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Table 1 Kinetic rate laws used in the small example network.

From: 13C labeling experiments at metabolic nonstationary conditions: An exploratory study

Reaction

Mechanism

Inhibitor

Kinetic

upt

Michaelis-Menten, 1 Inhibitor

A

v max A K m A ( 1 + A K I ) + A e x ( A K I ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWG2bGDdaWgaaqaaiGbc2gaTjabcggaHjabcIha4bqabaGaemyqaeeabaGaem4saS0aaSbaaeaacqWGTbqBcqWGbbqqaeqaamaabmaabaGaeGymaeJaey4kaSYaaSaaaeaacqWGbbqqaeaacqWGlbWsdaWgaaqaaiabdMeajbqabaaaaaGaayjkaiaawMcaaiabgUcaRiabdgeabnaaBaaabaGaemyzauMaemiEaGhabeaadaqadaqaamaalaaabaGaemyqaeeabaGaem4saS0aaSbaaeaacqWGjbqsaeqaaaaaaiaawIcacaGLPaaaaaaaaa@4792@

v1

reversible Michaelis-Menten

 

v max ( A B K e q ) K m A ( 1 + B K m P ) + A MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWG2bGDdaWgaaqaaiGbc2gaTjabcggaHjabcIha4bqabaWaaeWaaeaacqWGbbqqcqGHsisldaWcaaqaaiabdkeacbqaaiabdUealnaaBaaabaGaemyzauMaemyCaehabeaaaaaacaGLOaGaayzkaaaabaGaem4saS0aaSbaaeaacqWGTbqBcqWGbbqqaeqaamaabmaabaGaeGymaeJaey4kaSYaaSaaaeaacqWGcbGqaeaacqWGlbWsdaWgaaqaaiabd2gaTjabdcfaqbqabaaaaaGaayjkaiaawMcaaiabgUcaRiabdgeabbaaaaa@48AA@

v2

2 Substrate Hill-Kinetic

 

v max B h A E h B ( K m A + B h A ) ( K m B + E h B ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWG2bGDdaWgaaqaaiGbc2gaTjabcggaHjabcIha4bqabaGaemOqai0aaWbaaeqabaGaemiAaGMaemyqaeeaaiabdweafnaaCaaabeqaaiabdIgaOjabdkeacbaaaeaadaqadaqaaiabdUealnaaBaaabaGaemyBa0MaemyqaeeabeaacqGHRaWkcqWGcbGqdaahaaqabeaacqWGObaAcqWGbbqqaaaacaGLOaGaayzkaaWaaeWaaeaacqWGlbWsdaWgaaqaaiabd2gaTjabdkeacbqabaGaey4kaSIaemyrau0aaWbaaeqabaGaemiAaGMaemOqaieaaaGaayjkaiaawMcaaaaaaaa@4CBF@

v3

Michaelis-Menten, 1 competitive Inhibitor

D

v max C K m A ( 1 + D K I ) + C MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWG2bGDdaWgaaqaaiGbc2gaTjabcggaHjabcIha4bqabaGaem4qameabaGaem4saS0aaSbaaeaacqWGTbqBcqWGbbqqaeqaamaabmaabaGaeGymaeJaey4kaSYaaSaaaeaacqWGebaraeaacqWGlbWsdaWgaaqaaiabdMeajbqabaaaaaGaayjkaiaawMcaaiabgUcaRiabdoeadbaaaaa@3FB4@

v4

Michaelis-Menten, 1 competitive Inhibitor

C

v max D K m A ( 1 + C K I ) + D MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWG2bGDdaWgaaqaaiGbc2gaTjabcggaHjabcIha4bqabaGaemiraqeabaGaem4saS0aaSbaaeaacqWGTbqBcqWGbbqqaeqaamaabmaabaGaeGymaeJaey4kaSYaaSaaaeaacqWGdbWqaeaacqWGlbWsdaWgaaqaaiabdMeajbqabaaaaaGaayjkaiaawMcaaiabgUcaRiabdseaebaaaaa@3FB6@

v5

reversible Michaelis-Menten

 

v max ( A E K e q ) K m A ( 1 + E K m P ) + B MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWG2bGDdaWgaaqaaiGbc2gaTjabcggaHjabcIha4bqabaWaaeWaaeaacqWGbbqqcqGHsisldaWcaaqaaiabdweafbqaaiabdUealnaaBaaabaGaemyzauMaemyCaehabeaaaaaacaGLOaGaayzkaaaabaGaem4saS0aaSbaaeaacqWGTbqBcqWGbbqqaeqaamaabmaabaGaeGymaeJaey4kaSYaaSaaaeaacqWGfbqraeaacqWGlbWsdaWgaaqaaiabd2gaTjabdcfaqbqabaaaaaGaayjkaiaawMcaaiabgUcaRiabdkeacbaaaaa@48B8@

v6

Michaelis-Menten

 

v max E K m A + E MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWG2bGDdaWgaaqaaiGbc2gaTjabcggaHjabcIha4bqabaGaemyraueabaGaem4saS0aaSbaaeaacqWGTbqBcqWGbbqqaeqaaiabgUcaRiabdweafbaaaaa@38E5@