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.
Highlights
Catalytic processes are ubiquitous in cellular physiology
Our second result is a consequence of the main result: we prove that the flux–force relation is satisfied at the coarse-grained level by any catalytic mechanism for which only one single cycle emerges in step 2 of the presented procedure, as in example 3.1
The focus on the turnover led many people to identify the net effect of the enzyme with a single effective reaction, describing its kinetics with the Michaelis–Menten equation
Summary
Biocatalysts are involved in metabolism, cell signaling, transcription and translation of genetic information, as well as replication. All these processes and pathways involve a few but rather dozens to hundreds, sometimes thousands of different enzymes. For many enzymes the catalytic mechanisms are not known Even if such detailed information was at hand, including detailed catalytic machanisms into a large scale model is typically unfeasable for numerical simulations. Larger biochemical reaction networks contain the enzymes as single reactions following enzymatic kinetics. This simplified description captures only the essential dynamical features of the catalytic action, condensed into a single reaction
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