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| [[Image:Bond stretching energy.png|thumb|right|A [[Force field (chemistry)|force field]] is used to minimize the bond stretching energy of this ethane molecule.]]
| | Custom. The author's name is Dalton although it's not the maximum masucline name out there. To drive is one of some of the things he loves most. His wife and him chose to exist in in South Carolina with his family loves the program. Auditing is where his primary income comes from. He 's running and maintaining per blog here: http://circuspartypanama.com<br><br>Also visit my homepage: [http://circuspartypanama.com clash of clans triche] |
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| '''Molecular mechanics''' uses [[classical mechanics]] to model [[molecular]] systems. The potential energy of all systems in molecular mechanics is calculated using [[Force field (chemistry)|force field]]s. 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.
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| All-atomistic molecular mechanics methods have the following properties:
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| * Each atom is simulated as a single particle
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| * Each particle is assigned a radius (typically the [[van der Waals radius]]), polarizability, and a constant net charge (generally derived from quantum calculations and/or experiment)
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| * Bonded interactions are treated as "springs" with an equilibrium distance equal to the experimental or calculated bond length
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| Variations on this theme are possible; for example, many simulations have historically used a "united-atom" representation in which each terminal [[methyl group]] or intermediate [[methylene bridge|methylene unit]] was considered a single particle, and large protein systems are commonly simulated using a "bead" model that assigns two to four particles per [[amino acid]].
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| ==Functional form==
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| [[Image:MM PEF.png|thumb|right|Molecular mechanics potential energy function with continuum solvent.]]
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| The following functional abstraction, known as a potential function or [[Force field (chemistry)|force field]] in Chemistry, calculates the molecular system's potential energy (E) in a given conformation as a sum of individual energy terms.
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| <math>\ E = E_\text{covalent} + E_\text{noncovalent} \, </math>
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| where the components of the covalent and noncovalent contributions are given by the following summations:
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| <math>\ E_\text{covalent} = E_\text{bond} + E_\text{angle} + E_\text{dihedral}</math>
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| <math>\ E_\text{noncovalent} = E_\text{electrostatic} + E_\text{van der Waals} </math>
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| The [[Potential energy of protein|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 oscillator|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 (software)|Gaussian]]. For accurate reproduction of vibrational spectra, the [[Morse potential]] can be used instead, at computational cost. 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).
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| 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 force|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''<sup>−6</sup> and repulsive forces as ''r''<sup>−12</sup>, where r represents the distance between two atoms. The repulsive part ''r''<sup>−12</sup> is however unphysical, because repulsion increases exponentially. Description of van der Waals forces by the Lennard-Jones 6–12 potential introduces inaccuracies, which become significant at short distances.<ref>{{cite journal | author = Zgarbova M. ''et al.'' | year = 2010 | title = | url = | journal = Phys. Chem. Chem. Phys. | volume = 12 | issue = | pages = 10476–10493 | doi = 10.1039/C002656E |bibcode = 2010PCCP...1210476Z }}</ref> 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.
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| 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]]). The basic functional form is the [[Coulomb's law|Coulomb potential]], which only falls off as ''r''<sup>−1</sup>. 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 [[Ewald_summation#Particle_mesh_Ewald_.28PME.29_method|particle mesh Ewald]] (PME) and the [[Fast_multipole_method|multipole algorithm]].
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| 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 (chemistry)|force field]]. Parameterization is typically done through agreement with experimental values and theoretical calculations results.
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| Each force field is parameterized to be internally consistent, but the parameters are generally not transferable from one force field to another.
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| ==Areas of application==
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| One of the molecular mechanics application is energy minimization. That is, the [[force field (chemistry)|force field]] is used as an [[Optimization (mathematics)|optimization]] criterion and the (local) minimum searched by an appropriate algorithm (e.g. [[Gradient descent|steepest descent]]). Global energy optimization can be accomplished using [[simulated annealing]], the [[Metropolis–Hastings algorithm|Metropolis algorithm]] and other [[Monte Carlo method|Monte Carlo]] methods, or using different deterministic methods of discrete or continuous optimization. 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 [[enthalpy|enthalpic]] component of [[Gibbs free energy|free energy]], and only this component is included during energy minimization. However, the analysis of equilibrium between different states requires also [[conformational entropy]] be included, which is possible but rarely done.
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| Molecular mechanics potential energy functions have been used to calculate binding constants,<ref name=Kuhn>{{cite journal |author=Kuhn B, Kollman PA |title=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 |journal=Journal of Medicinal Chemistry |volume=43 |issue=20 |pages=3786–91 |date=October 2000|pmid=11020294 |doi=10.1021/jm000241h}}</ref><ref name=huo>{{cite journal |author=Huo S, Massova I, Kollman PA |title=Computational alanine scanning of the 1:1 human growth hormone-receptor complex |journal=J Comput Chem |volume=23 |issue=1 |pages=15–27 |date=January 2002|pmid=11913381 |doi=10.1002/jcc.1153}}</ref><ref name=Mobley>{{cite journal |author=Mobley DL, Graves AP, Chodera JD, McReynolds AC, Shoichet BK, Dill KA |title=Predicting absolute ligand binding free energies to a simple model site |journal=J Mol Biol. |volume=371 |issue=4 |pages=1118–34 |date=August 2007|pmid=17599350 |pmc=2104542 |doi=10.1016/j.jmb.2007.06.002}}</ref><ref name=Wang>{{cite journal |author=Wang J, Kang X, Kuntz ID, Kollman PA |title=Hierarchical database screenings for HIV-1 reverse transcriptase using a pharmacophore model, rigid docking, solvation docking, and MM-PB/SA |journal=Journal of Medicinal Chemistry |volume=48 |issue=7 |pages=2432–44 |date=April 2005|pmid=15801834 |doi=10.1021/jm049606e}}</ref><ref name=Kollman>{{cite journal |author=Kollman PA, Massova I, Reyes C, ''et al.'' |title=Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models |journal=Acc Chem Res. |volume=33 |issue=12 |pages=889–97 |date=December 2000|pmid=11123888 |doi=10.1021/ar000033j}}</ref> protein folding kinetics,<ref name=Snow>{{cite journal |author=Snow CD, Nguyen H, Pande VS, Gruebele M |title=Absolute comparison of simulated and experimental protein-folding dynamics |journal=Nature |volume=420 |issue=6911 |pages=102–6 |date=November 2002|pmid=12422224 |doi=10.1038/nature01160 |bibcode = 2002Natur.420..102S }}</ref> protonation equilibria,<ref name=Barth>{{cite journal |author=Barth P, Alber T, Harbury PB |title=Accurate, conformation-dependent predictions of solvent effects on protein ionization constants |journal=Proc Natl Acad Sci U.S.A. |volume=104 |issue=12 |pages=4898–903 |date=March 2007|pmid=17360348 |pmc=1829236 |doi=10.1073/pnas.0700188104 |bibcode = 2007PNAS..104.4898B }}</ref> [[docking (molecular)|active site coordinates]],<ref name=Mobley/><ref name=Chakrabarti>{{cite journal |author=Chakrabarti R, Klibanov AM, Friesner RA |title=Computational prediction of native protein ligand-binding and enzyme active site sequences |journal=Proc Natl Acad Sci U.S.A. |volume=102 |issue=29 |pages=10153–8 |date=July 2005|pmid=15998733 |pmc=1177389 |doi=10.1073/pnas.0504023102 |bibcode = 2005PNAS..10210153C }}</ref> and to [[protein design|design binding sites]].<ref name=Boas>{{cite journal |author=Boas FE, Harbury PB |title=Design of Protein-Ligand Binding Based on the Molecular-Mechanics Energy Model |journal=J Mol Biol. |volume=380 |issue=2 |pages=415–24 |date=July 2008|pmid=18514737 |doi=10.1016/j.jmb.2008.04.001 |pmc=2569001 }}</ref>
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| ==Environment and solvation==
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| 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 model]]s 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. 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). 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.
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| ==Software packages==
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| {{main|List of software for molecular mechanics modeling}}
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| This is a limited list; many more packages are available.
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| {{columns-list|3|
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| *[http://multiscalelab.org/acemd ACEMD - GPU MD]
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| *[[Abalone (molecular mechanics)|Abalone]]
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| *[[AMBER]]
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| *[http://www.biomolecular-modeling.com/Products.html Ascalaph]
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| *[[BOSS (molecular mechanics)|BOSS]]
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| *[[CHARMM]]
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| *[http://www.cosmos-software.de/ce_intro.html COSMOS]
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| *[http://cytosolve.com/ CytoSolve]
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| *[[Ghemical]]
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| *[[GROMOS]]
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| *[[GROMACS]]
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| *[[Internal Coordinate Mechanics|ICM]]
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| *[[MacroModel]]
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| *[[MDynaMix]]
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| *[[NAMD]]
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| *[[Q-Chem]]
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| *[[Spartan (software) | Spartan]]
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| *[http://www.exorga.com/ StruMM3D (STR3DI32)]
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| *[[TINKER]]
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| *[http://www.zeden.org/ Zodiac]
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| *[[X-PLOR]]
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| *[[Yasara]]
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| *[[LAMMPS]]
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| }}
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| ==See also==
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| {{columns-list|2|
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| * [[Molecular graphics]]
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| * [[Molecular dynamics]]
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| * [[Molecule editor]]
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| * [[Force field (chemistry)]]
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| * [[Force field implementation]]
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| * [[Molecular design software]]
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| * [[Molecular modeling on GPU]]
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| * [[List of software for molecular mechanics modeling|Software for molecular mechanics modeling]]
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| * [[List of software for Monte Carlo molecular modeling|Software for Monte Carlo molecular modeling]]
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| }}
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| ==References==
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| *{{cite book |author=Allinger NL, Burkert U |title=Molecular Mechanics |publisher=An American Chemical Society Publication |year=1982 |isbn=0-8412-0885-9 }}
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| *{{cite journal |author=Box VG |title=The Molecular Mechanics of Quantized Valence Bonds |journal=J Mol Model. |volume=3 |issue=3 |pages=124–41 |date=March 1997 |doi=10.1007/s008940050026 }}
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| *{{cite journal |author=Box VG |title=The anomeric effect of monosaccharides and their derivatives. Insights from the new QVBMM molecular mechanics force field |journal=Heterocycles |volume=48 |issue=11 |pages=2389–417 |date=12 November 1998|url=http://cat.inist.fr/?aModele=afficheN&cpsidt=10678043 |doi=10.3987/REV-98-504}}
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| *{{cite journal |author=Box VG |title=Stereo-electronic effects in polynucleotides and their double helices |journal=J Mol Struct. |volume=689 |issue=1–2 |pages=33–41 |year=2004 |doi=10.1016/j.molstruc.2003.10.019 |bibcode = 2004JMoSt.689...33B }}
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| *{{cite book |author=Becker OM |title=Computational biochemistry and biophysics |publisher=Marcel Dekker |location=New York, N.Y. |year=2001 |isbn=0-8247-0455-X }}
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| *{{cite journal |author=Mackerell AD |title=Empirical force fields for biological macromolecules: overview and issues |journal=J Comput Chem |volume=25 |issue=13 |pages=1584–604 |date=October 2004|pmid=15264253 |doi=10.1002/jcc.20082 }}
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| *{{cite book |author=Schlick T |title=Molecular modeling and simulation: an interdisciplinary guide |publisher=Springer |location=Berlin |year=2002 |isbn=0-387-95404-X }}
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| *{{cite book |author=Krishnan Namboori; Ramachandran, K. S.; Deepa Gopakumar |title=Computational Chemistry and Molecular Modeling: Principles and Applications |publisher=Springer |location=Berlin |year=2008 |isbn=3-540-77302-9 }}<ref>http://www.amrita.edu/cen/ccmm</ref>
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| {{Reflist}}
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| ==External links==
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| *[http://dissertations.ub.rug.nl/faculties/science/1996/h.bekker/ Molecular dynamics simulation methods revised]
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| *[http://www.layruoru.com/dokuwiki/doku.php/molecular_mechanics_-_it_is_simple Molecular mechanics - it is simple]
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| {{DEFAULTSORT:Molecular Mechanics}}
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| [[Category:Molecular physics]]
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| [[Category:Computational chemistry]]
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| [[Category:Intermolecular forces]]
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| [[Category:Molecular modelling]]
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