Supplementary Figure 1.
A Mathematical Model for the Flow of Carbon Through the Branched Chain Amino Acid Pathways of Escherichia coli K12.

(* call Cellerator and kMech into Mathematica Kernel *) << myPadRight.m ; <br /> << cellerator.m ; << kMech.m ; Off[General :: "spell1"] ; Off[General :: "spell"] ;

myPadRight Version 0.3 for Cellerator Loaded.

Cellerator™ Version 1.0 update 3.1002, loaded at Oct. 7, 2003, 17:28:17\n©2001,2002 Jet Propulsion Laboratory, California Institute of Technology.  U.S. Government Sponsorship Acknowledged. All rights reserved. \nPatent Pending (USPTO App 09993291).\nThe contents of this file may not be copied, distributed or transferred without written permission.

Cellerator™ 1.0 update 3.1002 load (using Mathematica Version 4.2 for Microsoft Windows (June 5, 2002)) complete at October 7, 2003 17:28:21

kMech is loaded

(* kMech Input of Enzyme Mechanisms for the Mathematical Modeling of    L - isoleucine (ILE), L - valine (VAL), and L - leucine (LEU) Biosynthesis *) ILESynthesis = Union[ {{Underoverscript[{Thr} ==> {aKB, NH3}, {{Val}, {Ile}}, arg3], GMWC[nGMWC -> nTDA, cGMWC -> cTDA, LGMWC -> L0TDA, vmax -> kcat$TDA, KGMWC -> {KmThr, KaVal, KiIle}]}}, {{Overscript[                     aKB ↔ propionylCoA, KDC], kfKDCaKB, krKDCaKB, kcat$KDC$aKB}}, Enz[Overscript[{Pyr, aKB} ↔ {CO 2 , a AHB}, AHASI, AHASICH3CO], PingPong[kfAHASIPyr, krAHASIPyr, kcat$AHASI$Pyr, kfAHASIaKB, krAHASIaKB, kcat$AHASI$aKB], NCI[Val, kfiAHASIPyrVal, kriAHASIPyrVal, kfiAHASIaKBVal, kriAHASIaKBVal, residualRateAHASIValaKB]], Enz[Overscript[{Pyr, aKB} ↔ {CO 2 , aAHB}, AHASII, AHASIICH3CO], PingPong[kfAHASIIPyr, krAHASIIPyr, kcat$AHASII$Pyr, kfAHASIIaKB, krAHASIIaKB, kcat$AHASII$aKB]], Enz[Overscript[{Pyr, aKB} ↔ {CO 2 , a AHB}, AHASIII, AHASIIICH3CO], PingPong[kfAHASIIIPyr, krAHASIIIPyr, kcat$AHASIII$Pyr, kfAHASIIIaKB, krAHASIIIaKB, kcat$AHASIII$aKB], NCI[Val, kfiAHASIIIPyrVal, kriAHASIIIPyrVal, kfiAHASIIIaKBVal, kriAHASIIIaKBVal, residualRateAHASIIIValaKB]], Enz[Overscript[{aAHB, NADPH} ↔ {aDMV, NADP}, IR], BiBi[kfIRaAHB, krIRaAHB, kcat$IR$aAHB]], {{Overscript[aDMV ↔ aKMV, DAD], kfDADaDMV, krDADaDMV, kcat$DAD$aDMV}}, Enz[Overscript[{Glu, aKMV} ↔ {aKG, Ile}, TB, TBNH2], PingPong[fkfTBGlu, fkrTBGlu, fkcat$TB$Glu, fkfTBaKMV, fkrTBaKMV, fkcat$TB$aKMV]], Enz[Overscript[{Ile, aKG} ↔ {aKMV, Glu}, TB, TBNH2], PingPong[rkfTBIle, rkrTBIle, rkcat$TB$Ile, rkfTBaKG, rkrTBaKG, rkcat$TB$aKG]], {{Overscript[exIle ↔ Ile, LIVI], kfLIVIexIle, krLIVIexIle, kcat$LIVI$exIle}}, {{Overscript[exIle ↔ Ile, LIVII], kfLIVIIexIle, krLIVIIexIle, kcat$LIVII$exIle}}, {{aKMV -> acetylCoA, kcat$aKMV}}, {{Ile -> protein, kcat$Ile}}] ; VALSynthesis = Union[ Enz[Overscript[{Pyr, Pyr} ↔ {CO 2 , a AL}, AHASI, AHASICH3CO], PingPong[kfAHASIPyr, krAHASIPyr, kcat$AHASI$Pyr, kfAHASIPyr2, krAHASIPyr2, kcat$AHASI$Pyr2], NCI[Val, kfiAHASIPyrVal, kriAHASIPyrVal, kfiAHASIPyr2Val, kriAHASIPyr2Val, residualRateAHASIValPyr2]], Enz[Overscript[{Pyr, Pyr} ↔ {CO 2 , a AL}, AHASII, AHASIICH3CO], PingPong[kfAHASIIPyr, krAHASIIPyr, kcat$AHASII$Pyr, kfAHASIIPyr2, krAHASIIPyr2, kcat$AHASII$Pyr2]], Enz[Overscript[{Pyr, Pyr} ↔ {CO 2 , a AL}, AHASIII, AHASIIICH3CO], PingPong[kfAHASIIIPyr, krAHASIIIPyr, kcat$AHASIII$Pyr, kfAHASIIIPyr2, krAHASIIIPyr2, kcat$AHASIII$Pyr2], NCI[Val, kfiAHASIIIPyrVal, kriAHASIIIPyrVal, kfiAHASIIIPyr2Val, kriAHASIIIPyr2Val, residualRateAHASIIIValPyr2]], Enz[Overscript[{aAL, NADPH} ↔ {aDHIV, NADP}, IR], BiBi[kfIRaAL, krIRaAL, kcat$IR$aAL]], {{Overscript[aDHIV ↔ aKIV, DAD], kfDADaDHIV, krDADaDHIV, kcat$DAD$aDHIV}}, Enz[Overscript[{Ala, aKIV} ↔ {Pyr, Val}, TC, TCNH2], PingPong[fkfTCAla, fkrTCAla, fkcat$TC$Ala, fkfTCaKIV, fkrTCaKIV, fkcat$TC$aKIV]], Enz[Overscript[{Val, Pyr} ↔ {aKIV, Ala}, TC, TCNH2], PingPong[rkfTCVal, rkrTCVal, rkcat$TC$Val, rkfTCPyr, rkrTCPyr, rkcat$TC$Pyr]], Enz[Overscript[{Glu, aKIV} ↔ {aKG, Val}, TB, TBNH2], PingPong[fkfTBGlu, fkrTBGlu, fkcat$TB$Glu, fkfTBaKIV, fkrTBaKIV, fkcat$TB$aKIV]], Enz[Overscript[{Val, aKG} ↔ {aKIV, Glu}, TB, TBNH2], PingPong[rkfTBVal, rkrTBVal, rkcat$TB$Val, rkfTBaKG, rkrTBaKG, rkcat$TB$aKG]], {{Overscript[exVal ↔ Val, LIVI], kfLIVIexVal, krLIVIexVal, kcat$LIVI$exVal}}, {{Overscript[exVal ↔ Val, LIVII], kfLIVIIexVal, krLIVIIexVal, kcat$LIVII$exVal}}, {{aKIV -> pantothenate, kcat$aKIV}}, {{Val -> protein, kcat$Val}}] ; LEUSynthesis = Union[ Enz[Overscript[{acetylCoA, aKIV} ↔ {CoA , aIPM}, IPMS, IPMSacetyl], PingPong[kfIPMSacetylCoA, krIPMSacetylCoA, kcat$IPMS$acetylCoA, kfIPMSaKIV, krIPMSaKIV, kcat$IPMS$aKIV], CI[Leu, kfiIPMSLeu, kriIPMSLeu], NCI[Leu, kfiIPMSacetylLeu, kriIPMSacetylLeu]], {{Overscript[aIPM ↔ bIPM, IPMI], kfIPMIaIPM, krIPMIaIPM, kcat$IPMI$aIPM}}, {{Overscript[bIPM ↔ aIPM, IPMI], kfIPMIbIPM, krIPMIbIPM, kcat$IPMI$bIPM}}, Enz[Overscript[{bIPM, NAD} ↔ {aKIC, NADH}, IPMDH], BiBi[kfIPMDHbIPM, krIPMDHbIPM, kcat$IPMDH$bIPM]], Enz[Overscript[{Glu, aKIC} ↔ {aKG, Leu}, TB, TBNH2], PingPong[fkfTBGlu, fkrTBGlu, fkcat$TB$Glu, fkfTBaKIC, fkrTBaKIC, fkcat$TB$aKIC]], Enz[Overscript[{Leu, aKG} ↔ {aKIC, Glu}, TB, TBNH2], PingPong[rkfTBLeu, rkrTBLeu, rkcat$TB$Leu, rkfTBaKG, rkrTBaKG, rkcat$TB$aKG]], {{aKIC -> glutarylCoA, kcat$aKIC}}, {{Overscript[exLeu ↔ Leu, LIVI], kfLIVIexLeu, krLIVIexLeu, kcat$LIVI$exLeu}}, {{Overscript[exLeu ↔ Leu, LIVII], kfLIVIIexLeu, krLIVIIexLeu, kcat$LIVII$exLeu}}, {{Overscript[exLeu ↔ Leu, LS], kfLSexLeu, krLSexLeu, kcat$LS$exLeu}}, {{Leu -> protein, kcat$Leu}}] ; ILE$VAL$LEU$Synthesis = Union[ILESynthesis, VALSynthesis, LEUSynthesis]

(* kMech - generated Elementary Reactions for Cellerator *)

{{aKIC -> glutarylCoA, kcat$aKIC}, {aKIV -> pantothenate, kcat$aKIV}, {aKMV -> acetylCoA, kcat$aKMV}, {Ile -> protein, kcat$Ile}, {Leu -> protein, kcat$Leu}, {Val -> protein, kcat$Val}, {$Complex$acetylCoA$IPMS$ -> CoA + IPMSacetyl, kcat$IPMS$acetylCoA}, {$Complex$aKB$AHASICH3CO$ -> aAHB + AHASI, kcat$AHASI$aKB}, {$Complex$aKB$AHASICH3CO$Val$ -> aAHB + $Complex$AHASICH3CO$Val$, kcat$AHASI$aKB residualRateAHASIValaKB}, {$Complex$aKB$AHASIICH3CO$ -> aAHB + AHASII, kcat$AHASII$aKB}, {$Complex$aKB$AHASIIICH3CO$ -> aAHB + AHASIII, kcat$AHASIII$aKB}, {$Complex$aKB$AHASIIICH3CO$Val$ -> aAHB + $Complex$AHASIIICH3CO$Val$, kcat$AHASIII$aKB residualRateAHASIIIValaKB}, {$Complex$aKG$TBNH2$ -> Glu + TB, rkcat$TB$aKG}, {$Complex$aKIC$TBNH2$ -> Leu + TB, fkcat$TB$aKIC}, {$Complex$aKIV$IPMSacetyl$ -> aIPM + IPMS, kcat$IPMS$aKIV}, {$Complex$aKIV$TBNH2$ -> TB + Val, fkcat$TB$aKIV}, {$Complex$aKIV$TCNH2$ -> TC + Val, fkcat$TC$aKIV}, {$Complex$aKMV$TBNH2$ -> Ile + TB, fkcat$TB$aKMV}, {$Complex$Ala$TC$ -> Pyr + TCNH2, fkcat$TC$Ala}, {$Complex$Glu$TB$ -> aKG + TBNH2, fkcat$TB$Glu}, {$Complex$Ile$TB$ -> aKMV + TBNH2, rkcat$TB$Ile}, {$Complex$IPMDH$bIPM$NAD$ -> aKIC + IPMDH + NADH, kcat$IPMDH$bIPM}, {$Complex$IR$aAHB$NADPH$ -> aDMV + IR + NADP, kcat$IR$aAHB}, {$Complex$IR$aAL$NADPH$ -> aDHIV + IR + NADP, kcat$IR$aAL}, {$Complex$Leu$TB$ -> aKIC + TBNH2, rkcat$TB$Leu}, {$Complex$Pyr$AHASICH3CO$ -> aAL + AHASI, kcat$AHASI$Pyr2}, {$Complex$Pyr$AHASICH3CO$Val$ -> aAL + $Complex$AHASICH3CO$Val$, kcat$AHASI$Pyr2 residualRateAHASIValPyr2}, {$Complex$Pyr$AHASIICH3CO$ -> aAL + AHASII, kcat$AHASII$Pyr2}, {$Complex$Pyr$AHASIIICH3CO$ -> aAL + AHASIII, kcat$AHASIII$Pyr2}, {$Complex$Pyr$AHASIIICH3CO$Val$ -> aAL + $Complex$AHASIIICH3CO$Val$, kcat$AHASIII$Pyr2 residualRateAHASIIIValPyr2}, {$Complex$Pyr$AHASIII$ -> AHASIIICH3CO + CO2, kcat$AHASIII$Pyr}, {$Complex$Pyr$AHASIII$Val$ -> CO2 + $Complex$AHASIII$Val$, kcat$AHASIII$Pyr residualRateAHASIIIValaKB}, {$Complex$Pyr$AHASIII$Val$ -> CO2 + $Complex$AHASIII$Val$, kcat$AHASIII$Pyr residualRateAHASIIIValPyr2}, {$Complex$Pyr$AHASII$ -> AHASIICH3CO + CO2, kcat$AHASII$Pyr}, {$Complex$Pyr$AHASI$ -> AHASICH3CO + CO2, kcat$AHASI$Pyr}, {$Complex$Pyr$AHASI$Val$ -> CO2 + $Complex$AHASI$Val$, kcat$AHASI$Pyr residualRateAHASIValaKB}, {$Complex$Pyr$AHASI$Val$ -> CO2 + $Complex$AHASI$Val$, kcat$AHASI$Pyr residualRateAHASIValPyr2}, {$Complex$Pyr$TCNH2$ -> Ala + TC, rkcat$TC$Pyr}, {$Complex$Val$TB$ -> aKIV + TBNH2, rkcat$TB$Val}, {$Complex$Val$TC$ -> aKIV + TCNH2, rkcat$TC$Val}, {Underoverscript[{Thr} ==> {aKB, NH3}, {{Val}, {Ile}}, arg3], GMWC[nGMWC -> nTDA, cGMWC -> cTDA, LGMWC -> L0TDA, vmax -> kcat$TDA, KGMWC -> {KmThr, KaVal, KiIle}]}, {AHASICH3CO + aKB ↔ $Complex$aKB$AHASICH3CO$, kfAHASIaKB, krAHASIaKB}, {AHASIICH3CO + aKB ↔ $Complex$aKB$AHASIICH3CO$, kfAHASIIaKB, krAHASIIaKB}, {AHASIIICH3CO + aKB ↔ $Complex$aKB$AHASIIICH3CO$, kfAHASIIIaKB, krAHASIIIaKB}, {acetylCoA + IPMS ↔ $Complex$acetylCoA$IPMS$, kfIPMSacetylCoA, krIPMSacetylCoA}, {aKIV + IPMSacetyl ↔ $Complex$aKIV$IPMSacetyl$, kfIPMSaKIV, krIPMSaKIV}, {IPMS + Leu ↔ $Complex$IPMS$Leu$, kfiIPMSLeu, kriIPMSLeu}, {IPMSacetyl + Leu ↔ $Complex$IPMSacetyl$Leu$, kfiIPMSacetylLeu, kriIPMSacetylLeu}, {bIPM + IPMDH + NAD ↔ $Complex$IPMDH$bIPM$NAD$, kfIPMDHbIPM, krIPMDHbIPM}, {aAHB + IR + NADPH ↔ $Complex$IR$aAHB$NADPH$, kfIRaAHB, krIRaAHB}, {aAL + IR + NADPH ↔ $Complex$IR$aAL$NADPH$, kfIRaAL, krIRaAL}, {AHASI + Pyr ↔ $Complex$Pyr$AHASI$, kfAHASIPyr, krAHASIPyr}, {AHASICH3CO + Pyr ↔ $Complex$Pyr$AHASICH3CO$, kfAHASIPyr2, krAHASIPyr2}, {AHASII + Pyr ↔ $Complex$Pyr$AHASII$, kfAHASIIPyr, krAHASIIPyr}, {AHASIICH3CO + Pyr ↔ $Complex$Pyr$AHASIICH3CO$, kfAHASIIPyr2, krAHASIIPyr2}, {AHASIII + Pyr ↔ $Complex$Pyr$AHASIII$, kfAHASIIIPyr, krAHASIIIPyr}, {AHASIIICH3CO + Pyr ↔ $Complex$Pyr$AHASIIICH3CO$, kfAHASIIIPyr2, krAHASIIIPyr2}, {Glu + TB ↔ $Complex$Glu$TB$, fkfTBGlu, fkrTBGlu}, {Ile + TB ↔ $Complex$Ile$TB$, rkfTBIle, rkrTBIle}, {Leu + TB ↔ $Complex$Leu$TB$, rkfTBLeu, rkrTBLeu}, {aKG + TBNH2 ↔ $Complex$aKG$TBNH2$, rkfTBaKG, rkrTBaKG}, {aKIC + TBNH2 ↔ $Complex$aKIC$TBNH2$, fkfTBaKIC, fkrTBaKIC}, {aKIV + TBNH2 ↔ $Complex$aKIV$TBNH2$, fkfTBaKIV, fkrTBaKIV}, {aKMV + TBNH2 ↔ $Complex$aKMV$TBNH2$, fkfTBaKMV, fkrTBaKMV}, {Ala + TC ↔ $Complex$Ala$TC$, fkfTCAla, fkrTCAla}, {aKIV + TCNH2 ↔ $Complex$aKIV$TCNH2$, fkfTCaKIV, fkrTCaKIV}, {Pyr + TCNH2 ↔ $Complex$Pyr$TCNH2$, rkfTCPyr, rkrTCPyr}, {AHASI + Val ↔ $Complex$AHASI$Val$, kfiAHASIPyrVal, kriAHASIPyrVal}, {AHASICH3CO + Val ↔ $Complex$AHASICH3CO$Val$, kfiAHASIaKBVal, kriAHASIaKBVal}, {AHASICH3CO + Val ↔ $Complex$AHASICH3CO$Val$, kfiAHASIPyr2Val, kriAHASIPyr2Val}, {AHASIII + Val ↔ $Complex$AHASIII$Val$, kfiAHASIIIPyrVal, kriAHASIIIPyrVal}, {AHASIIICH3CO + Val ↔ $Complex$AHASIIICH3CO$Val$, kfiAHASIIIaKBVal, kriAHASIIIaKBVal}, {AHASIIICH3CO + Val ↔ $Complex$AHASIIICH3CO$Val$, kfiAHASIIIPyr2Val, kriAHASIIIPyr2Val}, {TB + Val ↔ $Complex$Val$TB$, rkfTBVal, rkrTBVal}, {TC + Val ↔ $Complex$Val$TC$, rkfTCVal, rkrTCVal}, {aKB + $Complex$AHASICH3CO$Val$ ↔ $Complex$aKB$AHASICH3CO$Val$, kfAHASIaKB, krAHASIaKB}, {Pyr + $Complex$AHASICH3CO$Val$ ↔ $Complex$Pyr$AHASICH3CO$Val$, kfAHASIPyr2, krAHASIPyr2}, {aKB + $Complex$AHASIIICH3CO$Val$ ↔ $Complex$aKB$AHASIIICH3CO$Val$, kfAHASIIIaKB, krAHASIIIaKB}, {Pyr + $Complex$AHASIIICH3CO$Val$ ↔ $Complex$Pyr$AHASIIICH3CO$Val$, kfAHASIIIPyr2, krAHASIIIPyr2}, {Pyr + $Complex$AHASIII$Val$ ↔ $Complex$Pyr$AHASIII$Val$, kfAHASIIIPyr, krAHASIIIPyr}, {Pyr + $Complex$AHASI$Val$ ↔ $Complex$Pyr$AHASI$Val$, kfAHASIPyr, krAHASIPyr}, {Val + $Complex$aKB$AHASICH3CO$ ↔ $Complex$aKB$AHASICH3CO$Val$, kfiAHASIaKBVal, kriAHASIaKBVal}, {Val + $Complex$aKB$AHASIIICH3CO$ ↔ $Complex$aKB$AHASIIICH3CO$Val$, kfiAHASIIIaKBVal, kriAHASIIIaKBVal}, {Leu + $Complex$aKIV$IPMSacetyl$ ↔ $Complex$aKIV$IPMSacetyl$Leu$, kfiIPMSacetylLeu, kriIPMSacetylLeu}, {aKIV + $Complex$IPMSacetyl$Leu$ ↔ $Complex$aKIV$IPMSacetyl$Leu$, kfIPMSaKIV, krIPMSaKIV}, {Val + $Complex$Pyr$AHASICH3CO$ ↔ $Complex$Pyr$AHASICH3CO$Val$, kfiAHASIPyr2Val, kriAHASIPyr2Val}, {Val + $Complex$Pyr$AHASIIICH3CO$ ↔ $Complex$Pyr$AHASIIICH3CO$Val$, kfiAHASIIIPyr2Val, kriAHASIIIPyr2Val}, {Val + $Complex$Pyr$AHASIII$ ↔ $Complex$Pyr$AHASIII$Val$, kfiAHASIIIPyrVal, kriAHASIIIPyrVal}, {Val + $Complex$Pyr$AHASI$ ↔ $Complex$Pyr$AHASI$Val$, kfiAHASIPyrVal, kriAHASIPyrVal}, {Overscript[aDHIV ↔ aKIV, DAD], kfDADaDHIV, krDADaDHIV, kcat$DAD$aDHIV}, {Overscript[aDMV ↔ aKMV, DAD], kfDADaDMV, krDADaDMV, kcat$DAD$aDMV}, {Overscript[aIPM ↔ bIPM, IPMI], kfIPMIaIPM, krIPMIaIPM, kcat$IPMI$aIPM}, {Overscript[aKB ↔ propionylCoA, KDC], kfKDCaKB, krKDCaKB, kcat$KDC$aKB}, {Overscript[bIPM ↔ aIPM, IPMI], kfIPMIbIPM, krIPMIbIPM, kcat$IPMI$bIPM}, {Overscript[exIle ↔ Ile, LIVI], kfLIVIexIle, krLIVIexIle, kcat$LIVI$exIle}, {Overscript[exIle ↔ Ile, LIVII], kfLIVIIexIle, krLIVIIexIle, kcat$LIVII$exIle}, {Overscript[exLeu ↔ Leu, LIVI], kfLIVIexLeu, krLIVIexLeu, kcat$LIVI$exLeu}, {Overscript[exLeu ↔ Leu, LIVII], kfLIVIIexLeu, krLIVIIexLeu, kcat$LIVII$exLeu}, {Overscript[exLeu ↔ Leu, LS], kfLSexLeu, krLSexLeu, kcat$LS$exLeu}, {Overscript[exVal ↔ Val, LIVI], kfLIVIexVal, krLIVIexVal, kcat$LIVI$exVal}, {Overscript[exVal ↔ Val, LIVII], kfLIVIIexVal, krLIVIIexVal, kcat$LIVII$exVal}}

(* Cellerator - interpreted Ordinary Differential Equations (ODEs) and Equations for the MWC Model and Substrate Generators . *) interpret[ILE$VAL$LEU$Synthesis]

(* Modifications for Substrate Generators : The generated ODEs require some modifications to include the constant substrate fluxes for the steady state simulation 1. Substrate Generators :        Set the first derivatives of the following substrates to 0      to simulate constant flux      Thr '[t] == 0, Pyr '[t] == 0, NADPH '[t] == 0, Glu '[t] == 0,          Ala '[t] == 0, exIle^'[t] == 0, exVal^'[t] == 0, exLeu^'[t] == 0,          acetylCoA^'[t] == 0, NAD^'[t] == 0, *)

{myODEs, myVars} = {{aAHB^'[t] == -kfIRaAHB aAHB[t] IR[t] NADPH[t] + kcat$AHASI$aKB $Complex$aKB$AHASICH3CO$[t] + kcat$AHASI$aKB residualRateAHASIValaKB $Complex$aKB$AHASICH3CO$Val$[t] + kcat$AHASII$aKB $Complex$aKB$AHASIICH3CO$[t] + kcat$AHASIII$aKB $Complex$aKB$AHASIIICH3CO$[t] + kcat$AHASIII$aKB residualRateAHASIIIValaKB $Complex$aKB$AHASIIICH3CO$Val$[t] + krIRaAHB $Complex$IR$aAHB$NADPH$[t], aAL^'[t] == -kfIRaAL aAL[t] IR[t] NADPH[t] + krIRaAL $Complex$IR$aAL$NADPH$[t] + kcat$AHASI$Pyr2 $Complex$Pyr$AHASICH3CO$[t] + kcat$AHASI$Pyr2 residualRateAHASIValPyr2 $Complex$Pyr$AHASICH3CO$Val$[t] + kcat$AHASII$Pyr2 $Complex$Pyr$AHASIICH3CO$[t] + kcat$AHASIII$Pyr2 $Complex$Pyr$AHASIIICH3CO$[t] + kcat$AHASIII$Pyr2 residualRateAHASIIIValPyr2 $Complex$Pyr$AHASIIICH3CO$Val$[t], acetylCoA^'[t] == 0, aDHIV^'[t] == -kfDADaDHIV aDHIV[t] DAD[t] + krDADaDHIV $Complex$aDHIV$DAD$[t] + kcat$IR$aAL $Complex$IR$aAL$NADPH$[t], aDMV^'[t] == -kfDADaDMV aDMV[t] DAD[t] + krDADaDMV $Complex$aDMV$DAD$[t] + kcat$IR$aAHB $Complex$IR$aAHB$NADPH$[t], AHASI^'[t] == -kfAHASIPyr AHASI[t] Pyr[t] - kfiAHASIPyrVal AHASI[t] Val[t] + kriAHASIPyrVal $Complex$AHASI$Val$[t] + kcat$AHASI$aKB $Complex$aKB$AHASICH3CO$[t] + kcat$AHASI$Pyr2 $Complex$Pyr$AHASICH3CO$[t] + krAHASIPyr $Complex$Pyr$AHASI$[t], AHASICH3CO^'[t] == -kfAHASIaKB AHASICH3CO[t] aKB[t] - kfAHASIPyr2 AHASICH3CO[t] Pyr[t] - kfiAHASIaKBVal AHASICH3CO[t] Val[t] + kriAHASIaKBVal $Complex$AHASICH3CO$Val$[t] + krAHASIaKB $Complex$aKB$AHASICH3CO$[t] + krAHASIPyr2 $Complex$Pyr$AHASICH3CO$[t] + kcat$AHASI$Pyr $Complex$Pyr$AHASI$[t], AHASII^'[t] == -kfAHASIIPyr AHASII[t] Pyr[t] + kcat$AHASII$aKB $Complex$aKB$AHASIICH3CO$[t] + kcat$AHASII$Pyr2 $Complex$Pyr$AHASIICH3CO$[t] + krAHASIIPyr $Complex$Pyr$AHASII$[t], AHASIICH3CO^'[t] == -kfAHASIIaKB AHASIICH3CO[t] aKB[t] - kfAHASIIPyr2 AHASIICH3CO[t] Pyr[t] + krAHASIIaKB $Complex$aKB$AHASIICH3CO$[t] + krAHASIIPyr2 $Complex$Pyr$AHASIICH3CO$[t] + kcat$AHASII$Pyr $Complex$Pyr$AHASII$[t], AHASIII^'[t] == -kfAHASIIIPyr AHASIII[t] Pyr[t] - kfiAHASIIIPyrVal AHASIII[t] Val[t] + kriAHASIIIPyrVal $Complex$AHASIII$Val$[t] + kcat$AHASIII$aKB $Complex$aKB$AHASIIICH3CO$[t] + kcat$AHASIII$Pyr2 $Complex$Pyr$AHASIIICH3CO$[t] + krAHASIIIPyr $Complex$Pyr$AHASIII$[t], AHASIIICH3CO^'[t] == -kfAHASIIIaKB AHASIIICH3CO[t] aKB[t] - kfAHASIIIPyr2 AHASIIICH3CO[t] Pyr[t] - kfiAHASIIIaKBVal AHASIIICH3CO[t] Val[t] + kriAHASIIIaKBVal $Complex$AHASIIICH3CO$Val$[t] + krAHASIIIaKB $Complex$aKB$AHASIIICH3CO$[t] + krAHASIIIPyr2 $Complex$Pyr$AHASIIICH3CO$[t] + kcat$AHASIII$Pyr $Complex$Pyr$AHASIII$[t], aIPM^'[t] == -kfIPMIaIPM aIPM[t] IPMI[t] + krIPMIaIPM $Complex$aIPM$IPMI$[t] + kcat$IPMS$aKIV $Complex$aKIV$IPMSacetyl$[t] + kcat$IPMI$bIPM $Complex$bIPM$IPMI$[t], aKB^'[t] == -kfAHASIaKB AHASICH3CO[t] aKB[t] - kfAHASIIaKB AHASIICH3CO[t] aKB[t] - kfAHASIIIaKB AHASIIICH3CO[t] aKB[t] - kfKDCaKB aKB[t] KDC[t] + (kcat$TDA TDA[t] ((cTDA L0TDA (1 + Ile[t]/KiIle)^nTDA Thr[t] (1 + (cTDA Thr[t])/KmThr)^(-1 + nTDA))/KmThr + (Thr[t] (1 + Thr[t]/KmThr)^(-1 + nTDA) (1 + Val[t]/KaVal)^nTDA)/KmThr))/(L0TDA (1 + Ile[t]/KiIle)^nTDA (1 + (cTDA Thr[t])/KmThr)^nTDA + (1 + Thr[t]/KmThr)^nTDA (1 + Val[t]/KaVal)^nTDA) - kfAHASIaKB aKB[t] $Complex$AHASICH3CO$Val$[t] - kfAHASIIIaKB aKB[t] $Complex$AHASIIICH3CO$Val$[t] + krAHASIaKB $Complex$aKB$AHASICH3CO$[t] + krAHASIaKB $Complex$aKB$AHASICH3CO$Val$[t] + krAHASIIaKB $Complex$aKB$AHASIICH3CO$[t] + krAHASIIIaKB $Complex$aKB$AHASIIICH3CO$[t] + krAHASIIIaKB $Complex$aKB$AHASIIICH3CO$Val$[t] + krKDCaKB $Complex$aKB$KDC$[t], aKG^'[t] == -rkfTBaKG aKG[t] TBNH2[t] + rkrTBaKG $Complex$aKG$TBNH2$[t] + fkcat$TB$Glu $Complex$Glu$TB$[t], aKIC^'[t] == -kcat$aKIC aKIC[t] - fkfTBaKIC aKIC[t] TBNH2[t] + fkrTBaKIC $Complex$aKIC$TBNH2$[t] + kcat$IPMDH$bIPM $Complex$IPMDH$bIPM$NAD$[t] + rkcat$TB$Leu $Complex$Leu$TB$[t], aKIV^'[t] == -kcat$aKIV aKIV[t] - kfIPMSaKIV aKIV[t] IPMSacetyl[t] - fkfTBaKIV aKIV[t] TBNH2[t] - fkfTCaKIV aKIV[t] TCNH2[t] + kcat$DAD$aDHIV $Complex$aDHIV$DAD$[t] + krIPMSaKIV $Complex$aKIV$IPMSacetyl$[t] + krIPMSaKIV $Complex$aKIV$IPMSacetyl$Leu$[t] + fkrTBaKIV $Complex$aKIV$TBNH2$[t] + fkrTCaKIV $Complex$aKIV$TCNH2$[t] - kfIPMSaKIV aKIV[t] $Complex$IPMSacetyl$Leu$[t] + rkcat$TB$Val $Complex$Val$TB$[t] + rkcat$TC$Val $Complex$Val$TC$[t], aKMV^'[t] == -kcat$aKMV aKMV[t] - fkfTBaKMV aKMV[t] TBNH2[t] + kcat$DAD$aDMV $Complex$aDMV$DAD$[t] + fkrTBaKMV $Complex$aKMV$TBNH2$[t] + rkcat$TB$Ile $Complex$Ile$TB$[t], Ala^'[t] == 0, bIPM^'[t] == -kfIPMIbIPM bIPM[t] IPMI[t] - kfIPMDHbIPM bIPM[t] IPMDH[t] NAD[t] + kcat$IPMI$aIPM $Complex$aIPM$IPMI$[t] + krIPMIbIPM $Complex$bIPM$IPMI$[t] + krIPMDHbIPM $Complex$IPMDH$bIPM$NAD$[t], CO2^'[t] == kcat$AHASIII$Pyr $Complex$Pyr$AHASIII$[t] + kcat$AHASIII$Pyr residualRateAHASIIIValaKB $Complex$Pyr$AHASIII$Val$[t] + kcat$AHASII$Pyr $Complex$Pyr$AHASII$[t] + kcat$AHASI$Pyr $Complex$Pyr$AHASI$[t] + kcat$AHASI$Pyr residualRateAHASIValaKB $Complex$Pyr$AHASI$Val$[t], CoA^'[t] == kcat$IPMS$acetylCoA $Complex$acetylCoA$IPMS$[t], DAD^'[t] == -kfDADaDHIV aDHIV[t] DAD[t] - kfDADaDMV aDMV[t] DAD[t] + kcat$DAD$aDHIV $Complex$aDHIV$DAD$[t] + krDADaDHIV $Complex$aDHIV$DAD$[t] + kcat$DAD$aDMV $Complex$aDMV$DAD$[t] + krDADaDMV $Complex$aDMV$DAD$[t], exIle^'[t] == 0, exLeu^'[t] == 0, exVal^'[t] == 0, Glu^'[t] == 0, glutarylCoA^'[t] == kcat$aKIC aKIC[t], Ile^'[t] == -kcat$Ile Ile[t] - rkfTBIle Ile[t] TB[t] + fkcat$TB$aKMV $Complex$aKMV$TBNH2$[t] + kcat$LIVII$exIle $Complex$exIle$LIVII$[t] + kcat$LIVI$exIle $Complex$exIle$LIVI$[t] + rkrTBIle $Complex$Ile$TB$[t], IPMDH^'[t] == -kfIPMDHbIPM bIPM[t] IPMDH[t] NAD[t] + kcat$IPMDH$bIPM $Complex$IPMDH$bIPM$NAD$[t] + krIPMDHbIPM $Complex$IPMDH$bIPM$NAD$[t], IPMI^'[t] == -kfIPMIaIPM aIPM[t] IPMI[t] - kfIPMIbIPM bIPM[t] IPMI[t] + kcat$IPMI$aIPM $Complex$aIPM$IPMI$[t] + krIPMIaIPM $Complex$aIPM$IPMI$[t] + kcat$IPMI$bIPM $Complex$bIPM$IPMI$[t] + krIPMIbIPM $Complex$bIPM$IPMI$[t], IPMS^'[t] == -kfIPMSacetylCoA acetylCoA[t] IPMS[t] - kfiIPMSLeu IPMS[t] Leu[t] + krIPMSacetylCoA $Complex$acetylCoA$IPMS$[t] + kcat$IPMS$aKIV $Complex$aKIV$IPMSacetyl$[t] + kriIPMSLeu $Complex$IPMS$Leu$[t], IPMSacetyl^'[t] == -kfIPMSaKIV aKIV[t] IPMSacetyl[t] - kfiIPMSacetylLeu IPMSacetyl[t] Leu[t] + kcat$IPMS$acetylCoA $Complex$acetylCoA$IPMS$[t] + krIPMSaKIV $Complex$aKIV$IPMSacetyl$[t] + kriIPMSacetylLeu $Complex$IPMSacetyl$Leu$[t], IR^'[t] == -kfIRaAHB aAHB[t] IR[t] NADPH[t] - kfIRaAL aAL[t] IR[t] NADPH[t] + kcat$IR$aAHB $Complex$IR$aAHB$NADPH$[t] + krIRaAHB $Complex$IR$aAHB$NADPH$[t] + kcat$IR$aAL $Complex$IR$aAL$NADPH$[t] + krIRaAL $Complex$IR$aAL$NADPH$[t], KDC^'[t] == -kfKDCaKB aKB[t] KDC[t] + kcat$KDC$aKB $Complex$aKB$KDC$[t] + krKDCaKB $Complex$aKB$KDC$[t], Leu^'[t] == -kcat$Leu Leu[t] - kfiIPMSLeu IPMS[t] Leu[t] - kfiIPMSacetylLeu IPMSacetyl[t] Leu[t] - rkfTBLeu Leu[t] TB[t] + fkcat$TB$aKIC $Complex$aKIC$TBNH2$[t] - kfiIPMSacetylLeu Leu[t] $Complex$aKIV$IPMSacetyl$[t] + kriIPMSacetylLeu $Complex$aKIV$IPMSacetyl$Leu$[t] + kcat$LIVII$exLeu $Complex$exLeu$LIVII$[t] + kcat$LIVI$exLeu $Complex$exLeu$LIVI$[t] + kcat$LS$exLeu $Complex$exLeu$LS$[t] + kriIPMSacetylLeu $Complex$IPMSacetyl$Leu$[t] + kriIPMSLeu $Complex$IPMS$Leu$[t] + rkrTBLeu $Complex$Leu$TB$[t], LIVI^'[t] == -kfLIVIexIle exIle[t] LIVI[t] - kfLIVIexLeu exLeu[t] LIVI[t] - kfLIVIexVal exVal[t] LIVI[t] + kcat$LIVI$exIle $Complex$exIle$LIVI$[t] + krLIVIexIle $Complex$exIle$LIVI$[t] + kcat$LIVI$exLeu $Complex$exLeu$LIVI$[t] + krLIVIexLeu $Complex$exLeu$LIVI$[t] + kcat$LIVI$exVal $Complex$exVal$LIVI$[t] + krLIVIexVal $Complex$exVal$LIVI$[t], LIVII^'[t] == -kfLIVIIexIle exIle[t] LIVII[t] - kfLIVIIexLeu exLeu[t] LIVII[t] - kfLIVIIexVal exVal[t] LIVII[t] + kcat$LIVII$exIle $Complex$exIle$LIVII$[t] + krLIVIIexIle $Complex$exIle$LIVII$[t] + kcat$LIVII$exLeu $Complex$exLeu$LIVII$[t] + krLIVIIexLeu $Complex$exLeu$LIVII$[t] + kcat$LIVII$exVal $Complex$exVal$LIVII$[t] + krLIVIIexVal $Complex$exVal$LIVII$[t], LS^'[t] == -kfLSexLeu exLeu[t] LS[t] + kcat$LS$exLeu $Complex$exLeu$LS$[t] + krLSexLeu $Complex$exLeu$LS$[t], NAD^'[t] == 0, NADH^'[t] == kcat$IPMDH$bIPM $Complex$IPMDH$bIPM$NAD$[t], NADP^'[t] == kcat$IR$aAHB $Complex$IR$aAHB$NADPH$[t] + kcat$IR$aAL $Complex$IR$aAL$NADPH$[t], NADPH^'[t] == 0, NH3^'[t] == (kcat$TDA TDA[t] ((cTDA L0TDA (1 + Ile[t]/KiIle)^nTDA Thr[t] (1 + (cTDA Thr[t])/KmThr)^(-1 + nTDA))/KmThr + (Thr[t] (1 + Thr[t]/KmThr)^(-1 + nTDA) (1 + Val[t]/KaVal)^nTDA)/KmThr))/(L0TDA (1 + Ile[t]/KiIle)^nTDA (1 + (cTDA Thr[t])/KmThr)^nTDA + (1 + Thr[t]/KmThr)^nTDA (1 + Val[t]/KaVal)^nTDA), pantothenate^'[t] == kcat$aKIV aKIV[t], propionylCoA^'[t] == kcat$KDC$aKB $Complex$aKB$KDC$[t], protein^'[t] == kcat$Ile Ile[t] + kcat$Leu Leu[t] + kcat$Val Val[t], Pyr^'[t] == 0, TB^'[t] == -fkfTBGlu Glu[t] TB[t] - rkfTBIle Ile[t] TB[t] - rkfTBLeu Leu[t] TB[t] - rkfTBVal TB[t] Val[t] + rkcat$TB$aKG $Complex$aKG$TBNH2$[t] + fkcat$TB$aKIC $Complex$aKIC$TBNH2$[t] + fkcat$TB$aKIV $Complex$aKIV$TBNH2$[t] + fkcat$TB$aKMV $Complex$aKMV$TBNH2$[t] + fkrTBGlu $Complex$Glu$TB$[t] + rkrTBIle $Complex$Ile$TB$[t] + rkrTBLeu $Complex$Leu$TB$[t] + rkrTBVal $Complex$Val$TB$[t], TBNH2^'[t] == -rkfTBaKG aKG[t] TBNH2[t] - fkfTBaKIC aKIC[t] TBNH2[t] - fkfTBaKIV aKIV[t] TBNH2[t] - fkfTBaKMV aKMV[t] TBNH2[t] + rkrTBaKG $Complex$aKG$TBNH2$[t] + fkrTBaKIC $Complex$aKIC$TBNH2$[t] + fkrTBaKIV $Complex$aKIV$TBNH2$[t] + fkrTBaKMV $Complex$aKMV$TBNH2$[t] + fkcat$TB$Glu $Complex$Glu$TB$[t] + rkcat$TB$Ile $Complex$Ile$TB$[t] + rkcat$TB$Leu $Complex$Leu$TB$[t] + rkcat$TB$Val $Complex$Val$TB$[t], TC^'[t] == -fkfTCAla Ala[t] TC[t] - rkfTCVal TC[t] Val[t] + fkcat$TC$aKIV $Complex$aKIV$TCNH2$[t] + fkrTCAla $Complex$Ala$TC$[t] + rkcat$TC$Pyr $Complex$Pyr$TCNH2$[t] + rkrTCVal $Complex$Val$TC$[t], TCNH2^'[t] == -fkfTCaKIV aKIV[t] TCNH2[t] - rkfTCPyr Pyr[t] TCNH2[t] + fkrTCaKIV $Complex$aKIV$TCNH2$[t] + fkcat$TC$Ala $Complex$Ala$TC$[t] + rkrTCPyr $Complex$Pyr$TCNH2$[t] + rkcat$TC$Val $Complex$Val$TC$[t], TDA^'[t] == 0, Thr^'[t] == 0, Val^'[t] == -kcat$Val Val[t] - kfiAHASIPyrVal AHASI[t] Val[t] - kfiAHASIaKBVal AHASICH3CO[t] Val[t] - kfiAHASIIIPyrVal AHASIII[t] Val[t] - kfiAHASIIIaKBVal AHASIIICH3CO[t] Val[t] - rkfTBVal TB[t] Val[t] - rkfTCVal TC[t] Val[t] + kriAHASIaKBVal $Complex$AHASICH3CO$Val$[t] + kriAHASIIIaKBVal $Complex$AHASIIICH3CO$Val$[t] + kriAHASIIIPyrVal $Complex$AHASIII$Val$[t] + kriAHASIPyrVal $Complex$AHASI$Val$[t] - kfiAHASIaKBVal Val[t] $Complex$aKB$AHASICH3CO$[t] + kriAHASIaKBVal $Complex$aKB$AHASICH3CO$Val$[t] - kfiAHASIIIaKBVal Val[t] $Complex$aKB$AHASIIICH3CO$[t] + kriAHASIIIaKBVal $Complex$aKB$AHASIIICH3CO$Val$[t] + fkcat$TB$aKIV $Complex$aKIV$TBNH2$[t] + fkcat$TC$aKIV $Complex$aKIV$TCNH2$[t] + kcat$LIVII$exVal $Complex$exVal$LIVII$[t] + kcat$LIVI$exVal $Complex$exVal$LIVI$[t] - kfiAHASIPyr2Val Val[t] $Complex$Pyr$AHASICH3CO$[t] + kriAHASIPyr2Val $Complex$Pyr$AHASICH3CO$Val$[t] - kfiAHASIIIPyr2Val Val[t] $Complex$Pyr$AHASIIICH3CO$[t] + kriAHASIIIPyr2Val $Complex$Pyr$AHASIIICH3CO$Val$[t] - kfiAHASIIIPyrVal Val[t] $Complex$Pyr$AHASIII$[t] + kriAHASIIIPyrVal $Complex$Pyr$AHASIII$Val$[t] - kfiAHASIPyrVal Val[t] $Complex$Pyr$AHASI$[t] + kriAHASIPyrVal $Complex$Pyr$AHASI$Val$[t] + rkrTBVal $Complex$Val$TB$[t] + rkrTCVal $Complex$Val$TC$[t], $Complex$acetylCoA$IPMS$^'[t] == kfIPMSacetylCoA acetylCoA[t] IPMS[t] - kcat$IPMS$acetylCoA $Complex$acetylCoA$IPMS$[t] - krIPMSacetylCoA $Complex$acetylCoA$IPMS$[t], $Complex$aDHIV$DAD$^'[t] == kfDADaDHIV aDHIV[t] DAD[t] - kcat$DAD$aDHIV $Complex$aDHIV$DAD$[t] - krDADaDHIV $Complex$aDHIV$DAD$[t], $Complex$aDMV$DAD$^'[t] == kfDADaDMV aDMV[t] DAD[t] - kcat$DAD$aDMV $Complex$aDMV$DAD$[t] - krDADaDMV $Complex$aDMV$DAD$[t], $Complex$AHASICH3CO$Val$^'[t] == kfiAHASIaKBVal AHASICH3CO[t] Val[t] - kriAHASIaKBVal $Complex$AHASICH3CO$Val$[t] - kfAHASIaKB aKB[t] $Complex$AHASICH3CO$Val$[t] - kfAHASIPyr2 Pyr[t] $Complex$AHASICH3CO$Val$[t] + krAHASIaKB $Complex$aKB$AHASICH3CO$Val$[t] + kcat$AHASI$aKB residualRateAHASIValaKB $Complex$aKB$AHASICH3CO$Val$[t] + krAHASIPyr2 $Complex$Pyr$AHASICH3CO$Val$[t] + kcat$AHASI$Pyr2 residualRateAHASIValPyr2 $Complex$Pyr$AHASICH3CO$Val$[t], $Complex$AHASIIICH3CO$Val$^'[t] == kfiAHASIIIaKBVal AHASIIICH3CO[t] Val[t] - kriAHASIIIaKBVal $Complex$AHASIIICH3CO$Val$[t] - kfAHASIIIaKB aKB[t] $Complex$AHASIIICH3CO$Val$[t] - kfAHASIIIPyr2 Pyr[t] $Complex$AHASIIICH3CO$Val$[t] + krAHASIIIaKB $Complex$aKB$AHASIIICH3CO$Val$[t] + kcat$AHASIII$aKB residualRateAHASIIIValaKB $Complex$aKB$AHASIIICH3CO$Val$[t] + krAHASIIIPyr2 $Complex$Pyr$AHASIIICH3CO$Val$[t] + kcat$AHASIII$Pyr2 residualRateAHASIIIValPyr2 $Complex$Pyr$AHASIIICH3CO$Val$[t], $Complex$AHASIII$Val$^'[t] == kfiAHASIIIPyrVal AHASIII[t] Val[t] - kriAHASIIIPyrVal $Complex$AHASIII$Val$[t] - kfAHASIIIPyr Pyr[t] $Complex$AHASIII$Val$[t] + krAHASIIIPyr $Complex$Pyr$AHASIII$Val$[t] + kcat$AHASIII$Pyr residualRateAHASIIIValaKB $Complex$Pyr$AHASIII$Val$[t], $Complex$AHASI$Val$^'[t] == kfiAHASIPyrVal AHASI[t] Val[t] - kriAHASIPyrVal $Complex$AHASI$Val$[t] - kfAHASIPyr Pyr[t] $Complex$AHASI$Val$[t] + krAHASIPyr $Complex$Pyr$AHASI$Val$[t] + kcat$AHASI$Pyr residualRateAHASIValaKB $Complex$Pyr$AHASI$Val$[t], $Complex$aIPM$IPMI$^'[t] == kfIPMIaIPM aIPM[t] IPMI[t] - kcat$IPMI$aIPM $Complex$aIPM$IPMI$[t] - krIPMIaIPM $Complex$aIPM$IPMI$[t], $Complex$aKB$AHASICH3CO$^'[t] == kfAHASIaKB AHASICH3CO[t] aKB[t] - kcat$AHASI$aKB $Complex$aKB$AHASICH3CO$[t] - krAHASIaKB $Complex$aKB$AHASICH3CO$[t] - kfiAHASIaKBVal Val[t] $Complex$aKB$AHASICH3CO$[t] + kriAHASIaKBVal $Complex$aKB$AHASICH3CO$Val$[t], $Complex$aKB$AHASICH3CO$Val$^'[t] == kfAHASIaKB aKB[t] $Complex$AHASICH3CO$Val$[t] + kfiAHASIaKBVal Val[t] $Complex$aKB$AHASICH3CO$[t] - krAHASIaKB $Complex$aKB$AHASICH3CO$Val$[t] - kriAHASIaKBVal $Complex$aKB$AHASICH3CO$Val$[t] - kcat$AHASI$aKB residualRateAHASIValaKB $Complex$aKB$AHASICH3CO$Val$[t], $Complex$aKB$AHASIICH3CO$^'[t] == kfAHASIIaKB AHASIICH3CO[t] aKB[t] - kcat$AHASII$aKB $Complex$aKB$AHASIICH3CO$[t] - krAHASIIaKB $Complex$aKB$AHASIICH3CO$[t], $Complex$aKB$AHASIIICH3CO$^'[t] == kfAHASIIIaKB AHASIIICH3CO[t] aKB[t] - kcat$AHASIII$aKB $Complex$aKB$AHASIIICH3CO$[t] - krAHASIIIaKB $Complex$aKB$AHASIIICH3CO$[t] - kfiAHASIIIaKBVal Val[t] $Complex$aKB$AHASIIICH3CO$[t] + kriAHASIIIaKBVal $Complex$aKB$AHASIIICH3CO$Val$[t], $Complex$aKB$AHASIIICH3CO$Val$^'[t] == kfAHASIIIaKB aKB[t] $Complex$AHASIIICH3CO$Val$[t] + kfiAHASIIIaKBVal Val[t] $Complex$aKB$AHASIIICH3CO$[t] - krAHASIIIaKB $Complex$aKB$AHASIIICH3CO$Val$[t] - kriAHASIIIaKBVal $Complex$aKB$AHASIIICH3CO$Val$[t] - kcat$AHASIII$aKB residualRateAHASIIIValaKB $Complex$aKB$AHASIIICH3CO$Val$[t], $Complex$aKB$KDC$^'[t] == kfKDCaKB aKB[t] KDC[t] - kcat$KDC$aKB $Complex$aKB$KDC$[t] - krKDCaKB $Complex$aKB$KDC$[t], $Complex$aKG$TBNH2$^'[t] == rkfTBaKG aKG[t] TBNH2[t] - rkcat$TB$aKG $Complex$aKG$TBNH2$[t] - rkrTBaKG $Complex$aKG$TBNH2$[t], $Complex$aKIC$TBNH2$^'[t] == fkfTBaKIC aKIC[t] TBNH2[t] - fkcat$TB$aKIC $Complex$aKIC$TBNH2$[t] - fkrTBaKIC $Complex$aKIC$TBNH2$[t], $Complex$aKIV$IPMSacetyl$^'[t] == kfIPMSaKIV aKIV[t] IPMSacetyl[t] - kcat$IPMS$aKIV $Complex$aKIV$IPMSacetyl$[t] - krIPMSaKIV $Complex$aKIV$IPMSacetyl$[t] - kfiIPMSacetylLeu Leu[t] $Complex$aKIV$IPMSacetyl$[t] + kriIPMSacetylLeu $Complex$aKIV$IPMSacetyl$Leu$[t], $Complex$aKIV$IPMSacetyl$Leu$^'[t] == kfiIPMSacetylLeu Leu[t] $Complex$aKIV$IPMSacetyl$[t] - kriIPMSacetylLeu $Complex$aKIV$IPMSacetyl$Leu$[t] - krIPMSaKIV $Complex$aKIV$IPMSacetyl$Leu$[t] + kfIPMSaKIV aKIV[t] $Complex$IPMSacetyl$Leu$[t], $Complex$aKIV$TBNH2$^'[t] == fkfTBaKIV aKIV[t] TBNH2[t] - fkcat$TB$aKIV $Complex$aKIV$TBNH2$[t] - fkrTBaKIV $Complex$aKIV$TBNH2$[t], $Complex$aKIV$TCNH2$^'[t] == fkfTCaKIV aKIV[t] TCNH2[t] - fkcat$TC$aKIV $Complex$aKIV$TCNH2$[t] - fkrTCaKIV $Complex$aKIV$TCNH2$[t], $Complex$aKMV$TBNH2$^'[t] == fkfTBaKMV aKMV[t] TBNH2[t] - fkcat$TB$aKMV $Complex$aKMV$TBNH2$[t] - fkrTBaKMV $Complex$aKMV$TBNH2$[t], $Complex$Ala$TC$^'[t] == fkfTCAla Ala[t] TC[t] - fkcat$TC$Ala $Complex$Ala$TC$[t] - fkrTCAla $Complex$Ala$TC$[t], $Complex$bIPM$IPMI$^'[t] == kfIPMIbIPM bIPM[t] IPMI[t] - kcat$IPMI$bIPM $Complex$bIPM$IPMI$[t] - krIPMIbIPM $Complex$bIPM$IPMI$[t], $Complex$exIle$LIVII$^'[t] == kfLIVIIexIle exIle[t] LIVII[t] - kcat$LIVII$exIle $Complex$exIle$LIVII$[t] - krLIVIIexIle $Complex$exIle$LIVII$[t], $Complex$exIle$LIVI$^'[t] == kfLIVIexIle exIle[t] LIVI[t] - kcat$LIVI$exIle $Complex$exIle$LIVI$[t] - krLIVIexIle $Complex$exIle$LIVI$[t], $Complex$exLeu$LIVII$^'[t] == kfLIVIIexLeu exLeu[t] LIVII[t] - kcat$LIVII$exLeu $Complex$exLeu$LIVII$[t] - krLIVIIexLeu $Complex$exLeu$LIVII$[t], $Complex$exLeu$LIVI$^'[t] == kfLIVIexLeu exLeu[t] LIVI[t] - kcat$LIVI$exLeu $Complex$exLeu$LIVI$[t] - krLIVIexLeu $Complex$exLeu$LIVI$[t], $Complex$exLeu$LS$^'[t] == kfLSexLeu exLeu[t] LS[t] - kcat$LS$exLeu $Complex$exLeu$LS$[t] - krLSexLeu $Complex$exLeu$LS$[t], $Complex$exVal$LIVII$^'[t] == kfLIVIIexVal exVal[t] LIVII[t] - kcat$LIVII$exVal $Complex$exVal$LIVII$[t] - krLIVIIexVal $Complex$exVal$LIVII$[t], $Complex$exVal$LIVI$^'[t] == kfLIVIexVal exVal[t] LIVI[t] - kcat$LIVI$exVal $Complex$exVal$LIVI$[t] - krLIVIexVal $Complex$exVal$LIVI$[t], $Complex$Glu$TB$^'[t] == fkfTBGlu Glu[t] TB[t] - fkcat$TB$Glu $Complex$Glu$TB$[t] - fkrTBGlu $Complex$Glu$TB$[t], $Complex$Ile$TB$^'[t] == rkfTBIle Ile[t] TB[t] - rkcat$TB$Ile $Complex$Ile$TB$[t] - rkrTBIle $Complex$Ile$TB$[t], $Complex$IPMDH$bIPM$NAD$^'[t] == kfIPMDHbIPM bIPM[t] IPMDH[t] NAD[t] - kcat$IPMDH$bIPM $Complex$IPMDH$bIPM$NAD$[t] - krIPMDHbIPM $Complex$IPMDH$bIPM$NAD$[t], $Complex$IPMSacetyl$Leu$^'[t] == kfiIPMSacetylLeu IPMSacetyl[t] Leu[t] + krIPMSaKIV $Complex$aKIV$IPMSacetyl$Leu$[t] - kriIPMSacetylLeu $Complex$IPMSacetyl$Leu$[t] - kfIPMSaKIV aKIV[t] $Complex$IPMSacetyl$Leu$[t], $Complex$IPMS$Leu$^'[t] == kfiIPMSLeu IPMS[t] Leu[t] - kriIPMSLeu $Complex$IPMS$Leu$[t], $Complex$IR$aAHB$NADPH$^'[t] == kfIRaAHB aAHB[t] IR[t] NADPH[t] - kcat$IR$aAHB $Complex$IR$aAHB$NADPH$[t] - krIRaAHB $Complex$IR$aAHB$NADPH$[t], $Complex$IR$aAL$NADPH$^'[t] == kfIRaAL aAL[t] IR[t] NADPH[t] - kcat$IR$aAL $Complex$IR$aAL$NADPH$[t] - krIRaAL $Complex$IR$aAL$NADPH$[t], $Complex$Leu$TB$^'[t] == rkfTBLeu Leu[t] TB[t] - rkcat$TB$Leu $Complex$Leu$TB$[t] - rkrTBLeu $Complex$Leu$TB$[t], $Complex$Pyr$AHASICH3CO$^'[t] == kfAHASIPyr2 AHASICH3CO[t] Pyr[t] - kcat$AHASI$Pyr2 $Complex$Pyr$AHASICH3CO$[t] - krAHASIPyr2 $Complex$Pyr$AHASICH3CO$[t] - kfiAHASIPyr2Val Val[t] $Complex$Pyr$AHASICH3CO$[t] + kriAHASIPyr2Val $Complex$Pyr$AHASICH3CO$Val$[t], $Complex$Pyr$AHASICH3CO$Val$^'[t] == kfAHASIPyr2 Pyr[t] $Complex$AHASICH3CO$Val$[t] + kfiAHASIPyr2Val Val[t] $Complex$Pyr$AHASICH3CO$[t] - krAHASIPyr2 $Complex$Pyr$AHASICH3CO$Val$[t] - kriAHASIPyr2Val $Complex$Pyr$AHASICH3CO$Val$[t] - kcat$AHASI$Pyr2 residualRateAHASIValPyr2 $Complex$Pyr$AHASICH3CO$Val$[t], $Complex$Pyr$AHASIICH3CO$^'[t] == kfAHASIIPyr2 AHASIICH3CO[t] Pyr[t] - kcat$AHASII$Pyr2 $Complex$Pyr$AHASIICH3CO$[t] - krAHASIIPyr2 $Complex$Pyr$AHASIICH3CO$[t], $Complex$Pyr$AHASIIICH3CO$^'[t] == kfAHASIIIPyr2 AHASIIICH3CO[t] Pyr[t] - kcat$AHASIII$Pyr2 $Complex$Pyr$AHASIIICH3CO$[t] - krAHASIIIPyr2 $Complex$Pyr$AHASIIICH3CO$[t] - kfiAHASIIIPyr2Val Val[t] $Complex$Pyr$AHASIIICH3CO$[t] + kriAHASIIIPyr2Val $Complex$Pyr$AHASIIICH3CO$Val$[t], $Complex$Pyr$AHASIIICH3CO$Val$^'[t] == kfAHASIIIPyr2 Pyr[t] $Complex$AHASIIICH3CO$Val$[t] + kfiAHASIIIPyr2Val Val[t] $Complex$Pyr$AHASIIICH3CO$[t] - krAHASIIIPyr2 $Complex$Pyr$AHASIIICH3CO$Val$[t] - kriAHASIIIPyr2Val $Complex$Pyr$AHASIIICH3CO$Val$[t] - kcat$AHASIII$Pyr2 residualRateAHASIIIValPyr2 $Complex$Pyr$AHASIIICH3CO$Val$[t], $Complex$Pyr$AHASIII$^'[t] == kfAHASIIIPyr AHASIII[t] Pyr[t] - kcat$AHASIII$Pyr $Complex$Pyr$AHASIII$[t] - krAHASIIIPyr $Complex$Pyr$AHASIII$[t] - kfiAHASIIIPyrVal Val[t] $Complex$Pyr$AHASIII$[t] + kriAHASIIIPyrVal $Complex$Pyr$AHASIII$Val$[t], $Complex$Pyr$AHASIII$Val$^'[t] == kfAHASIIIPyr Pyr[t] $Complex$AHASIII$Val$[t] + kfiAHASIIIPyrVal Val[t] $Complex$Pyr$AHASIII$[t] - krAHASIIIPyr $Complex$Pyr$AHASIII$Val$[t] - kriAHASIIIPyrVal $Complex$Pyr$AHASIII$Val$[t] - kcat$AHASIII$Pyr residualRateAHASIIIValaKB $Complex$Pyr$AHASIII$Val$[t], $Complex$Pyr$AHASII$^'[t] == kfAHASIIPyr AHASII[t] Pyr[t] - kcat$AHASII$Pyr $Complex$Pyr$AHASII$[t] - krAHASIIPyr $Complex$Pyr$AHASII$[t], $Complex$Pyr$AHASI$^'[t] == kfAHASIPyr AHASI[t] Pyr[t] - kcat$AHASI$Pyr $Complex$Pyr$AHASI$[t] - krAHASIPyr $Complex$Pyr$AHASI$[t] - kfiAHASIPyrVal Val[t] $Complex$Pyr$AHASI$[t] + kriAHASIPyrVal $Complex$Pyr$AHASI$Val$[t], $Complex$Pyr$AHASI$Val$^'[t] == kfAHASIPyr Pyr[t] $Complex$AHASI$Val$[t] + kfiAHASIPyrVal Val[t] $Complex$Pyr$AHASI$[t] - krAHASIPyr $Complex$Pyr$AHASI$Val$[t] - kriAHASIPyrVal $Complex$Pyr$AHASI$Val$[t] - kcat$AHASI$Pyr residualRateAHASIValaKB $Complex$Pyr$AHASI$Val$[t], $Complex$Pyr$TCNH2$^'[t] == rkfTCPyr Pyr[t] TCNH2[t] - rkcat$TC$Pyr $Complex$Pyr$TCNH2$[t] - rkrTCPyr $Complex$Pyr$TCNH2$[t], $Complex$Val$TB$^'[t] == rkfTBVal TB[t] Val[t] - rkcat$TB$Val $Complex$Val$TB$[t] - rkrTBVal $Complex$Val$TB$[t], $Complex$Val$TC$^'[t] == rkfTCVal TC[t] Val[t] - rkcat$TC$Val $Complex$Val$TC$[t] - rkrTCVal $Complex$Val$TC$[t]}, {aAHB, aAL, acetylCoA, aDHIV, aDMV, AHASI, AHASICH3CO, AHASII, AHASIICH3CO, AHASIII, AHASIIICH3CO, aIPM, aKB, aKG, aKIC, aKIV, aKMV, Ala, bIPM, CO2, CoA, DAD, exIle, exLeu, exVal, Glu, glutarylCoA, Ile, IPMDH, IPMI, IPMS, IPMSacetyl, IR, KDC, Leu, LIVI, LIVII, LS, NAD, NADH, NADP, NADPH, NH3, pantothenate, propionylCoA, protein, Pyr, TB, TBNH2, TC, TCNH2, TDA, Thr, Val, $Complex$acetylCoA$IPMS$, $Complex$aDHIV$DAD$, $Complex$aDMV$DAD$, $Complex$AHASICH3CO$Val$, $Complex$AHASIIICH3CO$Val$, $Complex$AHASIII$Val$, $Complex$AHASI$Val$, $Complex$aIPM$IPMI$, $Complex$aKB$AHASICH3CO$, $Complex$aKB$AHASICH3CO$Val$, $Complex$aKB$AHASIICH3CO$, $Complex$aKB$AHASIIICH3CO$, $Complex$aKB$AHASIIICH3CO$Val$, $Complex$aKB$KDC$, $Complex$aKG$TBNH2$, $Complex$aKIC$TBNH2$, $Complex$aKIV$IPMSacetyl$, $Complex$aKIV$IPMSacetyl$Leu$, $Complex$aKIV$TBNH2$, $Complex$aKIV$TCNH2$, $Complex$aKMV$TBNH2$, $Complex$Ala$TC$, $Complex$bIPM$IPMI$, $Complex$exIle$LIVII$, $Complex$exIle$LIVI$, $Complex$exLeu$LIVII$, $Complex$exLeu$LIVI$, $Complex$exLeu$LS$, $Complex$exVal$LIVII$, $Complex$exVal$LIVI$, $Complex$Glu$TB$, $Complex$Ile$TB$, $Complex$IPMDH$bIPM$NAD$, $Complex$IPMSacetyl$Leu$, $Complex$IPMS$Leu$, $Complex$IR$aAHB$NADPH$, $Complex$IR$aAL$NADPH$, $Complex$Leu$TB$, $Complex$Pyr$AHASICH3CO$, $Complex$Pyr$AHASICH3CO$Val$, $Complex$Pyr$AHASIICH3CO$, $Complex$Pyr$AHASIIICH3CO$, $Complex$Pyr$AHASIIICH3CO$Val$, $Complex$Pyr$AHASIII$, $Complex$Pyr$AHASIII$Val$, $Complex$Pyr$AHASII$, $Complex$Pyr$AHASI$, $Complex$Pyr$AHASI$Val$, $Complex$Pyr$TCNH2$, $Complex$Val$TB$, $Complex$Val$TC$}} ;

(* Inputs for Values of K m , K i and k cat for each Enzyme . Lambda Approximation Functions : Kf[] , Kf2S[] for k f ,                                          Kr[] for k r Omega Approximation Functions : Kfi[] for k fi ,                                          Kri[] for k ri . *) Lamda = 100 ; <br /> Omega = 1 ; myKs = {<br />         nTDA -> 4, cTDA -> 0.013, L0TDA -> 1.05, kcat$TDA -> 6000, KmThr -> 2700, KaVal -> 550, KiIle -> 15,                                        (* TDA feedback resistant mutant, KiIle = 100000 *) KmKDCaKB = 1000 ; kcat$KDC$aKB = 3000 ; kfKDCaKB -> Kf[KmKDCaKB, kcat$KDC$aKB, Lamda], krKDCaKB -> Kr[kcat$KDC$aKB, Lamda], KmAHASIPyr = 10 ; kcat$AHASI$Pyr = 7000 ; kfAHASIPyr -> Kf[KmAHASIPyr, kcat$AHASI$Pyr, Lamda], krAHASIPyr -> Kr[kcat$AHASI$Pyr, Lamda], KmAHASIaKB = 5000 ; kcat$AHASI$aKB = 7000 ; kfAHASIaKB -> Kf[KmAHASIaKB, kcat$AHASI$aKB, Lamda], krAHASIaKB -> Kr[kcat$AHASI$aKB, Lamda], residualRateAHASIValaKB -> 0, KiAHASIVal = 200 ; kfiAHASIPyrVal -> Kfi[KmAHASIPyr, kcat$AHASI$Pyr, Lamda, Omega], kriAHASIPyrVal -> Kri[KmAHASIPyr, kcat$AHASI$Pyr, Lamda, Omega, KiAHASIVal], kfiAHASIaKBVal -> Kfi[KmAHASIaKB, kcat$AHASI$aKB, Lamda, Omega], kriAHASIaKBVal -> Kri[KmAHASIaKB, kcat$AHASI$aKB, Lamda, Omega, KiAHASIVal], KmAHASIIPyr = 10 ; kcat$AHASII$Pyr = 7000 ; kfAHASIIPyr -> Kf[KmAHASIIPyr, kcat$AHASII$Pyr, Lamda], krAHASIIPyr -> Kr[kcat$AHASII$Pyr, Lamda], KmAHASIIaKB = 150 ; kcat$AHASII$aKB = 7000 ; kfAHASIIaKB -> Kf[KmAHASIIaKB, kcat$AHASII$aKB, Lamda], krAHASIIaKB -> Kr[kcat$AHASII$aKB, Lamda], KmAHASIIIPyr = 10 ; kcat$AHASIII$Pyr = 7000 ; kfAHASIIIPyr -> Kf[KmAHASIIIPyr, kcat$AHASIII$Pyr, Lamda], krAHASIIIPyr -> Kr[kcat$AHASIII$Pyr, Lamda], KmAHASIIIaKB = 150 ; kcat$AHASIII$aKB = 7000 ; kfAHASIIIaKB -> Kf[KmAHASIIIaKB, kcat$AHASIII$aKB, Lamda], krAHASIIIaKB -> Kr[kcat$AHASIII$aKB, Lamda], residualRateAHASIIIValaKB -> 0.15, KiAHASIIIVal = 20 ; kfiAHASIIIPyrVal -> Kfi[KmAHASIIIPyr, kcat$AHASIII$Pyr, Lamda, Omega], kriAHASIIIPyrVal -> Kri[KmAHASIIIPyr, kcat$AHASIII$Pyr, Lamda, Omega, KiAHASIIIVal], kfiAHASIIIaKBVal -> Kfi[KmAHASIIIaKB, kcat$AHASIII$aKB, Lamda, Omega], kriAHASIIIaKBVal -> Kri[KmAHASIIIaKB, kcat$AHASIII$aKB, Lamda, Omega, KiAHASIIIVal], KmIRaAHB = 780 ; KmIRNADPH = 15 ; kcat$IR$aAHB = 4700 ; kfIRaAHB -> Kf2S[KmIRaAHB, KmIRNADPH, kcat$IR$aAHB, Lamda], krIRaAHB -> Kr[kcat$IR$aAHB, Lamda], KmDADaDMV = 750 ; kcat$DAD$aDMV = 24000 ; kfDADaDMV -> Kf[KmDADaDMV, kcat$DAD$aDMV, Lamda], krDADaDMV -> Kr[kcat$DAD$aDMV, Lamda], KmTBGlu = 1000 ; fkcat$TB$Glu = 2000 ; fkfTBGlu -> Kf[KmTBGlu, fkcat$TB$Glu, Lamda], fkrTBGlu -> Kr[fkcat$TB$Glu, Lamda], KmTBaKMV = 200 ; fkcat$TB$aKMV = 1500 ; fkfTBaKMV -> Kf[KmTBaKMV, fkcat$TB$aKMV, Lamda], fkrTBaKMV -> Kr[fkcat$TB$aKMV, Lamda], KmTBIle = 600 ; rkcat$TB$Ile = 3000 ; rkfTBIle -> Kf[KmTBIle, rkcat$TB$Ile, Lamda], rkrTBIle -> Kr[rkcat$TB$Ile, Lamda], KmTBaKG = 2500 ; rkcat$TB$aKG = 2100 ; rkfTBaKG -> Kf[KmTBaKG, rkcat$TB$aKG, Lamda], rkrTBaKG -> Kr[rkcat$TB$aKG, Lamda], KmLIVIexIle = 7 ; kcat$LIVI$exIle = 200 ; kfLIVIexIle -> Kf[KmLIVIexIle, kcat$LIVI$exIle, Lamda], krLIVIexIle -> Kr[kcat$LIVI$exIle, Lamda], KmLIVIIexIle = 1 ; kcat$LIVII$exIle = 1 ; kfLIVIIexIle -> Kf[KmLIVIIexIle, kcat$LIVII$exIle, Lamda], krLIVIIexIle -> Kr[kcat$LIVII$exIle, Lamda], kcat$aKMV -> 5, kcat$Ile -> 0.2, KmAHASIPyr = 10 ; kcat$AHASI$Pyr = 7000 ; kfAHASIPyr -> Kf[KmAHASIPyr, kcat$AHASI$Pyr, Lamda], krAHASIPyr -> Kr[kcat$AHASI$Pyr, Lamda], KmAHASIPyr2 = 1000 ; kcat$AHASI$Pyr2 = 7000 ; kfAHASIPyr2 -> Kf[KmAHASIPyr2, kcat$AHASI$Pyr2, Lamda], krAHASIPyr2 -> Kr[kcat$AHASI$Pyr2, Lamda], residualRateAHASIValPyr2 -> 0, KiAHASIVal = 200 ; kfiAHASIPyrVal -> Kfi[KmAHASIPyr, kcat$AHASI$Pyr, Lamda, Omega], kriAHASIPyrVal -> Kri[KmAHASIPyr, kcat$AHASI$Pyr, Lamda, Omega, KiAHASIVal], kfiAHASIPyr2Val -> Kfi[KmAHASIPyr2, kcat$AHASI$Pyr2, Lamda, Omega], kriAHASIPyr2Val -> Kri[KmAHASIPyr2, kcat$AHASI$Pyr2, Lamda, Omega, KiAHASIVal], KmAHASIIPyr = 10 ; kcat$AHASII$Pyr = 7000 ; kfAHASIIPyr -> Kf[KmAHASIIPyr, kcat$AHASII$Pyr, Lamda], krAHASIIPyr -> Kr[kcat$AHASII$Pyr, Lamda], KmAHASIIPyr2 = 10000 ; kcat$AHASII$Pyr2 = 7000 ; kfAHASIIPyr2 -> Kf[KmAHASIIPyr2, kcat$AHASII$Pyr2, Lamda], krAHASIIPyr2 -> Kr[kcat$AHASII$Pyr2, Lamda], KmAHASIIIPyr = 10 ; kcat$AHASIII$Pyr = 7000 ; kfAHASIIIPyr -> Kf[KmAHASIIIPyr, kcat$AHASIII$Pyr, Lamda], krAHASIIIPyr -> Kr[kcat$AHASIII$Pyr, Lamda], KmAHASIIIPyr2 = 7000 ; kcat$AHASIII$Pyr2 = 7000 ; kfAHASIIIPyr2 -> Kf[KmAHASIIIPyr2, kcat$AHASIII$Pyr2, Lamda], krAHASIIIPyr2 -> Kr[kcat$AHASIII$Pyr2, Lamda], residualRateAHASIIIValPyr2 -> 0.15, KiAHASIIIVal = 20 ; kfiAHASIIIPyrVal -> Kfi[KmAHASIIIPyr, kcat$AHASIII$Pyr, Lamda, Omega], kriAHASIIIPyrVal -> Kri[KmAHASIIIPyr, kcat$AHASIII$Pyr, Lamda, Omega, KiAHASIIIVal], kfiAHASIIIPyr2Val -> Kfi[KmAHASIIIPyr2, kcat$AHASIII$Pyr2, Lamda, Omega], kriAHASIIIPyr2Val -> Kri[KmAHASIIIPyr2, kcat$AHASIII$Pyr2, Lamda, Omega, KiAHASIIIVal], KmIRaAL = 290 ; KmIRNADPH = 15 ; kcat$IR$aAL = 1100 ; kfIRaAL -> Kf2S[KmIRaAL, KmIRNADPH, kcat$IR$aAL, Lamda], krIRaAL -> Kr[kcat$IR$aAL, Lamda], KmDADaDHIV = 2800 ; kcat$DAD$aDHIV = 24000 ; kfDADaDHIV -> Kf[KmDADaDHIV, kcat$DAD$aDHIV, Lamda], krDADaDHIV -> Kr[kcat$DAD$aDHIV, Lamda], KmTBGlu = 1000 ; fkcat$TB$Glu = 2000 ; fkfTBGlu -> Kf[KmTBGlu, fkcat$TB$Glu, Lamda], fkrTBGlu -> Kr[fkcat$TB$Glu, Lamda], KmTBaKIV = 300 ; fkcat$TB$aKIV = 930 ; fkfTBaKIV -> Kf[KmTBaKIV, fkcat$TB$aKIV, Lamda], fkrTBaKIV -> Kr[fkcat$TB$aKIV, Lamda], KmTBVal = 2700 ; rkcat$TB$Val = 2000 ; rkfTBVal -> Kf[KmTBVal, rkcat$TB$Val, Lamda], rkrTBVal -> Kr[rkcat$TB$Val, Lamda], KmTBaKG = 2500 ; rkcat$TB$aKG = 2100 ; rkfTBaKG -> Kf[KmTBaKG, rkcat$TB$aKG, Lamda], rkrTBaKG -> Kr[rkcat$TB$aKG, Lamda], KmTCAla = 100 ; fkcat$TC$Ala = 2000 ; fkfTCAla -> Kf[KmTCAla, fkcat$TC$Ala, Lamda], fkrTCAla -> Kr[fkcat$TC$Ala, Lamda], KmTCaKIV = 100 ; fkcat$TC$aKIV = 1500 ; fkfTCaKIV -> Kf[KmTCaKIV, fkcat$TC$aKIV, Lamda], fkrTCaKIV -> Kr[fkcat$TC$aKIV, Lamda], KmTCVal = 3000 ;    rkcat$TC$Val = 3000 ; rkfTCVal -> Kf[KmTCVal, rkcat$TC$Val, Lamda], rkrTCVal -> Kr[rkcat$TC$Val, Lamda], KmTCPyr = 2000 ; rkcat$TC$Pyr = 3000 ; rkfTCPyr -> Kf[KmTCPyr, rkcat$TC$Pyr, Lamda], rkrTCPyr -> Kr[rkcat$TC$Pyr, Lamda], KmLIVIexVal = 2 ; kcat$LIVI$exVal = 500 ; kfLIVIexVal -> Kf[KmLIVIexVal, kcat$LIVI$exVal, Lamda], krLIVIexVal -> Kr[kcat$LIVI$exVal, Lamda], KmLIVIIexVal = 1 ; kcat$LIVII$exVal = 1 ; kfLIVIIexVal -> Kf[KmLIVIIexVal, kcat$LIVII$exVal, Lamda], krLIVIIexVal -> Kr[kcat$LIVII$exVal, Lamda], kcat$aKIV -> 70, kcat$Val -> 0.2, KmIPMSacetylCoA = 200 ; kcat$IPMS$acetylCoA = 1000 ; kfIPMSacetylCoA -> Kf[KmIPMSacetylCoA, kcat$IPMS$acetylCoA, Lamda], krIPMSacetylCoA -> Kr[kcat$IPMS$acetylCoA, Lamda], KmIPMSaKIV = 60 ; kcat$IPMS$aKIV = 1000 ; kfIPMSaKIV -> Kf[KmIPMSaKIV, kcat$IPMS$aKIV, Lamda], krIPMSaKIV -> Kr[kcat$IPMS$aKIV, Lamda], KiIPMSLeu = 200 ; kfiIPMSLeu -> Kfi[KmIPMSacetylCoA, kcat$IPMS$acetylCoA, Lamda, Omega], kriIPMSLeu -> Kri[KmIPMSacetylCoA, kcat$IPMS$acetylCoA, Lamda, Omega, KiIPMSLeu], KiIPMSacetylLeu = 500 ; kfiIPMSacetylLeu -> Kfi[KmIPMSaKIV, kcat$IPMS$aKIV, Lamda, Omega], kriIPMSacetylLeu -> Kri[KmIPMSaKIV, kcat$IPMS$aKIV, Lamda, Omega, KiIPMSacetylLeu], KmIPMIaIPM = 100 ; kcat$IPMI$aIPM = 1000 ; kfIPMIaIPM -> Kf[KmIPMIaIPM, kcat$IPMI$aIPM, Lamda], krIPMIaIPM -> Kr[kcat$IPMI$aIPM, Lamda], KmIPMIbIPM = 100 ; kcat$IPMI$bIPM = 1000 ; kfIPMIbIPM -> Kf[KmIPMIbIPM, kcat$IPMI$bIPM, Lamda], krIPMIbIPM -> Kr[kcat$IPMI$bIPM, Lamda], KmIPMDHbIPM = 105 ; KmIPMDHNAD = 320 ; kcat$IPMDH$bIPM = 4000 ; kfIPMDHbIPM -> Kf2S[KmIPMDHbIPM, KmIPMDHNAD, kcat$IPMDH$bIPM, Lamda], krIPMDHbIPM -> Kr[kcat$IPMDH$bIPM, Lamda], KmTBGlu = 1000 ; fkcat$TB$Glu = 2000 ; fkfTBGlu -> Kf[KmTBGlu, fkcat$TB$Glu, Lamda], fkrTBGlu -> Kr[fkcat$TB$Glu, Lamda], KmTBaKIC = 200 ; fkcat$TB$aKIC = 3600 ; fkfTBaKIC -> Kf[KmTBaKIC, fkcat$TB$aKIC, Lamda], fkrTBaKIC -> Kr[fkcat$TB$aKIC, Lamda], KmTBLeu = 4400 ; rkcat$TB$Leu = 2800 ; rkfTBLeu -> Kf[KmTBLeu, rkcat$TB$Leu, Lamda], rkrTBLeu -> Kr[rkcat$TB$Leu, Lamda], KmTBaKG = 2500 ; rkcat$TB$aKG = 2100 ; rkfTBaKG -> Kf[KmTBaKG, rkcat$TB$aKG, Lamda], rkrTBaKG -> Kr[rkcat$TB$aKG, Lamda], KmLIVIexLeu = 4 ; kcat$LIVI$exLeu = 100 ; kfLIVIexLeu -> Kf[KmLIVIexLeu, kcat$LIVI$exLeu, Lamda], krLIVIexLeu -> Kr[kcat$LIVI$exLeu, Lamda], KmLIVIIexLeu = 1 ; kcat$LIVII$exLeu = 1 ; kfLIVIIexLeu -> Kf[KmLIVIIexLeu, kcat$LIVII$exLeu, Lamda], krLIVIIexLeu -> Kr[kcat$LIVII$exLeu, Lamda], KmLSexLeu = 0.5 ; kcat$LS$exLeu = 100 ; kfLSexLeu -> Kf[KmLSexLeu, kcat$LS$exLeu, Lamda], krLSexLeu -> Kr[kcat$LS$exLeu, Lamda], kcat$aKIC -> 25, kcat$Leu -> 0.01 } ;

(* <br />    Inputs for Values of Substrate and Enzyme Concentrations ( m M ) <br /> *) myICs = { Thr[0] == 520, Pyr[0] == 1000, Leu[0] == 0, Ala[0] == 2000, Glu[0] == 2000, Ile[0] == 0, Val[0] == 0, aKB[0] == 0, NH3[0] == 0, aAHB[0] == 0, aDMV[0] == 0, aKMV[0] == 0, aKG[0] == 0, aAL[0] == 0, aDHIV[0] == 0, aKIV[0] == 0, aIPM[0] == 0, bIPM[0] == 0, aKIC[0] == 0, propionylCoA[0] == 0, glutarylCoA[0] == 0, pantothenate[0] == 0, acetylCoA[0] == 1000, CoA[0] == 0, NADP[0] == 0, NADPH[0] == 1000, NAD[0] == 1000, NADH[0] == 0, CO2[0] == 0, protein[0] == 0, TDA[0] == 3, KDC[0] == 2, AHASI[0] == 10, AHASICH3CO[0] == 0, AHASII[0] == 0,                       (* E . coli K12 has no active AHASII *) AHASIICH3CO[0] == 0, AHASIII[0] == 2, AHASIIICH3CO[0] == 0, IR[0] == 13.5, DAD[0] == 7, TB[0] == 2.5, TBNH2[0] == 0, TC[0] == 2, TCNH2[0] == 0, IPMS[0] == 5, IPMSacetyl[0] == 0, IPMI[0] == 6, IPMDH[0] == 5, LIVI[0] == 10, LIVII[0] == 0, LS[0] == 8,                                                         (* extracellular amino acid treatment *) exVal[0] == 0,                            (* 1000 for valine growth inhibition *) exIle[0] == 0,                            (* 500 for isoleucine rescue *) exLeu[0] == 0, $Complex$aKB$KDC$[0] == 0, $Complex$Pyr$AHASI$[0] == 0, $Complex$AHASI$Val$[0] == 0, $Complex$Pyr$AHASI$Val$[0] == 0, $Complex$AHASICH3CO$Val$[0] == 0, $Complex$aKB$AHASICH3CO$[0] == 0, $Complex$aKB$AHASICH3CO$Val$[0] == 0, $Complex$Pyr$AHASICH3CO$[0] == 0, $Complex$Pyr$AHASICH3CO$Val$[0] == 0, $Complex$Pyr$AHASII$[0] == 0, $Complex$aKB$AHASIICH3CO$[0] == 0, $Complex$Pyr$AHASIICH3CO$[0] == 0, $Complex$Pyr$AHASIII$[0] == 0, $Complex$AHASIII$Val$[0] == 0, $Complex$Pyr$AHASIII$Val$[0] == 0, $Complex$AHASIIICH3CO$Val$[0] == 0, $Complex$aKB$AHASIIICH3CO$[0] == 0, $Complex$aKB$AHASIIICH3CO$Val$[0] == 0, $Complex$Pyr$AHASIIICH3CO$[0] == 0, $Complex$Pyr$AHASIIICH3CO$Val$[0] == 0, $Complex$IR$aAHB$NADPH$[0] == 0, $Complex$IR$aAL$NADPH$[0] == 0, $Complex$aDHIV$DAD$[0] == 0, $Complex$aDMV$DAD$[0] == 0, $Complex$Glu$TB$[0] == 0, $Complex$aKMV$TBNH2$[0] == 0, $Complex$aKIV$TBNH2$[0] == 0, $Complex$Ile$TB$[0] == 0, $Complex$Val$TB$[0] == 0, $Complex$aKG$TBNH2$[0] == 0, $Complex$Ala$TC$[0] == 0, $Complex$aKIV$TCNH2$[0] == 0, $Complex$Val$TC$[0] == 0, $Complex$Pyr$TCNH2$[0] == 0, $Complex$exIle$LIVI$[0] == 0, $Complex$exIle$LIVII$[0] == 0, $Complex$exVal$LIVI$[0] == 0, $Complex$exVal$LIVII$[0] == 0, $Complex$acetylCoA$IPMS$[0] == 0, $Complex$aKIV$IPMSacetyl$[0] == 0, $Complex$IPMS$Leu$[0] == 0, $Complex$IPMSacetyl$Leu$[0] == 0, $Complex$aKIV$IPMSacetyl$Leu$[0] == 0, $Complex$aIPM$IPMI$[0] == 0, $Complex$bIPM$IPMI$[0] == 0, $Complex$IPMDH$bIPM$NAD$[0] == 0, $Complex$aKIC$TBNH2$[0] == 0, $Complex$Leu$TB$[0] == 0, $Complex$exLeu$LIVI$[0] == 0, $Complex$exLeu$LIVII$[0] == 0, $Complex$exLeu$LS$[0] == 0} ;

(* Call the Mathematica NDSolve Function to Solve the ODEs with Given Values of Kinetic Parameters and Substrate and Enzyme Concentrations Listed Above . *) tmax = 100 ;      (* minutes *) mySolution = NDSolve[Join[myODEs /. myKs, myICs], myVars, {t, 0, tmax}, MaxSteps -> 3000]

{{aAHB -> InterpolatingFunction[{{0.`, 100.`}}, <>], aAL -> InterpolatingFunction[{{0.`, 100.`}}, <>], acetylCoA -> InterpolatingFunction[{{0.`, 100.`}}, <>], aDHIV -> InterpolatingFunction[{{0.`, 100.`}}, <>], aDMV -> InterpolatingFunction[{{0.`, 100.`}}, <>], AHASI -> InterpolatingFunction[{{0.`, 100.`}}, <>], AHASICH3CO -> InterpolatingFunction[{{0.`, 100.`}}, <>], AHASII -> InterpolatingFunction[{{0.`, 100.`}}, <>], AHASIICH3CO -> InterpolatingFunction[{{0.`, 100.`}}, <>], AHASIII -> InterpolatingFunction[{{0.`, 100.`}}, <>], AHASIIICH3CO -> InterpolatingFunction[{{0.`, 100.`}}, <>], aIPM -> InterpolatingFunction[{{0.`, 100.`}}, <>], aKB -> InterpolatingFunction[{{0.`, 100.`}}, <>], aKG -> InterpolatingFunction[{{0.`, 100.`}}, <>], aKIC -> InterpolatingFunction[{{0.`, 100.`}}, <>], aKIV -> InterpolatingFunction[{{0.`, 100.`}}, <>], aKMV -> InterpolatingFunction[{{0.`, 100.`}}, <>], Ala -> InterpolatingFunction[{{0.`, 100.`}}, <>], bIPM -> InterpolatingFunction[{{0.`, 100.`}}, <>], CO2 -> InterpolatingFunction[{{0.`, 100.`}}, <>], CoA -> InterpolatingFunction[{{0.`, 100.`}}, <>], DAD -> InterpolatingFunction[{{0.`, 100.`}}, <>], exIle -> InterpolatingFunction[{{0.`, 100.`}}, <>], exLeu -> InterpolatingFunction[{{0.`, 100.`}}, <>], exVal -> InterpolatingFunction[{{0.`, 100.`}}, <>], Glu -> InterpolatingFunction[{{0.`, 100.`}}, <>], glutarylCoA -> InterpolatingFunction[{{0.`, 100.`}}, <>], Ile -> InterpolatingFunction[{{0.`, 100.`}}, <>], IPMDH -> InterpolatingFunction[{{0.`, 100.`}}, <>], IPMI -> InterpolatingFunction[{{0.`, 100.`}}, <>], IPMS -> InterpolatingFunction[{{0.`, 100.`}}, <>], IPMSacetyl -> InterpolatingFunction[{{0.`, 100.`}}, <>], IR -> InterpolatingFunction[{{0.`, 100.`}}, <>], KDC -> InterpolatingFunction[{{0.`, 100.`}}, <>], Leu -> InterpolatingFunction[{{0.`, 100.`}}, <>], LIVI -> InterpolatingFunction[{{0.`, 100.`}}, <>], LIVII -> InterpolatingFunction[{{0.`, 100.`}}, <>], LS -> InterpolatingFunction[{{0.`, 100.`}}, <>], NAD -> InterpolatingFunction[{{0.`, 100.`}}, <>], NADH -> InterpolatingFunction[{{0.`, 100.`}}, <>], NADP -> InterpolatingFunction[{{0.`, 100.`}}, <>], NADPH -> InterpolatingFunction[{{0.`, 100.`}}, <>], NH3 -> InterpolatingFunction[{{0.`, 100.`}}, <>], pantothenate -> InterpolatingFunction[{{0.`, 100.`}}, <>], propionylCoA -> InterpolatingFunction[{{0.`, 100.`}}, <>], protein -> InterpolatingFunction[{{0.`, 100.`}}, <>], Pyr -> InterpolatingFunction[{{0.`, 100.`}}, <>], TB -> InterpolatingFunction[{{0.`, 100.`}}, <>], TBNH2 -> InterpolatingFunction[{{0.`, 100.`}}, <>], TC -> InterpolatingFunction[{{0.`, 100.`}}, <>], TCNH2 -> InterpolatingFunction[{{0.`, 100.`}}, <>], TDA -> InterpolatingFunction[{{0.`, 100.`}}, <>], Thr -> InterpolatingFunction[{{0.`, 100.`}}, <>], Val -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$acetylCoA$IPMS$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aDHIV$DAD$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aDMV$DAD$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$AHASICH3CO$Val$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$AHASIIICH3CO$Val$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$AHASIII$Val$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$AHASI$Val$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aIPM$IPMI$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKB$AHASICH3CO$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKB$AHASICH3CO$Val$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKB$AHASIICH3CO$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKB$AHASIIICH3CO$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKB$AHASIIICH3CO$Val$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKB$KDC$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKG$TBNH2$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKIC$TBNH2$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKIV$IPMSacetyl$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKIV$IPMSacetyl$Leu$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKIV$TBNH2$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKIV$TCNH2$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$aKMV$TBNH2$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Ala$TC$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$bIPM$IPMI$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$exIle$LIVII$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$exIle$LIVI$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$exLeu$LIVII$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$exLeu$LIVI$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$exLeu$LS$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$exVal$LIVII$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$exVal$LIVI$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Glu$TB$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Ile$TB$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$IPMDH$bIPM$NAD$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$IPMSacetyl$Leu$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$IPMS$Leu$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$IR$aAHB$NADPH$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$IR$aAL$NADPH$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Leu$TB$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Pyr$AHASICH3CO$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Pyr$AHASICH3CO$Val$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Pyr$AHASIICH3CO$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Pyr$AHASIIICH3CO$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Pyr$AHASIIICH3CO$Val$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Pyr$AHASIII$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Pyr$AHASIII$Val$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Pyr$AHASII$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Pyr$AHASI$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Pyr$AHASI$Val$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Pyr$TCNH2$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Val$TB$ -> InterpolatingFunction[{{0.`, 100.`}}, <>], $Complex$Val$TC$ -> InterpolatingFunction[{{0.`, 100.`}}, <>]}}

(* List of Substrates, Intermediates and Products for Graphic Outputs Displayed Below *) metabolites = { Thr, Pyr, aKB, aAHB, aAL, NADPH, aDMV, aDHIV, aKMV, aKIV, acetylCoA, aIPM, bIPM, NAD, aKIC, Glu, Ala, aKG, Ile, Val, Leu } ;

(* Display Results of Simulation of Branched Chain Amino Acid Simulation : Rates of Production of Metabolic Intermediates and End - products . X axis is Time (min) , and Y axis is Concentration ( m M ) *) displayTime = 20 ; Show[GraphicsArray[Partition[Map[Plot[#[t] /. mySolution, {t, 0, displayTime}, PlotLabel -> #, PlotRange -> All, DisplayFunction -> Identity] &, metabolites], 3] ] ] ;

[Graphics:HTMLFiles/index_19.gif]

(* MWC Model for L - Threonine Deaminase (TDA) in E . coli K12 *) n = 4 ; (* from Supplementary Figure 3 *) c = 0.013 ; L 0 = 1.05 ; (* Substrate : threonine (THR) *) <br /> KmThr = 2700 ;    (* uM *) (* Inhibitor : isoleucine (ILE) ; Activator : valine (VAL) *) <br /> KiIle = 15 ;                                   (* TDA feedback resistant mutant, KiIle = 100000 *) KaVal = 550 ; <br /> R[t_] = (1 + Thr[t]/KmThr)^n/((1 + Thr[t]/KmThr)^n + (L 0 (1 + Ile[t]/KiIle)^n)/(1 + Val[t]/KaVal)^n (1 + c Thr[t]/KmThr)^n) ; <br /> Yf[t_] = (((Thr[t]/KmThr (1 + Thr[t]/KmThr)^(n - 1)) + (L 0 (1 + Ile[t]/KiIle)^n)/(1 + Val[t]/KaVal)^n Thr[t]/KmThr c (1 + c Thr[t]/KmThr)^(n - 1))/((1 + Thr[t]/KmThr)^n + (L 0 (1 + Ile[t]/KiIle)^n)/(1 + Val[t]/KaVal)^n (1 + c Thr[t]/KmThr)^n)) ;

(* Display of Fraction of TDA in the Active R State and the Fractional Saturation (Yf) of TDA with substrate (MWC model) *) Plot[R[t] /. mySolution, {t, 0, displayTime}, PlotLabel -> R, PlotRange -> {0, 0.6}] ;

[Graphics:HTMLFiles/index_22.gif]

Plot[Yf[t] /. mySolution, {t, 0, displayTime}, PlotLabel -> Yf, PlotRange -> {0, 0.1}] ;

[Graphics:HTMLFiles/index_24.gif]

Converted by Mathematica  (October 8, 2003)