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Center for Nonlinear Studies |
Biological networks are intrinsically stochastic due to thermodynamics, and stochasticity in genetic circuits can significantly affect cell fate in many critical cellular processes. The discrete Chemical Master Equation (dCME) provides a fundamental framework to model detailed stochastic biological reaction networks. However, it is challenging to directly solve a dCME that involves a nontrivial number of species due to the explosion of the size of the discrete state space. I have developed the multi-finite buffer method (mb-dCME) to address this challenging issue. A bank of finite buffers is introduced to control the total size of the state space by putting a limit on the number of each synthesis and degradation reaction that can occur. In comparison to previous methods, dramatically reduced state space can be optimally enumerated using the mb-dCME, and transition rate matrix efficiently constructed. The probability of boundary states has been proved as a certificate for state space truncation error. And we also provide an a priori approach to efficiently estimate the buffer sizes. The mb-dCME method can be generally applied to directly solve both steady state and time evolution probability landscapes of biological networks with nontrivial number of molecular species and reactions. It can also be used to directly solve the rare event first passage time distribution of realistic biological reaction networks, which mostly relies on sampling approaches. The mb-dCME method has been successfully applied to decipher the control mechanism behind the efficiency and stability of the phage λ (a virus of E. coli) genetic switch for the lysogenic maintenance and lytic induction. Our results not only correctly predicted experimental outcomes in wild-type phage λ and mutants, but also identified the most critical cooperative interaction largely responsible for the emergence of stability of lysogenic maintenance. I will then briefly discuss my recent ongoing work using mb-dCME to study the stochastic behavior of HIV-1 Tat genetic circuit, which plays a key role in controlling the latency and transactivation of the HIV. Lastly, I will discuss how the mb-dCME method and stochastic modeling of genetic circuits can be integrated into a multi-scale model to simulate the spatio-temporal dynamics of a population of cells. Using human skin wound healing as a running example, I will show how our method can help reveal the potential regulatory mechanisms in this complex cellular process, in which the behavior of each single cell is stochastically controlled by both intracellular genetic circuits and intercellular communication networks to achieve complex tissue-level coordination. The same idea can be potentially applied to model the cell population dynamics in immune systems with viral infections.
Host: Ruy Ribeiro and Alan Perelson