Nonequilibrium steady state of biochemical cycle kinetics under non-isothermal conditions

TL;DR

This paper extends the steady-state theory of biochemical cycle kinetics to non-isothermal conditions, deriving new thermodynamic relations and reaction-rate formulas that account for temperature differences within subsystems, relevant to living organisms.

Contribution

It introduces a generalized nonequilibrium steady-state theory for non-isothermal biochemical cycles, providing revised reaction-rate formulas consistent with thermodynamics.

Findings

New thermodynamic relation between reaction rates and potentials under non-isothermal conditions

Revised reaction-rate formulas that improve upon isothermal approximations

Prediction that net flux can oppose temperature gradient without chemical driving force

Abstract

Nonequilibrium steady state of isothermal biochemical cycle kinetics has been extensively studied, but much less investigated under non-isothermal conditions. However, once the heat exchange between subsystems is rather slow, the isothermal assumption of the whole system meets great challenge, which is indeed the case inside many kinds of living organisms. Here we generalize the nonequilibrium steady-state theory of isothermal biochemical cycle kinetics, in the master-equation models, to the situation in which the temperatures of subsystems can be far from uniform. We first obtain a new thermodynamic relation between the chemical reaction rates and thermodynamic potentials under such a non-isothermal circumstances, which immediately implies simply applying the isothermal transition-state rate formula for each chemical reaction in terms of only the reactants' temperature, is not thermodynamically consistent. Therefore, we mathematically derive several revised reaction-rate formulas which not only obey the new thermodynamic relation but also approximate the exact reaction rate better than the rate formula under isothermal condition. The new thermodynamic relation also predicts that in the transporter system with different temperatures inside and outside the membrane, the net flux of the transported molecules can possibly even go against the temperature gradient in the absence of the chemical driving force.