Deficiency, Kinetic Invertibility, and Catalysis in Stochastic Chemical Reaction Networks

Abstract

Stochastic chemical processes are described by the chemical master equation satisfying the law of mass-action. We first ask whether the dual master equation, which has the same steady state as the chemical master equation, but with inverted reaction currents, satisfies the law of mass-action, namely, still describes a chemical process. We prove that the answer depends on the topological property of the underlying chemical reaction network known as deficiency. The answer is yes only for deficiency-zero networks. It is no for all other networks, implying that their steady-state currents cannot be inverted by controlling the kinetic constants of the reactions. Hence, the network deficiency imposes a form of non-invertibility to the chemical dynamics. We then ask whether catalytic chemical networks are deficiency-zero. We prove that the answer is no when they are driven out of equilibrium due to the exchange of some species with the environment.

References in corpus (7)

• Path-integral analysis of fluctuation theorems for general Langevin processes
• Stochastic thermodynamics of chemical reaction networks
• Thermodynamic uncertainty relation and thermodynamic speed limit in deterministic chemical reaction networks
• Nonequilibrium Thermodynamics of Non-Ideal Chemical Reaction Networks
• Negative differential response in chemical reactions
• Thermodynamics of Concentration vs Flux Control in Chemical Reaction Networks
• Stochastic approach to entropy production in chemical chaos

Cited by in corpus (3)

• Nonequilibrium Thermodynamics of Non-Ideal Reaction-Diffusion Systems: Implications for Active Self-Organization
• Characterizing the Conditions for Indefinite Growth in Open Chemical Reaction Networks
• What is a chemostat? Insights from hybrid dynamics and stochastic thermodynamics