Coarse-grained dynamics of transiently-bound fast linkers

TL;DR

This paper develops a mathematically justified coarse-grained model for transiently-bound fast linkers that preserves detailed balance, enabling accurate simulations of complex systems with multiple linkers and force-dependent unbinding.

Contribution

It provides a multiscale averaging framework that simplifies linker dynamics while maintaining equilibrium properties, applicable to diverse biological and physical systems.

Findings

The coarse-grained model preserves detailed balance at equilibrium.

Simulations confirm the validity of the derived effective dynamics.

Framework applies to systems with multiple, stiffening, or force-dependent linkers.

Abstract

Transient bonds between fast linkers and slower particles are widespread in physical and biological systems. In spite of their diverse structure and function, a commonality is that the linkers diffuse on timescales much faster compared to the overall motion of the particles they bind to. This limits numerical and theoretical approaches that need to resolve these diverse timescales with high accuracy. Many models, therefore, resort to effective, yet ad-hoc, dynamics, where linker motion is only accounted for when bound. This paper provides a mathematical justification for such coarse-grained dynamics that preserves detailed balance at equilibrium. Our derivation is based on multiscale averaging techniques and is broadly applicable. We verify our results with simulations on a minimal model of fast linker binding to a slow particle. We show how our framework can be applied to various systems, including those with multiple linkers, stiffening linkers upon binding, or slip bonds with force-dependent unbinding. Importantly, the preservation of detailed balance only sets the ratio of the binding to the unbinding rates, but it does not constrain the detailed expression of binding kinetics. We conclude by discussing how various choices of binding kinetics may affect macroscopic dynamics.