Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California, United States of America.
PLoS Comput Biol. 2019 Aug 30;15(8):e1007308. doi: 10.1371/journal.pcbi.1007308. eCollection 2019 Aug.
We present a novel surrogate modeling method that can be used to accelerate the solution of uncertainty quantification (UQ) problems arising in nonlinear and non-smooth models of biological systems. In particular, we focus on dynamic flux balance analysis (DFBA) models that couple intracellular fluxes, found from the solution of a constrained metabolic network model of the cellular metabolism, to the time-varying nature of the extracellular substrate and product concentrations. DFBA models are generally computationally expensive and present unique challenges to UQ, as they entail dynamic simulations with discrete events that correspond to switches in the active set of the solution of the constrained intracellular model. The proposed non-smooth polynomial chaos expansion (nsPCE) method is an extension of traditional PCE that can effectively capture singularities in the DFBA model response due to the occurrence of these discrete events. The key idea in nsPCE is to use a model of the singularity time to partition the parameter space into two elements on which the model response behaves smoothly. Separate PCE models are then fit in both elements using a basis-adaptive sparse regression approach that is known to scale well with respect to the number of uncertain parameters. We demonstrate the effectiveness of nsPCE on a DFBA model of an E. coli monoculture that consists of 1075 reactions and 761 metabolites. We first illustrate how traditional PCE is unable to handle problems of this level of complexity. We demonstrate that over 800-fold savings in computational cost of uncertainty propagation and Bayesian estimation of parameters in the substrate uptake kinetics can be achieved by using the nsPCE surrogates in place of the full DFBA model simulations. We then investigate the scalability of the nsPCE method by utilizing it for global sensitivity analysis and maximum a posteriori estimation in a synthetic metabolic network problem with a larger number of parameters related to both intracellular and extracellular quantities.
我们提出了一种新颖的代理建模方法，可用于加速解决非线性和非光滑生物系统模型中出现的不确定性量化 (UQ) 问题。特别是，我们专注于动态通量平衡分析 (DFBA) 模型，该模型将从细胞代谢的约束代谢网络模型的解中找到的细胞内通量与细胞外基质和产物浓度的时变性质联系起来。DFBA 模型通常计算成本高昂，并且对 UQ 提出了独特的挑战，因为它们需要涉及离散事件的动态模拟，这些离散事件对应于约束细胞内模型解的活动集中的开关。所提出的非光滑多项式混沌扩展 (nsPCE) 方法是传统 PCE 的扩展，它可以有效地捕获由于这些离散事件的发生而导致的 DFBA 模型响应中的奇点。nsPCE 的关键思想是使用奇点时间的模型将参数空间划分为两个元素，模型响应在这两个元素上表现平滑。然后，使用已知的基于基的稀疏回归方法在这两个元素中分别拟合 PCE 模型，该方法在不确定参数数量方面具有良好的扩展能力。我们使用包含 1075 个反应和 761 个代谢物的大肠杆菌单培养物的 DFBA 模型演示了 nsPCE 的有效性。我们首先说明传统 PCE 如何无法处理这种复杂程度的问题。我们证明，通过使用 nsPCE 代理模型代替完整的 DFBA 模型模拟，可以在不确定性传播和底物摄取动力学参数的贝叶斯估计方面节省超过 800 倍的计算成本。然后，我们通过在具有更多与细胞内和细胞外数量相关参数的合成代谢网络问题中使用它进行全局敏感性分析和最大后验估计，来研究 nsPCE 方法的可扩展性。
