Quantifying <i>Geobacter sulfurreducens</i> growth: A mathematical model based on acetate concentration as an oxidizing substrate

Abstract

<abstract><p>We developed a mathematical model to simulate dynamics associated with the proliferation of <italic>Geobacter</italic> and ultimately optimize cellular operation by analyzing the interaction of its components. The model comprises two segments: an initial part comprising a logistic form and a subsequent segment that incorporates acetate oxidation as a saturation term for the microbial nutrient medium. Given that four parameters can be obtained by minimizing the square root of the mean square error between experimental <italic>Geobacter</italic> growth and the mathematical model, the model underscores the importance of incorporating nonlinear terms. The determined parameter values closely align with experimental data, providing insights into the mechanisms that govern <italic>Geobacter</italic> proliferation. Furthermore, the model has been transformed into a scaleless equation with only two parameters to simplify the exploration of qualitative properties. This allowed us to conduct stability analysis of the fixed point and construct a co-dimension two bifurcation diagram.</p></abstract>