Analytic Partition Function Zeros of the Wako-Saito-Munoz-Eaton beta-hairpin Model

TL;DR

This paper derives an analytic formula for the density of states and partition function zeros of a beta-hairpin model, revealing their distribution patterns and physical implications for folding transitions and hydrophobic core effects.

Contribution

It provides the first analytic expressions for partition function zeros in a specific beta-hairpin model, linking zero distribution to folding behavior and structural features.

Findings

Zeros are uniformly distributed on a circle indicating a first-order-like transition.

Introduction of hydrophobic core results in zeros on two concentric circles.

Exact zeros for complex native contact structures closely match concentric circle patterns.

Abstract

An analytic formula for the density of states of Wako-Saito-Munoz-Eaton model, for a simple class of beta-hairpins, is obtained. Under certain simplifying assumptions on the structure of the native contacts and the values of local entropy, the partition function zeros are also obtained in analytic forms. The zeros are uniformly distributed on a circle, exhibiting a first-order-like nature of the folding transition. After introducing hydrophobic core at the central region of the hairpin, the zeros are shown to distribute uniformly on two concentric circles corresponding to the hydrophobic collapse and the transition to the fully folded conformations. The dependence of the distribution of the zeros on the position of the hydrophobic core, is shown to have a clear physical interpretation. The exact partition function zeros for a hairpin with a more complex structure of native contacts, the 16 C-terminal residues of streptococcal protein G B1, are also numerically computed, and their loci are also shown to be closely approximated by concentric circles.