Thermodynamic ranking of pathways in reaction networks

Abstract: Chemical Reaction Networks (CRNs) provide a powerful framework for modeling complex systems due to their compositionality, which makes them well-suited for analyzing interactions of subsystems within larger aggregate systems. This work presents a thermodynamic formalism for ranking CRN pathways under fixed throughput currents (fixed velocities of species flowing in and out of the system), where pathways represent subnetworks capable of performing the stipulated chemical conversion. We define a thermodynamic cost function for pathways derived from the large-deviation theory of stochastic CRNs, which decomposes into two components: an ongoing maintenance cost to sustain a non-equilibrium steady state (NESS), and a restriction cost, quantifying the ongoing improbability of neutralizing reactions outside the specified pathway. Applying this formalism to detailed-balanced CRNs in the linear response regime, we prove that the resistance of a CRN decreases as reactions are added that support the throughput current, and that the maintenance cost, the restriction cost, and the thermodynamic cost of nested pathways are bounded below by those of their hosting network. Extending the analysis far from equilibrium, we find that while cost is non-decreasing for progressively more restricted nested pathways near equilibrium, multimolecular CRN examples can be found that assign lower costs to more restricted pathways at far-from-equilibrium NESSs. The possibility to reduce the resistance of a network at fixed throughput, while also simplifying the network, may have implications for enzyme family evolution, in which novel reaction mechanisms may first lead to a proliferation of pathways through non-specific catalysis, but later selection for specificity may benefit both from species retention, and more efficient use of autocatalysts to improve throughput.