Salazar Yolocuauhtli, Valle Paul A, Rodríguez Emmanuel, Soto-Cruz Nicolás O, Páez-Lerma Jesús B, Reyes-Sánchez Francisco J
Postgraduate Program in Engineering, Tecnológico Nacional de México/IT Durango, Blvd. Felipe Pescador 1830 Ote., Durango 34080, Mexico.
Postgraduate Program in Engineering Sciences, BioMath Research Group, Tecnológico Nacional de México/IT Tijuana, Blvd. Alberto Limón Padilla s/n, Tijuana 22454, Mexico.
Entropy (Basel). 2023 Mar 14;25(3):497. doi: 10.3390/e25030497.
This paper presents results concerning mechanistic modeling to describe the dynamics and interactions between biomass growth, glucose consumption and ethanol production in batch culture fermentation by (). The mathematical model was formulated based on the biological assumptions underlying each variable and is given by a set of three coupled nonlinear first-order Ordinary Differential Equations. The model has ten parameters, and their values were fitted from the experimental data of 17 strains by means of a computational algorithm design in Matlab. The latter allowed us to determine that seven of these parameters share the same value among all the strains, while three parameters concerning biomass maximum growth rate, and ethanol production due to biomass and glucose had specific values for each strain. These values are presented with their corresponding standard error and 95% confidence interval. The goodness of fit of our system was evaluated both qualitatively by in silico experimentation and quantitative by means of the coefficient of determination and the Akaike Information Criterion. Results regarding the fitting capabilities were compared with the classic model given by the logistic, Pirt, and Luedeking-Piret Equations. Further, nonlinear theories were applied to investigate local and global dynamics of the system, the Localization of Compact Invariant Sets Method was applied to determine the so-called localizing domain, i.e., lower and upper bounds for each variable; whilst Lyapunov's stability theories allowed to establish sufficient conditions to ensure asymptotic stability in the nonnegative octant, i.e., R+,03. Finally, the predictive ability of our mechanistic model was explored through several numerical simulations with expected results according to microbiology literature on batch fermentation.
本文展示了关于机理建模的结果，该建模用于描述分批培养发酵中生物量生长、葡萄糖消耗和乙醇生产之间的动态变化及相互作用。数学模型是基于每个变量背后的生物学假设建立的，由一组三个耦合的非线性一阶常微分方程给出。该模型有十个参数，其值通过Matlab中的一种计算算法设计，根据17种菌株的实验数据进行拟合。后者使我们能够确定其中七个参数在所有菌株中具有相同的值，而与生物量最大生长速率以及生物量和葡萄糖产生的乙醇相关的三个参数在每种菌株中具有特定值。这些值及其相应的标准误差和95%置信区间一同列出。我们系统的拟合优度通过计算机模拟进行定性评估，并通过决定系数和赤池信息准则进行定量评估。将拟合能力的结果与逻辑斯蒂方程、皮尔特方程和吕德金 - 皮雷特方程给出的经典模型进行了比较。此外，应用非线性理论研究系统的局部和全局动态，应用紧致不变集定位方法确定所谓的定位域，即每个变量的上下界；而李雅普诺夫稳定性理论则用于建立充分条件，以确保在非负卦限(R_{+}^{3})中的渐近稳定性。最后，通过根据分批发酵的微生物学文献进行的几次数值模拟，探索了我们机理模型的预测能力，并得到了预期结果。
