Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to mimic this forcing. No general formulation exists for forcing an arbitrary large kinetic model in a manner that is still consistent with the existence of a non-equilibrium steady state. We prove a theorem that guarantees the existence of a non-equilibrium steady state for chemical kinetic models, assuming two conditions; that every reaction is mass balanced , and that reaction kinetic rate laws never lead to a negative molecule concentration. These conditions can be verified in polynomial time and , flexible enough to permit a novel method of forcing a system away from equilibrium. In an expository biochemical example we show how a reversible, mass balanced  with thermodynamically infeasible kinetic parameters, can be used to perpetually force a kinetic model of anaerobic glycolysis in a manner consistent with the existence of a steady state. Our definition of easily testable existence conditions is foundational for efforts to reliably compute non-equilibrium steady states in genome-scale biochemical kinetic models.
Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to mimic this forcing. We provide a general formulation to force an arbitrary large kinetic model in a manner that is still consistent with the existence of a non-equilibrium steady state. We can guarantee the existence of a non-equilibrium steady state assuming only two conditions; that every reaction is mass balanced and that continuous kinetic reaction rate laws never lead to a negative molecule concentration. These conditions can be verified in polynomial time and are flexible enough to permit one to force a system away from equilibrium. In an expository biochemical example we show how a reversible, mass balanced perpetual reaction, with thermodynamically infeasible kinetic parameters, can be used to perpetually force a kinetic model of anaerobic glycolysis in a manner consistent with the existence of a steady state. Easily testable existence conditions are foundational for efforts to reliably compute non-equilibrium steady states in genome-scale biochemical kinetic models.
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