Department of Statistics, Sungkyunkwan University, Seoul, South Korea.
J Comput Biol. 2023 May;30(5):609-618. doi: 10.1089/cmb.2022.0201. Epub 2023 Mar 10.
Ordinary differential equations (ODEs) are widely used for elucidating dynamic processes in various fields. One of the applications of ODEs is to describe dynamics of gene regulatory networks (GRNs), which is a critical step in understanding disease mechanisms. However, estimation of ODE models for GRNs is challenging because of inflexibility of the model and noisy data with complex error structures such as heteroscedasticity, correlations between genes, and time dependency. In addition, either a likelihood or Bayesian approach is commonly used for estimation of ODE models, but both approaches have benefits and drawbacks in their own right. Data cloning is a maximum likelihood (ML) estimation method through the Bayesian framework. Since it works in the Bayesian framework, it is free from local optimum problems that are common drawbacks of ML methods. Also, its inference is invariant for the selection of prior distributions, which is a major issue in Bayesian methods. This study proposes an estimation method of ODE models for GRNs through data cloning. The proposed method is demonstrated through simulation and it is applied to real gene expression time-course data.
常微分方程（ODE）广泛用于阐明各个领域的动态过程。ODE 的应用之一是描述基因调控网络（GRN）的动态，这是理解疾病机制的关键步骤。然而，由于模型的不灵活性和具有复杂误差结构（如异方差、基因之间的相关性和时间依赖性）的嘈杂数据，GRN 的 ODE 模型的估计具有挑战性。此外，通常使用似然或贝叶斯方法来估计 ODE 模型，但这两种方法都有其自身的优点和缺点。数据克隆是一种通过贝叶斯框架进行最大似然（ML）估计的方法。由于它在贝叶斯框架中工作，因此它不受 ML 方法常见的局部最优问题的影响。此外，其推断对于先验分布的选择是不变的，这是贝叶斯方法的一个主要问题。本研究提出了一种通过数据克隆估计 GRN 的 ODE 模型的方法。通过模拟对所提出的方法进行了演示，并将其应用于真实的基因表达时间序列数据。
