Directed information flow in reaction networks under energy constraints: A framework for communication and optimal design applications

Biological information processing is constrained by energetic costs, making it natural to treat information flow and dissipation jointly. We develop a unified framework for continuous-time chemical reaction networks (CRNs) that couples trajectory-level mutual and directed information between disjoint species sets with process-based stochastic thermodynamics for open, multi-reservoir systems. The formulation covers causal conditioning and indistinguishable reactions at the subnetwork level arising from multiple reservoir coupling or projection. To ensure stringent use of stochastic thermodynamics across disciplines, we compile a unified account that treats coarse-graining and multi-reservoir modeling correctly when estimating dissipation. We also give a conversion from species–reaction graphs to local-independence graphs on reactions and link local independence to causally conditioned directed information. Applications are twofold: First, the framework yields a rigorous continuous-time communication model over a CRN, with messages source-encoded by time-dependent chemostat protocols. Capacity is posed over trajectory distributions under principled thermodynamic costs. Graph tools enable a functionality-based classification that distinguishes between encoding reactions and reactions that constitute the transmission path. This facilitates characterizing degrees of freedom in the chemical noisy channel coding problem. Second, we advocate directed information as an objective for naturally evolved and engineered biochemical circuits under finite energy budgets. Case studies with minimal promoter-switching models illustrate framework application and visualize trade-offs between information flow and dissipation.