Often sharp changes in cellular behavior are triggered by thresholded events, i.e., by the attainment of a threshold value of a relevant cellular or molecular dynamical variable. Since the governing variable itself typically undergoes noisy or stochastic dynamics, there is a corresponding variability in the times when the same change occurs in each cell of a population. This time is called the "first passage" time and the corresponding process is a "first passage" (FP) process, referring to the event when a random variable first passes the threshold value. In this review we first present and elucidate fundamentals of the FP formalism within a unified conceptual framework, which naturally integrates the existing techniques. We then discuss applications thereof, with emphasis on the practical use of FP techniques in biophysical systems. Our focus here is on covering a diverse set of analytical techniques; the number of reviewed biological applications is thus limited, out of necessity. We focus on three specific areas: channel transport; receptor binding and adhesion; and single-cell growth and division.
Stochastic synthesis-degradation processes: first-passage properties and connections with resetting
Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）
Mean first passage times of higher-dimensional velocity jump processes
California State University at Northridge（北岭加州州立大学）；University of California at Los Angeles（加利福尼亚大学洛杉矶分校）；University of Notre Dame（圣母大学）；University of Alberta（阿尔伯塔大学）
