The Thermodynamic Links between Substrate, Enzyme, and Microbial Dynamics in Michaelis-Menten-Monod Kinetics

Abstract

<p>Accurate prediction of the temperature response of the velocity v of a biochemical reaction has wide applications in cell biology, reaction design, and biomass yield enhancement. Here, we introduce a simple but comprehensive mechanistic approach that uses thermodynamics and biochemical kinetics to describe and link the reaction rate and Michaelis–Menten constants (k_T and K_T) with the biomass yield and mortality rate (Y_T and δ_T) as explicit functions of <i>T</i>. The temperature control is exerted by catabolic enthalpy at low temperatures and catabolic entropy at high temperatures, whereas changes in cell and enzyme–substrate heat capacity shift the anabolic electron use efficiency e_A and the maximum reaction velocity v_max. We show that cells have optimal growth when the catabolic (differential) free energy of activation decreases the cell free energy harvest required to duplicate their internal structures as long as electrons for anabolism are available. With the described approach, we accurately predicted observed glucose fermentation and ammonium nitrification dynamics across a wide temperature range with a minimal number of thermodynamics parameters, and we highlight how kinetic parameters are linked to each other using first principles.</p>