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Table 3 Convenience rate laws for common reaction stoichiometries

From: Bringing metabolic networks to life: convenience rate law and thermodynamic constraints

Reaction formula Rate law Turnover rates k ± c a t MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGRbWAdaqhaaWcbaGaeyySaelabaacbaGae83yamMae8xyaeMae8hDaqhaaaaa@342E@ Irreversible
A ↔ B k + c a t a ˜ k c a t b ˜ 1 + a ˜ + b ˜ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaaieaacqWFJbWycqWFHbqycqWF0baDaaGccuWGHbqygaacaiabgkHiTiabdUgaRnaaDaaaleaacqGHsislaeaacqWFJbWycqWFHbqycqWF0baDaaGccuWGIbGygaacaaqaaiabigdaXiabgUcaRiqbdggaHzaaiaGaey4kaSIafmOyaiMbaGaaaaaaaa@42CB@ k V ( k ˜ A M k ˜ B M ) ± 1 / 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGRbWAdaahaaWcbeqaaGqaaiab=zfawbaakiabcIcaOmaalaaabaGafm4AaSMbaGaadaqhaaWcbaGae8xqaeeabaGae8xta0eaaaGcbaGafm4AaSMbaGaadaqhaaWcbaGae8NqaieabaGae8xta0eaaaaakiabcMcaPmaaCaaaleqabaGaeyySaeRaeGymaeJaei4la8IaeGOmaidaaaaa@3DB9@ k + c a t a ˜ 1 + a ˜ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaaieaacqWFJbWycqWFHbqycqWF0baDaaGccuWGHbqygaacaaqaaiabigdaXiabgUcaRiqbdggaHzaaiaaaaaaa@37C2@
A + X ↔ B k + c a t a ˜ x ˜ k c a t b ˜ 1 + a ˜ + x ˜ + a ˜ x ˜ + b ˜ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaaieaacqWFJbWycqWFHbqycqWF0baDaaGccuWGHbqygaacaiqbdIha4zaaiaGaeyOeI0Iaem4AaS2aa0baaSqaaiabgkHiTaqaaiab=ngaJjab=fgaHjab=rha0baakiqbdkgaIzaaiaaabaGaeGymaeJaey4kaSIafmyyaeMbaGaacqGHRaWkcuWG4baEgaacaiabgUcaRiqbdggaHzaaiaGafmiEaGNbaGaacqGHRaWkcuWGIbGygaacaaaaaaa@4A81@ k V ( k ˜ A M k ˜ X M k ˜ B M ) ± 1 / 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGRbWAdaahaaWcbeqaaGqaaiab=zfawbaakiabcIcaOmaalaaabaGafm4AaSMbaGaadaqhaaWcbaGae8xqaeeabaGae8xta0eaaOGafm4AaSMbaGaadaqhaaWcbaGae8hwaGfabaGae8xta0eaaaGcbaGafm4AaSMbaGaadaqhaaWcbaGae8NqaieabaGae8xta0eaaaaakiabcMcaPmaaCaaaleqabaGaeyySaeRaeGymaeJaei4la8IaeGOmaidaaaaa@41B2@ k + c a t a ˜ x ˜ 1 + a ˜ + x ˜ + a ˜ x ˜ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaaieaacqWFJbWycqWFHbqycqWF0baDaaGccuWGHbqygaacaiqbdIha4zaaiaaabaGaeGymaeJaey4kaSIafmyyaeMbaGaacqGHRaWkcuWG4baEgaacaiabgUcaRiqbdggaHzaaiaGafmiEaGNbaGaaaaaaaa@3F78@
A + X ↔ B + Y k + c a t a ˜ x ˜ k c a t b ˜ y ˜ 1 + a ˜ + x ˜ + a ˜ x ˜ + b ˜ + y ˜ + b ˜ y ˜ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaaieaacqWFJbWycqWFHbqycqWF0baDaaGccuWGHbqygaacaiqbdIha4zaaiaGaeyOeI0Iaem4AaS2aa0baaSqaaiabgkHiTaqaaiab=ngaJjab=fgaHjab=rha0baakiqbdkgaIzaaiaGafmyEaKNbaGaaaeaacqaIXaqmcqGHRaWkcuWGHbqygaacaiabgUcaRiqbdIha4zaaiaGaey4kaSIafmyyaeMbaGaacuWG4baEgaacaiabgUcaRiqbdkgaIzaaiaGaey4kaSIafmyEaKNbaGaacqGHRaWkcuWGIbGygaacaiqbdMha5zaaiaaaaaaa@523F@ k V ( k ˜ A M k ˜ X M k ˜ B M k ˜ Y M ) ± 1 / 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGRbWAdaahaaWcbeqaaGqaaiab=zfawbaakiabcIcaOmaalaaabaGafm4AaSMbaGaadaqhaaWcbaGae8xqaeeabaGae8xta0eaaOGafm4AaSMbaGaadaqhaaWcbaGae8hwaGfabaGae8xta0eaaaGcbaGafm4AaSMbaGaadaqhaaWcbaGae8NqaieabaGae8xta0eaaOGafm4AaSMbaGaadaqhaaWcbaGae8xwaKfabaGae8xta0eaaaaakiabcMcaPmaaCaaaleqabaGaeyySaeRaeGymaeJaei4la8IaeGOmaidaaaaa@45AD@ k + c a t a ˜ x ˜ 1 + a ˜ + x ˜ + a ˜ x ˜ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaaieaacqWFJbWycqWFHbqycqWF0baDaaGccuWGHbqygaacaiqbdIha4zaaiaaabaGaeGymaeJaey4kaSIafmyyaeMbaGaacqGHRaWkcuWG4baEgaacaiabgUcaRiqbdggaHzaaiaGafmiEaGNbaGaaaaaaaa@3F78@
2 A ↔ B k + c a t a ˜ 2 k c a t b ˜ 1 + a ˜ + a ˜ 2 + b ˜ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaaieaacqWFJbWycqWFHbqycqWF0baDaaGccuWGHbqygaacamaaCaaaleqabaGaeGOmaidaaOGaeyOeI0Iaem4AaS2aa0baaSqaaiabgkHiTaqaaiab=ngaJjab=fgaHjab=rha0baakiqbdkgaIzaaiaaabaGaeGymaeJaey4kaSIafmyyaeMbaGaacqGHRaWkcuWGHbqygaacamaaCaaaleqabaGaeGOmaidaaOGaey4kaSIafmOyaiMbaGaaaaaaaa@4759@ k V ( ( k ˜ A M ) 2 k ˜ B M ) ± 1 / 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGRbWAdaahaaWcbeqaaGqaaiab=zfawbaakiabcIcaOmaalaaabaGaeiikaGIafm4AaSMbaGaadaqhaaWcbaGae8xqaeeabaGae8xta0eaaOGaeiykaKYaaWbaaSqabeaacqaIYaGmaaaakeaacuWGRbWAgaacamaaDaaaleaacqWFcbGqaeaacqWFnbqtaaaaaOGaeiykaKYaaWbaaSqabeaacqGHXcqScqaIXaqmcqGGVaWlcqaIYaGmaaaaaa@4094@ k + cat a ˜ 2 1 + a ˜ + a ˜ 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaacqqGJbWycqqGHbqycqqG0baDaaGccuWGHbqygaacamaaCaaaleqabaGaeGOmaidaaaGcbaGaeGymaeJaey4kaSIafmyyaeMbaGaacqGHRaWkcuWGHbqygaacamaaCaaaleqabaGaeGOmaidaaaaaaaa@3C43@
2 A ↔ B + Y k + c a t a ˜ 2 k c a t b ˜ y ˜ 1 + a ˜ + a ˜ 2 + b ˜ + y ˜ + b ˜ y ˜ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaaieaacqWFJbWycqWFHbqycqWF0baDaaGccuWGHbqygaacamaaCaaaleqabaGaeGOmaidaaOGaeyOeI0Iaem4AaS2aa0baaSqaaiabgkHiTaqaaiab=ngaJjab=fgaHjab=rha0baakiqbdkgaIzaaiaGafmyEaKNbaGaaaeaacqaIXaqmcqGHRaWkcuWGHbqygaacaiabgUcaRiqbdggaHzaaiaWaaWbaaSqabeaacqaIYaGmaaGccqGHRaWkcuWGIbGygaacaiabgUcaRiqbdMha5zaaiaGaey4kaSIafmOyaiMbaGaacuWG5bqEgaacaaaaaaa@4F17@ k V ( ( k ˜ A M ) 2 k ˜ B M k ˜ Y M ) ± 1 / 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGRbWAdaahaaWcbeqaaGqaaiab=zfawbaakiabcIcaOmaalaaabaGaeiikaGIafm4AaSMbaGaadaqhaaWcbaGae8xqaeeabaGae8xta0eaaOGaeiykaKYaaWbaaSqabeaacqaIYaGmaaaakeaacuWGRbWAgaacamaaDaaaleaacqWFcbGqaeaacqWFnbqtaaGccuWGRbWAgaacamaaDaaaleaacqWFzbqwaeaacqWFnbqtaaaaaOGaeiykaKYaaWbaaSqabeaacqGHXcqScqaIXaqmcqGGVaWlcqaIYaGmaaaaaa@448F@ k + cat a ˜ 2 1 + a ˜ + a ˜ 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaacqqGJbWycqqGHbqycqqG0baDaaGccuWGHbqygaacamaaCaaaleqabaGaeGOmaidaaaGcbaGaeGymaeJaey4kaSIafmyyaeMbaGaacqGHRaWkcuWGHbqygaacamaaCaaaleqabaGaeGOmaidaaaaaaaa@3C43@
2 A + X ↔ B k + c a t a ˜ 2 x ˜ k c a t b ˜ ( 1 + a ˜ + a ˜ 2 ) ( 1 + x ˜ ) + b ˜ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaaieaacqWFJbWycqWFHbqycqWF0baDaaGccuWGHbqygaacamaaCaaaleqabaGaeGOmaidaaOGafmiEaGNbaGaacqGHsislcqWGRbWAdaqhaaWcbaGaeyOeI0cabaGae83yamMae8xyaeMae8hDaqhaaOGafmOyaiMbaGaaaeaacqGGOaakcqaIXaqmcqGHRaWkcuWGHbqygaacaiabgUcaRiqbdggaHzaaiaWaaWbaaSqabeaacqaIYaGmaaGccqGGPaqkcqGGOaakcqaIXaqmcqGHRaWkcuWG4baEgaacaiabcMcaPiabgUcaRiqbdkgaIzaaiaaaaaaa@4F9F@ k V ( ( k ˜ A M ) 2 k ˜ X M k ˜ B M ) ± 1 / 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGRbWAdaahaaWcbeqaaGqaaiab=zfawbaakiabcIcaOmaalaaabaGaeiikaGIafm4AaSMbaGaadaqhaaWcbaGae8xqaeeabaGae8xta0eaaOGaeiykaKYaaWbaaSqabeaacqaIYaGmaaGccuWGRbWAgaacamaaDaaaleaacqWFybawaeaacqWFnbqtaaaakeaacuWGRbWAgaacamaaDaaaleaacqWFcbGqaeaacqWFnbqtaaaaaOGaeiykaKYaaWbaaSqabeaacqGHXcqScqaIXaqmcqGGVaWlcqaIYaGmaaaaaa@448D@ k + cat a ˜ 2 x ˜ ( 1 + a ˜ + a ˜ 2 ) ( 1 + x ˜ ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdUgaRnaaDaaaleaacqGHRaWkaeaacqqGJbWycqqGHbqycqqG0baDaaGccuWGHbqygaacamaaCaaaleqabaGaeGOmaidaaOGafmiEaGNbaGaaaeaacqGGOaakcqaIXaqmcqGHRaWkcuWGHbqygaacaiabgUcaRiqbdggaHzaaiaWaaWbaaSqabeaacqaIYaGmaaGccqGGPaqkcqGGOaakcqaIXaqmcqGHRaWkcuWG4baEgaacaiabcMcaPaaaaaa@4493@
  1. The rate laws follow from the enzyme mechanism and reflect the reaction stoichiometry; for each case, the thermodynamically independent expression of the turnover rates and the irreversible form are also shown. We use the shortcuts a ˜ = a / k A M MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGHbqygaacaiabg2da9iabdggaHjabc+caViabdUgaRnaaDaaaleaacqqGbbqqaeaacqqGnbqtaaaaaa@34F3@ and k ˜ A M = k A G k A M MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGRbWAgaacamaaDaaaleaaieaacqWFbbqqaeaacqWFnbqtaaGccqGH9aqpcqWGRbWAdaqhaaWcbaGae8xqaeeabaGae83raCeaaOGaem4AaS2aa0baaSqaaiab=feabbqaaiab=1eanbaaaaa@38E8@ for metabolite A and analogous shortcuts for the other metabolites. For brevity, the prefactors for enzyme concentration and enzyme regulation are not shown.