A semi-analytical description of protein folding that incorporates detailed geometrical information

摘要

Much has been done to study the interplay between geometric and energetic effects on the protein folding energy landscape. Numerical techniques such as molecular dynamics simulations are able to maintain a precise geometrical representation of the protein. Analytical approaches, however, often focus on the energetic aspects of folding, including geometrical information only in an average way. Here, we investigate a semi-analytical expression of folding that explicitly includes geometrical effects. We consider a Hamiltonian corresponding to a Gaussian filament with structure-based interactions. The model captures local features of protein folding often averaged over by mean-field theories, for example, loop contact formation and excluded volume. We explore the thermodynamics and folding mechanisms of beta-hairpin and alpha-helical structures as functions of temperature and Q, the fraction of native contacts formed. Excluded volume is shown to be an important component of a protein Hamiltonian, since it both dominates the cooperativity of the folding transition and alters folding mechanisms. Understanding geometrical effects in analytical formulae will help illuminate the consequences of the approximations required for the study of larger proteins. © 2011 American Institute of Physics Article Outline INTRODUCTION MODEL AND METHODS Partition function with microscopic Hamiltonian Solving the model Low temperature limit and entropy crisis Partition function factors into energetic and geometric parts Elucidating the dependence on the order parameter Q RESULTS AND DISCUSSION Excluded volume and cooperativity Implicit repulsive effect of the Gaussian chain Excluded volume results in increased cooperativity Comparison between energetic and entropic cooperativity Excluded volume in simple protein-like native state geometries Repulsive effects depend on native contact map α-helix versus β-hairpin Relaxation of constraints Q dependence of thermodynamical functions Contact ordering with Q Geometric properties are a robust feature of the landscape Entropy and geometrical information CONCLUSIONS