An Ising-Like model for protein mechanical unfolding

TL;DR

This paper extends a simplified protein model to include external forces, enabling exact thermodynamic solutions and analysis of protein unfolding mechanics, with applications to titin and PIN1 molecules.

Contribution

It introduces a generalized Ising-like model for protein unfolding that incorporates external forces and allows exact thermodynamic calculations.

Findings

Force-extension curves for titin were determined.

Kinetic barriers in protein unfolding were identified.

The free energy landscape of PIN1 was computed using an extended Jarzynski equality.

Abstract

The mechanical unfolding of proteins is investigated by extending the Wako-Saito-Munoz-Eaton model, a simplified protein model with binary degrees of freedom, which has proved successful in describing the kinetics of protein folding. Such a model is generalized by including the effect of an external force, and its thermodynamics turns out to be exactly solvable. We consider two molecules, the 27th immunoglobulin domain of titin and protein PIN1. In the case of titin we determine equilibrium force-extension curves and study nonequilibrium phenomena in the frameworks of dynamic loading and force clamp protocols, verifying theoretical laws and finding the position of the kinetic barrier which hinders the unfolding of the molecule. The PIN1 molecule is used to check the possibility of computing the free energy landscape as a function of the molecule length by means of an extended form of the Jarzynski equality.