Thermodynamically Consistent Coarse Graining of Biocatalysts beyond Michaelis--Menten

TL;DR

This paper introduces a thermodynamically consistent coarse-graining method for biocatalysts that extends enzyme kinetics to complex systems, enabling systematic thermodynamic analysis of large biochemical networks.

Contribution

It provides a novel coarse-graining procedure that maintains thermodynamic consistency and applies to active transporters and molecular machines, broadening the scope of enzyme kinetics.

Findings

The method yields stoichiometries, reaction fluxes, and Gibbs energies at the coarse level.

It clarifies conditions for flux-force relations to hold in coarse-grained networks.

The second law does not always imply alignment of currents and forces in biochemical systems.

Abstract

Starting from the detailed catalytic mechanism of a biocatalyst we provide a coarse-graining procedure which, by construction, is thermodynamically consistent. This procedure provides stoichiometries, reaction fluxes (rate laws), and reaction forces (Gibbs energies of reaction) for the coarse-grained level. It can treat active transporters and molecular machines, and thus extends the applicability of ideas that originated in enzyme kinetics. Our results lay the foundations for systematic studies of the thermodynamics of large-scale biochemical reaction networks. Moreover, we identify the conditions under which a relation between one-way fluxes and forces holds at the coarse-grained level as it holds at the detailed level. In doing so, we clarify the speculations and broad claims made in the literature about such a general flux--force relation. As a further consequence we show that, in contrast to common belief, the second law of thermodynamics does not require the currents and the forces of biochemical reaction networks to be always aligned.