%0 Journal Article
%T The Principle of Stationary Action in Biophysics: Stability in Protein Folding
%A Walter Simmons
%A Joel L. Weiner
%J Journal of Biophysics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/697529
%X 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. 1. Descriptive Introduction Processes that proceed reliably from a variety of initial conditions to a unique final state, regardless of changing conditions, are of obvious importance in biophysics. Proteins in an appropriate solution fold to unique forms and serve as a flagship example of stable processes in biology. In this paper, we suggest how the action principle in classical mechanics could be used to analyze the stability of the protein folding process, which is of obvious importance per se, but because the techniques described here follow from fundamental physics, this approach will also be useful in the study of the stability of other biophysical processes. In this introduction, we present a number of technical issues in a descriptive style. Technical details are discussed in a later section. The action principle is a traditional starting point for classical mechanics. The action is a path integral of the difference between kinetic and potential energy (the Lagrangian), between an initial and final time over a trajectory . (The trajectory is implicit here.) The action is a scalar. The energy terms are written in generalized coordinates which take into account some or all constraints on the motion. The use of generalized coordinates makes this formalism particularly suited to moving parts of a complicated mechanical system. Standard
%U http://www.hindawi.com/journals/jbp/2013/697529/