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The analysis of non-equilibrium steady states of biochemical reactionnetworks relies on finding the configurations of fluxes and chemical potentialssatisfying stoichiometric (mass balance) and thermodynamic (energy balance)constraints. Efficient methods to explore such states are crucial to predictreaction directionality, calculate physiologic ranges of variability, estimatecorrelations, and reconstruct the overall energy balance of the network fromthe underlying molecular processes. While different techniques for sampling thespace generated by mass balance constraints are currently available,thermodynamics is generically harder to incorporate. Here we introduce a methodto sample the free energy landscape of a reaction network at steady state. Inits most general form, it allows to calculate distributions of fluxes andconcentrations starting from trial functions that may contain prior biochemicalinformation. We apply our method to the human red blood cell's metabolicnetwork, whose space of mass-balanced flux states has been sampled extensivelyin recent years. Specifically, we profile its thermodynamically feasible fluxconfigurations, characterizing in detail how fluctuations of fluxes andpotentials are correlated. Based on this, we derive the cell's energy balancein terms of entropy production, chemical work done and thermodynamicefficiency.

Computing fluxes and chemical potential distributions in biochemical networks: energy balance analysis of the human red blood cell