Local imperfect feedback control in non-equilibrium biophysical systems enabled by thermodynamic constraints

TL;DR

This paper explores how non-equilibrium biological systems can achieve robust control using local, imperfect feedback mechanisms constrained by thermodynamics, enabling environmental adaptation without complex network design.

Contribution

It introduces a thermodynamic constraint that allows simple local feedback rules to ensure stability and adaptation in non-equilibrium biological models.

Findings

Thermodynamic constraints enable local feedback for environmental tracking.

Local stability implies global stability in systems with up to two regulators.

Basin of attraction remains large even in higher-dimensional systems.

Abstract

Understanding how biological systems achieve robust control despite relying on imperfect local information remains a challenging problem. Here, we consider non-equilibrium models which are generically used to describe natural and synthetic biological processes, such as gene regulation and protein conformational dynamics, and investigate their capacity for effective control using imperfect local feedback mechanisms. We derive a thermodynamic constraint on the response of non-equilibrium steady-state properties to changes in the driving forces. We show that this constraint enables linear, local, and easily implementable feedback rules to achieve environmental tracking and adaptation without consideration of network topology. In particular, we demonstrate that local stability of these feedback dynamics implies global stability for systems with one or two chemical regulators, regardless of the network topology. For higher-dimensional systems, global stability is not guaranteed. However, in part due to simplifications in attractor landscapes implied by our thermodynamic constraint, we find the basin of attraction remains significantly larger than would be expected from linear approximation alone. Our findings provide insight into how biological and synthetically engineered systems can respond effectively to environmental changes given only minimal feedback, without highly engineered interactions or precise parameter tuning.