Table 1 Summary of modeling assumptions and equation terms affected by them

From: A coarse-grained bacterial cell model for resource-aware analysis and design of synthetic gene circuits

Assumption

Equations

Relevant termsa,b

mRNA synthesis

Negligible transcriptional couplings

(15), (16), (21)

Fi ⋅ ci ⋅ αi ⋅ λ

Constitutive metabolic gene expression

(15)

Fa ≡ 1

mRNA synthesis rate proportional to cell growth rate

(15), (16), (21)

Fi ⋅ ci ⋅ αi ⋅ λ

Protein synthesis

Translational couplings captured by effective rate constants

(17), (18)

\(\frac{\epsilon ({t}^{c})}{{n}_{i}}\cdot \frac{{{{{{{{{\boldsymbol{m}}}}}}}}}_{{{{{{{{\boldsymbol{i}}}}}}}}}/{{{{{{{{\boldsymbol{k}}}}}}}}}_{{{{{{{{\boldsymbol{i}}}}}}}}}}{{{{{{{{\bf{1}}}}}}}}+\frac{{{{{{{{\bf{1}}}}}}}}}{{{{{{{{\bf{1}}}}}}}}-{\overline{{{{{{{{\boldsymbol{\phi }}}}}}}}}}_{{{{{{{{\boldsymbol{q}}}}}}}}}}{{{{{{{{\boldsymbol{\sum }}}}}}}}}_{{{{{{{{\boldsymbol{j}}}}}}}}{{{{{{{\boldsymbol{\in }}}}}}}}\{{{{{{{{\boldsymbol{a}}}}}}}},{{{{{{{\boldsymbol{r}}}}}}}}\}}{{{{{{{{\boldsymbol{m}}}}}}}}}_{{{{{{{{\boldsymbol{j}}}}}}}}}/{{{{{{{{\boldsymbol{k}}}}}}}}}_{{{{{{{{\boldsymbol{j}}}}}}}}}}R\)

Housekeeping protein mass fraction fixed

(17), (18), (22)

\({\phi }_{q}\equiv {\overline{\phi }}_{q}\equiv 0.59\)

Housekeeping gene expression not modeled explicitly

(17), (18), (22)

\(\frac{{m}_{i}/{k}_{i}}{1+\frac{{{{{{{{\bf{1}}}}}}}}}{{{{{{{{\bf{1}}}}}}}}-{\overline{{{{{{{{\boldsymbol{\phi }}}}}}}}}}_{{{{{{{{\boldsymbol{q}}}}}}}}}}{\sum }_{j\in \{a,r\}}{m}_{j}/{k}_{j}}\)

Degradation and dilution of species

mRNA degradation rate comparable to cell growth rate

(15), (16)

−(λ + βi)mi

Protein degradation rate negligible compared to cell growth rate

(17), (18)

−λpi

tRNA degradation rate negligible compared to cell growth rate

(19), (20)

−λtc, −λtu

Cell growth rate regulation

Cell growth rate maintains constant protein mass per unit of cell volume

(25)

\(\lambda (\epsilon,B)=\frac{\epsilon B}{M}\)

Translation elongation

Translation elongation rate governed by Michaelis-Menten kinetics

(26)

\(\epsilon ({t}^{c})={\epsilon }_{{{{{{\rm{max}}}}}}}\frac{{t}^{c}}{{t}^{c}+{K}_{\epsilon }}\)

Protein precursor synthesis

tRNA aminoacylation rate governed by Michaelis-Menten kinetics

(27)

\(\nu ({t}^{u},\sigma )={{{{{{{{\boldsymbol{\nu }}}}}}}}}_{{{{{{{{\mathbf{{{max}}}}}}}}}}}\sigma \frac{{{{{{{{{\boldsymbol{t}}}}}}}}}^{{{{{{{{\boldsymbol{u}}}}}}}}}}{{{{{{{{{\boldsymbol{t}}}}}}}}}^{{{{{{{{\boldsymbol{u}}}}}}}}}+{{{{{{{{\boldsymbol{K}}}}}}}}}_{{{{{{{{\boldsymbol{\nu }}}}}}}}}}\)

Culture medium’s nutrient quality captured by the nutrient quality factor σ

(27)

\(\nu ({t}^{u},\sigma )={\nu }_{{{{{{\rm{max}}}}}}}{{{{{{{\boldsymbol{\sigma }}}}}}}}\frac{{t}^{u}}{{t}^{u}+{K}_{\nu }}\)

Flux-parity resource allocation

ppGpp level reflects the ratio of charged and uncharged tRNA concentrations

(28)

\(T=\frac{{t}^{c}}{{t}^{u}}\propto \frac{1}{[{{{{{\rm{ppGpp}}}}}}]}\)

Ribosome synthesis regulated by ppGpp

(29)

\({F}_{r}(T)=\frac{T}{T+\tau }\)

tRNA and ribosome synthesis co-regulated

(30)

ψ(T) = ψmax Fr(T)

  1. aGeneric index i means that the term pertains to both a and r genes.
  2. bWhere not all factors of a term reflect the assumption, the relevant part is given in bold.
Back to article page