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Protein PKa Calculations
In computational biology, protein p''K''a calculations are used to estimate the p''K''a values of amino acids as they exist within proteins. These calculations complement the p''K''a values reported for amino acids in their free state, and are used frequently within the fields of molecular modeling, structural bioinformatics, and computational biology. Amino acid p''K''a values p''K''a values of amino acid side chains play an important role in defining the pH-dependent characteristics of a protein. The pH-dependence of the activity displayed by enzymes and the pH-dependence of protein stability, for example, are properties that are determined by the p''K''a values of amino acid side chains. The p''K''a values of an amino acid side chain in solution is typically inferred from the p''K''a values of model compounds (compounds that are similar to the side chains of amino acids). See Amino acid for the p''K''a values of all amino acid side chains inferred in such a way. There are also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Biology
Computational biology refers to the use of data analysis, mathematical modeling and computational simulations to understand biological systems and relationships. An intersection of computer science, biology, and big data, the field also has foundations in applied mathematics, chemistry, and genetics. It differs from biological computing, a subfield of computer engineering which uses bioengineering to build computers. History Bioinformatics, the analysis of informatics processes in biological systems, began in the early 1970s. At this time, research in artificial intelligence was using network models of the human brain in order to generate new algorithms. This use of biological data pushed biological researchers to use computers to evaluate and compare large data sets in their own field. By 1982, researchers shared information via punch cards. The amount of data grew exponentially by the end of the 1980s, requiring new computational methods for quickly interpreting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson–Boltzmann Equation
The Poisson–Boltzmann equation is a useful equation in many settings, whether it be to understand physiology, physiological interfaces, polymer science, electron interactions in a semiconductor, or more. It aims to describe the distribution of the electric potential in solution in the direction normal to a charged surface. This distribution is important to determine how the electrostatic interactions will affect the molecules in solution. The Poisson–Boltzmann equation is derived via Mean field theory, mean-field assumptions. From the Poisson–Boltzmann equation many other equations have been derived with a number of different assumptions. Origins Background and derivation The Poisson–Boltzmann equation describes a model proposed independently by Louis Georges Gouy and David Leonard Chapman in 1910 and 1913, respectively. In the Double layer (surface science)#Gouy-Chapman, Gouy-Chapman model, a charged solid comes into contact with an ionic solution, creating a layer of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bennett Acceptance Ratio
The Bennett acceptance ratio method (BAR) is an algorithm for estimating the difference in free energy between two systems (usually the systems will be simulated on the computer). It was suggested by Charles H. Bennett in 1976. Preliminaries Take a system in a certain super (i.e. Gibbs) state. By performing a Metropolis Monte Carlo walk it is possible to sample the landscape of states that the system moves between, using the equation : p(\text_x \rightarrow \text_y) = \min \left(e ^ , 1 \right) = M(\beta \, \Delta U) where Δ''U'' = ''U''(State''y'') − ''U''(State''x'') is the difference in potential energy, β = 1/''kT'' (''T'' is the temperature in kelvins, while ''k'' is the Boltzmann constant), and M(x) \equiv \min(e^ , 1) is the Metropolis function. The resulting states are then sampled according to the Boltzmann distribution of the super state at temperature ''T''. Alternatively, if the system is dynamically simulated in the canonical ensemble (als ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jarzynski Equality
The Jarzynski equality (JE) is an equation in statistical mechanics that relates free energy differences between two states and the irreversible work along an ensemble of trajectories joining the same states. It is named after the physicist Christopher Jarzynski (then at the University of Washington and Los Alamos National Laboratory, currently at the University of Maryland) who derived it in 1996. Fundamentally, the Jarzynski equality points to the fact that the fluctuations in the work satisfy certain constraints separately from the average value of the work that occurs in some process. Overview In thermodynamics, the free energy difference \Delta F = F_B - F_A between two states ''A'' and ''B'' is connected to the work ''W'' done on the system through the ''inequality'': : \Delta F \leq W , with equality holding only in the case of a quasistatic process, i.e. when one takes the system from ''A'' to ''B'' infinitely slowly (such that all intermediate states are in thermody ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic Integration
Thermodynamic integration is a method used to compare the difference in free energy between two given states (e.g., A and B) whose potential energies U_A and U_B have different dependences on the spatial coordinates. Because the free energy of a system is not simply a function of the phase space coordinates of the system, but is instead a function of the Boltzmann-weighted integral over phase space (i.e. partition function), the free energy difference between two states cannot be calculated directly from the potential energy of just two coordinate sets (for state A and B respectively). In thermodynamic integration, the free energy difference is calculated by defining a thermodynamic path between the states and integrating over ensemble-averaged enthalpy changes along the path. Such paths can either be real chemical processes or alchemical processes. An example alchemical process is the Kirkwood's coupling parameter method. Derivation Consider two systems, A and B, with poten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free-energy Perturbation
Free energy perturbation (FEP) is a method based on statistical mechanics that is used in computational chemistry for computing free energy differences from molecular dynamics or Metropolis Monte Carlo simulations. The FEP method was introduced by Robert W. Zwanzig in 1954. According to the free-energy perturbation method, the free energy difference for going from state A to state B is obtained from the following equation, known as the ''Zwanzig equation'': :\Delta F(\mathbf \rightarrow \mathbf) = F_\mathbf - F_\mathbf = -k_\mathrm T \ln \left \langle \exp \left ( - \frac \right ) \right \rangle _\mathbf where ''T'' is the temperature, ''k''B is Boltzmann's constant, and the angular brackets denote an average over a simulation run for state A. In practice, one runs a normal simulation for state A, but each time a new configuration is accepted, the energy for state B is also computed. The difference between states A and B may be in the atom types involved, in which case the Δ'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wang And Landau Algorithm
The Wang and Landau algorithm, proposed by Fugao Wang and David P. Landau, is a Monte Carlo method designed to estimate the density of states of a system. The method performs a non-Markovian random walk to build the density of states by quickly visiting all the available energy spectrum. The Wang and Landau algorithm is an important method to obtain the density of states required to perform a multicanonical simulation. The Wang–Landau algorithm can be applied to any system which is characterized by a cost (or energy) function. For instance, it has been applied to the solution of numerical integrals and the folding of proteins. The Wang–Landau sampling is related to the metadynamics algorithm.Christoph Junghans, Danny Perez, and Thomas Vogel. "Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang–Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics." Journal of Chemical Theory and Computation 10.5 (2014): 1843-1847. doibr>10.1021/ct5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metropolis Monte Carlo
A metropolis () is a large city or conurbation which is a significant economic, political, and cultural center for a country or region, and an important hub for regional or international connections, commerce, and communications. A big city belonging to a larger urban agglomeration, but which is not the core of that agglomeration, is not generally considered a metropolis but a part of it. The plural of the word is ''metropolises'', although the Latin plural is ''metropoles'', from the Greek ''metropoleis'' (). For urban centers outside metropolitan areas that generate a similar attraction on a smaller scale for their region, the concept of the regiopolis ("regio" for short) was introduced by urban and regional planning researchers in Germany in 2006. Etymology Metropolis (μητρόπολις) is a Greek word, coming from μήτηρ, ''mḗtēr'' meaning "mother" and πόλις, ''pólis'' meaning "city" or "town", which is how the Greek colonies of antiquity referred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henderson–Hasselbalch Equation
In chemistry and biochemistry, the Henderson–Hasselbalch equation :\ce = \ceK_\ce + \log_ \left( \frac \right) relates the pH of a chemical solution of a weak acid to the numerical value of the acid dissociation constant, ''K''a, of acid and the ratio of the concentrations, \frac of the acid and its conjugate base in an equilibrium. : \mathrm For example, the acid may be acetic acid :\mathrm The Henderson–Hasselbalch equation can be used to estimate the pH of a buffer solution by approximating the actual concentration ratio as the ratio of the analytical concentrations of the acid and of a salt, MA. The equation can also be applied to bases by specifying the protonated form of the base as the acid. For example, with an amine, \mathrm :\mathrm Derivation, assumptions and limitations A simple buffer solution consists of a solution of an acid and a salt of the conjugate base of the acid. For example, the acid may be acetic acid and the salt may be sodium acetat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Titration
Titration (also known as titrimetry and volumetric analysis) is a common laboratory method of quantitative chemical analysis to determine the concentration of an identified analyte (a substance to be analyzed). A reagent, termed the ''titrant'' or ''titrator'', is prepared as a standard solution of known concentration and volume. The titrant reacts with a solution of ''analyte'' (which may also be termed the ''titrand'') to determine the analyte's concentration. The volume of titrant that reacted with the analyte is termed the ''titration volume''. History and etymology The word "titration" descends from the French word ''titrer'' (1543), meaning the proportion of gold or silver in coins or in works of gold or silver; i.e., a measure of fineness or purity. ''Tiltre'' became ''titre'', which thus came to mean the "fineness of alloyed gold", and then the "concentration of a substance in a given sample". In 1828, the French chemist Joseph Louis Gay-Lussac first used ''titre'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 err ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson's Equation
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate electrostatic or gravitational (force) field. It is a generalization of Laplace's equation, which is also frequently seen in physics. The equation is named after French mathematician and physicist Siméon Denis Poisson. Statement of the equation Poisson's equation is \Delta\varphi = f where \Delta is the Laplace operator, and f and \varphi are real or complex-valued functions on a manifold. Usually, f is given and \varphi is sought. When the manifold is Euclidean space, the Laplace operator is often denoted as and so Poisson's equation is frequently written as \nabla^2 \varphi = f. In three-dimensional Cartesian coordinates, it takes the form \left( \frac + \frac + \frac \right)\va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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