Topologically protected modes in non-equilibrium stochastic systems

TL;DR

This paper demonstrates that non-equilibrium biochemical systems can exhibit topologically protected boundary modes, providing a robust mechanism for function despite disorder, by linking topological invariants to steady-state localization.

Contribution

It introduces a topological framework for biochemical networks, showing how winding numbers predict localized steady states at interfaces, enhancing understanding of robustness in non-equilibrium systems.

Findings

Topologically protected boundary modes exist in non-equilibrium biochemical systems.

Mismatch in winding numbers guarantees localized steady states at interfaces.

Robustness of biochemical functions can be explained by topological invariants.

Abstract

Non-equilibrium driving of biochemical reactions is believed to enable their robust functioning despite the presence of thermal fluctuations and other sources of disorder. Such robust functions include sensory adaptation, enhanced enyzmatic specificity and maintenance of coherent oscillations. Non-equilibrium biochemical reactions can be modeled as a master equation whose rate constants break detailed balance. We find that non equilibrium fluxes can support topologically protected boundary modes that resemble similar modes in electronic and mechanical systems. We show that when a biochemical network can be decomposed into two ordered bulks that meet at a possibly disordered interferace, the ordered bulks can be each associated with a topologically invariant winding number. If the winding numbers are mismatched, we are guaranteed that the steady state distribution is localized at the interface between the bulks, even in the presence of strong disorder in reaction rates. We argue that our work provides a framework for how biochemical systems can use non equilibrium driving to achieve robust function.