We formulate a mathematical model of bacterial populations in a chemostat setting that also accounts for thermodynamic growth inhibition as a consequence of chemical reactions. Using only elementary mathematical and chemical arguments, we carry this out for two systems: a simple toy model with a single species, a single substrate, and a single reaction product, and a more involved model that describes bioreduction of uranium[VI] into uranium[IV]. We find that in contrast to most traditional chemostat models, as a consequence of thermodynamic inhibition the equilibria concentrations of nutrient substrates might depend on their inflow concentration and not only on reaction parameters and the reactor’s dilution rate. Simulation results of the uranium degradation model indicate that thermodynamic growth inhibition quantitatively alters the solution of the model. This suggests that neglecting thermodynamic inhibition effects in systems where they play a role might lead to wrong model predictions and under- or over-estimate the efficacy of the process under investigation.

中文翻译：

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恒化器模型中的热力学抑制

我们在恒化器设置中制定了细菌种群的数学模型，该模型还解释了由于化学反应导致的热力学生长抑制。仅使用基本的数学和化学参数，我们对两个系统执行此操作：具有单一物种、单一底物和单一反应产物的简单玩具模型，以及描述铀 [VI] 生物还原为铀的更复杂模型[四]。我们发现，与大多数传统的恒化器模型相比，作为热力学抑制的结果，营养底物的平衡浓度可能取决于它们的流入浓度，而不仅取决于反应参数和反应器的稀释率。铀降解模型的模拟结果表明，热力学生长抑制定量地改变了模型的解。这表明在它们起作用的系统中忽略热力学抑制效应可能会导致错误的模型预测，并低估或高估所研究过程的功效。