This work presents a novel, differentiable, way of solving dynamic Flux Balance Analysis (dFBA) problems by embedding flux balance analysis of metabolic network models within lumped bulk kinetics for biochemical processes. The proposed methodology utilizes transformation of the bounds of the embedded linear programming problem of flux balance analysis via a logarithmic barrier (interior point) approach. By exploiting the first-order optimality conditions of the interior-point problem, and with further transformations, the approach results in a system of implicit ordinary differential equations. Results from four case studies, show that the CPU and wall-times obtained using the proposed method are competitive with existing state-of-the art approaches for solving dFBA simulations, for problem sizes up to genome-scale. The differentiability of the proposed approach allows, using existing commercial packages, its application to the optimal control of dFBA problems at a genome-scale size, thus outperforming existing formulations as shown by two dynamic optimization case studies.

通过将代谢网络模型的通量平衡分析嵌入生化过程的集总体积动力学中，这项工作提出了解决动态通量平衡分析（dFBA）问题的新颖，可微分方法。所提出的方法通过对数势垒（内点）方法利用了通量平衡分析的嵌入式线性规划问题的界线变换。通过利用内点问题的一阶最优条件，并进行进一步的变换，该方法导致了一个隐式常微分方程组。四个案例研究的结果表明，使用提出的方法获得的CPU时间和壁挂时间与解决dFBA模拟的现有技术水平（与问题规模最大的基因组规模）相比具有竞争优势。