Thermodynamics of unicellular life: Entropy production rate as function of the balanced growth rate

A bstract In isothermal chemical reaction networks, reaction rates depend solely on the reactant concentrations setting their thermodynamic driving force. Living cells can, in addition, alter reaction rates in their enzyme-catalysed networks by changing enzyme concentrations. This gives them control over their metabolic activities, as function of conditions. Thermodynamics dictates that the steady-state entropy production rate (EPR) of an isothermal chemical reaction network rises with its reaction rates. Here we ask whether microbial cells that change their metabolism as function of growth rate can break this relation by shifting to a metabolism with a lower thermodynamic driving force at faster growth. We address this problem by focussing on balanced microbial growth in chemostats. Since the driving force can then be determined and the growth rate can be set, chemostats allow for the calculation of the (specific) EPR. First we prove that the EPR of a steady-state chemical reaction network rises with its driving force. Next, we study an example metabolic network with enzyme-catalysed reactions to illustrate that maximisation of specific flux can indeed lead to selection of a pathway with a lower driving force. Following this idea, we investigate microbes that change their metabolic network responsible for catabolism from an energetically-efficient mode to a less efficient mode as function of their growth rate. This happens for instance during a shift from complete degradation of glucose at slow growth to partial degradation at fast growth. If partial degradation liberates less free energy, fast growth can occur at a reduced driving force and possibly a reduced EPR. We analyse these metabolic shifts using three models for chemostat cultivation of the yeast Saccharomyces cerevisiae that are calibrated with experimental data. We also derive a criterion to predict when EPR drops after a metabolic switch that generalises to other organisms. Both analyses gave however inconclusive results, as current experimental evidence proved insufficient. We indicate which experiments are required to get a better understanding of the behaviour of the EPR during metabolic shifts in unicellular organisms.