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Substitution Model
In biology, a substitution model, also called models of sequence evolution, are Markov models that describe changes over evolutionary time. These models describe evolutionary changes in macromolecules, such as DNA sequences or protein sequences, that can be represented as sequence of symbols (e.g., A, C, G, and T in the case of DNA or the 20 "standard" proteinogenic amino acids in the case of proteins). Substitution models are used to calculate the likelihood of phylogenetic trees using multiple sequence alignment data. Thus, substitution models are central to maximum likelihood estimation of phylogeny as well as Bayesian inference in phylogeny. Estimates of evolutionary distances (numbers of substitutions that have occurred since a pair of sequences diverged from a common ancestor) are typically calculated using substitution models (evolutionary distances are used as input for distance methods such as neighbor joining). Substitution models are also central to phylogenetic inv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Model
In probability theory, a Markov model is a stochastic model used to Mathematical model, model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property). Generally, this assumption enables reasoning and computation with the model that would otherwise be Intractability (complexity), intractable. For this reason, in the fields of predictive modelling and probabilistic forecasting, it is desirable for a given model to exhibit the Markov property. Introduction Andrey Andreyevich Markov (14 June 1856 – 20 July 1922) was a Russian mathematician best known for his work on stochastic processes. A primary subject of his research later became known as the Markov chain. There are four common Markov models used in different situations, depending on whether every sequential state is observable or not, and whether the system is to be adjusted on the basis of observation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagonalizable Matrix
In linear algebra, a square matrix A is called diagonalizable or non-defective if it is matrix similarity, similar to a diagonal matrix. That is, if there exists an invertible matrix P and a diagonal matrix D such that . This is equivalent to (Such D are not unique.) This property exists for any linear map: for a dimension (vector space), finite-dimensional vector space a linear map T:V\to V is called diagonalizable if there exists an Basis (linear algebra)#Ordered bases and coordinates, ordered basis of V consisting of eigenvectors of T. These definitions are equivalent: if T has a matrix (mathematics), matrix representation A = PDP^ as above, then the column vectors of P form a basis consisting of eigenvectors of and the diagonal entries of D are the corresponding eigenvalues of with respect to this eigenvector basis, T is represented by Diagonalization is the process of finding the above P and and makes many subsequent computations easier. One can raise a diag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transversion
Transversion, in molecular biology, refers to a point mutation in DNA in which a single (two ring) purine ( A or G) is changed for a (one ring) pyrimidine ( T or C), or vice versa. A transversion can be spontaneous, or it can be caused by ionizing radiation or alkylating agents. It can only be reversed by a spontaneous reversion. Ratio of transitions to transversions Although there are two possible transversions but only one possible transition per base, transition mutations are more likely than transversions because substituting a single ring structure for another single ring structure is more likely than substituting a double ring for a single ring. Also, transitions are less likely to result in amino acid substitutions (due to wobble base pair), and are therefore more likely to persist as "silent substitutions" in populations as single nucleotide polymorphisms (SNPs). A transversion usually has a more pronounced effect than a transition because the second and third nucle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Models Of DNA Evolution
A number of different Markov models of DNA sequence evolution have been proposed. These substitution models differ in terms of the parameters used to describe the rates at which one nucleotide replaces another during evolution. These models are frequently used in molecular phylogenetic analyses. In particular, they are used during the calculation of likelihood of a tree (in Bayesian and maximum likelihood approaches to tree estimation) and they are used to estimate the evolutionary distance between sequences from the observed differences between the sequences. Introduction These models are phenomenological descriptions of the evolution of DNA as a string of four discrete states. These Markov models do not explicitly depict the mechanism of mutation nor the action of natural selection. Rather they describe the relative rates of different changes. For example, mutational biases and purifying selection favoring conservative changes are probably both responsible for the relative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pyrimidine
Pyrimidine (; ) is an aromatic, heterocyclic, organic compound similar to pyridine (). One of the three diazines (six-membered heterocyclics with two nitrogen atoms in the ring), it has nitrogen atoms at positions 1 and 3 in the ring. The other diazines are pyrazine (nitrogen atoms at the 1 and 4 positions) and pyridazine (nitrogen atoms at the 1 and 2 positions). In nucleic acids, three types of nucleobases are pyrimidine derivatives: cytosine (C), thymine (T), and uracil (U). Occurrence and history The pyrimidine ring system has wide occurrence in nature as substituted and ring fused compounds and derivatives, including the nucleotides cytosine, thymine and uracil, thiamine (vitamin B1) and alloxan. It is also found in many synthetic compounds such as barbiturates and the HIV drug zidovudine. Although pyrimidine derivatives such as alloxan were known in the early 19th century, a laboratory synthesis of a pyrimidine was not carried out until 1879, when Grimaux repor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Purine
Purine is a heterocyclic aromatic organic compound that consists of two rings (pyrimidine and imidazole) fused together. It is water-soluble. Purine also gives its name to the wider class of molecules, purines, which include substituted purines and their tautomers. They are the most widely occurring nitrogen-containing heterocycles in nature. Dietary sources Purines are found in high concentration in meat and meat products, especially internal organs, such as liver and kidney, and in various seafoods, high-fructose beverages, alcohol, and yeast products. Examples of high-purine food sources include anchovies, sardines, liver, beef, kidneys, brains, monkfish, dried mackerel, and shrimp. Foods particularly rich in hypoxanthine, adenine, and guanine lead to higher blood levels of uric acid. Foods having more than 200 mg of hypoxanthine per 100 g, particularly animal and fish meats containing hypoxanthine as more than 50% of total purines, are more likely to increase uri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nucleotide
Nucleotides are Organic compound, organic molecules composed of a nitrogenous base, a pentose sugar and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both of which are essential biomolecules within all Life, life-forms on Earth. Nucleotides are obtained in the diet and are also synthesized from common Nutrient, nutrients by the liver. Nucleotides are composed of three subunit molecules: a nucleobase, a pentose, five-carbon sugar (ribose or deoxyribose), and a phosphate group consisting of one to three phosphates. The four nucleobases in DNA are guanine, adenine, cytosine, and thymine; in RNA, uracil is used in place of thymine. Nucleotides also play a central role in metabolism at a fundamental, cellular level. They provide chemical energy—in the form of the nucleoside triphosphates, adenosine triphosphate (ATP), guanosine triphosphate (GTP), cytidine triphosphate (CTP), and uridine triph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonsense Mutation
In genetics, a nonsense mutation is a point mutation in a sequence of DNA that results in a ''nonsense codon'', or a premature stop codon in the transcribed mRNA, and leads to a truncated, incomplete, and possibly nonfunctional protein product. Nonsense mutations are not always harmful; the functional effect of a nonsense mutation depends on many aspects, such as the location of the stop codon within the coding DNA. For example, the effect of a nonsense mutation depends on the proximity of the nonsense mutation to the original stop codon, and the degree to which functional subdomains of the protein are affected. As nonsense mutations leads to premature termination of polypeptide chains; they are also called chain termination mutations. Missense mutations differ from nonsense mutations since they are point mutations that exhibit a single nucleotide change to cause substitution of a different amino acid. A nonsense mutation also differs from a nonstop mutation, which is a point muta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Codon
Genetic code is a set of rules used by living cells to translate information encoded within genetic material (DNA or RNA sequences of nucleotide triplets or codons) into proteins. Translation is accomplished by the ribosome, which links proteinogenic amino acids in an order specified by messenger RNA (mRNA), using transfer RNA (tRNA) molecules to carry amino acids and to read the mRNA three nucleotides at a time. The genetic code is highly similar among all organisms and can be expressed in a simple table with 64 entries. The codons specify which amino acid will be added next during protein biosynthesis. With some exceptions, a three-nucleotide codon in a nucleic acid sequence specifies a single amino acid. The vast majority of genes are encoded with a single scheme (see the RNA codon table). That scheme is often called the canonical or standard genetic code, or simply ''the'' genetic code, though variant codes (such as in mitochondria) exist. History Efforts to understan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proteins
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, responding to stimuli, providing structure to cells and organisms, and transporting molecules from one location to another. Proteins differ from one another primarily in their sequence of amino acids, which is dictated by the nucleotide sequence of their genes, and which usually results in protein folding into a specific 3D structure that determines its activity. A linear chain of amino acid residues is called a polypeptide. A protein contains at least one long polypeptide. Short polypeptides, containing less than 20–30 residues, are rarely considered to be proteins and are commonly called peptides. The individual amino acid residues are bonded together by peptide bonds and adjacent amino acid residues. The sequence of amino acid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simon Tavaré
Simon Tavaré (born 1952) is a British researcher who is the founding Director of the Herbert and Florence Irving Institute of Cancer Dynamics at Columbia University. Prior to joining Columbia, he was Director of the Cancer Research UK Cambridge Institute, Professor of Cancer Research at the Department of Oncology and Professor in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge. Education Tavaré was educated at Oundle School and the University of Sheffield where he was awarded a Bachelor of Science degree in 1974, a Master of Science degree in 1975, and a PhD in 1979. Research and career Tavaré is a computational biologist and statistician, with his research focusing on three main areas: statistical methods for the analysis of next‑generation sequencing data, evolutionary approaches to cancer and methods for the analysis of genomics data. Tavaré's research has been funded by Cancer Research UK, the Royal Society, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stationarity (statistics)
In mathematics and statistics, a stationary process (also called a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose statistical properties, such as mean and variance, do not change over time. More formally, the joint probability distribution of the process remains the same when shifted in time. This implies that the process is statistically consistent across different time periods. Because many statistical procedures in time series analysis assume stationarity, non-stationary data are frequently transformed to achieve stationarity before analysis. A common cause of non-stationarity is a trend in the mean, which can be due to either a unit root or a deterministic trend. In the case of a unit root, stochastic shocks have permanent effects, and the process is not mean-reverting. With a deterministic trend, the process is called trend-stationary, and shocks have only transitory effects, with the variable tending towards a determin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
