The logic layout of the TOL network of Pseudomonas putida pWW0 plasmid stems from a metabolic amplifier motif (MAM) that optimizes biodegradation of m-xylene

Table 1 Equations and threshold inequalities used to simulate the TOL network

N°	PL equations for the TOL model	Description
1	dupper/dt = k ⁰ _upper * s ⁺ (XylR, θ _XylR ) s* ⁺ (m _xyl , θ _mxyl ) - g _upper * upper	Upper pathway expression
2	dXylS/dt = k ⁰ _XylS + k ¹ _XylS * s ⁺ (XylR, θ _XylR ) s* ⁺ (m _xyl , θ _mxyl ) - g _XylS * XylS	XylS expression
3	dmeta/dt = k ⁰ _meta * s ⁺ (XylS, θ ² _XylSh ) + k ¹ _meta * s ⁺ (XylS, θ ¹ _XylSi ) s* ⁺ (upper, θ _upper ) s* ⁺ (m _xyl , θ _mxyl ) - g _meta * meta	Meta pathway expression
4	dXylR/dt = k ⁰ _XylR - g _XylR * XylR	XylR expression
	Parameter inequalities
	zero _upper <θ _upper < k ⁰ _upper /g _upper < max _upper	Parameter inequalities for equation 1
	zero _XylS < θ ¹ _XylSi < k ⁰ _XylS /g _XylS < θ ² _XylSh < (k ⁰ _XylS + k ¹ _XylS )/g _XylS < max _XylS	Parameter inequalities for equation 2
	zero _meta < θ _meta < k ⁰ _meta /g _meta < k ¹ _meta /g _meta < (k ⁰ _meta + k ¹ _meta )/g _meta < max _meta	Parameter inequalities for equation 3
	zero _XylR <θ _XylR < k ⁰ _XylR /g _XylR < max _XylR	Parameter inequalities for equation 4
	Alternative parameter inequalities
	zero _XylS < θ ¹ _XylSi < k ⁰ _XylS /g _XylS < (k ⁰ _XylS + k ¹ _XylS )/g _XylS < θ ² _XylSh < max _XylS	No XylS hyper-expression condition (for eq. 2)
	zero _upper < k ⁰ _upper /g _upper <θ _upper < max _upper	No XylSa condition (for eq.1)