Topology-dependent protein folding rates analyzed by a stereochemical model

Abstract

It is an experimental fact that gross topological parameters of the native structure of small proteins presenting two-state kinetics, as relative contact order chi, correlate with the logarithm of their respective folding rate constant kappa(f). However, reported results show specific cases for which the (chi,log kappa(f)) dependence does not follow the overall trend of the entire collection of experimental data. Therefore, an interesting point to be clarified is to what extent the native topology alone can explain these exceptional data. In this work, the structural determinants of the folding kinetics are investigated by means of a 27-mer lattice model, in that each native is represented by a compact self-avoiding (CSA) configuration. The hydrophobic effect and steric constraints are taken as basic ingredients of the folding mechanism, and each CSA configuration is characterized according to its composition of specific patterns (resembling basic structural elements such as loops, sheets, and helices). Our results suggest that (i) folding rate constants are largely influenced by topological details of the native structure, as configurational pattern types and their combinations, and (ii) global parameters, as the relative contact order, may not be effective to detect them. Distinct pattern types and their combinations are determinants of what we call here the "content of secondary-type" structure (sigma) of the native: high sigma implies a large kappa(f). The largest part of all CSA configurations presents a mix of distinct structural patterns, which determine the chixlog kappa(f) linear dependence: Those structures not presenting a proper chi-dependent balance of patterns have their folding kinetics affected with respect to the pretense linear correlation between chi and log kappa(f). The basic physical mechanism relating sigma and kappa(f) involves the concept of cooperativity: If the native is composed of patterns producing a spatial order rich in effective short-range contacts, a properly designed sequence undertakes a fast folding process. On the other hand, the presence of some structural patterns, such as long loops, may reduce substantially the folding performance. This fact is illustrated through natives having a very similar topology but presenting a distinct folding rate kappa(f), and by analyzing structures having the same chi but different sigma.