Collaborative Research: Semiparametric ODE Models for Complex Gene Regulatory Networks

基因调控在细胞的生长、分裂和对环境刺激的反应等活动和功能中起着重要作用。细胞内基因及其表达产物（rna和蛋白质）之间的调控相互作用交织成复杂而动态的基因调控网络（grn）。最近的技术突破使GRNs的大规模实验研究成为可能。GRN分析的一个核心问题是阐明网络拓扑结构和动态，从而产生研究中的生物特性。然而，这些网络数据的规模和复杂性给从中提取有用信息带来了严峻的挑战。该项目旨在开发统计和计算工具来揭示grn的底层结构、动态和功能。新的统计理论和推理方法将被开发，以解决建模和分析大规模GRNs的理论和计算挑战。这项研究的结果将建立一个新的框架来剖析动态和复杂的生物网络，特别是在我们的案例研究中调节细胞增殖的GRN。传统的grn统计分析通常假设网络节点之间的相互作用可以用线性函数或低阶多项式来描述。然而，生物过程通常是复杂的，网络节点之间的分子相互作用可能无法用简单的函数来准确描述。该项目的主要目标是开发新颖灵活的统计方法，通过从连续值或离散值基因表达的时间过程实验数据中学习非线性相互作用来解剖和重建grn。具体来说，我们将开发新的建模和分析方法，使用半参数常微分方程（ode）来研究grn，并将开发最先进的计算工具来表征grn的结构和动力学，以帮助科学家解决由grn调节的关键细胞系统。该项目分为两部分。第一部分侧重于方法和理论，包括三个目标：(1)开发新的自动化统计程序，用于研究大型复杂grn的局部模式和动态结构；(2)对grn的拓扑特征和调控相互作用建立有效的统计推断；(3)开发分析大规模grn的高效计算算法和软件。本研究开发的方法将为使用ode对grn的拓扑和动态建模提供有价值的工具。在第二部分中，我们将关注真实的数据应用程序。具体而言，我们将在第一部分中应用新开发的工具分析视网膜母细胞瘤(Rb)-E2F基因网络，该基因网络在控制细胞增殖及其内部基因调控中起关键作用。

Gene regulation plays a fundamental role in cellular activities and functions, such as growth, division, and responses to environmental stimuli. The regulatory interactions among genes and their expression products (RNAs and proteins) intertwine into complex and dynamic gene regulatory networks (GRNs) in cells. Recent technical breakthrough has enabled large-scale experimental studies of GRNs. A central question in GRN analysis is to elucidate network topologies and dynamics that give rise to biological properties at study. However, the magnitude and complexity of these network data pose serious challenges in extracting useful information from within. This project aims to develop statistical and computational tools to reveal underlying structure, dynamics, and functionality of GRNs. New statistical theory and inference methods will be developed to tackle theoretical and computational challenges in modeling and analyzing large-scale GRNs. Results from this research will establish a novel framework to dissect dynamical and complex biological networks, and particularly a GRN that regulates cell proliferation in our case study.Traditional statistical analysis of GRNs typically assumes that interactions between network nodes can be described by linear functions or low-order polynomials. However, biological processes are usually complex and molecular interactions between network nodes may not be accurately described by simple functions. The main goal of this project is to develop novel and flexible statistical approaches to dissect and reconstruct GRNs by learning nonlinear interactions from time-course experimental data, with either continuous- or discrete-valued gene expression. Specifically, we will develop new modeling and analysis approaches to study GRNs using semiparametric ordinary differential equations (ODEs), and will develop state of art computational tools to characterize the structures and dynamics of GRNs, to help scientists address crucial cellular systems regulated by GRNs. The project has two parts. The first part focuses on Methods and Theory, consisting of three aims: (1) to develop new and automated statistical procedures for studying local patterns and dynamic structures in large and complex GRNs; (2) to establish valid statistical inferences on topological features and regulatory interactions of GRNs; and (3) to develop efficient computational algorithms and software for analyzing large-scale GRNs. Developed methods from this research will provide valuable tools for modeling the topologies and dynamics of GRNs using ODEs. In the second part, we will focus on real data applications. Specifically, we will apply newly developed tools in the first part to analyze a retinoblastoma (Rb)-E2F gene network, which plays a key role in controlling cell proliferation and the gene regulation within.