Optimization of Time-Course Experiments for Kinetic Model Discrimination

Systems biology relies heavily on the construction of quantitative models of biochemical networks. These models must have predictive power to help unveiling the underlying molecular mechanisms of cellular physiology, but it is also paramount that they are consistent with the data resulting from key experiments. Often, it is possible to find several models that describe the data equally well, but provide significantly different quantitative predictions regarding particular variables of the network. In those cases, one is faced with a problem of model discrimination, the procedure of rejecting inappropriate models from a set of candidates in order to elect one as the best model to use for prediction.
In this work, a method is proposed to optimize the design of enzyme kinetic assays with the goal of selecting a model among a set of candidates. We focus on models with systems of ordinary differential equations as the underlying mathematical description. The method provides a design where an extension of the Kullback-Leibler distance, computed over the time courses predicted by the models, is maximized. Given the asymmetric nature this measure, a generalized differential evolution algorithm for multi-objective optimization problems was used.
The kinetics of yeast glyoxalase I (EC 4.4.1.5) was chosen as a difficult test case to evaluate the method. Although a single-substrate kinetic model is usually considered, a two-substrate mechanism has also been proposed for this enzyme. We designed an experiment capable of discriminating between the two models by optimizing the initial substrate concentrations of glyoxalase I, in the presence of the subsequent pathway enzyme, glyoxalase II (EC 3.1.2.6). This discriminatory experiment was conducted in the laboratory and the results indicate a two-substrate mechanism for the kinetics of yeast glyoxalase I.

系统生物学高度依赖生化网络定量模型的构建。此类模型不仅需具备预测能力，以助力揭示细胞生理学的潜在分子机制，同时还必须与关键实验所得数据保持一致，这一点至关重要。通常情况下，可能存在多个能够同等程度拟合实验数据的模型，但针对网络中特定变量，它们所给出的定量预测却存在显著差异。在此类场景下，研究者将面临模型判别（model discrimination）问题：即从候选模型集合中剔除不合适的模型，以选出最优模型用于预测的标准化流程。
本研究提出一种方法，用于优化酶动力学实验的设计，以实现从候选模型集合中筛选最优模型。本研究聚焦于以常微分方程组作为底层数学描述的模型。该方法通过最大化基于各模型预测的时间历程计算得到的Kullback-Leibler距离（Kullback-Leibler distance）的扩展形式，来生成最优实验设计方案。鉴于该度量具备非对称性，本研究采用了面向多目标优化问题的广义差分进化算法。
本研究选取酵母乙二醛酶I（glyoxalase I，EC 4.4.1.5）的动力学特性作为评估该方法的颇具挑战性的测试案例。尽管该领域通常仅采用单底物动力学模型，但已有研究针对该酶提出了双底物催化机制。本研究通过优化乙二醛酶I的初始底物浓度，并在该通路后续酶乙二醛酶II（glyoxalase II，EC 3.1.2.6）存在的条件下，设计出了可有效区分这两种模型的实验方案。该判别实验已在实验室完成，实验结果证实酵母乙二醛酶I的动力学特性符合双底物催化机制。