Overview of molecular forces: Potential energy functions and simulation methods

Oliver Smart
(c) O.S. Smart 1996, all rights reserved
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Potential energy functions

We have briefly reviewed the variety of interactions which are important in protein interactions and seen suitable simple mathematical forms for their representation. These are drawn together to form a potential energy function:

This function can be used to calculate a value for the potential energy (PEF(R)) for any conformation of a given protein - defined by the (normally Cartesian) coordinate vector R. A number of important points can be made:

Simulation methods

This section provides a very brief introduction into what the uses of potential energy functions are in protein studies.

Energy minimization

This is in many ways the simplest simulation procedure. The basic idea is that starting from some structure (R we find its potential energy using the potential energy function given as equation (1) above. The coordinate vector R is then varied using an optimization procedure so as to minimize the potential energy PEF(R).

Very often these methods are used if a distorted structure is produced - e.g. a homology based model. Energy minimization can then relieve short interatomic distances while maintaining important structural features.

Energy minimization can be used to help to solve experimental structures:

Extensive notes on optimization procedures are available from the M.Sc. Molecular Modelling and Bioinformatics at Birkbeck.

Molecular Dynamics

In molecular dynamics studies the motion of a molecule is simulated as a function of time. A simple description is that Newton's second law of motion:

is solved to find how the position for each atom of the system xi varies with t. To find the forces on each atom (Fi) the derivative vector (or gradient) of equation 1 is calculated. Factors such as the temperature and pressure of the system can be included in the treatment.

Molecular dynamics simulation procedures are very popular in the protein field. They have the advantage that they can treat systems where motion is essentially diffusive in character - important because of the role of water in protein structure. The procedures can be used to calculate "ensemble average" properties - recent advances have included the ability to calculate free energy differences between (slightly) different ligands or conformations of a protein. A disadvantage of conventional molecular dynamics procedures is that they can only tackle motions with a relatively short time scale - one nanosecond is the approximate upper limit with current computers.

Other methods

Very many other methods use potential energy functions for the study of proteins conformation and dynamics. An example of this is the Path Energy Minimization procedure - which aims to find routes for large scale conformational transitions of proteins (developed by the author of this section of the course).


Useful sources of information to start to learn more about this topic:

S.J. Weiner, P.A. Kollman, D.A. Case, U.C. Singh, G. Alagona, S. Profeta Jr. and P. Weiner. "A new force field for the molecular mechanical simulation of nucleic acids and proteins". J. Am. Chem. Soc. , 106:765-784 (1984).
The original paper describing the AMBER potential energy function. An interesting if slightly heavy going paper describing the process of developing an energy function, source of parameters etc.. For further details of the AMBER program and energy function then why not look at the AMBER home page at the University of Calfornia, San Francisco.

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