Elastic energy of proteins and the stages of protein folding

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 $R_g\sim N^{\nu }$ in different regions. It shows three folding stages characterized by the progression with exponents $\nu =3/5,3/7,2/5$, 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.

References in corpus (2)

• Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two- and Three-Dimensional Self-Avoiding Walks
• Dynamics of Alpha-Helix Formation in the CSAW Model

Cited by in corpus (4)

• Elastic Energy and Phase Structure in a Continuous Spin Ising Chain with Applications to the Protein Folding Problem
• Frequency-Rank Correlations of Rhodopsin Mutations with Tuned Hydropathic Roughness Based on Self-Organized Criticality
• Multiple scales and phases in discrete chains with application to folded proteins
• Long range correlations and folding angle in polymers with applications to α-helical proteins