Table 3.

Propensity functions for the stochastic lac operon model

Reaction		Propensity function∗†‡
1	$\varnothing \stackrel{k_{\text{sMR}}}{\to }{\mathrm{M}}_{\mathrm{R}}$	${\alpha }_1=V_{\text{E.coli}}·N_{\text{A}}·k_{\text{sMR}}$
2	${\mathrm{M}}_{\mathrm{R}}\stackrel{k_{\text{sR}}}{\to }{\mathrm{M}}_{\mathrm{R}}+\mathrm{R}$	${\alpha }_2=k_{\text{sR}}·{\mathrm{M}}_{\mathrm{R}}$
3	$2\mathrm{R}\stackrel{k_{2\mathrm{R}}}{\to }{\mathrm{R}}_2$	${\alpha }_3=\frac{k_{2\mathrm{R}}}{V_{\text{E.coli}}·N_{\mathrm{A}}}·\mathrm{R}·\left(\mathrm{R}-1\right)$
4	${\mathrm{R}}_2\stackrel{k_{-2\mathrm{R}}}{\to }2\mathrm{R}$	${\alpha }_4=k_{-2\mathrm{R}}·{\mathrm{R}}_2$
5	${\mathrm{R}}_2+\mathrm{O}\stackrel{k_{\mathrm{r}}}{\to }{\mathrm{R}}_2\mathrm{O}$	${\alpha }_5=\frac{k_{\mathrm{r}}}{V_{\text{E.coli}}·N_{\mathrm{A}}}·{\mathrm{R}}_2·\mathrm{O}$
6	${\mathrm{R}}_2\mathrm{O}\stackrel{k_{-\mathrm{r}}}{\to }{\mathrm{R}}_2+\mathrm{O}$	${\alpha }_6=k_{-\mathrm{r}}·{\mathrm{R}}_{2}O$
7	$2\mathrm{I}+{\mathrm{R}}_2\stackrel{k_{\text{dr}1}}{\to }{\mathrm{I}}_2{\mathrm{R}}_2$	${\alpha }_7=\frac{k_{\text{dr}1}}{{\left(V_{\text{E.coli}}·N_{\mathrm{A}}\right)}^2}·{\mathrm{R}}_2·\mathrm{I}·\left(\mathrm{I}-1\right)$
8	${\mathrm{I}}_2{\mathrm{R}}_2\stackrel{k_{-\text{dr}1}}{\to }2\mathrm{I}+{\mathrm{R}}_2$	${\alpha }_8=k_{-\text{dr}1}·I_2{\mathrm{R}}_2$
9	$2\mathrm{I}+{\mathrm{R}}_2\mathrm{O}\stackrel{k_{\text{dr}2}}{\to }{\mathrm{I}}_2{\mathrm{R}}_2+\mathrm{O}$	${\alpha }_9=\frac{k_{\text{dr}2}}{{\left(V_{\text{E.coli}}·N_{\mathrm{A}}\right)}^2}·{\mathrm{R}}_2\mathrm{O}·\text{I}·\left(\text{I}-1\right)$
10	${\mathrm{I}}_2{\mathrm{R}}_2+\mathrm{O}\stackrel{k_{-\text{dr}2}}{\to }2\mathrm{I}+{\mathrm{R}}_2\mathrm{O}$	${\alpha }_{10}=\frac{k_{-\text{dr}2}}{V_{\text{E.coli}}·N_{\mathrm{A}}}·{\mathrm{I}}_2{\mathrm{R}}_2·\mathrm{O}$
11	$\mathrm{O}\stackrel{k_{\text{sMY}}}{\to }\mathrm{O}+{\mathrm{M}}_{\mathrm{Y}}$	${\alpha }_{11}=k_{\text{sMY}}·\mathrm{O}$
12	${\mathrm{M}}_{\mathrm{Y}}\stackrel{k_{1\text{sMY}}}{\to }{\mathrm{M}}_{\mathrm{Y}}+\mathrm{Y}$	${\alpha }_{12}=k_{1\text{sMY}}·{\mathrm{M}}_{\mathrm{Y}}$
13	${\mathrm{M}}_{\mathrm{Y}}\stackrel{k_{0\text{sMY}}}{\to }{\mathrm{M}}_{\mathrm{Y}}+\mathrm{Y}$	${\alpha }_{12}=k_{0\text{sMY}}·{\mathrm{M}}_{\mathrm{Y}}$
14	$\mathrm{Y}+{\mathrm{I}}_{\text{ex}}\stackrel{k_{\mathrm{p}}}{\to }\mathrm{Y}{\mathrm{I}}_{\text{ex}}$	${\alpha }_{13}=k_{\mathrm{p}}·\left[{\mathrm{I}}_{\text{ex}}\right]·\mathrm{Y}$
15	$\mathrm{Y}{\mathrm{I}}_{\text{ex}}\stackrel{k_{-\mathrm{p}}}{\to }\mathrm{Y}+{\mathrm{I}}_{\text{ex}}$	${\alpha }_{14}=k_{-\mathrm{p}}·\mathrm{Y}{\mathrm{I}}_{\text{ex}}$
16	$\mathrm{Y}{\mathrm{I}}_{\text{ex}}\stackrel{k_{\text{ft}}}{\to }\mathrm{Y}+\mathrm{I}$	${\alpha }_{15}=k_{\text{ft}}·\mathrm{Y}{\mathrm{I}}_{\text{ex}}$
17§	${\mathrm{I}}_{\text{ex}}\stackrel{k_{\mathrm{t}}}{\to }\mathrm{I}$	${\alpha }_{16}=V_{\text{E.coli}}·N_{\mathrm{A}}·k_{\mathrm{t}}·\left[{\mathrm{I}}_{\mathrm{ex}}\right]$
18	$\mathrm{I}\stackrel{k_{-\mathrm{t}}}{\to }{\mathrm{I}}_{\text{ex}}$	${\alpha }_{17}=k_{\mathrm{t}}·\mathrm{I}$
19	${\mathrm{M}}_{\mathrm{R}}\stackrel{{\lambda }_{\text{MR}}}{\to }\varnothing$	${\alpha }_{18}={\lambda }_{\text{MR}}·{\mathrm{M}}_{\mathrm{R}}$
20	${\mathrm{M}}_{\mathrm{Y}}\stackrel{{\lambda }_{\text{MY}}}{\to }\varnothing$	${\alpha }_{19}={\lambda }_{\text{MY}}·{\mathrm{M}}_{\mathrm{Y}}$
21	$\mathrm{R}\stackrel{{\lambda }_{\mathrm{R}}}{\to }\varnothing$	${\alpha }_{20}={\lambda }_{\mathrm{R}}·\mathrm{R}$
22	${\mathrm{R}}_2\stackrel{{\lambda }_{\mathrm{R}2}}{\to }\varnothing$	${\alpha }_{21}={\lambda }_{\mathrm{R}2}·{\mathrm{R}}_2$
23	$\mathrm{Y}\stackrel{{\lambda }_{\mathrm{Y}}}{\to }\varnothing$	${\alpha }_{22}={\lambda }_{\mathrm{Y}}·\mathrm{Y}$
24	$\mathrm{Y}{\mathrm{I}}_{\text{ex}}\stackrel{{\lambda }_{\mathrm{Y}{\mathrm{I}}_{\text{ex}}}}{\to }\mathrm{I}$	${\alpha }_{22}={\lambda }_{\text{YIex}}·\mathrm{Y}{\mathrm{I}}_{\text{ex}}$
25	${\mathrm{I}}_2{\mathrm{R}}_2\stackrel{{\lambda }_{\mathrm{I}2\mathrm{R}2}}{\to }2\mathrm{I}$	${\alpha }_{23}={\lambda }_{\mathrm{I}2\mathrm{R}2}·{\mathrm{I}}_2{\mathrm{R}}_2$

^∗Variables without brackets denote the number of molecules of the corresponding species.

^†All propensity functions are in units of min⁻¹.

^‡Avogadro's number is N_A = 6.0221367 × 10¹⁴ nmol⁻¹.

^§For the stochastic modeling of I_ex-related processes, see Appendix 3.