Table 1 Equations of our mathematical model*
From: Cell cycle control and environmental response by second messengers in Caulobacter crescentus
(1) | d[ cdG]/dt | = | \(k_{\mathrm {s.cdG}}\cdot {\!\mathrm {[\!DGC]}}\cdot {\frac {K_{1}^{2}}{K_{1}^{2}+[\text {cdG}]^{2}}}\cdot {\frac {[\text {GTP}]^{2}}{[\text {GTP}]^{2}+K_{\mathrm {m1}}^{2}}}-k_{\mathrm {d.cdG}}\cdot {\mathrm {[\!PDE]}}\cdot {\frac {\mathrm {[cdG]}}{\mathrm {[cdG]}+K_{\mathrm {m2}}}}\) |
(2) | d[ (p)ppGpp]/dt | = | \(k_{\mathrm {s.(p)ppGpp}}\cdot {\left \{\text {SpoT}_{\text {sd}}\right \}}\cdot {\frac {[\text {GTP}]}{[\text {GTP}]+K_{\mathrm {m3}}}}-k_{\mathrm {d.(p)ppGpp}}\cdot {\left \{\text {SpoT}_{\text {hd}}\right \}}\cdot {\frac {[\mathrm {(p)ppGpp}]}{[\mathrm {(p)ppGpp}]+K_{\mathrm {m4}}}}\) |
(3) | d[ GTP]/dt | = | \(k_{\mathrm {s.GTP}}\cdot {[\text {GMP}]}-k_{\mathrm {d.GTP}}\cdot {[\text {GTP}]}-k_{\mathrm {s.(p)ppGpp}}\cdot {\left \{\text {SpoT}_{\text {sd}}\right \}}\cdot {\frac {[\text {GTP}]}{[\text {GTP}]+K_{\mathrm {m3}}}}\) |
\(+k_{\mathrm {d.(p)ppGpp}}\cdot {\left \{\text {SpoT}_{\text {hd}}\right \}}\cdot {\frac {[\mathrm {(p)ppGpp}]}{[\mathrm {(p)ppGpp}]+K_{\mathrm {m4}}}}-2\cdot {k_{\mathrm {s.cdG}}\cdot {\mathrm {[\!DGC]}}\cdot {\frac {K_{1}^{2}}{K_{1}^{2}+[\text {cdG}]^{2}}}\cdot {\frac {[\text {GTP}]^{2}}{[\text {GTP}]^{2}+K_{\mathrm {m1}}^{2}}}}\) | |||
(4) | d[ GMP]/dt | = | \(2\cdot {k_{\mathrm {d.cdG}}\cdot {\mathrm {[PDE]}}\cdot {\frac {\mathrm {[cdG]}}{\mathrm {[cdG]}+K_{\mathrm {m2}}}}}+k_{\mathrm {d.GTP}}\cdot {[\!\text {GTP}]}-k_{\mathrm {s.GTP}}\cdot {[\!\text {GMP}]}\) |
(5) | d[ EI∼P]tot/dt | = | \(k_{1}\cdot {\frac {K_{4}+\epsilon [\text {Gln}]}{K_{4}+[\text {Gln}]}}\cdot [\!\text {EI}^{\text {PEP}}]\,-\,k_{-1}\cdot \left [\!\text {EI}\!\sim \mathrm {P}^{\text {Pyr}}\right ]\!-k_{2}\cdot [\!\text {EI}\!\sim {\mathrm {P}}]_{\text {tot}}[\!\text {NPr}]+k_{-2}\cdot [\!\text {NPr}\!\sim {\mathrm {P}}][\text {EI}]]_{\text {tot}}\) |
(6) | d[ NPr∼P]/dt | = | k2·[ EI ∼ P]]tot[ NPr] −k−2·[NPr ∼ P][ EI]tot − (k3·[ NPr ∼ P][ EIIA] −k−3·[ NPr][EIIA ∼ P]) |
(7) | d[ EIIA∼P]/dt | = | k3·[ NPr∼P][EIIA]−k−3·[ NPr][ EIIA∼P] |
(8) | [EI][PEP] | = | \(\phantom {\dot {i}\!}\!K_{{\mathrm {d}}_{1}}\cdot [\!\text {EI}^{\text {PEP}}]\) |
(9) | [ EI∼P][Pyr] | = | \(\phantom {\dot {i}\!}\!K_{\mathrm {d}_{2}} \cdot \left [\!\text {EI}\sim {\mathrm {P}}^{\text {Pyr}}\right ]\) |
(10) | [ EI]T | = | [EI]+ [ EIPEP]+ [ EI∼PPyr]+[EI ∼ P] |
(11) | [ NPr]T | = | [ NPr]+[ NPr∼P] |
(12) | [ EIIA]T | = | [ EIIA]+[ EIIA∼P] |