A Simple Model for Protein Folding

Abstract

We describe a simple Ising-like statistical mechanical model for folding proteins based on the α-carbon contact map of the native structure. In this model residues can adopt two microscopic states corresponding to the native and non-native conformations. In order to exactly enumerate the large number of possible configurations, structure is considered to grow as continuous sequences of native residues, with no more than two sequences in each molecule. Inter-residue contacts can only form within each sequence and between residues of the two native sequences. As structure grows there is a tradeoff between the stabilizing effect of inter-residue contacts and the entropy losses from ordering residues in their native conformation and from forming a disordered loop to connect two continuous sequences. Folding kinetics are calculated from the dynamics on the free energy profile, as in Kramers' reaction rate theory. Although non-native interactions responsible for roughness in the energy landscape are not explicitly considered in the model, they are implicitly included by determining the absolute rates for motion on the free energy profile. With the exception of α-helical proteins, the kinetic progress curves exhibit single exponential time courses, consistent with two state behavior, as observed experimentally. The calculated folding rates are in remarkably good agreement with the measured values for the 25 two-state proteins investigated, with a correlation coefficient of 0.8. With its coarse-grained description of both the energy and entropy, and only three independently adjustable parameters, the model may be regarded as the simplest possible analytical model of protein folding capable of predicting experimental properties of specific proteins.