Table of Contents
Journal of Biophysics
Volume 2013, Article ID 697529, 7 pages
http://dx.doi.org/10.1155/2013/697529
Research Article

The Principle of Stationary Action in Biophysics: Stability in Protein Folding

1Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822, USA
2Department of Mathematics, University of Hawaii at Manoa, Honolulu, HI 96822, USA

Received 22 May 2013; Revised 18 October 2013; Accepted 1 November 2013

Academic Editor: Kuo-Chen Chou

Copyright © 2013 Walter Simmons and Joel L. Weiner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We conceptualize protein folding as motion in a large dimensional dihedral angle space. We use Lagrangian mechanics and introduce an unspecified Lagrangian to study the motion. The fact that we have reliable folding leads us to conjecture the totality of paths forms caustics that can be recognized by the vanishing of the second variation of the action. There are two types of folding processes: stable against modest perturbations and unstable. We also conjecture that natural selection has picked out stable folds. More importantly, the presence of caustics leads naturally to the application of ideas from catastrophe theory and allows us to consider the question of stability for the folding process from that perspective. Powerful stability theorems from mathematics are then applicable to impose more order on the totality of motions. This leads to an immediate explanation for both the insensitivity of folding to solution perturbations and the fact that folding occurs using very little free energy. The theory of folding, based on the above conjectures, can also be used to explain the behavior of energy landscapes, the speed of folding similar to transition state theory, and the fact that random proteins do not fold.