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e_coli_13C_xch.r
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e_coli_13C_xch.r
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# 2014-28-08 millard@insa-toulouse.fr
#
# Model of the glycolytic and pentose phosphate pathways of E. coli
# published in the following paper:
#
# Impact of kinetic isotope effects in isotope labeling experiments
# by P. Millard, S. Sokol, J.C. Portais and P. Mendes
#
# A graphical representation of this network in SBGN format can be
# found in Figure 2 of the paper.
#
# 'rxn' : list containing the topology of the metabolic network, the
# carbon atom transitions, and the rate laws
# 'kp' : named vector of parameters
#
# note: in this version, reversible reactions are converted to two
# irreversible reactions to consider isotope exchange between
# metabolite pools
#
# Copyright 2014, INRA, France
# License: GNU General Public License v2 (see license.txt for details)
# network definition
# reaction substrate(s) product(s) carbon atom transitions rate law
rxn=list('PTS'= list('su'=c('GLC','PEP'), 'pr'=c('G6P','PYR'), 'tr'=c('abcdef','ghi','abcdef','ghi'), 'eq'="65*PTSrmaxPTS*GLC*(PEP/PYR)/((PTSKPTSa1+PTSKPTSa2*(PEP/PYR)+PTSKPTSa3*GLC+GLC*(PEP/PYR))*(1+G6P**PTSnPTSg6p/PTSKPTSg6p))"),
'PGI'= list('su'=c('G6P',''), 'pr'=c('F6P',''), 'tr'=c('abcdef','','abcdef',''), 'eq'="PGIrmaxPGI*G6P/(PGIKPGIg6p*(1+F6P/(PGIKPGIf6p*(1+PGN/PGIKPGIf6ppginh))+PGN/PGIKPGIg6ppginh)+G6P)"),
'PGIrev'= list('su'=c('F6P',''), 'pr'=c('G6P',''), 'tr'=c('abcdef','','abcdef',''), 'eq'="PGIrmaxPGI*F6P/(PGIKPGIeq*(PGIKPGIg6p*(1+F6P/(PGIKPGIf6p*(1+PGN/PGIKPGIf6ppginh))+PGN/PGIKPGIg6ppginh)+G6P))"),
'GPM'= list('su'=c('G6P',''), 'pr'=c('G1P',''), 'tr'=c('abcdef','','abcdef',''), 'eq'="PGMrmaxPGM*G6P/(PGMKPGMg6p*(1+G1P/PGMKPGMg1p)+G6P)"),
'GPMrev'= list('su'=c('G1P',''), 'pr'=c('G6P',''), 'tr'=c('abcdef','','abcdef',''), 'eq'="PGMrmaxPGM*G1P/(PGMKPGMeq*(PGMKPGMg6p*(1+G1P/PGMKPGMg1p)+G6P))"),
'G6PDH'= list('su'=c('G6P',''), 'pr'=c('PGN',''), 'tr'=c('abcdef','','abcdef',''), 'eq'="G6PDHrmaxG6PDH*G6P*cnadp/((G6P+G6PDHKG6PDHg6p)*(1+cnadph/G6PDHKG6PDHnadphg6pinh)*(G6PDHKG6PDHnadp*(1+cnadph/G6PDHKG6PDHnadphnadpinh)+cnadp))"),
'PFK'= list('su'=c('F6P',''), 'pr'=c('FBP',''), 'tr'=c('abcdef','','abcdef',''), 'eq'="PFKrmaxPFK*catp*F6P/((catp+PFKKPFKatps*(1+cadp/PFKKPFKadpc))*(F6P+PFKKPFKf6ps*(1+PEP/PFKKPFKpep+cadp/PFKKPFKadpb+camp/PFKKPFKampb)/(1+cadp/PFKKPFKadpa+camp/PFKKPFKampa))*(1+PFKLPFK/(1+F6P*(1+cadp/PFKKPFKadpa+camp/PFKKPFKampa)/(PFKKPFKf6ps*(1+PEP/PFKKPFKpep+cadp/PFKKPFKadpb+camp/PFKKPFKampb)))**PFKnPFK))"),
'TA'= list('su'=c('GAP','S7P'), 'pr'=c('F6P','E4P'), 'tr'=c('abc','defghij','defabc','ghij'), 'eq'="TArmaxTA*GAP*S7P"),
'TK1'= list('su'=c('R5P','X5P'), 'pr'=c('GAP','S7P'), 'tr'=c('abcde','fghij','cde','abfghij'), 'eq'="TK1rmaxTKa*R5P*X5P"),
'TK2'= list('su'=c('E4P','X5P'), 'pr'=c('GAP','F6P'), 'tr'=c('abcd','efghi','ghi','efabcd'), 'eq'="TK2rmaxTKb*X5P*E4P"),
'TArev'= list('su'=c('F6P','E4P'), 'pr'=c('GAP','S7P'), 'tr'=c('defabc','ghij','abc','defghij'), 'eq'="TArmaxTA*E4P*F6P/TAKTAeq"),
'TK1rev'= list('su'=c('GAP','S7P'), 'pr'=c('R5P','X5P'), 'tr'=c('cde','abfghij','abcde','fghij'), 'eq'="TK1rmaxTKa*S7P*GAP/TK1KTKaeq"),
'TK2rev'= list('su'=c('GAP','F6P'), 'pr'=c('E4P','X5P'), 'tr'=c('ghi','efabcd','abcd','efghi'), 'eq'="TK2rmaxTKb*F6P*GAP/TK2KTKbeq"),
'MURSYN'= list('su'=c('F6P',''), 'pr'=c('',''), 'tr'=c('abcdef','','',''), 'eq'="MURSYNv*2"),
'ALD'= list('su'=c('FBP',''), 'pr'=c('DHAP','GAP'), 'tr'=c('abcdef','','cba','def'), 'eq'="ALDrmaxALDO*FBP/(ALDkALDOfdp+FBP+ALDkALDOgap*DHAP/(ALDkALDOeq*ALDVALDOblf)+ALDkALDOdhap*GAP/(ALDkALDOeq*ALDVALDOblf)+FBP*GAP/ALDkALDOgapinh+GAP*DHAP/(ALDVALDOblf*ALDkALDOeq))"),
'ALDrev'= list('su'=c('DHAP','GAP'), 'pr'=c('FBP',''), 'tr'=c('cba','def','abcdef',''), 'eq'="ALDrmaxALDO*(GAP*DHAP/ALDkALDOeq)/(ALDkALDOfdp+FBP+ALDkALDOgap*DHAP/(ALDkALDOeq*ALDVALDOblf)+ALDkALDOdhap*GAP/(ALDkALDOeq*ALDVALDOblf)+FBP*GAP/ALDkALDOgapinh+GAP*DHAP/(ALDVALDOblf*ALDkALDOeq))"),
'GAPDH'= list('su'=c('GAP',''), 'pr'=c('BPG',''), 'tr'=c('abc','','abc',''), 'eq'="GAPDHrmaxGAPDH*(GAP*cnad)/((GAPDHKGAPDHgap*(1+BPG/GAPDHKGAPDHpgp)+GAP)*(GAPDHKGAPDHnad*(1+cnadh/GAPDHKGAPDHnadh)+cnad))"),
'GAPDHrev'= list('su'=c('BPG',''), 'pr'=c('GAP',''), 'tr'=c('abc','','abc',''), 'eq'="GAPDHrmaxGAPDH*(BPG*cnadh/GAPDHKGAPDHeq)/((GAPDHKGAPDHgap*(1+BPG/GAPDHKGAPDHpgp)+GAP)*(GAPDHKGAPDHnad*(1+cnadh/GAPDHKGAPDHnadh)+cnad))"),
'TPI'= list('su'=c('DHAP',''), 'pr'=c('GAP',''), 'tr'=c('abc','','cba',''), 'eq'="TPIrmaxTIS*(DHAP)/(TPIkTISdhap*(1+GAP/TPIkTISgap)+DHAP)"),
'TPIrev'= list('su'=c('GAP',''), 'pr'=c('DHAP',''), 'tr'=c('abc','','cba',''), 'eq'="TPIrmaxTIS*(GAP/TPIkTISeq)/(TPIkTISdhap*(1+GAP/TPIkTISgap)+DHAP)"),
'GDH'= list('su'=c('DHAP',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="GDHrmaxG3PDH*DHAP/(GDHKG3PDHdhap+DHAP)"),
'PGK'= list('su'=c('BPG',''), 'pr'=c('PG3',''), 'tr'=c('abc','','abc',''), 'eq'="PGKrmaxPGK*(cadp*BPG)/((PGKKPGKadp*(1+catp/PGKKPGKatp)+cadp)*(PGKKPGKpgp*(1+PG3/PGKKPGKpg3)+BPG))"),
'PGKrev'= list('su'=c('PG3',''), 'pr'=c('BPG',''), 'tr'=c('abc','','abc',''), 'eq'="PGKrmaxPGK*(catp*PG3/PGKKPGKeq)/((PGKKPGKadp*(1+catp/PGKKPGKatp)+cadp)*(PGKKPGKpgp*(1+PG3/PGKKPGKpg3)+BPG))"),
'SERSYN'= list('su'=c('PG3',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="SERSYNrmaxSerSynth*PG3/(SERSYNKSerSynthpg3+PG3)"),
'PGMrev'= list('su'=c('PG2',''), 'pr'=c('PG3',''), 'tr'=c('abc','','abc',''), 'eq'="PGMrmaxPGluMu*(PG2/PGMKPGluMueq)/(PGMKPGluMupg3*(1+PG2/PGMKPGluMupg2)+PG3)"),
'ENOrev'= list('su'=c('PEP',''), 'pr'=c('PG2',''), 'tr'=c('abc','','abc',''), 'eq'="ENOrmaxENO*(PEP/ENOKENOeq)/(ENOKENOpg2*(1+PEP/ENOKENOpep)+PG2)"),
'PGM'= list('su'=c('PG3',''), 'pr'=c('PG2',''), 'tr'=c('abc','','abc',''), 'eq'="PGMrmaxPGluMu*(PG3)/(PGMKPGluMupg3*(1+PG2/PGMKPGluMupg2)+PG3)"),
'ENO'= list('su'=c('PG2',''), 'pr'=c('PEP',''), 'tr'=c('abc','','abc',''), 'eq'="ENOrmaxENO*(PG2)/(ENOKENOpg2*(1+PEP/ENOKENOpep)+PG2)"),
'PYK'= list('su'=c('PEP',''), 'pr'=c('PYR',''), 'tr'=c('abc','','abc',''), 'eq'="PYKrmaxPK*PEP*(PEP/PYKKPKpep+1)**(PYKnPK-1)*cadp/(PYKKPKpep*(PYKLPK*((1+catp/PYKKPKatp)/(FBP/PYKKPKfdp+camp/PYKKPKamp+1))**PYKnPK+(PEP/PYKKPKpep+1)**PYKnPK)*(cadp+PYKKPKadp))"),
'PPC'= list('su'=c('PEP',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="PPCrmaxpepCxylase*PEP*(1+(FBP/PPCKpepCxylasefdp)**PPCnpepCxylasefdp)/(PPCKpepCxylasepep+PEP)"),
'SYN1'= list('su'=c('PEP',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="SYN1rmaxSynth1*PEP/(SYN1KSynth1pep+PEP)"),
'SYN2'= list('su'=c('PYR',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="SYN2rmaxSynth2*PYR/(SYN2KSynth2pyr+PYR)"),
'DAHPSYN'= list('su'=c('E4P','PEP'), 'pr'=c('',''), 'tr'=c('abcd','efg','',''), 'eq'="DAHPSYNrmaxDAHPS*E4P**DAHPSYNnDAHPSe4p*PEP**DAHPSYNnDAHPSpep/((DAHPSYNKDAHPSe4p+E4P**DAHPSYNnDAHPSe4p)*(DAHPSYNKDAHPSpep+PEP**DAHPSYNnDAHPSpep))"),
'PDH'= list('su'=c('PYR',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="PDHrmaxPDH*PYR**PDHnPDH/(PDHKPDHpyr+PYR**PDHnPDH)"),
'GND'= list('su'=c('PGN',''), 'pr'=c('RB5P',''), 'tr'=c('abcdef','','abcde',''), 'eq'="GNDrmaxPGDH*PGN*cnadp/((PGN+GNDKPGDHpg)*(cnadp+GNDKPGDHnadp*(1+cnadph/GNDKPGDHnadphinh)*(1+catp/GNDKPGDHatpinh)))"),
'RPI'= list('su'=c('RB5P',''), 'pr'=c('R5P',''), 'tr'=c('abcde','','abcde',''), 'eq'="RPIrmaxR5PI*(RB5P)"),
'RPE'= list('su'=c('RB5P',''), 'pr'=c('X5P',''), 'tr'=c('abcde','','abcde',''), 'eq'="RPErmaxRu5P*(RB5P)"),
'RPIrev'= list('su'=c('R5P',''), 'pr'=c('RB5P',''), 'tr'=c('abcde','','abcde',''), 'eq'="RPIrmaxR5PI*(R5P/RPIKR5PIeq)"),
'RPErev'= list('su'=c('X5P',''), 'pr'=c('RB5P',''), 'tr'=c('abcde','','abcde',''), 'eq'="RPErmaxRu5P*(X5P/RPEKRu5Peq)"),
'RPP'= list('su'=c('R5P',''), 'pr'=c('',''), 'tr'=c('abcde','','',''), 'eq'="RPPrmaxRPPK*R5P/(RPPKRPPKrib5p+R5P)"),
'G1PAT'= list('su'=c('G1P',''), 'pr'=c('',''), 'tr'=c('abcdef','','',''), 'eq'="G1PATrmaxG1PAT*G1P*catp*(1+(FBP/G1PATKG1PATfdp)**G1PATnG1PATfdp)/((G1PATKG1PATatp+catp)*(G1PATKG1PATg1p+G1P))"),
'G6Pdilution'= list('su'=c('G6P',''), 'pr'=c('',''), 'tr'=c('abcdef','','',''), 'eq'="mu*G6P"),
'F6Pdilution'= list('su'=c('F6P',''), 'pr'=c('',''), 'tr'=c('abcdef','','',''), 'eq'="mu*F6P"),
'FDPdilution'= list('su'=c('FBP',''), 'pr'=c('',''), 'tr'=c('abcdef','','',''), 'eq'="mu*FBP"),
'GAPdilution'= list('su'=c('GAP',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="mu*GAP"),
'DHAPdilution'= list('su'=c('DHAP',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="mu*DHAP"),
'BPGdilution'= list('su'=c('BPG',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="mu*BPG"),
'PG3dilution'= list('su'=c('PG3',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="mu*PG3"),
'PG2dilution'= list('su'=c('PG2',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="mu*PG2"),
'PEPdilution'= list('su'=c('PEP',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="mu*PEP"),
'RB5Pdilution'= list('su'=c('RB5P',''), 'pr'=c('',''), 'tr'=c('abcde','','',''), 'eq'="mu*RB5P"),
'R5Pdilution'= list('su'=c('R5P',''), 'pr'=c('',''), 'tr'=c('abcde','','',''), 'eq'="mu*R5P"),
'X5Pdilution'= list('su'=c('X5P',''), 'pr'=c('',''), 'tr'=c('abcde','','',''), 'eq'="mu*X5P"),
'S7Pdilution'= list('su'=c('S7P',''), 'pr'=c('',''), 'tr'=c('abcdefg','','',''), 'eq'="mu*S7P"),
'PYRdilution'= list('su'=c('PYR',''), 'pr'=c('',''), 'tr'=c('abc','','',''), 'eq'="mu*PYR"),
'PGNdilution'= list('su'=c('PGN',''), 'pr'=c('',''), 'tr'=c('abcdef','','',''), 'eq'="mu*PGN"),
'E4Pdilution'= list('su'=c('E4P',''), 'pr'=c('',''), 'tr'=c('abcd','','',''), 'eq'="mu*E4P"),
'G1Pdilution'= list('su'=c('G1P',''), 'pr'=c('',''), 'tr'=c('abcdef','','',''), 'eq'="mu*G1P"))
# kinetic parameters
kp=c('PTSrmaxPTS'=7829.78,
'PTSKPTSa1'=3082.3,
'PTSKPTSa2'=0.01,
'PTSKPTSa3'=245.3,
'PTSnPTSg6p'=3.66,
'PTSKPTSg6p'=2.15,
'PGIrmaxPGI'=650.988,
'PGIKPGIeq'=0.1725,
'PGIKPGIg6p'=2.9,
'PGIKPGIf6p'=0.266,
'PGIKPGIf6ppginh'=0.2,
'PGIKPGIg6ppginh'=0.2,
'PGMrmaxPGM'=0.839824,
'PGMKPGMeq'=0.196,
'PGMKPGMg6p'=1.038,
'PGMKPGMg1p'=0.0136,
'G6PDHrmaxG6PDH'=1.3802,
'G6PDHKG6PDHg6p'=14.4,
'G6PDHKG6PDHnadphg6pinh'=6.43,
'G6PDHKG6PDHnadp'=0.0246,
'G6PDHKG6PDHnadphnadpinh'=0.01,
'cnadph'=0.062,
'PFKrmaxPFK'=1840.58,
'PFKKPFKatps'=0.123,
'PFKKPFKadpc'=4.14,
'PFKKPFKf6ps'=0.325,
'PFKKPFKpep'=3.26,
'PFKKPFKadpb'=3.89,
'PFKKPFKampb'=3.2,
'PFKKPFKadpa'=128,
'PFKKPFKampa'=19.1,
'PFKLPFK'=5629070,
'PFKnPFK'=11.1,
'cadp'=0.582,
'camp'=0.954783,
'TArmaxTA'=10.8716,
'TAKTAeq'=1.05,
'TK1rmaxTKa'=9.47338,
'TK1KTKaeq'=1.2,
'TK2rmaxTKb'=86.5586,
'TK2KTKbeq'=10,
'MURSYNv'=0.00043711,
'ALDrmaxALDO'=17.4146,
'ALDkALDOeq'=0.144,
'ALDkALDOfdp'=1.75,
'ALDkALDOgap'=0.088,
'ALDVALDOblf'=2,
'ALDkALDOdhap'=0.088,
'ALDkALDOgapinh'=0.6,
'GAPDHrmaxGAPDH'=921.594,
'GAPDHKGAPDHeq'=0.63,
'GAPDHKGAPDHgap'=0.683,
'GAPDHKGAPDHpgp'=0.0000104,
'GAPDHKGAPDHnad'=0.252,
'GAPDHKGAPDHnadh'=1.09,
'cnad'=1.4644,
'cnadh'=0.0934,
'TPIrmaxTIS'=68.6747,
'TPIkTISeq'=1.39,
'TPIkTISdhap'=2.8,
'TPIkTISgap'=0.3,
'TRPv'=0.001037,
'GDHrmaxG3PDH'=0.0116204,
'GDHKG3PDHdhap'=1,
'PGKrmaxPGK'=3021.77,
'PGKKPGKeq'=1934.4,
'PGKKPGKadp'=0.185,
'PGKKPGKatp'=0.653,
'PGKKPGKpgp'=0.0468,
'PGKKPGKpg3'=0.473,
'SERSYNrmaxSerSynth'=0.0257121,
'SERSYNKSerSynthpg3'=1,
'PGMrmaxPGluMu'=89.0497,
'PGMKPGluMueq'=0.188,
'PGMKPGluMupg3'=0.2,
'PGMKPGluMupg2'=0.369,
'ENOrmaxENO'=330.448,
'ENOKENOeq'=6.73,
'ENOKENOpg2'=0.1,
'ENOKENOpep'=0.135,
'PYKrmaxPK'=0.0611315,
'PYKKPKpep'=0.31,
'PYKnPK'=4,
'PYKLPK'=1000,
'PYKKPKatp'=22.5,
'PYKKPKfdp'=0.19,
'PYKKPKamp'=0.2,
'PYKKPKadp'=0.26,
'PPCrmaxpepCxylase'=0.107021,
'PPCKpepCxylasefdp'=0.7,
'PPCnpepCxylasefdp'=4.21,
'PPCKpepCxylasepep'=4.07,
'SYN1rmaxSynth1'=0.019539,
'SYN1KSynth1pep'=1,
'SYN2rmaxSynth2'=0.0736186,
'SYN2KSynth2pyr'=1,
'DAHPSYNrmaxDAHPS'=0.107953,
'DAHPSYNnDAHPSe4p'=2.6,
'DAHPSYNnDAHPSpep'=2.2,
'DAHPSYNKDAHPSe4p'=0.035,
'DAHPSYNKDAHPSpep'=0.0053,
'PDHrmaxPDH'=6.05953,
'PDHnPDH'=3.68,
'PDHKPDHpyr'=1159,
'METSYNv'=0.0022627,
'GNDrmaxPGDH'=16.2324,
'GNDKPGDHpg'=37.5,
'GNDKPGDHnadp'=0.0506,
'GNDKPGDHnadphinh'=0.0138,
'GNDKPGDHatpinh'=208,
'catp'=4.27,
'cnadp'=0.196759,
'RPIrmaxR5PI'=4.83841,
'RPIKR5PIeq'=4,
'RPErmaxRu5P'=6.73903,
'RPEKRu5Peq'=1.4,
'RPPrmaxRPPK'=0.0129005,
'RPPKRPPKrib5p'=0.1,
'G1PATrmaxG1PAT'=0.00752546,
'G1PATKG1PATfdp'=0.119,
'G1PATnG1PATfdp'=1.2,
'G1PATKG1PATatp'=4.42,
'G1PATKG1PATg1p'=3.2,
'mu'=0.0000278)