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 ∼0.4 nM. This threshold is not controlled by the Gibbs free energy equation of methanogenesis from H₂ + HCO ₃ ^- 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 ∼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.