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Table 1 Mathematical model to capture counts of intercellular mRNA (M), LacZ (E) and lactose (L) as reproduced from [27]. A summary of key symbols is listed in Table 2 with constants explained in Table 4

From: PROKARYO: an illustrative and interactive computational model of the lactose operon in the bacterium Escherichia coli

\(\dot {M} = D k_{M} P_{D} P_{R} - \gamma _{M} M\) (5)
\(\dot {E} = k_{E} M - \gamma _{E} E\) (6)
\(\dot {L} = k_{L} \beta _{L} \beta _{G} Q - 2 \phi _{M} \mathcal {M} B - \gamma _{L} L\) (7)
A=L (8)
Q=E (9)
B=E/4 (10)
\(P_{D} = \frac {p_{p} (1\, +\, p_{c} (K_{\textit {pc}}\, -\, 1))}{1\, +\, p_{p} p_{c} (k_{\textit {pc}}\, -\, 1)}\) (11)
\(p_{c} = \frac {K^{n_{h}}_{G}}{K^{n_{h}}_{G}\, +\, Ge^{n_{h}}}\) (12)
\(P_{R} = \frac {1}{1\, +\, \rho (A)\, +\, \frac {\xi _{123} \rho (A)}{(1\, +\, \xi _{2} \rho (A))(1\, +\, \xi _{3} \rho (A))}}\) (13)
\(\rho (A) = \rho _{\textit {max}} \left (\frac {K_{A}}{K_{A}\, +\, A}\right)^{\!\!4}\) (14)
\(\beta _{L} = \frac {Le}{k_{L}\, +\, Le}\) (15)
\(\beta _{G} = 1 - \phi _{G} \frac {Ge}{k_{G}\, +\, Ge}\) (16)
\(\mathcal {M}= \frac {L}{k_{M}\, +\, L}\) (17)