St John Peter C, Doyle Francis J
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA.
BMC Syst Biol. 2013 Jul 29;7:71. doi: 10.1186/1752-0509-7-71.
The dynamics of gene regulation play a crucial role in a cellular control: allowing the cell to express the right proteins to meet changing needs. Some needs, such as correctly anticipating the day-night cycle, require complicated oscillatory features. In the analysis of gene regulatory networks, mathematical models are frequently used to understand how a network's structure enables it to respond appropriately to external inputs. These models typically consist of a set of ordinary differential equations, describing a network of biochemical reactions, and unknown kinetic parameters, chosen such that the model best captures experimental data. However, since a model's parameter values are uncertain, and since dynamic responses to inputs are highly parameter-dependent, it is difficult to assess the confidence associated with these in silico predictions. In particular, models with complex dynamics - such as oscillations - must be fit with computationally expensive global optimization routines, and cannot take advantage of existing measures of identifiability. Despite their difficulty to model mathematically, limit cycle oscillations play a key role in many biological processes, including cell cycling, metabolism, neuron firing, and circadian rhythms.
In this study, we employ an efficient parameter estimation technique to enable a bootstrap uncertainty analysis for limit cycle models. Since the primary role of systems biology models is the insight they provide on responses to rate perturbations, we extend our uncertainty analysis to include first order sensitivity coefficients. Using a literature model of circadian rhythms, we show how predictive precision is degraded with decreasing sample points and increasing relative error. Additionally, we show how this method can be used for model discrimination by comparing the output identifiability of two candidate model structures to published literature data.
Our method permits modellers of oscillatory systems to confidently show that a model's dynamic characteristics follow directly from experimental data and model structure, relaxing assumptions on the particular parameters chosen. Ultimately, this work highlights the importance of continued collection of high-resolution data on gene and protein activity levels, as they allow the development of predictive mathematical models.
基因调控动力学在细胞控制中起着至关重要的作用，使细胞能够表达正确的蛋白质以满足不断变化的需求。有些需求，比如正确预测昼夜周期，需要复杂的振荡特征。在基因调控网络分析中，数学模型经常被用来理解网络结构如何使其能够对外部输入做出适当反应。这些模型通常由一组描述生化反应网络的常微分方程以及未知的动力学参数组成，这些参数的选择要使模型能最好地捕捉实验数据。然而，由于模型的参数值不确定，且对输入的动态响应高度依赖参数，因此很难评估这些计算机模拟预测的可信度。特别是，具有复杂动力学（如振荡）的模型必须通过计算成本高昂的全局优化程序来拟合，并且无法利用现有的可识别性度量方法。尽管极限环振荡在数学上难以建模，但它在许多生物过程中起着关键作用，包括细胞周期、新陈代谢、神经元放电和昼夜节律。
在本研究中，我们采用一种有效的参数估计技术，对极限环模型进行自展不确定性分析。由于系统生物学模型的主要作用是提供对速率扰动响应的见解，我们将不确定性分析扩展到包括一阶灵敏度系数。使用一个昼夜节律的文献模型，我们展示了预测精度如何随着采样点的减少和相对误差的增加而降低。此外，我们展示了如何通过将两个候选模型结构的输出可识别性与已发表的文献数据进行比较，将该方法用于模型判别。
我们的方法使振荡系统的建模者能够自信地表明，模型的动态特性直接源于实验数据和模型结构，放宽了对所选特定参数的假设。最终，这项工作强调了持续收集基因和蛋白质活性水平高分辨率数据的重要性，因为这些数据有助于开发预测性数学模型。
