基于小样本数据的高维生物系统重构理论及算法与应用

Mathematical modeling based on biological and medical data is an important step forwards revealing life phenomena and understanding human complex diseases while the related research has become an international frontier. However, how to mine disciplinary knowledge from high-through data with small samples and how to integrate it into the complete information on systems of interest need to solve such issues as system reconstruction and computational modeling. Our preliminary results indicate that rather than being a drawback, high dimensional data with small samples may provide a global view with rich information on the system of interest and also reflect insight on the accumulated effects of long time dynamics. We will focus on theory, method and algorithm for reconstruction of high-dimensional systems based on nonlinear noisy data with small samples, including building and inference, computational modeling and algorithms, analysis and elucidation of the mechanisms of dynamic molecular networks. Furthermore, we will use the theoretical methods and results to study the nature progression of COPD and the novel recovery process after bypass surgery, including building the related dynamical molecular networks, studying dynamical properties of the related mathematical models, describing the mechanism of regulation and control of the networks, and establishing dynamic network marks. We believe that our theoretical and application research will be able to lay theoretical foundation and provide methodology for interpreting complex life phenomena and understanding the pathogenesis of complex diseases based on experimental data with small samples.

基于生物、医学数据建立数学模型是揭示生命现象以及理解人类复杂疾病机理的重要一步，相关研究已成为国际研究热点。然而，如何从小样本高通量数据中挖掘出有规律性的知识，并整合这些知识形成对系统的整体认识，需要解决诸如系统重构与可计算建模等问题。我们在前期研究中发现，小样本高维数据并不是缺陷，而是可以对有关系统提供全局有用的信息，并能反映出系统长时间动力行为的积累效果。本项目将研究基于小样本、非线性、噪声数据的高维动力系统重构理论、方法与算法，包括相应动态分子网络的构建与推断、可计算模型与算法、运行机制分析与阐明等，并应用理论方法与结果构建慢性阻塞性肺病状态(正常，COPD，治疗后)转化过程的动态分子调控网络，研究有关数学模型的动力学性质和有关网络的调节控制机理，确立动态网络标记物等。本项目的理论与应用研究将为基于小样本实验数据解释复杂生命现象和探索复杂疾病机理奠定理论基础并提供方法论。

基于生物、医学数据建立数学模型是揭示生命现象以及理解人类复杂疾病机理的重要一步，相关研究已成为国际研究热点。然而，如何从小样本高通量数据中挖掘出有规律性的知识，并整合这些知识形成对系统的整体认识，需要解决诸如系统重构与可计算建模等问题。我们发展和建立起一种基于实验或测量数据预测新数据的理论或方法，能够方便于生物/疾病系统或网络的重构；建立起生化反应网络的数学建模与理论分析的二项矩方法，解决了广泛使用的矩封闭方法的收敛性问题；我们建立的理论与方法，甚至能为基于正常状态和疾病状态的小样本数据，寻找和发现复杂疾病早期诊断准确和可靠的、疾病特定性的生物标志物，并预测动态药物的敏感性和耐药性。

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