Discrete Kinetic Models from Funneled Energy Landscape Simulations

Nicholas P Schafer,Elizabeth A Komives,Ryan M B Hoffman,Peter G Wolynes,Patricio O Craig,Anat Burger

doi:10.1371/journal.pone.0050635

Abstract

A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK). In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an “inside-out”, nucleation-propagation like character.

Highlights

Energy landscape theory and the principle of minimal frustration, which provide both simple models and interpretative frameworks [1,2], have contributed greatly to our understanding of the protein folding process
Protein folding can be understood as a diffusive process across a rugged, biased, and structurally correlated energy landscape with weak transient trapping
We describe a free energy based method that can be used to derive kinetic equations that are similar to those derived using clustering based approaches but that take into account what has been learned about natural protein folding

Summary

Introduction

Energy landscape theory and the principle of minimal frustration, which provide both simple models and interpretative frameworks [1,2], have contributed greatly to our understanding of the protein folding process. Proteins have evolved to minimize the effects of roughness of their energy landscapes by ensuring a significant stability gap between the unfolded ensemble and the native state. This leads to landscapes that resemble the highdimensional analog of a rugged funnel. All-atom simulations of fast folding proteins are just becoming reliable [6] and give results largely consistent with the rugged funnel landscape picture [7]. Model building is only part of the challenge facing theorists working on protein folding since, even on a minimally frustrated landscape, many seemingly distinct detailed mechanisms of folding are possible

Methods

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Conclusion