Molecular Mechanics

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Revision as of 08:32, 26 August 2008

Molecular Mechanics or force-field methods use classical type models to predict the energy of a molecule as a function of its conformation. It is an empirical method of calculating the dynamics of molecules, in which bonds between atoms are represented by springs obeying Hooke's law, and additional terms representing bond angle bending, torsional interactions, and van der Waals-type interactions are included.

This allows predictions of:

• Equilibrium geometries and transition states
• Relative energies between conformers or between different molecules

Molecular mechanics can be used to supply the potential energy for molecular dynamics computations on large molecules. However, they are not appropriate for bond-breaking reactions.

Molecular mechanics methods are based on the following principles:

• Nuclei and electrons are lumped into atom-like particles.
• Atom-like particles are spherical (radii obtained from measurements or theory) and have a net charge (obtained from theory).
• Interactions are based on springs and classical potentials.
• Interactions must be preassigned to specific sets of atoms.
• Interactions determine the spatial distribution of atom-like particles and their energies.

Functional Form

Schematic representation of the four key contributions to a molecular mechanics force field

In its simplest representation, the molecular mechanics equation is

E = Es + Eb + Ew + Enb

where Es is the energy involved in the deformation of a bond, either by stretching or compression, Eb is the energy involved in angle bending, Ew is the torsional angle energy, and Enb is the energy involved in interactions between atoms that are not directly bonded.

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.g. 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. 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. However, the analysis of equilibrium between different states requires also conformational entropy be included, which is possible but rarely done.

Molecular mechanics potential energy functions have been used to calculate binding constants <ref name="Kuhn">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).</ref> <ref name="huo">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).</ref> <ref name="Mobley">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).</ref> <ref name="Wang">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).</ref> <ref name="Kollman">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).</ref>, protein folding kinetics<ref name="Snow">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).</ref>, protonation equilibria<ref name="Barth">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).</ref>, active site coordinates<ref name="Mobley">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).</ref> <ref name="Chakrabarti">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).</ref>, and to design binding sites.<ref name="Boas">F. E. Boas and P. B. Harbury, "Design of protein-ligand binding based on the molecular-mechanics energy model," J. Mol. Biol. 380, 415-424. (2008).</ref>

Molecular Mechanics and Molecular Dynamics (MD) are related but different. Main purpose of MD is modeling of molecular motions, although it is also applied for optimization, for example using simulated annealing. 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. But MD may also be based on quantum chemical methods like DFT. MM is also loosely used to define a set of techniques in molecular modeling.

Software Packages

• AMBER
• Ascalaph
• CHARMM
• Ghemical
• GROMOS
• GROMACS
• MDynaMix
• NAMD
• STR3DI32
• TINKER
• Zodiac

References

• U. Burkert and N.L. Allinger, Molecular Mechanics, 1982, ISBN 0-8412-0885-9
• Vernon G. S. Box, The Molecular Mechanics of Quantized Valence Bonds, J. Mol. Model., 3, 124, 1997
• Vernon G. S. Box, The anomeric effect of monosaccharides and their derivatives. Insights from the new QVBMM molecular mechanics force field, Heterocycles, 48, 2389 1998
• Vernon G. S. Box, Stereo-electronic effects in polynucleotides and their double helices, J. Mol. Struct., 689, 33-41 2004
• O. Becker, A.D. MacKerell, Jr., B. Roux and M. Watanabe, Editors, Computational Biochemistry and Biophysics, Marcel Dekker Inc., New York, 2001, ISBN 0-8247-0455-X
• MacKerell, A.D., Jr., Empirical Force Fields for Biological Macromolecules: Overview and Issues, Journal of Computational Chemistry, 25: 1584-1604, 2004
• Schlick, T. Molecular Modeling and Simulation: An Interdisciplinary Guide. Springer-Verlag, New York, NY: 2002. ISBN 0-387-95404-X.
• K.I.Ramachandran, G Deepa and Krishnan Namboori. P.K.Computational Chemistry and Molecular Modeling Principles and Applications ISBN 978-3-540-77302-3 Springer-Verlag GmbH (2008)[1]

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