Columbia University Irving Medical Center, 630 West 168th Street, New York, NY, 10032, USA.
J Math Biol. 2020 Jun;80(7):2395-2430. doi: 10.1007/s00285-020-01499-6. Epub 2020 May 18.
Organisms have evolved a variety of mechanisms to cope with the unpredictability of environmental conditions, and yet mainstream models of metabolic regulation are typically based on strict optimality principles that do not account for uncertainty. This paper introduces a dynamic metabolic modelling framework that is a synthesis of recent ideas on resource allocation and the powerful optimal control formulation of Ramkrishna and colleagues. In particular, their work is extended based on the hypothesis that cellular resources are allocated among elementary flux modes according to the principle of maximum entropy. These concepts both generalise and unify prior approaches to dynamic metabolic modelling by establishing a smooth interpolation between dynamic flux balance analysis and dynamic metabolic models without regulation. The resulting theory is successful in describing 'bet-hedging' strategies employed by cell populations dealing with uncertainty in a fluctuating environment, including heterogenous resource investment, accumulation of reserves in growth-limiting conditions, and the observed behaviour of yeast growing in batch and continuous cultures. The maximum entropy principle is also shown to yield an optimal control law consistent with partitioning resources between elementary flux mode families, which has important practical implications for model reduction, selection, and simulation.
生物已经进化出了多种机制来应对环境条件的不可预测性，然而代谢调控的主流模型通常基于不考虑不确定性的严格最优性原则。本文介绍了一个动态代谢建模框架，它是对资源分配的最新思想和 Ramkrishna 等人的强大最优控制公式的综合。特别是，根据细胞资源根据最大熵原理在基本通量模式之间分配的假设，对他们的工作进行了扩展。这些概念通过在没有调节的情况下在动态通量平衡分析和动态代谢模型之间建立平滑插值，对动态代谢建模的先前方法进行了概括和统一。所得到的理论成功地描述了细胞群体在波动环境中应对不确定性时采用的“赌注对冲”策略，包括异质资源投资、在生长限制条件下积累储备，以及在分批和连续培养中观察到的酵母生长行为。最大熵原理还产生了一个与基本通量模式家族之间分配资源一致的最优控制律，这对模型简化、选择和模拟具有重要的实际意义。
