Fig. 3.

For a stable protein, no feedback provides the lowest noise in event timing for a fixed mean FPT. Protein trajectories obtained using the stochastic simulation algorithm for a stochastic gene expression model with positive feedback (Left), no feedback (Middle), and negative feedback (Right) (42). The threshold for event timing is assumed to be 500 protein molecules and feedback is implemented by assuming a linear form of transcription rates as $k_i=c_1+c_{2}i$. The value of $c_2$ is taken as $0.05{\text{min}}^{-1}$ for positive feedback and $-0.05{\text{min}}^{-1}$ for negative feedback. For each feedback, the parameter $c_1$ is taken such that the mean FPT is kept constant (40 min). The mRNA half-life is assumed to be $2.7\text{min}$, and proteins are translated from mRNAs at a rate $0.5{\text{min}}^{-1}$, which corresponds to a mean burst size of $b=2$. Histograms on the top represent distribution of FPT from 10,000 Monte Carlo simulations.