Effects of different burst form on gene expression dynamic and first-passage time

Timing of events in many cellular processes, such as cell-cycle control, cell differentiation, and so on, depend on regulatory proteins reaching critical threshold levels. The time at which special protein cross up the threshold levels is called as the first-passage time(FPT). Here, we theoretically show that geometric conditional burst has unneglectable effects on gene expression and FPT. More precisely, if the mean of protein is fixed and the same burst size, conditional geometric burst increase the mean and noise of FPT compared with the geometric distribution. If the mean of FPT is fixed and the same burst size, conditional geometric burst increase noise of FPT compared with the geometric distribution.