Substitution Matrix
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Substitution Matrix
In bioinformatics and evolutionary biology, a substitution matrix describes the frequency at which a character in a nucleotide sequence or a protein sequence changes to other character states over evolutionary time. The information is often in the form of log odds of finding two specific character states aligned and depends on the assumed number of evolutionary changes or sequence dissimilarity between compared sequences. It is an application of a stochastic matrix. Substitution matrices are usually seen in the context of amino acid or DNA sequence alignments, where they are used to calculate similarity scores between the aligned sequences. Background In the process of evolution, from one generation to the next the amino acid sequences of an organism's proteins are gradually altered through the action of DNA mutations. For example, the sequence ALEIRYLRD could mutate into the sequence ALEINYLRD in one step, and possibly AQEINYQRD over a longer period of evolutionary t ...
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Bioinformatics
Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combines biology, chemistry, physics, computer science, information engineering, mathematics and statistics to analyze and interpret the biological data. Bioinformatics has been used for '' in silico'' analyses of biological queries using computational and statistical techniques. Bioinformatics includes biological studies that use computer programming as part of their methodology, as well as specific analysis "pipelines" that are repeatedly used, particularly in the field of genomics. Common uses of bioinformatics include the identification of candidates genes and single nucleotide polymorphisms (SNPs). Often, such identification is made with the aim to better understand the genetic basis of disease, unique adaptations, desirable properties (e ...
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Sequence Homology
Sequence homology is the biological homology between DNA, RNA, or protein sequences, defined in terms of shared ancestry in the evolutionary history of life. Two segments of DNA can have shared ancestry because of three phenomena: either a speciation event (orthologs), or a duplication event (paralogs), or else a horizontal (or lateral) gene transfer event (xenologs). Homology among DNA, RNA, or proteins is typically inferred from their nucleotide or amino acid sequence similarity. Significant similarity is strong evidence that two sequences are related by evolutionary changes from a common ancestral sequence. Alignments of multiple sequences are used to indicate which regions of each sequence are homologous. Identity, similarity, and conservation The term "percent homology" is often used to mean "sequence similarity”, that is the percentage of identical residues (''percent identity''), or the percentage of residues conserved with similar physicochemical properties (' ...
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Substitution Model
In biology, a substitution model, also called models of DNA sequence evolution, are Markov models that describe changes over evolutionary time. These models describe evolutionary changes in macromolecules (e.g., DNA sequences) represented as sequence of symbols (A, C, G, and T in the case of DNA). 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 input for distance methods such as neighbor joining). Substitution models are also central to phylogenetic invariants because they are necessary to predict site pattern frequencies given a tree topology. Substitution models a ...
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Neighbor-joining
In bioinformatics, neighbor joining is a bottom-up (agglomerative) clustering method for the creation of phylogenetic trees, created by Naruya Saitou and Masatoshi Nei in 1987. Usually based on DNA or protein sequence data, the algorithm requires knowledge of the distance between each pair of taxa (e.g., species or sequences) to create the phylogenetic tree. The algorithm Neighbor joining takes a distance matrix, which specifies the distance between each pair of taxa, as input. The algorithm starts with a completely unresolved tree, whose topology corresponds to that of a star network, and iterates over the following steps, until the tree is completely resolved, and all branch lengths are known: # Based on the current distance matrix, calculate a matrix Q (defined below). # Find the pair of distinct taxa i and j (i.e. with i \neq j) for which Q(i,j) is smallest. Make a new node that joins the taxa i and j, and connect the new node to the central node. For example, in part (B ...
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Maximum Likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimation theory, estimating the Statistical parameter, parameters of an assumed probability distribution, given some observed data. This is achieved by Mathematical optimization, maximizing a likelihood function so that, under the assumed statistical model, the Realization (probability), observed data is most probable. The point estimate, point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is Differentiable function, differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when ...
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BLAST
Blast or The Blast may refer to: * Explosion, a rapid increase in volume and release of energy in an extreme manner *Detonation, an exothermic front accelerating through a medium that eventually drives a shock front Film * ''Blast'' (1997 film), starring Andrew Divoff * ''Blast'' (2000 film), starring Liesel Matthews * ''Blast'' (2004 film), an action comedy film * ''Blast!'' (1972 film) or ''The Final Comedown'', an American drama * ''BLAST!'' (2008 film), a documentary about the BLAST telescope * '' A Blast'', a 2014 film directed by Syllas Tzoumerkas Magazines * ''Blast'' (magazine), a 1914–15 literary magazine of the Vorticist movement * ''Blast'' (U.S. magazine), a 1933–34 American short-story magazine * ''The Blast'' (magazine), a 1916–17 American anarchist periodical Music * Blast (American band), a hardcore punk band * Blast (Russian band), an indie band * ''Blast'' (album), by Holly Johnson, 1989 * ''The Blast'' (album), by Yuvan Shankar Raja, 1999 * " ...
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Steven Henikoff
Steven Henikoff is a scientist at the Fred Hutchinson Cancer Research Center, and an HHMI Investigator. His field of study is chromatin-related transcriptional regulation. He earned his BS in chemistry at the University of Chicago. He earned his PhD in biochemistry and molecular biology from Harvard University in the lab of Matt Meselson in 1977. He did a postdoctoral fellowship at the University of Washington. His research has been funded by the National Science Foundation, National Institutes of Health, and HHMI. In 1992, Steven Henikoff, together with his wife Jorja Henikoff, introduced the BLOSUM substitution matrices. The BLOSUM matrices are widely used for sequence alignment of proteins. In 2005, Henikoff was elected to the National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineer ...
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BLOSUM
In bioinformatics, the BLOSUM (BLOcks SUbstitution Matrix) matrix is a substitution matrix used for sequence alignment of proteins. BLOSUM matrices are used to score alignments between evolutionarily divergent protein sequences. They are based on local alignments. BLOSUM matrices were first introduced in a paper by Steven Henikoff and Jorja Henikoff. They scanned the BLOCKS database for very conserved regions of protein families (that do not have gaps in the sequence alignment) and then counted the relative frequencies of amino acids and their substitution probabilities. Then, they calculated a log-odds score for each of the 210 possible substitution pairs of the 20 standard amino acids. All BLOSUM matrices are based on observed alignments; they are not extrapolated from comparisons of closely related proteins like the PAM Matrices. Biological background The genetic instructions of every replicating cell in a living organism are contained within its DNA. Throughout the cell's ...
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Margaret Oakley Dayhoff
Margaret Belle (Oakley) Dayhoff (March 11, 1925 – February 5, 1983) was an American physical chemist and a pioneer in the field of bioinformatics. Dayhoff was a professor at Georgetown University Medical Center and a noted research biochemist at the National Biomedical Research Foundation, where she pioneered the application of mathematics and computational methods to the field of biochemistry. She dedicated her career to applying the evolving computational technologies to support advances in biology and medicine, most notably the creation of protein and nucleic acid databases and tools to interrogate the databases. She originated one of the first substitution matrices, point accepted mutations (''PAM''). The one-letter code used for amino acids was developed by her, reflecting an attempt to reduce the size of the data files used to describe amino acid sequences in an era of punch-card computing. Her PhD degree was from Columbia University in the Department of Chemist ...
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Point Accepted Mutation
A point accepted mutation — also known as a PAM — is the replacement of a single amino acid in the primary structure of a protein with another single amino acid, which is accepted by the processes of natural selection. This definition does not include all point mutations in the DNA of an organism. In particular, silent mutations are not point accepted mutations, nor are mutations that are lethal or that are rejected by natural selection in other ways. A PAM matrix is a matrix where each column and row represents one of the twenty standard amino acids. In bioinformatics, PAM matrices are sometimes used as substitution matrices to score sequence alignments for proteins. Each entry in a PAM matrix indicates the likelihood of the amino acid of that row being replaced with the amino acid of that column through a series of one or more point accepted mutations during a specified evolutionary interval, rather than these two amino acids being aligned due to chance. Different PAM matri ...
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Score (statistics)
In statistics, the score (or informant) is the gradient of the log-likelihood function with respect to the parameter vector. Evaluated at a particular point of the parameter vector, the score indicates the steepness of the log-likelihood function and thereby the sensitivity to infinitesimal changes to the parameter values. If the log-likelihood function is continuous over the parameter space, the score will vanish at a local maximum or minimum; this fact is used in maximum likelihood estimation to find the parameter values that maximize the likelihood function. Since the score is a function of the observations that are subject to sampling error, it lends itself to a test statistic known as ''score test'' in which the parameter is held at a particular value. Further, the ratio of two likelihood functions evaluated at two distinct parameter values can be understood as a definite integral of the score function. Definition The score is the gradient (the vector of partial derivat ...
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