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A force field is used to minimize the bond stretching energy of this ethane molecule.
A force field is used to minimize the bond stretching energy of this ethane molecule. In the context of Molecular mechanics, a force field (also called a forcefield) refers to the functional form and Parameter sets used

The term molecular mechanics refers to the use of Newtonian mechanics to model molecular systems. Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by The potential energy of all systems in molecular mechanics is calculated using force fields. In the context of Molecular mechanics, a force field (also called a forcefield) refers to the functional form and Parameter sets used Molecular mechanics can be used to study small molecules as well as large biological systems or material assemblies with many thousands to millions of atoms.

All-atomistic molecular mechanics methods have the following properties:

Variations on this theme are possible; for example, many simulations have historically used a "united-atom" representation in which methyl and methylene groups were represented as a single particle, and large protein systems are commonly simulated using a "bead" model that assigns two to four particles per amino acid. Van der Waals Volume The van der Waals volume, V, also called the atomic volume or molecular volume, is the atomic property most directly In Chemistry, a methyl group is a Hydrophobic Alkyl Functional group named after Methane (4 Methylene is the chemical species R2C named after Methane, in which two of the carbon atom's valence electrons form no bonds In Chemistry, an amino acid is a Molecule containing both Amine and Carboxyl Functional groups In Biochemistry, this

Contents

Functional Form

Molecular mechanics potential energy function with continuum solvent.
Molecular mechanics potential energy function with continuum solvent.

The following functional abstraction, known as a potential function or force field in Chemistry, calculates the molecular system's potential energy (E) in a given conformation as a sum of individual energy terms. In the context of Molecular mechanics, a force field (also called a forcefield) refers to the functional form and Parameter sets used

\ E = E_{covalent} + E_{noncovalent}

where the components of the covalent and noncolvalent contributions are given by the following summations:

\ E_{covalent} = E_{bond} + E_{angle} + E_{dihedral}

\ E_{noncovalent} = E_{electrostatic} + E_{van der Waals}

The exact functional form of the potential function, or force field, depends on the particular simulation program being used. Generally the bond and angle terms are modeled as harmonic potentials centered around equilibrium bond-length values derived from experiment or theoretical calculations of electronic structure performed with software which does ab-initio type calculations such as Gaussian. This article is about the harmonic oscillator in classical mechanics Generally the word Gaussian pertains to Carl Friedrich Gauss and his ideas For accurate reproduction of vibrational spectra, the Morse potential can be used instead, at computational cost. The Morse potential, named after physicist Philip M Morse, is a convenient model for the Potential energy of a Diatomic molecule. The dihedral or torsional terms typically have multiple minima and thus cannot be modeled as harmonic oscillators, though their specific functional form varies with the implementation. This class of terms may include "improper" dihedral terms, which function as correction factors for out-of-plane deviations (for example, they can be used to keep benzene rings planar). Benzene, or benzol, is an organic Chemical compound and a known Carcinogen with the molecular formula C 6 H 6

The non-bonded terms are much more computationally costly to calculate in full, since a typical atom is bonded to only a few of its neighbors, but interacts with every other atom in the molecule. Fortunately the van der Waals term falls off rapidly - it is typically modeled using a "6-12 Lennard-Jones potential", which means that attractive forces fall off with distance as r-6 and repulsive forces as r-12, where r represents the distance between two atoms. The Van der Waals equation is an Equation of state that can be derived from a special form of the potential between a pair of molecules (hard-sphere repulsion A pair of neutral atoms or molecules is subject to two distinct forces in the limit of large separation and small separation an attractive force at long ranges ( van der Waals force, or Generally a cutoff radius is used to speed up the calculation so that atom pairs whose distances are greater than the cutoff have a van der Waals interaction energy of zero.

The electrostatic terms are notoriously difficult to calculate well because they do not fall off rapidly with distance, and long-range electrostatic interactions are often important features of the system under study (especially for proteins). Proteins are large Organic compounds made of Amino acids arranged in a linear chain and joined together by Peptide bonds between the Carboxyl The basic functional form is the Coulomb potential, which only falls off as r-1. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form A variety of methods are used to address this problem, the simplest being a cutoff radius similar to that used for the van der Waals terms. However, this introduces a sharp discontinuity between atoms inside and atoms outside the radius. Switching or scaling functions that modulate the apparent electrostatic energy are somewhat more accurate methods that multiply the calculated energy by a smoothly varying scaling factor from 0 to 1 at the outer and inner cutoff radii. Other more sophisticated but computationally intensive methods are known as particle mesh Ewald (PME) and the multipole algorithm.

In addition to the functional form of each energy term, a useful energy function must be assigned parameters for force constants, van der Waals multipliers, and other constant terms. These terms, together with the equilibrium bond, angle, and dihedral values, partial charge values, atomic masses and radii, and energy function definitions, are collectively known as a force field. In the context of Molecular mechanics, a force field (also called a forcefield) refers to the functional form and Parameter sets used Parameterization is typically done through agreement with experimental values and theoretical calculations results.

Each force field is parameterized to be internally consistent, but the parameters are generally not transferable from one force field to another. For example, the MM3 force field has 46 sets of parameters for oxygen and 18 sets for carbon (in different functional groups). MM3 has no parameters for lone pairs of electrons. On the other hand, the molecular recognition features of STR3DI32 enables it to use one set of parameters for each hybridization type of each atom (three sets of parameters for each of the second row elements, etc. ), and it is parameterized for lone pairs of electrons. These molecular recognition features of STR3DI32 allow for an easy usage of data from MM3 files. However, starting with the simple Cartesian coordinate data, one would require considerable effort to produce a MM3 file. Most molecular modelers, and STR3DI32, can generate MM2, and other, files which can be read by MM3.

Areas of application

The prototypical Molecular Mechanics application is energy minimization. That is, the force field is used as an optimization criterion and the (local) minimum searched by an appropriate algorithm (e. In the context of Molecular mechanics, a force field (also called a forcefield) refers to the functional form and Parameter sets used In Mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function g. steepest descent). For the analytical method called "steepest descent" see Method of steepest descent. Global energy optimization can be accomplished using simulated annealing, the Metropolis algorithm and other Monte Carlo methods, or using different deterministic methods of discrete or continuous optimization. Simulated annealing (SA is a generic probabilistic Meta-algorithm for the Global optimization problem namely locating a good approximation to the In Mathematics and Physics, the Metropolis-Hastings algorithm is a method for creating a Markov chain that can be used to generate a sequence of Monte Carlo methods are a class of Computational Algorithms that rely on repeated Random sampling to compute their results The main aim of optimization methods is finding the lowest energy conformation of a molecule or identifying a set of low-energy conformers that are in equilibrium with each other. The force field represents only the enthalpic component of free energy, and only this component is included during energy minimization. In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of In Thermodynamics, the Gibbs free energy ( IUPAC recommended name Gibbs energy or Gibbs function) is a Thermodynamic potential which However, the analysis of equilibrium between different states requires also conformational entropy be included, which is possible but rarely done. Conformational entropy is the Entropy associated with the physical arrangement of a Polymer chain that assumes a compact or globular state in solution

Molecular mechanics potential energy functions have been used to calculate binding constants [1] [2] [3] [4] [5], protein folding kinetics[6], protonation equilibria[7], active site coordinates[3] [8], and to design binding sites. In the field of Molecular modeling, docking is a method which predicts the preferred orientation of one molecule to a second when bound to each other to form Protein design is the design of new Protein molecules from scratch or the deliberate design of a new molecule by making calculated variations on a known structure [9]

Molecular Mechanics and Molecular Dynamics (MD) are related but different. Molecular dynamics ( MD) is a form of Computer simulation in which atoms and molecules are allowed to interact for a period of time by approximations of Main purpose of MD is modeling of molecular motions, although it is also applied for optimization, for example using simulated annealing. Simulated annealing (SA is a generic probabilistic Meta-algorithm for the Global optimization problem namely locating a good approximation to the MM implements more "static" energy minimization methods to study the potential energy surfaces of different molecular systems. However, MM can also provide important dynamic parameters, such as energy barriers between different conformers or steepness of a potential energy surface around a local minimum. MD and MM are usually based on the same classical force fields. In the context of Molecular mechanics, a force field (also called a forcefield) refers to the functional form and Parameter sets used But MD may also be based on quantum chemical methods like DFT. Quantum chemistry is a branch of Theoretical chemistry, which applies Quantum mechanics and Quantum field theory to address issues and problems in Density functional theory (DFT is a quantum mechanical theory used in Physics and Chemistry to investigate the Electronic structure (principally MM is also loosely used to define a set of techniques in molecular modeling. Molecular modelling is a collective term that refers to theoretical methods and computational techniques to model or mimic the behaviour of Molecules The techniques

Environment and Solvation

There are several ways of defining the environment surrounding the molecule or molecules of interest in molecular mechanics. A system can be simulated in vacuum (known as a gas-phase simulation) with no surrounding environment at all, but this is usually not desirable because it introduces artifacts in the molecular geometry, especially in charged molecules. Surface charges that would ordinarily interact with solvent molecules instead interact with each other, producing molecular conformations that are unlikely to be present in any other environment. The "best" way to solvate a system is to place explicit water molecules in the simulation box with the molecules of interest and treat the water molecules as interacting particles like those in the molecule. A variety of water models exist with increasing levels of complexity, representing water as a simple hard sphere (a united-atom approach), as three separate particles with fixed bond angles, or even as four or five separate interaction centers to account for unpaired electrons on the oxygen atom. Computational chemistry, classical water models are used for the simulation of Water clusters liquid water, and aqueous solutions with explicit solvent Unsurprisingly, the more complex the water model, the more computationally intensive the simulation. A compromise approach has been found in implicit solvation, which replaces the explicitly represented water molecules with a mathematical expression that reproduces the average behavior of water molecules (or other solvents such as lipids). Implicit solvation (sometimes known as continuum solvation) is a method of representing Solvent as a continuous medium instead of individual “explicit” solvent This method is useful for preventing artifacts that arise from vacuum simulations and reproduces bulk solvent properties well, but cannot reproduce situations in which individual water molecules have interesting interactions with the molecules under study.

Software Packages

Limited list; many more are available

See also

Force field in Chemistry
Software for molecular mechanics modeling

References

  1. ^ B. Kuhn and P. A. Kollman, "Binding of a diverse set of ligands to avidin and streptavidin: an accurate quantitative prediction of their relative affinities by a combination of molecular mechanics and continuum solvent models," J Med Chem 43, 3786-3791 (2000).
  2. ^ S. Huo, I. Massova and P. A. Kollman, "Computational alanine scanning of the 1:1 human growth hormone-receptor complex," J Comput Chem 23, 15-27 (2002).
  3. ^ a b D. L. Mobley, A. P. Graves, J. D. Chodera, A. C. McReynolds, B. K. Shoichet and K. A. Dill, "Predicting absolute ligand binding free energies to a simple model site," J Mol Biol 371, 1118-1134 (2007).
  4. ^ J. Wang, X. Kang, I. D. Kuntz and P. A. Kollman, "Hierarchical database screenings for HIV-1 reverse transcriptase using a pharmacophore model, rigid docking, solvation docking, and MM-PB/SA," J Med Chem 48, 2432-2444 (2005).
  5. ^ P. A. Kollman, I. Massova, C. Reyes, B. Kuhn, S. Huo, L. Chong, M. Lee, T. Lee, Y. Duan, W. Wang, O. Donini, P. Cieplak, J. Srinivasan, D. A. Case and T. E. Cheatham, 3rd, "Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models," Acc Chem Res 33, 889-897 (2000).
  6. ^ C. D. Snow, H. Nguyen, V. S. Pande and M. Gruebele, "Absolute comparison of simulated and experimental protein-folding dynamics," Nature 420, 102-106 (2002).
  7. ^ P. Barth, T. Alber and P. B. Harbury, "Accurate, conformation-dependent predictions of solvent effects on protein ionization constants," Proc Natl Acad Sci U S A 104, 4898-4903 (2007).
  8. ^ R. Chakrabarti, A. M. Klibanov and R. A. Friesner, "Computational prediction of native protein ligand-binding and enzyme active site sequences," Proc Natl Acad Sci U S A 102, 10153-10158 (2005).
  9. ^ F. E. Boas and P. B. Harbury, "Design of protein-ligand binding based on the molecular-mechanics energy model," J. Mol. Biol. In press. (2008).

Dictionary

molecular mechanics

-noun

  1. (chemistry) A non-rigorous method of computing the structures, energies, and some properties of molecules by assuming they behave like small balls connected by springs.
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