Mathematical modelling of growth and metabolism in anaerobic microbes : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Palmerston North, New Zealand

Abstract

The growth rates of microbes can be thermodynamically limited by unfavourable ratios of energy substrates and end products. This thesis explored and expanded mathematical models that apply to a broad range of anaerobic microbes with different metabolisms, especially at low substrate to product ratios. The rates considered here fall into four categories based on how they are derived. Prima facie these rates are unrelated; however, for large concentrations of substrate they are in agreement. A new term based on the properties of the ATP synthase enzyme was added to a model derived from the Briggs-Haldane rate to allow the microbe to vary the energy required to produce ATP (∆GATP) at low substrate concentrations. Experimental data were used to show that different values of ∆GATP were better suited for predicting Kapp and Smin, substrate concentration values corresponding to half-maximal growth rate and growth shutoff, respectively. This term allowed growth to continue in challenging thermodynamic conditions by optimising ∆GATP to maximise the growth rate. When ∆GATP was considered variable between biologically relevant limits, the model predicted the measured Kapp and Smin values from the dataset. Results from the model were compared with experimental data reported at multiple times as growth occurs. The results agreed qualitatively for batch cultures with and without thermodynamic inhibition. The model produced results that were consistent with experimental data for a continuous culture for two strains of microbe. In addition, it was adapted for modelling direct competition between the two strains which compete for the same energy substrate. Modelling this competition identified conditions for stable coexistence, a result that has yet to be shown analytically. Different approaches for modelling metabolisms where multiple substrates are simultaneously required to produce ATP were explored, with a focus on four variations of an analogy between microbes and enzymes. This analysis identified several rates that may have applications in different situations, and also identified a derivation for a widely-used empirical rate as a special case. An extension of a rate based on statistical mechanics to multiple substrates also showed promise.