A mathematical model for the kinetics of Methanobacterium bryantii M.o.H. considering hydrogen thresholds

We develop a kinetic model that builds on the foundation of classic Monod kinetics, but incorporates new phenomena such as substrate thresholds and survival mode observed in experiments with the H2-oxidizing methanogen Methanobacterium bryantii M.o.H. We apply our model to the experimental data presented in our companion paper on H2 thresholds. The model accurately describes H2 consumption, CH4 generation, biomass growth, substrate thresholds, and survival state during batch experiments. Methane formation stops when its Gibbs free energy is equal zero, although this does not interrupt H2 oxidation. The thermodynamic threshold for H2 oxidation occurs when the free energy for oxidizing H2 and transferring electrons to biomass is no longer negative, at approximately 0.4 nM. This threshold is not controlled by the Gibbs free energy equation of methanogenesis from H2 + HCO3- as we show in our companion paper. Beyond this threshold, the microorganisms shift to a low-maintenance metabolism called "the survival state" in response to extended H2 starvation; adding the starvation response as another new feature of the kinetic model. A kinetic threshold (or S (min)), a natural feature of the Monod kinetics, is also captured by the model at H2 concentration of around approximately 2,400 nM. S (min) is the minimum substrate concentration to maintain steady-state biomass concentration. Our model will be useful for interpreting threshold results and designing new studies to understand thresholds and their ecological implications.