Skip to main content

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[ EIP]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[ NPrP]/dt = k2·[ EI P]]tot[ NPr] −k−2·[NPr P][ EI]tot − (k3·[ NPr P][ EIIA] −k−3·[ NPr][EIIA P])
(7) d[ EIIAP]/dt = k3·[ NPrP][EIIA]−k−3·[ NPr][ EIIAP]
(8) [EI][PEP] = \(\phantom {\dot {i}\!}\!K_{{\mathrm {d}}_{1}}\cdot [\!\text {EI}^{\text {PEP}}]\)
(9) [ EIP][Pyr] = \(\phantom {\dot {i}\!}\!K_{\mathrm {d}_{2}} \cdot \left [\!\text {EI}\sim {\mathrm {P}}^{\text {Pyr}}\right ]\)
(10) [ EI]T = [EI]+ [ EIPEP]+ [ EIPPyr]+[EI P]
(11) [ NPr]T = [ NPr]+[ NPrP]
(12) [ EIIA]T = [ EIIA]+[ EIIAP]
  1. *{SpoT\(_{\text {sd}}\}= \frac {\alpha }{1+\alpha }\), {SpoT\(_{\text {hd}}\}=\frac {1}{1+\alpha },\alpha =K_{\text {SpoT}}\cdot \frac {[\text {NPr} \sim \mathrm {P}]}{[\text {NPr} \sim \mathrm {P}]+K_{2}}/\frac {K_{3}}{[\text {EIIA} \sim \mathrm {P}]+K_{3}}\). {SpoTsd}and {SpoThd}represent the fraction of total SpoT for synthetase and hydrolase, respectively