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Self-consistent Mean Field (biology)
The self-consistent mean field (SCMF) method is an adaptation of mean field theory used in protein structure prediction to determine the optimal amino acid side chain packing given a fixed protein backbone. It is faster but less accurate than dead-end elimination and is generally used in situations where the protein of interest is too large for the problem to be tractable by DEE. General principles Like dead-end elimination, the SCMF method explores conformational space by discretizing the dihedral angles of each side chain into a set of rotamers for each position in the protein sequence. The method iteratively develops a probabilistic description of the relative population of each possible rotamer at each position, and the probability of a given structure is defined as a function of the probabilities of its individual rotamer components. The basic requirements for an effective SCMF implementation are: # A well-defined finite set of discrete independent variables # A precompu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Field Theory
In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of freedom (the number of values in the final calculation of a statistic that are free to vary). Such models consider many individual components that interact with each other. The main idea of MFT is to replace all interactions to any one body with an average or effective interaction, sometimes called a ''molecular field''. This reduces any many-body problem into an effective one-body problem. The ease of solving MFT problems means that some insight into the behavior of the system can be obtained at a lower computational cost. MFT has since been applied to a wide range of fields outside of physics, including statistical inference, graphical models, neuroscience, artificial intelligence, epidemic models, queueing theory, computer-network ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Protein secondary structure, secondary and Protein tertiary structure, tertiary structure from Protein primary structure, 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 addresses Levinthal's paradox. Accurate structure prediction has important applications in medicine (for example, in drug design) and biotechnology (for example, in novel enzyme design). Starting in 1994, the performance of current methods is assessed biannually in the ''Critical Assessment of Structure Prediction'' (CASP) experiment. A continuous evaluation of protein structure prediction web servers is performed by the community project ''Continuous Automated Model EvaluatiOn'' (CAMEO3D). Protein structure a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amino Acid
Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although over 500 amino acids exist in nature, by far the most important are the 22 α-amino acids incorporated into proteins. Only these 22 appear in the genetic code of life. Amino acids can be classified according to the locations of the core structural functional groups ( alpha- , beta- , gamma- amino acids, etc.); other categories relate to polarity, ionization, and side-chain group type ( aliphatic, acyclic, aromatic, polar, 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 on Earth and its emergence. Amino acids are formally named by the IUPAC- IUBMB Joint Commi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Side Chain
In organic chemistry and biochemistry, a side chain is a substituent, chemical group that is attached to a core part of the molecule called the "main chain" or backbone chain, backbone. The side chain is a hydrocarbon branching element of a molecule that is attached to a larger hydrocarbon backbone. It is one factor in determining a molecule's properties and reactivity. A side chain is also known as a pendant chain, but a pendant group (side group) has a different definition. Conventions The placeholder R is often used as a generic placeholder for alkyl (saturated hydrocarbon) group side chains in structural formulae. To indicate other non-carbon groups in structure diagrams, X, Y, or Z are often used. History The ''R'' symbol was introduced by 19th-century French chemist Charles Frédéric Gerhardt, who advocated its adoption on the grounds that it would be widely recognizable and intelligible given its correspondence in multiple European languages to the initial letter of "r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tertiary Structure
Protein tertiary structure is the three-dimensional shape of a protein. The tertiary structure will have a single polypeptide chain "backbone" with one or more protein secondary structures, the protein domains. Amino acid side chains and the backbone may interact and bond in a number of ways. The interactions and bonds of side chains within a particular protein determine its tertiary structure. The protein tertiary structure is defined by its atomic coordinates. These coordinates may refer either to a protein domain or to the entire tertiary structure. A number of these structures may bind to each other, forming a quaternary structure. History The science of the tertiary structure of proteins has progressed from one of hypothesis to one of detailed definition. Although Emil Fischer had suggested proteins were made of polypeptide chains and amino acid side chains, it was Dorothy Maud Wrinch who incorporated geometry into the prediction of protein structures. Wrinch demon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dead-end Elimination
The dead-end elimination algorithm (DEE) is a method for minimizing a function over a discrete set of independent variables. The basic idea is to identify "dead ends", i.e., combinations of variables that are not necessary to define a global minimum because there is always a way of replacing such a combination with a better or equivalent one. Then we can refrain from further searching such combinations. Hence, dead-end elimination is the mirror image of dynamic programming, in which "good" combinations are identified and explored further. Although the method itself is general, it has been developed and applied mainly to the problems of predicting and designing the structures of proteins (and in this wise was cited in the Scientific Background to the 2024 Nobel Prize in Chemistry).https://www.nobelprize.org/uploads/2024/10/advanced-chemistryprize2024.pdf It is closely related to the notion of dominance in optimization also known as substitutability in a Constraint Satisfactio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotamer
In chemistry, rotamers are chemical species that differ from one another primarily due to rotations about one or more single bonds. Various arrangements of atoms in a molecule that differ by rotation about single bonds can also be referred to as conformations. Conformers/rotamers differ little in their energies, so they are almost never separable in a practical sense. Rotations about single bonds are subject to small energy barriers. When the time scale for interconversion is long enough for isolation of individual rotamers (usually arbitrarily defined as a half-life of interconversion of 1000 seconds or longer), the species are termed atropisomers (''see:'' atropisomerism). The ring-flip of substituted cyclohexanes constitutes a common form of conformers. The study of the energetics of bond rotation is referred to as conformational analysis. In some cases, conformational analysis can be used to predict and explain product selectivity, mechanisms, and rates of reactions. Conform ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Distribution
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. The distribution is expressed in the form: :p_i \propto \exp\left(- \frac \right) where is the probability of the system being in state , is the exponential function, is the energy of that state, and a constant of the distribution is the product of the Boltzmann constant and thermodynamic temperature . The symbol \propto denotes proportionality (see for the proportionality constant). The term ''system'' here has a wide meaning; it can range from a collection of 'sufficient number' of atoms or a single atom to a macroscopic system such as a natural gas storage tank. Therefore, the Boltzmann distribution can be used to sol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simulated Annealing
Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA can find the global optimum. It is often used when the search space is discrete (for example the traveling salesman problem, the boolean satisfiability problem, protein structure prediction, and job-shop scheduling). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to exact algorithms such as gradient descent or branch and bound. The name of the algorithm comes from annealing in metallurgy, a technique involving heating and controlled cooling of a material to alter its physical properties. Both are attributes of the material that depend on their thermodynamic free energy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the molar gas constant, in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating Johnson–Nyquist noise, thermal noise in resistors. The Boltzmann constant has Dimensional analysis, dimensions of energy divided by temperature, the same as entropy and heat capacity. It is named after the Austrian scientist Ludwig Boltzmann. As part of the 2019 revision of the SI, the Boltzmann constant is one of the seven "Physical constant, defining constants" that have been defined so as to have exact finite decimal values in SI units. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly joules per kelvin, with the effect of defining the SI unit ke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the profession, professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of Mathematical analysis, applied analysis, most notably differential equations; approximation theory (broadly construed, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
