Table 1.

The network topology formulated as a system of chemical equations. Note that R ₂=∅ and is not represented in the actual model but merely introduced here for ease of notation. The factor L is defined in Eq. 1. The symbols p _i represent the gene from which the porins are transcribed. The factor $\mathcal{\mathscr{H}}:=E_0^2/(0.001^2+E_0^2)$ denotes a Hill function; it prevents gene expression when there is no internal energy in the cell. In all experiments reported here $d_{\{P_i,E_i\}}$ were set proportional to the growth rate, i.e. the reaction rate of R.VIII, while d _R is an evolvable parameter acting on a much faster time-scale

Substrate	Product	Reaction rate	Reaction number
N i	E i+R i	$k_{N_i}\frac{N_i}{N_i+K_{N_i}}{P}_i\mathit{\text{bm}}$	R.I
E i	E 0	$k_{E_i}{E}_i$	R.II
p 1+E 0	p 1+P 1	$\left(\text{leak1}+k_{P_1}\frac{E_1^H}{E_1^H+K_{P_1}^H}{E}_0\right)L\mathit{\text{bm}}\mathcal{\mathscr{H}}$	R.III
p 2+E 0	p 2+P 2	$\left(\text{leak2}+k_{P_2}\frac{E_2^H}{E_2^H+K_{P_2}^H}\frac{K_R^H}{R^H+K_R^H}{E}_0\right)L\mathit{\text{bm}}\mathcal{\mathscr{H}}$	R.IV
R 1+P 2	B 2	k b R 1 P 2	R.V
B 2	R 1+P 2	k ub B 2	R.VI
{P i,E i,R 1}	∅	$d_{\{P_i,E_i,R_1\}}$	R.VII
E 0	b m	$g\mathit{\text{bm}}\frac{E_0}{E_0+K_g}$	R.VIII