From: Genetic toggle switch controlled by bacterial growth rate
Model parametrization | Symbol | Value | Parameter range for E. coli |
---|---|---|---|
Doubling time | T | 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(t,T) | \(V_{0}(T)e^{\ln (2)\frac {t}{T}}\) | ^{b} |
Number of gene copies averaged over all genome loci | S(T) | \(\begin {array}{ll} \frac {9T}{80}+\frac {175}{T}-6.5 & T<30\\ \frac {T}{80}+\frac {85}{T}-0.5 & 30\leq T<60\\ 1+\frac {40}{T} & T\geq 60\\ \end {array}\) | ^{c} |
Approximate S(T) | S _{ appr }(T) | \(\frac {1}{\ln (2)}\left (\frac {T}{40}+\frac {1}{2}\right)\left (2^{\frac {40}{T}}-1\right)\) | ^{c} |
Gene repression by protein dimer binding | r _{ g }(t,T) | \({5,20,35}\times \frac {10^{-4}}{V(t,T)}\) | ^{d} |
Gene activation by protein dimer unbinding | k _{ g } | 2×10^{−3} | ^{d} |
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) | \(2V_{0}(T)\frac {40}{T}\times 10^{-2}\) | 10^{−2}÷10[1/s]^{f} |
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 } | 10^{−1} | \(\begin {array}{c} 5\times 10^{-8}\div 1.9\times 10^{3} \\ {[}1/\textit {s}]\textsuperscript {h}\end {array} \) |
mRNA degradation | r _{ m } | 3×10^{−3} | 10^{−2}÷6×10^{−4}[1/s]^{i} |
Protein monomer degradation | - | 0 (only dilution) | \( \begin {array}{c} 1.4\times 10^{-5}\div 10^{-2}\\ {[}1/\textit {s}]\textsuperscript {j}\end {array}\) |