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This paper addresses the challenge of enforcing thermodynamic consistency, specifically detailed balance via Wegscheider conditions, in parameter optimization and Bayesian inference of biochemical reaction networks. The authors propose a novel approach that penalizes parameters violating detailed balance, rather than explicitly imposing these conditions through network reparameterization. This method successfully maintains agreement with observed dynamics while yielding posterior samples that approximately satisfy thermodynamic constraints, even in complex biological systems.
Biochemical models can appear to fit data well while violating fundamental physical laws, but a simple penalty term can enforce thermodynamic consistency without sacrificing accuracy.
Subcellular signaling pathways regulating, e.g., cell division or synaptic plasticity, are often modeled as dynamical networks of reactions satisfying the law of mass action. To remain physically grounded, these models must satisfy different physical conservation laws, such as conservation of energy. This gives rise to thermodynamic constraints formalized by the Wegscheider conditions, which ensure that the system is in detailed balance at thermodynamic equilibrium. Explicitly imposing Wegscheider conditions requires identifying cycles in the reaction network. This can become computationally cumbersome, especially in large, complex systems. Furthermore, even when these constraints are explicitly available, enforcing them requires choosing a reparameterization of the network, which may introduce asymmetries among the parameters and affect numerical conditioning. Moreover, this approach often causes inverse uncertainty quantification methods like Markov chain Monte Carlo (MCMC) to struggle. Instead of imposing Wegscheider conditions directly in the parameter space, we propose an approach for promoting physical consistency by penalizing parameters that violate detailed balance. We first illustrate the approach on a simple reaction network containing a single cycle. We show that parameter values inferred without thermodynamic constraints can reproduce the experimental data seemingly accurately, while substantially violating the Wegscheider condition. In contrast, the proposed approach preserves the agreement with the observed dynamics while yielding posterior samples that approximately satisfy the thermodynamic constraint. We further apply the approach to a model of PKA-calcineurin signaling in synaptic long-term depression, demonstrating its applicability to a more complex biochemical reaction network.