Table 4.

Statistical characteristic of stochastic SNAIL dynamics (at stationary state). Where, N is a normalizing factor, and τ is lag duration. τ_1/2 represents the average time at which a cell's SNAIL level changes by 50% due to stochasticity in its expression.

characteristics	expression
mean, μ	S0
variance, σ2	${\displaystyle \frac{{\sigma }_n^2\hspace{0.17em}{S}_0}{2{\gamma }_{\mathrm{SNAIL}}}}$
coefficient of variation, CV	${\sigma }_n\sqrt{{\displaystyle \frac{1\hspace{0.17em}}{2{\gamma }_{\mathrm{SNAIL}}\hspace{0.17em}{S}_0}}}$
probability density function, p.d.f.	${\displaystyle \frac{1}{N}\exp \left({\displaystyle \frac{-{\gamma }_{\mathrm{SNAIL}}\hspace{0.17em}{(S-S_0)}^2}{{\sigma }_n^2\hspace{0.17em}{S}_0}}\right)}$
autocorrelation function, A ($\mathit{\tau }$)	$\exp \left(-{\displaystyle \frac{{\gamma }_{\mathrm{SNAIL}}\hspace{0.17em}\tau }{S_0}}\right)$)
50% decorrelation time, ${\mathit{\tau }}_{1/2}$	${\displaystyle \frac{S_0\hspace{0.17em}\ln 2}{{\gamma }_{\mathrm{SNAIL}}}}$