Minimum Problems

Piela L, Kostrowicki J and Scheraga H A 1989 The multiple-minima problem in the conformational analysis of molecules. Deformation of the potential energy hypersurface by the diffusion equation method J. Phys. Chem. 93 3339... 

Q and H A Scheraga 1987. Monte-Carlo-minimization Approach to the Multiple-minima Problem... 

Li Z Q and H A Scheraga 1987. Monte Carlo Minimization Approach to the Multiple Minima Problem, in Protein Folding. Proceedings of the National Academy of Sciences USA 84 6611-6615. 

An approach to overcome the multi minima problem of proteins is simulated annealing (SA) run. Besides global molecular properties such as structural and thermal motions, functional properties of fast biological reactions can also be studied by MD. 

Purisima, E.O. Scheraga, H.A., An approach to the multiple-minima problem by relaxing dimensionality, Proc. Natl Acad. Sci. USA 1986, 83, 2782-2786... 

Cvijovic, D. and Klinowski, J. (1995) Taboo search—an approach to the multiple minima problem. Science 267, 664—666. 

Z. Li and H. A. Scheraga. Monte carlo minimization approach to the multiple minima problem in protein folding. Proc. Nat. Acad. Sci. U.S.A., 84 6611-6615, 1987. 

Challenging the Multiple Minima Problem Example of Protein Folding... 

The multiple minima problem is ubiquitous in mathematical description of reality (physics, chemistry, biology, economy, etc.), and (R) is only an example of it. It is very unlikely that such kind of problems will find analytical solution, and thus, one has to rely on computers. The hope is that for certain class of approximations one can simplify (R) enough to overcome the multiple minima problem by extensive calculations. 

The protein folding, notorious for an astronomic number of possible conformations, is only an example of the multiple minima problem, inherently connected to all applications of theory to structural chemistry (isomers, supramolecular structures etc.). The multiple minima problem is also virtually ubiquitous in other sciences, and whenever a mathematical description is used, the situation is encountered more and more often. Despite the complexity of the protein folding, remarkable achievements in the prediction of the 3D structure of globular proteins are possible nowadays. 

It is instructive to see what kind of concepts have been used to overcome the multiple minima problem in this particular case, with a hope that a similar approach could help in other domains. Here is the list of decisive steps ... 

L. Piela, H.A. Scheraga, On the multiple-minima problem in the conformational analysis of polypeptides. I. Backbone degrees of freedom for a perturbed a-helix. Biopolymers 26, S33-S58 (1987)... 

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