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Contact Order
The contact order of a protein is a measure of the locality of the inter-amino acid contacts in the protein's native state tertiary structure. It is calculated as the average sequence distance between residues that form native contacts in the folded protein divided by the total length of the protein. Higher contact orders indicate longer folding times, and low contact order has been suggested as a predictor of potential downhill folding, or protein folding that occurs without a free energy barrier. This effect is thought to be due to the lower loss of conformational entropy associated with the formation of local as opposed to nonlocal contacts. Relative contact order (CO) is formally defined as: :CO=\sum^\Delta S_ where ''N'' is the total number of contacts, Δ''Si,j'' is the sequence separation, in residues, between contacting residues ''i'' and ''j'', and ''L'' is the total number of residues in the protein. The value of contact order typically ranges from 5% to 25% for single- ...
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Protein
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 residue ...
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Objective Function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized. The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century. In the context of economics, for example, this ...
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Circuit Topology
The circuit topology of a folded linear polymer refers to the arrangement of its intra-molecular contacts. Examples of linear polymers with intra-molecular contacts are nucleic acids and proteins. Proteins fold via formation of contacts of various nature, including hydrogen bonds, disulfide bonds, and beta-beta interactions. Contacts in the genome are established via protein bridges including CTCF and cohesins and are measured by technologies including Hi-C. Circuit topology categorises the topological arrangement of these physical contacts, that are referred to as hard contacts. Furthermore, chains can fold via knotting (or formation of "soft" contacts). Circuit topology uses a similar language to categorise both "soft" and "hard" contacts, and provides a full description of a folded linear chain. A simple example of a folded chain is a chain with two hard contacts. For a chain with two binary contacts, three arrangements are available: parallel, series and crossed. For a chain ...
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Homology (biology)
In biology, homology is similarity due to shared ancestry between a pair of structures or genes in different taxa. A common example of homologous structures is the forelimbs of vertebrates, where the wings of bats and birds, the arms of primates, the front flippers of whales and the forelegs of four-legged vertebrates like dogs and crocodiles are all derived from the same ancestral tetrapod structure. Evolutionary biology explains homologous structures adapted to different purposes as the result of descent with modification from a common ancestor. The term was first applied to biology in a non-evolutionary context by the anatomist Richard Owen in 1843. Homology was later explained by Charles Darwin's theory of evolution in 1859, but had been observed before this, from Aristotle onwards, and it was explicitly analysed by Pierre Belon in 1555. In developmental biology, organs that developed in the embryo in the same manner and from similar origins, such as from matching p ...
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Sequence Alignment
In bioinformatics, a sequence alignment is a way of arranging the sequences of DNA, RNA, or protein to identify regions of similarity that may be a consequence of functional, structural, or evolutionary relationships between the sequences. Aligned sequences of nucleotide or amino acid residues are typically represented as rows within a matrix. Gaps are inserted between the residues so that identical or similar characters are aligned in successive columns. Sequence alignments are also used for non-biological sequences, such as calculating the distance cost between strings in a natural language or in financial data. Interpretation If two sequences in an alignment share a common ancestor, mismatches can be interpreted as point mutations and gaps as indels (that is, insertion or deletion mutations) introduced in one or both lineages in the time since they diverged from one another. In sequence alignments of proteins, the degree of similarity between amino acids occupying a parti ...
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Molecular Dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanical force fields. The method is applied mostly in chemical physics, materials science, and biophysics. Because molecular systems typically consist of a vast number of particles, it is impossible to determine the properties of such complex systems analytically; MD simulation circumvents this problem by using numerical methods. However, long MD simulations are mathematically ill-conditioned, generating cumulative errors in ...
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Phi Value Analysis
Phi value analysis, \phi analysis, or \phi-value analysis is an experimental protein engineering technique for studying the structure of the folding transition state of small protein domains that fold in a two-state manner. The structure of the folding transition state is hard to find using methods such as protein NMR or X-ray crystallography because folding transitions states are mobile and partly unstructured by definition. In \phi -value analysis, the folding kinetics and conformational folding stability of the wild-type protein are compared with those of point mutants to find ''phi values''. These measure the mutant residue's energetic contribution to the folding transition state, which reveals the degree of native structure around the mutated residue in the transition state, by accounting for the relative free energies of the unfolded state, the folded state, and the transition state for the wild-type and mutant proteins. The protein's residues are mutated one by one to ...
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Transition State
In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked with the double dagger ‡ symbol. As an example, the transition state shown below occurs during the SN2 reaction of bromoethane with a hydroxide anion: The activated complex of a reaction can refer to either the transition state or to other states along the reaction coordinate between reactants and products, especially those close to the transition state.Peter Atkins and Julio de Paula, ''Physical Chemistry'' (8th ed., W.H. Freeman 2006), p.809 According to the transition state theory, once the reactants have passed through the transition state configuration, they always continue to form products. History of concept The concept of a transition state has been important in many theories of the rates at which chemical reactions occ ...
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Rosetta@Home
Rosetta@home is a volunteer computing project researching protein structure prediction on the Berkeley Open Infrastructure for Network Computing (BOINC) platform, run by the Baker laboratory at the University of Washington. Rosetta@home aims to predict protein–protein docking and design new proteins with the help of about fifty-five thousand active volunteered computers processing at over 487,946 GigaFLOPS on average as of September 19, 2020. Foldit, a Rosetta@home videogame, aims to reach these goals with a crowdsourcing approach. Though much of the project is oriented toward basic research to improve the accuracy and robustness of proteomics methods, Rosetta@home also does applied research on malaria, Alzheimer's disease, and other pathologies. Like all BOINC projects, Rosetta@home uses idle computer processing resources from volunteers' computers to perform calculations on individual workunits. Completed results are sent to a central project server where they are validate ...
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Global Optimization
Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function g(x) is equivalent to the minimization of the function f(x):=(-1)\cdot g(x). Given a possibly nonlinear and non-convex continuous function f:\Omega\subset\mathbb^n\to\mathbb with the global minima f^* and the set of all global minimizers X^* in \Omega, the standard minimization problem can be given as :\min_f(x), that is, finding f^* and a global minimizer in X^*; where \Omega is a (not necessarily convex) compact set defined by inequalities g_i(x)\geqslant0, i=1,\ldots,r. Global optimization is distinguished from local optimization by its focus on finding the minimum or maximum over the given set, as opposed to finding ''local'' minima or maxima. Finding an arbitrary local minimum is relatively str ...
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Amino Acid
Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although hundreds of amino acids exist in nature, by far the most important are the alpha-amino acids, which comprise proteins. Only 22 alpha amino acids appear in the genetic code. Amino acids can be classified according to the locations of the core structural functional groups, as Alpha and beta carbon, alpha- , beta- , gamma- or delta- amino acids; other categories relate to Chemical polarity, polarity, ionization, and side chain group type (aliphatic, Open-chain compound, acyclic, aromatic, containing hydroxyl or sulfur, etc.). In the form of proteins, amino acid '' residues'' form the second-largest component (water being the largest) of human muscles and other tissues. Beyond their role as residues in proteins, amino acids participate in a number of processes such as neurotransmitter transport and biosynthesis. It is thought that they played a key role in enabling life ...
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Protein Structure Prediction
Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its secondary and tertiary structure from primary structure. Structure prediction is different from the inverse problem of protein design. Protein structure prediction is one of the most important goals pursued by computational biology; and it is important in medicine (for example, in drug design) and biotechnology (for example, in the design of novel enzymes). Starting in 1994, the performance of current methods is assessed biannually in the CASP experiment (Critical Assessment of Techniques for Protein Structure Prediction). A continuous evaluation of protein structure prediction web servers is performed by the community project CAMEO3D. Protein structure and terminology Proteins are chains of amino acids joined together by peptide bonds. Many conformations of this chain are possible due to the rotation of the main chain abou ...
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