  Inside individual cells, expression of genes is stochastic across organisms
ranging from bacterial to human cells. A ubiquitous feature of stochastic
expression is burst-like synthesis of gene products, which drives considerable
intercellular variability in protein levels across an isogenic cell population.
One common mechanism by which cells control such stochasticity is negative
feedback regulation, where a protein inhibits its own synthesis. For a single
gene that is expressed in bursts, negative feedback can affect the burst
frequency or the burst size. In order to compare these feedback types, we study
a piecewise deterministic model for gene expression of a self-regulating gene.
Mathematically tractable steady-state protein distributions are derived and
used to compare the noise suppression abilities of the two feedbacks. Results
show that in the low noise regime, both feedbacks are similar in term of their
noise buffering abilities. Intriguingly, feedback in burst size outperforms the
feedback in burst frequency in the high noise regime. Finally, we discuss
various regulatory strategies by which cells implement feedback to control
burst sizes of expressed proteins at the level of single cells.
