(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]
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