Computational Modelling of Metabolic Burden and Substrate Toxicity in Escherichia coli Carrying a Synthetic Metabolic Pathway

. 2019 Nov 11;7(11):553. doi: 10.3390/microorganisms7110553

Monod + Hill [27]:	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S]} - [B] \cdot \frac{k {[X]}^{n}}{{K_{i}}^{n} + {[X]}^{n}}$	(A3)
Monod + Aiba-Edward [65]:	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S]} - [B] \cdot \frac{k [X]}{K_{X} + [X]} \cdot exp (\frac{- [X]}{K_{i}})$	(A4)
Monod + Andrews [66]:	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S]} - [B] \cdot \frac{k}{(1 + \frac{K_{X}}{[X]}) (1 + \frac{[X]}{K_{i}})}$	(A5)
Monod + Haldane-Andrews [66]:	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S]} - [B] \cdot \frac{k [X]}{K_{X} + [X] + \frac{{[X]}^{2}}{K_{i}}}$	(A6)
Monod + Monod:	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S]} - [B] \cdot \frac{k [X]}{K_{X} + [X]}$	(A7)
Monod + Moser [64]:	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S]} - [B] \cdot \frac{k {[X]}^{n}}{K_{X} + {[X]}^{n}}$	(A8)
Monod + Tessier [63]:	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S]} - [B] \cdot k (1 - exp (\frac{- [X]}{K_{i}}))$	(A9)
Monod + Tessier-type [65]:	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S]} - [B] \cdot k (exp (\frac{- [X]}{K_{i}}) - exp (\frac{- [X]}{K_{X}}))$	(A10)
competitive inhibition:	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} (1 + \frac{[X]}{K_{i}}) + [S]}$	(A11)
non-competitive inhibition:	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max}}{1 + \frac{[X]}{K_{i}}} \cdot \frac{[S]}{K_{S} + [S]}$	(A12)
uncompetitive inhibition:	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S] (1 + \frac{[X]}{K_{i}})}$	(A13)
non-competitive inhibition using negative Hill	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S]} \cdot \frac{k \cdot {K_{i}}^{n}}{{K_{i}}^{n} + {[X]}^{n}}$	(A14)
non-competitive inhibition using negative Moser	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S]} \cdot \frac{k \cdot K_{i}}{K_{i} + {[X]}^{n}}$	(A15)
non-competitive exponential inhibition	$\frac{d [B]}{d t} = [B] \cdot \frac{μ_{\max} [S]}{K_{S} + [S]} \cdot \frac{k}{{K_{i}}^{[X]}}$	(A16)