Tiejun Li, Peking University
Energy landscape and rare events for biological jump processes
The construction of energy landscape for bio-dynamics is attracting more and more attention recent years. In this talk, I will introduce the strategy to construct the landscape from its connection with rare events, which relies on the large deviation theory for Gillespie-type jump dynamics. In the application to a typical genetic switching model, the two-scale large deviation theory is developed to take into account the fast switching of DNA states. The comparison with other proposals are also discussed. We demonstrate different diffusive limits arise when considering different regimes for genetic translation and switching processes. I will also talk about its applications in understanding the S-phase checkpoint activation mechanism for budding yeast. This is a joint work with Fangting Li, Xiaoguang Li, Cheng Lv and Peijie Zhou.