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

From: 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

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 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 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 upper < max upper No XylSa condition (for eq.1)