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Competitive exclusion in a DAE model for microbial electrolysis cells
Mathematical Biosciences and Engineering ( IF 2.6 ) Pub Date : 2020-09-16 , DOI: 10.3934/mbe.2020329
Harry J Dudley 1 , Zhiyong Jason Ren 2 , David M Bortz 1
Affiliation  

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 resembles a chemostat or continuous stirred tank reactor (CSTR). It consists of ordinary differential equations for concentrations of substrate, microorganisms, and an extracellular mediator involved in electron transfer. There is also 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 electric current and the resulting 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. This states that only microbes which grow at the lowest substrate concentration will survive as t → ∞.
We show that if methanogens can grow at the lowest substrate concentration, then the equilibrium corresponding to competitive exclusion by methanogens is globally asymptotically stable. The analogous result for electroactive bacteria is not necessarily true. In fact we show that local asymptotic stability of competitive exclusion by electroactive bacteria is not guaranteed, even in a simplified version of the model. In this case, even if electroactive bacteria can grow at the lowest substrate concentration, a few additional conditions are required to guarantee local asymptotic stability. We provide numerical simulations supporting these arguments. Our results suggest operating conditions that are most conducive to success of electroactive bacteria and the resulting current and hydrogen production in MECs. This will help identify when producing methane or electricity and hydrogen is favored.


中文翻译:

DAE模型中微生物电解池的竞争排斥

微生物电解池(MEC)是利用电活性细菌执行细胞外电子转移,使氢从可生物降解的底物产生的装置。在我们之前的工作中,我们开发和分析了微机电方程的微分-代数方程(DAE)模型。该模型类似于化学恒温器或连续搅拌釜反应器(CSTR)。它由用于底物,微生物和参与电子转移的细胞外介质浓度的常微分方程组成。电流和氢的产生也有代数约束。我们的目标是确定产甲烷的古细菌与电活性细菌之间竞争的结果,因为只有后者会产生电流并产生氢气。我们在模型的两个与工业相关的版本中研究渐近稳定性。许多Chemostat模型的一个重要方面是竞争排斥的原理。这说明只有在最低底物浓度下生长的微生物才能生存t →∞。
我们表明,如果产甲烷菌可以在最低的底物浓度下生长,那么对应于产甲烷菌竞争性排斥的平衡是全局渐近稳定的。电活性细菌的类似结果不一定正确。实际上,我们证明,即使在模型的简化版本中,也不能保证电活性细菌竞争排斥的局部渐近稳定性。在这种情况下,即使电活性细菌可以在最低的底物浓度下生长,也需要一些其他条件来保证局部渐近稳定性。我们提供了支持这些论点的数值模拟。我们的结果表明,最有利于电活性细菌成功以及在MEC中产生电流和产氢的运行条件。
更新日期:2020-09-16
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