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Gene expression is inherently a noisy process which manifests as cell-to-cellvariability in time evolution of proteins. Consequently, events that trigger atcritical threshold levels of regulatory proteins exhibit stochasticity in theirtiming. An important contributor to the noise in gene expression is translationbursts which correspond to randomness in number of proteins produced in asingle mRNA lifetime. Modeling timing of an event as a first-passage time (FPT)problem, we explore the effect of burst size distribution on event timing.Towards this end, the probability density function of FPT is computed for agene expression model with burst size drawn from a generic non-negativedistribution. Analytical formulas for FPT moments are provided in terms ofknown vectors and inverse of a matrix. The effect of burst size distribution isinvestigated by looking at how the feedback regulation strategy that minimizesnoise in timing around a given time deviates from the case when burst isdeterministic. Interestingly, results show that the feedback strategy fordeterministic burst case is quite robust to change in burst size distribution,and deviations from it are confined to about 20% of the optimal value. Thesefindings facilitate an improved understanding of noise regulation in eventtiming.

Effect of gene-expression bursts on stochastic timing of cellular events