Table 1 Variables and parameters of the mathematical model.

I

IPTG concentration

mM

G

Concentration of GFP protein

molecules per cell

L ^F

Free LacI molecules, i.e. not bound to operator sites or IPTG molecule

molecules per cell

L ^I

LacI molecules bound to IPTG

molecules per cell

M _G

mRNA molecules of GFP

molecules per cell

M _L

mRNA molecules of LacI

molecules per cell

$D_{G/L}^F$

Free Repressor/Reporter plasmids

plasmids per cell

$D_{G/L}^L$

Repressor/Reporter plasmids bound to LacI molecules

plasmids per cell

$D_{G/L}^I$

Repressor/Reporter plasmids bound to induced LacI molecules

plasmids per cell

$D_G^0$

Number of Reporter plasmids per cell

80

plasmids per cell

$D_L^0$

Number of Repressor plasmids per cell

$D_G^0/{3.75}^{\S }=21.33$

plasmids per cell

λ _G/L

Protein degradation rate

0.0214^§

min^-1

${\lambda }_{G/L}^M$

mRNA degradation rate

0.271[39]

min^-1

α _G

GFP rate of synthesis

540λ _G = 11.54[40]

min^-1

Α _L

LacI rate of synthesis

α _G /4 = 2.88

min^-1

${\alpha }_G^M$

GFP transcription rate

0.56^†

min^-1

${\alpha }_L^M$

LacI transcription rate

${\alpha }_G^M/{1.23}^{\S }=0.45$

min^-1

$K_x^L$

Equilibrium binding constant of the complex LacI-O_x

$K_1^L$

0.13[41]

molecules per cell

$K_2^L$

1.63[41]

molecules per cell

$K_s^L$

0.0394^†

molecules per cell

$K_x^I$

Equilibrium binding constant for the binding of induced LacI molecule to the operator sequence O_x

$K_1^I$

25336^†

molecules per cell

$K_2^I$

∞

molecules per cell

$K_s^I$

313^†

molecules per cell

K ^LI

Equilibrium binding constant for the binding IPTG-LacI

0.2890^†

mM

n

Cooperativity of the binding LacI-IPTG

1.8688^†

τ ^LI

Time constant of LacI binding to the operator sequences

0.02[43]

min

τ ^DI

Time constant of induced-LacI binding to the operator sequences

*

min

τ ^DL

Time constant of the binding LacI-IPTG

*

min