Fröhlich Fabian, Thomas Philipp, Kazeroonian Atefeh, Theis Fabian J, Grima Ramon, Hasenauer Jan
Helmholtz Zentrum München - German Research Center for Environmental Health, Institute of Computational Biology, Neuherberg, Germany.
Technische Universität München, Center for Mathematics, Chair of Mathematical Modeling of Biological Systems, Garching, Germany.
PLoS Comput Biol. 2016 Jul 22;12(7):e1005030. doi: 10.1371/journal.pcbi.1005030. eCollection 2016 Jul.
Quantitative mechanistic models are valuable tools for disentangling biochemical pathways and for achieving a comprehensive understanding of biological systems. However, to be quantitative the parameters of these models have to be estimated from experimental data. In the presence of significant stochastic fluctuations this is a challenging task as stochastic simulations are usually too time-consuming and a macroscopic description using reaction rate equations (RREs) is no longer accurate. In this manuscript, we therefore consider moment-closure approximation (MA) and the system size expansion (SSE), which approximate the statistical moments of stochastic processes and tend to be more precise than macroscopic descriptions. We introduce gradient-based parameter optimization methods and uncertainty analysis methods for MA and SSE. Efficiency and reliability of the methods are assessed using simulation examples as well as by an application to data for Epo-induced JAK/STAT signaling. The application revealed that even if merely population-average data are available, MA and SSE improve parameter identifiability in comparison to RRE. Furthermore, the simulation examples revealed that the resulting estimates are more reliable for an intermediate volume regime. In this regime the estimation error is reduced and we propose methods to determine the regime boundaries. These results illustrate that inference using MA and SSE is feasible and possesses a high sensitivity.
定量机理模型是剖析生化途径以及全面理解生物系统的宝贵工具。然而，要实现定量，这些模型的参数必须从实验数据中估计。在存在显著随机波动的情况下，这是一项具有挑战性的任务，因为随机模拟通常耗时过长，而使用反应速率方程（RREs）的宏观描述不再准确。因此，在本手稿中，我们考虑矩封闭近似（MA）和系统规模展开（SSE），它们近似随机过程的统计矩，并且往往比宏观描述更精确。我们为MA和SSE引入基于梯度的参数优化方法和不确定性分析方法。使用模拟示例以及通过将其应用于促红细胞生成素诱导的JAK/STAT信号传导数据来评估这些方法的效率和可靠性。该应用表明，即使仅可获得总体平均数据，与RRE相比，MA和SSE也能提高参数的可识别性。此外，模拟示例表明，对于中等体积范围，所得估计更可靠。在这个范围内，估计误差减小，我们提出了确定范围边界的方法。这些结果表明，使用MA和SSE进行推断是可行的，并且具有很高的灵敏度。
