the condensation. [ 15 ] [ 16 ] Many sulfinamides are commercially available in both ( R )- and ( S )-forms. The two most commonly used are the Davis p -toluene-sulfinamide and the Ellman tert -butanesulfinamide [ 8 ] [ 15 ] [ 16 ]
The p -toluene-sulfinyl imines have been used for the highly diastereoselective asymmetric synthesis of α- amino acids , [ 18 ] [ 19 ] β-amino acids, [ 20 ] [ 21 ] syn- and anti-2,3-diamino esters, [ 22 ] α-amino aldehydes and ketones, [ 23 ] [ 24 ] β-amino ketones, [ 25 ] [ 26 ] α-amino phosphonates, [ 27 ] [ 28 ] aziridine 2-carboxylates, [ 29 ] [ 30 ] and aziridine 2-phosphonates. [ 31 ] Many of these same transformations can be carried out with tert-butylsulfinyl imines. [ 8 ] For the asymmetric synthesis of amines, tert-butylsulfinyl imines are required as lithium and Grignard reagents react at the sulfinyl sulfur in p -toluene-sulfinyl imines. [ 8 ] Mild acid treatment readily removes the N -sulfinyl group in the sulfinamide products affording the free amine derivatives. An advantage of tert-butylsulfinyl imines is that acid treatment of the corresponding sulfinamides leads to easily removal by-products [ 8 ] | https://en.wikipedia.org/wiki/N-Sulfinyl_imine |
An n -body choreography is a periodic solution to the n-body problem in which all the bodies are equally spread out along a single orbit . [ 1 ] The term was originated in 2000 by Chenciner and Montgomery. [ 1 ] [ 2 ] [ 3 ] One such orbit is a circular orbit, with equal masses at the corners of an equilateral triangle; another is the figure-8 orbit, first discovered numerically in 1993 by Cristopher Moore [ 4 ] and subsequently proved to exist by Chenciner and Montgomery. Choreographies can be discovered using variational methods , [ 1 ] and more recently, topological approaches have been used to attempt a classification in the planar case. [ 5 ] Having knowledge of specific solutions such as choreographies can be incredibly useful as it is not possible to solve the N-body problem for N > 2 through explicit means.
Numerical methods using computers have been crucial in the discovery and understanding of choreographies from their inception. In 1993, Moore employed a numerical implementation of the direct method from the calculus of variations to uncover the "eight" choreography. Later, during the rediscovery period between 1999 and 2000, Carles Simó dispelled doubts surrounding the validity of complex existence proofs through meticulous numerical investigations. [ 6 ]
The numerical implementation process can be distilled into a gradient search within a finite-dimensional approximation of the path space. One approach involves discretizing the path at uniform time intervals. Another effective method entails expressing the action as a function of the Fourier components of the choreography curve and truncating the Fourier series at a finite order. Convergence can be verified by increasing the truncation order and observing the alterations in the resulting minimizing Fourier coefficients. If these changes fall within a specified tolerance range, the result can be considered successful. For further refinements, consult the works of Simó or Moore and Nauenberg. [ 7 ]
In 2013, Montaldi and Steckles categorized all possible symmetry groups of planar 𝑛-body collision-free choreographies, which can be divided into two infinite families and, in the case of odd values of 𝑛, three exceptional groups. The second part of their study involves the development of the equivariant fundamental group, which is employed to identify the topology of the space of loops possessing a particular symmetry. They demonstrate that this topology is linked to certain cosets of the pure braid group in the full braid group, as well as the centralizers of elements within the corresponding coset. Furthermore, their work refines the symmetry classification by categorizing the connected components of the set of loops with a given symmetry, leading to the discovery of many new choreographies in 𝑛-body systems that are governed by a strong force potential. [ 8 ]
This classical mechanics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N-body_choreography |
In physics , the n -body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally . [ 1 ] Solving this problem has been motivated by the desire to understand the motions of the Sun , Moon , planets , and visible stars . In the 20th century, understanding the dynamics of globular cluster star systems became an important n -body problem. [ 2 ] The n -body problem in general relativity is considerably more difficult to solve due to additional factors like time and space distortions.
The classical physical problem can be informally stated as the following:
Given the quasi-steady orbital properties (instantaneous position, velocity and time) [ 3 ] of a group of celestial bodies, predict their interactive forces; and consequently, predict their true orbital motions for all future times. [ 4 ]
The two-body problem has been completely solved and is discussed below, as well as the famous restricted three-body problem . [ 5 ]
Knowing three orbital positions of a planet's orbit – positions obtained by Sir Isaac Newton from astronomer John Flamsteed [ 6 ] – Newton was able to produce an equation by straightforward analytical geometry, to predict a planet's motion; i.e., to give its orbital properties: position, orbital diameter, period and orbital velocity. [ 7 ] Having done so, he and others soon discovered over the course of a few years, those equations of motion did not predict some orbits correctly or even very well. [ 8 ] Newton realized that this was because gravitational interactive forces amongst all the planets were affecting all their orbits.
The aforementioned revelation strikes directly at the core of what the n-body issue physically is: as Newton understood, it is not enough to just provide the beginning location and velocity, or even three orbital positions, in order to establish a planet's actual orbit; one must also be aware of the gravitational interaction forces. Thus came the awareness and rise of the n -body "problem" in the early 17th century. These gravitational attractive forces do conform to Newton's laws of motion and to his law of universal gravitation, but the many multiple ( n -body) interactions have historically made any exact solution intractable. Ironically, this conformity led to the wrong approach.
After Newton's time the n -body problem historically was not stated correctly because it did not include a reference to those gravitational interactive forces. Newton does not say it directly but implies in his Principia the n -body problem is unsolvable because of those gravitational interactive forces. [ 9 ] Newton said [ 10 ] in his Principia , paragraph 21:
And hence it is that the attractive force is found in both bodies. The Sun attracts Jupiter and the other planets, Jupiter attracts its satellites and similarly the satellites act on one another. And although the actions of each of a pair of planets on the other can be distinguished from each other and can be considered as two actions by which each attracts the other, yet inasmuch as they are between the same, two bodies they are not two but a simple operation between two termini. Two bodies can be drawn to each other by the contraction of rope between them. The cause of the action is twofold, namely the disposition of each of the two bodies; the action is likewise twofold, insofar as it is upon two bodies; but insofar as it is between two bodies it is single and one ...
Newton concluded via his third law of motion that "according to this Law all bodies must attract each other." This last statement, which implies the existence of gravitational interactive forces, is key.
As shown below, the problem also conforms to Jean Le Rond D'Alembert 's non-Newtonian first and second Principles and to the nonlinear n -body problem algorithm, the latter allowing for a closed form solution for calculating those interactive forces.
The problem of finding the general solution of the n -body problem was considered very important and challenging. Indeed, in the late 19th century King Oscar II of Sweden , advised by Gösta Mittag-Leffler , established a prize for anyone who could find the solution to the problem. The announcement was quite specific:
Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly .
In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prizeworthy. The prize was awarded to Poincaré , even though he did not solve the original problem. (The first version of his contribution even contained a serious error. [ 11 ] ) The version finally printed contained many important ideas which led to the development of chaos theory . The problem as stated originally was finally solved by Karl Fritiof Sundman for n = 3 and generalized to n > 3 by L. K. Babadzanjanz [ 12 ] [ 13 ] and Qiudong Wang . [ 14 ]
The n -body problem considers n point masses m i , i = 1, 2, …, n in an inertial reference frame in three dimensional space ℝ 3 moving under the influence of mutual gravitational attraction. Each mass m i has a position vector q i . Newton's second law says that mass times acceleration m i d 2 q i / dt 2 is equal to the sum of the forces on the mass. Newton's law of gravity says that the gravitational force felt on mass m i by a single mass m j is given by [ 15 ] F i j = G m i m j ‖ q j − q i ‖ 2 ⋅ ( q j − q i ) ‖ q j − q i ‖ = G m i m j ( q j − q i ) ‖ q j − q i ‖ 3 , {\displaystyle \mathbf {F} _{ij}={\frac {Gm_{i}m_{j}}{\left\|\mathbf {q} _{j}-\mathbf {q} _{i}\right\|^{2}}}\cdot {\frac {\left(\mathbf {q} _{j}-\mathbf {q} _{i}\right)}{\left\|\mathbf {q} _{j}-\mathbf {q} _{i}\right\|}}={\frac {Gm_{i}m_{j}\left(\mathbf {q} _{j}-\mathbf {q} _{i}\right)}{\left\|\mathbf {q} _{j}-\mathbf {q} _{i}\right\|^{3}}},} where G is the gravitational constant and ‖ q j − q i ‖ is the magnitude of the distance between q i and q j ( metric induced by the l 2 norm ).
Summing over all masses yields the n -body equations of motion :
m i d 2 q i d t 2 = ∑ j = 1 j ≠ i n G m i m j ( q j − q i ) ‖ q j − q i ‖ 3 = − ∂ U ∂ q i {\displaystyle m_{i}{\frac {d^{2}\mathbf {q} _{i}}{dt^{2}}}=\sum _{j=1 \atop j\neq i}^{n}{\frac {Gm_{i}m_{j}\left(\mathbf {q} _{j}-\mathbf {q} _{i}\right)}{\left\|\mathbf {q} _{j}-\mathbf {q} _{i}\right\|^{3}}}=-{\frac {\partial U}{\partial \mathbf {q} _{i}}}}
where U is the self-potential energy
U = − ∑ 1 ≤ i < j ≤ n G m i m j ‖ q j − q i ‖ . {\displaystyle U=-\sum _{1\leq i<j\leq n}{\frac {Gm_{i}m_{j}}{\left\|\mathbf {q} _{j}-\mathbf {q} _{i}\right\|}}.}
Defining the momentum to be p i = m i d q i / dt , Hamilton's equations of motion for the n -body problem become [ 16 ] d q i d t = ∂ H ∂ p i d p i d t = − ∂ H ∂ q i , {\displaystyle {\frac {d\mathbf {q} _{i}}{dt}}={\frac {\partial H}{\partial \mathbf {p} _{i}}}\qquad {\frac {d\mathbf {p} _{i}}{dt}}=-{\frac {\partial H}{\partial \mathbf {q} _{i}}},} where the Hamiltonian function is H = T + U {\displaystyle H=T+U} and T is the kinetic energy T = ∑ i = 1 n ‖ p i ‖ 2 2 m i . {\displaystyle T=\sum _{i=1}^{n}{\frac {\left\|\mathbf {p} _{i}\right\|^{2}}{2m_{i}}}.}
Hamilton's equations show that the n -body problem is a system of 6 n first-order differential equations , with 6 n initial conditions as 3 n initial position coordinates and 3 n initial momentum values.
Symmetries in the n -body problem yield global integrals of motion that simplify the problem. [ 17 ] Translational symmetry of the problem results in the center of mass C = ∑ i = 1 n m i q i ∑ i = 1 n m i {\displaystyle \mathbf {C} ={\frac {\displaystyle \sum _{i=1}^{n}m_{i}\mathbf {q} _{i}}{\displaystyle \sum _{i=1}^{n}m_{i}}}} moving with constant velocity, so that C = L 0 t + C 0 , where L 0 is the linear velocity and C 0 is the initial position. The constants of motion L 0 and C 0 represent six integrals of the motion. Rotational symmetry results in the total angular momentum being constant A = ∑ i = 1 n q i × p i , {\displaystyle \mathbf {A} =\sum _{i=1}^{n}\mathbf {q} _{i}\times \mathbf {p} _{i},} where × is the cross product . The three components of the total angular momentum A yield three more constants of the motion. The last general constant of the motion is given by the conservation of energy H . Hence, every n -body problem has ten integrals of motion.
Because T and U are homogeneous functions of degree 2 and −1, respectively, the equations of motion have a scaling invariance : if q i ( t ) is a solution, then so is λ −2/3 q i ( λt ) for any λ > 0 . [ 18 ]
The moment of inertia of an n -body system is given by I = ∑ i = 1 n m i q i ⋅ q i = ∑ i = 1 n m i ‖ q i ‖ 2 {\displaystyle I=\sum _{i=1}^{n}m_{i}\mathbf {q} _{i}\cdot \mathbf {q} _{i}=\sum _{i=1}^{n}m_{i}\left\|\mathbf {q} _{i}\right\|^{2}} and the virial is given by Q = 1 / 2 dI / dt . Then the Lagrange–Jacobi formula states that [ 19 ] d 2 I d t 2 = 2 T − U . {\displaystyle {\frac {d^{2}I}{dt^{2}}}=2T-U.}
For systems in dynamic equilibrium , the longterm time average of ⟨ d 2 I / dt 2 ⟩ is zero. Then on average the total kinetic energy is half the total potential energy, ⟨ T ⟩ = 1 / 2 ⟨ U ⟩ , which is an example of the virial theorem for gravitational systems. [ 20 ] If M is the total mass and R a characteristic size of the system (for example, the radius containing half the mass of the system), then the critical time for a system to settle down to a dynamic equilibrium is [ 21 ] t c r = ( G M R 3 ) − 1 / 2 . {\displaystyle t_{\mathrm {cr} }=\left({\frac {GM}{R^{3}}}\right)^{-1/2}.}
Any discussion of planetary interactive forces has always started historically with the two-body problem. The purpose of this section is to relate the real complexity in calculating any planetary forces. Note in this Section also, several subjects, such as gravity , barycenter , Kepler's Laws , etc.; and in the following Section too ( Three-body problem ) are discussed on other Wikipedia pages. Here though, these subjects are discussed from the perspective of the n -body problem.
The two-body problem ( n = 2 ) was completely solved by Johann Bernoulli (1667–1748) by classical theory (and not by Newton) by assuming the main point-mass was fixed; this is outlined here. [ 22 ] Consider then the motion of two bodies, say the Sun and the Earth, with the Sun fixed, then: m 1 a 1 = G m 1 m 2 r 12 3 ( r 2 − r 1 ) Sun–Earth m 2 a 2 = G m 1 m 2 r 21 3 ( r 1 − r 2 ) Earth–Sun {\displaystyle {\begin{aligned}m_{1}\mathbf {a} _{1}&={\frac {Gm_{1}m_{2}}{r_{12}^{3}}}(\mathbf {r} _{2}-\mathbf {r} _{1})&&\quad {\text{Sun–Earth}}\\m_{2}\mathbf {a} _{2}&={\frac {Gm_{1}m_{2}}{r_{21}^{3}}}(\mathbf {r} _{1}-\mathbf {r} _{2})&&\quad {\text{Earth–Sun}}\end{aligned}}}
The equation describing the motion of mass m 2 relative to mass m 1 is readily obtained from the differences between these two equations and after canceling common terms gives: α + η r 3 r = 0 {\displaystyle \mathbf {\alpha } +{\frac {\eta }{r^{3}}}\mathbf {r} =\mathbf {0} } Where
The equation α + η / r 3 r = 0 is the fundamental differential equation for the two-body problem Bernoulli solved in 1734. Notice for this approach forces have to be determined first, then the equation of motion resolved. This differential equation has elliptic, or parabolic or hyperbolic solutions. [ 23 ] [ 24 ] [ 25 ]
It is incorrect to think of m 1 (the Sun) as fixed in space when applying Newton's law of universal gravitation, and to do so leads to erroneous results. The fixed point for two isolated gravitationally interacting bodies is their mutual barycenter , and this two-body problem can be solved exactly, such as using Jacobi coordinates relative to the barycenter.
Dr. Clarence Cleminshaw calculated the approximate position of the Solar System's barycenter, a result achieved mainly by combining only the masses of Jupiter and the Sun. Science Program stated in reference to his work:
The Sun contains 98 per cent of the mass in the solar system, with the superior planets beyond Mars accounting for most of the rest. On the average, the center of the mass of the Sun–Jupiter system, when the two most massive objects are considered alone, lies 462,000 miles from the Sun's center, or some 30,000 miles above the solar surface! Other large planets also influence the center of mass of the solar system, however. In 1951, for example, the systems' center of mass was not far from the Sun's center because Jupiter was on the opposite side from Saturn, Uranus and Neptune. In the late 1950s, when all four of these planets were on the same side of the Sun, the system's center of mass was more than 330,000 miles from the solar surface, Dr. C. H. Cleminshaw of Griffith Observatory in Los Angeles has calculated. [ 26 ]
The Sun wobbles as it rotates around the Galactic Center , dragging the Solar System and Earth along with it. What mathematician Kepler did in arriving at his three famous equations was curve-fit the apparent motions of the planets using Tycho Brahe 's data, and not curve-fitting their true circular motions about the Sun (see figure). Both Robert Hooke and Newton were well aware that Newton's Law of Universal Gravitation did not hold for the forces associated with elliptical orbits. [ 10 ] In fact, Newton's Universal Law does not account for the orbit of Mercury, the asteroid belt's gravitational behavior, or Saturn's rings . [ 27 ] Newton stated (in section 11 of the Principia ) that the main reason, however, for failing to predict the forces for elliptical orbits was that his math model was for a body confined to a situation that hardly existed in the real world, namely, the motions of bodies attracted toward an unmoving center. Some present physics and astronomy textbooks do not emphasize the negative significance of Newton's assumption and end up teaching that his mathematical model is in effect reality. It is to be understood that the classical two-body problem solution above is a mathematical idealization . See also Kepler's first law of planetary motion .
This section relates a historically important n -body problem solution after simplifying assumptions were made.
In the past not much was known about the n -body problem for n ≥ 3 . [ 28 ] The case n = 3 has been the most studied. Many earlier attempts to understand the three-body problem were quantitative, aiming at finding explicit solutions for special situations.
Moulton's solution may be easier to visualize (and definitely easier to solve) if one considers the more massive body (such as the Sun ) to be stationary in space, and the less massive body (such as Jupiter ) to orbit around it, with the equilibrium points ( Lagrangian points ) maintaining the 60° spacing ahead of, and behind, the less massive body almost in its orbit (although in reality neither of the bodies are truly stationary, as they both orbit the center of mass of the whole system—about the barycenter). For sufficiently small mass ratio of the primaries, these triangular equilibrium points are stable, such that (nearly) massless particles will orbit about these points as they orbit around the larger primary (Sun). The five equilibrium points of the circular problem are known as the Lagrangian points. See figure below:
In the restricted three-body problem math model figure above (after Moulton), the Lagrangian points L 4 and L 5 are where the Trojan planetoids resided (see Lagrangian point ); m 1 is the Sun and m 2 is Jupiter. L 2 is a point within the asteroid belt. It has to be realized for this model, this whole Sun-Jupiter diagram is rotating about its barycenter. The restricted three-body problem solution predicted the Trojan planetoids before they were first seen. The h -circles and closed loops echo the electromagnetic fluxes issued from the Sun and Jupiter. It is conjectured, contrary to Richard H. Batin's conjecture (see References), the two h 1 are gravity sinks, in and where gravitational forces are zero, and the reason the Trojan planetoids are trapped there. The total amount of mass of the planetoids is unknown.
The restricted three-body problem assumes the mass of one of the bodies is negligible. [ citation needed ] For a discussion of the case where the negligible body is a satellite of the body of lesser mass, see Hill sphere ; for binary systems, see Roche lobe . Specific solutions to the three-body problem result in chaotic motion with no obvious sign of a repetitious path. [ citation needed ]
The restricted problem (both circular and elliptical) was worked on extensively by many famous mathematicians and physicists, most notably by Poincaré at the end of the 19th century. Poincaré's work on the restricted three-body problem was the foundation of deterministic chaos theory. [ citation needed ] In the restricted problem, there exist five equilibrium points . Three are collinear with the masses (in the rotating frame) and are unstable. The remaining two are located on the third vertex of both equilateral triangles of which the two bodies are the first and second vertices.
Inspired by the circular restricted three-body problem, the four-body problem can be greatly simplified by considering a smaller body to have a small mass compared to the other three massive bodies, which in turn are approximated to describe circular orbits. This is known as the bicircular restricted four-body problem (also known as bicircular model) and it can be traced back to 1960 in a NASA report written by Su-Shu Huang. [ 31 ] This formulation has been highly relevant in the astrodynamics , mainly to model spacecraft trajectories in the Earth-Moon system with the addition of the gravitational attraction of the Sun. The former formulation of the bicircular restricted four-body problem can be problematic when modelling other systems than the Earth-Moon-Sun, so the formulation was generalized by Negri and Prado [ 32 ] to expand the application range and improve the accuracy without loss of simplicity.
The planetary problem is the n -body problem in the case that one of the masses is much larger than all the others. A prototypical example of a planetary problem is the Sun– Jupiter – Saturn system, where the mass of the Sun is about 1000 times larger than the masses of Jupiter or Saturn. [ 18 ] An approximate solution to the problem is to decompose it into n − 1 pairs of star–planet Kepler problems , treating interactions among the planets as perturbations. Perturbative approximation works well as long as there are no orbital resonances in the system, that is none of the ratios of unperturbed Kepler frequencies is a rational number. Resonances appear as small denominators in the expansion.
The existence of resonances and small denominators led to the important question of stability in the planetary problem: do planets, in nearly circular orbits around a star, remain in stable or bounded orbits over time? [ 18 ] [ 33 ] In 1963, Vladimir Arnold proved using KAM theory a kind of stability of the planetary problem: there exists a set of positive measure of quasiperiodic orbits in the case of the planetary problem restricted to the plane. [ 33 ] In the KAM theory, chaotic planetary orbits would be bounded by quasiperiodic KAM tori. Arnold's result was extended to a more general theorem by Féjoz and Herman in 2004. [ 34 ]
A central configuration q 1 (0), …, q N (0) is an initial configuration such that if the particles were all released with zero velocity, they would all collapse toward the center of mass C . [ 33 ] Such a motion is called homothetic . Central configurations may also give rise to homographic motions in which all masses moves along Keplerian trajectories (elliptical, circular, parabolic, or hyperbolic), with all trajectories having the same eccentricity e . For elliptical trajectories, e = 1 corresponds to homothetic motion and e = 0 gives a relative equilibrium motion in which the configuration remains an isometry of the initial configuration, as if the configuration was a rigid body. [ 35 ] Central configurations have played an important role in understanding the topology of invariant manifolds created by fixing the first integrals of a system.
Solutions in which all masses move on the same curve without collisions are called choreographies. [ 36 ] A choreography for n = 3 was discovered by Lagrange in 1772 in which three bodies are situated at the vertices of an equilateral triangle in the rotating frame. A figure eight choreography for n = 3 was found numerically by C. Moore in 1993 [ 37 ] and generalized and proven by A. Chenciner and R. Montgomery in 2000. [ 38 ] Since then, many other choreographies have been found for n ≥ 3 .
For every solution of the problem, not only applying an isometry or a time shift but also a reversal of time (unlike in the case of friction) gives a solution as well. [ citation needed ]
In the physical literature about the n -body problem ( n ≥ 3 ), sometimes reference is made to "the impossibility of solving the n -body problem" (via employing the above approach). [ citation needed ] However, care must be taken when discussing the 'impossibility' of a solution, as this refers only to the method of first integrals (compare the theorems by Abel and Galois about the impossibility of solving algebraic equations of degree five or higher by means of formulas only involving roots).
One way of solving the classical n -body problem is "the n -body problem by Taylor series ".
We start by defining the system of differential equations : [ citation needed ] d 2 x i ( t ) d t 2 = G ∑ k = 1 k ≠ i n m k ( x k ( t ) − x i ( t ) ) | x k ( t ) − x i ( t ) | 3 , {\displaystyle {\frac {d^{2}\mathbf {x} _{i}(t)}{dt^{2}}}=G\sum _{k=1 \atop k\neq i}^{n}{\frac {m_{k}\left(\mathbf {x} _{k}(t)-\mathbf {x} _{i}(t)\right)}{\left|\mathbf {x} _{k}(t)-\mathbf {x} _{i}(t)\right|^{3}}},}
As x i ( t 0 ) and d x i ( t 0 ) / dt are given as initial conditions, every d 2 x i ( t ) / dt 2 is known. Differentiating d 2 x i ( t ) / dt 2 results in d 3 x i ( t ) / dt 3 which at t 0 which is also known, and the Taylor series is constructed iteratively. [ clarification needed ]
In order to generalize Sundman's result for the case n > 3 (or n = 3 and c = 0 [ clarification needed ] ) one has to face two obstacles:
Lastly, Sundman's result was generalized to the case of n > 3 bodies by Qiudong Wang in the 1990s. [ 39 ] Since the structure of singularities is more complicated, Wang had to leave out completely the questions of singularities. The central point of his approach is to transform, in an appropriate manner, the equations to a new system, such that the interval of existence for the solutions of this new system is [0,∞) .
There can be two types of singularities of the n -body problem:
The latter ones are called Painlevé's conjecture (no-collisions singularities). Their existence has been conjectured for n > 3 by Painlevé (see Painlevé conjecture ). Examples of this behavior for n = 5 have been constructed by Xia [ 40 ] and a heuristic model for n = 4 by Gerver. [ 41 ] Donald G. Saari has shown that for 4 or fewer bodies, the set of initial data giving rise to singularities has measure zero. [ 42 ]
While there are analytic solutions available for the classical (i.e. nonrelativistic) two-body problem and for selected configurations with n > 2 , in general n -body problems must be solved or simulated using numerical methods. [ 21 ]
For a small number of bodies, an n -body problem can be solved using direct methods , also called particle–particle methods . These methods numerically integrate the differential equations of motion. Numerical integration for this problem can be a challenge for several reasons. First, the gravitational potential is singular; it goes to infinity as the distance between two particles goes to zero. The gravitational potential may be "softened" to remove the singularity at small distances: [ 21 ] U ε = ∑ 1 ≤ i < j ≤ n G m i m j ‖ q j − q i ‖ 2 + ε 2 {\displaystyle U_{\varepsilon }=\sum _{1\leq i<j\leq n}{\frac {Gm_{i}m_{j}}{\sqrt {\left\|\mathbf {q} _{j}-\mathbf {q} _{i}\right\|^{2}+\varepsilon ^{2}}}}} Second, in general for n > 2 , the n -body problem is chaotic , [ 43 ] which means that even small errors in integration may grow exponentially in time. Third, a simulation may be over large stretches of model time (e.g. millions of years) and numerical errors accumulate as integration time increases.
There are a number of techniques to reduce errors in numerical integration. [ 21 ] Local coordinate systems are used to deal with widely differing scales in some problems, for example an Earth–Moon coordinate system in the context of a solar system simulation. Variational methods and perturbation theory can yield approximate analytic trajectories upon which the numerical integration can be a correction. The use of a symplectic integrator ensures that the simulation obeys Hamilton's equations to a high degree of accuracy and in particular that energy is conserved.
Direct methods using numerical integration require on the order of 1 / 2 n 2 computations to evaluate the potential energy over all pairs of particles, and thus have a time complexity of O ( n 2 ) . For simulations with many particles, the O ( n 2 ) factor makes large-scale calculations especially time-consuming. [ 21 ]
A number of approximate methods have been developed that reduce the time complexity relative to direct methods: [ 21 ]
In astrophysical systems with strong gravitational fields, such as those near the event horizon of a black hole , n -body simulations must take into account general relativity ; such simulations are the domain of numerical relativity . Numerically simulating the Einstein field equations is extremely challenging [ 21 ] and a parameterized post-Newtonian formalism (PPN), such as the Einstein–Infeld–Hoffmann equations , is used if possible. The two-body problem in general relativity is analytically solvable only for the Kepler problem, in which one mass is assumed to be much larger than the other. [ 44 ]
Most work done on the n -body problem has been on the gravitational problem. But there exist other systems for which n -body mathematics and simulation techniques have proven useful.
In large scale electrostatics problems, such as the simulation of proteins and cellular assemblies in structural biology , the Coulomb potential has the same form as the gravitational potential, except that charges may be positive or negative, leading to repulsive as well as attractive forces. [ 45 ] Fast Coulomb solvers are the electrostatic counterpart to fast multipole method simulators. These are often used with periodic boundary conditions on the region simulated and Ewald summation techniques are used to speed up computations. [ 46 ]
In statistics and machine learning , some models have loss functions of a form similar to that of the gravitational potential: a sum of kernel functions over all pairs of objects, where the kernel function depends on the distance between the objects in parameter space. [ 47 ] Example problems that fit into this form include all-nearest-neighbors in manifold learning , kernel density estimation , and kernel machines . Alternative optimizations to reduce the O ( n 2 ) time complexity to O ( n ) have been developed, such as dual tree algorithms, that have applicability to the gravitational n -body problem as well.
A technique in Computational fluid dynamics called Vortex Methods sees the vorticity in a fluid domain discretized onto particles which are then advected with the velocity at their centers. Because the fluid velocity and vorticity are related via a Poisson's equation , the velocity can be solved in the same manner as gravitation and electrostatics: as an n -body summation over all vorticity-containing particles. The summation uses the Biot-Savart law , with vorticity taking the place of electrical current. [ 48 ] In the context of particle-laden turbulent multiphase flows, determining an overall disturbance field generated by all particles is an n -body problem. If the particles translating within the flow are much smaller than the flow's Kolmogorov scale, their linear Stokes disturbance fields can be superposed, yielding a system of 3 n equations for 3 components of disturbance velocities at the location of n particles. [ 49 ] [ 50 ] | https://en.wikipedia.org/wiki/N-body_problem |
In physics and astronomy , an N -body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity (see n -body problem for other applications). N -body simulations are widely used tools in astrophysics , from investigating the dynamics of few-body systems like the Earth - Moon - Sun system to understanding the evolution of the large-scale structure of the universe . [ 1 ] In physical cosmology , N -body simulations are used to study processes of non-linear structure formation such as galaxy filaments and galaxy halos from the influence of dark matter . Direct N -body simulations are used to study the dynamical evolution of star clusters .
The 'particles' treated by the simulation may or may not correspond to physical objects which are particulate in nature. For example, an N-body simulation of a star cluster might have a particle per star, so each particle has some physical significance. On the other hand, a simulation of a gas cloud cannot afford to have a particle for each atom or molecule of gas as this would require on the order of 10 23 particles for each mole of material (see Avogadro constant ), so a single 'particle' would represent some much larger quantity of gas (often implemented using Smoothed Particle Hydrodynamics ). This quantity need not have any physical significance, but must be chosen as a compromise between accuracy and manageable computer requirements.
Dark matter plays an important role in the formation of galaxies. The time evolution of the density f (in phase space) of dark matter particles, can be described by the collisionless Boltzmann equation
d f d t = ∂ f ∂ t + v ⋅ ∇ f − ∂ f ∂ v ⋅ ∇ Φ {\displaystyle {\frac {df}{dt}}={\frac {\partial f}{\partial t}}+\mathbf {v} \cdot \nabla f-{\frac {\partial f}{\partial \mathbf {v} }}\cdot \nabla \Phi }
In the equation, v {\displaystyle \mathbf {v} } is the velocity, and Φ is the gravitational potential given by Poisson's Equation . These two coupled equations are solved in an expanding background Universe, which is governed by the Friedmann equations , after determining the initial conditions of dark matter particles. The conventional method employed for initializing positions and velocities of dark matter particles involves moving particles within a uniform Cartesian lattice or a glass-like particle configuration. [ 2 ] This is done by using a linear theory approximation or a low-order perturbation theory . [ 3 ]
In direct gravitational N -body simulations, the equations of motion of a system of N particles under the influence of their mutual gravitational forces are integrated numerically without any simplifying approximations. These calculations are used in situations where interactions between individual objects, such as stars or planets, are important to the evolution of the system.
The first direct gravitational N -body simulations were carried out by Erik Holmberg at the Lund Observatory in 1941, determining the forces between stars in encountering galaxies via the mathematical equivalence between light propagation and gravitational interaction: putting light bulbs at the positions of the stars and measuring the directional light fluxes at the positions of the stars by a photo cell, the equations of motion can be integrated with O ( N ) {\displaystyle O(N)} effort. [ 4 ] The first purely calculational simulations were then done by Sebastian von Hoerner at the Astronomisches Rechen-Institut in Heidelberg , Germany. Sverre Aarseth at the University of Cambridge (UK) dedicated his entire scientific life to the development of a series of highly efficient N -body codes for astrophysical applications which use adaptive (hierarchical) time steps, an Ahmad-Cohen neighbour scheme and regularization of close encounters. Regularization is a mathematical trick to remove the singularity in the Newtonian law of gravitation for two particles which approach each other arbitrarily close. Sverre Aarseth's codes are used to study the dynamics of star clusters, planetary systems and galactic nuclei. [ citation needed ]
Many simulations are large enough that the effects of general relativity in establishing a Friedmann-Lemaitre-Robertson-Walker cosmology are significant. This is incorporated in the simulation as an evolving measure of distance (or scale factor ) in a comoving coordinate system, which causes the particles to slow in comoving coordinates (as well as due to the redshifting of their physical energy). However, the contributions of general relativity and the finite speed of gravity can otherwise be ignored, as typical dynamical timescales are long compared to the light crossing time for the simulation, and the space-time curvature induced by the particles and the particle velocities are small. The boundary conditions of these cosmological simulations are usually periodic (or toroidal), so that one edge of the simulation volume matches up with the opposite edge.
N -body simulations are simple in principle, because they involve merely integrating the 6 N ordinary differential equations defining the particle motions in Newtonian gravity . In practice, the number N of particles involved is usually very large (typical simulations include many millions, the Millennium simulation included ten billion) and the number of particle-particle interactions needing to be computed increases on the order of N 2 , and so direct integration of the differential equations can be prohibitively computationally expensive. Therefore, a number of refinements are commonly used.
Numerical integration is usually performed over small timesteps using a method such as leapfrog integration . However all numerical integration leads to errors. Smaller steps give lower errors but run more slowly. Leapfrog integration is roughly 2nd order on the timestep, other integrators such as Runge–Kutta methods can have 4th order accuracy or much higher.
One of the simplest refinements is that each particle carries with it its own timestep variable, so that particles with widely different dynamical times don't all have to be evolved forward at the rate of that with the shortest time.
There are two basic approximation schemes to decrease the computational time for such simulations. These can reduce the computational complexity to O(N log N) or better, at the loss of accuracy.
In tree methods , such as a Barnes–Hut simulation , an octree is usually used to divide the volume into cubic cells and only interactions between particles from nearby cells need to be treated individually; particles in distant cells can be treated collectively as a single large particle centered at the distant cell's center of mass (or as a low-order multipole expansion). This can dramatically reduce the number of particle pair interactions that must be computed. To prevent the simulation from becoming swamped by computing particle-particle interactions, the cells must be refined to smaller cells in denser parts of the simulation which contain many particles per cell. For simulations where particles are not evenly distributed, the well-separated pair decomposition methods of Callahan and Kosaraju yield optimal O( n log n ) time per iteration with fixed dimension.
Another possibility is the particle mesh method in which space is discretised on a mesh and, for the purposes of computing the gravitational potential , particles are assumed to be divided between the surrounding 2x2 vertices of the mesh. The potential energy Φ can be found with the Poisson equation
∇ 2 Φ = 4 π G ρ , {\displaystyle \nabla ^{2}\Phi =4\pi G{\rho },\,}
where G is Newton's constant and ρ {\displaystyle \rho } is the density (number of particles at the mesh points). The fast Fourier transform can solve this efficiently by going to the frequency domain where the Poisson equation has the simple form
Φ ^ = − 4 π G ρ ^ k 2 , {\displaystyle {\hat {\Phi }}=-4\pi G{\frac {\hat {\rho }}{k^{2}}},}
where k → {\displaystyle {\vec {k}}} is the comoving wavenumber and the hats denote Fourier transforms. Since g → = − ∇ → Φ {\displaystyle {\vec {g}}=-{\vec {\nabla }}\Phi } , the gravitational field can now be found by multiplying by − i k → {\displaystyle -i{\vec {k}}} and computing the inverse Fourier transform (or computing the inverse transform and then using some other method). Since this method is limited by the mesh size, in practice a smaller mesh or some other technique (such as combining with a tree or simple particle-particle algorithm) is used to compute the small-scale forces. Sometimes an adaptive mesh is used, in which the mesh cells are much smaller in the denser regions of the simulation.
Several different gravitational perturbation algorithms are used to get fairly accurate estimates of the path of objects in the Solar System .
People often decide to put a satellite in a frozen orbit .
The path of a satellite closely orbiting the Earth can be accurately modeled starting from the 2-body elliptical orbit around the center of the Earth, and adding small corrections due to the oblateness of the Earth , gravitational attraction of the Sun and Moon, atmospheric drag, etc.
It is possible to find a frozen orbit without calculating the actual path of the satellite.
The path of a small planet, comet, or long-range spacecraft can often be accurately modeled starting from the 2-body elliptical orbit around the Sun, and adding small corrections from the gravitational attraction of the larger planets in their known orbits.
Some characteristics of the long-term paths of a system of particles can be calculated directly. The actual path of any particular particle does not need to be calculated as an intermediate step. Such characteristics include Lyapunov stability , Lyapunov time , various measurements from ergodic theory , etc.
Although there are millions or billions of particles in typical simulations, they typically correspond to a real particle with a very large mass, typically 10 9 solar masses . This can introduce problems with short-range interactions between the particles such as the formation of two-particle binary systems. As the particles are meant to represent large numbers of dark matter particles or groups of stars, these binaries are unphysical. To prevent this, a softened Newtonian force law is used, which does not diverge as the inverse-square radius at short distances. Most simulations implement this quite naturally by running the simulations on cells of finite size. It is important to implement the discretization procedure in such a way that particles always exert a vanishing force on themselves.
Softening is a numerical trick used in N-body techniques to prevent numerical divergences when a particle comes too close to another (and the force goes to infinity). This is obtained by modifying the regularized gravitational potential of each particle as
Φ = − 1 r 2 + ϵ 2 , {\displaystyle \Phi =-{\frac {1}{\sqrt {r^{2}+\epsilon ^{2}}}},}
(rather than 1/r) where ϵ {\displaystyle \epsilon } is the softening parameter. The value of the softening parameter should be set small enough to keep simulations realistic.
N -body simulations give findings on the large-scale dark matter distribution and the structure of dark matter halos. According to simulations of cold dark matter, the overall distribution of dark matter on a large scale is not entirely uniform. Instead, it displays a structure resembling a network, consisting of voids, walls, filaments, and halos. Also, simulations show that the relationship between the concentration of halos and factors such as mass, initial fluctuation spectrum, and cosmological parameters is linked to the actual formation time of the halos. [ 5 ] In particular, halos with lower mass tend to form earlier, and as a result, have higher concentrations due to the higher density of the Universe at the time of their formation. Shapes of halos are found to deviate from being perfectly spherical. Typically, halos are found to be elongated and become increasingly prolate towards their centers. However, interactions between dark matter and baryons would affect the internal structure of dark matter halos. Simulations that model both dark matters and baryons are needed to study small-scale structures.
Many simulations simulate only cold dark matter , and thus include only the gravitational force. Incorporating baryons , leptons and photons into the simulations dramatically increases their complexity and often radical simplifications of the underlying physics must be made. However, this is an extremely important area and many modern simulations are now trying to understand processes that occur during galaxy formation which could account for galaxy bias .
Reif and Tate [ 6 ] prove that if the n -body reachability problem is defined as follows – given n bodies satisfying a fixed electrostatic potential law, determining if a body reaches a destination ball in a given time bound where we require a poly( n ) bits of accuracy and the target time is poly( n ) is in PSPACE .
On the other hand, if the question is whether the body eventually reaches the destination ball, the problem is PSPACE-hard. These bounds are based on similar complexity bounds obtained for ray tracing .
The simplest implementation of N-body simulations where n ≥ 3 {\textstyle n\geq 3} is a naive propagation of orbiting bodies; naive implying that the only forces acting on the orbiting bodies is the gravitational force which they exert on each other. In object-oriented programming languages, such as C++ , some boilerplate code is useful for establishing the fundamental mathematical structures as well as data containers required for propagation; namely state vectors , and thus vectors , and some fundamental object containing this data, as well as the mass of an orbiting body. This method is applicable to other types of N-body simulations as well; a simulation of point masses with charges would use a similar method, however the force would be due to attraction or repulsion by interaction of electric fields. Regardless, acceleration of particle is a result of summed force vectors, divided by the mass of the particle:
a → = 1 m ∑ F → {\displaystyle {\vec {a}}={\frac {1}{m}}\sum {\vec {F}}}
An example of a programmatically stable and scalable method for containing kinematic data for a particle is the use of fixed length arrays, which in optimised code allows for easy memory allocation and prediction of consumed resources; as seen in the following C++ code:
Note that OrbitalEntity contains enough room for a state vector, where:
Additionally, OrbitalEntity contains enough room for a mass value.
Commonly, N-body simulations will be systems based on some type of equations of motion ; of these, most will be dependent on some initial configuration to "seed" the simulation. In systems such as those dependent on some gravitational or electric potential, the force on a simulation entity is independent on its velocity. Hence, to seed the forces of the simulation, merely initial positions are needed, but this will not allow propagation- initial velocities are required. Consider a planet orbiting a star- it has no motion, but is subject to gravitational attraction to its host star. As a time progresses, and time steps are added, it will gather velocity according to its acceleration. For a given instant in time, t n {\displaystyle t_{n}} , the resultant acceleration of a body due to its neighbouring masses is independent of its velocity, however, for the time step t n + 1 {\displaystyle t_{n+1}} , the resulting change in position is significantly different due the propagation's inherent dependency on velocity. In basic propagation mechanisms, such as the symplectic euler method to be used below, the position of an object at t n + 1 {\displaystyle t_{n+1}} is only dependent on its velocity at t n {\displaystyle t_{n}} , as the shift in position is calculated via
r → t n + 1 = r → t n + v → t n ⋅ Δ t {\displaystyle {\vec {r}}_{t_{n+1}}={\vec {r}}_{t_{n}}+{\vec {v}}_{t_{n}}\cdot \Delta t}
Without acceleration, v → t n {\textstyle {\vec {v}}_{t_{n}}} is static, however, from the perspective of an observer seeing only position, it will take two time steps to see a change in velocity.
A solar-system-like simulation can be accomplished by taking average distances of planet equivalent point masses from a central star. To keep code simple, a non-rigorous approach based on semi-major axes and mean velocities will be used. Memory space for these bodies must be reserved before the bodies are configured; to allow for scalability, a malloc command may be used:
where N_ASTEROIDS is a variable which will remain at 0 temporarily, but allows for future inclusion of significant numbers of asteroids, at the users discretion. A critical step for the configuration of simulations is to establish the time ranges of the simulation, t 0 {\displaystyle t_{0}} to t end {\displaystyle t_{\text{end}}} , as well as the incremental time step d t {\displaystyle dt} which will progress the simulation forward:
The positions and velocities established above are interpreted to be correct for t = t 0 {\displaystyle t=t_{0}} .
The extent of a simulation would logically be for the period where t 0 ≤ t < t end {\displaystyle t_{0}\leq t<t_{\text{end}}} .
An entire simulation can consist of hundreds, thousands, millions, billions, or sometimes trillions of time steps. At the elementary level, each time step (for simulations with particles moving due to forces exerted on them) involves
The above can be implemented quite simply with a while loop which continues while t {\displaystyle t} exists in the aforementioned range:
Focusing on the inner four rocky planets in the simulation, the trajectories resulting from the above propagation is shown below: | https://en.wikipedia.org/wiki/N-body_simulation |
In quantum chemistry , n -electron valence state perturbation theory ( NEVPT ) is a perturbative treatment applicable to multireference CASCI-type wavefunctions . It can be considered as a generalization of the well-known second-order Møller–Plesset perturbation theory to multireference complete active space cases. The theory is directly integrated into many quantum chemistry packages such as MOLCAS , Molpro , DALTON , PySCF and ORCA .
The research performed into the development of this theory led to various implementations. The theory here presented refers to the deployment for the single-state NEVPT, where the perturbative correction is applied to a single electronic state.
Research implementations has been also developed for quasi-degenerate cases, where a set of electronic states undergo the perturbative correction at the same time, allowing interaction among themselves. The theory development makes use of the quasi-degenerate formalism by Lindgren and the Hamiltonian multipartitioning technique from Zaitsevskii and Malrieu.
Let Ψ m ( 0 ) {\displaystyle \Psi _{m}^{(0)}} be a zero-order CASCI wavefunction, defined as a linear combination of Slater determinants
obtained diagonalizing the true Hamiltonian H ^ {\displaystyle {\hat {\mathcal {H}}}} inside the CASCI space
where P ^ C A S {\displaystyle {\hat {\mathcal {P}}}_{\rm {CAS}}} is the projector inside the CASCI space.
It is possible to define perturber wavefunctions in NEVPT as zero-order wavefunctions of the outer space (external to CAS) where k {\displaystyle k} electrons are removed from the inactive part (core and virtual orbitals) and added to the valence part (active orbitals). At second order of perturbation − 2 ≤ k ≤ 2 {\displaystyle -2\leq k\leq 2} . Decomposing the zero-order CASCI wavefunction as an antisymmetrized product of the inactive part Φ c {\displaystyle \Phi _{c}} and a valence part Ψ m v {\displaystyle \Psi _{m}^{v}}
then the perturber wavefunctions can be written as
The pattern of inactive orbitals involved in the procedure can be grouped as a collective index l {\displaystyle l} , so to represent the various perturber wavefunctions as Ψ l , μ k {\displaystyle \Psi _{l,\mu }^{k}} , with μ {\displaystyle \mu } an enumerator index for the different wavefunctions. The number of these functions is relative to the degree of contraction of the resulting perturbative space.
Supposing indexes i {\displaystyle i} and j {\displaystyle j} referring to core orbitals, a {\displaystyle a} and b {\displaystyle b} referring to active orbitals and r {\displaystyle r} and s {\displaystyle s} referring to virtual orbitals, the possible excitation schemes are:
These cases always represent situations where interclass electronic excitations happen. Other three excitation schemes involve a single interclass excitation plus an intraclass excitation internal to the active space:
A possible approach is to define the perturber wavefunctions into Hilbert spaces S l k {\displaystyle S_{l}^{k}} defined by those determinants with given k and l labels. The determinants characterizing these spaces can be written as a partition comprising the same inactive (core + virtual) part Φ l − k {\displaystyle \Phi _{l}^{-k}} and all possible valence (active) parts Ψ I k {\displaystyle \Psi _{I}^{k}}
The full dimensionality of these spaces can be exploited to obtain the definition of the perturbers, by diagonalizing the Hamiltonian inside them
This procedure is impractical given its high computational cost: for each S l k {\displaystyle S_{l}^{k}} space, a diagonalization of the true Hamiltonian must be performed. Computationally, is preferable to improve the theoretical development making use of the modified Dyall's Hamiltonian H ^ D {\displaystyle {\hat {\mathcal {H}}}^{D}} . This Hamiltonian behaves like the true Hamiltonian inside the CAS space, having the same eigenvalues and eigenvectors of the true Hamiltonian projected onto the CAS space. Also, given the decomposition for the wavefunction defined before, the action of the Dyall's Hamiltonian can be partitioned into
stripping out the constant contribution of the inactive part and leaving a
subsystem to be solved for the valence part
The total energy E l , μ k {\displaystyle E_{l,\mu }^{k}} is the sum of E μ k {\displaystyle E_{\mu }^{k}} and the energies of the orbitals involved in the definition of the inactive part Φ l − k {\displaystyle \Phi _{l}^{-k}} . This introduces the possibility to perform a single diagonalization of the valence Dyall's Hamiltonian on the CASCI zero-order wavefunction and evaluate the perturber energies using the property depicted above.
A different choice in the development of the NEVPT approach is to choose a single function for each space S l k {\displaystyle S_{l}^{k}} , leading to the Strongly Contracted (SC) scheme. A set of perturbative operators are used to produce a single function for each space, defined as the projection inside each space P ^ S l k {\displaystyle {\hat {\mathcal {P}}}_{S_{l}^{k}}} of the application of the Hamiltonian to the contracted zero order wavefunction. In other words,
where P ^ S l k {\displaystyle {\hat {\mathcal {P}}}_{S_{l}^{k}}} is the projector onto the subspace. This can be equivalently written as the application of a specific part of the Hamiltonian to the zero-order wavefunction
For each space, appropriate operators can be devised. We will not present their definition, as it could result overkilling. Suffice to say that the resulting perturbers are not normalized, and their norm
plays an important role in the Strongly Contracted development. To evaluate these norms, the spinless density matrix of rank not higher than three between the Ψ m ( 0 ) {\displaystyle \Psi _{m}^{(0)}} functions are needed.
An important property of the Ψ l k {\displaystyle \Psi _{l}^{k}} is that any other function of the space S l k {\displaystyle S_{l}^{k}} which is orthogonal to Ψ l k {\displaystyle \Psi _{l}^{k}} do not interact with the zero-order wavefunction through the true Hamiltonian. It is possible to use the Ψ l k {\displaystyle \Psi _{l}^{k}} functions as a basis set for the expansion of the first-order correction to the wavefunction, and also for the expression of the zero-order Hamiltonian by means of a spectral decomposition
where | Ψ l k ′ ⟩ {\displaystyle \left|\Psi _{l}^{k}{}^{\prime }\right\rangle } are the normalized | Ψ l k ⟩ {\displaystyle \left|\Psi _{l}^{k}\right\rangle } .
The expression for the first-order correction to the wavefunction is therefore
and for the energy is
This result still misses a definition of the perturber energies E l k {\displaystyle E_{l}^{k}} , which can be defined in a computationally advantageous approach by means of the Dyall's Hamiltonian
leading to
Developing the first term and extracting the inactive part of the Dyall's Hamiltonian it can be obtained
with Δ ϵ l {\displaystyle \Delta \epsilon _{l}} equal to the sum of the orbital energies of the newly occupied virtual orbitals minus the orbital energies of the unoccupied core orbitals.
The term that still needs to be evaluated is the bracket involving the commutator. This can be obtained developing each V {\displaystyle V} operator and substituting. To obtain the final result it is necessary to evaluate Koopmans matrices and density matrices involving only active indexes. An interesting case is represented by the contribution for the V i j r s ( 0 ) {\displaystyle V_{ijrs}^{(0)}} case, which is trivial and can be demonstrated identical to the Møller–Plesset second-order contribution
NEVPT2 can therefore be seen as a generalized form of MP2 to multireference wavefunctions.
An alternative approach, named Partially Contracted (PC) is to define the perturber wavefunctions in a subspace S ¯ l k {\displaystyle {\overline {S}}_{l}^{k}} of S l k {\displaystyle S_{l}^{k}} with dimensionality higher than one (like in case of the Strongly Contracted approach). To define this subspace, a set of functions Φ {\displaystyle \Phi } is generated by means of the V l k {\displaystyle V_{l}^{k}} operators, after decontraction of their formulation. For example, in the case of the V r s i − 1 {\displaystyle V_{rsi}^{-1}} operator
The Partially Contracted approach makes use of functions Φ r i s a = E r i E s a Ψ m ( 0 ) {\displaystyle \Phi _{risa}=E_{ri}E_{sa}\Psi _{m}^{(0)}} and Φ r i s a = E s i E r a Ψ m ( 0 ) {\displaystyle \Phi _{risa}=E_{si}E_{ra}\Psi _{m}^{(0)}} . These functions must be orthonormalized and purged of linear dependencies which may arise. The resulting set spans the S ¯ r s i − 1 {\displaystyle {\overline {S}}_{rsi}^{-1}} space.
Once all the S ¯ l k {\displaystyle {\overline {S}}_{l}^{k}} spaces have been defined, we can obtain as usual a set of perturbers from the diagonalization of the Hamiltonian (true or Dyall) inside this space
As usual, the evaluation of the Partially Contracted perturbative correction by means of the Dyall Hamiltonian involves simply manageable entities for nowadays computers.
Although the Strongly Contracted approach makes use of a perturbative space with very low flexibility, in general it provides values in very good agreement with those obtained by the more decontracted space defined for the Partially Contracted approach. This can be probably explained by the fact that the Strongly Contracted perturbers are a good average of the totally decontracted perturbative space.
The Partially Contracted evaluation has a very little overhead in computational cost with respect to the Strongly Contracted one, therefore they are normally evaluated together.
NEVPT is blessed with many important properties, making the approach very solid and reliable. These properties arise both from the theoretical approach used and on the Dyall's Hamiltonian particular structure: | https://en.wikipedia.org/wiki/N-electron_valence_state_perturbation_theory |
N -linked glycosylation is the attachment of an oligosaccharide , a carbohydrate consisting of several sugar molecules, sometimes also referred to as glycan , to a nitrogen atom (the amide nitrogen of an asparagine (Asn) residue of a protein ), in a process called N -glycosylation , studied in biochemistry . [ 1 ] The resulting protein is called an N-linked glycan , or simply an N-glycan .
This type of linkage is important for both the structure [ 2 ] and function [ 3 ] of many eukaryotic proteins. The N -linked glycosylation process occurs in eukaryotes and widely in archaea , but very rarely in bacteria . The nature of N -linked glycans attached to a glycoprotein is determined by the protein and the cell in which it is expressed. [ 4 ] It also varies across species . Different species synthesize different types of N -linked glycan.
There are two types of bonds involved in a glycoprotein: bonds between the saccharides residues in the glycan and the linkage between the glycan chain and the protein molecule.
The sugar moieties are linked to one another in the glycan chain via glycosidic bonds . These bonds are typically formed between carbons 1 and 4 of the sugar molecules. The formation of glycosidic bond is energetically unfavourable, therefore the reaction is coupled to the hydrolysis of two ATP molecules. [ 4 ]
On the other hand, the attachment of a glycan residue to a protein requires the recognition of a consensus sequence . N -linked glycans are almost always attached to the nitrogen atom of an asparagine (Asn) side chain that is present as a part of Asn–X– Ser / Thr consensus sequence, where X is any amino acid except proline (Pro). [ 4 ]
In animal cells, the glycan attached to the asparagine is almost inevitably N -acetylglucosamine (GlcNAc) in the β-configuration. [ 4 ] This β-linkage is similar to glycosidic bond between the sugar moieties in the glycan structure as described above. Instead of being attached to a sugar hydroxyl group, the anomeric carbon atom is attached to an amide nitrogen. The energy required for this linkage comes from the hydrolysis of a pyrophosphate molecule. [ 4 ]
The biosynthesis of N -linked glycans occurs via three major steps: [ 4 ]
Synthesis, en bloc transfer and initial trimming of precursor oligosaccharide occurs in the endoplasmic reticulum (ER). Subsequent processing and modification of the oligosaccharide chain are carried out in the Golgi apparatus . [ citation needed ]
The synthesis of glycoproteins is thus spatially separated in different cellular compartments. Therefore, the type of N -glycan synthesized, depends on its accessibility to the different enzymes present within these cellular compartments. [ citation needed ]
However, in spite of the diversity, all N -glycans are synthesized through a common pathway with a common core glycan structure. [ 4 ] The core glycan structure is essentially made up of two N -acetyl glucosamine and three mannose residues. This core glycan is then elaborated and modified further, resulting in a diverse range of N -glycan structures. [ 4 ]
The process of N -linked glycosylation starts with the formation of dolichol -linked GlcNAc sugar. Dolichol is a lipid molecule composed of repeating isoprene units. This molecule is found attached to the membrane of the ER. Sugar molecules are attached to the dolichol through a pyrophosphate linkage [ 4 ] (one phosphate was originally linked to dolichol, and the second phosphate came from the nucleotide sugar). The oligosaccharide chain is then extended through the addition of various sugar molecules in a stepwise manner to form a precursor oligosaccharide. [ citation needed ]
The assembly of this precursor oligosaccharide occurs in two phases: Phase I and II. [ 4 ] Phase I takes place on the cytoplasmic side of the ER and Phase II takes place on the luminal side of the ER. [ citation needed ]
The precursor molecule, ready to be transferred to a protein, consists of two GlcNAc, nine mannose, and three glucose molecules.
Once the precursor oligosaccharide is formed, the completed glycan is then transferred to the nascent polypeptide in the lumen of the ER membrane. This reaction is driven by the energy released from the cleavage of the pyrophosphate bond between the dolichol-glycan molecule.
There are three conditions to fulfill before a glycan is transferred to a nascent polypeptide: [ 4 ]
Oligosaccharyltransferase is the enzyme responsible for the recognition of the consensus sequence and the transfer of the precursor glycan to a polypeptide acceptor which is being translated in the endoplasmic reticulum lumen. N -linked glycosylation is, therefore, a co-translational event. [ citation needed ]
N -glycan processing is carried out in endoplasmic reticulum and the Golgi body. Initial trimming of the precursor molecule occurs in the ER and the subsequent processing occurs in the Golgi.
Upon transferring the completed glycan onto the nascent polypeptide, two glucose residues are removed from the structure. Enzymes known as glycosidases remove some sugar residues. These enzymes can break glycosidic linkages by using a water molecule. These enzymes are exoglycosidases as they only work on monosaccharide residues located at the non-reducing end of the glycan. [ 4 ] This initial trimming step is thought to act as a quality control step in the ER to monitor protein folding .
Once the protein is folded correctly, two glucose residues are removed by glucosidase I and II. The removal of the final third glucose residue signals that the glycoprotein is ready for transit from the ER to the cis -Golgi. [ 4 ] ER mannosidase catalyses the removal of this final glucose. However, if the protein is not folded properly, the glucose residues are not removed and thus the glycoprotein can't leave the endoplasmic reticulum. A chaperone protein ( calnexin / calreticulin ) binds to the unfolded or partially folded protein to assist protein folding.
The next step involves further addition and removal of sugar residues in the cis-Golgi. These modifications are catalyzed by glycosyltransferases and glycosidases respectively. In the cis -Golgi, a series of mannosidases remove some or all of the four mannose residues in α-1,2 linkages. [ 4 ] Whereas in the medial portion of the Golgi, glycosyltransferases add sugar residues to the core glycan structure, giving rise to the three main types of glycans: high mannose, hybrid and complex glycans.
The order of addition of sugars to the growing glycan chains is determined by the substrate specificities of the enzymes and their access to the substrate as they move through secretory pathway . Thus, the organization of this machinery within a cell plays an important role in determining which glycans are made. [ citation needed ]
Golgi enzymes play a key role in determining the synthesis of the various types of glycans. The order of action of the enzymes is reflected in their position in the Golgi stack:
Similar N -glycan biosynthesis pathway have been found in prokaryotes and Archaea. [ 6 ] However, compared to eukaryotes, the final glycan structure in eubacteria and archaea does not seem to differ much from the initial precursor made in the endoplasmic reticulum. In eukaryotes, the original precursor oligosaccharide is extensively modified en route to the cell surface. [ 4 ]
N -linked glycans have intrinsic and extrinsic functions. [ 4 ] [ 7 ]
Within the immune system, the N -linked glycans on an immune cell's surface will help dictate that migration pattern of the cell, e.g. immune cells that migrate to the skin have specific glycosylations that favor homing to that site. [ 8 ] The glycosylation patterns on the various immunoglobulins including IgE, IgM, IgD, IgA, and IgG bestow them with unique effector functions by altering their affinities for Fc and other immune receptors. [ 8 ] Glycans may also be involved in "self" and "non self" discrimination, which may be relevant to the pathophysiology of various autoimmune diseases. [ 8 ]
In some cases, interaction between the N-glycan and the protein stabilizes the protein through complex electronic effects. [ 11 ]
Changes in N -linked glycosylation has been associated with different diseases including rheumatoid arthritis , [ 12 ] type 1 diabetes , [ 13 ] Crohn's disease , [ 14 ] and cancers. [ 15 ] [ 16 ]
Mutations in eighteen genes involved in N -linked glycosylation result in a variety of diseases, most of which involve the nervous system . [ 3 ] [ 16 ]
Many therapeutic proteins in the market are antibodies , which are N -linked glycoproteins. For example, Etanercept , Infliximab and Rituximab are N -glycosylated therapeutic proteins.
The importance of N -linked glycosylation is becoming increasingly evident in the field of pharmaceuticals . [ 17 ] Although bacterial or yeast protein production systems have significant potential advantages such as high yield and low cost, problems arise when the protein of interest is a glycoprotein. Most prokaryotic expression systems such as E. coli cannot carry out post-translational modifications . On the other hand, eukaryotic expression hosts such as yeast and animal cells, have different glycosylation patterns. The proteins produced in these expression hosts are often not identical to human protein and thus, cause immunogenic reactions in patients. For example, S.cerevisiae (yeast) often produce high-mannose glycans which are immunogenic.
Non-human mammalian expression systems such as CHO or NS0 cells have the machinery required to add complex, human-type glycans. However, glycans produced in these systems can differ from glycans produced in humans, as they can be capped with both N -glycolylneuraminic acid (Neu5Gc) and N -acetylneuraminic acid (Neu5Ac), whereas human cells only produce glycoproteins containing N -acetylneuraminic acid. Furthermore, animal cells can also produce glycoproteins containing the galactose-alpha-1,3-galactose epitope, which can induce serious allergenic reactions, including anaphylactic shock , in people who have Alpha-gal allergy .
These drawbacks have been addressed by several approaches such as eliminating the pathways that produce these glycan structures through genetic knockouts. Furthermore, other expression systems have been genetically engineered to produce therapeutic glycoproteins with human-like N -linked glycans. These include yeasts such as Pichia pastoris , [ 18 ] insect cell lines, green plants, [ 19 ] and even bacteria. | https://en.wikipedia.org/wiki/N-linked_glycosylation |
N-philes are group of radical molecules which are specifically attracted to the C=N bonds , defying often the selectivity rules of electrophilic attack. N-philes can often masquerade as electrophiles, where acyl radicals are excellent examples which interact with pi electrons of aryl groups.
This organic chemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N-philes |
Quantum mechanics was first applied to optics , and interference in particular, by Paul Dirac . [ 1 ] Richard Feynman , in his Lectures on Physics , uses Dirac's notation to describe thought experiments on double-slit interference of electrons . [ 2 ] Feynman's approach was extended to N -slit interferometers for either single-photon illumination, or narrow- linewidth laser illumination, that is, illumination by indistinguishable photons , by Frank Duarte . [ 3 ] [ 4 ] The N -slit interferometer was first applied in the generation and measurement of complex interference patterns . [ 3 ] [ 4 ]
In this article the generalized N -slit interferometric equation, derived via Dirac's notation, is described. Although originally derived to reproduce and predict N -slit interferograms, [ 3 ] [ 4 ] this equation also has applications to other areas of optics.
In this approach the probability amplitude for the propagation of a photon from a source s to an interference plane x , via an array of slits j , is given using Dirac's bra–ket notation as [ 3 ]
This equation represents the probability amplitude of a photon propagating from s to x via an array of j slits. Using a wavefunction representation for probability amplitudes, [ 1 ] and defining the probability amplitudes as [ 3 ] [ 4 ] [ 5 ]
where θ j and Φ j are the incidence and diffraction phase angles, respectively. Thus, the overall probability amplitude can be rewritten as
where
and
after some algebra, the corresponding probability becomes [ 3 ] [ 4 ] [ 5 ]
where N is the total number of slits in the array, or transmission grating, and the term in parentheses represents the phase that is directly related to the exact path differences derived from the geometry of the N -slit array ( j ), the intra interferometric distance, and the interferometric plane x . [ 5 ] In its simplest version, the phase term can be related to the geometry using
where k is the wavenumber , and L m and L m − 1 represent the exact path differences. Here the Dirac – Duarte (DD) interferometric equation is a probability distribution that is related to the intensity distribution measured experimentally. [ 6 ] The calculations are performed numerically. [ 5 ]
The DD interferometric equation applies to the propagation of a single photon, or the propagation of an ensemble of indistinguishable photons, and enables the accurate prediction of measured N -slit interferometric patterns continuously from the near to the far field. [ 5 ] [ 6 ] Interferograms generated with this equation have been shown to compare well with measured interferograms for both even ( N = 2, 4, 6... ) and odd ( N = 3, 5, 7... ) values of N from 2 to 1600. [ 5 ] [ 7 ]
At a practical level, the N -slit interferometric equation was introduced for imaging applications [ 5 ] and is routinely applied to predict N -slit laser interferograms, both in the near and far field. Thus, it has become a valuable tool in the alignment of large, and very large, N -slit laser interferometers [ 8 ] [ 9 ] used in the study of clear air turbulence and the propagation of interferometric characters for secure laser communications in space . Other analytical applications are described below.
The N -slit interferometric equation has been applied to describe classical phenomena such as interference , diffraction , refraction ( Snell's law ), and reflection , in a rational and unified approach, using quantum mechanics principles. [ 7 ] [ 10 ] In particular, this interferometric approach has been used to derive generalized refraction equations for both positive and negative refraction , [ 11 ] thus providing a clear link between diffraction theory and generalized refraction. [ 11 ]
From the phase term, of the interferometric equation, the expression
can be obtained, where M = 0, 2, 4... .
For n 1 = n 2 , this equation can be written as [ 7 ] [ 10 ]
which is the generalized diffraction grating equation . Here, θ m is the angle of incidence, φ m is the angle of diffraction, λ is the wavelength, and m = 0, 1, 2... is the order of diffraction.
Under certain conditions, d m ≪ λ , which can be readily obtained experimentally, the phase term becomes [ 7 ] [ 10 ]
which is the generalized refraction equation, [ 11 ] where θ m is the angle of incidence, and φ m now becomes the angle of refraction.
Furthermore, the N -slit interferometric equation has been applied to derive the cavity linewidth equation applicable to dispersive oscillators, such as the multiple-prism grating laser oscillators : [ 12 ]
In this equation, Δ θ is the beam divergence and the overall intracavity angular dispersion is the quantity in parentheses.
Researchers working on Fourier-transform ghost imaging consider the N -slit interferometric equation [ 3 ] [ 5 ] [ 10 ] as an avenue to investigate the quantum nature of ghost imaging. [ 13 ] Also, the N -slit interferometric approach is one of several approaches applied to describe basic optical phenomena in a cohesive and unified manner. [ 14 ]
Note: given the various terminologies in use, for N -slit interferometry, it should be made explicit that the N -slit interferometric equation applies to two-slit interference, three-slit interference, four-slit interference, etc.
The Dirac principles and probabilistic methodology used to derive the N -slit interferometric equation have also been used to derive the polarization quantum entanglement probability amplitude [ 15 ]
and corresponding probability amplitudes depicting the propagation of multiple pairs of quanta. [ 16 ]
A comparison of the Dirac approach with classical methods, in the performance of interferometric calculations, has been done by Travis S. Taylor et al . [ 17 ] These authors concluded that the interferometric equation, derived via the Dirac formalism, was advantageous in the very near field.
Some differences between the DD interferometric equation and classical formalisms can be summarized as follows:
So far there has been no published comparison with more general classical approaches based on the Huygens–Fresnel principle or Kirchhoff's diffraction formula . | https://en.wikipedia.org/wiki/N-slit_interferometric_equation |
N-terminal acetylation is the protein modification that occurs on the α-amino acid group at the N-termini of proteins. The backbone amino group on the first amino acid (α-amino group) on a protein N-terminus gets an acetyl group (-COCH 3 ) via acetyl-CoA, and this process is catalyzed by enzymes called N-terminal acetyltransferases (NATs). [ 1 ] This changes the chemical properties by making the protein more hydrophobic. Adding an acetyl group on the N-terminus of proteins is to date not shown to be reversible.
Acetylation of a protein is adding an acetyl group on one or several amino acids in the protein. This protein modification can happen internally on an ε- amino acid group of a protein. An internal acetylation is called lysine acetylation, as it is an internal lysine (K) that is added an acetyl group (-COCH 3 ). This process is catalyzed by enzymes named lysine acetyltransferases (KATs) by using acetyl-CoA as donor. This process can be reversed, meaning that the acetyl group can be removed by lysine deacetylases (KDACs). [ 2 ]
There are seven human N-terminal acetyltransferases discovered to date, named NatA, NatB, NatC, NatD, NatE, NatF, and NatH. [ 1 ] There is a group of plant NATs discovered called NatG. [ 3 ] [ 4 ]
NatA, NatB, NatC, NatD and NatE work co-translationally by binding to the ribosome . NatD/NAA40 is in itself ribosome-binding, whereas the remaining four of these NATs bind to the ribosome via an auxiliary subunit. NatF and NatH modify proteins post-translationally and are as far as we know monomeric enzymes. NatA targets about 38% of the human proteome, NatB almost 21%, whereas NatC, NatE and NatF together target in total 21% of the human proteome. [ 1 ] That means that the different NATs in total acetylate over 80% of the human proteome , making N-terminal acetylation a highly abundant protein modification.
NatA was the first NAT to be described, [ 5 ] and its structure consists of the catalytic subunit NAA10 and the auxiliary subunit NAA15 which together is called the NatA complex. The NatA complex also binds to HYPK (Huntingtin-interacting protein K) which can stabilize the NatA complex. NatA targets proteins starting with S , A , T , G , V and C , and has the largest substrate pool of all the NATs. However, NAA10 can also work independently of NAA15, and acetylate proteins on its own. NatB consists of the catalytic subunit NAA20 and the auxiliary subunit NAA25. The target proteins of NatB are those that have N-termini starting with the amino acids MD, ME, MN and MQ. NatC consists of the catalytic subunit NAA30, and NAA35 which anchors the ribosome and NAA38 whose role is still not known. The targets of NatC are MI-, ML-, MF-, MY- and MK-starting protein N-termini.
NatD consists of one catalytic unit called NAA40 with high substrate selectivity, targeting only histones H2A and H4 and some proteins starting with SGRGK. NatE consists of the unit NAA50 which binds to the NatA complex and HYPK, and this NatE complex targets MS-, MT-, MA-, MV-, ML-, MI-, MF-, MY- and MK-starting N-termini. NatF consists of the catalytic NAA60 and is localized to the cytosolic side of the Golgi membrane, and it is the only known NAT that is specifically targeting membrane proteins. [ 6 ] [ 7 ] The targets of NatF are MI-, ML-, MF-, MY- and MK-starting membrane proteins . NatH consist of the catalytic NAA80 . It is highly specific and targets only actins , including cytoplasmic β-actin and γ-actin. [ 8 ] [ 9 ] NatH works post-translationally in the cytosol on actin at the final maturation stage of actin and it interacts with profilin which promotes actin N-terminal acetylation [ 10 ] [ 11 ]
NatG is a group of plant NATs that was discovered in 2015. NatG consists of several plant-specific GNAT proteins with dual functions as KATs and NATs targets chloroplast proteins with N-termini starting with A, M , T, S. [ 4 ] [ 12 ]
Most proteins in the human body have this protein modification, and there are several cellular and biological functions of N-terminal acetylation. As a general overview, the N-terminal acetylation functions like a label, and the target could be to relocate a protein to a different subcellular location , activate a protein for its proper function. An example is that N-terminally acetylated actin is part of keeping a normal functional cytoskeleton . [ 8 ] [ 13 ] A modified protein could target the protein for degradation, [ 14 ] and for some proteins it can do the opposite and protect it from degradation. [ 15 ] An important role of NatC is to protect proteins from degradation otherwise mediated by ubiquitin ligases . [ 16 ] In human and plant cells, NatA can also protect proteins from degradation by ubiquitin ligases and thereby stabilize these. [ 17 ] [ 18 ] There are also reports of N-terminal acetylation could have a stabilizing effect depending on the protein in question. [ 19 ]
Lack of N-terminal acetylation has been associated with different pathologies in recent years. Pathogenic variants in the coding DNA region of the NATs may result in a NAT with reduced enzymatic activity. There have been found several patient mutations like this where NatA has been affected. The first case of NatA defect in 2011 had severe consequences, involving developmental delay, heart failures, aged appearance and a short life span. [ 20 ] Pathogenic variants have also been found in the coding region of NAA20, where the patients have developed various symptoms like speech delay, epilepsy and cognitive impairment due to weakening of the NatB complex formation. [ 21 ] [ 22 ] Other diseases linked to lack of N-terminal acetylation involve NatF, where lack of NAA60 activity had shown to cause primary familial brain calcifications . [ 23 ] N-terminal acetyltransferases have also been linked to cancer progression, including NAA10, NAA20, NAA30, NAA40 and NAA50. [ 1 ] Due to the large number of proteins having these modifications, often malfunction in the N-terminal acetyltransferases the human body have so called pleiotropic effects. As there are several diseases linked to lack of N-terminal acetylation, it is important to investigate genetic variants that lead to disease, but also to do research on the basal functions of NATs to reveal new therapeutic angles for these diseases. | https://en.wikipedia.org/wiki/N-terminal_acetylation |
N-terminal prohormone of brain natriuretic peptide (NT-proBNP or BNPT) is a 76 amino acid long protein that is cleaved from the N-terminal end of the 108 amino acid long prohormone proBNP to release brain natriuretic peptide 32 (BNP, also known as B-type natriuretic peptide). [ 1 ] [ 2 ] [ 3 ]
Both BNP and NT-proBNP levels in the blood are used for screening, diagnosis of acute congestive heart failure (CHF) and may be useful to establish prognosis in heart failure, as both markers are typically higher in patients with worse outcome. [ 4 ] The plasma concentrations of both BNP and NT-proBNP are also typically increased in patients with asymptomatic or symptomatic left ventricular dysfunction and is associated with coronary artery disease , myocardial ischemia , and severity of aortic valve stenosis . [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ]
There is no level of BNP that perfectly separates patients with and without heart failure. [ 13 ]
In screening for congenital heart disease in pediatric patients, an NT-proBNP cut-off value of 91 pg/mL could differentiate an acyanotic heart disease (ACNHD) patient from a healthy patient with a sensitivity of 84% and specificity of 42%. [ 14 ] On the other hand, an NT-proBNP cut-off value of 318 pg/mL is more appropriate in differing patients with congenital nonspherocytic hemolytic disease (CNHD) from healthy patients, with 94% sensitivity and 97% specificity. [ 14 ] An NT-proBNP value of 408 pg/mL has been estimated to be 83% sensitive and 57% specific in differentiating patients with ACNHD from patients with CNHD. [ 14 ] In patients with non-severe asymptomatic aortic valve stenosis, increased age- and sex adjusted NT-proBNP levels alone and combined with a 50% or greater increase from baseline had been found associated with increased event rates of aortic valve stenosis related events ( cardiovascular death , hospitalization with heart failure due to progression of aortic valve stenosis, or aortic valve replacement surgery). [ 15 ] In severe aortic valve stenosis , NT-proBNP provide important prognostic information beyond clinical and echocardiographic evaluation. [ 16 ]
While discussed in Canadian medical journals in the mid to late 2000s, [ 17 ] the test is not widely used. It was only approved for use in Alberta in February 2012. [ 18 ]
The test has been widely used in the life insurance industry to screen applicants as part of the routine requirements when applying for a life insurance policy. It is also inexpensive and can be measured from blood samples routinely drawn as part of the application process. The test can be used to evaluate for a number of health conditions. [ 10 ] [ 19 ] [ 20 ] | https://en.wikipedia.org/wiki/N-terminal_prohormone_of_brain_natriuretic_peptide |
The N-terminal telopeptide ( NTX ), also known as amino-terminal collagen crosslinks , is the N-terminal telopeptide of fibrillar collagens such as collagen type I and type II . It is used as a biomarker to measure the rate of bone turnover . NTX can be measured in the urine (uNTX) or serum (serum NTX). [ 1 ] The peptide consists of eight amino acids with the sequence YDEKSTGG. [ 2 ]
Evaluating an individual's rate of bone turnover, termed bone remodeling , directly may be important in assessing his or her potential nonsurgical treatment response as well as evaluating his or her risk of developing complications during healing following surgical intervention. To determine an individual's rate of bone turnover, numerous biomarkers are available in the body fluids that can be correlated to this rate, and one such biomarker is NTX. [ 1 ]
However, while NTX does fluctuate in a very sensitive manner in line with bone resorption patterns, they are not very specific , in that they may vary spontaneously without physiologic intervention. For example, NTX levels may drop by 50% from day to day with no treatment, [ 3 ] thus, making NTX levels unconvincing evidence of treatment effect. [ 4 ]
Conversely, the serum CTX biomarker, described in 2000 by Rosen, appears to be a much more effective and valuable indicator of bone resorption rate. [ 4 ] | https://en.wikipedia.org/wiki/N-terminal_telopeptide |
N - tert -Butylbenzenesulfinimidoyl chloride is a useful oxidant for organic synthesis reactions. [ 1 ] It is a good electrophile , and the sulfimide S=N bond can be attacked by nucleophiles , such as alkoxides , enolates , and amide ions. The nitrogen atom in the resulting intermediate is basic , and can abstract an α-hydrogen to create a new double bond .
This reagent can be synthesized quickly and in near-quantitative yield by reacting phenyl thioacetate with tert-butyldichloroamine in hot benzene . After the reaction is complete, the product can be isolated as a yellow, moisture-sensitive solid by vacuum distillation . [ 2 ]
A nucleophile , such as an alkoxide ( 1 ), attacks the S=N bond in 2 . The resulting intermediate ( 3 ) collapses and ejects chloride ion, which is a good leaving group . The resulting sulfimide has two resonance forms - 4a and 4b . Because of this, the nitrogen is basic, and via a five-membered ring transition state , it can abstract the hydrogen adjacent to the oxygen . This forms a new C=O bond and ejects a neutral sulfenamide ( 5 ), giving ketone 6 as the product. N - tert -Butylbenzenesulfinimidoyl chloride reacts with enolates, amides, and primary alkoxides by the same general mechanism.
The Swern oxidation , which converts primary and secondary alcohols to aldehydes and ketones, respectively, also uses a sulfur-containing compound ( DMSO ) as the oxidant and proceeds by a similar mechanism. In the Swern oxidation, elimination also occurs via a five-membered ring transition state, but the basic species is a sulfur ylide instead of a negatively charged nitrogen. Several other oxidation reactions also make use of DMSO as the oxidant and pass through a similar transition state (see #See also ).
Reacting an aldehyde with a Grignard reagent or organolithium and treating the resulting secondary alkoxide with N - tert -butylbenzenesulfinimidoyl chloride is a convenient one-pot reaction for converting aldehydes to ketones. While Grignards can be used for this reaction, organolithium compounds give higher yields, due to the higher reactivity of a lithium alkoxide compared to the corresponding magnesium salt. In some cases, an equivalent of DMPU , a Lewis base , will increase yields. For example, treating benzaldehyde with n -butyllithium and N - tert -butylbenzenesulfinimidoyl chloride in THF gives 1-phenyl-1-pentanone in good yield. [ 3 ]
N - tert -Butylbenzenesulfinimidoyl chloride can also be used to synthesize imines from amines . Imines synthesized in this fashion have been shown to undergo a one-pot Mannich reaction with 1,3-dicarbonyl compounds, such as malonate esters and 1,3-diketones . In this example, Cbz -protected benzylamine is deprotonated using n -butyllithium, then treated with N - tert -butylbenzenesulfinimidoyl chloride to form the protected imine. Dimethyl malonate acts as the nucleophile and reacts with the imine to give the final product, a Mannich base . [ 4 ] | https://en.wikipedia.org/wiki/N-tert-Butylbenzenesulfinimidoyl_chloride |
In mathematics , an N -topological space is a set equipped with N arbitrary topologies. If τ 1 , τ 2 , ..., τ N are N topologies defined on a nonempty set X , then the N -topological space is denoted by ( X , τ 1 , τ 2 ,..., τ N ).
For N = 1, the structure is simply a topological space .
For N = 2, the structure becomes a bitopological space introduced by J. C. Kelly. [ 1 ]
Let X = { x 1 , x 2 , ...., x n } be any finite set. Suppose A r = { x 1 , x 2 , ..., x r }. Then the collection τ 1 = { φ , A 1 , A 2 , ..., A n = X } will be a topology on X . If τ 1 , τ 2 , ..., τ m be m such topologies (chain topologies) defined on X , then the structure ( X , τ 1 , τ 2 , ..., τ m ) is an m -topological space .
This topology-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N-topological_space |
N1 -Acetyl-5-methoxykynuramine ( AMK ) is a metabolite of melatonin that could improve memory by acting on the melatonin receptors . AMK is produced from the metabolization of melatonin by the kynuramine pathway in the brain. [ 1 ] It significantly increased the phosphorylation of both ERK and CREB in the hippocampus . [ 2 ] It also helps scavenge free radicals. [ 3 ] AMK is highly reactive towards dioxygen (O 2 ) radicals because of AMK's N 2- amino group. [ 4 ]
Studies have shown that melatonin , along with its metabolites N1-acetyl-N2-formyl-5-methoxykynuramine (AFMK) and N1-acetyl-5-methoxykynuramine (AMK), can suppress the activation of cyclooxygenase-2 (COX-2) and inducible nitric oxide synthase (iNOS). This leads to reduced production of prostaglandin E₂ (PGE₂) and nitric oxide, respectively. COX-2 is a key enzyme involved in inflammation and its activation is triggered by lipopolysaccharide (LPS) in macrophages . Elevated levels of COX-2 expression have been linked to various disorders, such as cancer and neurodegeneration. COX-2 and iNOS are identified as newly recognized molecular targets and this supports the possible therapeutic role of melatonin, AFMK, and AMK in managing inflammatory responses. [ 5 ]
AMK is naturally synthesized in the human skin and its concentration varies depending on the degree of melanin pigmentation. It has been shown to reduce cell proliferation in keratinocytes and cancerous melanocytes . When epidermal melanocytes and melanoma cells were cultured with AMK, a decrease in cell count was observed compared to cells exposed only to the control treatment. Studies have shown that these antiproliferative effects were maintained even when AMK is administered in the presence of L-tyrosine . [ 6 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N1-Acetyl-5-methoxykynuramine |
N1-Methylguanosine (also 1-Methylguanosine or m 1 G ) is a modified nucleoside , derived from guanosine through the addition of a methyl group to the nitrogen atom at position 1 of the guanine base. This modification results in a fixed positive charge on the purine ring. It occurs in all transfer RNAs (tRNAs) that read codons starting with C except in those tRNAs that read CAN codons. [ 1 ] [ 2 ]
m 1 G can help prevent errors in protein synthesis, and lower levels can cause significant errors, reduction of protein output, and lower cell viability. Additionally, as a RNA component, it is excreted in urine and elevated levels may be usable as an indicator of certain cancers.
The most extensively studied function of m 1 G is in tRNA, where it is typically found at position 37 (m 1 G37), immediately 3' to the anticodon . This modification is critical for maintaining translational fidelity. [ 3 ] The presence of m1G37, with its positive charge and steric bulk, helps prevent frameshift errors during protein synthesis , particularly at codons susceptible to +1 frame-shifting, by stabilizing the codon-anticodon interaction and ensuring correct alignment within the ribosome . [ 1 ] Loss of m1G37 modification can lead to significant translational errors, global reduction of protein output, [ 4 ] and reduced cell viability. [ 5 ] [ 6 ] In addition to its presence in position 37, m 1 G is also found in position 9 of many cytosolic and mitochondrial tRNAs. [ 7 ] The presence of m 1 G in tRNA has also been identified as part of the epitranscriptome . [ 7 ]
The methylation of guanosine at the N-1 position is catalyzed by specific RNA methyltransferase enzymes using S-adenosyl methionine (SAM) as the methyl donor. In bacteria, the enzyme responsible for m 1 G37 formation is TrmD (tRNA (guanine 37 -N1)-methyltransferase). [ 1 ] TrmD is essential for the viability of many bacteria, making it an attractive target for the development of new antibiotics . In archaea and eukaryotes, the orthologous enzyme is Trm5. [ 7 ] Despite catalyzing the same reaction, Trm5 enzymes differ significantly in structure and mechanism from bacterial TrmD. [ citation needed ]
Modified nucleosides, generated from the catabolism of RNA, are excreted in urine. [ 8 ] Altered levels of RNA turnover and modification often occur in disease states, particularly cancer . [ 9 ] Consequently, urinary concentrations of various modified nucleosides, including m 1 G, have been investigated as potential non-invasive biomarkers . [ 9 ] Studies have reported elevated urinary m 1 G levels, along with other modified nucleosides, in patients with various malignancies, including breast cancer , lung cancer , leukemia , ovarian cancer , and renal cell carcinoma , often correlating with tumor stage or progression. [ 9 ] | https://en.wikipedia.org/wiki/N1-Methylguanosine |
Dinitrogen difluoride is a chemical compound with the formula N 2 F 2 . It is a gas at room temperature, and was first identified in 1952 as the thermal decomposition product of the fluorine azide ( FN 3 ). It has the structure F−N=N−F and exists in both cis and trans isomers , as typical for diimides .
The cis isomer has C 2v symmetry and the trans isomer has C 2h symmetry. These isomers can interconvert, but the process is slow enough at low temperature that the two can separated by low-temperature fractionation . [ clarification needed ] The trans isomer is less thermodynamically stable [ 2 ] but can be stored in glass vessels. The cis isomer attacks glass over a time scale of about 2 weeks to form silicon tetrafluoride and nitrous oxide : [ 3 ] [ page needed ]
Most preparations of dinitrogen difluoride give mixtures of the two isomers, but they can be prepared independently.
An aqueous method involves N , N -difluoro urea with concentrated potassium hydroxide . This gives a 40% yield with three times more of the trans isomer. [ 4 ]
Difluoramine forms a solid unstable compound with potassium fluoride (or rubidium fluoride or caesium fluoride ) which decomposes to dinitrogen difluoride. [ 4 ]
It can also be prepared by photolysis of tetrafluorohydrazine and bromine : [ 5 ]
The cis form of difluorodiazene will react with strong fluoride ion acceptors such as antimony pentafluoride to form the linear [ 6 ] [N≡N−F] + cation (fluorodiazonium cation [ 6 ] ) which forms a salt with the formula [N≡N−F] + [SbF 6 ] − (fluorodiazonium hexafluoroantimonate(V)).
Analogous reaction of cis -difluorodiazene with arsenic pentafluoride gives white solid salt with the formula [N≡N−F] + [AsF 6 ] − [ 6 ] (fluorodiazonium hexafluoroarsenate(V)).
In the solid phase, the observed N≡N and N−F bond distances in the [N≡N−F] + cation are 1.089(9) and 1.257(8) Å respectively, among the shortest experimentally observed N-N and N-F bonds. | https://en.wikipedia.org/wiki/N2F2 |
The N2K Consortium is a collaborative multinational effort by American , Chilean and Japanese astronomers to find additional extrasolar planets around stars that are
not already being surveyed. The N2K is shorthand for the set of roughly 2,000 of the nearest and most luminous main sequence stars that were selected to be newly surveyed. Target stars have a B - V color index value between 0.4 and 1.2, a visual magnitude brighter than 10.5, and a distance of less than 110 pc from the Sun . They were selected based upon their high metallicity , which is the abundance of elements other than hydrogen and helium. [ 1 ]
The observing campaign uses the Keck , Magellan and Subaru telescopes, plus automated telescopes at Fairborn Observatory . Each star is observed three times over a period of several days, then checked for short period variations in radial velocity. This variation is a characteristic of gravitational perturbation caused by a hot Jupiter. Those stars showing radial velocity variations are then checked with the automated photometric telescopes from Fairborn Observatory. [ 1 ]
During a two-year run beginning in 2004, the N2K Consortium was predicted to detect about 60 new hot Jupiters. [ 1 ] However, by 2009, only seven planets with orbital periods of up to five days had been discovered. They orbit the following stars: [ 2 ] | https://en.wikipedia.org/wiki/N2K_Consortium |
Nickel (II) nitrate is the inorganic compound Ni(NO 3 ) 2 or any hydrate thereof. In the hexahydrate, the nitrate anions are not bonded to nickel. Other hydrates have also been reported: Ni(NO 3 ) 2 . 9H 2 O, Ni(NO 3 ) 2 . 4H 2 O, and Ni(NO 3 ) 2 . 2H 2 O. [ 3 ]
It is prepared by the reaction of nickel oxide with nitric acid:
The anhydrous nickel nitrate is typically not prepared by heating the hydrates. Rather it is generated by the reaction of hydrates with dinitrogen pentoxide or of nickel carbonyl with dinitrogen tetroxide : [ 3 ]
The hydrated nitrate is often used as a precursor to supported nickel catalysts. [ 3 ]
Nickel(II) compounds with oxygenated ligands often feature octahedral coordination geometry. Two polymorphs of the tetrahydrate Ni(NO 3 ) 2 . 4H 2 O have been crystallized. In one the monodentate nitrate ligands are trans [ 4 ] while in the other they are cis. [ 5 ]
Nickel(II) nitrate is primarily used in electrotyping and electroplating of metallic nickel.
In heterogeneous catalysis, nickel(II) nitrate is used to impregnate alumina . Pyrolysis of the resulting material gives forms of Raney nickel and Urushibara nickel . [ 6 ] In homogeneous catalysis , the hexahydrate is a precatalyst for cross coupling reactions . [ 7 ] | https://en.wikipedia.org/wiki/N2NiO6 |
Dinitrogen dioxide is an inorganic compound having molecular formula N 2 O 2 . Many structural isomers are possible. The covalent bonding pattern O=N–N=O (a non-cyclic dimer of nitric oxide (NO)) is predicted to be the most stable isomer based on ab initio calculations and is the only one that has been experimentally produced. [ 1 ] In the solid form, the molecules have C 2v symmetry : the entire structure is planar, with the two oxygen atoms cis across the N–N bond. The O–N distance is 1.15 Å, the N–N distance is 2.33 Å, and the O=N–N angle is 95°. [ 2 ] | https://en.wikipedia.org/wiki/N2O2 |
Dinitrogen trioxide (also known as nitrous anhydride ) is the inorganic compound with the formula N 2 O 3 . It is a nitrogen oxide . It forms upon mixing equal parts of nitric oxide and nitrogen dioxide and cooling the mixture below −21°C (−6°F): [ 4 ]
Dinitrogen trioxide is only isolable at low temperatures (i.e., in the liquid and solid phases ). In liquid and solid states, it has a deep blue color. [ 2 ] At higher temperatures the equilibrium favors the constituent gases, with K D = 193 kPa (25°C). [ 5 ] [ clarification needed ]
This compound is sometimes called "nitrogen trioxide", but this name properly refers to another compound, the (uncharged) nitrate radical •NO 3 .
Dinitrogen trioxide molecule contains an N –N bond. One of the numerous resonant structures of the molecule of dinitrogen trioxide is O=N−NO 2 , which can be described as a nitroso group −N=O attached to a nitro group −NO 2 by a single bond between the two nitrogen atoms. This isomer is considered as the " anhydride " of the unstable nitrous acid ( HNO 2 ), and produces it when mixed with water , although an alternative structure might be anticipated for the true anhydride of nitrous acid (i.e., O=N−O−N=O ). This isomer can be produced from the reaction of tetrabutylammonium nitrite and triflic anhydride in dichloromethane solution at −30°C. [ 6 ]
If the nitrous acid is not then used up quickly, it decomposes into nitric oxide and nitric acid . Nitrite salts are sometimes produced by adding N 2 O 3 to water solutions of bases :
Typically, N–N bonds are similar in length to that in hydrazine (145 pm ). Dinitrogen trioxide, however, has an unusually long N–N bond at 186 pm. Some other nitrogen oxides also possess long N–N bonds, including dinitrogen tetroxide (175 pm). The N 2 O 3 molecule is planar and exhibits C s symmetry . The dimensions displayed on the picture below come from microwave spectroscopy of low-temperature , gaseous N 2 O 3 : [ 4 ]
Similar to nitronium nitrate , this molecule can also co-exist in equilibrium with an ionic gas called nitrosonium nitrite ([NO] + [NO2] – ) [ 7 ] | https://en.wikipedia.org/wiki/N2O3 |
Dinitrogen tetroxide , commonly referred to as nitrogen tetroxide ( NTO ), and occasionally (usually among ex-USSR/Russian rocket engineers) as amyl , is the chemical compound N 2 O 4 . It is a useful reagent in chemical synthesis. It forms an equilibrium mixture with nitrogen dioxide . Its molar mass is 92.011 g/mol.
Dinitrogen tetroxide is a powerful oxidizer that is hypergolic (spontaneously reacts) upon contact with various forms of hydrazine , which has made the pair a common bipropellant for rockets.
Dinitrogen tetroxide could be regarded as two nitro groups (-NO 2 ) bonded together. It forms an equilibrium mixture with nitrogen dioxide . [ 5 ] The molecule is planar with an N-N bond distance of 1.78 Å and N-O distances of 1.19 Å. The N-N distance corresponds to a weak bond, since it is significantly longer than the average N-N single bond length of 1.45 Å. [ 6 ] This exceptionally weak σ bond (amounting to overlapping of the sp 2 hybrid orbitals of the two NO 2 units [ 7 ] ) results from the simultaneous delocalization of the bonding electron pair across the whole N 2 O 4 molecule, and the considerable electrostatic repulsion of the doubly occupied molecular orbitals of each NO 2 unit. [ 8 ]
Unlike NO 2 , N 2 O 4 is diamagnetic since it has no unpaired electrons. [ 9 ] The liquid is also colorless but can appear as a brownish yellow liquid due to the presence of NO 2 according to the following equilibrium: [ 9 ]
Higher temperatures push the equilibrium towards nitrogen dioxide. Inevitably, some dinitrogen tetroxide is a component of smog containing nitrogen dioxide.
Solid N 2 O 4 is white, and melts at −11.2 °C. [ 9 ]
Nitrogen tetroxide is made by the catalytic oxidation of ammonia (the Ostwald process ): steam is used as a diluent to reduce the combustion temperature. In the first step, the ammonia is oxidized into nitric oxide :
Most of the water is condensed out, and the gases are further cooled; the nitric oxide that was produced is oxidized to nitrogen dioxide, which is then dimerized into nitrogen tetroxide:
and the remainder of the water is removed as nitric acid . The gas is essentially pure nitrogen dioxide, which is condensed into dinitrogen tetroxide in a brine-cooled liquefier. [ 10 ]
Dinitrogen tetroxide can also be made through the reaction of concentrated nitric acid and metallic copper. This synthesis is practical in a laboratory setting. Dinitrogen tetroxide can also be produced by heating metal nitrates. [ 11 ] The oxidation of copper by nitric acid is a complex reaction forming various nitrogen oxides of varying stability which depends on the concentration of the nitric acid, presence of oxygen, and other factors. The unstable species further react to form nitrogen dioxide which is then purified and condensed to form dinitrogen tetroxide.
Nitrogen tetroxide is used as an oxidizing agent in one of the most important rocket propellant systems because it can be stored as a liquid at room temperature. Pedro Paulet , a Peruvian polymath , reported in 1927 that he had experimented in the 1890s with a rocket engine that used spring-loaded nozzles that periodically introduced vaporized nitrogen tetroxide and a petroleum benzine to a spark plug for ignition, with the engine putting out 300 pulsating explosions per minute. [ 12 ] [ 13 ] Paulet would go on to visit the German rocket association Verein für Raumschiffahrt (VfR) and on March 15, 1928, Valier applauded Paulet's liquid-propelled rocket design in the VfR publication Die Rakete , saying the engine had "amazing power". [ 14 ] Paulet would soon be approached by Nazi Germany to help develop rocket technology, though he refused to assist and never shared the formula for his propellant. [ 15 ]
In early 1944, research on the usability of dinitrogen tetroxide as an oxidizing agent for rocket fuel was conducted by German scientists, although the Germans only used it to a very limited extent as an additive for S-Stoff (fuming nitric acid). It became the storable oxidizer of choice for many rockets in both the United States and USSR by the late 1950s. It is a hypergolic propellant in combination with a hydrazine -based rocket fuel . One of the earliest uses of this combination was on the Titan family of rockets used originally as ICBMs and then as launch vehicles for many spacecraft. Used on the U.S. Gemini and Apollo spacecraft and also on the Space Shuttle , it continues to be used as station-keeping propellant on most geo-stationary satellites, and many deep-space probes. It is also the primary oxidizer for Russia's Proton rocket .
When used as a propellant, dinitrogen tetroxide is usually referred to simply as nitrogen tetroxide and the abbreviation NTO is extensively used. Additionally, NTO is often used with the addition of a small percentage of nitric oxide that reacts to form dinitrogen trioxide , which inhibits stress-corrosion cracking of titanium alloys, and in this form, propellant-grade NTO is referred to as mixed oxides of nitrogen ( MON ) and can be distinguished by its green-blue color. Larger additions of nitric oxide, up to 25-30%, also lower the freezing point of NTO, improving storability in space conditions. [ 16 ] Most spacecraft now use MON instead of NTO; for example, the Space Shuttle reaction control system used MON3 (NTO containing 3% NO by weight). [ 17 ]
On 24 July 1975, NTO poisoning affected three U.S. astronauts on the final descent to Earth after the Apollo-Soyuz Test Project flight. This was due to a switch accidentally left in the wrong position, which allowed the attitude control thrusters to fire after the cabin fresh air intake was opened, allowing NTO fumes to enter the cabin. One crew member lost consciousness during descent. Upon landing, the crew was hospitalized for five days for chemical-induced pneumonia and pulmonary edema . [ 18 ] [ 19 ]
The tendency of N 2 O 4 to reversibly break into NO 2 has led to research into its use in advanced power generation systems as a so-called dissociating gas. [ 20 ] "Cool" dinitrogen tetroxide is compressed and heated, causing it to dissociate into nitrogen dioxide at half the molecular weight. This hot nitrogen dioxide is expanded through a turbine, cooling it and lowering the pressure, and then cooled further in a heat sink, causing it to recombine into nitrogen tetroxide at the original molecular weight. It is then much easier to compress to start the entire cycle again. Such dissociative gas Brayton cycles have the potential to considerably increase efficiencies of power conversion equipment. [ 21 ]
The high molecular weight and smaller volumetric expansion ratio of nitrogen dioxide compared to steam allows the turbines to be more compact. [ 22 ]
N 2 O 4 was the main component of the "nitrin" working fluid in the decommissioned Pamir-630D portable nuclear reactor which operated from 1985 to 1987. [ 23 ]
Nitric acid is manufactured on a large scale via N 2 O 4 . This species reacts with water to give both nitrous acid and nitric acid :
The coproduct HNO 2 upon heating disproportionates to NO and more nitric acid. When exposed to oxygen, NO is converted back into nitrogen dioxide:
The resulting NO 2 and N 2 O 4 can be returned to the cycle to give the mixture of nitrous and nitric acids again.
N 2 O 4 undergoes molecular autoionization to give [NO + ] [NO 3 − ], with the former nitrosonium ion being a strong oxidant. Various anhydrous transition metal nitrate complexes can be prepared from N 2 O 4 and base metal. [ 24 ]
where M = Cu , Zn , or Sn .
If metal nitrates are prepared from N 2 O 4 in completely anhydrous conditions, a range of covalent metal nitrates can be formed with many transition metals. This is because there is a thermodynamic preference for the nitrate ion to bond covalently with such metals rather than form an ionic structure. Such compounds must be prepared in anhydrous conditions, since the nitrate ion is a much weaker ligand than water, and if water is present the simple nitrate of the hydrated metal ion will form. The anhydrous nitrates concerned are themselves covalent, and many, e.g. anhydrous copper nitrate , are volatile at room temperature. Anhydrous titanium nitrate sublimes in vacuum at only 40 °C. Many of the anhydrous transition metal nitrates have striking colours. This branch of chemistry was developed by Cliff Addison and Norman Logan at the University of Nottingham in the UK during the 1960s and 1970s when highly efficient desiccants and dry boxes started to become available.
In even slightly basic solvents, N 2 O 4 adds to alkenes radically, giving mixtures of nitro compounds and nitrite esters . Pure or in entirely nonbasic solvents, the compounds autoionizes as above, to give nitroso compounds and nitrate esters . [ 25 ] | https://en.wikipedia.org/wiki/N2O4 |
Dinitrogen pentoxide (also known as nitrogen pentoxide or nitric anhydride ) is the chemical compound with the formula N 2 O 5 . It is one of the binary nitrogen oxides , a family of compounds that contain only nitrogen and oxygen . It exists as colourless crystals that sublime slightly above room temperature, yielding a colorless gas. [ 4 ]
Dinitrogen pentoxide is an unstable and potentially dangerous oxidizer that once was used as a reagent when dissolved in chloroform for nitrations but has largely been superseded by nitronium tetrafluoroborate ( NO 2 BF 4 ).
N 2 O 5 is a rare example of a compound that adopts two structures depending on the conditions. The solid is a salt, nitronium nitrate , consisting of separate nitronium cations [NO 2 ] + and nitrate anions [NO 3 ] − ; but in the gas phase and under some other conditions it is a covalently-bound molecule. [ 5 ]
N 2 O 5 was first reported by the French chemist Henri Deville in 1840, who prepared it by treating silver nitrate ( AgNO 3 ) with chlorine . [ 6 ] [ 7 ]
Pure solid N 2 O 5 is a salt , consisting of separated linear nitronium ions NO + 2 and planar trigonal nitrate anions NO − 3 . Both nitrogen centers have oxidation state +5. It crystallizes in the space group D 4 6 h ( C 6/ mmc ) with Z = 2, with the NO − 3 anions in the D 3 h sites and the NO + 2 cations in D 3 d sites. [ 8 ]
The vapor pressure P (in atm) as a function of temperature T (in kelvin ), in the range 211 to 305 K (−62 to 32 °C), is well approximated by the formula
being about 48 torr at 0 °C, 424 torr at 25 °C, and 760 torr at 32 °C (9 °C below the melting point). [ 9 ]
In the gas phase, or when dissolved in nonpolar solvents such as carbon tetrachloride , the compound exists as covalently-bonded molecules O 2 N−O−NO 2 . In the gas phase, theoretical calculations for the minimum-energy configuration indicate that the O−N−O angle in each −NO 2 wing is about 134° and the N−O−N angle is about 112°. In that configuration, the two −NO 2 groups are rotated about 35° around the bonds to the central oxygen, away from the N−O−N plane. The molecule thus has a propeller shape, with one axis of 180° rotational symmetry ( C 2 ) [ 10 ]
When gaseous N 2 O 5 is cooled rapidly ("quenched"), one can obtain the metastable molecular form, which exothermically converts to the ionic form above −70 °C. [ 11 ]
Gaseous N 2 O 5 absorbs ultraviolet light with dissociation into the free radicals nitrogen dioxide NO 2 • and nitrogen trioxide NO 3 • (uncharged nitrate). The absorption spectrum has a broad band with maximum at wavelength 160 nm . [ 12 ]
A recommended laboratory synthesis entails dehydrating nitric acid ( HNO 3 ) with phosphorus(V) oxide : [ 11 ]
Another laboratory process is the reaction of lithium nitrate LiNO 3 and bromine pentafluoride BrF 5 , in the ratio exceeding 3:1. The reaction first forms nitryl fluoride FNO 2 that reacts further with the lithium nitrate: [ 8 ]
The compound can also be created in the gas phase by reacting nitrogen dioxide NO 2 or N 2 O 4 with ozone : [ 13 ]
However, the product catalyzes the rapid decomposition of ozone: [ 13 ]
Dinitrogen pentoxide is also formed when a mixture of oxygen and nitrogen is passed through an electric
discharge. [ 8 ] Another route is the reactions of Phosphoryl chloride POCl 3 or nitryl chloride NO 2 Cl with silver nitrate AgNO 3 [ 8 ] [ 14 ]
Dinitrogen pentoxide reacts with water ( hydrolyses ) to produce nitric acid HNO 3 . Thus, dinitrogen pentoxide is the anhydride of nitric acid: [ 11 ]
Solutions of dinitrogen pentoxide in nitric acid can be seen as nitric acid with more than 100% concentration. The phase diagram of the system H 2 O − N 2 O 5 shows the well-known negative azeotrope at 60% N 2 O 5 (that is, 70% HNO 3 ), a positive azeotrope at 85.7% N 2 O 5 (100% HNO 3 ), and another negative one at 87.5% N 2 O 5 ("102% HNO 3 "). [ 15 ]
The reaction with hydrogen chloride HCl also gives nitric acid and nitryl chloride NO 2 Cl : [ 16 ]
Dinitrogen pentoxide eventually decomposes at room temperature into NO 2 and O 2 . [ 17 ] [ 13 ] Decomposition is negligible if the solid is kept at 0 °C, in suitably inert containers. [ 8 ]
Dinitrogen pentoxide reacts with ammonia NH 3 to give several products, including nitrous oxide N 2 O , ammonium nitrate NH 4 NO 3 , nitramide NH 2 NO 2 and ammonium dinitramide NH 4 N(NO 2 ) 2 , depending on reaction conditions. [ 18 ]
Dinitrogen pentoxide between high temperatures of 600 and 1,100 K (327–827 °C), is decomposed in two successive stoichiometric steps:
In the shock wave, N 2 O 5 has decomposed stoichiometrically into nitrogen dioxide and oxygen . At temperatures of 600 K and higher, nitrogen dioxide is unstable with respect to nitrogen oxide NO and oxygen. The thermal decomposition of 0.1 mM nitrogen dioxide at 1000 K is known to require about two seconds. [ 19 ]
Apart from the decomposition of N 2 O 5 at high temperatures, it can also be decomposed in carbon tetrachloride CCl 4 at 30 °C (303 K). [ 20 ] Both N 2 O 5 and NO 2 are soluble in CCl 4 and remain in solution while oxygen is insoluble and escapes. The volume of the oxygen formed in the reaction can be measured in a gas burette. After this step we can proceed with the decomposition, measuring the quantity of O 2 that is produced over time because the only form to obtain O 2 is with the N 2 O 5 decomposition. The equation below refers to the decomposition of N 2 O 5 in CCl 4 :
And this reaction follows the first order rate law that says:
N 2 O 5 can also be decomposed in the presence of nitric oxide NO :
The rate of the initial reaction between dinitrogen pentoxide and nitric oxide of the elementary unimolecular decomposition. [ 21 ]
Dinitrogen pentoxide, for example as a solution in chloroform , has been used as a reagent to introduce the −NO 2 functionality in organic compounds . This nitration reaction is represented as follows:
where Ar represents an arene moiety. [ 22 ] The reactivity of the NO + 2 can be further enhanced with strong acids that generate the "super- electrophile " HNO 2+ 2 .
In this use, N 2 O 5 has been largely replaced by nitronium tetrafluoroborate [NO 2 ] + [BF 4 ] − . This salt retains the high reactivity of NO + 2 , but it is thermally stable, decomposing at about 180 °C (into NO 2 F and BF 3 ).
Dinitrogen pentoxide is relevant to the preparation of explosives. [ 7 ] [ 23 ]
In the atmosphere , dinitrogen pentoxide is an important reservoir of the NO x species that are responsible for ozone depletion : its formation provides a null cycle with which NO and NO 2 are temporarily held in an unreactive state. [ 24 ] Mixing ratios of several parts per billion by volume have been observed in polluted regions of the nighttime troposphere. [ 25 ] Dinitrogen pentoxide has also been observed in the stratosphere [ 26 ] at similar levels, the reservoir formation having been postulated in considering the puzzling observations of a sudden drop in stratospheric NO 2 levels above 50 °N, the so-called ' Noxon cliff '.
Variations in N 2 O 5 reactivity in aerosols can result in significant losses in tropospheric ozone , hydroxyl radicals , and NO x concentrations. [ 27 ] Two important reactions of N 2 O 5 in atmospheric aerosols are hydrolysis to form nitric acid [ 28 ] and reaction with halide ions, particularly Cl − , to form ClNO 2 molecules which may serve as precursors to reactive chlorine atoms in the atmosphere. [ 29 ] [ 30 ]
N 2 O 5 is a strong oxidizer that forms explosive mixtures with organic compounds and ammonium salts. The decomposition of dinitrogen pentoxide produces the highly toxic nitrogen dioxide gas. | https://en.wikipedia.org/wiki/N2O5 |
Lead(II) nitrate is an inorganic compound with the chemical formula Pb ( NO 3 ) 2 . It commonly occurs as a colourless crystal or white powder and, unlike most other lead(II) salts , is soluble in water .
Known since the Middle Ages by the name plumbum dulce , the production of lead(II) nitrate from either metallic lead or lead oxide in nitric acid was small-scale, for direct use in making other lead compounds . In the nineteenth century lead(II) nitrate began to be produced commercially in Europe and the United States. Historically, the main use was as a raw material in the production of pigments for lead paints , but such paints have been superseded by less toxic paints based on titanium dioxide . Other industrial uses included heat stabilization in nylon and polyesters , and in coatings of photothermographic paper. Since around the year 2000, lead(II) nitrate has begun to be used in gold cyanidation .
Lead(II) nitrate is toxic and must be handled with care to prevent inhalation, ingestion and skin contact. Due to its hazardous nature , the limited applications of lead(II) nitrate are under constant scrutiny.
Lead nitrate was first identified in 1597 by the alchemist Andreas Libavius , who called the substance plumbum dulce , meaning "sweet lead", because of its taste. [ 5 ] It is produced commercially by reaction of metallic lead with concentrated nitric acid in which it is sparingly soluble. [ 6 ] [ 7 ] It has been produced as a raw material for making pigments such as chrome yellow (lead(II) chromate, PbCrO 4 ) and chrome orange (basic lead(II) chromate, Pb 2 CrO 5 ) and Naples yellow . These pigments were used for dyeing and printing calico and other textiles. [ 8 ] It has been used as an oxidizer in black powder and together with lead azide in special explosives . [ 9 ]
Lead nitrate is produced by reaction of lead(II) oxide with concentrated nitric acid: [ 10 ]
It may also be obtained by evaporation of the solution obtained by reacting metallic lead with dilute nitric acid . [ 11 ]
Solutions and crystals of lead(II) nitrate are formed in the processing of lead– bismuth wastes from lead refineries. [ 12 ]
The crystal structure of solid lead(II) nitrate has been determined by neutron diffraction . [ 13 ] [ 14 ] The compound crystallizes in the cubic system with the lead atoms in a face-centred cubic system. Its space group is Pa3 Z=4 ( Bravais lattice notation), with each side of the cube with length 784 picometres .
The black dots represent the lead atoms, the white dots the nitrate groups 27 picometres above the plane of the lead atoms, and the blue dots the nitrate groups the same distance below this plane. In this configuration, every lead atom is bonded to twelve oxygen atoms ( bond length : 281 pm). All N–O bond lengths are identical, at 127 picometres. [ 15 ]
Research interest in the crystal structure of lead(II) nitrate was partly based on the possibility of free internal rotation of the nitrate groups within the crystal lattice at elevated temperatures, but this did not materialise. [ 14 ]
Lead nitrate is an oxidizer and has been used as such in pyrotechnics . [ 9 ] It is soluble in water and dilute nitric acid.
Basic nitrates are formed when alkali is added to a solution. Pb 2 (OH) 2 (NO 3 ) 2 is the predominant species formed at low pH . At higher pH Pb 6 (OH) 5 NO 3 is formed. [ 17 ] The cation Pb 6 O(OH) 6 4+ is unusual in having an oxide ion inside a cluster of 3 face-sharing PbO 4 tetrahedra. [ 18 ] There is no evidence for the formation of the hydroxide, Pb(OH) 2 , in aqueous solution below pH 12.
Solutions of lead nitrate can be used to form co-ordination complexes. Lead(II) is a hard acceptor ; it forms stronger complexes with nitrogen and oxygen electron-donating ligands. For example, combining lead nitrate and pentaethylene glycol (shortened to EO5 in the referenced paper) in a solution of acetonitrile and methanol followed by slow evaporation produced the compound [ Pb(NO 3 ) 2 EO5]. [ 19 ] In the crystal structure for this compound, the EO5 chain is wrapped around the lead ion in an equatorial plane similar to that of a crown ether . The two bidentate nitrate ligands are in trans configuration . The total coordination number is 10, with the lead ion in a bicapped square antiprism molecular geometry .
The complex formed by lead nitrate with a bithiazole bidentate N-donor ligand is binuclear. The crystal structure shows that the nitrate group forms a bridge between two lead atoms. [ 20 ] One aspect of this type of complexes is the presence of a physical gap in the coordination sphere ; i.e., the ligands are not placed symmetrically around the metal ion. This is potentially due to a lone pair of lead electrons, also found in lead complexes with an imidazole ligand. [ 21 ]
Lead nitrate has been used as a heat stabiliser in nylon and polyesters, as a coating for photothermographic paper, and in rodenticides . [ 10 ]
Heating lead nitrate is convenient means of making nitrogen dioxide :
In the gold cyanidation process, addition of lead(II) nitrate solution improves the leaching process. Only limited amounts (10 to 100 milligrams lead nitrate per kilogram gold) are required. [ 22 ] [ 23 ]
In organic chemistry, it may be used in the preparation of isothiocyanates from dithiocarbamates . [ 24 ] Its use as a bromide scavenger during S N 1 substitution has been reported. [ 25 ]
Lead(II) nitrate is toxic, and ingestion may lead to acute lead poisoning, as is applicable for all soluble lead compounds. [ 26 ] All inorganic lead compounds are classified by the International Agency for Research on Cancer (IARC) as probably carcinogenic to humans (Category 2A). [ 27 ] They have been linked to renal cancer and glioma in experimental animals and to renal cancer, brain cancer and lung cancer in humans, although studies of workers exposed to lead are often complicated by concurrent exposure to arsenic . [ 28 ] Lead is known to substitute for zinc in a number of enzymes , including δ-aminolevulinic acid dehydratase (porphobilinogen synthase) in the haem biosynthetic pathway and pyrimidine-5′-nucleotidase , important for the correct metabolism of DNA and can therefore cause fetal damage. [ 29 ] | https://en.wikipedia.org/wiki/N2O6Pb |
Palladium(II) nitrate is the inorganic compound with the formula Pd(NO 3 ) 2 .(H 2 O) x where x = 0 or 2. The anhydrous and dihydrate are deliquescent solids. According to X-ray crystallography , both compounds feature square planar Pd(II) with unidentate nitrate ligands. The anhydrous compound, which is a coordination polymer , is yellow. [ 1 ] [ 2 ]
As a solution in nitric acid, Pd(NO 3 ) 2 catalyzes the conversion of alkenes to dinitrate esters. Its pyrolysis affords palladium oxide . [ 3 ]
Hydrated palladium nitrate may be prepared by dissolving palladium oxide hydrate in dilute nitric acid followed by crystallization. The nitrate crystallizes as yellow-brown deliquescent prisms. The anhydrous material is obtained by treating palladium metal with fuming nitric acid . [ 1 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N2O6Pd |
Strontium nitrate is an inorganic compound composed of the elements strontium , nitrogen and oxygen with the formula Sr ( NO 3 ) 2 . This colorless solid is used as a red colorant and oxidizer in pyrotechnics .
Strontium nitrate is typically generated by the reaction of nitric acid on strontium carbonate . [ 2 ]
Like many other strontium salts, strontium nitrate is used to produce a rich red flame in fireworks and road flares . The oxidizing properties of this salt are advantageous in such applications. [ 3 ]
Strontium nitrate can aid in eliminating and lessening skin irritations. When mixed with glycolic acid , strontium nitrate reduces the sensation of skin irritation significantly better than using glycolic acid alone. [ 4 ]
As a divalent ion with an ionic radius similar to that of Ca 2+ (1.13 Å and 0.99 Å respectively), Sr 2+ ions resembles calcium's ability to traverse calcium-selective ion channels and trigger neurotransmitter release from nerve endings. It is thus used in electrophysiology experiments.
In his short story " A Germ-Destroyer ", Rudyard Kipling refers to strontium nitrate as the main ingredient of the titular fumigant . | https://en.wikipedia.org/wiki/N2O6Sr |
Uranyl nitrate is a water-soluble yellow uranium salt with the formula UO 2 (NO 3 ) 2 · n H 2 O . The hexa-, tri-, and dihydrates are known. [ 3 ] The compound is mainly of interest because it is an intermediate in the preparation of nuclear fuels. In the nuclear industry, it is commonly referred to as yellow salt.
Uranyl nitrate can be prepared by reaction of uranium salts with nitric acid . It is soluble in water , ethanol , and acetone . As determined by neutron diffraction , the uranyl center is characteristically linear with short U=O distances. In the equatorial plane of the complex are six U-O bonds to bidentate nitrate and two water ligands. At 245 pm , these U-O bonds are much longer than the U=O bonds of the uranyl center. [ 1 ]
Uranyl nitrate is important for nuclear reprocessing . It is the compound of uranium that results from dissolving the decladded spent nuclear fuel rods or yellowcake in nitric acid, for further separation and preparation of uranium hexafluoride for isotope separation for preparing of enriched uranium . A special feature of uranyl nitrate is its solubility in tributyl phosphate ( PO(OC 4 H 9 ) 3 ), which allows uranium to be extracted from the nitric acid solution. Its high solubility is attributed to the formation of the lipophilic adduct UO 2 (NO 3 ) 2 (OP(OBu) 3 ) 2 . [ citation needed ]
During the first half of the 19th century, many photosensitive metal salts had been identified as candidates for photographic processes , among them uranyl nitrate. The prints thus produced were called uranium prints or uranotypes.
The first uranium printing processes were invented by Scotsman J. Charles Burnett between 1855 and 1857, and used this compound as the sensitive salt. Burnett authored a 1858 article comparing "Printing by the Salts of the Uranic and Ferric Oxides"
The process employs the ability of the uranyl ion to pick up two electrons and reduce to the lower oxidation state of uranium(IV) under ultraviolet light.
Uranotypes can vary from print to print from a more neutral, brown russet to strong Bartolozzi red, with a very long tone grade. Surviving prints are slightly radioactive , a property which serves as a means of non-destructively identifying them.
Several other more elaborate photographic processes employing the compound appeared and vanished during the second half of the 19th century with names like Wothlytype, Mercuro-Uranotype and the Auro-Uranium process. Uranium papers were manufactured commercially at least until the end of the 19th century, vanishing due to the superior sensitivity and practical advantages of silver halides . From the 1930s through the 1950s Kodak Books described a uranium toner (Kodak T-9) using uranium nitrate hexahydrate. [ citation needed ]
Along with uranyl acetate it is used as a negative stain for viruses in electron microscopy ; in tissue samples it stabilizes nucleic acids and cell membranes . [ citation needed ]
Uranyl nitrates are common starting materials for the synthesis of other uranyl compounds because the nitrate ligand is easily replaced by other anions. It reacts with oxalate to give uranyl oxalate . Treatment with hydrochloric acid gives uranyl chloride . [ 4 ]
Uranyl nitrate is an oxidizing and highly toxic compound. When ingested, it causes severe chronic kidney disease and acute tubular necrosis and is a lymphocyte mitogen . Target organs include the kidneys , liver , lungs and brain . It also represents a severe fire and explosion risk when heated or subjected to shock in contact with oxidizable substances. [ citation needed ] | https://en.wikipedia.org/wiki/N2O8U |
Triazane is an inorganic compound with the chemical formula NH 2 NHNH 2 or N 3 H 5 . [ 2 ] Triazane is the third simplest acyclic azane after ammonia and hydrazine . It can be synthesized from hydrazine but is unstable and cannot be isolated in the free base form, only as salt forms such as triazanium sulfate. [ 3 ] Attempts to convert triazanium salts to the free base release only diazene and ammonia . [ 4 ] Triazane was first synthesized as a ligand of the silver complex ion: tris(μ 2 -triazane-κ 2 N 1 , N 3 )disilver(2+). [ clarification needed ] Triazane has also been synthesized in electron-irradiated ammonia ices and detected as a stable gas-phase product after sublimation . [ 5 ]
Several compounds containing the triazane skeleton are known, including 1-methyl-1-nitrosohydrazine ( NH 2 −N(CH 3 )−N=O ), produced from the solventless reaction of methylhydrazine ( CH 3 NHNH 2 ) and an alkyl nitrite (R−O−N=O):
1-Methyl-1-nitrosohydrazine is a colorless solid, sensitive to impact, but not to friction. It melts at 45 °C and decomposes at 121 °C.
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N3H5 |
Scandium(III) nitrate , Sc(NO 3 ) 3 , is an ionic compound. It is an oxidizer , as all nitrates are. The salt is applied in optical coatings, catalysts, electronic ceramics and the laser industry.
Scandium nitrate can be prepared by the reaction between scandium metal with dinitrogen tetroxide . [ 1 ]
The anhydrous form can also be obtained by the reaction between scandium chloride and dinitrogen pentoxide . [ 2 ] The tetrahydrate can be obtained from the reaction between scandium hydroxide and nitric acid . [ 3 ]
Scandium nitrate is a white solid which dissolves in water and ethanol . [ 4 ] It has multiple hydrated forms, including the dihydrate, trihydrate, and tetrahydrate. The tri- and tetrahydrate exist in the monoclinic crystal system . Upon heating in air to 50 °C, the tetrahydrate transforms into the dihydrate, which at 60 °C further converts to Sc 4 O 3 (NO 3 ) 3 ·6.5H 2 O. At 140–220 °C, Sc 4 O 5 (NO 3 ) 3 is formed. [ 2 ]
Scandium nitrate has been found to form clusters when in an aqueous solution which can affect its behavior and properties in various ways. Small Angle neutron scattering [ 5 ] has been used in experiments to show the clusters can contain as many as 10 scandium ions. This number depends on the concentration of the original scandium nitrate in the solution.
Scandium nitrate has been found to be a successful catalyst in chemical reactions such as Beckmann rearrangement of ketoximes to amides [ 6 ] and the isomerization of allylic alcohols to aldehydes. The catalytic success of scandium nitrate can be increased by modifying its structure in ways such as adding a co catalyst. Scandium nitrate is also the precursor for the synthesis of other scandium based compounds such as scandium oxide or scandium hydroxide. Scandium nitrate has also been investigated for its potential in luminescent materials due to its ability to strongly emit in the blue region of the spectrum. | https://en.wikipedia.org/wiki/N3O9Sc |
The molecular formula N 4 O (molar mass: 72.03 g/mol, exact mass: 72.0072 u) may refer to: | https://en.wikipedia.org/wiki/N4O |
Nitryl azide ( tetranitrogen dioxide ) is an inorganic compound with the chemical formula N 3 −N O 2 . It is an unstable nitrogen oxide consisting of a covalent nitrogen –nitrogen bond between a nitro group and an azide group. It has been detected by infrared spectroscopy as a short-lived product of the reaction between sodium azide and nitronium hexafluoroantimonate : [ 1 ]
The compound quickly decomposes to form nitrous oxide . Calculations suggest that this process occurs via an oxatetrazole oxide intermediate: [ 2 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N4O2 |
Trinitramide is a compound of nitrogen and oxygen with the molecular formula N (N O 2 ) 3 . The compound was detected and described in 2010 by researchers at the Royal Institute of Technology (KTH) in Sweden . [ 1 ] It is made of a nitrogen atom bonded to three nitro groups ( −NO 2 ).
Earlier, there had been speculation [ by whom? ] whether trinitramide could exist. [ need quotation to verify ] Theoretical calculations by Montgomery and Michels in 1993 showed that the compound was likely to be stable. [ 2 ]
Trinitramide is prepared by the nitration reaction of either potassium dinitramide or ammonium dinitramide with nitronium tetrafluoroborate in acetonitrile at low temperatures. [ 1 ]
Trinitramide has a potential use as one of the most efficient and least polluting of rocket propellant oxidizers , as it is chlorine -free. [ 3 ] This is potentially an important development, because the Tsiolkovsky rocket equation implies that even small improvements in specific impulse yields a similar change in delta-v , which can make large improvements in the size of practical rocket launch payloads.
The density impulse (impulse per volume) of a trinitramide based propellant could be 20 to 30 percent better than most existing formulations, [ 4 ] however the specific impulse (impulse per mass) of formulations with liquid oxygen is higher. [ 1 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/N4O6 |
Tetrasulfur tetranitride is an inorganic compound with the formula S 4 N 4 . This vivid orange, opaque, crystalline explosive is the most important binary sulfur nitride , which are compounds that contain only the elements sulfur and nitrogen . It is a precursor to many S-N compounds and has attracted wide interest for its unusual structure and bonding. [ 1 ] [ 2 ]
Nitrogen and sulfur have similar electronegativities . When the properties of atoms are so highly similar , they often form extensive families of covalently bonded structures and compounds. Indeed, a large number of S-N and S-NH compounds are known with S 4 N 4 as their parent.
S 4 N 4 adopts an unusual "extreme cradle" structure, with D 2d point group symmetry . It can be viewed as a derivative of a (hypothetical) eight-membered ring (or more simply a 'deformed' eight-membered ring) of alternating sulfur and nitrogen atoms. The pairs of sulfur atoms across the ring are separated by 2.586 Å , resulting in a cage-like structure as determined by single crystal X-ray diffraction. [ 3 ] The nature of the transannular S–S interactions remains a matter of investigation because it is significantly shorter than the sum of the van der Waals radii [ 4 ] but has been explained in the context of molecular orbital theory . [ 1 ] One pair of the transannular S atoms have valence 4, and the other pair of the transannular S atoms have valence 2. [ citation needed ] The bonding in S 4 N 4 is considered to be delocalized , which is indicated by the fact that the bond distances between neighboring sulfur and nitrogen atoms are nearly identical. S 4 N 4 has been shown to co-crystallize with benzene and the C 60 molecule. [ 5 ]
S 4 N 4 is stable to air . It is, however, unstable in the thermodynamic sense with a positive enthalpy of formation of +460 kJ/mol. This endothermic enthalpy of formation originates in the difference in energy of S 4 N 4 compared to its highly stable decomposition products:
S 4 N 4 is shock and friction sensitive and because one of its decomposition products is a gas, it is considered a primary explosive. [ 1 ] [ 6 ] Purer samples tend to be more sensitive. [ 7 ] Small samples can be detonated by striking with a hammer. S 4 N 4 is thermochromic , changing from pale yellow below −30 °C to orange at room temperature to deep red above 100 °C. [ 1 ]
S 4 N 4 was first prepared in 1835 by M. Gregory by the reaction of disulfur dichloride with ammonia , [ 8 ] a process that has been optimized: [ 9 ]
Coproducts of this reaction include heptasulfur imide ( S 7 NH ) and elemental sulfur, and the latter equilibrates with more S 4 N 4 and ammonium sulfide : [ 10 ]
A related synthesis employs [NH 4 ]Cl instead: [ 1 ]
An alternative synthesis entails the use of (((CH 3 ) 3 Si) 2 N) 2 S as a precursor with pre-formed S–N bonds. (((CH 3 ) 3 Si) 2 N) 2 S is prepared by the reaction of lithium bis(trimethylsilyl)amide and SCl 2 .
The (((CH 3 ) 3 Si) 2 N) 2 S reacts with the combination of SCl 2 and SO 2 Cl 2 to form S 4 N 4 , trimethylsilyl chloride , and sulfur dioxide : [ 11 ]
S 4 N 4 is a Lewis base at nitrogen. It binds to strong Lewis acids , such as SbCl 5 and SO 3 , or H[BF 4 ] :
The cage is distorted in these adducts . [ 1 ]
S 4 N 4 reacts with metal complexes, but the bonding situation may be quite complex. The cage remains intact in some cases but in other cases, it is degraded. [ 2 ] [ 12 ] For example, the soft Lewis acid CuCl forms a coordination polymer : [ 1 ]
Reportedly, [Pt 2 Cl 4 (P(CH 3 ) 2 Ph ) 2 ] initially forms a complex with S 4 N 4 at sulfur. This compound, upon standing, isomerizes to additionally bond through a nitrogen atom. S 4 N 4 oxidatively adds to Vaska's complex ( [Ir(Cl)(CO)(P Ph 3 ) 2 ] to form a hexacoordinate iridium complex where the S 4 N 4 binds through two sulfur atoms and one nitrogen atom. [ 2 ]
Dilute NaOH hydrolyzes S 4 N 4 as follows, yielding thiosulfate and trithionate : [ 1 ]
More concentrated base yields sulfite :
Many S-N compounds are prepared from S 4 N 4 . [ 13 ]
In electrophilic substitution or 1,3-dipolar cycloaddition reactions, S 4 N 4 behaves as a combination of the dithionitronium synthon and the sulfide synthon. Thus it adds to arenes and electron-rich alkynes to give 1,2,5‑ thiadiazoles . [ 14 ] Electron-poor alkynes attack S 4 N 4 to give a different cycloadduct of stoichiometry RC(NS) 2 SCR ′ . [ 15 ] [ 14 ] With electron-rich alkenes , S 4 N 4 behaves as a Diels-Alder diene. [ 14 ]
Passing gaseous S 4 N 4 over silver metal yields the low temperature superconductor polythiazyl or polysulfurnitride (transition temperature (0.26±0.03) K [ 16 ] ), often simply called "(SN) x ". In the conversion, the silver first becomes sulfided, and the resulting Ag 2 S catalyzes the conversion of the S 4 N 4 into the four-membered ring S 2 N 2 , which readily polymerizes . [ 1 ]
Oxidation of S 4 N 4 with elemental chlorine gives thiazyl chloride , [ citation needed ] but milder reagents give S 4 N + 3 :
That cation is relatively non- electrophilic and planar, with a delocalized π system . However, it adds triphenylphosphine to give [S(NPPh 3 ) 3 ] 3+ [Cl − ] 3 , a triimide analogue to sulfur trioxide . Conversely, S 4 N + 3 salts react with aluminum azide to recover S 4 N 4 . [ 14 ]
Treatment with tetramethylammonium azide produces the similar 10-π heterocycle [S 3 N 3 ] − :
In a related reaction, the use of the bis(triphenylphosphine)iminium azide gives a salt containing the blue [NS 4 ] − anion: [ 13 ]
[NS 4 ] − has a chain structure approximated by the resonance [S=S=N−S−S − ] ↔ [ − S−S−N=S=S] .
Reaction with piperidine generates [S 4 N 5 ] − :
A related cation is also known, i.e. [S 4 N 5 ] + .
Triphenylphosphine abstracts a sulfur atom, replacing it with another triphenylphosphine moiety: [ 14 ]
S 4 N 4 is a categorized as a primary explosive that is shock and friction sensitive. While comparable to pentaerythritol tetranitrate (PETN) in terms of impact sensitivity, its friction sensitivity is equal to or even lower than lead azide. [ 17 ] Purer samples are more shock-sensitive than those contaminated with elemental sulfur. [ 9 ] [ 7 ] | https://en.wikipedia.org/wiki/N4S4 |
In computational biology , N50 and L50 are statistics of a set of contig or scaffold lengths. The N50 is similar to a mean or median of lengths, but has greater weight given to the longer contigs. It is used widely in genome assembly , especially in reference to contig lengths within a draft assembly. There are also the related U50 , UL50 , UG50 , UG50% , N90 , NG50 , and D50 statistics.
To provide a better assessment of assembly output for viral and microbial datasets, a new metric called U50 should be used. The U50 identifies unique, target-specific contigs by using a reference genome as baseline, aiming at circumventing some limitations that are inherent to the N50 metric. The use of the U50 metric allows for a more accurate measure of assembly performance by analyzing only the unique, non-overlapping contigs. Most viral and microbial sequencing have high background noise (i.e., host and other non-targets), which contributes to having a skewed, misrepresented N50 value - this is corrected by U50 . [ 1 ]
N50 statistic defines assembly quality in terms of contiguity . Given a set of contigs, the N50 is defined as the sequence length of the shortest contig at 50% of the total assembly length. It can be thought of as the point of half of the mass of the distribution; the number of bases from all contigs longer than the N50 will be close to the number of bases from all contigs shorter than the N50 . For example, consider 9 contigs with the lengths 2,3,4,5,6,7,8,9, and 10; their sum is 54, half of the sum is 27, and the size of the genome also happens to be 54. Then, 50% of this assembly would be 10 + 9 + 8 = 27 (half the length of the sequence). Thus the N50=8, which is the size of the contig which, along with the larger contigs, contain half of sequence of a particular genome. Note: When comparing N50 values from different assemblies, the assembly sizes must be the same size in order for N50 to be meaningful.
N50 can be described as a weighted median statistic such that 50% of the entire assembly is contained in contigs or scaffolds equal to or larger than this value.
Given a set of contigs, each with its own length, the L50 is defined as count of smallest number of contigs whose length sum makes up half of genome size. From the example above the L50=3.
The N90 statistic is less than or equal to the N50 statistic; it is the length for which the collection of all contigs of that length or longer contains at least 90% of the sum of the lengths of all contigs.
Note that N50 is calculated in the context of the assembly size rather than the genome size. Therefore, comparisons of N50 values derived from assemblies of significantly different lengths are usually not informative, even if for the same genome. To address this, the authors of the Assemblathon competition came up with a new measure called NG50 . The NG50 statistic is the same as N50 except that it is 50% of the known or estimated genome size that must be of the NG50 length or longer. This allows for meaningful comparisons between different assemblies. In the typical case that the assembly size is not more than the genome size, the NG50 statistic will not be more than the N50 statistic.
The D50 statistic (also termed D50 test ) is similar to the N50 statistic in definition though it is generally not used to describe genome assemblies. The D50 statistic is the lowest value d for which the sum of the lengths of the largest d lengths is at least 50% of the sum of all of the lengths. [ 2 ]
U50 is the length of the smallest contig such that 50% of the sum of all unique, target-specific contigs is contained in contigs of size U50 or larger. [ 1 ]
UL50 is the number of contigs whose length sum produces U50.
UG50 is the length of the smallest contig such that 50% of the reference genome is contained in unique, target-specific contigs of size UG50 or larger.
UG50% is the estimated percent coverage length of the UG50 in direct relation to the length of the reference genome. The calculation is (100 × (UG50/Length of reference genome). The UG50% , as a percentage-based metric, can be used to compare assembly results from different samples or studies.
Consider two fictional, highly simplified genome assemblies, A and B, that are derived from two different species. Assembly A contains six contigs of lengths 80 kbp , 70 kbp, 50 kbp, 40 kbp, 30 kbp, and 20 kbp. The sum size of assembly A is 290 kbp, the N50 contig length is 70 kbp because 80 + 70 is greater than 50% of 290, and the L50 contig count is 2 contigs. The contig lengths of assembly B are the same as those of assembly A, except for the presence of two additional contigs with lengths of 10 kbp and 5 kbp. The size of assembly B is 305 kbp, the N50 contig length drops to 50 kbp because 80 + 70 + 50 is greater than 50% of 305, and the L50 contig count is 3 contigs. This example illustrates that one can sometimes increase the N50 length simply by removing some of the shortest contigs or scaffolds from an assembly.
If the estimated or known size of the genome from the fictional species A is 500 kbp then the NG50 contig length is 30 kbp because 80 + 70 + 50 + 40 + 30 is greater than 50% of 500. In contrast, if the estimated or known size of the genome from species B is 350 kbp then it has an NG50 contig length of 50 kbp because 80 + 70 + 50 is greater than 50% of 350.
N50 can be found mathematically for a list L of positive integers as follows:
For example: If L = (2, 2, 2, 3, 3, 4, 8, 8), then L' consists of six 2's, six 3's, four 4's, and sixteen 8's. That is, L' has twice as many 2s as L ; it has three times as many 3s as L ; it has four times as many 4s; etc. The median of the 32-element set L' is the average of the 16th smallest element, 4, and 17th smallest element, 8, so the N50 is 6. We can see that the sum of all values in the list L that are smaller than or equal to the N50 of 6 is 16 = 2+2+2+3+3+4 and the sum of all values in the list L that are larger than or equal to 6 is also 16 = 8+8. For comparison with the N50 of 6, note that the mean of the list L is 4 while the median is 3.
To recapitulate in a more visual way, we have:
Values of the list L = (2, 2, 2, 3, 3, 4, 8, 8)
Values of the new list L' = (2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8)
Ranks of L' values = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | https://en.wikipedia.org/wiki/N50,_L50,_and_related_statistics |
This is a table of UN/NA numbers (United Nations and North American numbers) exceptions of hazardous materials .
[ 1 ] | https://en.wikipedia.org/wiki/NA/UN_exceptions |
NABERS , the National Australian Built Environment Rating System is an Australian national initiative, managed by the Government of New South Wales ' Department of Climate Change, Energy, the Environment and Water (New South Wales) on behalf of the Australian Government , that measures and compares the environmental performance of Australian buildings and tenancies.
There are NABERS rating tools for commercial office buildings to measure greenhouse gas emissions , energy efficiency , water efficiency , waste efficiency and indoor environment quality . There are also energy/greenhouse and water rating tools for hotels , shopping centres and data centres .
A key feature of the initiative is the use of independent 'Accredited Assessors' to conduct ratings. Assessors are required to attend training, pass an exam and complete two supervised assessments before they receive full accreditation. [ 1 ] While there are no formal pre-requisites to attend the training, most Assessors have experience in the building services, property or energy management industries. Building owners and tenants can use the online 'self-assessment' tool, however they cannot promote these results. Only ratings that have been certified by the NABERS National Administrator can be promoted using the NABERS trademark .
NABERS rating helps you to accurately measure, understand, and communicate the environmental performance of your building while identifying areas for cost savings and future improvements. It provides a rating that is valid for twelve months from one to six stars for building efficiency across these measures:
Ratings can be applied to the following built environment sectors:
The vision statement of NABERS is 'To support a more sustainable built environment through a relevant, reliable and practical measure of building performance '.
The NABERS tools attempt to provide an accurate measurement of how efficiently building owners and tenants are providing their services without penalising them for factors that are beyond their control .
For example, if the primary service that an office building owner provides is safe , lit and comfortable office space the NABERS Energy for offices tool would consider how much space is being used, how much energy is being used to supply services to the space, and then statistically adjusts for factors like the climate - which will influence how much energy is used for heating and cooling .
To obtain a NABERS Energy for offices rating, consumption data for the building (such as electricity and gas bills) is collected by Accredited Assessors along with data about a number of other aspects of the building such as its size, hours of occupation, climate location and density of occupation. Data requirements are set out in a document called 'The NABERS Energy and Water for Offices Rules for Collecting and Using Data v.3.0' . This data is then input into the NABERS rating calculator [ 2 ] which statistically adjusts for these factors so that the building can have its consumption fairly benchmarked against its peers. The result of this calculation is a star rating on a six-star scale, where zero is very poor performance and six is market-leading. [ 3 ]
The procedure for an office water rating is similar to conducting an office energy rating. The main differences are that it is water rather than energy bills that are used, and some data such as the hours of operation are not required. Unlike office energy ratings, which can either be for the base building, tenancies or whole building, office water ratings are only available for whole buildings.
Like NABERS for offices, NABERS Energy for data centres has three distinct rating types to reflect the different interests and responsibilities from data centres owners, operators and tenants – Infrastructure (co-location owner), Whole Facility (data centre owner) and IT Equipment (data centre tenant) ratings. The tool is designed to rate the majority of data centres in Australia, provide a direct comparison with other rateable data centres, and allow an individual data centre to measure and compare performance over time.
The NABERS Data Centre IT Equipment Rating is designed for organisations that control and manage their own IT equipment ( servers , storage and networking devices ). The IT Equipment rating measures features that are closely related to the primary functions of a data centre ( processing , storage and networking ) and that all data centres provide, regardless of how they provide them. NABERS uses two IT equipment metrics:
The NABERS performance benchmark model predicts the industry median greenhouse gas emissions for a given amount of data centre processing and storage capacity. This means that if a data centre consumes more energy than the benchmark model predicts, the site is less energy efficient than the industry median (set at 3 stars), while if it consumes less energy it is more efficient than the median.
To obtain a NABERS Energy for data centres IT Equipment rating, energy consumption data for the IT equipment over a 28- to 40-day period is collected by Accredited Assessors along with data about the total unformatted storage capacity and total processing capacity as above.
The Infrastructure Rating measures the energy efficiency in delivering support services to the IT equipment, using the widely accepted industry Power Usage Effectiveness (PUE) ratio that is converted into kilogram of emissions with some modification for climate and shared cooling services. To obtain an infrastructure rating, 12 months of energy consumption data for IT equipment and infrastructure services is collected by Accredited Assessors along with the climate location of the data centre. [ 4 ]
The Whole Facility rating measures the energy efficiency of the whole data centre by assessing the processing and storage capacity and the industry median energy efficiency for infrastructure services compared with the overall energy consumption of the data centre. It is a combination of both the IT Equipment and Infrastructure rating benchmarks To obtain a NABERS Energy for data centres Whole Facility rating, 12 months of energy consumption data for the data centre is collected by Accredited Assessors along with the processing and storage capacity and climate location of the data centre.
There are a number of building environmental certification systems across the world, such as LEED , Green Star , BRE Environmental Assessment Method (BREEAM) and Display Energy Certificates (DECs) . The key features of NABERS as a system are that it is based on performance rather than design, assessments are carried out by third-party 'Accredited Assessors', it is based on third party verifiable data (such as utility bills), ratings undergo government quality assurance checks and it distinguishes between the environmental impact of a building's shared services and its tenancies. While other rating systems across the world share some of these features, none share all of them.
While NABERS Energy is a voluntary rating scheme for buildings, its success has been at least partly driven by its extensive use in energy initiatives by government and industry throughout Australia. Some programs include:
NABERS Energy for offices is considered by many to have been successful, as over 82% of the Australian national office market has now been rated with either a base building or whole building rating. Factors behind the success of the tool are largely attributed to its ability to differentiate between the base building and tenants energy end uses and strong government support. [ 11 ] Far fewer tenancy energy ratings have been conducted however and there has also been far less uptake of the other tools.
Australian government legislation that requires owners of office buildings to disclose the energy efficiency of the building to prospective tenants or buyers. Known operationally as the Commercial Building Disclosure (CBD) program, a certified NABERS Energy rating is the main energy efficiency indicator required of building owners. [ 12 ] | https://en.wikipedia.org/wiki/NABERS |
NADPH oxidase (nicotinamide adenine dinucleotide phosphate oxidase) is a membrane-bound enzyme complex that faces the extracellular space. It can be found in the plasma membrane as well as in the membranes of phagosomes used by neutrophil white blood cells to engulf microorganisms. Human isoforms of the catalytic component of the complex include NOX1 , NOX2 , NOX3 , NOX4 , NOX5 , DUOX1 , and DUOX2 . [ 1 ]
NADPH oxidase catalyzes the production of a superoxide free radical by transferring one electron to oxygen from NADPH . [ 2 ]
In mammals, NADPH oxidase is found in two types: one in white blood cells (neutrophilic) and the other in vascular cells, differing in biochemical structure and functions. [ 3 ] Neutrophilic NADPH oxidase produces superoxide almost instantaneously, whereas the vascular enzyme produces superoxide in minutes to hours. [ 4 ] Moreover, in white blood cells, superoxide has been found to transfer electrons across the membrane to extracellular oxygen, while in vascular cells, the radical anion appears to be released mainly intracellularly. [ 5 ] [ 6 ]
The isoform found in neutrophils is made up of six subunits. These subunits are:
There are several vascular isoforms of the complex which use paralogs the NOX2 subunit:
There are two further paralogs of NOX2 subunit in the thyroid:
The whole structure of the membrane-bound vascular enzyme is composed of five parts: two cytosolic subunits (p47phox and p67phox), a cytochrome b558 which consists of gp91phox, p22phox and a small G protein Rac. [ 3 ] Generation of the superoxide in vascular NADPH occurs by a one-electron reduction of oxygen via the gp91phox subunit, using reduced NADPH as the electron donor. The small G protein carries an essential role in the activation of the oxidase by switching between a GDP-bound (inactive) and GTP-linked (active) forms. [ 8 ]
NADPH oxidases (NOXes) are one of the major sources of cellular reactive oxygen species (ROS) , and they still are the focus of extensive research interest due to their exclusive function in producing ROS under normal physiological conditions. The NADPH oxidase complex is dormant under normal circumstances but is activated to assemble in the membranes during respiratory burst . The activated NADPH oxidase generates superoxide which has roles in animal immune response and plant signalling. [ 9 ]
Superoxide can be produced in phagosomes which have ingested bacteria and fungi , or it can be produced outside of the cell. [ 10 ] In macrophages, superoxide kills bacteria and fungi by mechanisms that are not yet fully understood. [ 11 ] [ 12 ] Superoxide spontaneously dismutates to form peroxide which is then protonated to produce hydrogen peroxide. Opinions are polarised as to how the oxidase kills microbes in neutrophils. On the one hand it is thought that hydrogen peroxide acts as substrate for myeloperoxidase to produce hypochlorous acid. [ 13 ] It may also inactivate critical metabolic enzymes, initiate lipid peroxidation , damage iron-sulphur clusters , [ 14 ] and liberate redox-active iron, which allows the generation of indiscriminate oxidants such as the hydroxyl radical. [ 12 ] An alternative view is that the oxidase elevates the pH in the vacuole to about 9.0, which is optimal for the neutral proteases that degranulate from the cytoplasmic granules (where they are inactive at pH ~5.5) and it pumps potassium into the vacuole, which solubilises the enzymes, and it is the activated proteases that kill and digest the microbes. [ 15 ]
In insects , NOXes had some functions clarified. Arthropods have three NOX types (NOX4-art, an arthropod-specific p22-phox-independent NOX4, and two calcium-dependent enzymes, DUOX). [ 16 ] [ 17 ] [ 18 ] In the gut, DUOX-dependent ROS production from bacteria-stimulated Drosophila melanogaster mucosa is an important pathogen-killing mechanism [ 19 ] and can increase defecation as a defense response. [ 20 ] In Aedes aegypti , DUOX is involved in the control of the gut indigenous microbiota. [ 21 ] Rhodnius prolixus has calcium activated DUOX, which is involved in eggshell hardening, [ 22 ] and NOX5, which is involved in the control of gut motility and blood digestion. [ 23 ] [ 24 ]
Careful regulation of NADPH oxidase activity is crucial to maintain a healthy level of ROS in the body. The enzyme is dormant in resting cells but becomes rapidly activated by several stimuli, including bacterial products and cytokines. [ 25 ] Vascular NADPH oxidases are regulated by a variety of hormones and factors known to be important players in vascular remodeling and disease. These include thrombin , platelet-derived growth factor (PDGF), tumor necrosis factor (TNFa), lactosylceramide , interleukin-1 , and oxidized LDL . [ 26 ] It is also stimulated by agonists and arachidonic acid . [ 26 ] Conversely, assembly of the complex can be inhibited by apocynin and diphenylene iodonium . Apocynin decreases influenza-induced lung inflammation in mice in vivo and so may have clinical benefits in the treatment of influenza. [ 27 ]
Ang-1 triggers NOX2, NOX4, and the mitochondria to release ROS and that ROS derived from these sources play distinct roles in the regulation of the Ang-1/Tie 2 signaling pathway and pro-angiogenic responses. [ 28 ]
Superoxides are crucial in killing foreign bacteria in the human body. Consequently, under-activity can lead to an increased susceptibility to organisms such as catalase-positive microbes, and over-activity can lead to oxidative stress and cell damage.
Excessive production of ROS in vascular cells causes many forms of cardiovascular disease including hypertension , atherosclerosis , myocardial infarction , and ischemic stroke . [ 29 ] Atherosclerosis is caused by the accumulation of macrophages containing cholesterol ( foam cells ) in artery walls (in the intima ). ROS produced by NADPH oxidase activate an enzyme that makes the macrophages adhere to the artery wall (by polymerizing actin fibers). This process is counterbalanced by NADPH oxidase inhibitors, and by antioxidants. An imbalance in favor of ROS produces atherosclerosis. In vitro studies have found that the NADPH oxidase inhibitors apocynin and diphenyleneiodonium, along with the antioxidants N-acetyl-cysteine and resveratrol, depolymerized the actin, broke the adhesions, and allowed foam cells to migrate out of the intima. [ 30 ] [ 31 ]
One study suggests a role for NADPH oxidase in ketamine -induced loss of neuronal parvalbumin and GAD67 expression. [ 32 ] Similar loss is observed in schizophrenia , and the results may point at the NADPH oxidase as a possible player in the pathophysiology of the disease. [ 33 ] Nitro blue tetrazolium is used in a diagnostic test, in particular, for chronic granulomatous disease, a disease in which there is a defect in NADPH oxidase; therefore, the phagocyte is unable to make the reactive oxygen species or radicals required for bacterial killing, resulting in bacteria thriving within the phagocyte. The higher the blue score the better the cell is at producing reactive oxygen species.
It has also been shown that NADPH oxidase plays a role in the mechanism that induces the formation of sFlt-1 , a protein that deactivates certain proangiogenic factors that play a role in the development of the placenta, by facilitating the formation of reactive oxygen species , which are suspected intermediaries in sFlt-1 formation. These effects are in part responsible for inducing pre-eclampsia in pregnant women [ 34 ]
Mutations in the NADPH oxidase subunit genes cause several Chronic Granulomatous Diseases (CGD), characterized by extreme susceptibility to infection. [ 26 ] These include:
In these diseases, cells have a low capacity for phagocytosis, and persistent bacterial infections occur. Areas of infected cells are common, granulomas. A similar disorder called neutrophil immunodeficiency syndrome is linked to a mutation in the RAC2, also a part of the complex.
NADPH oxidase can be inhibited by apocynin , nitric oxide (NO), and diphenylene iodonium . Apocynin acts by preventing the assembly of the NADPH oxidase subunits. Apocynin decreases influenza-induced lung inflammation in mice in vivo and so may have clinical benefits in the treatment of influenza. [ 27 ]
Inhibition of NADPH oxidase by NO blocks the source of oxidative stress in the vasculature. NO donor drugs ( nitrovasodilators ) have therefore been used for more than a century to treat coronary artery disease , hypertension , and heart failure by preventing excess superoxide from deteriorating healthy vascular cells. [ 3 ]
More advanced NADPH oxidase inhibitors include GKT-831 (Formerly GKT137831 ), a dual Inhibitor of isoforms NOX4 and NOX1 [ 35 ] which was patented in 2007. [ 36 ] The compound was initially developed for Idiopathic pulmonary fibrosis and obtained orphan drug designation by the FDA and EMA at end of 2010. [ 37 ] | https://en.wikipedia.org/wiki/NAD(P)H_oxidase |
In molecular biology , the NAD+ five-prime cap (NAD+ 5' cap) refers to a molecule of nicotinamide adenine dinucleotide ( NAD+ ), a nucleoside-containing metabolite, covalently bonded the 5' end of cellular mRNA . While the more common methylated guanosine ( m7G ) cap is added to RNA by a capping complex that associates with RNA polymerase II ( RNAP II ), [ 1 ] the NAD cap is added during transcriptional initiation by the RNA polymerase itself, acting as a non-canonical initiating nucleotide (NCIN). [ 2 ] As such, while m7G capping can only occur in organisms possessing specialized capping complexes, because NAD capping is performed by RNAP itself, it is hypothesized to occur in most, if not all, organisms. [ 2 ]
The NAD+ 5' cap has been observed in bacteria , [ 3 ] contrary to the long-held belief that prokaryotes lacked 5'-capped RNA , [ 4 ] as well as on the 5' cap of eukaryotic mRNA , [ 5 ] in place of the m7G cap. This modification also potentially allows for selective degradation of RNA]within prokaryotes as different pathways are involved in the degradation of NAD+-capped and uncapped 5′-triphosphate-RNAs.
In eukaryotic cells, while the more commonly observed m7G cap promotes the stability of the mRNA and supports translation , [ 6 ] the NAD+ cap targets the RNA transcript for decay, facilitated by the non-canonical decapping enzyme, DXO. [ 7 ] Considering the centrality of NAD in redox chemistry and post-translational protein modification , its attachment to RNA represents potentially undiscovered pathways in RNA metabolism and regulation. [ 8 ]
In prokaryotes , the 5' NAD+ modification is established by bacterial RNAP during transcription initiation [ 4 ] and has been shown to display functions analogous to those of the eukaryotic 5' cap. [ 7 ] In-vitro transcribed NAD-modified RNA was shown to be more resistant to RNase E , the main enzyme in the decay pathway of E. coli . [ 7 ] NAD-modification further was shown to decelerate RNA processing by RNA pyrophosphohydrolase (RppH), [ 7 ] which is known to trigger RNase-E-mediated decay through the conversion of 5′-triphosphate-RNA to 5′-monophosphate-RNA. [ 9 ] Nudc, a nudix phosphohydrolase , can decap NAD-RNA through hydrolyzing NAD(H) into NMN(H) and AMP, [ 10 ] causing RNase-E-mediated decay, but is inactive against 5′-triphosphate-RNA. [ 7 ] This 5' modification allows for the selective initiation of degradation for a subset of RNAs as the NAD-capped RNAs are stabilized in the presence of RppH, but are decapped by Nudc, while the 5′-triphosphate-RNAs are susceptible to RppH but not Nudc. [ 11 ]
Next generation sequencing ( NGS ) of the NAD-RNA conjugates in E. coli revealed an abundance of a specific group of small regulatory RNAs (sRNAs) which are known to be involved in stress response systems, as well as enzymes involved in cellular metabolism . [ 12 ] The small number of RNA transcripts with a NAD cap might allow the cell to selectively degrade these RNAs separate from other pathways. [ 8 ] Considering that the stress responses are known to affect NAD+ concentration, [ 13 ] this finding further supports the possibility of undiscovered pathways linking the energetic state of a cell to mRNA turnover.
NAD capping has also been suggested to recruit specific proteins to the 5' end of the RNA as NAD is one of the most common protein ligands . [ 8 ] NAD-binding pockets are well characterized in many proteins and could help the localization of the RNA to an enzyme or receptor . Many NAD-utilizing metabolic enzymes can also bind to RNA , [ 12 ] presenting the possibility of unknown ribonucleoprotein complexes.
NAD+ 5' capped RNA have been found in yeast , [ 2 ] humans , [ 4 ] and Arabidopsis thaliana . [ 14 ] In eukaryotes , the NAD+ cap is removed by non-canonical decapping enzymes from the DXO family. [ 15 ] DeNADing by DXO results in a 5' end monophosphate RNA [ 15 ] distinct from NudC which results in NMN plus 5′ monophosphate RNA. [ 10 ] Importantly, DXO is ~6 fold more efficient at decapping NAD+ compared to m7G , [ 6 ] suggesting that it selectively degrades NAD-capped RNA rather than the more common m7G cap, similar to NudC.
The m7G cap has been shown to promote translation through recruitment of the initiation complex onto the mRNA . [ 16 ] However, the NAD+-cap does not provide a similar function as NAD+-capped and polyadenylated mRNA displayed similar levels of translation in vitro to uncapped mRNA . [ 7 ] Additionally, the 5' NAD+ cap further promotes decay of the RNA it is attached to, [ 6 ] NAD+-capped and polyadenylated mRNA were demonstrated in vitro to be less stable than mRNAs lacking a 5' cap , [ 7 ] suggesting that the NAD+ modification is actively facilitating DXO-mediated RNA decay. [ 6 ]
While the relationship between RNA-binding proteins, such as glyceraldehyde-3-phosphate dehydrogenase ( GAPDH ), [ 17 ] and NAD+ concentration is established, the NAD+ cap has been hypothesized to represent a direct link between RNA expression levels and cellular metabolism. [ 6 ] It is known that energy stresses such as glucose deprivation [ 13 ] and caloric restriction [ 18 ] influence NAD+ concentrations and can possibly impact NAD+ capping. Additionally, as low-nutrient conditions can affect mRNA stability, [ 19 ] and seeing as NAD+ caps promote mRNA decay, it is possible that the energetic state of a cell could affect NAD+-capping and thus mRNA turnover. [ 6 ] Certain findings, such as the higher abundance of NAD+-capped transcripts in stationary-phase bacteria [ 2 ] as well as yeast grown on synthetic media, [ 5 ] point toward this possibility. | https://en.wikipedia.org/wiki/NAD+_Five-prime_cap |
3PFN
65220
192185
ENSG00000008130
ENSMUSG00000029063
O95544
P58058
NM_001353642
NM_001159637 NM_138671 NM_001355599
NP_001340571
NP_001153109 NP_619612 NP_001342528
NAD + kinase (EC 2.7.1.23, NADK) is an enzyme that converts nicotinamide adenine dinucleotide (NAD + ) into NADP + through phosphorylating the NAD + coenzyme . [ 6 ] NADP + is an essential coenzyme that is reduced to NADPH primarily by the pentose phosphate pathway to provide reducing power in biosynthetic processes such as fatty acid biosynthesis and nucleotide synthesis . [ 7 ] The structure of the NADK from the archaean Archaeoglobus fulgidus has been determined. [ 1 ]
In humans, the genes NADK [ 8 ] and MNADK [ 9 ] encode NAD + kinases localized in cytosol [ 8 ] and mitochondria, [ 9 ] respectively. Similarly, yeast have both cytosolic and mitochondrial isoforms, and the yeast mitochondrial isoform accepts both NAD + and NADH as substrates for phosphorylation. [ 10 ] [ 11 ]
The reaction catalyzed by NADK is
NADK phosphorylates NAD + at the 2’ position of the ribose ring that carries the adenine moiety. It is highly selective for its substrates, NAD and ATP, and does not tolerate modifications either to the phosphoryl acceptor, NAD, or the pyridine moiety of the phosphoryl donor, ATP. [ 8 ] NADK also uses metal ions to coordinate the ATP in the active site. In vitro studies with various divalent metal ions have shown that zinc and manganese are preferred over magnesium, while copper and nickel are not accepted by the enzyme at all. [ 8 ] A proposed mechanism involves the 2' alcohol oxygen acting as a nucleophile to attack the gamma-phosphoryl of ATP, releasing ADP.
NADK is highly regulated by the redox state of the cell. Whereas NAD is predominantly found in its oxidized state NAD + , the phosphorylated NADP is largely present in its reduced form, as NADPH. [ 12 ] [ 13 ] Thus, NADK can modulate responses to oxidative stress by controlling NADP synthesis. Bacterial NADK is shown to be inhibited allosterically by both NADPH and NADH. [ 14 ] NADK is also reportedly stimulated by calcium / calmodulin binding in certain cell types, such as neutrophils. [ 15 ] NAD kinases in plants and sea urchin eggs have also been found to bind calmodulin. [ 16 ] [ 17 ]
Due to the essential role of NADPH in lipid and DNA biosynthesis and the hyperproliferative nature of most cancers, NADK is an attractive target for cancer therapy. Furthermore, NADPH is required for the antioxidant activities of thioredoxin reductase and glutaredoxin . [ 18 ] [ 19 ] Thionicotinamide and other nicotinamide analogs are potential inhibitors of NADK, [ 20 ] and studies show that treatment of colon cancer cells with thionicotinamide suppresses the cytosolic NADPH pool to increase oxidative stress and synergizes with chemotherapy. [ 21 ]
While the role of NADK in increasing the NADPH pool appears to offer protection against apoptosis , there are also cases where NADK activity appears to potentiate cell death. Genetic studies done in human haploid cell lines indicate that knocking out NADK may protect from certain non-apoptotic stimuli. [ 22 ] | https://en.wikipedia.org/wiki/NAD+_kinase |
NAIL-MS (short for nucleic acid isotope labeling coupled mass spectrometry ) is a technique based on mass spectrometry used for the investigation of nucleic acids and its modifications . It enables a variety of experiment designs to study the underlying mechanism of RNA biology in vivo . For example, the dynamic behaviour of nucleic acids in living cells, especially of RNA modifications , can be followed in more detail. [ 1 ]
NAIL-MS is used to study RNA modification mechanisms. Therefore, cells in culture are first fed with stable isotope labeled nutrients and the cells incorporate these into their biomolecules. After purification of the nucleic acids, most often RNA , analysis is done by mass spectrometry. Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of ions . Pairs of chemically identical nucleosides of different stable-isotope composition can be differentiated in a mass spectrometer due to their mass difference. Unlabeled nucleosides can therefore be distinguished from their stable isotope labeled isotopologues . For most NAIL-MS approaches it is crucial that the labeled nucleosides are more than 2 Da heavier than the unlabeled ones. This is because 1.1% of naturally occurring carbon atoms are 13 C isotopes. In the case of nucleosides this leads to a mass increase of 1 Da in ~10% of the nucleosides. This signal would disturb the final evaluation of the measurement.
NAIL-MS can be used to investigate RNA modification dynamics by changing the labeled nutrients of the corresponding growth medium during the experiment. Furthermore, cell populations can be compared directly with each other without effects of purification bias. Furthermore, it can be used for the production of biosynthetic isotopologues of most nucleosides which are needed for quantification by mass spectrometry and even for the discovery of yet unknown RNA modifications. [ 2 ] [ 3 ] [ 4 ]
In general, cells are cultivated in unlabeled or stable (non-radioactive) isotope labeled media. For example, the medium can contain glucose labeled with six carbon-13 atoms ( 13 C) instead of the normal carbon-12 ( 12 C). Cells growing in this medium, will, depending on model organism, incorporate the heavy glucose into all of their RNA molecules. Thereafter, all nucleotides are 5 Da heavier than their unlabeled isotopologues due to a complete carbon labeling of the ribose. After cultivation and appropriate labeling of the cells, they are generally harvested using phenol/chloroform/guanidinium isothiocyanate. Other extraction methods are possible and sometimes needed (e.g. for yeast). RNA is then isolated by Phenol-Chloroform extraction and iso -Propanol precipitation. Further purification of specific RNA species (e.g. rRNA, tRNA) is usually done by size-exclusion chromatography (SEC) but other approaches are available as well. For most applications the final product needs to be enzymatically digested to nucleosides before analysis by LC-MS . Therefore, digestion enzymes such as benzonase , NP1 and CIP are used. [ 5 ] [ 6 ] Typically, a triple quadrupole in MRM mode is used for the measurements.
How the labeling of RNA molecules is achieved depends on the model organism. For E.coli ( bacteria ) the minimum medium M9 can be used and supplemented with the stable isotope labeled variants of the needed salts. This enables labeling with 13 C-carbon, 15 N-nitrogen, 34 S-sulfur and 2 H-hydrogen. [ 7 ] In S.cerevisiae ( yeast ) there are currently two possibilities: First, the use of commercially available complete growth medium, which enables labeling with 13 C-carbon and/or 15 N-nitrogen and second the use of minimal YNB medium which has to be supplemented with several amino acids and glucose which can be added as stable isotope labeled variants in order to achieve 13 C-carbon, 15 N-nitrogen and 2 H-hydrogen labeling of RNA. [ 8 ]
While labeling in model organisms like E.coli and S.cerevisiae is fairly simple, stable isotope labeling in cell culture is much more challenging as the composition of the growth media is much more complex. Neither the supplementation of stable isotope labeled glucose nor the supplementation of stable isotope labeled variants of simple precursors of nucleoside biosynthesis such as glutamine and/or aspartate is sufficient for a defined mass increase higher than 2 Da. Instead, most cells kept in cell culture can be fed with stable isotope labeled methionine for labeling of methyl groups and with stable isotope labeled variants of adenin and uridine for labeling of the nucleoside's base body. [ 9 ] Special care must be taken when supplementing the medium with FBS (fetal bovine serum), as it also contains small metabolites used for the biosynthesis of nucleosides. The use of dialyzed FBS is therefore advisable when defined labeling of all nucleosides is desired.
With NAIL-MS different experiment designs are possible.
NAIL-MS can be used to produce stable isotope labeled internal standards (ISTD). Therefore, cells are grown in medium which results in complete labeling of all nucleosides. The purified mix of nucleosides can then be used as ISTD which is needed for accurate absolute quantification of nucleosides by mass spectrometry. This mixture of labeled nucleosides is also referred to as SILIS (stable isotope labeled internal standard). [ 10 ] The advantage of this approach is, that all modifications present in an organism can thereby be biosynthesized as labeled compounds. The production of SILIS was already done before the term NAIL-MS emerged.
A comparative NAIL-MS experiment is quite similar to a SILAC experiment but for RNA instead of proteins. First, two populations of the respective cells are cultivated. One of the cell populations is fed with growth medium containing unlabeled nutrients, whereas the second population is fed with growth medium containing stable isotope labeled nutrients. The cells then incorporate the respective isotopologues into their RNA molecules. One of the cell populations serves as a control group whereas the other is subject to the associated research (e.g. KO strain, stress). Upon harvesting of the two cell populations they are mixed and co-processed together to exclude purification-bias. Due to the distinct masses of incorporated nutrients into the nucleosides a differentiation of the two cell populations is possible by mass spectrometry.
Upon initiation of a pulse-chase experiment the medium is switched from medium(1) to medium(2). The two media must only differ in their isotope content. Thereby it is possible to distinguish between RNA molecules already existent before experiment initiation (= RNA molecules grown in medium(1)) and RNA molecules that are newly transcribed after experiment initiation (= RNA molecules grown in medium(2)). This allows the detailed study of modification dynamics in vivo . The supplementation of labeled methionine in either medium(1) or medium(2) allows the tracing of methylation processes. Other isotopically labeled metabolites potentially allow for further modification analysis.
Altogether NAIL-MS enables the investigation of RNA modification dynamics by mass spectrometry. With this technique, enzymatic demethylation has been observed for several RNA damages inside living bacteria. [ 4 ] [ 7 ]
For the discovery of uncharacterized modifications cells are grown in unlabeled or 13 C‑labeled or 15 N‑labeled or 2 H‑labeled or 34 S‑labeled medium. Unknown signals occurring during mass spectrometry are then inspected in all differentially labeled cultures. If retention times of unknown compounds with appropriately divergent m/z values overlap, a sum formula of the compound can be postulated by calculating the mass differences of the overlapping signal in the differentially labeled cultures. With this method several new RNA modifications could be discovered. This experimental design also was the initial idea that started the concept of NAIL-MS.
NAIL-MS can also be applied to oligonucleotide analysis by mass spectrometry. This is useful when the sequence information is to be retained. [ 11 ] | https://en.wikipedia.org/wiki/NAIL-MS |
NAPQI , also known as NAPBQI or N -acetyl- p -benzoquinone imine, is a toxic byproduct produced during the xenobiotic metabolism of the analgesic paracetamol (acetaminophen). [ 1 ] It is normally produced only in small amounts, and then almost immediately detoxified in the liver.
However, under some conditions in which NAPQI is not effectively detoxified (usually in the case of paracetamol overdose ), it causes severe damage to the liver. This becomes apparent 3–4 days after ingestion and may result in death from fulminant liver failure several days after the overdose.
In adults, the primary metabolic pathway for paracetamol is glucuronidation . [ 1 ] This yields a relatively non-toxic metabolite, which is excreted into bile and passed out of the body. A small amount of the drug is metabolized via the cytochrome P-450 pathway (to be specific, CYP3A4 and CYP2E1 ) into NAPQI, which is extremely toxic to liver tissue, as well as being a strong biochemical oxidizer. [ 1 ] In an average adult, only a small amount (approximately 10% of a therapeutic paracetamol dose) of NAPQI is produced, which is inactivated by conjugation with glutathione (GSH). The amount of NAPQI produced differs in certain populations. [ citation needed ]
The minimum dosage at which paracetamol causes toxicity usually is 7.5 to 10g in the average person. [ 2 ] The lethal dose is usually between 10 g and 15 g. [ citation needed ] Concurrent alcohol intake lowers these thresholds significantly. Chronic alcoholics may be more susceptible to adverse effects due to reduced glutathione levels. [ 3 ] Other populations may experience effects at lower or higher dosages depending on differences in P-450 enzyme activity and other factors which affect the amount of NAPQI produced. In general, however, the primary concern is accidental or intentional paracetamol overdose.
When a toxic dose of paracetamol is ingested, the normal glucuronide pathway is saturated and large amounts of NAPQI are produced. Liver reserves of glutathione are depleted by conjugation with this excess NAPQI. The mechanism by which toxicity results is complex, but is believed to involve reaction between unconjugated NAPQI and critical proteins as well as increased susceptibility to oxidative stress caused by the depletion of glutathione. [ 4 ]
The prognosis is good for paracetamol overdoses if treatment is initiated up to 8 hours after the drug has been taken. Most hospitals stock the antidote ( acetylcysteine ), which replenishes the liver's supply of glutathione , allowing the NAPQI to be metabolized safely. [ 1 ] Without early administration of the antidote, fulminant liver failure follows, often in combination with kidney failure, and death generally occurs within several days.
NAPQI becomes toxic when GSH is depleted by an overdose of acetaminophen, Glutathione is an essential antidote to overdose. Glutathione conjugates to NAPQI and helps to detoxify it. In this capacity, it protects cellular protein thiol groups, which would otherwise become covalently modified; when all GSH has been spent, NAPQI begins to bind to certain enzymes like N-10 formyltetrahydrofolate dehydrogenase and glutamate dehydrogenase, reducing their activity and killing the cells in the process. This, along with the depletion of GSH which significantly impairs the function of mitochondria, plays a significant role in the development of paracetamol toxicity. [ 5 ]
The preferred treatment for an overdose of this painkiller is the administration of N -acetyl- L -cysteine (either via oral or IV administration) [ 6 ] ), which is processed by cells to L -cysteine and used in the de novo synthesis of GSH. | https://en.wikipedia.org/wiki/NAPQI |
The NASA Fine Art Program was established in 1962. NASA administrator, James Webb , jump-started the program by recommending artists to become involved in the agency. [ 1 ] Artists, including Norman Rockwell , Robert Rauschenberg , Malcolm H. Smith and Andy Warhol were commissioned to record the history of space exploration through the eyes of artists. The first director of the Art Program was James Dean (NASA) . [ 2 ] Using artists of different mediums and genres serves the purpose of educating different audiences about NASA and space exploration. [ 3 ] To give the artists the best experience possible, NASA allowed them unprecedented access to sites and materials. Participants were present at suit-up, launch sites, and press releases. [ 2 ] All works, from sketches to finished products, were given to NASA for use in museums and exhibitions. [ 4 ] The collection now includes 2,500 works by more than 350 artists. The program still exists today but is much smaller. [ 5 ]
James Webb , an administrator from 1961 to 1968, put the program into effect. Webb wanted to use art to capture the emotions and importance of what NASA was doing. [ 5 ] James Dean (an artist and NASA employee) became the head of the program with the help of Hereward Lester Cooke , a curator of National Galleys. [ 5 ] To insure that the program would succeed, Cooke looked at similar programs that the air force had and decided that the program needed three things done: Use only commissioned artists, keep all of the sketches that the artists drew while they were observing, and give artists an idea of how to represent NASA, but still let them create whatever they wanted. [ 6 ]
Artists first time observing a mission was the last Mercury launch, with Gordon Cooper's Faith 7. [ 7 ] Robert McCall , Mitchell Jamieson , Peter Hurd , John McCoy , Lamar Dodd , Paul Calle and Robert Shore were the first group of artists chosen. [ 6 ] Each artists was paid $800 for their services as well as the freedom to create whatever they wanted. [ 7 ] The art created during the last Mercury launch made it possible for the program to continue. [ 5 ]
In July 1969 the program had its biggest event. It captured the attention of the public so, the number of artists grew. Mission Control at NASA's Johnson Space Center in Houston and NASA's Kennedy Space Center in Florida are just two of the locations artist chose to observe. Soon after the mission, the director of the National Art gallery asked Dean to use the art created during the mission. [ 7 ] | https://en.wikipedia.org/wiki/NASA_Art_Program |
The NASA Astrobiology Institute ( NAI ) was established in 1998 by the National Aeronautics and Space Administration (NASA) [ 1 ] "to develop the field of astrobiology and provide a scientific framework for flight missions." [ 2 ] In December 2019 the institute's activities were suspended. [ 3 ]
The NAI is a virtual, [ 4 ] distributed organization that integrates astrobiology research and training programs in concert with the national and international science communities. [ 5 ]
Although NASA had explored the idea of forming an astrobiology institute in the past, when the Viking biological experiments returned negative results for life on Mars , the public lost interest and federal funds for exobiology dried up. In 1996, the announcement of possible traces of ancient life in the Allan Hills 84001 meteorite from Mars led to new interest in the subject. At the same time, NASA developed the Origins Program , broadening its reach from exobiology to astrobiology , the study of the origin, evolution, distribution, and future of life in the universe. [ 1 ]
In 1998, $9 million was set aside to fund the NASA Astrobiology Institute (NAI), an interdisciplinary research effort using the expertise of different scientific research institutions and universities from across the country, centrally linked to Ames Research Center in Mountain View, California . Gerald Soffen former Project Scientist with the Viking program , helped coordinate the new institute. [ 1 ] In May, [ 5 ] NASA selected eleven science teams, each with a Principal Investigator (PI). [ 6 ] NAI was established in July with Scott Hubbard as interim Director. [ 5 ] Nobel laureate Baruch S. Blumberg was appointed the first Director of the institute, and served from May 15, 1999 – October 14, 2002. [ 7 ]
The NASA Astrobiology Program includes the NAI as one of four components, including the Exobiology and Evolutionary Biology Program; the Astrobiology Science and Technology Instrument Development (ASTID) Program; and the Astrobiology Science and Technology for Exploring Planets (ASTEP) Program. [ 2 ] Program budgets for fiscal year 2008 were as follows: NAI, $16 million; Grants for the Exobiology and Evolutionary Biology Program, $11 million; ASTID, $9 million; ASTEP, $5 million. [ 5 ]
As of 2018, the NAI has 10 teams including about 600 researchers distributed across ~100 institutions. It also has 13 international partner organizations. Some past and present teams are: [ 8 ] [ 9 ]
NAI has partnership program with other international astrobiology organizations to provide collaborative opportunities for its researchers within the global science community. [ 10 ]
Selected, significant topics of interdisciplinary research by NAI as of 2008: [ 5 ] | https://en.wikipedia.org/wiki/NASA_Astrobiology_Institute |
Since its establishment in 1958, NASA has conducted research on a range of topics. Because of its unique structure, work happens at various field centers and different research areas are concentrated in those centers. [ 1 ] Depending on the technology, hardware and expertise needed, research may be conducted across a range of centers. [ 2 ]
The Aeronautics Research Mission Directorate (ARMD) is one of five mission directorates within NASA , the other four being the Exploration Systems Development Mission Directorate, the Space Operations Mission Directorate, the Science Mission Directorate , and the Space Technology Mission Directorate. [ 3 ] The ARMD is responsible for NASA's aeronautical research, which benefits the commercial , military , and general aviation sectors. The current NASA associate administrator heading ARMD is Robert A. Pearce who has held the position since 2019. [ 4 ]
ARMD is involved in the creation of the Next Generation Air Transportation System (NextGen). [ 5 ]
A 2014 audit by the NASA Office of Inspector General reported that ARMD "solicits input from industry, academia, and other Federal agencies regarding research needs and...uses this information to develop its research plans", and concluded that the directorate supported "advancement of the nation's civil aeronautics research and technology objectives consistent with the National Plan" established in 2006. [ 6 ]
A variety of large-scale medical studies are being conducted in space by the National Space Biomedical Research Institute (NSBRI). Prominent among these is the Advanced Diagnostic Ultrasound in Microgravity Study, in which astronauts (including former ISS Commanders Leroy Chiao and Gennady Padalka ) perform ultrasound scans under the guidance of remote experts to diagnose and potentially treat hundreds of medical conditions in space. Usually there is no physician on board the International Space Station, and diagnosis of medical conditions is challenging. Astronauts are susceptible to a variety of health risks including decompression sickness , barotrauma, immunodeficiencies, loss of bone and muscle, orthostatic intolerance due to volume loss, sleep disturbances , and radiation injury. Ultrasound offers a unique opportunity to monitor these conditions in space. This study's techniques are now being applied to cover professional and Olympic sports injuries as well as ultrasound performed by non-expert operators in populations such as medical and high school students. It is anticipated that remote guided ultrasound will have application on Earth in emergency and rural care situations, where access to a trained physician is often rare. [ 7 ] [ 8 ] [ 9 ]
In one of the nation's largest restoration projects, NASA technology helps state and federal government reclaim 15,100 acres (61 km 2 ) of salt evaporation ponds in South San Francisco Bay. Satellite sensors are used by scientists to study the effect of salt evaporation on local ecology. [ 10 ]
NASA has started Energy Efficiency and Water Conservation Program as an agency-wide program directed to prevent pollution and reduce energy and water utilization. It helps to ensure that NASA meets its federal stewardship responsibilities for the environment. [ 11 ]
Main page: NASA Earth Science
Understanding of natural and human-induced changes on the global environment (such as global warming ) is the main objective of NASA's Earth science . NASA currently has more than a dozen Earth science spacecraft/instruments in orbit studying all aspects of the Earth system (oceans, land, atmosphere, biosphere , cryosphere ), with several more planned for launch in the next few years. [ 12 ] The earth science research program was created and funded in the 1980s under the administrations of Ronald Reagan and George H. W. Bush . [ 13 ] [ 14 ]
NASA is working in cooperation with National Renewable Energy Laboratory (NREL). The goal is to produce worldwide solar resource maps with great local detail. [ 15 ] NASA was also one of the main participants in the evaluation innovative technologies for the cleanup of the sources for dense non-aqueous phase liquids (DNAPLs). On April 6, 1999, the agency signed The Memorandum of Agreement (MOA) along with the United States Environmental Protection Agency , DOE , and USAF authorizing all the above organizations to conduct necessary tests at the John F. Kennedy Space center. The main purpose was to evaluate two innovative in-situ remediation technologies, thermal removal and oxidation destruction of DNAPLs. [ 16 ] National Space Agency made a partnership with Military Services and Defense Contract Management Agency named the "Joint Group on Pollution Prevention". The group is working on reduction or elimination of hazardous materials or processes. [ 17 ]
On May 8, 2003, Environmental Protection Agency recognized NASA as the first federal agency to directly use landfill gas to produce energy at one of its facilities—the Goddard Space Flight Center , Greenbelt, Maryland. [ 18 ]
In 1975, NASA was directed by legislation to research and monitor the upper atmosphere. This led to Upper Atmosphere Research Program and later the Earth Observing System (EOS) satellites in the 1990s to monitor ozone depletion . [ 19 ] The first comprehensive worldwide measurements were obtained in 1978 with the Nimbus 7 satellite and NASA scientists at the Goddard Institute for Space Studies . [ 20 ]
Within the Earth science program, NASA researches and publishes on climate issues. [ 21 ] Its statements concur with the interpretation that the global climate is heating . [ 22 ] Bob Walker, who has advised president-elect Donald Trump on space issues, has advocated that NASA shut down its climate study operations. [ 23 ] The Washington Post reported that NASA scientists copied data on climate change held on U.S. government computers, out of a fear that a Trump administration would end access to data on climate change. [ 24 ] | https://en.wikipedia.org/wiki/NASA_research |
Nucleic acid sequence-based amplification, commonly referred to as NASBA , is a method in molecular biology which is used to produce multiple copies of single stranded RNA. [ 1 ] NASBA is a two-step process that takes RNA and anneals specially designed primers, then utilizes an enzyme cocktail to amplify it. [ 2 ]
Nucleic acid amplification is a technique used to produce several copies of a specific segment of RNA/DNA. [ 3 ] Amplified RNA and DNA can be used for a variety of applications, such as genotyping, sequencing, and detection of bacteria or viruses. [ 4 ] There are two different types of amplification, non-isothermal and isothermal. [ 5 ] Non-isothermal amplification produces multiple copies of RNA/DNA through reiterative cycling between different temperatures. [ 6 ] Isothermal amplification produces multiple copies of RNA/DNA at a constant reaction temperature. [ 7 ] NASBA takes single stranded RNA, anneals primers to it at 65°C, and then amplifies it at 41°C to produce multiple copies of single stranded RNA. [ 8 ] In order for successful amplification to occur, an enzyme cocktail containing, Avian Myeloblastosis Reverse Transcriptase (AMV-RT), RNase H, and RNA polymerase is used. [ 9 ] AMV-RT synthesizes a complementary DNA strand (cDNA) from the RNA template once the primer is annealed. [ 10 ] RNase H then degrades the RNA template and the other primer binds to the cDNA to form double stranded DNA, which RNA polymerase uses to synthesize copies of RNA. [ 11 ] One key aspect of NASBA is that the starting material and end product is always single stranded RNA. That being said, it can be used to amplify DNA, but the DNA must be translated into RNA in order for successful amplification to occur.
Loop-mediated isothermal amplification (LAMP) is another isothermal amplification technique.
NASBA was developed by J Compton in 1991, who defined it as "a primer-dependent technology that can be used for the continuous amplification of nucleic acids in a single mixture at one temperature". [ 12 ] Immediately after the invention of NASBA it was used for the rapid diagnosis and quantification of HIV-1 in patient sera. [ 13 ] Although RNA can also be amplified by PCR using a reverse transcriptase (in order to synthesize a complementary DNA strand as a template), NASBA's main advantage is that it works under isothermal conditions – usually at a constant temperature of 41 °C or two different temperatures, depending on the primers and enzymes used. Even when two different temperatures are applied, it is still considered isothermal, because it does not cycle back and forth between those temperatures. NASBA can be used in medical diagnostics as an alternative to PCR that is quicker and more sensitive in some circumstances. [ 14 ]
Explained briefly, NASBA works as follows:
The NASBA technique has been used to develop rapid diagnostic tests for several pathogenic viruses with single-stranded RNA genomes, e.g. influenza A, [ 16 ] zika virus, foot-and-mouth disease virus, [ 17 ] severe acute respiratory syndrome ( SARS )-associated coronavirus , [ 18 ] human bocavirus (HBoV) [ 19 ] and also parasites like Trypanosoma brucei . [ 20 ]
Recently, NASBA reaction with fluoresce, dipstick and next generation sequencing readout has been developed for COVID-19 diagnosis. [ 21 ] | https://en.wikipedia.org/wiki/NASBA_(molecular_biology) |
The Institute for Problems of Cryobiology and Cryomedicine in Kharkiv is one of the institutes of the National Academy of Science of Ukraine , and is the largest institute devoted to cryobiology research in the world.
Established in 1972, the focus of the research is on cryoinjury, cryosurgery , cryopreservation , lyophilization and hypothermia . [ 1 ] Since 1985 the Institute has published the open access peer-reviewed scientific journal Problems of Cryobiology and Cryomedicine . [ 2 ] | https://en.wikipedia.org/wiki/NASU_Institute_of_Cryobiology_and_Cryomedicine_Issues |
Institute of Pulse Processes and Technologies (IPPT) of the National Academy of Sciences of Ukraine is a research institute of the National Academy of Sciences of Ukraine.
In 1959 on an initiative of young enthusiasts and support of the Mykolaiv city authorities there was created a joint laboratory for studying a new phenomenon at that time as high-voltage charge in water (see electrohydrodynamics ) and processes that accompany it.
Institute was established in 1991 on the basis of Planning and Design Bureau of Electrohydraulics of National Academy of Sciences of Ukraine , which existed in Mykolaiv since 1962. It specializes in studies of physical and technical aspects of high-voltage electric discharge in condensed matter, the creation of highly environmentally friendly resource and energy saving pulse technology on its basis.
IPPT is a scientific-industrial complex that includes the Institute, a research plant and research and development center "VEGA". The structure of the institute - five academic departments (electrophysical studies dept., dept. of pulse energy conversion processes and their management, dept. of methods and techniques of pulsed impact onto liquid metals and crystallizing alloys, dept. of the intensification of production of minerals, dept. of pulse electrical systems), and three engineering department.
More than 1000 technological systems for the foundry, metallurgical, mining and other industries were developed in the IPPT. The following unique facilities were created: Laboratory park for studying the physical processes in the electric explosion, pulsed power capacitors laboratory for the study of processes in the cores of rock at a pressure of 500 atmospheres and temperatures up to 1000 °C and metallographic and metallophysical complexes.
Since 1977 the Institute and its predecessor are publishing a collection of scientific papers. | https://en.wikipedia.org/wiki/NASU_Institute_of_Pulse_Processes_and_Technologies |
The NATO Software Engineering Conferences were held in 1968 and 1969. The conferences were attended by international experts on computer software who aimed to define best practices for software development grounded in the application of engineering principles. The result of the conferences were two reports, one for the 1968 conference and the other for the 1969 conference, that outlined how software should be developed. [ 1 ] [ 2 ] The conferences played a major role in gaining general acceptance for the term software engineering . [ 3 ]
In the 1960s, the computer industry was experiencing rapid growth, leading to increasing complexity in software development. This period saw the emergence of what was later termed the " software crisis ", characterized by projects that were over budget, overdue, and unreliable. [ 4 ] To address these challenges, the NATO Science Committee convened two conferences to explore ways to improve software development practices by applying engineering principles. [ 1 ]
The first conference took place in Garmisch , Germany, from 7 to 11 October 1968. [ 1 ] It was attended by 50 leading computer scientists and practitioners from 11 countries, including Edsger Dijkstra , Friedrich L. Bauer , Alan Perlis , and Peter Naur . [ 4 ] The term "software engineering" was deliberately chosen as the conference title to provoke thought regarding the need for disciplined approaches in software development. [ 4 ]
During the conference, participants discussed issues such as software reliability, project management, and the challenges of large-scale software systems. [ 1 ] The concept of the "software crisis" was a central theme, highlighting the difficulties in producing high-quality software on time and within budget. [ 4 ] The conference emphasized the importance of adopting engineering principles in software development to improve reliability and efficiency.
The conference resulted in a report edited by Peter Naur and Brian Randell, which compiled the discussions and recommendations made during the event. [ 1 ] The editors faced the challenge of capturing the dynamic discussions and diverse viewpoints, ultimately producing a document that emphasized the need for formal methodologies and better project management in software development. [ 4 ]
Following the success of the first conference, a second conference was held in Rome, Italy, from 27 to 31 October 1969. [ 2 ] The goal was to delve deeper into the technical aspects of software engineering. However, the atmosphere differed from the first conference, with less consensus among participants and a lack of clear direction. [ 4 ]
Discussions at the Rome conference focused on software design techniques, methodologies, and tools. [ 2 ] The conference highlighted the communication gap between different groups involved in software development, emphasizing the need for better collaboration. [ 4 ] There was also a proposal to establish an international software engineering institute, but it did not gain sufficient support. [ 4 ] Additionally, the conference brought to light the differing opinions on how software engineering should evolve, with debates over the balance between theoretical approaches and practical applications.
The report from the second conference was edited by John Buxton and Brian Randell. [ 2 ] The editors faced challenges due to the lack of clear consensus among participants, making the compilation of the report more difficult than the previous year. [ 4 ] Despite these difficulties, the report provided insights into the state of software engineering at the time and highlighted areas needing further research and development.
The NATO Software Engineering Conferences were instrumental in establishing software engineering as a recognized discipline. [ 4 ] The conferences popularized the term "software engineering" and brought attention to the critical issues facing the software industry at the time. [ 4 ]
The reports from these conferences influenced academia and industry, leading to the development of new methodologies, tools, and educational programs. [ 4 ] They prompted further discussions on software reliability, project management, and the application of engineering principles to software development. The conferences are considered seminal events in the history of software engineering, setting the foundation for the discipline and inspiring future conferences and research in the field. [ 5 ] | https://en.wikipedia.org/wiki/NATO_Software_Engineering_Conferences |
The NAT (Non Animal Technologies) Database is a freely accessible, free of cost database containing various non-animal research methods that are being developed worldwide. These include, for example, modern in-vitro methods with human cells or in-silico methods ( computer modelling ).
In order to avoid animal testing and promote animal-free research, the association Doctors Against Animal Experiments published the NAT database on animal-free research methods on 29 July 2020. It held 250 entries at the time. The database currently as of May 2024 contains almost 1,700 entries. [ 1 ]
In order to close the gap between the enormous number of animal-free methods available and the fact that they are almost impossible to find, the association has created the bilingual NAT (Non-Animal-Technologies) database. The freely available database includes a wide variety of non-animal methods from all over the world, ranging from state-of-the-art methods based on human cells to complex computer models. The NAT database supports scientists in their search for animal-free methods for their respective research questions, but is also intended for politicians, representatives of authorities, journalists, and the interested public. The search mask allows a keyword search and also offers the possibility to filter by subject area, model, country, or date of publication. The entries contain a summary of the method along with related sources and information on the responsible researchers and institutes. [ 2 ] [ 3 ] [ 4 ]
The idea to develop the NAT database was born in 2020 because a platform that offered a comprehensive overview of modern animal-free technologies being developed worldwide simply didn't exist. On the one hand, DDAE is delighted with the uniqueness of our NAT database. On the other hand, it is a great disappointment that government authorities have not yet ensured that such a database is available to the scientific community. In order to abolish animal testing, it is essential that the great non-animal research methods that exist are also made available. Such an overview is invaluable for scientists working in this field, as it helps, for example, to find co-operation partners to establish animal-free methods. The database is equally important for authorities and decision-makers. In order to be able to reject applications for animal experiments, those responsible must be able to identify non-animal methods that can be used instead in a quick and targeted manner. So far, neither the federal government of Germany nor the EU has ensured that such a platform is made available.
At the end of 2020, the Federal Budget Committee made available €3 million, which was to be used, among other things, to create such a database. So far, however, this has not happened. Only the so-called Federal 3R Network has been set up, which is a kind of general information platform on the topic of 3Rs (refinement, reduction, and replacement of animal experiments). [ 5 ] [ 6 ] Since the launch of the NAT database, the association's scientific team, led by Dr. Tamara Zietek, has been working continuously to research and select new animal-free technologies in order to add new entries. The methods and projects that are to be entered into the database are first filtered out from a large number of publications based animal-free technologies. The organisation ensures that different biomedical disciplines are represented (e.g. oncology or toxicology), as well as different models (e.g. 3-dimensional cell models or computer-based methods). The association's science team writes a summary of the method. A crucial part of the database is the language it is written in: as easily as possible to understand, so that non-scientists are able to benefit from the database as well and understand the methods described. In addition, references, contact persons, and the associated institutes where the method was developed are entered as well. Since the NAT database is bilingual, all this has to be done in German and English. Before a new entry is added to the database, it has to pass a final quality check with regard to content and language.
The database found many supporters. For example, it was supported by the Berlin State Animal Welfare Commissioner with public funds. Those funds were to be used, amongst others, for the entry of animal-free methods published by the European Centre for the Validation of Alternative Methods (ECVAM). The ECVAM is part of the European Commission and has published a total of 7 reports on non-animal models in biomedical research over the past 2 years. These contain thousands of animal-free procedures from various specialist areas such as neurodegenerative diseases, respiratory diseases, breast cancer, cardiovascular diseases, and autoimmune diseases. With funding from the state of Berlin and the support of external partners, hundreds of methods have been selected from reports and entered into the NAT database. [ 7 ] The main aim of the association is to ensure that the NAT database reaches as many people as possible, especially scientists and young researchers. The NAT database has been included in the DBIS (Database Information System) and is therefore available to students and staff in over 340 university libraries. [ 8 ]
The NAT database has so far been honoured with 2 prizes: the international Lush Prize 2022 and the Animal Welfare Prize by the State of Lower Saxony also in 2022. [ 9 ] | https://en.wikipedia.org/wiki/NAT_Database |
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