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A stochastic model of autoregulated bursty gene expression by Kumar et al.[Phys. Rev. Lett. 113, 268105 (2014)] has been exactly solved in steady-stateconditions under the implicit assumption that protein numbers are sufficientlylarge such that fluctuations in protein numbers due to reversibleprotein-promoter binding can be ignored. Here we derive an alternative modelthat takes into account these fluctuations and hence can be used to study lowprotein number effects. The exact steady-state protein number distributions isderived as a sum of Gaussian hypergeometric functions. We use the theory tostudy how promoter switching rates and the type of feedback influence the sizeof protein noise and noise-induced bistability. Furthermore we show that ourmodel predictions for the protein number distribution are significantlydifferent from those of Kumar et al. when the protein mean is small, geneswitching is fast, and protein binding is faster than unbinding.

Small protein number effects in stochastic models of autoregulated bursty gene expression