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e_coli_13C_noxch.r

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