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

TL;DR

This paper introduces a novel method to sample the energy landscape of biochemical networks at steady state, enabling detailed analysis of fluxes, chemical potentials, and energy balance in the human red blood cell.

Contribution

It presents a new approach to incorporate thermodynamics into sampling biochemical network states, improving energy balance analysis.

Findings

Characterized thermodynamically feasible flux configurations.

Analyzed correlations between fluxes and potentials.

Derived the energy balance, entropy production, and efficiency of the red blood cell.

Abstract

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