  Gene expression is inherently a noisy process which manifests as cell-to-cell
variability in time evolution of proteins. Consequently, events that trigger at
critical threshold levels of regulatory proteins exhibit stochasticity in their
timing. An important contributor to the noise in gene expression is translation
bursts which correspond to randomness in number of proteins produced in a
single 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 a
gene expression model with burst size drawn from a generic non-negative
distribution. Analytical formulas for FPT moments are provided in terms of
known vectors and inverse of a matrix. The effect of burst size distribution is
investigated by looking at how the feedback regulation strategy that minimizes
noise in timing around a given time deviates from the case when burst is
deterministic. Interestingly, results show that the feedback strategy for
deterministic burst case is quite robust to change in burst size distribution,
and deviations from it are confined to about 20% of the optimal value. These
findings facilitate an improved understanding of noise regulation in event
timing.

Subcellular Processes