Bayer AG, Leverkusen, Germany.
Process Dynamics and Operations group, TU Dortmund University, Dortmund, Germany.
Biotechnol Bioeng. 2020 Jul;117(7):2058-2073. doi: 10.1002/bit.27340. Epub 2020 May 12.
In macroscopic dynamic models of fermentation processes, elementary modes (EM) derived from metabolic networks are often used to describe the reaction stoichiometry in a simplified manner and to build predictive models by parameterizing kinetic rate equations for the EM. In this procedure, the selection of a set of EM is a key step which is followed by an estimation of their reaction rates and of the associated confidence bounds. In this paper, we present a method for the computation of reaction rates of cellular reactions and EM as well as an algorithm for the selection of EM for process modeling. The method is based on the dynamic metabolic flux analysis (DMFA) proposed by Leighty and Antoniewicz (2011, Metab Eng, 13(6), 745-755) with additional constraints, regularization and analysis of uncertainty. Instead of using estimated uptake or secretion rates, concentration measurements are used directly to avoid an amplification of measurement errors by numerical differentiation. It is shown that the regularized DMFA for EM method is significantly more robust against measurement noise than methods using estimated rates. The confidence intervals for the estimated reaction rates are obtained by bootstrapping. For the selection of a set of EM for a given st oichiometric model, the DMFA for EM method is combined with a multiobjective genetic algorithm. The method is applied to real data from a CHO fed-batch process. From measurements of six fed-batch experiments, 10 EM were identified as the smallest subset of EM based upon which the data can be described sufficiently accurately by a dynamic model. The estimated EM reaction rates and their confidence intervals at different process conditions provide useful information for the kinetic modeling and subsequent process optimization.
在发酵过程的宏观动态模型中，常从代谢网络中提取基本代谢途径（EM）来简化描述反应计量关系，并通过对 EM 的动力学速率方程进行参数化来构建预测模型。在这个过程中，选择一组 EM 是一个关键步骤，之后需要对它们的反应速率及其相关置信区间进行估计。在本文中，我们提出了一种用于计算细胞反应和 EM 反应速率的方法，以及一种用于选择用于过程建模的 EM 的算法。该方法基于 Leighty 和 Antoniewicz（2011，Metab Eng，13(6)，745-755）提出的动态代谢通量分析（DMFA），并增加了约束、正则化和不确定性分析。该方法直接使用浓度测量值而不是估计的摄取或分泌速率，以避免数值微分对测量误差的放大。结果表明，与使用估计速率的方法相比，正则化 EM 的 DMFA 方法对测量噪声具有更高的鲁棒性。通过自举法获得估计反应速率的置信区间。对于给定的计量模型选择一组 EM，DMFA 方法与多目标遗传算法相结合。该方法应用于 CHO 补料分批过程的真实数据。从六个补料分批实验的测量中，确定了 10 个 EM 作为基于此可以充分准确描述动态模型数据的最小 EM 子集。在不同过程条件下估计的 EM 反应速率及其置信区间为动力学建模和后续过程优化提供了有用的信息。
