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Bull Math Biol. 2020 Jun 13;82(6):76. doi: 10.1007/s11538-020-00758-3.
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.
我们构建了一个在恒化器环境下的细菌种群的数学模型，该模型还考虑了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论据，我们对两个系统进行了推导：一个简单的单物种、单基质和单反应产物的玩具模型，以及一个更复杂的描述铀[VI]生物还原为铀[IV]的模型。我们发现，与大多数传统的恒化器模型不同，由于热力学抑制，营养基质的平衡浓度可能取决于它们的流入浓度，而不仅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，热力学生长抑制会定量改变模型的解。这表明，在热力学抑制作用起作用的系统中忽略这些影响可能会导致错误的模型预测，并低估或高估所研究过程的效果。
