Mathematical modeling is an overarching approach for assessing the complexity of microbial electrosynthesis (MES) and for complementing the relevant experimental research. By describing and linking compartments, components, and processes with appropriate mathematical equations, MES and the corresponding bioelectrodes and complete bioelectrochemical systems can be analyzed and predicted across several temporal and local scales. Thereby, insights into fundamental phenomena and mechanisms, in addition to process engineering and design can be obtained. However, a substantial lack of knowledge about extracellular electron transfer mechanisms and electrotrophic microorganisms presumably prevented the development of adequate models of MES, especially of biocathodes, so far. To propel efforts regarding this demanding task, this chapter provides a comprehensive overview of the relevant compartments, components and processes, appropriate model strategies, and a discussion on potential modeling pitfalls. By adapting an established approach to assessing the energetics of microorganism, an instruction for calculating stoichiometry, thermodynamics, and kinetics, with the example of electro-autotrophic growth at cathodes, is presented. Models of bioanodes and fundamental electrochemical equations are described to provided strategies for calculating cathodic electron-uptake reactions and connecting them to the microbial metabolism. Finally, differential equations are detailed for coupling the distinct compartments of a bioelectrochemical system. Although MES comprises anodic and cathodic reactions, the present chapter focuses on biocathodes representing a functional connection between cathode and electron-accepting microorganisms. Graphical Abstract.
Keywords: Autotrophy; Biocathode; Cathodic extracellular electron transfer; Microbial electrochemical technologies; Microbial fuel cells.