A theoretical derivation of the monod equation with a kinetics sense
A theoretical derivation of the monod equation with a kinetics sense
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DOI：
10.1016/j.bej.2019.107305
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发表时间：
2019-10-15
影响因子：
3.9
通讯作者：
Jaime Vernon-Carter, E.
中科院分区：
文献类型：
--
作者：
Alvarez-Ramirez, Jose;Meraz, M.;Jaime Vernon-Carter, E.
莫诺德方程已被广泛用于模拟微生物生长，但没有机制基础，其推导是纯经验的。在这项工作中，开发了一种基于简单动力学方案推导莫诺德方程的方法。所考虑的微生物生长过程包括两个连续的步骤，即(i)基质-细胞“复合物”的形成，以及（ii）细胞繁殖的基质代谢。该方法脱离质量作用定律，采用奇异摄动法推导控制微生物生长动力学的微分方程。在此背景下，得到了由自催化效应诱导的二次项修正的Monod方程。用文献报道的恶臭杆菌降解苯、苯酚和甲苯的实验数据验证了该模型的有效性。
The Monod equation has been extensively used for modeling microbial growth, but has no mechanistic basis and its derivation is purely empirical. In this work an approach was developed for deriving the Monod equation based on a simple kinetics scheme. The microbial growth process considered involved two consecutive steps, i.e., (i) the formation of a substrate-cell "complex", and (ii) the metabolism of the substrate for cell reproduction. By departing from the law of mass action, the approach uses a singular perturbation method for derivation of the differential equations governing the microbial growth dynamics. Within this context, a Monod equation corrected by a quadratic term induced by auto-catalyst effects was obtained. The proposed model was validated with experimental data reported in the literature for the degradation of benzene, phenol and toluene by P. putida.