Division of Plant and Crop Sciences, School of Biosciences, University of Nottingham, Sutton Bonington LE12 5RD, United Kingdom; School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
J Theor Biol. 2018 Nov 14;457:66-78. doi: 10.1016/j.jtbi.2018.05.028. Epub 2018 Jul 21.
Developing effective strategies to use models in conjunction with experimental data is essential to understand the dynamics of biological regulatory networks. In this study, we demonstrate how combining parameter estimation with asymptotic analysis can reveal the key features of a network and lead to simplified models that capture the observed network dynamics. Our approach involves fitting the model to experimental data and using the profile likelihood to identify small parameters and cases where model dynamics are insensitive to changing particular individual parameters. Such parameter diagnostics provide understanding of the dominant features of the model and motivate asymptotic model reductions to derive simpler models in terms of identifiable parameter groupings. We focus on the particular example of biosynthesis of the plant hormone gibberellin (GA), which controls plant growth and has been mutated in many current crop varieties. This pathway comprises two parallel series of enzyme-substrate reactions, which have previously been modelled using the law of mass action (Middleton et al., 2012). Considering the GA20ox-mediated steps, we analyse the identifiability of the model parameters using published experimental data; the analysis reveals the ratio between enzyme and GA levels to be small and motivates us to perform a quasi-steady state analysis to derive a reduced model. Fitting the parameters in the reduced model reveals additional features of the pathway and motivates further asymptotic analysis which produces a hierarchy of reduced models. Calculating the Akaike information criterion and parameter confidence intervals enables us to select a parsimonious model with identifiable parameters. As well as demonstrating the benefits of combining parameter estimation and asymptotic analysis, the analysis shows how GA biosynthesis is limited by the final GA20ox-mediated steps in the pathway and generates a simple mathematical description of this part of the GA biosynthesis pathway.
开发有效的策略，将模型与实验数据结合使用，对于理解生物调控网络的动态至关重要。在本研究中，我们展示了如何结合参数估计和渐近分析，揭示网络的关键特征，并得到简化模型，以捕捉观察到的网络动态。我们的方法包括将模型拟合到实验数据，并使用似然比来识别小参数和模型动态对特定个体参数变化不敏感的情况。这种参数诊断提供了对模型主要特征的理解，并促使进行渐近模型简化，以便以可识别的参数分组形式得到更简单的模型。我们专注于植物激素赤霉素（GA）生物合成的特殊例子，它控制植物生长，并且在许多当前的作物品种中发生了突变。该途径包含两个平行的酶-底物反应系列，以前曾使用质量作用定律（Middleton 等人，2012 年）对其进行建模。考虑到 GA20ox 介导的步骤，我们使用已发表的实验数据分析模型参数的可识别性；分析揭示了酶和 GA 水平之间的比值很小，并促使我们进行准稳态分析，以得到简化模型。在简化模型中拟合参数揭示了途径的其他特征，并促使进一步的渐近分析，产生了一系列简化模型。计算赤霉素生物合成途径的简化模型和渐近分析有助于选择具有可识别参数的简约模型。除了展示结合参数估计和渐近分析的好处外，该分析还展示了 GA 生物合成如何受到途径中最终的 GA20ox 介导步骤的限制，并生成了 GA 生物合成途径这一部分的简单数学描述。
