  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.
