From: Bringing metabolic networks to life: convenience rate law and thermodynamic constraints
Quantity
Symbol
unit
Formula
Gibbs free energy of formation
G i ( 0 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGhbWrdaqhaaWcbaGaemyAaKgabaGaeiikaGIaeGimaaJaeiykaKcaaaaa@31EB@
kJ/mol
G i ( 0 ) = R T ln k i G MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGhbWrdaqhaaWcbaGaemyAaKgabaGaeiikaGIaeGimaaJaeiykaKcaaOGaeyypa0JaemOuaiLaemivaqLagiiBaWMaeiOBa4Maem4AaS2aa0baaSqaaiabdMgaPbqaaGqaaiab=Deahbaaaaa@3C22@
Gibbs fr. en. for substrate binding
Δ G l i ( 0 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqHuoarcqWGhbWrdaqhaaWcbaGaemiBaWMaemyAaKgabaGaeiikaGIaeGimaaJaeiykaKcaaaaa@34B2@
Δ G l i ( 0 ) = R T ln k l i M MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqHuoarcqWGhbWrdaqhaaWcbaGaemiBaWMaemyAaKgabaGaeiikaGIaeGimaaJaeiykaKcaaOGaeyypa0JaemOuaiLaemivaqLagiiBaWMaeiOBa4Maem4AaS2aa0baaSqaaiabdYgaSjabdMgaPbqaaGqaaiab=1eanbaaaaa@4056@
Equilibrium constant
k l e q MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGRbWAdaqhaaWcbaGaemiBaWgabaacbaGae8xzauMae8xCaehaaaaa@3258@
-
ln k l e q = − ∑ i n i l ln k i G MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacyGGSbaBcqGGUbGBcqWGRbWAdaqhaaWcbaGaemiBaWgabaacbaGae8xzauMae8xCaehaaOGaeyypa0JaeyOeI0YaaabuaeaacqWGUbGBdaWgaaWcbaGaemyAaKMaemiBaWgabeaaaeaacqWGPbqAaeqaniabggHiLdGccyGGSbaBcqGGUbGBcqWGRbWAdaqhaaWcbaGaemyAaKgabaGae83raCeaaaaa@45A5@
Turnover rate
k ± l c a t MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGRbWAdaqhaaWcbaGaeyySaeRaemiBaWgabaacbaGae83yamMae8xyaeMae8hDaqhaaaaa@358F@
1/s
ln k ± l c a t = ln k l V ∓ 1 2 ∑ i n i l ( ln k i G + ln k l i M ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacyGGSbaBcqGGUbGBcqWGRbWAdaqhaaWcbaGaeyySaeRaemiBaWgabaacbaGae83yamMae8xyaeMae8hDaqhaaOGaeyypa0JagiiBaWMaeiOBa4Maem4AaS2aa0baaSqaaiabdYgaSbqaaiab=zfawbaakiabloHiTnaalaaabaGaeGymaedabaGaeGOmaidaamaaqafabaGaemOBa42aaSbaaSqaaiabdMgaPjabdYgaSbqabaaabaGaemyAaKgabeqdcqGHris5aOGaeiikaGIagiiBaWMaeiOBa4Maem4AaS2aa0baaSqaaiabdMgaPbqaaiab=DeahbaakiabgUcaRiGbcYgaSjabc6gaUjabdUgaRnaaDaaaleaacqWGSbaBcqWGPbqAaeaacqWFnbqtaaGccqGGPaqkaaa@5CD7@
Maximal velocity
v ± l max MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG2bGDdaqhaaWcbaGaeyySaeRaemiBaWgabaGagiyBa0MaeiyyaeMaeiiEaGhaaaaa@35C3@
mM/s
ln v ± l m a x = ln E l + ln k l V ∓ 1 2 ∑ i n i l ( ln k i G + ln k l i M ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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1eanbaakiabcMcaPaaa@635B@