The Ability of Flux Balance Analysis to Predict Evolution of Central Metabolism Scales with the Initial Distance to the Optimum

The most powerful genome-scale framework to model metabolism, flux balance analysis (FBA), is an evolutionary optimality model. It hypothesizes selection upon a proposed optimality criterion in order to predict the set of internal fluxes that would maximize fitness. Here we present a direct test of the optimality assumption underlying FBA by comparing the central metabolic fluxes predicted by multiple criteria to changes measurable by a 13C-labeling method for experimentally-evolved strains. We considered datasets for three Escherichia coli evolution experiments that varied in their length, consistency of environment, and initial optimality. For ten populations that were evolved for 50,000 generations in glucose minimal medium, we observed modest changes in relative fluxes that led to small, but significant decreases in optimality and increased the distance to the predicted optimal flux distribution. In contrast, seven populations evolved on the poor substrate lactate for 900 generations collectively became more optimal and had flux distributions that moved toward predictions. For three pairs of central metabolic knockouts evolved on glucose for 600–800 generations, there was a balance between cases where optimality and flux patterns moved toward or away from FBA predictions. Despite this variation in predictability of changes in central metabolism, two generalities emerged. First, improved growth largely derived from evolved increases in the rate of substrate use. Second, FBA predictions bore out well for the two experiments initiated with ancestors with relatively sub-optimal yield, whereas those begun already quite optimal tended to move somewhat away from predictions. These findings suggest that the tradeoff between rate and yield is surprisingly modest. The observed positive correlation between rate and yield when adaptation initiated further from the optimum resulted in the ability of FBA to use stoichiometric constraints to predict the evolution of metabolism despite selection for rate.

作为目前最强大的基因组规模代谢建模框架，通量平衡分析（flux balance analysis, FBA）是一种进化最优性模型。其基于预设的最优性准则进行选择假设，以预测可最大化适应度的胞内通量集。本研究通过将多种准则预测的中心代谢通量，与实验进化菌株经13C同位素标记法可检测到的通量变化进行对比，直接检验了FBA的核心最优性假设。我们选取了三项大肠杆菌（Escherichia coli）进化实验的数据集，这些实验在进化时长、环境一致性以及初始最优性水平上存在差异。针对10个在葡萄糖基本培养基中进化50000代的菌株种群，我们观察到相对通量出现小幅变化，导致最优性出现小幅但显著的下降，且与预测的最优通量分布之间的距离增大。与之相反，7个在贫瘠底物乳酸中进化900代的菌株种群，整体最优性得到提升，其通量分布也更贴近FBA的预测结果。针对3组在葡萄糖培养基中进化600~800代的中心代谢基因敲除菌株对，最优性与通量模式分别出现了向FBA预测靠拢或偏离的情况，二者占比相当。尽管中心代谢通量变化的可预测性存在上述差异，我们仍得到了两项共性结论。其一，生长速率的提升主要源于进化过程中底物利用速率的提高。其二，当初始菌株的底物得率相对偏低时，FBA的预测效果良好；而当初始菌株的得率已处于较高水平时，进化后的通量分布往往会略微偏离FBA的预测。上述结果表明，底物利用速率与得率之间的权衡关系出乎意料地微弱。当进化起始于远离最优状态的条件下时，速率与得率呈现出正相关关系，这使得即便选择压力指向底物利用速率，FBA仍可通过化学计量约束来准确预测代谢的进化过程。