近二十年来的研究证实：基因表达是一个随机的，不连续的过程，它使得处于相同环境下细胞的表型及功能呈现出多样性。这一颠覆性发现引导我们去重新探讨生命的本质，也衍生出了若干亟待解决的数学问题。本项目将通过建立实验驱动的数学模型，结合微分方程、动力系统、随机分析、统计等方法，试图引入新的数学手段来更完整地刻画基因表达的随机特征。我们将探讨基因表达噪声产生的根源及其对细胞群体行为的影响，信号转导网络对外部信号的应答机制，基因表达在细胞层面随机性与器官层面确定性关系等重要问题。通过研究登革病毒在伊蚊体内激发的抗菌肽基因表达的非线性动力学行为, 我们将阐述Wolbachia感染引导的虫媒病控制生化机制，为登革热和寨卡的防控提供理论支持。我们期望该项工作一方面能为生物医学工作者的研究提供新的思路，另一方面也能为数学工作者提出新的数学问题、引领更多青年学者进入分子生物学研究的前沿领域。

The experiments in the last 20 years have shown that gene expression is a stochastic and discontinuous process in single cells: Even under homogeneous environmental conditions, cells in a population of identical genes exhibit apparent phenotypic heterogeneity. These findings have revolutionized our basic views on cells and generated many fundamental questions on the core principles of life. In this program, we plan to characterize quantitatively and systematically the stochastic behaviors of gene expression by developing experimental data-driven mathematical models and using innovative methods from differential equations, dynamical systems, stochastic analysis, statistics, and numerical simulations. We are aiming at exploring the major biochemical steps leading to gene expression noise and their physiological consequences, the response of signal transduction networks to the external stimuli, and how the noise in individual cells is filtered to ascertain the function robustness of cell population. By studying the nonlinear dynamics in the activation and repression of anti-microbial peptide genes in mosquitoes, we attempt to elaborate the mechanisms underlying the Wolbachia-driven control of Dengue and Zika viruses. It is hoped that our effort will not only generate new ideas for biomedical researchers, but also propose challenging questions for the mathematicians who are motivated to explore the essence of life.