A Unified Model of $\alpha$-Helix/$\beta$-Sheet/Random-Coil Transition in Proteins

TL;DR

This paper presents a simple, unified model for protein conformational transitions among alpha-helix, beta-sheet, and random coil states, incorporating both short and long-range interactions and new parameters for beta structures.

Contribution

It introduces three novel parameters to describe beta structures and explores how their interplay with existing factors influences conformational transitions.

Findings

Increasing local constraint or long-range bonding promotes beta-sheet formation.

Transition sharpness depends on the competition between short and long-range interactions.

Entropy from beta-strand grouping significantly affects the partition function and structural differences.

Abstract

The theory of transition between $\alpha$-helix, $\beta$-sheet and random coil conformation of a protein is discussed through a simple model, that includes both short and long-range interactions. Besides the bonding parameter and helical initiation factor in Zimm-Bragg model, three new parameters are introduced to describe beta structure: the local constraint factor for a single residue to be contained in a $\beta$-strand, the long-range bonding parameter that accounts for the interaction between a pair of bonded $\beta$-strands, and a correction factor for the initiation of a $\beta$-sheet. Either increasing local constraint factor or long-range bonding parameter can cause a transition from $\alpha$-helix or random coil conformation to $\beta$-sheet conformation. The sharpness of transition depends on the competition between short and long-range interactions. Other effective factors, such as the chain length and temperature, are also discussed. In this model, the entropy due to different ways to group $\beta$-strands into different $\beta$-sheets gives rise to significant contribution to partition function, and makes major differences between beta structure and helical structure.