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

Abstract

The nonequilibrium steady state of isothermal biochemical cycle kinetics has been extensively studied, but that under non-isothermal conditions has been much less extensively investigated. When the heat exchange between subsystems is slow, the isothermal assumption of the whole system breaks down, as is true for many types of living organisms. Here, starting with a four-state model of molecular transporter across the cell membrane, we generalize the nonequilibrium steady-state theory of isothermal biochemical cycle kinetics to the circumstances with non-uniform temperatures of subsystems in terms of general master equation models. We obtain a new thermodynamic relationship between the chemical reaction rates and thermodynamic potentials in non-isothermal circumstances, based on the overdamped dynamics along the continuous reaction coordinate. We show that the entropy production can vary up to 3% in real cells, even when the temperature difference across the cell membrane is only approximately 1 K. We then decompose the total thermodynamic driving force into its thermal and chemical components and predict that the net flux of molecules transported by the molecular transporter can potentially go against the temperature gradient in the absence of a chemical driving force. Furthermore, we demonstrate that the simple application of the isothermal transition-state rate formula for each chemical reaction in terms of only the reactant' temperature is not thermodynamically consistent. Therefore, we mathematically derive several revised reaction rate formulas that are not only consistent with the new thermodynamic relationship but also approximate the exact reaction rate better than Kramers' rate formula under isothermal conditions. as this is driven not only by chemical potential differences but also by the temperature gradient across the cell membrane [17].Under isothermal or non-isothermal circumstances, mesoscopic biochemical cycle kinetics can be modeled using the master equation model. The theory of stochastic thermodynamics in terms of the master equation model has already been well developed, and the entropy production rate is expressed in terms of the transition rates between discrete states [4,11,12]. After taking the ensemble average, the mesoscopic stochastic thermodynamics should be consistent with the macroscopic nonequilibrium thermodynamics framework [22,23]. Such consistency under isothermal conditions has been illustrated previously [1,4,[24][25][26].The problem of transport processes across a thermal gradient has been considered before in [16,17]. These references discussed the transport of ions across a plasma membrane, when the temperature inside the cell is different from the temperature in the extracellular medium. However, the temperature at the membrane interface where the molecular transporter occupies is assumed to be independent of the reaction coordinates. This assumption is quite uncertain and evades the circumstances when the assumption is not valid.In our paper, we remove this assumption, an...

Dissipation-driven selection of states in non-equilibrium chemical networks

“…Relying on equilibrium thermodynamics is thus unlikely to provide a route to explain the emergence of life 6 . The potential relevance of non-equilibrium conditions in this context has also been highlighted in several recent works 7 – 9 .…”

Dissipation-Driven Selection under Finite Diffusion: Hints from Equilibrium and Separation of Time Scales

“…It would be interesting to push forward the parallel between theoretical idealised systems and experimentally feasible procedures, in order to verify these theoretical predictions. Moreover, observing features of non-isothermal chemistry might also ignite the study of the origins of life problems from the point of view of non-equilibrium statistical mechanics and thermodynamics [29][30][31][32][33][34].…”

Dissipation-driven selection under finite diffusion: hints from equilibrium and separation of time-scales

“…It would be interesting to push forward the parallel between theoretical idealized systems and experimentally feasible procedures, in order to verify these theoretical predictions. Moreover, observing features of non-isothermal chemistry might also ignite the study of origin of life problems from the point of view of non-equilibrium statistical mechanics and thermodynamics [29][30][31][32][33][34].…”