Modeling telomere shortening process

Cell senescence has attracted much attention in the long history of human beings, and telomere shortening (TS) is one of the main concerns in the study of cell senescence. To reveal the microscopic mechanism of TS process, we model it based on molecular stochastic process from the perspective of nonequilibrium statistical physics. We associate the TS process with the continuous time random walk and derive the Fokker-Planck equation to describe the length distribution of the TS. We further modify the model describing the TS process, similar to the anomalous tempered diffusion, and derive the Feynman-Kac equation characterizing the functional distribution of the TS process. Finally, we study the statistics related to the critical telomere length lc, including the occupation time and first passage time. These two kinds of statistics help us understand the time scale of cell senescence.