Microbial electrolysis cells (MECs) are devices that employ electroactive bacteria to perform extracellular electron transfer, enabling hydrogen generation from biodegradable substrates. Previously we analyzed a regular, semi-explicit, index 1 differential-algebraic equation (DAE) model for MECs. The model consists of ordinary differential equations (ODE) resembling chemostats or continuous stirred tank reactors (CSTRs), an ODE for a mediator involved in electron transfer, and an algebraic constraint for electric current and hydrogen production. This work characterizes asymptotic stability of equilibria in two biologically relevant versions of the model. Our goal is to determine the outcome of competition between methanogenic archaea and electroactive bacteria, because only the latter contribute to  electric current and  hydrogen production. We investigate global asymptotic stability in a modelwith finitely many species, Monod kinetics, different removal rates, and a constraint based on the Nernst and Butler-Volmer equations. If methanogens can grow at the lowest substrate concentration, then the equilibrium corresponding to competitive exclusion by methanogens is globally asymptotically stable. Establishing the analogous result for electroactive bacteria has proven challenging. As a first step towards characterizing stability of an electroactive-only equilibrium, we consider local asymptotic stability in a model with three types of microbes, general monotone kinetics, equal removal rates, and a general constraint . In this model , even if electroactive bacteria can grow at the lowest substrate concentration, a few additional conditions are required to guarantee local asymptotic stability. We also provide numerical simulations supporting these arguments. Our results suggest operating conditions that are most conducive to success of electroactive bacteria and current or hydrogen production  .
Microbial electrolysis cells (MECs) are devices that employ electroactive bacteria to perform extracellular electron transfer, enabling hydrogen generation from biodegradable substrates. In our previous work, we developed and analyzed a differential-algebraic equation (DAE) model for MECs. The model consists of ordinary differential equations (ODE) resembling chemostats or continuous stirred tank reactors (CSTRs), an ODE for an extracellular mediator involved in electron transfer, and an algebraic constraint for electric current and hydrogen production. Our goal is to determine the outcome of competition between methanogenic archaea and electroactive bacteria, because only the latter contribute to both electric current and correlated hydrogen production. We investigate asymptotic stability in two industrially relevant versions of the model. An important aspect of many chemostat models is the principle of competitive exclusion, which states that only the URLanisms which can grow at the lowest substrate concentration will survive. We show that if methanogens can grow at the lowest substrate concentration, then the equilibrium corresponding to competitive exclusion by methanogens is globally stable. The analogous result for electroactive bacteria is not necessarily true. We show that local asymptotic stability of competitive exclusion by electroactive bacteria is not guaranteed, even in a simplified model . In this case , even if electroactive bacteria can grow at the lowest substrate concentration, a few additional conditions are required to guarantee local stability. We also provide numerical simulations supporting these arguments. Our results suggest operating conditions that are most conducive to success of electroactive bacteria and current or hydrogen production in MECs. This will help identify when methane production or electricity and hydrogen production are favored .
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