Table 1:

Terminology and parameterization of transcription rates.

Kinetic rates	Units	Parameterization $\left\{k_{\text{ini}},k_{\text{on}},k_{\text{off}}\right\}$	Parameterization $\left\{k_{\text{ini}},\langle n\rangle ,{\tau }_n\right\}$
Pol II initiation rate $k_{\text{ini}}$	[min−1]	$k_{\text{ini}}$	$k_{\text{ini}}$
Promoter switching on-rate $k_{\text{on}}$	[min−1]	$k_{\text{on}}$	$\frac{\langle n\rangle }{{\tau }_n}$
Promoter switching off-rate $k_{\text{off}}$	[min−1]	$k_{\text{off}}$	$\frac{1-\langle n\rangle }{{\tau }_n}$
Bursting parameters	Units	Parameterization $\left\{k_{\text{ini}},k_{\text{on}},k_{\text{off}}\right\}$	Parameterization $\left\{k_{\text{ini}},\langle n\rangle ,{\tau }_n\right\}$
Promoter mean occupancy $\langle n\rangle$	#	$\frac{k_{\text{on}}}{\left(k_{\text{on}}+k_{\text{off}}\right)}=k_{\text{on}}{\tau }_n$	$\langle n\rangle$
Switching correlation time ${\tau }_n$	[min]	$\frac{1}{\left(k_{\text{on}}+k_{\text{off}}\right)}$	${\tau }_n$
Burst size $b$	#	$\frac{k_{\text{ini}}}{k_{\text{off}}}$	$\frac{k_{\text{ini}}{\tau }_n}{1-\langle n\rangle }$
Burst frequency $f$	[min−1]	$\frac{k_{\text{on}}{k}_{\text{off}}}{\left(k_{\text{on}}+k_{\text{off}}\right)}=k_{\text{off}}\langle n\rangle$	$\frac{\langle n\rangle \left(1-\langle n\rangle \right)}{{\tau }_n}$
Mean transcript synthesis rate	[min−1]	$\frac{k_{\text{ini}}{k}_{\text{on}}}{\left(k_{\text{on}}+k_{\text{off}}\right)}$	$k_{\text{ini}}\langle n\rangle$

Within the context of the two-state model the most intuitive parameterization is given by the kinetic rates $k_{\text{ini}},k_{\text{on}}$ and $k_{\text{off}}$. However, fluctuation analysis in transcriptional activity and inference approach both revealed that the three independent and uncorrelated variables $k_{\text{ini}},{\tau }_n$ and $\langle n\rangle$ provides a more natural parameterization, in which only $\langle n\rangle$ is modulated, while $k_{\text{ini}}$ and ${\tau }_n$ are both constant. Bursting parameters are clearly identified in both parameterizations.