Thermodynamic ranking of pathways in reaction networks

One of the puzzles left open by energetic analyses of irreversible stochastic processes is that boundary conditions that prevent the performance of work or the dissipation of heat make no contribution to an entropy-production budget; yet we see ubiquitously in both engineered and living systems that both transient and persistent energy costs are paid to create and maintain such boundaries. We wish to know whether there are inherent limits for the costs of such phenomena, and common units in which those can be traded off against more familiar costs measured in terms of heat dissipation. We give this problem a concrete framing in the context of CRNs, for the problem of extracting a topologically restricted pathway from a larger distributed network, through activation of some reactions and selective elimination of others. We define a thermodynamic cost function for pathways derived from large-deviation theory of stochastic CRNs, which decomposes into two components: an ongoing maintenance cost to sustain a 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 make use of their formal equivalence to electrical circuits. 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. For small CRNs, we show how catalytic and inhibitory mechanisms can drastically alter pathway costs, enabling unfavorable pathways to become favorable and approach the cost of the hosting pathway. Our results provide insights into the thermodynamic principles governing open CRNs and offer a foundation for understanding the evolution of metabolic networks.