Exactly Solvable Model for Helix-Coil-Sheet Transitions in Protein Systems

TL;DR

This paper introduces an exactly solvable statistical mechanical model for protein secondary structure transitions, capturing helix, sheet, and coil phases with long-range interactions, providing insights into thermodynamic behavior.

Contribution

It presents a novel, exactly solvable Potts model incorporating long-range contacts to study helix-sheet-coil transitions in proteins.

Findings

Exact partition function derived using transfer matrices

Identifies phase transitions between structural states

Provides thermodynamic insights into protein folding

Abstract

In view of the important role helix-sheet transitions play in protein aggregation, we introduce a simple model to study secondary structural transitions of helix-coil-sheet systems using a Potts model starting with an effective Hamiltonian. This energy function depends on four parameters that approximately describe entropic and enthalpic contributions to the stability of a polypeptide in helical and sheet conformations. The sheet structures involve long-range interactions between residues which are far in sequence, but are in contact in real space. Such contacts are included in the Hamiltonian. Using standard statistical mechanical techniques, the partition function is solved exactly using transfer matrices. Based on this model, we study thermodynamic properties of polypeptides, including phase transitions between helix, sheet, and coil structures.