Elastic energy of proteins and the stages of protein folding

¹  Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University - Beijing 100084, China
²  Physics Department, Massachusetts Institute of Technology - Cambridge, MA 02139, USA

Corresponding author: jzlei@mail.tsinghua.edu.cn

Received: 18 July 2009
Accepted: 22 November 2009

Abstract

We propose a universal elastic energy for proteins, which depends only on the radius of gyration R_g and the residue number N. It is constructed using physical arguments based on the hydrophobic effect and hydrogen bonding. Adjustable parameters are fitted to data from the computer simulation of the folding of a set of proteins using the CSAW (conditioned self-avoiding walk) model. The elastic energy gives rise to scaling relations of the form in different regions. It shows three folding stages characterized by the progression with exponents , which we identify as the unfolded stage, pre-globule, and molten globule, respectively. The pre-globule goes over to the molten globule via a break in behavior akin to a first-order phase transition, which is initiated by a sudden acceleration of hydrogen bonding.