Irreversible thermodynamics of open chemical networks. I. Emergent cycles and broken conservation laws

chemical reaction networks, with special regard to metabolic networks regulating cellular physiology
and biochemical functions. We first introduce closed networks “in a box”, whose thermodynamics is
subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed
balance. We further digress on the role of solvents and on the seemingly unacknowledged property
of network independence of free energy landscapes. We then open the system by assuming that the
concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated
by the environment via contact with reservoirs, or because nearly constant in a time window.
As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues
in the network of internal species: Emergent irreversible cycles are associated with nonvanishing
affinities, whose symmetries are dictated by the breakage of conservation laws. These central results
are resumed in the relation a + b = sY between the number of fundamental affinities a, that of broken
conservation laws b and the number of chemostats sY. We decompose the steady state entropy
production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg’s theory of
network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency
and tight coupling, of free energy transduction, and of thermodynamic constraints for network
reconstruction.