报告题目：A complete spectral characterization for a stochastic autoregulated gene expression model

报告人：贾晨研究员（北京计算科学研究中心）

报告时间：2023年12月21日14:30-15:30

报告地点：复杂系统研究所（商学楼四层）

报告人简介：贾晨，特聘研究员，博士生导师，国家级人才计划入选者。于北京大学数学科学学院取得学士学位与博士学位，博士毕业后赴美任助理研究员，随后回国并加入北京计算科学研究中心。主要从事数学、生物学、物理学等交叉领域的研究，特别是复杂生化网络的随机动力学与随机热力学研究。目前任中国运筹学会计算系统生物学分会青年理事，中国工业与应用数学学会数学生命科学专委会委员，中国生物信息学学会网络生物学专委会委员，中国生物信息学学会算法研究专委会委员。以第一或通讯作者发表学术论文40余篇，多项研究工作发表在PRX、Cell子刊、SIAM汇刊、PCB、JCP、AAP、EJP、JMB等相关领域的权威杂志。

报告摘要：In this study, we obtain an exact time-dependent solution of the chemical master equation (CME) of an extension of the two-state telegraph model describing bursty or non-bursty protein expression in the presence of positive or negative autoregulation. Using the method of spectral decomposition, we show that the eigenfunctions of the generating function solution of the CME are Heun functions, while the eigenvalues can be determined by solving a continued fraction equation. Our solution generalizes and corrects a previous time-dependent solution for the CME of a gene circuit describing non-bursty protein expression in the presence of negative autoregulation [Phys. Rev. E 83: 062902 (2011)]. In particular, we clarify that the eigenvalues are generally not real as previously claimed. We also investigate the relationship between different types of dynamic behavior and the type of feedback, the protein burst size, and the gene switching rate.

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