Fig. 2.

Relative positions of the event threshold and the steady-state protein level determine noise in timing. Noise in the FPT ($C{V}_T^2$) is plotted as a function of the event threshold ($X$) for different mean protein burst sizes $b$ and decay rates $\gamma$. For $\gamma \ne 0$, the noise is high at small values of $X$ and decreases with increasing $X$, which is similar to the $C{V}_T^2$ versus $X$ trend when $\gamma =0$ (dashed lines). After attaining a minima at an intermediate value of $X$, $C{V}_T^2$ increases with further increase in $X$. The minimum value of $C{V}_T^2$ is achieved at $X\approx x_{ss}/2$ for a birth–death process, and this optimal point shifts to the right as $b$ is increased while keeping $x_{ss}$ fixed by commensurate change in $k$. The steady-state protein level and the decay rate are taken as $x_{ss}=300$ molecules, and $\gamma =0.01$ per min.