Transition in relaxation paths in allosteric molecules: enzymatic kinetically constrained model

TL;DR

This paper introduces a statistical physics model of allosteric molecules with enzymatic reactions, revealing slow, logarithmic relaxation dynamics with multiple plateaus, driven by kinetic constraints and cooperativity.

Contribution

The study extends classic allosteric models by incorporating enzymatic reactions, demonstrating complex relaxation behaviors and kinetic transitions not linked to equilibrium.

Findings

Relaxation is logarithmic with multiple plateaus.

Kinetic constraints cause symmetry breaking in relaxation trajectories.

Model captures slow dynamics similar to glasses.

Abstract

A hierarchy of timescales is ubiquitous in biological systems, where enzymatic reactions play an important role because they can hasten the relaxation to equilibrium. We introduced a statistical physics model of interacting spins that also incorporates enzymatic reactions to extend the classic model for allosteric regulation. Through Monte Carlo simulations, we found that the relaxation dynamics are much slower than the elementary reactions and are logarithmic in time with several plateaus, as is commonly observed for glasses. This is because of the kinetic constraints from the cooperativity via the competition for an enzyme, which has different affinity for molecules with different structures. Our model showed symmetry breaking in the relaxation trajectories that led to inherently kinetic transitions without any correspondence to the equilibrium state. In this paper, we discuss the relevance of these results for diverse responses in biology.