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Table 1 Model parameters

From: Genetic toggle switch controlled by bacterial growth rate

Model parametrization



Parameter range for E. coli

Doubling time


from 20 to 120 [min]

20 [min] ÷ days

Scaled cell volume just after division (t=0)

V 0(T)

\(\frac {1}{6}\left (\frac {40}{T}\right)^{2}+\frac {1}{3}\)

0.4÷3[μ m 3]a

Cell volume


\(V_{0}(T)e^{\ln (2)\frac {t}{T}}\)


Number of gene copies averaged over all genome loci


\(\begin {array}{ll} \frac {9T}{80}+\frac {175}{T}-6.5 & T<30\\ \frac {T}{80}+\frac {85}{T}-0.5 & 30\leq T<60\\ 1+\frac {40}{T} & T\geq 60\\ \end {array}\)


Approximate S(T)

S appr (T)

\(\frac {1}{\ln (2)}\left (\frac {T}{40}+\frac {1}{2}\right)\left (2^{\frac {40}{T}}-1\right)\)


Gene repression by protein dimer binding

r g (t,T)

\({5,20,35}\times \frac {10^{-4}}{V(t,T)}\)


Gene activation by protein dimer unbinding

k g



mRNA transcription from active gene

k m (T)

\(\frac {5}{S(T)}\times 10^{-3}\)

≤ 0.8[1/s]e

Protein translation

k p (T)

\(2V_{0}(T)\frac {40}{T}\times 10^{-2}\)


Dimer formation

k d (t,T)

\(\frac {10^{-3}}{V(t,T)}\)

\(\begin {array}{c} 1.6\times 10^{-6}\div 9.5 \\ {[}1/(\text {mlcl}\times \textit {s})]\textsuperscript {g}\end {array}\)

Dimer dissociation to monomers

r d


\(\begin {array}{c} 5\times 10^{-8}\div 1.9\times 10^{3} \\ {[}1/\textit {s}]\textsuperscript {h}\end {array} \)

mRNA degradation

r m



Protein monomer degradation


0 (only dilution)

\( \begin {array}{c} 1.4\times 10^{-5}\div 10^{-2}\\ {[}1/\textit {s}]\textsuperscript {j}\end {array}\)

  1. aCell volume measurements from [30]. Cell size measured as cross-sectional area in range: 2÷7.5[μ m 2] [25, 26]. (Mass/cell) range: 1.3÷5.9[OD460 units /109 cells] [5]. V 0 was fitted based on cross-sectional area measurements which are correlated well with cell mass measurements by optical density of the culture [25]
  2. bExponential cell growth based on [30, 31]
  3. cAverage number of genome equivalents/cell: 1.6÷4 [5]. Average number of ori range: 2÷9 [5, 25]. Average number of ter range: 1.2÷2.1 [5]
  4. dGene switching is causing mRNA bursts observed at an E. coli promoter [32]
  5. eFor E. coli maximal transcription rate: 0.16−0.84/s [33]
  6. fTranslation initiation intervals are of the order of seconds, although they are specific for each mRNA [34]. In E. coli translation initiation rate may vary at least 1000-fold [35]; maximal peptide chain elongation rate: 20a a/s [36, 37]; average peptide chain elongation rate: 12a a/s [33]
  7. gAll cell types: 9.8×102/(M×s)÷5.7×109/(M×s) [38]; for 1 μ m 3 volume cell: 1.63×10−6/(mlcl×s)÷9.47/(mlcl×s)
  8. hAll cell types: 5×10−8/s÷1.9×103/s [38]
  9. iThe vast majority of mRNAs in a bacterial cell are very unstable, with a half-life of about 3 min (decay rate 3×10−3/s) – bacterial mRNAs are both rapidly synthesized and rapidly degraded [39]. In E. coli mRNA half-lives span between 1 and 18 min (decay rates 10−2/s÷6×10−4/s) [40]
  10. jMost of bacterial proteins are very stable, with degradation rates: 1.4×10−5÷5.6×10−5/s [41]