Entropic flux balance analysis

Author: Ronan Fleming, University of Galway

INTRODUCTION

Entropic flux balance analysis [1] maximises the (unnormalised) entropy of unidirectional fluxes ( and ) and optionally a linear function of external net fluxes w, subject to mass balance constraints, optionally coupling constraints, box constraints on net flux, and zero lower bounds on unidirectional fluxes. This ensures that predicted steady state fluxes are thermodynamically feasible, assuming one is given a model that admits a thermodynamically feasible flux. A method for finding the largest subset of a given model that admits a thermodynamically feasible flux is described in this paper [3] and this tutorial [4]. Given a generic model of metabolism and context-specific omics data, this paper [5] and this tutorial [6] explain how to extract a context-specific model that admits a thermodynamically feasible internal net flux vector, using the XomicsToModel protocol [5].
Entropic flux balance analysis is mathematically represented by the optimisation problem
where N is the internal reaction stoichiometric matrix (all reactions bass balanced), B is the external reaction stoichiometric matrix (all reactions mass imbalanced), b may be used to represent any known fixed input (negative) or output (positive) of molecular species from the system, and zero otherwise. The variables to the right of the : are the corresponding dual variables to each constraint.
A variation of this is quadratically constrained entropic flux balance analysis [2], which allows one to penalise deviation of predicted net flux from experimentally measured net flux. This is represented by the following optimisation problem
where H may be used to add penalties, e.g., is the standard deviation in measured net flux h.

MATERIALS - EQUIPMENT SETUP

Mosek installation required

PROCEDURE

Set the directory for results
basePath='~/work/sbgCloud';
resultsDirectory=[basePath '/programModelling/projects/thermoModel/results/entropicFBA'];
Set the model to load
modelToUse='iDopaNeuro';
%modelToUse='ecoli_core';
%modelToUse = 'fork';
%modelToUse = 'single';
%modelToUse='recon3';
 
if ~exist('model','var')
switch modelToUse
case 'single'
driver_singleModel
case 'fork'
driver_forkModel
 
case 'ecoli_core'
dataDirectory=[basePath '/data'];
load([dataDirectory '/models/published/e_coli_core.mat']);
if ~isfield(model,'SConsistentMetBool') || ~isfield(model,'SConsistentRxnBool')
massBalanceCheck=0;
[~, ~, ~, ~, ~, ~, model, ~] = findStoichConsistentSubset(model, massBalanceCheck, 0);
end
model.lb(ismember(model.rxns,'BIOMASS_Ecoli_core_w_GAM'))=0.1;
case 'recon3'
%COBRA.models/mat/Recon3DModel_301_xomics_input.mat
load(which('Recon3DModel_301_xomics_input.mat'))
 
%change onto uMol/gDW/hr
model.lb = model.lb;
model.ub = model.ub;
case 'iDopaNeuro'
%load('~/drive/sbgCloud/projects/iDopaNeuro/results/codeResults/iDN1/iDopaNeuroC/iDopaNeuroC.mat')
load('~/drive/sbgCloud/projects/variationalKinetics/data/iDopaNeuro/iDopaNeuroC.mat')
model = iDopaNeuroC;
clear iDopaNeuroC
model.lb(ismember(model.rxns,'ATPM')) = model.lb(ismember(model.rxns,'ATPM'))/2;
 
%problematic reactions
% {'34DHPHEt'} {'3, 4-Dihydroxy-L-Phenylalanine Transport' } -0.53635 0 {'34dhphe[e] <=> 34dhphe[c] '}
% {'URAt' } {'Uracil Transport via Faciliated Diffusion'} -0.0013626 0 {'ura[e] <=> ura[c] ' }
model.lb(ismember(model.rxns,'34DHPHEt'))=-1e4;
model.ub(ismember(model.rxns,'34DHPHEt'))= 1e4;
model.lb(ismember(model.rxns,'URAt'))=-1e4;
model.ub(ismember(model.rxns,'URAt'))= 1e4;
end
end
Examine the constraints on the model
printConstraints(model,-1e4,1e4,model.SIntRxnBool)
Forward_Reaction, 0 bound Name lb ub equation _________________________ ________________________________________________________________ __ _______ _______________________________________________________________________________________________________________________ {'10FTHF6GLUtl' } {'6-Glutamyl-10Fthf Transport, Lysosomal' } 0 10000 {'10fthf6glu[c] -> 10fthf6glu[l] ' } {'1PPDCRp' } {'Delta1-Piperideine-2-Carboxylate Reductase, Perixosomal' } 0 10000 {'h[x] + 1pipdn2c[x] + nadh[x] -> Lpipecol[x] + nad[x] ' } {'2OXOADOXm' } {'2-Oxoadipate:Lipoamde 2-Oxidoreductase (Decarboxylating And '} 0 10000 {'nad[m] + 2oxoadp[m] + coa[m] -> nadh[m] + co2[m] + glutcoa[m] ' } {'34DHPHAMT' } {'3, 4-Dihydroxyphenylacetate:Amet O-Methyltransferase' } 0 10000 {'34dhpha[c] + amet[c] -> h[c] + ahcys[c] + homoval[c] ' } {'34DHPLACOX' } {'3, 4-Dihydroxyphenylacetaldehyde:NAD+ Oxidoreductase' } 0 10000 {'h2o[c] + nad[c] + 34dhpac[c] -> 2 h[c] + nadh[c] + 34dhpha[c] ' } {'34DHXMANDACOX' } {'3, 4-Dihydroxymandelaldehyde:NAD+ Oxidoreductase' } 0 10000 {'h2o[c] + nad[c] + 34dhmald[c] -> 2 h[c] + nadh[c] + 34dhoxmand[c] ' } {'34HPLFM' } {'3- (4-Hydroxyphenyl-)Lactate Formation' } 0 10000 {'h[m] + nadh[m] + 34hpp[m] -> nad[m] + 34hpl[m] ' } {'3DSPHR' } {'3-Dehydrosphinganine Reductase' } 0 10000 {'h[c] + nadph[c] + 3dsphgn[c] -> nadp[c] + sphgn[c] ' } {'3HLYTCL' } {'3-Hydroxy-L-Tyrosine Carboxy-Lyase' } 0 10000 {'h[c] + 34dhphe[c] -> co2[c] + dopa[c] ' } {'3SALACBOXL' } {'3-Sulfino-L-Alanine Carboxy-Lyase' } 0 10000 {'2 h[c] + 3sala[c] -> co2[c] + hyptaur[c] ' } {'3SALAOX' } {'Cysteinesulfinic Acid Oxidase' } 0 10000 {'o2[c] + 2 h[c] + 2 3sala[c] -> 2 Lcyst[c] ' } {'3SALATAi' } {'3-Sulfino-Alanine Transaminase (Irreversible)' } 0 10000 {'h[c] + akg[c] + 3sala[c] -> glu_L[c] + 3snpyr[c] ' } {'3SPYRSP' } {'3-Sulfinopyruvate Hydrolase (Spotaneous Reaction)' } 0 10000 {'h2o[c] + 3snpyr[c] -> h[c] + pyr[c] + so3[c] ' } {'41R1H2MAE12BOOX' } {'4-[ (1R)-1-Hydroxy-2- (Methylamino)Ethyl]-1, 2-Benzenediol:O'} 0 10000 {'h2o[c] + o2[c] + adrnl[c] -> h2o2[c] + 34dhmald[c] + mma[c] ' } {'42A12BOOX' } {'4- (2-Aminoethyl)-1, 2-Benzenediol:Oxygen Oxidoreductase (De'} 0 10000 {'h2o[c] + o2[c] + dopa[c] -> h2o2[c] + nh4[c] + 34dhpac[c] ' } {'4HBZCOAFm' } {'4-Hydroxybenzoyl Coenzyme A Formation' } 0 10000 {'h2o[m] + nad[m] + coa[m] + coucoa[m] -> h[m] + nadh[m] + 4hbzcoa[m] + accoa[m] ' } {'4HBZFm' } {'4-Hydroxybenzoate Formation' } 0 10000 {'h2o[m] + 4hbzcoa[m] -> h[m] + coa[m] + 4hbz[m] ' } {'4MOPt2im' } {'4-Methyl-2-Oxopentanoate Mitochondrial Transport via Proton '} 0 10000 {'h[c] + 4mop[c] -> h[m] + 4mop[m] ' } {'7DHFtl' } {'7-Glutamyl-Dhf Transport, Lysosomal' } 0 10000 {'7dhf[c] -> 7dhf[l] ' } {'AASAD3m' } {'L-Aminoadipate-Semialdehyde Dehydrogenase (NADH), Mitochondr'} 0 10000 {'h2o[m] + nad[m] + L2aadp6sa[m] -> 2 h[m] + L2aadp[m] + nadh[m] ' } {'ACACT1x' } {'Acetyl Coenzyme A C-Acetyltransferase' } 0 10000 {'2 accoa[x] -> coa[x] + aacoa[x] ' } {'ACGALK' } {'N-Acetylgalactosamine Kinase' } 0 10000 {'atp[c] + acgal[c] -> h[c] + adp[c] + acgal1p[c] ' } {'ACGALK2' } {'N-Acetylgalactosamine Kinase (ITP)' } 0 10000 {'acgal[c] + itp[c] -> h[c] + acgal1p[c] + idp[c] ' } {'ACGAM6PSi' } {'N-Acetylglucosamine-6-Phosphate Synthase' } 0 10000 {'accoa[c] + gam6p[c] -> h[c] + coa[c] + acgam6p[c] ' } {'ACGAMK' } {'N-Acetylglucosamine Kinase' } 0 10000 {'atp[c] + acgam[c] -> h[c] + adp[c] + acgam6p[c] ' } {'ACGAMtly' } {'N-Acetyl-Glucosamine Lysosomal Efflux' } 0 10000 {'acgam[l] -> acgam[c] ' } {'ACITL' } {'ATP-Citrate Lyase' } 0 10000 {'atp[c] + coa[c] + cit[c] -> adp[c] + pi[c] + accoa[c] + oaa[c] ' } {'ACNAM9PL2' } {'N-Acetylneuraminate 9-Phosphate Pyruvate-Lyase (Pyruvate-Pho'} 0 10000 {'h2o[c] + pep[c] + man6p[c] -> pi[c] + kdnp[c] ' } {'ACOAD8m' } {'Acyl Coenzyme A Dehydrogenase (Isovaleryl Coenzyme A), Mitoc'} 0 10000 {'fad[m] + ivcoa[m] -> fadh2[m] + 3mb2coa[m] ' } {'ACP1_FMN_' } {'Acid Phosphatase (FMN)' } 0 10000 {'h2o[c] + fmn[c] -> pi[c] + ribflv[c] ' } {'ADMDC' } {'Adenosylmethionine Decarboxylase' } 0 10000 {'h[c] + amet[c] -> co2[c] + ametam[c] ' } {'ADNCYC' } {'Adenylate Cyclase' } 0 10000 {'atp[c] -> ppi[c] + camp[c] ' } {'ADRNLPVESSEC' } {'Adrenaline Secretion via Secretory Vesicle (ATP Driven)' } 0 10000 {'h2o[c] + atp[c] + adrnl[c] -> h[c] + adp[c] + pi[c] + adrnl[e] ' } {'ADSK' } {'Adenylyl-Sulfate Kinase' } 0 10000 {'atp[c] + aps[c] -> h[c] + adp[c] + paps[c] ' } {'ADSL1' } {'Adenylosuccinate Lyase' } 0 10000 {'dcamp[c] -> amp[c] + fum[c] ' } {'ADSL2' } {'Adenylosuccinate Lyase' } 0 10000 {'25aics[c] -> fum[c] + aicar[c] ' } {'AGPAT1' } {'1-Acylglycerol-3-Phosphate O-Acyltransferase 1' } 0 10000 {'2 h[c] + Rtotal2coa[c] + alpa_hs[c] -> coa[c] + pa_hs[c] ' } {'AGTim' } {'Alanine-Glyoxylate Transaminase (Irreversible), Mitochondria'} 0 10000 {'ala_L[m] + glx[m] -> pyr[m] + gly[m] ' } {'AKGDm' } {'2-Oxoglutarate Dehydrogenase' } 0 10000 {'akg[m] + nad[m] + coa[m] -> nadh[m] + co2[m] + succoa[m] ' } {'ALAASNNaEx' } {'L-Alanine/L-Asparagine Na-Dependent Exchange (Ala-L In)' } 0 10000 {'na1[e] + ala_L[e] + asn_L[c] -> na1[c] + ala_L[c] + asn_L[e] ' } {'ALAGLNNaEx' } {'L-Alanine/L-Glutamine Na-Dependent Exchange (Ala-L In)' } 0 10000 {'na1[e] + ala_L[e] + gln_L[c] -> na1[c] + ala_L[c] + gln_L[e] ' } {'ALASm' } {'5-Aminolevulinate Synthase' } 0 10000 {'h[m] + gly[m] + succoa[m] -> coa[m] + co2[m] + 5aop[m] ' } {'ALAt4' } {'Alanine-Sodium Symporter' } 0 10000 {'na1[e] + ala_L[e] -> na1[c] + ala_L[c] ' } {'ALCD21_L' } {'Alcohol Dehydrogenase (L-1, 2-Propanediol)' } 0 10000 {'nad[c] + 12ppd_S[c] -> h[c] + nadh[c] + lald_L[c] ' } {'ALDD2xm' } {'Aldehyde Dehydrogenase (Acetylaldehyde, NAD), Mitochondrial' } 0 10000 {'h2o[m] + nad[m] + acald[m] -> 2 h[m] + nadh[m] + ac[m] ' } {'ALDD2y' } {'Aldehyde Dehydrogenase (Acetaldehyde, NADP)' } 0 10000 {'h2o[c] + nadp[c] + acald[c] -> 2 h[c] + nadph[c] + ac[c] ' } {'ALOX5' } {'Arachidonate 5-Lipoxygenase' } 0 10000 {'o2[c] + arachd[c] -> 5HPET[c] ' } {'ALOX52' } {'Arachidonate 5-Lipoxygenase' } 0 10000 {'5HPET[c] -> h2o[c] + leuktrA4[c] ' } {'ALR2' } {'Aldose Reductase (Methylglyoxal)' } 0 10000 {'h[c] + nadph[c] + mthgxl[c] -> nadp[c] + acetol[c] ' } {'ALR3' } {'Aldose Reductase (Acetol)' } 0 10000 {'h[c] + nadph[c] + acetol[c] -> nadp[c] + 12ppd_S[c] ' } {'AMPDA' } {'Adenosine Monophosphate Deaminase' } 0 10000 {'h2o[c] + h[c] + amp[c] -> nh4[c] + imp[c] ' } {'APRTO2' } {'N-Acetylputrescine: Oxygen Oxireductase (Deaminating)' } 0 10000 {'h2o[c] + o2[c] + aprut[c] -> h2o2[c] + nh4[c] + n4abutn[c] ' } {'ARGLYSex' } {'Arginine/Lysine Exchanger (Arg In)' } 0 10000 {'lys_L[c] + arg_L[e] -> lys_L[e] + arg_L[c] ' } {'ARGSS' } {'Argininosuccinate Synthase' } 0 10000 {'atp[c] + asp_L[c] + citr_L[c] -> h[c] + amp[c] + ppi[c] + argsuc[c] ' } {'R_group_phosphotase_1'} {'R Group Phosphotase 1' } 0 10000 {'atp[c] + coa[c] + Rtotal[c] -> amp[c] + ppi[c] + Rtotalcoa[c] ' } {'R_group_phosphotase_2'} {'R Group Phosphotase 2' } 0 10000 {'atp[c] + coa[c] + Rtotal2[c] -> amp[c] + ppi[c] + Rtotal2coa[c] ' } {'ASAH1' } {'N-Acylsphingosine Amidohydrolase' } 0 10000 {'h2o[l] + crm_hs[l] -> Rtotal[l] + sphings[l] ' } {'ASNALANaEx' } {'L-Alanine/L-Asparagine Na-Dependent Exchange (Asn-L In)' } 0 10000 {'na1[e] + ala_L[c] + asn_L[e] -> na1[c] + ala_L[e] + asn_L[c] ' } {'ASNNm' } {'L-Asparaginase, Mitochondrial' } 0 10000 {'h2o[m] + asn_L[m] -> asp_L[m] + nh4[m] ' } {'ASNS1' } {'Asparagine Synthase (Glutamine-Hydrolysing)' } 0 10000 {'h2o[c] + atp[c] + asp_L[c] + gln_L[c] -> h[c] + glu_L[c] + amp[c] + ppi[c] + asn_L[c] ' } {'ASNt4' } {'L-Asparagine Transport in via Sodium Symport' } 0 10000 {'na1[e] + asn_L[e] -> na1[c] + asn_L[c] ' } {'ASNtm' } {'L-Asparagine Transport, Mitochondrial' } 0 10000 {'asn_L[c] -> asn_L[m] ' } {'ASPDt6' } {'D-Aspartate Transport via Na, H Symport And K Antiport' } 0 10000 {'h[e] + 3 na1[e] + asp_D[e] + k[c] -> h[c] + 3 na1[c] + asp_D[c] + k[e] ' } {'ASPGLUm' } {'Aspartate-Glutamate Mitochondrial Shuttle' } 0 10000 {'h[c] + glu_L[c] + asp_L[m] -> h[m] + glu_L[m] + asp_L[c] ' } {'ASPNATm' } {'Aspartate N-Acetyltransferase, Mitochondrial' } 0 10000 {'asp_L[m] + accoa[m] -> h[m] + coa[m] + Nacasp[m] ' } {'ASPt6' } {'L-Aspartate Transport via Na, H Symport And K Antiport' } 0 10000 {'h[e] + 3 na1[e] + k[c] + asp_L[e] -> h[c] + 3 na1[c] + asp_L[c] + k[e] ' } {'ATPasel' } {'V-Type ATPase, H+ Transporting, Lysosomal' } 0 10000 {'h2o[c] + atp[c] -> adp[c] + pi[c] + h[l] ' } {'ATPH1e' } {'ATP Diphosphohydrolase' } 0 10000 {'2 h2o[e] + atp[e] -> 2 h[e] + 2 pi[e] + amp[e] ' } {'ATPtm' } {'ADP/ATP Transporter, Mitochondrial' } 0 10000 {'adp[c] + atp[m] -> atp[c] + adp[m] ' } {'BAMPPALDOX' } {'Beta-Aminopropion Aldehyde:NAD+ Oxidoreductase' } 0 10000 {'h2o[c] + bamppald[c] + nad[c] -> 2 h[c] + nadh[c] + ala_B[c] ' } {'BPNT2' } {'3', 5'-Bisphosphate Nucleotidase (Paps)' } 0 10000 {'h2o[c] + paps[c] -> pi[c] + aps[c] ' } {'CAATPS' } {'Ca ATPase' } 0 10000 {'h2o[c] + atp[c] + ca2[c] -> adp[c] + pi[c] + h[e] + ca2[e] ' } {'CATm' } {'Catalase' } 0 10000 {'2 h2o2[m] -> 2 h2o[m] + o2[m] ' } {'CATp' } {'Catalase A, Peroxisomal' } 0 10000 {'2 h2o2[x] -> o2[x] + 2 h2o[x] ' } {'CBPPer' } {'Carbamoyl Phosphate Phosphotransferase, Endoplasmic Reticulu'} 0 10000 {'h[r] + glc_D[r] + cbp[r] -> co2[r] + nh4[r] + g6p[r] ' } {'CDS' } {'Phosphatidate Cytidylyltransferase' } 0 10000 {'h[c] + pa_hs[c] + ctp[c] -> ppi[c] + cdpdag_hs[c] ' } {'CEPTC' } {'Choline Phosphotransferase' } 0 10000 {'cdpchol[c] + dag_hs[c] -> h[c] + cmp[c] + pchol_hs[c] ' } {'CERK' } {'Ceramide Kinase' } 0 10000 {'atp[c] + crm_hs[c] -> h[c] + adp[c] + crmp_hs[c] ' } {'CGLYt3_2_' } {'Cys-Gly Transport in via Proton Symport' } 0 10000 {'2 h[e] + cgly[e] -> 2 h[c] + cgly[c] ' } {'CHLPCTD' } {'Choline Phosphate Cytididyltransferase' } 0 10000 {'h[c] + ctp[c] + cholp[c] -> ppi[c] + cdpchol[c] ' } {'CHOLK' } {'Choline Kinase' } 0 10000 {'atp[c] + chol[c] -> h[c] + adp[c] + cholp[c] ' } {'CHSTEROLtg' } {'Cholesterol Efflux (ATP Depedent), Golgi Apparatus' } 0 10000 {'h2o[c] + atp[c] + chsterol[g] -> h[c] + adp[c] + pi[c] + chsterol[c] ' } {'CK' } {'ATP Creatine Kinase' } 0 10000 {'atp[m] + creat[m] -> h[m] + adp[m] + pcreat[m] ' } {'CKc' } {'ATP Creatine Kinase, Cytosolic' } 0 10000 {'atp[c] + creat[c] -> h[c] + adp[c] + pcreat[c] ' } {'CMPSAS' } {'CMP Sialic Acid Synthase' } 0 10000 {'acnam[c] + ctp[c] -> ppi[c] + cmpacna[c] ' } {'COUCOAFm' } {'P-Coumaroyl Coenzyme A Formation' } 0 10000 {'coa[m] + atp[m] + T4hcinnm[m] -> coucoa[m] + amp[m] + ppi[m] ' } {'CREATtmdiffir' } {'Creatine Transport To/from Mitochondria via Diffusion' } 0 10000 {'creat[c] -> creat[m] ' } {'CRNCARtp' } {'Carnitine-Acetylcarnitine Carrier, Peroxisomal' } 0 10000 {'crn[c] + acrn[x] -> acrn[c] + crn[x] ' } {'CRTNsyn' } {'Creatinine Synthase' } 0 10000 {'pcreat[c] -> pi[c] + crtn[c] ' } {'CSm' } {'Citrate Synthase' } 0 10000 {'h2o[m] + accoa[m] + oaa[m] -> h[m] + coa[m] + cit[m] ' } {'CYSO' } {'Cysteine Oxidase' } 0 10000 {'o2[c] + cys_L[c] -> 2 h[c] + 3sala[c] ' } {'CYSTGLUex' } {'L-Cystine/L-Glutamate Exchanger' } 0 10000 {'glu_L[c] + Lcystin[e] -> Lcystin[c] + glu_L[e] ' } {'CYTDK1' } {'ATPcytidine 5-Phosphotransferase' } 0 10000 {'atp[c] + cytd[c] -> h[c] + adp[c] + cmp[c] ' } {'DAGK_hs' } {'Diacylglycerol Phosphate Kinase (Homo Sapiens)' } 0 10000 {'atp[c] + dag_hs[c] -> h[c] + adp[c] + pa_hs[c] ' } {'DASCBR' } {'Dehydroascorbate Reductase' } 0 10000 {'nadph[c] + dhdascb[c] -> nadp[c] + ascb_L[c] ' } {'DESAT16_2' } {'Palmitoyl Coenzyme A Desaturase (N-C16:0CoA -> N-C16:1CoA)' } 0 10000 {'o2[c] + h[c] + nadh[c] + pmtcoa[c] -> 2 h2o[c] + nad[c] + hdcoa[c] ' } {'DESAT18_5' } {'Stearoyl Coenzyme A Desaturase (N-C18:0CoA -> N-C18:1CoA)' } 0 10000 {'o2[c] + h[c] + nadh[c] + stcoa[c] -> 2 h2o[c] + nad[c] + od2coa[c] ' } {'DESAT22_1p' } {'Fatty Acyl Coenzyme A Desaturase (N-C22:4CoA -> N-C22:5CoA)' } 0 10000 {'h[x] + nadh[x] + o2[x] + adrncoa[x] -> nad[x] + 2 h2o[x] + dcsptn1coa[x] ' } {'DHCR242r' } {'24-Dehydrocholesterol Reductase [Precursor]' } 0 10000 {'fadh2[r] + chlstol[r] -> fad[r] + lthstrl[r] ' } {'DHCRD1' } {'Dihydroceramide Desaturase' } 0 10000 {'nadp[c] + dhcrm_hs[c] -> h[c] + nadph[c] + crm_hs[c] ' } {'DHCRD2' } {'Dihydroceramide Desaturase' } 0 10000 {'dhcrm_hs[c] + fad[c] -> crm_hs[c] + fadh2[c] ' } {'DHPR2' } {'6, 7-Dihydropteridine Reduction' } 0 10000 {'5mthf[c] + dhbpt[c] -> h[c] + thbpt[c] + mlthf[c] ' } {'DKMPPD' } {' 2, 3-Diketo-5-Methylthio-1-Phosphopentane Degradation React'} 0 10000 {'h2o[c] + o2[c] + dkmpp[c] -> 2 h[c] + pi[c] + for[c] + 2kmb[c] ' } {'DOLGLCP_Lter' } {'Dolichyl Beta-D-Glucosyl Phosphate Flippase (Liver)' } 0 10000 {'0.1 dolglcp_L[c] -> 0.1 dolglcp_L[r] ' } {'DOLGPP_Ler' } {'Dolichyl-Beta-D-Glucosyl-Phosphate Dolichylphosphohydrolase '} 0 10000 {'h2o[r] + 0.1 dolglcp_L[r] -> h[r] + 0.1 dolp_L[r] + glc_D[r] ' } {'DOLPMT4_Ler' } {'Dolichyl-Phosphate-Mannose-Glycolipid Alpha-Mannosyltransfer'} 0 10000 {'0.1 dolp_L[r] -> 0.1 dolp_L[c] ' } {'DOPABMO' } {'Dopamine Beta-Monooxygenase' } 0 10000 {'o2[c] + h[c] + dopa[c] + ascb_L[c] -> h2o[c] + nrpphr[c] + dhdascb[c] ' } {'DOPACHRMISO' } {'L-Dopachrome Isomerase 1' } 0 10000 {'o2[c] + 2 2c23dh56dhoxin[c] -> 2 h2o[c] + 2 L_dpchrm[c] ' } {'DOPASFt' } {'Transport of Dopamine 3-0-Sulfate (Diffusion)' } 0 10000 {'dopasf[c] -> dopasf[e] ' } {'DOPASULT' } {'Dopamine Sulfotransferase' } 0 10000 {'paps[c] + dopa[c] -> h[c] + pap[c] + dopasf[c] ' } {'DPGase' } {'Diphosphoglycerate Phosphatase' } 0 10000 {'h2o[c] + 23dpg[c] -> pi[c] + 3pg[c] ' } {'DPMVDx' } {'Diphosphomevalonate Decarboxylase' } 0 10000 {'atp[x] + 5dpmev[x] -> adp[x] + co2[x] + ipdp[x] + pi[x] ' } {'DRPA' } {'Deoxyribose-Phosphate Aldolase' } 0 10000 {'2dr5p[c] -> acald[c] + g3p[c] ' } {'DSAT' } {'Dihydrosphingosine N-Acyltransferase' } 0 10000 {'sphgn[c] + Rtotalcoa[c] -> h[c] + coa[c] + dhcrm_hs[c] ' } {'DUTPDPm' } {'DUTP Diphosphatase' } 0 10000 {'h2o[m] + dutp[m] -> h[m] + ppi[m] + dump[m] ' } {'DUTPDPn' } {'DUTP Diphosphatase, Nuclear' } 0 10000 {'h2o[n] + dutp[n] -> ppi[n] + h[n] + dump[n] ' } {'ETF' } {'Electron Transfer Flavoprotein' } 0 10000 {'fadh2[m] + etfox[m] -> fad[m] + etfrd[m] ' } {'ETFQO' } {'Electron Transfer Flavoprotein-Ubiquinone Oxidoreductase' } 0 10000 {'q10[m] + etfrd[m] -> q10h2[m] + etfox[m] ' } {'ETHAK' } {'Ethanolamine Kinase' } 0 10000 {'atp[c] + etha[c] -> h[c] + adp[c] + ethamp[c] ' } {'FACOAL160i' } {'C160 Fatty Acid Activation' } 0 10000 {'atp[c] + coa[c] + hdca[c] -> amp[c] + ppi[c] + pmtcoa[c] ' } {'FACOAL1821' } {'Fatty-Acid- Coenzyme A Ligase' } 0 10000 {'atp[c] + coa[c] + lnlc[c] -> amp[c] + ppi[c] + lnlccoa[c] ' } {'FACOAL80i' } {'Fatty-Acid- Coenzyme A Ligase (Octanoate)' } 0 10000 {'atp[c] + coa[c] + octa[c] -> amp[c] + ppi[c] + occoa[c] ' } {'FADH2tru' } {'Transport of FADH2, Endoplasmic Reticulum' } 0 10000 {'fadh2[c] -> fadh2[r] ' } {'FADtru' } {'Transport of FAD, Endoplasmic Reticulum' } 0 10000 {'fad[r] -> fad[c] ' } {'FAEL183' } {'Fatty-Acyl Coenzyme A Elongation (N-C18:3CoA)' } 0 10000 {'o2[c] + 5 h[c] + 4 nadph[c] + lnlncgcoa[c] + malcoa[c] -> 3 h2o[c] + 4 nadp[c] + co2[c] + coa[c] + dlnlcgcoa[c] ' } {'FAEL204' } {'Fatty-Acyl Coenzyme A Elongation (N-C20:4CoA)' } 0 10000 {'o2[c] + 5 h[c] + 4 nadph[c] + arachdcoa[c] + malcoa[c] -> 3 h2o[c] + 4 nadp[c] + co2[c] + coa[c] + adrncoa[c] ' } {'FAOXC160' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'7 h2o[m] + 7 nad[m] + 7 coa[m] + 7 fad[m] + pmtcoa[m] -> 7 h[m] + 7 nadh[m] + 8 accoa[m] + 7 fadh2[m] ' } {'FAOXC16080x' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'4 nad[x] + 4 coa[x] + pmtcoa[x] + 4 o2[x] + 4 h2o[x] -> 4 h[x] + 4 nadh[x] + 4 accoa[x] + occoa[x] + 4 h2o2[x] ' } {'FAOXC16180m' } {'Beta Oxidation Fatty Acid' } 0 10000 {'4 h2o[m] + 4 nad[m] + 4 coa[m] + 3 fad[m] + hdcoa[m] -> 4 h[m] + 4 nadh[m] + 4 accoa[m] + 3 fadh2[m] + occoa[m] ' } {'FAOXC180' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'h2o[m] + nad[m] + coa[m] + fad[m] + stcoa[m] -> h[m] + nadh[m] + accoa[m] + fadh2[m] + pmtcoa[m] ' } {'FAOXC180x' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'nad[x] + coa[x] + o2[x] + h2o[x] + stcoa[x] -> h[x] + nadh[x] + accoa[x] + pmtcoa[x] + h2o2[x] ' } {'FAOXC1811603m' } {'Beta Oxidation Fatty Acid' } 0 10000 {'5 h2o[m] + 5 nad[m] + 5 coa[m] + 4 fad[m] + odecoa[m] -> 5 h[m] + 5 nadh[m] + 5 accoa[m] + 4 fadh2[m] + occoa[m] ' } {'FAOXC183806x' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'5 nad[x] + 5 coa[x] + 2 o2[x] + 5 h2o[x] + lnlncgcoa[x] -> 5 h[x] + 5 nadh[x] + 5 accoa[x] + occoa[x] + 2 h2o2[x] '} {'FAOXC18480x' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'5 nad[x] + 5 coa[x] + o2[x] + 5 h2o[x] + strdnccoa[x] -> 5 h[x] + 5 nadh[x] + 5 accoa[x] + occoa[x] + h2o2[x] ' } {'FAOXC200180m' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'h2o[m] + nad[m] + coa[m] + fad[m] + arachcoa[m] -> h[m] + nadh[m] + accoa[m] + fadh2[m] + stcoa[m] ' } {'FAOXC200180x' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'nad[x] + coa[x] + o2[x] + h2o[x] + arachcoa[x] -> h[x] + nadh[x] + accoa[x] + h2o2[x] + stcoa[x] ' } {'FAOXC204' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'9 h2o[m] + 9 nad[m] + 9 coa[m] + 5 fad[m] + arachdcoa[m] -> 9 h[m] + 9 nadh[m] + 10 accoa[m] + 5 fadh2[m] ' } {'FAOXC2051843x' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'nad[x] + coa[x] + h2o[x] + tmndnccoa[x] -> h[x] + nadh[x] + accoa[x] + strdnccoa[x] ' } {'FAOXC2251836x' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'2 nad[x] + 2 coa[x] + 2 h2o[x] + dcsptn1coa[x] -> 2 h[x] + 2 nadh[x] + 2 accoa[x] + lnlncgcoa[x] ' } {'FAOXC2252053m' } {'Beta Oxidation of Long Chain Fatty Acid' } 0 10000 {'h2o[m] + o2[m] + nad[m] + coa[m] + dcsptn1coa[m] -> h[m] + nadh[m] + accoa[m] + h2o2[m] + tmndnccoa[m] ' } {'FAOXC80' } {'Beta Oxidation of Med/Long Chain Fatty Acid' } 0 10000 {'3 h2o[m] + 3 nad[m] + 3 coa[m] + 3 fad[m] + occoa[m] -> 3 h[m] + 3 nadh[m] + 4 accoa[m] + 3 fadh2[m] ' } {'FAS100COA' } {'Fatty Acyl Coenzyme A Synthase (N-C10:0CoA)' } 0 10000 {'3 h[c] + 2 nadph[c] + occoa[c] + malcoa[c] -> h2o[c] + 2 nadp[c] + co2[c] + coa[c] + dcacoa[c] ' } {'FAS120COA' } {'Fatty-Acyl Coenzyme A Synthase (N-C12:0CoA)' } 0 10000 {'3 h[c] + 2 nadph[c] + malcoa[c] + dcacoa[c] -> h2o[c] + 2 nadp[c] + co2[c] + coa[c] + ddcacoa[c] ' } {'FAS140COA' } {'Fatty-Acyl Coenzyme A Synthase (N-C14:0CoA)' } 0 10000 {'3 h[c] + 2 nadph[c] + malcoa[c] + ddcacoa[c] -> h2o[c] + 2 nadp[c] + co2[c] + coa[c] + tdcoa[c] ' } {'FAS160COA' } {'Fatty-Acyl Coenzyme A Synthase (N-C16:0CoA)' } 0 10000 {'3 h[c] + 2 nadph[c] + tdcoa[c] + malcoa[c] -> h2o[c] + 2 nadp[c] + co2[c] + coa[c] + pmtcoa[c] ' } {'FAS180COA' } {'Fatty-Acyl Coenzyme A Synthase (N-C18:0CoA)' } 0 10000 {'3 h[c] + 2 nadph[c] + pmtcoa[c] + malcoa[c] -> h2o[c] + 2 nadp[c] + co2[c] + coa[c] + stcoa[c] ' } {'FAS80COA_L' } {'Fatty Acyl Coenzyme A Synthase (N-C8:0CoA), Lumped Reaction' } 0 10000 {'9 h[c] + 6 nadph[c] + accoa[c] + 3 malcoa[c] -> 3 h2o[c] + 6 nadp[c] + 3 co2[c] + 3 coa[c] + occoa[c] ' } {'FBP26' } {'Fructose-2, 6-Bisphosphate 2-Phosphatase' } 0 10000 {'h2o[c] + f26bp[c] -> pi[c] + f6p[c] ' } {'FKYNH' } {'N-Formyl-L-Kynurenine Amidohydrolase' } 0 10000 {'h2o[c] + Lfmkynr[c] -> h[c] + for[c] + Lkynr[c] ' } {'FOLR2' } {'Folate Reductase' } 0 10000 {'nadph[c] + fol[c] -> nadp[c] + dhf[c] ' } {'FPGS2' } {'Folylpolyglutamate Synthetase' } 0 10000 {'atp[c] + glu_L[c] + 5thf[c] -> h[c] + adp[c] + pi[c] + 6thf[c] ' } {'FPGS3' } {'Folylpolyglutamate Synthetase' } 0 10000 {'atp[c] + glu_L[c] + 6thf[c] -> h[c] + adp[c] + pi[c] + 7thf[c] ' } {'FPGS4' } {'Folylpolyglutamate Synthetase (Dhf)' } 0 10000 {'atp[c] + 4 glu_L[c] + dhf[c] -> 3 h2o[c] + h[c] + adp[c] + pi[c] + 5dhf[c] ' } {'FPGS5' } {'Folylpolyglutamate Synthetase (Dhf)' } 0 10000 {'atp[c] + glu_L[c] + 5dhf[c] -> h[c] + adp[c] + pi[c] + 6dhf[c] ' } {'FPGS6' } {'Folylpolyglutamate Synthetase (Dhf)' } 0 10000 {'atp[c] + glu_L[c] + 6dhf[c] -> h[c] + adp[c] + pi[c] + 7dhf[c] ' } {'FPGS8' } {'Folylpolyglutamate Synthetase (10Fthf)' } 0 10000 {'10fthf5glu[c] + atp[c] + glu_L[c] -> 10fthf6glu[c] + h[c] + adp[c] + pi[c] ' } {'G5SDym' } {'Glutamate-5-Semialdehyde Dehydrogenase, Mitochondrial' } 0 10000 {'h[m] + nadph[m] + glu5p[m] -> nadp[m] + pi[m] + glu5sa[m] ' } {'G6PPer' } {'Glucose-6-Phosphate Phosphatase, Edoplasmic Reticular' } 0 10000 {'h2o[r] + g6p[r] -> glc_D[r] + pi[r] ' } {'GALtly' } {'Galactose Efflux from Lysosome' } 0 10000 {'gal[l] -> gal[c] ' } {'GBA' } {'Glucosylceramidase' } 0 10000 {'h2o[c] + gluside_hs[c] -> glc_D[c] + crm_hs[c] ' } {'GGH_10FTHF5GLUl' } {'Gamma-Glutamyl Hydrolase (10Fthf5Glu), Lysosomal' } 0 10000 {'10fthf5glu[l] + 4 h2o[l] -> 10fthf[l] + 4 glu_L[l] ' } {'GGH_10FTHF6GLUl' } {'Gamma-Glutamyl Hydrolase (10Fthf6Glu), Lysosomal' } 0 10000 {'10fthf6glu[l] + h2o[l] -> 10fthf5glu[l] + glu_L[l] ' } {'GGH_5DHFl' } {'Gamma-Glutamyl Hydrolase (5Dhf), Lysosomal' } 0 10000 {'4 h2o[l] + 5dhf[l] -> dhf[l] + 4 glu_L[l] ' } {'GGH_6DHFl' } {'Gamma-Glutamyl Hydrolase (6Dhf), Lysosomal' } 0 10000 {'h2o[l] + 6dhf[l] -> 5dhf[l] + glu_L[l] ' } {'GGH_7DHFl' } {'Gamma-Glutamyl Hydrolase (7Dhf), Lysosomal' } 0 10000 {'h2o[l] + 7dhf[l] -> 6dhf[l] + glu_L[l] ' } {'GLAl' } {'Galactosidase, Alpha' } 0 10000 {'h2o[l] + digalside_hs[l] -> galside_hs[l] + gal[l] ' } {'GLCAASE8ly' } {'Beta-Glucuronidase, Lysosomal' } 0 10000 {'h2o[l] + ha[l] -> glcur[l] + ha_deg1[l] ' } {'GLCAASE9ly' } {'Beta-Glucuronidase, Lysosomal' } 0 10000 {'2 h2o[l] + ha_pre1[l] -> acgam[l] + glcur[l] ' } {'GLCtly' } {'Glucose Efflux from Lysosome' } 0 10000 {'glc_D[l] -> glc_D[c] ' } {'GLCURter' } {'Glucuronate Endoplasmic Reticular Transport' } 0 10000 {'glcur[c] -> glcur[r] ' } {'GLNASNNaEx' } {'L-Glutamine/L-Asparagine Na-Dependent Exchange (Gln-L In)' } 0 10000 {'na1[e] + asn_L[c] + gln_L[e] -> na1[c] + asn_L[e] + gln_L[c] ' } {'GLNSERNaEx' } {'L-Serine/L-Glutamine Na-Dependent Exchange (Gln-L In)' } 0 10000 {'na1[e] + gln_L[e] + ser_L[c] -> na1[c] + gln_L[c] + ser_L[e] ' } {'GLNTHRNaEx' } {'L-Threonine/L-Glutamine Na-Dependent Exchange (Gln-L In)' } 0 10000 {'na1[e] + gln_L[e] + thr_L[c] -> na1[c] + gln_L[c] + thr_L[e] ' } {'GLNtm' } {'L-Glutamine Transport via Electroneutral Transporter' } 0 10000 {'gln_L[c] -> gln_L[m] ' } {'GLU5Km' } {'Glutamate 5-Kinase, Mitochondrial' } 0 10000 {'glu_L[m] + atp[m] -> adp[m] + glu5p[m] ' } {'GLUCYS' } {'Gamma-Glutamylcysteine Synthetase' } 0 10000 {'atp[c] + glu_L[c] + cys_L[c] -> h[c] + adp[c] + pi[c] + glucys[c] ' } {'GLUNm' } {'Glutaminase, Mitochondrial' } 0 10000 {'h2o[m] + gln_L[m] -> glu_L[m] + nh4[m] ' } {'GLUt6' } {'Glutamate Transport via Na, H Symport And K Antiport' } 0 10000 {'h[e] + 3 na1[e] + k[c] + glu_L[e] -> h[c] + 3 na1[c] + glu_L[c] + k[e] ' } {'GLUt7l' } {'Glutamate Transport, Lysosomal' } 0 10000 {'glu_L[l] -> glu_L[c] ' } {'GLUVESSEC' } {'L-Glutamate Secretion via Secretory Vesicle (ATP Driven)' } 0 10000 {'h2o[c] + atp[c] + glu_L[c] -> h[c] + adp[c] + pi[c] + glu_L[e] ' } {'GLYCLTDy' } {'Glycolate Dehydrogenase (NADP)' } 0 10000 {'h[c] + nadph[c] + glx[c] -> nadp[c] + glyclt[c] ' } {'GLYOp' } {'Glycine Oxidase, Perixosomal' } 0 10000 {'o2[x] + h2o[x] + gly[x] -> h2o2[x] + glx[x] + nh4[x] ' } {'GLYt4' } {'Transport of Glycine via Sodium Symport' } 0 10000 {'na1[e] + gly[e] -> na1[c] + gly[c] ' } {'GPAM_hs' } {'Glycerol-3-Phosphate Acyltransferase' } 0 10000 {'Rtotalcoa[c] + glyc3p[c] -> 2 h[c] + coa[c] + alpa_hs[c] ' } {'GTHO' } {'Glutathione Oxidoreductase' } 0 10000 {'h[c] + nadph[c] + gthox[c] -> nadp[c] + 2 gthrd[c] ' } {'GTHOm' } {'Glutathione Oxidoreductase' } 0 10000 {'h[m] + nadph[m] + gthox[m] -> nadp[m] + 2 gthrd[m] ' } {'GTHP' } {'Glutathione Peroxidase' } 0 10000 {'h2o2[c] + 2 gthrd[c] -> 2 h2o[c] + gthox[c] ' } {'GTHPe' } {'Glutathione Peroxidase, Extracellular' } 0 10000 {'2 gthrd[e] + h2o2[e] -> 2 h2o[e] + gthox[e] ' } {'GTHPm' } {'Glutathione Peroxidase, Mitochondria' } 0 10000 {'h2o2[m] + 2 gthrd[m] -> 2 h2o[m] + gthox[m] ' } {'GTHS' } {'Glutathione Synthetase' } 0 10000 {'atp[c] + gly[c] + glucys[c] -> h[c] + adp[c] + pi[c] + gthrd[c] ' } {'GUACYC' } {'Guanylate Cyclase' } 0 10000 {'gtp[c] -> 35cgmp[c] + ppi[c] ' } {'GULNter' } {'L-Gulonate Endoplasmic Reticular Export' } 0 10000 {'guln[r] -> guln[c] ' } {'H2CO3Dm' } {'Carboxylic Acid Dissociation' } 0 10000 {'h2o[m] + co2[m] -> h[m] + hco3[m] ' } {'H2O2tm' } {'Hydrogen Peroxide Mitochondrial Transport' } 0 10000 {'h2o2[c] -> h2o2[m] ' } {'HAS1' } {'Hyaluronan Synthase' } 0 10000 {'uacgam[c] + udpglcur[c] -> 2 h[c] + 2 udp[c] + ha_pre1[e] ' } {'HAS2' } {'Hyaluronan Synthase' } 0 10000 {'ha_pre1[e] + uacgam[c] + udpglcur[c] -> 2 h[c] + 2 udp[c] + ha[e] ' } {'HAtly' } {'Hyaluronan Transport, Extracellular to Lysosome' } 0 10000 {'ha[e] -> ha[l] ' } {'HISDC' } {'Histidine Decarboxylase' } 0 10000 {'h[c] + his_L[c] -> co2[c] + hista[c] ' } {'HISt4' } {'L-Histidine Transport in via Sodium Symport' } 0 10000 {'na1[e] + his_L[e] -> na1[c] + his_L[c] ' } {'HISTASE' } {'Histaminase' } 0 10000 {'h2o[c] + o2[c] + hista[c] -> h2o2[c] + nh4[c] + im4act[c] ' } {'HISTAVESSEC' } {'Histamine Secretion via Secretory Vesicle (ATP Driven)' } 0 10000 {'h2o[c] + atp[c] + hista[c] -> h[c] + adp[c] + pi[c] + hista[e] ' } {'HMGCOASi' } {'Hydroxymethylglutaryl Coenzyme A Synthase (Ir)' } 0 10000 {'h2o[c] + accoa[c] + aacoa[c] -> h[c] + coa[c] + hmgcoa[c] ' } {'HMGLm' } {'Hydroxymethylglutaryl Coenzyme A Lyase' } 0 10000 {'hmgcoa[m] -> accoa[m] + acac[m] ' } {'HMGLx' } {'Hydroxymethylglutaryl Coenzyme A Lyase' } 0 10000 {'hmgcoa[x] -> accoa[x] + acac[x] ' } {'HOMt4' } {'L-Homoserine via Sodium Symport' } 0 10000 {'na1[e] + hom_L[e] -> na1[c] + hom_L[c] ' } {'HPYRRy' } {'Hydroxypyruvate Reductase (NADPH)' } 0 10000 {'h[c] + nadph[c] + hpyr[c] -> nadp[c] + glyc_R[c] ' } {'HYPTROX' } {'Hypotaurine Oxidase' } 0 10000 {'o2[c] + 2 hyptaur[c] -> 2 taur[c] ' } {'ICDHxm' } {'Isocitrate Dehydrogenase (NAD+)' } 0 10000 {'nad[m] + icit[m] -> akg[m] + nadh[m] + co2[m] ' } {'ICDHy' } {'Isocitrate Dehydrogenase (NADP)' } 0 10000 {'nadp[c] + icit[c] -> nadph[c] + akg[c] + co2[c] ' } {'KDNH' } {'2-Keto-3Deoxy-D-Glycero-D-Galactononic Acid Phosphohydrolase'} 0 10000 {'h2o[c] + kdnp[c] -> pi[c] + kdn[c] ' } {'KYNAKGAT' } {'L-Kynurenine:2-Oxoglutarate Aminotransferase' } 0 10000 {'akg[c] + Lkynr[c] -> glu_L[c] + 4aphdob[c] ' } {'KYNATESYN' } {'4- (2-Aminophenyl)-2, 4-Dioxobutanoate Dehydratase' } 0 10000 {'4aphdob[c] -> h2o[c] + kynate[c] ' } {'LAPCOAl' } {'Lysosomal Acid Phosphorylase (CoA)' } 0 10000 {'h2o[l] + coa[l] -> pi[l] + dpcoa[l] ' } {'LCYSTCBOXL' } {'3-Sulfoalanine Carboxy-Lyase' } 0 10000 {'h[c] + Lcyst[c] -> co2[c] + taur[c] ' } {'LEUt4' } {'Transport of L-Leucine via Sodium Symport' } 0 10000 {'na1[e] + leu_L[e] -> na1[c] + leu_L[c] ' } {'L_LACDcm' } {'L-Lactate Dehydrogenase, Cytosolic/Mitochondrial' } 0 10000 {'2 ficytC[m] + lac_L[c] -> 2 h[c] + pyr[c] + 2 focytC[m] ' } {'L_LACtcm' } {'Transport of L-Lactate via Diffusion, Mitochondrial' } 0 10000 {'lac_L[c] -> lac_L[m] ' } {'L_LACtm' } {'Transport of L-Lactate, Mitochondrial' } 0 10000 {'h[c] + lac_L[c] -> h[m] + lac_L[m] ' } {'LPASE' } {'Lysophospholipase' } 0 10000 {'h2o[c] + lpchol_hs[c] -> h[c] + Rtotal[c] + g3pc[c] ' } {'LPS2' } {'Lipase' } 0 10000 {'h2o[c] + dag_hs[c] -> h[c] + Rtotal[c] + mag_hs[c] ' } {'LTA4H' } {'Leukotriene A-4 Hydrolase' } 0 10000 {'h2o[c] + leuktrA4[c] -> leuktrB4[c] ' } {'LYStiDF' } {'Transport of L-Lysine via Diffusion' } 0 10000 {'lys_L[e] -> lys_L[c] ' } {'LYStip' } {'Transport of L-Lysine, Peroxisomal (Irreversible)' } 0 10000 {'lys_L[c] -> lys_L[x] ' } {'MACOXO' } {'3-Methylimidazole Acetaldehyde:NAD+ Oxidoreductase' } 0 10000 {'h2o[c] + nad[c] + 3mldz[c] -> 2 h[c] + nadh[c] + 3mlda[c] ' } {'MAOX' } {'Methylamine Oxidase' } 0 10000 {'h2o[c] + o2[c] + mma[c] -> h2o2[c] + nh4[c] + fald[c] ' } {'MDRPD' } {' 5-Methylthio-5-Deoxy-D-Ribulose 1-Phosphate Dehydratase' } 0 10000 {'5mdru1p[c] -> h2o[c] + dkmpp[c] ' } {'ME1m' } {'Malic Enzyme (NAD), Mitochondrial' } 0 10000 {'nad[m] + mal_L[m] -> nadh[m] + co2[m] + pyr[m] ' } {'ME2' } {'Malic Enzyme (NADP)' } 0 10000 {'nadp[c] + mal_L[c] -> pyr[c] + nadph[c] + co2[c] ' } {'ME2m' } {'Malic Enzyme (NADP), Mitochondrial' } 0 10000 {'nadp[m] + mal_L[m] -> nadph[m] + co2[m] + pyr[m] ' } {'METLEUex' } {'Methionine/Leucine Exchange (Met In)' } 0 10000 {'leu_L[c] + met_L[e] -> met_L[c] + leu_L[e] ' } {'METS' } {'Methionine Synthase' } 0 10000 {'5mthf[c] + hcys_L[c] -> h[c] + met_L[c] + thf[c] ' } {'METt4' } {'L-Methionine Transport in via Sodium Symport' } 0 10000 {'na1[e] + met_L[e] -> na1[c] + met_L[c] ' } {'MEVK1x' } {'Mevalonate Kinase (ATP)' } 0 10000 {'atp[x] + mev_R[x] -> h[x] + adp[x] + 5pmev[x] ' } {'MGSA' } {'Methylglyoxal Synthase' } 0 10000 {'dhap[c] -> pi[c] + mthgxl[c] ' } {'MGSA2' } {'Methyglyoxylate Synthase 2 (from G3P)' } 0 10000 {'g3p[c] -> pi[c] + mthgxl[c] ' } {'MHISOR' } {'N-Methylhistamine:Oxygen Oxidoreductase (Deaminating)' } 0 10000 {'h2o[c] + o2[c] + mhista[c] -> h2o2[c] + nh4[c] + 3mldz[c] ' } {'MI1345PP' } {'Inositol-1, 3, 4, 5-Trisphosphate 5-Phosphatase' } 0 10000 {'h2o[c] + mi1345p[c] -> pi[c] + mi134p[c] ' } {'MI1PS' } {'Myo-Inositol-1-Phosphate Synthase' } 0 10000 {'g6p[c] -> mi1p_D[c] ' } {'MMSAD3m' } {'Methylmalonate-Semialdehyde Dehydrogenase (Malonic Semialdeh'} 0 10000 {'nad[m] + coa[m] + msa[m] -> nadh[m] + co2[m] + accoa[m] ' } {'MTAP' } {'5'-Methylthioadenosine Phosphorylase' } 0 10000 {'pi[c] + 5mta[c] -> ade[c] + 5mdr1p[c] ' } {'NABTNO' } {'N4-Acetylaminobutanal:NAD+ Oxidoreductase' } 0 10000 {'h2o[c] + nad[c] + n4abutn[c] -> 2 h[c] + nadh[c] + 4aabutn[c] ' } {'NACASPtm' } {'N-Acetyl-L-Aspartate Transport (Mitochondria to Cytosol)' } 0 10000 {'Nacasp[m] -> Nacasp[c] ' } {'NACHEX27ly' } {'Beta-N-Acetylhexosaminidase, Lysosomal' } 0 10000 {'h2o[l] + ha_deg1[l] -> acgam[l] + ha_pre1[l] ' } {'NADHtpu' } {'NADH Transporter, Peroxisome' } 0 10000 {'nadh[c] -> nadh[x] ' } {'NADPHtru' } {'Transport of NADPH, Endoplasmic Reticulum' } 0 10000 {'nadph[c] -> nadph[r] ' } {'NADPHtxu' } {'Transport of NADPH, Peroxisome' } 0 10000 {'nadph[c] -> nadph[x] ' } {'NADPtru' } {'Transport of NADP, Endoplasmic Reticulum' } 0 10000 {'nadp[r] -> nadp[c] ' } {'NADPtxu' } {'Transport of NADP, Peroxisome' } 0 10000 {'nadp[x] -> nadp[c] ' } {'NaKt' } {'Na+/K+ Exchanging ATPase' } 0 10000 {'h2o[c] + atp[c] + na1[c] + k[e] -> h[c] + adp[c] + pi[c] + na1[e] + k[c] ' } {'NDP6' } {'Nucleoside-Diphosphatase (dCDP)' } 0 10000 {'h2o[c] + dcdp[c] -> h[c] + pi[c] + dcmp[c] ' } {'NDP7er' } {'Nucleoside-Diphosphatase (UDP), Endoplasmic Reticulum' } 0 10000 {'h2o[r] + udp[r] -> h[r] + pi[r] + ump[r] ' } {'NDP8' } {'Nucleoside-Diphosphatase (dUDP)' } 0 10000 {'h2o[c] + dudp[c] -> h[c] + pi[c] + dump[c] ' } {'NICRNS' } {'Nicotinate D-Ribonucleoside Kinase' } 0 10000 {'atp[c] + nicrns[c] -> h[c] + adp[c] + nicrnt[c] ' } {'NMNATn' } {'Nicotinamide-Nucleotide Adenylyltransferase' } 0 10000 {'atp[n] + h[n] + nmn[n] -> ppi[n] + nad[n] ' } {'NMNS' } {'Nicotinamide Ribotide (NMN) Synthetase' } 0 10000 {'h[c] + ncam[c] + prpp[c] -> ppi[c] + nmn[c] ' } {'NORANMT' } {'Noradrenaline N-Methyltransferase' } 0 10000 {'amet[c] + nrpphr[c] -> h[c] + ahcys[c] + adrnl[c] ' } {'NP1' } {'Nucleotide Phosphatase' } 0 10000 {'h[c] + nac[c] + r1p[c] -> pi[c] + nicrns[c] ' } {'NTD2e' } {'5'-Nucleotidase (UMP), Extracellular' } 0 10000 {'h2o[e] + ump[e] -> pi[e] + uri[e] ' } {'NTD7e' } {'5'-Nucleotidase (AMP), Extracellular' } 0 10000 {'h2o[e] + amp[e] -> adn[e] + pi[e] ' } {'OCCOAtm' } {'Octanoyl Coenzyme A Transport, Diffusion' } 0 10000 {'occoa[c] -> occoa[m] ' } {'OIVD1m' } {'2-Oxoisovalerate Dehydrogenase (Acylating' } 0 0.92259 {'nad[m] + coa[m] + 4mop[m] -> nadh[m] + co2[m] + ivcoa[m] ' } {'ORNtiDF' } {'Ornithine Transport via Diffusion (Extracellular to Cytosol)'} 0 10000 {'orn[e] -> orn[c] ' } {'P45027A12m' } {'5-Beta-Cholestane-3-Alpha, 7-Alpha, 12-Alpha-Triol 27-Hydrox'} 0 10000 {'nadp[m] + xoltetrol[m] -> h[m] + nadph[m] + thcholst[m] ' } {'P45027A13m' } {'5-Beta-Cholestane-3-Alpha, 7-Alpha, 12-Alpha-Triol 27-Hydrox'} 0 10000 {'o2[m] + nadph[m] + thcholst[m] -> h2o[m] + nadp[m] + thcholstoic[m] ' } {'P45027A15m' } {'5-Beta-Cytochrome P450, Family 27, Subfamily A, Polypeptide '} 0 10000 {'o2[m] + h[m] + nadph[m] + xol7ah3[m] -> 2 h2o[m] + nadp[m] + xol7ah2al[m] ' } {'P45027A16m' } {'Cytochrome P450 27' } 0 10000 {'o2[m] + nadph[m] + xol7ah2al[m] -> h2o[m] + nadp[m] + dhcholestanate[m] ' } {'P45027A1m' } {'Cytochrome P450 27' } 0 10000 {'o2[m] + h[m] + nadph[m] + chsterol[m] -> h2o[m] + nadp[m] + xol27oh[m] ' } {'P450LTB4r' } {'Cytochrome P450 Leukotriene B4' } 0 10000 {'1.5 o2[r] + nadph[r] + leuktrB4woh[r] -> 2 h2o[r] + nadp[r] + leuktrB4wcooh[r] ' } {'PAFH' } {'Platelet-Activating Factor Acetylhydrolase' } 0 10000 {'h2o[c] + paf_hs[c] -> h[c] + ac[c] + ak2lgchol_hs[c] ' } {'PAFS' } {'Alkyl Glycerol Phosphocholine Acetyl Transferase' } 0 10000 {'accoa[c] + ak2lgchol_hs[c] -> coa[c] + paf_hs[c] ' } {'PAN4PP' } {'Phosphatase (Pan4P)' } 0 10000 {'h2o[c] + pan4p[c] -> pi[c] + ptth[c] ' } {'PCFLOPm' } {'Phosphatidylcholine Flippase' } 0 10000 {'h2o[c] + atp[c] + pchol_hs[m] -> h[c] + adp[c] + pi[c] + pchol_hs[c] ' } {'PCHOLP_hs' } {'Choline Phosphatase' } 0 10000 {'h2o[c] + pchol_hs[c] -> h[c] + pa_hs[c] + chol[c] ' } {'PCHOLPm_hs' } {'Choline Phosphatase' } 0 10000 {'h2o[m] + pchol_hs[m] -> h[m] + pa_hs[m] + chol[m] ' } {'PCREATtmdiffir' } {'Phosphocreatine Transport To/from Mitochondria via Diffusion'} 0 10000 {'pcreat[m] -> pcreat[c] ' } {'PDE1' } {'3', 5'-Cyclic-Nucleotide Phosphodiesterase' } 0 10000 {'h2o[c] + camp[c] -> h[c] + amp[c] ' } {'PDE4' } {'3', 5'-Cyclic-Nucleotide Phosphodiesterase' } 0 10000 {'h2o[c] + 35cgmp[c] -> h[c] + gmp[c] ' } {'PEFLIPm' } {'Phosphatidylethanolamine Flippase' } 0 10000 {'h2o[c] + atp[c] + pe_hs[c] -> h[c] + adp[c] + pi[c] + pe_hs[m] ' } {'PETOHMm_hs' } {'Phosphatidylethanolamine N-Methyltransferase' } 0 10000 {'3 amet[m] + pe_hs[m] -> 3 h[m] + 3 ahcys[m] + pchol_hs[m] ' } {'PFK26' } {'6-Phosphofructo-2-Kinase' } 0 10000 {'atp[c] + f6p[c] -> h[c] + adp[c] + f26bp[c] ' } {'PGCD' } {'Phosphoglycerate Dehydrogenase' } 0 10000 {'nad[c] + 3pg[c] -> h[c] + nadh[c] + 3php[c] ' } {'PGLer' } {'6-Phosphogluconolactonase, Endoplasmic Reticulum' } 0 10000 {'h2o[r] + 6pgl[r] -> h[r] + 6pgc[r] ' } {'PHEt4' } {'Transport of L-Phenylalanine via Sodium Symport' } 0 10000 {'na1[e] + phe_L[e] -> na1[c] + phe_L[c] ' } {'PHYQt' } {'Transport of Phylloquinone ' } 0 10000 {'h2o[c] + atp[c] + phyQ[e] -> h[c] + adp[c] + pi[c] + phyQ[c] ' } {'PI345P3P' } {'Phosphatidylinositol-3, 4, 5-Trisphosphate 3-Phosphatase' } 0 10000 {'h2o[c] + pail345p_hs[c] -> pi[c] + pail45p_hs[c] ' } {'PI345P5P' } {'Phosphatidylinositol-3, 4, 5-Trisphosphate 5-Phosphatase' } 0 10000 {'h2o[c] + pail345p_hs[c] -> pi[c] + pail34p_hs[c] ' } {'PI3P4K' } {'Phosphatidylinositol 3-Phosphate 4-Kinase' } 0 10000 {'atp[c] + pail3p_hs[c] -> h[c] + adp[c] + pail34p_hs[c] ' } {'PI3P5K' } {'Phosphatidylinositol 3-Phosphate 5-Kinase' } 0 10000 {'atp[c] + pail3p_hs[c] -> h[c] + adp[c] + pail35p_hs[c] ' } {'PI45P4P' } {'Phosphatidylinositol-4, 5-Bisphosphate 4-Phosphatase' } 0 10000 {'h2o[c] + pail45p_hs[c] -> pi[c] + pail5p_hs[c] ' } {'PI45P5P' } {'Phosphatidylinositol-4, 5-Bisphosphate 5-Phosphatase' } 0 10000 {'h2o[c] + pail45p_hs[c] -> pi[c] + pail4p_hs[c] ' } {'PI4P3K' } {'Phosphatidylinositol 4-Phosphate 3-Kinase' } 0 10000 {'atp[c] + pail4p_hs[c] -> h[c] + adp[c] + pail34p_hs[c] ' } {'PI4P5K' } {'Phosphatidylinositol 4-Phosphate 5-Kinase' } 0 10000 {'atp[c] + pail4p_hs[c] -> h[c] + adp[c] + pail45p_hs[c] ' } {'PI4PP' } {'Phosphatidylinositol-4-Phosphate 4-Phosphatase' } 0 10000 {'h2o[c] + pail4p_hs[c] -> pi[c] + pail_hs[c] ' } {'PI5P3K' } {'Phosphatidylinositol-5-Phosphate 3-Kinase' } 0 10000 {'atp[c] + pail5p_hs[c] -> h[c] + adp[c] + pail35p_hs[c] ' } {'PIK5' } {'Phosphatidylinositol 5-Kinase' } 0 10000 {'atp[c] + pail_hs[c] -> h[c] + adp[c] + pail5p_hs[c] ' } {'PIPLC' } {'Phosphatidylinositol Phospholipase C' } 0 10000 {'h2o[c] + pail_hs[c] -> h[c] + dag_hs[c] + mi1p_D[c] ' } {'PItg' } {'Phosphate Transport, Golgi Apparatus' } 0 10000 {'pi[g] -> pi[c] ' } {'PLA2_2' } {'Phospholipase A2' } 0 10000 {'h2o[c] + pchol_hs[c] -> h[c] + Rtotal2[c] + lpchol_hs[c] ' } {'PMEVKx' } {'Phosphomevalonate Kinase' } 0 10000 {'atp[x] + 5pmev[x] -> adp[x] + 5dpmev[x] ' } {'PMI12346PH' } {'5-Diphosphoinositol-1, 2, 3, 4, 6-Pentakisphosphate Diphosph'} 0 10000 {'h2o[c] + ppmi12346p[c] -> h[c] + pi[c] + minohp[c] ' } {'PNTOt5' } {'Pantothenate Sodium Symporter Ii' } 0 10000 {'h2o[c] + atp[c] + na1[e] + pnto_R[e] -> h[c] + adp[c] + pi[c] + na1[c] + pnto_R[c] ' } {'PPA2' } {'Inorganic Triphosphatase' } 0 10000 {'h2o[c] + pppi[c] -> h[c] + pi[c] + ppi[c] ' } {'PPAer' } {'Inorganic Diphosphatase, Endoplasmic Reticulum' } 0 10000 {'h2o[r] + ppi[r] -> h[r] + 2 pi[r] ' } {'PPAm' } {'Inorganic Diphosphatase' } 0 10000 {'h2o[m] + ppi[m] -> h[m] + 2 pi[m] ' } {'PPAn' } {'Inorganic Diphosphatase, Nuclear' } 0 10000 {'h2o[n] + ppi[n] -> h[n] + 2 pi[n] ' } {'PPAP' } {'Phosphatidic Acid Phosphatase' } 0 10000 {'h2o[c] + pa_hs[c] -> pi[c] + dag_hs[c] ' } {'PPD2CSPp' } {'Ppd2Cspp' } 0 10000 {'6a2ohxnt[x] -> 1pipdn2c[x] + h2o[x] ' } {'PRAGSr' } {'Phosphoribosylglycinamide Synthase' } 0 10000 {'atp[c] + gly[c] + pram[c] -> h[c] + adp[c] + pi[c] + gar[c] ' } {'PRASCS' } {'Phosphoribosylaminoimidazolesuccinocarboxamide Synthase' } 0 10000 {'atp[c] + asp_L[c] + 5aizc[c] -> h[c] + adp[c] + pi[c] + 25aics[c] ' } {'PRDX' } {'Peroxidase (Multiple Substrates)' } 0 10000 {'h2o2[c] + meoh[c] -> 2 h2o[c] + fald[c] ' } {'PROt4' } {'Na+/Proline-L Symporter' } 0 10000 {'na1[e] + pro_L[e] -> na1[c] + pro_L[c] ' } {'PSFLIPm' } {'Phosphatidylserine Flippase' } 0 10000 {'h2o[c] + atp[c] + ps_hs[c] -> h[c] + adp[c] + pi[c] + ps_hs[m] ' } {'PTE2x' } {'Peroxisomal Acyl Coenzyme A Thioesterase' } 0 10000 {'pmtcoa[x] + h2o[x] -> h[x] + coa[x] + hdca[x] ' } {'PTHPS' } {'6-Pyruvoyltetrahydropterin Synthase' } 0 10000 {'ahdt[c] -> pppi[c] + 6pthp[c] ' } {'PTRCAT1' } {'Putrescine Acetyltransferase' } 0 10000 {'accoa[c] + ptrc[c] -> h[c] + coa[c] + aprut[c] ' } {'PTRCOX1' } {'Putrescine:Oxygen Oxidoreductase (Deaminating)' } 0 10000 {'h2o[c] + o2[c] + ptrc[c] -> h2o2[c] + nh4[c] + 4abutn[c] ' } {'PYRt2m' } {'Pyruvate Mitochondrial Transport via Proton Symport' } 0 10000 {'h[c] + pyr[c] -> h[m] + pyr[m] ' } {'RDH3a' } {'Retinol Dehydrogenase (11-Cis, NADPH)' } 0 10000 {'nadp[c] + retinol_cis_11[c] -> h[c] + nadph[c] + retinal_11_cis[c] ' } {'SACCD3m' } {'Saccharopine Dehydrogenase (NADP, L-Lysine Forming), Mitocho'} 0 10000 {'h[m] + nadph[m] + akg[m] + lys_L[m] -> h2o[m] + nadp[m] + saccrp_L[m] ' } {'SADT' } {'Sulfate Adenylyltransferase' } 0 10000 {'h[c] + atp[c] + so4[c] -> ppi[c] + aps[c] ' } {'SAMHISTA' } {'S-Adenosyl-L-Methionine:Histamine N-Tele-Methyltransferase' } 0 10000 {'amet[c] + hista[c] -> h[c] + ahcys[c] + mhista[c] ' } {'SBTD_D2' } {'D-Sorbitol Dehydrogenase (D-Fructose Producing)' } 0 10000 {'nad[c] + sbt_D[c] -> h[c] + nadh[c] + fru[c] ' } {'SBTR' } {'D-Sorbitol Reductase' } 0 10000 {'h[c] + nadph[c] + glc_D[c] -> nadp[c] + sbt_D[c] ' } {'SERCYSNaEx' } {'L-Serine/L-Cysteine Na-Dependent Exchange (Ser-L In)' } 0 10000 {'na1[e] + cys_L[c] + ser_L[e] -> na1[c] + cys_L[e] + ser_L[c] ' } {'SERPT' } {'Serine C-Palmitoyltransferase' } 0 0.0001 {'h[c] + ser_L[c] + pmtcoa[c] -> co2[c] + 3dsphgn[c] + coa[c] ' } {'SERt4' } {'L-Serine via Sodium Symport' } 0 10000 {'na1[e] + ser_L[e] -> na1[c] + ser_L[c] ' } {'SFGTH' } {'S-Formylglutathione Hydralase' } 0 10000 {'h2o[c] + Sfglutth[c] -> h[c] + for[c] + gthrd[c] ' } {'SMS' } {'Sphingomyelin Synthase (Homo Sapiens)' } 0 10000 {'pchol_hs[c] + crm_hs[c] -> dag_hs[c] + sphmyln_hs[c] ' } {'SO4HCOtex' } {'Sulfate Transport via Bicarbonate Antiport' } 0 10000 {'2 hco3[c] + so4[e] -> 2 hco3[e] + so4[c] ' } {'SPODMm' } {'Superoxide Dismutase' } 0 10000 {'2 h[m] + 2 o2s[m] -> o2[m] + h2o2[m] ' } {'SPR' } {'Sepiapterin Reductase' } 0 10000 {'2 h[c] + 2 nadph[c] + 6pthp[c] -> 2 nadp[c] + thbpt[c] ' } {'SPRMS' } {'Spermine Synthase' } 0 10000 {'ametam[c] + spmd[c] -> h[c] + sprm[c] + 5mta[c] ' } {'SULFOX' } {'Sulfite Oxidase' } 0 10000 {'h2o[c] + so3[c] + 2 ficytC[m] -> 2 h[c] + 2 focytC[m] + so4[c] ' } {'T4HCINNMFM' } {'4-Hydroxycinnamate Formation' } 0 10000 {'34hpl[m] -> h2o[m] + T4hcinnm[m] ' } {'THBPT4ACAMDASE' } {'Tetrahydrobiopterin-4A-Carbinolamine Dehydratase' } 0 10000 {'thbpt4acam[c] -> h2o[c] + dhbpt[c] ' } {'THD1m' } {'NAD (P) Transhydrogenase' } 0 10000 {'nadp[m] + h[c] + nadh[m] -> h[m] + nadph[m] + nad[m] ' } {'THMTP' } {'Thiamine-Triphosphatase' } 0 10000 {'h2o[c] + thmtp[c] -> h[c] + pi[c] + thmpp[c] ' } {'THRALANaEx' } {'L-Alanine/L-Threonine Na-Dependent Exchange (Thr-L In)' } 0 10000 {'na1[e] + ala_L[c] + thr_L[e] -> na1[c] + ala_L[e] + thr_L[c] ' } {'THRCYSNaEx' } {'L-Cysteine/L-Threonine Na-Dependent Exchange (Thr-L In)' } 0 10000 {'na1[e] + cys_L[c] + thr_L[e] -> na1[c] + cys_L[e] + thr_L[c] ' } {'THRt4' } {'L-Threonine via Sodium Symport' } 0 10000 {'na1[e] + thr_L[e] -> na1[c] + thr_L[c] ' } {'THYMDt1' } {'Thymd Transport' } 0 10000 {'thymd[e] -> thymd[c] ' } {'TMDK1m' } {'Thymidine Kinase (ATP:Thymidine)' } 0 10000 {'atp[m] + thymd[m] -> h[m] + adp[m] + dtmp[m] ' } {'TMDPPK' } {'Thiamine-Diphosphate Kinase' } 0 10000 {'atp[c] + thmpp[c] -> adp[c] + thmtp[c] ' } {'TRDR' } {'Thioredoxin Reductase (NADPH)' } 0 10000 {'h[c] + nadph[c] + trdox[c] -> nadp[c] + trdrd[c] ' } {'TRPO2' } {'L-Tryptophan:Oxygen 2, 3-Oxidoreductase (Decyclizing)' } 0 10000 {'o2[c] + trp_L[c] -> Lfmkynr[c] ' } {'TYR3MO2' } {'Tyrosine 3-Monooxygenase' } 0 10000 {'o2[c] + thbpt[c] + tyr_L[c] -> 34dhphe[c] + thbpt4acam[c] ' } {'TYRCBOX' } {'L-Tyrosine Carboxy-Lyase' } 0 10000 {'h[c] + tyr_L[c] -> co2[c] + tym[c] ' } {'UAG2EMAi' } {'UDP-N-Acetyl-D-Glucosamine 2-Epimerase (Hydrolysis)' } 0 10000 {'h2o[c] + uacgam[c] -> h[c] + udp[c] + acmana[c] ' } {'UAGALDP' } {'UDP-N-Acetylgalactosamine Diphosphorylase' } 0 10000 {'h[c] + acgal1p[c] + utp[c] -> ppi[c] + udpacgal[c] ' } {'UDPDOLPT_L' } {'UDPglucose:Dolichyl-Phosphate Beta-D-Glucosyltransferase (Li'} 0 10000 {'0.1 dolp_L[c] + udpg[c] -> udp[c] + 0.1 dolglcp_L[c] ' } {'UDPGD' } {'UDPglucose 6-Dehydrogenase' } 0 10000 {'h2o[c] + 2 nad[c] + udpg[c] -> 3 h[c] + 2 nadh[c] + udpglcur[c] ' } {'UDPGNP' } {'UDPglucuronate Uridine-Diphosphohydrolase' } 0 10000 {'h2o[c] + udpglcur[c] -> h[c] + udp[c] + glcur[c] ' } {'UDPGP' } {'UDPglucose Pyrophosphohydrolase' } 0 10000 {'h2o[c] + udpg[c] -> 2 h[c] + g1p[c] + ump[c] ' } {'URIK1' } {'Uridine Kinase (ATP:Uridine)' } 0 10000 {'atp[c] + uri[c] -> h[c] + adp[c] + ump[c] ' } {'r0023' } {'NADH:Ferricytochrome-B5 Oxidoreductase' } 0 10000 {'nadh[c] + 2 HC00617[c] -> h[c] + nad[c] + 2 HC00619[c] ' } {'r0047' } {'Adenosine 5-Monophosphate Phosphohydrolase' } 0 10000 {'h2o[m] + amp[m] -> pi[m] + adn[m] ' } {'r0085' } {'2-Oxoglutaramate Amidohydrolase' } 0 10000 {'h2o[c] + HC00591[c] -> nh4[c] + akg[c] ' } {'r0086' } {'2-Oxoglutaramate Amidohydrolase' } 0 10000 {'h2o[m] + HC00591[m] -> akg[m] + nh4[m] ' } {'r0119' } {'Guanosine 5-Triphosphate Pyrophosphohydrolase' } 0 10000 {'h2o[c] + gtp[c] -> h[c] + ppi[c] + gmp[c] ' } {'r0142' } {'Sulfite:Oxygen Oxidoreductase' } 0 10000 {'h2o[m] + o2[m] + so3[m] -> h2o2[m] + so4[m] ' } {'r0145' } {'L-Arginine, NADPH:Oxygen Oxidoreductase (Nitric-Oxide-Formin'} 0 10000 {'2 o2[c] + 2 nadph[c] + arg_L[c] -> 2 h2o[c] + 2 nadp[c] + citr_L[c] + no[c] ' } {'r0153' } {'CTP:Pyruvate O2-Phosphotransferase' } 0 10000 {'h[c] + pep[c] + cdp[c] -> pyr[c] + ctp[c] ' } {'r0156' } {'L-Glutamine:Pyruvate Aminotransferase' } 0 10000 {'pyr[c] + gln_L[c] -> ala_L[c] + HC00591[c] ' } {'r0157' } {'L-Glutamine:Pyruvate Aminotransferase' } 0 10000 {'pyr[m] + gln_L[m] -> ala_L[m] + HC00591[m] ' } {'r0160' } {'L-Serine:Pyruvate Aminotransferase' } 0 0.28767 {'pyr[c] + ser_L[c] -> ala_L[c] + hpyr[c] ' } {'r0165' } {'UTP:Pyruvate O2-Phosphotransferase' } 0 10000 {'h[c] + udp[c] + pep[c] -> pyr[c] + utp[c] ' } {'r0166' } {'Uridine Triphosphate Pyrophosphohydrolase' } 0 10000 {'h2o[e] + utp[e] -> h[e] + ump[e] + ppi[e] ' } {'r0179' } {'Succinate-Semialdehyde:NADP+ Oxidoreductase' } 0 10000 {'h2o[m] + nadp[m] + sucsal[m] -> 2 h[m] + nadph[m] + succ[m] ' } {'r0186' } {'Ethanolamine-Phosphate Phospho-Lyase (Deaminating)' } 0 10000 {'h2o[c] + ethamp[c] -> nh4[c] + pi[c] + acald[c] ' } {'r0191' } {'UTP:D-Fructose-6-Phosphate 1-Phosphotransferase' } 0 10000 {'utp[c] + f6p[c] -> h[c] + udp[c] + fdp[c] ' } {'r0280' } {'DATP:Pyruvate O2-Phosphotransferase' } 0 10000 {'h[c] + pep[c] + dadp[c] -> pyr[c] + datp[c] ' } {'r0281' } {'Putrescine:Oxygen Oxidoreductase (Deaminating)' } 0 10000 {'h2o[e] + o2[e] + ptrc[e] -> nh4[e] + h2o2[e] + 4abutn[e] ' } {'r0301' } {'Xanthosine-5-Phosphate:Ammonia Ligase (AMP-Forming)' } 0 10000 {'nh4[c] + atp[c] + xmp[c] -> 2 h[c] + amp[c] + ppi[c] + gmp[c] ' } {'r0354' } {'Hexokinase' } 0 10000 {'itp[c] + glc_D[c] -> h[c] + idp[c] + g6p[c] ' } {'r0357' } {'Hexokinase' } 0 10000 {'itp[c] + fru[c] -> h[c] + idp[c] + f6p[c] ' } {'r0365' } {'3-Hydroxypropanoate:NAD+ Oxidoreductase ' } 0 10000 {'nad[m] + 3hpp[m] -> h[m] + nadh[m] + msa[m] ' } {'r0377' } {'ATP:Deoxycitidine 5-Phosphotransferase' } 0 10000 {'atp[c] + dcyt[c] -> h[c] + adp[c] + dcmp[c] ' } {'r0383' } {'Pyruvate:[Dihydrolipoyllysine-Residue Acetyltransferase]-Lip'} 0 10000 {'h[m] + pyr[m] + lpam[m] -> co2[m] + HC00682[m] ' } {'r0399' } {'L-Phenylalanine, Tetrahydrobiopterin:Oxygen Oxidoreductase ('} 0 10000 {'o2[c] + thbpt[c] + phe_L[c] -> h2o[c] + dhbpt[c] + tyr_L[c] ' } {'r0413' } {'DATP:Pyruvate O2-Phosphotransferase' } 0 10000 {'h[c] + pep[c] + dgdp[c] -> pyr[c] + dgtp[c] ' } {'r0423' } {'Isocitrate:NADP+ Oxidoreductase (Decarboxylating)' } 0 10000 {'nadp[m] + icit[m] -> h[m] + nadph[m] + HC01434[m] ' } {'r0426' } {'Isocitrate Hydro-Lyase ' } 0 10000 {'icit[m] -> h2o[m] + HC00342[m] ' } {'r0438' } {'Palmitoyl Coenzyme A:L-Carnitine O-Palmitoyltransferase' } 0 10000 {'crn[r] + lnlccoa[r] -> coa[r] + lnlccrn[r] ' } {'r0451' } {'2-Oxoadipate:Lipoamde 2-Oxidoreductase (Decarboxylating And '} 0 10000 {'h[m] + 2oxoadp[m] + lpam[m] -> co2[m] + HC01712[m] ' } {'r0456' } {'ATP:Deoxyguanosine 5-Phosphotransferase' } 0 10000 {'atp[c] + dgsn[c] -> h[c] + adp[c] + dgmp[c] ' } {'r0509' } {'Succinate:Ubiquinone Oxidoreductase' } 0 10000 {'q10[m] + succ[m] -> q10h2[m] + fum[m] ' } {'r0511' } {'Steroyl Coenzyme A, Hydrogen-Donor:Oxygen Oxidoreductase Pol'} 0 10000 {'o2[c] + 2 h[c] + stcoa[c] + 2 HC00619[c] -> 2 h2o[c] + odecoa[c] + 2 HC00617[c] ' } {'r0555' } {'Acetyl Coenzyme A:Enzyme N6- (Dihydrolipoyl)Lysine S-Acetylt'} 0 10000 {'coa[m] + HC00682[m] -> accoa[m] + dhlam[m] ' } {'r0557' } {'Glutaryl Coenzyme A:Dihydrolipoamide S-Succinyltransferase L'} 0 10000 {'coa[m] + HC01712[m] -> glutcoa[m] + dhlam[m] ' } {'r0568' } {' (5-L-Glutamyl)-L-Amino-Acid 5-Glutamyltransferase (Cyclizin'} 0 10000 {'glucys[c] -> cys_L[c] + 5oxpro[c] ' } {'r0578' } {'ATP:Pantothenate 4-Phosphotransferase' } 0 10000 {'atp[c] + ptth[c] -> h[c] + adp[c] + pan4p[c] ' } {'r0594' } {'L-2-Aminoadipate-6-Semialdehyde:NAD+ 6-Oxidoreductase Lysine'} 0 10000 {'h2o[c] + nad[c] + L2aadp6sa[c] -> 2 h[c] + L2aadp[c] + nadh[c] ' } {'r0596' } {'3-Hydroxyisobutyryl Coenzyme A Hydrolase ' } 0 10000 {'h2o[m] + 3hpcoa[m] -> h[m] + coa[m] + 3hpp[m] ' } {'r0655' } {'3-Methylbutanoyl Coenzyme A: (Acceptor) 2, 3-Oxidoreductase '} 0 10000 {'ivcoa[m] + q10[m] -> 3mb2coa[m] + q10h2[m] ' } {'r0666' } {'2- (Formamido)-N1- (5-Phosphoribosyl)Acetamidine Cyclo-Ligas'} 0 10000 {'atp[c] + fpram[c] -> 2 h[c] + adp[c] + pi[c] + air[c] ' } {'r0698' } {'Propanoyl Coenzyme A:Acetyl Coenzyme A C-Acyltransferase Bil'} 0 10000 {'4 h[x] + dcholcoa[x] + ppcoa[x] -> coa[x] + h2o[x] + dhcholestancoa[x] ' } {'r0853' } {'Facilitated Diffusion' } 0 10000 {'atp[c] + pi[m] -> pi[c] + atp[m] ' } {'r0924' } {'ATP-Binding Cassette (ABC) Tcdb:3.A.1.204.5' } 0 10000 {'h2o[r] + atp[r] + chsterol[r] -> adp[r] + h[r] + pi[r] + chsterol[e] ' } {'r0986' } {'Vesicular Transport' } 0 10000 {'lnlc[l] -> lnlc[r] ' } {'r1002' } {'Facilitated Diffusion' } 0 10000 {'crn[c] + lnlccrn[r] -> crn[r] + lnlccrn[c] ' } {'r1078' } {'Vesicular Transport' } 0 10000 {'tyr_L[c] -> tyr_L[m] ' } {'r1109' } {'Citrate Oxaloacetate-Lyase ( (Pro-3S)-Ch2Coo- ->Acetate)' } 0 10000 {'cit[m] -> ac[m] + oaa[m] ' } {'r1150' } {'Facilitated Diffusion' } 0 10000 {'pi[l] -> pi[c] ' } {'r1164' } {'Sterol O-Acyltransferase' } 0 10000 {'chsterol[r] + pmtcoa[r] -> coa[r] + HC02020[r] ' } {'r1168' } {'Sterol O-Acyltransferase' } 0 10000 {'chsterol[r] + lnlccoa[r] -> coa[r] + HC02024[r] ' } {'r1170' } {'Sterol O-Acyltransferase' } 0 10000 {'chsterol[r] + lnlncgcoa[r] -> coa[r] + HC02026[r] ' } {'r1171' } {'Sterol O-Acyltransferase' } 0 10000 {'chsterol[r] + arachdcoa[r] -> coa[r] + HC02027[r] ' } {'r1179' } {'Sterol Esterase' } 0 10000 {'h2o[r] + HC02024[r] -> h[r] + chsterol[r] + lnlc[r] ' } {'r1182' } {'Sterol Esterase' } 0 10000 {'h2o[r] + HC02026[r] -> h[r] + chsterol[r] + lnlncg[r] ' } {'r1183' } {'Sterol Esterase' } 0 10000 {'h2o[r] + HC02027[r] -> arachd[r] + h[r] + chsterol[r] ' } {'r1253' } {'Long-Chain-Fatty-Acid---Coa Ligase' } 0 10000 {'atp[r] + 8 h[r] + coa[r] + strdnc[r] -> amp[r] + ppi[r] + stcoa[r] ' } {'r1254' } {'Long-Chain-Fatty-Acid---Coa Ligase' } 0 10000 {'8 h[c] + atp[c] + coa[c] + strdnc[c] -> amp[c] + ppi[c] + stcoa[c] ' } {'r1260' } {'Long-Chain-Fatty-Acid---Coa Ligase' } 0 10000 {'atp[r] + coa[r] + lnlncg[r] -> amp[r] + ppi[r] + lnlncgcoa[r] ' } {'r1298' } {'Vesicular Transport' } 0 10000 {'lnlncg[l] -> lnlncg[r] ' } {'r1299' } {'Vesicular Transport' } 0 10000 {'lnlncg[c] -> lnlncg[l] ' } {'r1382' } {'Folylpolyglutamyl Synthetase' } 0 10000 {'6 atp[c] + 6 glu_L[c] + thf[c] -> 6 h[c] + 6 adp[c] + 6 pi[c] + 7thf[c] ' } {'r1383' } {'Gamma-Glutamyl Hydrolase' } 0 10000 {'6 h2o[c] + 7thf[c] -> 6 glu_L[c] + thf[c] ' } {'r1423' } {'Facilitated Diffusion' } 0 10000 {'pi[c] -> pi[e] ' } {'r1434' } {'Transport Reaction' } 0 10000 {'ala_L[c] -> ala_L[m] ' } {'r1435' } {'Transport Reaction' } 0 10000 {'ser_L[c] -> ser_L[m] ' } {'r1455' } {'Transport Reaction' } 0 10000 {'h[c] + phe_L[c] -> h[m] + phe_L[m] ' } {'r1493' } {'Utilized Transport' } 0 10000 {'gthrd[c] -> gthrd[e] ' } {'r1514' } {'ATP-Binding Cassette (ABC) Tcdb:3.A.1.211.1' } 0 10000 {'h2o[c] + atp[c] + arachd[c] -> h[c] + adp[c] + pi[c] + arachd[e] ' } {'r1515' } {'ATP-Binding Cassette (ABC) Tcdb:3.A.1.211.1' } 0 10000 {'h2o[c] + atp[c] + hdca[c] -> h[c] + adp[c] + pi[c] + hdca[e] ' } {'r1517' } {'ATP-Binding Cassette (ABC) Tcdb:3.A.1.211.1' } 0 10000 {'h2o[c] + atp[c] + strdnc[c] -> h[c] + adp[c] + pi[c] + strdnc[e] ' } {'r1518' } {'ATP-Binding Cassette (ABC) Tcdb:3.A.1.211.1' } 0 10000 {'h2o[c] + atp[c] + lnlc[c] -> h[c] + adp[c] + pi[c] + lnlc[e] ' } {'r1520' } {'ATP-Binding Cassette (ABC) Tcdb:3.A.1.211.1' } 0 10000 {'h2o[c] + atp[c] + lnlncg[c] -> h[c] + adp[c] + pi[c] + lnlncg[e] ' } {'r1530' } {'ATP-Binding Cassette (ABC) Tcdb:3.A.1.208.15' } 0 10000 {'h2o[c] + atp[c] + gthrd[c] -> h[c] + adp[c] + pi[c] + gthrd[e] ' } {'r1674' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + gly[e] + ser_L[c] -> na1[c] + gly[c] + ser_L[e] ' } {'r1725' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + ser_L[e] + leu_L[c] -> na1[c] + ser_L[c] + leu_L[e] ' } {'r1726' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + ser_L[e] + pro_L[c] -> na1[c] + ser_L[c] + pro_L[e] ' } {'r1735' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + ser_L[c] + met_L[e] -> na1[c] + ser_L[e] + met_L[c] ' } {'r1790' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + hom_L[c] + tyr_L[e] -> na1[c] + hom_L[e] + tyr_L[c] ' } {'r1810' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + ser_L[c] + leu_L[e] -> na1[c] + ser_L[e] + leu_L[c] ' } {'r1815' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + cys_L[c] + leu_L[e] -> na1[c] + cys_L[e] + leu_L[c] ' } {'r1834' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + thr_L[c] + pro_L[e] -> na1[c] + thr_L[e] + pro_L[c] ' } {'r1909' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + ile_L[e] + val_L[c] -> na1[c] + ile_L[c] + val_L[e] ' } {'r1912' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + gly[e] + lys_L[c] -> na1[c] + gly[c] + lys_L[e] ' } {'r1915' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + gly[e] + his_L[c] -> na1[c] + gly[c] + his_L[e] ' } {'r1919' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + orn[c] + ala_L[e] -> na1[c] + ala_L[c] + orn[e] ' } {'r1928' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + ser_L[e] + arg_L[c] -> na1[c] + ser_L[c] + arg_L[e] ' } {'r1944' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + orn[c] + phe_L[e] -> na1[c] + orn[e] + phe_L[c] ' } {'r1954' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + orn[c] + cys_L[e] -> na1[c] + cys_L[c] + orn[e] ' } {'r1962' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + lys_L[c] + pro_L[e] -> na1[c] + lys_L[e] + pro_L[c] ' } {'r1967' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + asn_L[e] + lys_L[c] -> na1[c] + asn_L[c] + lys_L[e] ' } {'r1975' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + his_L[c] + val_L[e] -> na1[c] + his_L[e] + val_L[c] ' } {'r1982' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + lys_L[c] + hom_L[e] -> na1[c] + lys_L[e] + hom_L[c] ' } {'r1989' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + orn[c] + ile_L[e] -> na1[c] + ile_L[c] + orn[e] ' } {'r1991' } {'Y+Lat2 Utilized Transport' } 0 10000 {'na1[e] + citr_L[c] + ile_L[e] -> na1[c] + ile_L[c] + citr_L[e] ' } {'r2381' } {'Mitochondrial Carrier (Mc) Tcdb:2.A.29.7.2' } 0 10000 {'h[c] + akg[m] + cit[c] -> h[m] + akg[c] + cit[m] ' } {'r2419' } {'Mitochondrial Carrier (Mc) Tcdb:2.A.29.2.7' } 0 10000 {'akg[c] + pi[m] -> pi[c] + akg[m] ' } {'r2471' } {'Major Facilitator (Mfs) Tcdb:2.A.18.8.1' } 0 10000 {'h[e] + ser_L[e] -> h[c] + ser_L[c] ' } {'r2473' } {'Major Facilitator (Mfs) Tcdb:2.A.1.4.5' } 0 10000 {'pi[r] + g6p[c] -> pi[c] + g6p[r] ' } {'r2512' } {'Utilized Transport' } 0 10000 {'crn[c] + lnlncg[r] -> crn[r] + lnlncg[c] ' } {'RE0565C' } {'RE0565C' } 0 10000 {'h[c] + stcoa[c] + malcoa[c] -> co2[c] + coa[c] + CE2251[c] ' } {'RE0569C' } {'RE0569C' } 0 10000 {'h[c] + arachcoa[c] + malcoa[c] -> co2[c] + coa[c] + CE2250[c] ' } {'RE0912C' } {'RE0912C' } 0 10000 {'paps[c] + CE2866[c] -> h[c] + pap[c] + CE2870[c] ' } {'RE1266C' } {'RE1266C' } 0 10000 {'o2[c] + 4mop[c] -> h[c] + co2[c] + CE2028[c] ' } {'RE1836X' } {'Propionyl Coenzyme A C2-Trimethyltridecanoyltransferase' } 0 10000 {'coa[x] + o2[x] + dhcholestancoa[x] -> h2o[x] + dcholcoa[x] + ppcoa[x] ' } {'RE2666C' } {'RE2666C' } 0 10000 {'udpgal[c] + galside_hs[c] -> h[c] + udp[c] + digalside_hs[c] ' } {'RE2717L' } {'Galactosylceramidase' } 0 10000 {'h2o[l] + C01747[l] -> sphings[l] + gal[l] ' } {'RE2985M' } {'Acyl Coenzyme A Oxidase' } 0 10000 {'o2[m] + arachdcoa[m] -> h2o2[m] + CE4795[m] ' } {'RE2998M' } {'Acyl Coenzyme A Oxidase' } 0 10000 {'o2[m] + CE0785[m] -> h2o2[m] + CE2432[m] ' } {'RE3052C' } {'RE3052C' } 0 10000 {'cpppg3[c] -> 6 h[c] + C05770[c] ' } {'RE3095C' } {'Peroxidase' } 0 10000 {'h2o2[c] + dopa[c] -> 2 h2o[c] + CE5276[c] ' } {'RE3201C' } {'Tyrosinase' } 0 10000 {'o2[c] + 56dihindlcrbxlt[c] -> h2o2[c] + CE1562[c] ' } {'RE3251M' } {'RE3251M' } 0 10000 {'o2[m] + h[m] + nadph[m] + xoltetrol[m] -> h2o[m] + nadp[m] + CE4874[m] ' } {'RE3346M' } {'Aldehyde Dehydrogenase (NAD+)' } 0 10000 {'2 h[m] + nadh[m] + thcholstoic[m] -> h2o[m] + nad[m] + CE4872[m] ' } {'RE3434C' } {'Leukotriene-B4 20-Monooxygenase' } 0 10000 {'o2[c] + h[c] + nadph[c] + CE4988[c] -> h2o[c] + nadp[c] + CE4989[c] ' } {'RE3435C' } {'Leukotriene-B4 20-Monooxygenase' } 0 10000 {'o2[c] + h[c] + nadph[c] + CE5945[c] -> h2o[c] + nadp[c] + CE5946[c] ' } {'RE3436C' } {'Leukotriene-B4 20-Monooxygenase' } 0 10000 {'o2[c] + h[c] + nadph[c] + CE4989[c] -> h2o[c] + nadp[c] + CE5945[c] ' } {'RE3525R' } {'Arachidonate 12-Lipoxygenase' } 0 10000 {'o2[r] + 2 C04805[r] -> 2 leuktrB4[r] ' } {'RE3624M' } {'Acyl Coenzyme A Oxidase' } 0 10000 {'o2[m] + CE4794[m] -> h2o2[m] + C05279[m] ' } {'RE3637C' } {'RE3637C' } 0 10000 {'uppg3[c] -> 6 h[c] + C05767[c] ' } {'FAOXC101C102x' } {'Fatty Acid Beta Oxidation (C10:1->C10:2), Peroxisomal' } 0 10000 {'o2[x] + dece4coa[x] -> h2o2[x] + dec24dicoa[x] ' } {'FAOXC16C14m' } {'Fatty Acid Beta Oxidation (C16->C14), Mitochondrial' } 0 10000 {'h2o[m] + nad[m] + coa[m] + fad[m] + pmtcoa[m] -> h[m] + nadh[m] + accoa[m] + fadh2[m] + tdcoa[m] ' } {'FAOXC4C2m' } {'Fatty Acid Beta Oxidation (C4->C2), Mitochondrial' } 0 10000 {'h2o[m] + nad[m] + coa[m] + fad[m] + btcoa[m] -> h[m] + nadh[m] + 2 accoa[m] + fadh2[m] ' } {'FAOXC5C5OHm' } {'Fatty Acid Beta Oxidation (C5->C5Oh), Mitochondrial' } 0 10000 {'h2o[m] + 3mb2coa[m] -> 3ivcoa[m] ' } {'FAOXC6C4m' } {'Fatty Acid Beta Oxidation (C6->C4), Mitochondrial' } 0 10000 {'h2o[m] + nad[m] + coa[m] + fad[m] + hxcoa[m] -> h[m] + nadh[m] + accoa[m] + fadh2[m] + btcoa[m] ' } {'FAOXC8C6m' } {'Fatty Acid Beta Oxidation (C8->C6), Mitochondrial' } 0 10000 {'h2o[m] + nad[m] + coa[m] + fad[m] + occoa[m] -> h[m] + nadh[m] + accoa[m] + fadh2[m] + hxcoa[m] ' } {'HEXCOAACBP' } {'Transport of Hexanoyl Coenzyme A (N-C6:0CoA) from Mitochondr'} 0 10000 {'hxcoa[m] -> hxcoa[c] ' } {'PRISTCOAtcx' } {'Transport of Pristanoylcoa from Cytosol to Peroxisomes.' } 0 10000 {'h2o[c] + atp[c] + pristcoa[c] -> h[c] + adp[c] + pi[c] + pristcoa[x] ' } {'SCP21cx' } {'Transport of Phytanoylcoa from Cytosol to Peroxisomes.' } 0 10000 {'h2o[c] + atp[c] + phytcoa[c] -> h[c] + adp[c] + pi[c] + phytcoa[x] ' } {'SUCCACT' } {'Activation of Succinate' } 0 10000 {'atp[c] + coa[c] + succ[c] -> amp[c] + ppi[c] + succoa[c] ' } {'TDCRNe' } {'Transport of Myristoyl Carnitine into Extra Cellular Space' } 0 10000 {'ttdcrn[c] -> ttdcrn[e] ' } {'34DHPHELAT1tc' } {'Transport of 3, 4-Dihydroxy-L-Phenylalanine by Lat1 in Assoc'} 0 10000 {'34dhphe[e] + leu_L[c] -> 34dhphe[c] + leu_L[e] ' } {'ASCBSVCTtc' } {'Transport of L-Ascorbate by Svct1 Or Svct2 Transporter' } 0 10000 {'h2o[c] + atp[c] + 2 na1[e] + ascb_L[e] -> h[c] + adp[c] + pi[c] + 2 na1[c] + ascb_L[c] ' } {'FOLTle' } {'Transport of Folate' } 0 10000 {'h[e] + fol[e] -> h[c] + fol[c] ' } {'GLNyLATthc' } {'Transport of Glutamine by Y+Lat1 Or Y+Lat2 with Symporter of'} 0 10000 {'h[e] + gln_L[e] + arg_L[c] -> h[c] + gln_L[c] + arg_L[e] ' } {'HISyLATtc' } {'Transport of L-Histidine by Y+Lat1 Or Y+Lat2 Transporters' } 0 10000 {'na1[e] + arg_L[c] + his_L[e] -> na1[c] + arg_L[e] + his_L[c] ' } {'LEUyLAThtc' } {'Transport of Leucine by Y+Lat1 Or Y+Lat2 with Symporter of H'} 0 10000 {'h[e] + arg_L[c] + leu_L[e] -> h[c] + arg_L[e] + leu_L[c] ' } {'LINOFATPtc' } {'Uptake of Linoleic Acid' } 0 10000 {'atp[c] + coa[c] + lnlc[e] -> amp[c] + ppi[c] + lnlccoa[c] ' } {'PALFATPtc' } {'Transport of Hexadecanoate' } 0 10000 {'atp[c] + coa[c] + hdca[e] -> amp[c] + ppi[c] + pmtcoa[c] ' } {'PNTORDe' } {'Release of Pantothenate' } 0 10000 {'pnto_R[c] -> pnto_R[e] ' } {'TAUPAT1c' } {'Transport of Taurine by Pat1' } 0 10000 {'h[e] + taur[e] -> h[c] + taur[c] ' } {'VITKtl' } {'Transport of Vitamin K into Lymph' } 0 10000 {'phyQ[c] -> phyQ[e] ' } {'4HPROLTASCT1' } {'Transport of Hydroxy-Proline ' } 0 10000 {'na1[e] + ala_L[e] + 4hpro_LT[c] -> na1[c] + ala_L[c] + 4hpro_LT[e] ' } {'ASPPROASCT1' } {'Aspartate Intake by System Asct-1 Transporter' } 0 10000 {'na1[e] + asp_L[e] + pro_L[c] -> na1[c] + asp_L[c] + pro_L[e] ' } {'CHOLESACATc' } {'Esterification of Cholesterol to Cholesterol Ester' } 0 10000 {'Rtotalcoa[c] + chsterol[c] -> coa[c] + xolest2_hs[c] ' } {'DPMVDc' } {'Diphosphomevalonate Decarboxylase, Cytosol' } 0 10000 {'atp[c] + 5dpmev[c] -> adp[c] + pi[c] + co2[c] + ipdp[c] ' } {'FADH2ETC' } {'Complex Ii Reaction for Respiratory Chain' } 0 10000 {'fadh2[m] + q10[m] -> fad[m] + q10h2[m] ' } {'G6PDH2c' } {'Glucose 6-Phosphate Dehydrogenase' } 0 10000 ...
printConstraints(model,-1e4,1e4,~model.SIntRxnBool)
Forward_Reaction, 0 bound Name lb ub equation _________________________ _____________________________________________________________ __ _____ _________________________ {'EX_34dhoxpeg[e]' } {'Exchange of 3, 4-Dihydroxyphenylethyleneglycol ' } 0 10000 {'34dhoxpeg[e] -> ' } {'EX_3mlda[e]' } {'Exchange of 3-Methylimidazoleacetic Acid ' } 0 10000 {'3mlda[e] -> ' } {'EX_adrnl[e]' } {'Exchange of Adrenaline ' } 0 10000 {'adrnl[e] -> ' } {'EX_amp[e]' } {'Exchange of AMP ' } 0 10000 {'amp[e] -> ' } {'EX_creat[e]' } {'Exchange of Creatine ' } 0 10000 {'creat[e] -> ' } {'EX_dag_hs[e]' } {'Exchange of Diglyceride' } 0 10000 {'dag_hs[e] -> ' } {'EX_gsn[e]' } {'Exchange of Guanosine' } 0 10000 {'gsn[e] -> ' } {'EX_gthox[e]' } {'Exchange of Oxidized Glutathione ' } 0 10000 {'gthox[e] -> ' } {'EX_hista[e]' } {'Exchange of Histamine ' } 0 10000 {'hista[e] -> ' } {'EX_imp[e]' } {'Exchange of IMP ' } 0 10000 {'imp[e] -> ' } {'EX_leuktrB4[e]' } {'Exchange of Leukotriene B4 ' } 0 10000 {'leuktrB4[e] -> ' } {'EX_mag_hs[e]' } {'Exchange of Monoacylglycerol 2 (Homo Sapiens) ' } 0 10000 {'mag_hs[e] -> ' } {'EX_no[e]' } {'Exchange of Nitric Oxide' } 0 10000 {'no[e] -> ' } {'EX_nrpphr[e]' } {'Exchange of Norepinephrine ' } 0 10000 {'nrpphr[e] -> ' } {'EX_xolest2_hs[e]' } {'Exchange of Cholesterol Ester (from FullR2) ' } 0 10000 {'xolest2_hs[e] -> ' } {'EX_4abutn[e]' } {'Exchange of 4-Ammoniobutanal' } 0 10000 {'4abutn[e] -> ' } {'EX_fad[e]' } {'Exchange of Flavin Adenine Dinucleotide Oxidized' } 0 10000 {'fad[e] -> ' } {'EX_fald[e]' } {'Exchange of Formaldehyde' } 0 10000 {'fald[e] -> ' } {'EX_HC02213[e]' } {'Exchange of Prostaglandin-E3 ' } 0 10000 {'HC02213[e] -> ' } {'EX_4hpro[e]' } {'Exchange of Hydroxy Proline' } 0 10000 {'4hpro_LT[e] -> ' } {'EX_leuleu[e]' } {'Exchange of Leucylleucine' } 0 10000 {'leuleu[e] -> ' } {'EX_34hpp[e]' } {'Exchange of 3- (4-Hydroxyphenyl)Pyruvate' } 0 10000 {'34hpp[e] -> ' } {'EX_3mob[e]' } {'Exchange of 3-Methyl-2-Oxobutanoate' } 0 10000 {'3mob[e] -> ' } {'EX_3mop[e]' } {'Exchange of 3-Methyl-2-Oxopentanoate' } 0 10000 {'3mop[e] -> ' } {'EX_4mop[e]' } {'Exchange of 4-Methyl-2-Oxopentanoate' } 0 10000 {'4mop[e] -> ' } {'EX_5mta[e]' } {'Exchange of 5-S-Methyl-5-Thioadenosine' } 0 10000 {'5mta[e] -> ' } {'EX_5oxpro[e]' } {'Exchange of 5-Oxoprolinate' } 0 10000 {'5oxpro[e] -> ' } {'EX_ahcys[e]' } {'Exchange of S-Adenosyl-L-Homocysteine' } 0 10000 {'ahcys[e] -> ' } {'EX_cbasp[e]' } {'Exchange of N-Carbamoyl-L-Aspartate' } 0 10000 {'cbasp[e] -> ' } {'EX_crtn[e]' } {'Exchange of Creatinine' } 0 10000 {'crtn[e] -> ' } {'EX_cyst_L[e]' } {'Exchange of L-Cystathionine' } 0 10000 {'cyst_L[e] -> ' } {'EX_ethamp[e]' } {'Exchange of Ethanolamine Phosphate' } 0 10000 {'ethamp[e] -> ' } {'EX_gudac[e]' } {'Exchange of Guanidinoacetic Acid' } 0 10000 {'gudac[e] -> ' } {'EX_kynate[e]' } {'Exchange of Kynurenic Acid' } 0 10000 {'kynate[e] -> ' } {'EX_xmp[e]' } {'Exchange of Xanthylic Acid' } 0 10000 {'xmp[e] -> ' } {'EX_argsuc[e]' } {'Exchange of L-Arginosuccinic Acid' } 0 10000 {'argsuc[e] -> ' } {'EX_3mtp[e]' } {'Exchange of 3-Methyl-Thio-Propionate' } 0 10000 {'3mtp[e] -> ' } {'EX_34hpl[e]' } {'Exchange of 3- (4-Hydroxyphenyl)Lactate' } 0 10000 {'34hpl[e] -> ' } {'EX_4aabutn[e]' } {'Exchange of 4-Acetamidobutanoate' } 0 10000 {'4aabutn[e] -> ' } {'EX_aclys[e]' } {'Exchange of Acetyl-Lysine' } 0 10000 {'aclys[e] -> ' } {'EX_C02712[e]' } {'Exchange of N-Acetylmethionine' } 0 10000 {'C02712[e] -> ' } {'EX_C04805[e]' } {'Exchange of 5(S)-HETE' } 0 10000 {'C04805[e] -> ' } {'EX_leuktrB4wcooh[e]'} {'Exchange of W-Carboxy Leukotriene B4' } 0 10000 {'leuktrB4wcooh[e] -> '} {'EX_Lpipecol[e]' } {'Exchange of L-Pipecolic Acid' } 0 10000 {'Lpipecol[e] -> ' } {'EX_magole_hs[e]' } {'Exchange of 1-Oleoylglycerol' } 0 10000 {'magole_hs[e] -> ' } {'EX_mi1p_D[e]' } {'Exchange of Myo-Inositol 1-Phosphate' } 0 10000 {'mi1p_D[e] -> ' } {'EX_urcan[e]' } {'Exchange of Urocanate' } 0 10000 {'urcan[e] -> ' } {'EX_dhbpt[e]' } {'Exchange of 6,7-Dihydrobiopterin' } 0 10000 {'dhbpt[e] -> ' } {'EX_thbpt[e]' } {'Exchange of 5,6,7,8-Tetrahydrobiopterin' } 0 10000 {'thbpt[e] -> ' } {'EX_argglygly[e]' } {'Exchange of ArgGlyGly' } 0 10000 {'argglygly[e] -> ' } {'EX_gluleu[e]' } {'Exchange of GluLeu' } 0 10000 {'gluleu[e] -> ' } {'EX_hisglylys[e]' } {'Exchange of HisGlyLys' } 0 10000 {'hisglylys[e] -> ' } {'EX_leuleutrp[e]' } {'Exchange of LeuLeuTrp' } 0 10000 {'leuleutrp[e] -> ' } {'EX_leuval[e]' } {'Exchange of LeuVal' } 0 10000 {'leuval[e] -> ' } {'EX_lysvaltrp[e]' } {'Exchange of LysValTrp' } 0 10000 {'lysvaltrp[e] -> ' } {'EX_phetrpleu[e]' } {'Exchange of PheTrpLeu' } 0 10000 {'phetrpleu[e] -> ' } {'EX_trpglyleu[e]' } {'Exchange of TrpGlyLeu' } 0 10000 {'trpglyleu[e] -> ' } {'EX_trpglyval[e]' } {'Exchange of TrpGlyVal' } 0 10000 {'trpglyval[e] -> ' } {'EX_homoval[e]' } {'Exchange of Homovanillate' } 0 10000 {'homoval[e] -> ' } {'EX_acgal[e]' } {'Exchange of N-Acetylgalactosamine ' } 0 10000 {'acgal[e] -> ' } {'EX_acnam[e]' } {'Exchange of N-Acetylneuraminate ' } 0 10000 {'acnam[e] -> ' } {'EX_pcreat[e]' } {'Exchange of Phosphocreatine' } 0 10000 {'pcreat[e] -> ' } {'EX_2obut[e]' } {'Exchange of 2-Oxobutanoate' } 0 10000 {'2obut[e] -> ' } {'EX_glcn[e]' } {'Exchange of D-Gluconate' } 0 10000 {'glcn[e] -> ' } {'EX_adn[e]' } {'Exchange of Adenosine' } 0 10000 {'adn[e] -> ' } {'EX_cgly[e]' } {'Exchange of Cysteinyl-Glycine ' } 0 10000 {'cgly[e] -> ' } {'EX_co2[e]' } {'Exchange of Carbon Dioxide ' } 0 10000 {'co2[e] -> ' } {'EX_cytd[e]' } {'Exchange of Cytidine' } 0 10000 {'cytd[e] -> ' } {'EX_glypro[e]' } {'Exchange of Glypro' } 0 10000 {'glypro[e] -> ' } {'EX_ppi[e]' } {'Exchange of Ppi' } 0 10000 {'ppi[e] -> ' } {'EX_for[e]' } {'Exchange of Formate ' } 0 10000 {'for[e] -> ' } {'EX_ac[e]' } {'Exchange of Acetate ' } 0 10000 {'ac[e] -> ' } {'EX_fru[e]' } {'Exchange of D-Fructose' } 0 10000 {'fru[e] -> ' } {'EX_glcur[e]' } {'Exchange of D-Glucuronate ' } 0 10000 {'glcur[e] -> ' } {'EX_xan[e]' } {'Exchange of Xanthine ' } 0 10000 {'xan[e] -> ' } {'EX_xyl_D[e]' } {'Exchange of D-Xylose ' } 0 10000 {'xyl_D[e] -> ' } {'EX_4hbz[e]' } {'Exchange of 4-Hydroxybenzoate' } 0 10000 {'4hbz[e] -> ' } {'EX_3mox4hoxm[e]' } {'Exchange of 3-Methoxy-4-Hydroxymandelate' } 0 10000 {'3mox4hoxm[e] -> ' } {'EX_2h3mv[e]' } {'Exchange of 2-Hydroxy-3-Methyl-Valerate' } 0 10000 {'2h3mv[e] -> ' } {'EX_2hiv[e]' } {'Exchange of 2-Hydroxy-Isovalerate' } 0 10000 {'2hiv[e] -> ' } {'EX_2m3hbu[e]' } {'Exchange of 2-Methyl-3-Hydroxy-Butyrate' } 0 10000 {'2m3hbu[e] -> ' } {'EX_2m3hvac[e]' } {'Exchange of 2-Methyl-3-Hydroxy-Valerate' } 0 10000 {'2m3hvac[e] -> ' } {'EX_3h3mglt[e]' } {'Exchange of 3-Hydroxy-3-Methyl-Glutarate' } 0 10000 {'3h3mglt[e] -> ' } {'EX_3mglutac[e]' } {'Exchange of 3-Methyl-Glutaconate' } 0 10000 {'3mglutac[e] -> ' } {'EX_mvlac[e]' } {'Exchange of Mevalonate-Lactone' } 0 10000 {'mvlac[e] -> ' } {'EX_3ohglutac[e]' } {'Excahnge of 3-Hydroxy-Glutarate' } 0 10000 {'3ohglutac[e] -> ' } {'EX_glutcon[e]' } {'Exchange of Glutaconate' } 0 10000 {'glutcon[e] -> ' } {'EX_sql[e]' } {'Exchange of Squalene' } 0 10000 {'sql[e] -> ' } {'EX_HC02020[e]' } {'Exchange of Cholesterol-Ester-Palm' } 0 10000 {'HC02020[e] -> ' } {'EX_xol24oh[e]' } {'Exchange of (24S)-24-Hydroxycholesterol' } 0 10000 {'xol24oh[e] -> ' } {'EX_xol27oh[e]' } {'Exchange of 26-Hydroxycholesterol' } 0 10000 {'xol27oh[e] -> ' } {'EX_34dhoxmand[e]' } {'Exchange of 3,4-Dihydroxymandelate' } 0 10000 {'34dhoxmand[e] -> ' } {'EX_C05767[e]' } {'Exchange of Uroporphyrin I' } 0 10000 {'C05767[e] -> ' } {'EX_C05770[e]' } {'Exchange of Coproporphyrin Iii' } 0 10000 {'C05770[e] -> ' } {'EX_mhista[e]' } {'Exchange of N(Tele)-Methylhistaminium' } 0 10000 {'mhista[e] -> ' } {'EX_ppbng[e]' } {'Exchange of Porphobilinogen' } 0 10000 {'ppbng[e] -> ' } {'EX_ametam[e]' } {'Exchange of S-Adenosylmethioninamine' } 0 10000 {'ametam[e] -> ' } {'EX_xylu_D[e]' } {'Exchange of Xylu_D' } 0 10000 {'xylu_D[e] -> ' } {'EX_sphings[e]' } {'Exchange of Sphingosine' } 0 10000 {'sphings[e] -> ' } {'EX_im4ac[e]' } {'Exchange of Imidazol-4-Ylacetate' } 0 10000 {'im4ac[e] -> ' } {'EX_mlthf[e]' } {'Exchange of 5,10-Methylenetetrahydrofolate' } 0 10000 {'mlthf[e] -> ' } {'EX_CE2705[e]' } {'Exchange of Quinonoid Dihydrobiopterin' } 0 10000 {'CE2705[e] -> ' } {'EX_fdp[e]' } {'Exchange of D-Fructose 1,6-Bisphosphate' } 0 10000 {'fdp[e] -> ' } {'EX_34dhpe[c]' } {'Exchange of 3, 4-Dihydroxyphenylethanol ' } 0 10000 {'34dhpe[e] -> ' } {'EX_pail_hs[e]' } {'Exchange of 1-Phosphatidyl-1D-Myo-Inositol' } 0 10000 {'pail_hs[e] -> ' } {'EX_caproic[e]' } {'Exchange for Caproic Acid' } 0 10000 {'caproic[e] -> ' } {'EX_M01966[e]' } {'Exchange for D-Glucose 1,6-Bisphosphate' } 0 10000 {'M01966[e] -> ' } {'EX_kdn[e]' } {'Exchange for 2-Keto-3-Deoxy-D-Glycero-D-Galactononic Acid'} 0 10000 {'kdn[e] -> ' } {'DM_CE5026[c]' } {'Demand for 5-S-Glutathionyl-L-Dopa' } 0 10000 {'CE5026[c] -> ' } {'DM_CE1261[c]' } {'Demand for 5-S-Cysteinyldopa' } 0 10000 {'CE1261[c] -> ' } {'DM_4glu56dihdind[c]'} {'Demand for 4-S-Glutathionyl-5,6-Dihydroxyindoline' } 0 10000 {'4glu56dihdind[c] -> '} {'DM_CE1562[c]' } {'Demand for 5,6-Indolequinone-2-Carboxylate' } 0 10000 {'CE1562[c] -> ' } {'DM_ind56qn[c]' } {'Demand for Indole-5,6-Quinone' } 0 10000 {'ind56qn[c] -> ' } {'DM_5cysdopa[c]' } {'Demand for 5-S-Cysteinyldopamine' } 0 10000 {'5cysdopa[c] -> ' } {'DM_CE5025[c]' } {'Demand for 5-S-Glutathionyl-Dopamine' } 0 10000 {'CE5025[c] -> ' } {'DM_CE4888[c]' } {'Demand for Dopaminochrome' } 0 10000 {'CE4888[c] -> ' } Reverse_Reaction, 0 bound Name lb ub equation _________________________ _______________________________ ________ __ __________________ {'EX_lys_L[e]'} {'Exchange of L-Lysine ' } -100.23 0 {'lys_L[e] <=> '} {'EX_met_L[e]'} {'Exchange of L-Methionine ' } -1.8909 0 {'met_L[e] <=> '} {'EX_o2[e]' } {'Exchange of Oxugen' } -1516.9 0 {'o2[e] <=> ' } {'EX_his_L[e]'} {'Exchange of L-Histidine' } -27.05 0 {'his_L[e] <=> '} {'EX_thr_L[e]'} {'Exchange of L-Threonine ' } -96.44 0 {'thr_L[e] <=> '} {'EX_phe_L[e]'} {'Exchange of L-Phenylalanine'} -47.547 0 {'phe_L[e] <=> '} {'EX_trp_L[e]'} {'Exchange of L-Tryptophan ' } -0.83573 0 {'trp_L[e] <=> '} Forward_Reaction, non-0 bound Name lb ub equation _____________________________ _______________________________________________________ __________ _________ __________________ {'EX_2hb[e]' } {'Exchange of 2-Hydroxybutyrate ' } 0.032705 0.067463 {'2hb[e] -> ' } {'EX_bhb[e]' } {'Transport of (R)-3-Hydroxybutanoate via H+ Symport'} 0.053865 0.14049 {'bhb[e] -> ' } {'EX_3hpp[e]' } {'Exchange of 3-Hydroxypropionate' } 0.02363 0.063418 {'3hpp[e] -> ' } {'EX_Nacasp[e]'} {'Exchange of N-Acetyl-L-Aspartate' } 0.32205 0.60337 {'Nacasp[e] -> '} {'EX_glyc_R[e]'} {'Exchange of D-Glycerate' } 0.28767 0.39303 {'glyc_R[e] -> '} {'EX_glyclt[e]'} {'Exchange of Glycolate' } 0.10791 0.14605 {'glyclt[e] -> '} {'EX_akg[e]' } {'Exchange of 2-Oxoglutarate ' } 0.1022 0.27196 {'akg[e] -> ' } {'EX_asn_L[e]' } {'Exchange of L-Asparagine' } 0.48669 2.393 {'asn_L[e] -> ' } {'EX_fum[e]' } {'Exchange of Fumarate' } 0.06551 0.15912 {'fum[e] -> ' } {'EX_lac_L[e]' } {'Exchange of L-Lactate ' } 196.46 284.62 {'lac_L[e] -> ' } {'EX_mal_L[e]' } {'Exchange of L-Malate' } 0.054241 0.15419 {'mal_L[e] -> ' } {'EX_orn[e]' } {'Exchange of Ornithine ' } 25.366 40.296 {'orn[e] -> ' } {'EX_pro_L[e]' } {'Exchange of L-Proline ' } 0.96137 1.7283 {'pro_L[e] -> ' } {'EX_ser_L[e]' } {'Exchange of L-Serine' } 2.79 3.856 {'ser_L[e] -> ' } {'EX_succ[e]' } {'Exchange of Succinate ' } 0.15368 0.24036 {'succ[e] -> ' } {'EX_ala_L[e]' } {'Exchange of L-Alanine' } 8.6953 11.925 {'ala_L[e] -> ' } {'EX_cit[e]' } {'Exchange of Citrate ' } 0.254 0.69304 {'cit[e] -> ' } {'EX_ura[e]' } {'Exchange of Uracil ' } 0.0070234 0.016635 {'ura[e] -> ' } {'EX_taur[e]' } {'Exchange of Taurine ' } 0.0022509 0.019592 {'taur[e] -> ' } {'EX_actyr[e]' } {'Exchange of N-Acetyl-Tyrosine' } 0.00018472 0.0056333 {'actyr[e] -> ' } {'EX_3hivac[e]'} {'Exchange of 3-Hydroxy-Isovalerate' } 0.92259 2.1672 {'3hivac[e] -> '} Reverse_Reaction, non-0 bound Name lb ub equation _____________________________ ____________________________________ ________ ________ __________________ {'EX_acglu[e]'} {'Exchange of N-Acetyl-L-Glutamate'} -0.27082 -0.18228 {'acglu[e] <=> '} {'EX_ile_L[e]'} {'Exchange of L-Isoleucine ' } -19.49 -8.4975 {'ile_L[e] <=> '} {'EX_leu_L[e]'} {'Exchange of L-Leucine ' } -18.323 -8.3021 {'leu_L[e] <=> '} {'EX_val_L[e]'} {'Exchange of L-Valine ' } -11.719 -2.6654 {'val_L[e] <=> '} {'EX_gly[e]' } {'Exchange of Glycine' } -25.654 -14.496 {'gly[e] <=> ' } {'EX_cys_L[e]'} {'Exchange of L-Cysteine' } -1.6574 -0.57181 {'cys_L[e] <=> '} {'EX_gln_L[e]'} {'Exchange of L-Glutamine' } -60.556 -3.9021 {'gln_L[e] <=> '} {'EX_arg_L[e]'} {'Exchange of L-Arginine ' } -6.0387 -1.8685 {'arg_L[e] <=> '} {'EX_etha[e]' } {'Exchange of Ethanolamine ' } -0.56504 -0.35439 {'etha[e] <=> ' } {'EX_glc_D[e]'} {'Exchange of D-Glucose ' } -298.95 -126.74 {'glc_D[e] <=> '} Reversible_Reaction Name lb ub equation _______________________ ________________________________________________________________ ___________ _________ __________________________ {'EX_34dhphe[e]' } {'Exchange of 3, 4-Dihydroxy-L-Phenylalanine ' } -10000 10000 {'34dhphe[e] <=> ' } {'EX_ala_B[e]' } {'Exchange of Beta-Alanine ' } -0.16633 0.33252 {'ala_B[e] <=> ' } {'EX_arachd[e]' } {'Exchange of Nc20:4 ' } -10000 10000 {'arachd[e] <=> ' } {'EX_atp[e]' } {'Exchange of ATP ' } -10000 10000 {'atp[e] <=> ' } {'EX_chol[e]' } {'Exchange of Choline' } -7.1675 10000 {'chol[e] <=> ' } {'EX_chsterol[e]' } {'Exchange of Cholesterol' } -10000 10000 {'chsterol[e] <=> ' } {'EX_dopa[e]' } {'Exchange of Dopamine ' } -10000 10000 {'dopa[e] <=> ' } {'EX_dopasf[e]' } {'Exchange of Dopamine 3-O-Sulfate ' } -10000 10000 {'dopasf[e] <=> ' } {'EX_gthrd[e]' } {'Exchange of Reduced Glutathione ' } -0.25182 10000 {'gthrd[e] <=> ' } {'EX_h2o2[e]' } {'Exchange of Hydrogen Peroxide ' } -10000 10000 {'h2o2[e] <=> ' } {'EX_hco3[e]' } {'Exchange of Bicarbonate ' } -4268.5 10000 {'hco3[e] <=> ' } {'EX_inost[e]' } {'Exchange of Myo-Inositol ' } -8.5039 10000 {'inost[e] <=> ' } {'EX_Lcystin[e]' } {'Exchange of L-Cystine ' } -7.7283 10000 {'Lcystin[e] <=> ' } {'EX_lneldc[e]' } {'Exchange of Linoelaidic Acid ' } -10000 10000 {'lneldc[e] <=> ' } {'EX_lnlc[e]' } {'Exchange of Linoleic Acid (All Cis C18:2) ' } -0.011596 10000 {'lnlc[e] <=> ' } {'EX_lnlncg[e]' } {'Exchange of Gamma-Linolenic Acid ' } -10000 10000 {'lnlncg[e] <=> ' } {'EX_octa[e]' } {'Exchange of Octanoate (N-C8:0)' } -0.035424 0.035424 {'octa[e] <=> ' } {'EX_strdnc[e]' } {'Exchange of Stearidonic Acid ' } -10000 10000 {'strdnc[e] <=> ' } {'EX_citr_L[e]' } {'Exchange of L-Citrulline ' } -0.0018322 0.039396 {'citr_L[e] <=> ' } {'EX_Lkynr[e]' } {'Exchange of L-Kynurenine' } -0.00094841 0.0078456 {'Lkynr[e] <=> ' } {'EX_CE2028[e]' } {'Exchange of Beta-Hydroxy-Beta-Methylbutyrate' } -10000 10000 {'CE2028[e] <=> ' } {'EX_acile_L[e]' } {'Exchange of Acetyl Isoleucine' } -0.0094463 0.0019905 {'acile_L[e] <=> ' } {'EX_acleu_L[e]' } {'Exchange of Acetyl Leucine' } -0.0076158 0.0018524 {'acleu_L[e] <=> ' } {'EX_asp_L[e]' } {'Exchange of L-Aspartate ' } -3.8654 10000 {'asp_L[e] <=> ' } {'EX_gal[e]' } {'Exchange of D-Galactose' } -10000 10000 {'gal[e] <=> ' } {'EX_glu_L[e]' } {'Exchange of L-Glutamate ' } -3.8654 10000 {'glu_L[e] <=> ' } {'EX_h[e]' } {'Exchange of Proton' } -10000 10000 {'h[e] <=> ' } {'EX_h2o[e]' } {'Exchange of Water ' } -10000 10000 {'h2o[e] <=> ' } {'EX_pi[e]' } {'Exchange of Phosphate ' } -144.37 10000 {'pi[e] <=> ' } {'EX_ribflv[e]' } {'Exchange of Riboflavin' } -0.12727 10000 {'ribflv[e] <=> ' } {'EX_so4[e]' } {'Exchange of Sulfate ' } -31.748 10000 {'so4[e] <=> ' } {'EX_thymd[e]' } {'Exchange of Thymidine ' } -0.1166 10000 {'thymd[e] <=> ' } {'EX_tyr_L[e]' } {'Exchange of L-Tyrosine ' } -5.5345 0.8733 {'tyr_L[e] <=> ' } {'EX_nh4[e]' } {'Exchange of Ammonia ' } -0.00019826 10000 {'nh4[e] <=> ' } {'EX_fol[e]' } {'Exchange of Folate' } -1.1658 10000 {'fol[e] <=> ' } {'EX_ptrc[e]' } {'Exchange of 1, 4-Butanediammonium' } -0.12682 1.6468 {'ptrc[e] <=> ' } {'EX_34dhpha[e]' } {'Exchange of 34Dhpha' } -10000 10000 {'34dhpha[e] <=> ' } {'EX_pyr[e]' } {'Exchange of Pyruvate ' } -0.73311 0.44965 {'pyr[e] <=> ' } {'EX_4abut[e]' } {'Exchange of 4-Aminobutanoate ' } -0.00026682 0.030803 {'4abut[e] <=> ' } {'EX_C09642[e]' } {'Exchange of (-)-Salsolinol' } -10000 10000 {'C09642[e] <=> ' } {'EX_dopa4sf[e]' } {'Exchange of Dopamine 4-O-Sulfate ' } -10000 10000 {'dopa4sf[e] <=> ' } {'EX_dopa4glcur[e]' } {'Exchange of Dopamine 4-O-Glucuronide ' } -10000 10000 {'dopa4glcur[e] <=> ' } {'EX_dopa3glcur[e]' } {'Exchange of Dopamine 3-O-Glucuronide ' } -10000 10000 {'dopa3glcur[e] <=> ' } {'EX_4glu56dihdind[e]'} {'Exchange of 4-S-Glutathionyl-5, 6-Dihydroxyindoline ' } -10000 10000 {'4glu56dihdind[e] <=> '} {'EX_5cysdopa[e]' } {'Exchange of 5-S-Cysteinyldopamine ' } -10000 10000 {'5cysdopa[e] <=> ' } {'EX_CE5025[e]' } {'Exchange of 5-S-Glutathionyl-Dopamine ' } -10000 10000 {'CE5025[e] <=> ' } {'EX_CE5629[e]' } {'Exchange of 6, 7-Dihydroxy-1, 2, 3, 4-Tetrahydroisoquinoline'} -10000 10000 {'CE5629[e] <=> ' } {'EX_CE5026[e]' } {'Exchange of 5-S-Glutathionyl-L-Dopa' } -10000 10000 {'CE5026[e] <=> ' } {'EX_CE1261[e]' } {'Exchange of 5-S-Cysteinyldopa' } -10000 10000 {'CE1261[e] <=> ' } {'EX_CE1554[e]' } {'Exchange of Acetyl-Alanine' } -10000 10000 {'CE1554[e] <=> ' } {'DM_ps_hs[c]' } {'Phosphatidylserine demand' } -10000 10000 {'ps_hs[c] <=> ' }
printCouplingConstraints(model,1);
coupledRxnId constraints ___________________________ __________________________________________________________________________________ {'Phosphatidylcholine' } {'PCHOLP_hs + PLA2_2 + SMS >= 2.025' } {'Adenosine Monophosphate'} {'AMPDA + NTD7 >= 0.2265' } {'Glutamate' } {'- ALATA_L + GLUCYS + GLUDxm + GLUDym - ASPTA - ILETA - LEUTA - VALTA >= 1.2225'} {'Aspartate' } {'ARGSS + ASPTA >= 1.1925' } {'Serine' } {'GHMT2r + r0060 >= 0.8625' } {'Arginine' } {'GLYAMDTRc + r0145 >= 0.7245' } {'Tyrosine' } {'TYR3MO2 + TYRTA + HMR_6728 + HMR_6874 >= 0.55875' } {'Histidine' } {'HISDC + HISD >= 1.095' } {'Leucine + Isoleucine' } {'ILETA + LEUTA >= 1.305' } {'Valine + Methionine' } {'METAT + VALTA >= 0.705' } {'Glycine' } {'GTHS - GHMT2r >= 0.7725' }
Set the data parameters for the entropic flux balance analysis problem
Linear optimisation direction
model.osenseStr = 'min';
Reaction parameters
model.cf=0.1;
model.cr=0.1;
model.g=2;
if 0
quad = zeros(size(model.S,2),1);
quad(~model.SIntRxnBool)=1;
model.Q=diag(quad);
end

Reaction parameters

Setting the bounds on reaction direction is important, because certain bounds may be incompatible with the existence of a thermodynamically feasible steady state
param.internalNetFluxBounds = 'original' maintains direction and magnitude of internal net flux from model.lb & model.ub
param.internalNetFluxBounds = 'directional' maintains direction of internal net flux from model.lb & model.ub but not magnitude
param.internalNetFluxBounds = 'none' removes lower and upper bounds on internal net flux
param.internalNetFluxBounds = 'random' random internal net flux direction, replacing constraints from model.lb & model.ub
param.internalNetFluxBounds='directional';
%param.internalNetFluxBounds='original';
%param.internalNetFluxBounds='none';
Maximum permitted internal flux
param.maxUnidirectionalFlux=100;
%model.vfl = [0;0;0]

Method parameters

param.method='fluxes';
%param.method='fluxConc';%param.method='fluxConcNorm';

Metabolite parameters (only relevant if a concentration method chosen)

Standard chemical potential
model.u0 = ones(1,size(model.S,1))*0;
Strictly positive weight on concentration entropy maximisation
model.f=1;
Scalar maximum permitted metabolite concentration
param.maxConc=1;

Solver parameters

Set the solver
%param.solver='pdco';
param.solver='mosek';
Minimum permitted internal flux required for exponential cone reformulation
if strcmp(param.solver,'mosek')
param.minUnidirectionalFlux=0;
end
Tolerances
param.feasTol=1e-7;
Printing level
param.printLevel=2;
param.debug = 1;

Entropic flux balance analysis

[solution,modelOut] = entropicFluxBalanceAnalysis(model,param);
Using directional internal net flux bounds only. Using existing external net flux bounds without modification. MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 Problem Name : Objective sense : minimize Type : LO (linear optimization problem) Constraints : 2965 Affine conic cons. : 0 Disjunctive cons. : 0 Cones : 0 Scalar variables : 3625 Matrix variables : 0 Integer variables : 0 Optimizer started. Presolve started. Eliminator started. Freed constraints in eliminator : 1219 Eliminator terminated. Linear dependency checker started. Linear dependency checker terminated. Eliminator started. Freed constraints in eliminator : 141 Eliminator terminated. Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 9 dual deps. : 0 Presolve terminated. Time: 0.02 Optimizer - threads : 18 Optimizer - solved problem : the primal Optimizer - Constraints : 512 Optimizer - Cones : 0 Optimizer - Scalar variables : 1700 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.01 Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 5040 after factor : 1.19e+04 Factor - dense dim. : 1 flops : 5.13e+05 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 8.1e+03 1.2e+03 2.7e+04 0.00e+00 2.524651910e+04 -1.187509009e+03 1.3e+02 0.03 1 3.5e+03 5.6e-01 1.1e+04 1.01e+00 9.340150454e+03 2.546036924e+03 5.5e+01 0.05 2 1.6e+03 2.6e-01 5.4e+03 1.21e+00 5.103765843e+03 2.145030639e+03 2.6e+01 0.05 3 6.0e+02 9.6e-02 2.0e+03 1.12e+00 2.290895208e+03 1.257801880e+03 9.4e+00 0.06 4 1.2e+02 1.9e-02 3.8e+02 1.05e+00 6.891441803e+02 4.922303657e+02 1.8e+00 0.06 5 4.0e+01 6.4e-03 1.3e+02 1.02e+00 4.330729771e+02 3.656226850e+02 6.3e-01 0.06 6 5.4e+00 8.8e-04 1.8e+01 1.02e+00 3.116637492e+02 3.025822720e+02 8.6e-02 0.06 7 1.8e+00 2.9e-04 5.9e+00 1.01e+00 2.971165650e+02 2.941345150e+02 2.8e-02 0.06 8 4.7e-01 7.6e-05 1.5e+00 1.00e+00 2.918325929e+02 2.910515001e+02 7.4e-03 0.07 9 3.4e-02 5.4e-06 1.1e-01 1.00e+00 2.900752738e+02 2.900195527e+02 5.3e-04 0.07 10 1.5e-02 2.5e-06 5.1e-02 9.93e-01 2.899968569e+02 2.899711094e+02 2.4e-04 0.07 11 9.4e-04 1.5e-07 3.1e-03 9.98e-01 2.899355375e+02 2.899339714e+02 1.5e-05 0.07 12 1.6e-05 2.6e-09 5.3e-05 1.00e+00 2.899307214e+02 2.899306947e+02 2.5e-07 0.08 13 1.1e-07 1.8e-11 3.7e-07 1.00e+00 2.899306171e+02 2.899306169e+02 1.7e-09 0.08 14 2.8e-08 1.2e-11 3.3e-08 1.00e+00 2.899306168e+02 2.899306168e+02 1.8e-13 0.08 Basis identification started. Primal basis identification phase started. Primal basis identification phase terminated. Time: 0.00 Dual basis identification phase started. Dual basis identification phase terminated. Time: 0.00 Basis identification terminated. Time: 0.00 Optimizer terminated. Time: 0.09 Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 2.8993061675e+02 nrm: 2e+02 Viol. con: 1e-07 var: 3e-09 Dual. obj: 2.8993061677e+02 nrm: 5e+00 Viol. con: 0e+00 var: 6e-12 Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 2.8993061677e+02 nrm: 2e+02 Viol. con: 7e-13 var: 1e-14 Dual. obj: 2.8993061677e+02 nrm: 7e+00 Viol. con: 2e-14 var: 8e-10 Optimizer summary Optimizer - time: 0.09 Interior-point - iterations : 14 time: 0.09 Basis identification - time: 0.00 Primal - iterations : 37 time: 0.00 Dual - iterations : 95 time: 0.00 Clean primal - iterations : 0 time: 0.00 Clean dual - iterations : 0 time: 0.00 Simplex - time: 0.00 Primal simplex - iterations : 0 time: 0.00 Dual simplex - iterations : 0 time: 0.00 Mixed integer - relaxations: 0 time: 0.00 solveCobraEP: LP part of EPproblem is feasible according to solveCobraLP with mosek. MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 Problem Name : Objective sense : minimize Type : CONIC (conic optimization problem) Constraints : 2965 Affine conic cons. : 3420 (10260 rows) Disjunctive cons. : 0 Cones : 0 Scalar variables : 7046 Matrix variables : 0 Integer variables : 0 Optimizer started. Presolve started. Linear dependency checker started. Linear dependency checker terminated. Eliminator started. Freed constraints in eliminator : 0 Eliminator terminated. Eliminator - tries : 1 time : 0.00 Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 25 dual deps. : 0 Presolve terminated. Time: 0.03 Optimizer - threads : 18 Optimizer - solved problem : the primal Optimizer - Constraints : 1960 Optimizer - Cones : 3420 Optimizer - Scalar variables : 11264 conic : 10260 Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.02 Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 1.19e+04 after factor : 2.06e+04 Factor - dense dim. : 0 flops : 7.95e+05 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 1.0e+04 1.2e+00 1.0e+04 0.00e+00 5.937759534e+03 -4.414972768e+03 1.0e+00 0.06 1 7.8e+03 9.2e-01 9.2e+03 -9.99e-01 8.329038595e+03 -2.020744460e+03 7.8e-01 0.08 2 7.1e+03 8.3e-01 8.7e+03 -9.96e-01 9.584261566e+03 -7.537052715e+02 7.1e-01 0.08 3 5.2e+03 6.1e-01 7.4e+03 -9.87e-01 1.460992409e+04 4.361323650e+03 5.2e-01 0.09 4 1.7e+03 2.0e-01 4.1e+03 -9.66e-01 5.216178440e+04 4.235234708e+04 1.7e-01 0.10 5 7.4e+02 8.7e-02 2.4e+03 -8.64e-01 1.028563864e+05 9.397331223e+04 7.4e-02 0.11 6 4.0e+02 4.6e-02 1.4e+03 -6.03e-01 1.076676790e+05 1.004097991e+05 4.0e-02 0.12 7 2.8e+02 3.3e-02 9.7e+02 -1.71e-01 8.893218123e+04 8.290489716e+04 2.8e-02 0.13 8 1.6e+02 1.9e-02 4.9e+02 8.31e-02 6.300096522e+04 5.880765531e+04 1.6e-02 0.13 9 1.1e+02 1.2e-02 2.7e+02 4.17e-01 4.940899724e+04 4.640012206e+04 1.1e-02 0.14 10 4.5e+01 5.3e-03 8.2e+01 6.09e-01 3.123427143e+04 2.979941887e+04 4.5e-03 0.16 11 1.4e+01 1.7e-03 1.6e+01 8.34e-01 2.194998655e+04 2.146636309e+04 1.4e-03 0.16 12 4.4e+00 5.2e-04 2.8e+00 9.56e-01 1.845528587e+04 1.830414181e+04 4.4e-04 0.17 13 1.3e+00 1.6e-04 4.8e-01 9.89e-01 1.743922038e+04 1.739390618e+04 1.3e-04 0.18 14 3.6e-01 4.3e-05 7.2e-02 9.98e-01 1.714335346e+04 1.713092359e+04 3.6e-05 0.19 15 8.7e-02 1.0e-05 8.4e-03 1.00e+00 1.705275421e+04 1.704978384e+04 8.7e-06 0.20 16 1.5e-02 1.7e-06 6.2e-04 9.99e-01 1.703018296e+04 1.702967748e+04 1.5e-06 0.21 17 2.2e-03 2.5e-07 3.4e-05 1.00e+00 1.702611788e+04 1.702604409e+04 2.2e-07 0.22 18 1.2e-03 1.5e-07 1.5e-05 1.00e+00 1.702582068e+04 1.702577846e+04 1.2e-07 0.23 19 2.1e-04 2.4e-08 1.0e-06 1.00e+00 1.702548983e+04 1.702548272e+04 2.1e-08 0.24 20 2.1e-04 2.4e-08 1.0e-06 1.00e+00 1.702548982e+04 1.702548271e+04 2.1e-08 0.25 21 2.1e-04 2.4e-08 1.0e-06 1.00e+00 1.702548968e+04 1.702548258e+04 2.1e-08 0.25 22 2.1e-04 2.4e-08 1.0e-06 1.00e+00 1.702548967e+04 1.702548258e+04 2.1e-08 0.27 23 2.1e-04 2.4e-08 1.0e-06 1.00e+00 1.702548966e+04 1.702548257e+04 2.1e-08 0.28 24 2.1e-04 2.4e-08 1.0e-06 1.00e+00 1.702548948e+04 1.702548241e+04 2.1e-08 0.28 25 2.1e-04 2.4e-08 1.0e-06 1.00e+00 1.702548946e+04 1.702548239e+04 2.1e-08 0.29 26 2.1e-04 2.4e-08 1.0e-06 1.00e+00 1.702548944e+04 1.702548238e+04 2.1e-08 0.30 27 2.1e-04 2.4e-08 1.0e-06 1.00e+00 1.702548912e+04 1.702548208e+04 2.1e-08 0.31 28 2.1e-04 2.4e-08 1.0e-06 1.00e+00 1.702548909e+04 1.702548206e+04 2.1e-08 0.32 29 2.0e-04 2.3e-08 9.3e-07 1.00e+00 1.702548550e+04 1.702547886e+04 2.0e-08 0.33 30 1.9e-04 2.3e-08 9.3e-07 1.00e+00 1.702548537e+04 1.702547873e+04 1.9e-08 0.34 31 1.9e-04 2.2e-08 8.8e-07 1.00e+00 1.702548330e+04 1.702547689e+04 1.9e-08 0.35 32 1.9e-04 2.2e-08 8.8e-07 1.00e+00 1.702548321e+04 1.702547681e+04 1.9e-08 0.36 33 1.8e-04 2.2e-08 8.5e-07 1.00e+00 1.702548189e+04 1.702547563e+04 1.8e-08 0.37 34 1.8e-04 2.1e-08 8.3e-07 1.00e+00 1.702548076e+04 1.702547461e+04 1.8e-08 0.38 35 1.8e-04 2.1e-08 8.3e-07 1.00e+00 1.702548072e+04 1.702547458e+04 1.8e-08 0.39 36 1.8e-04 2.1e-08 8.2e-07 1.00e+00 1.702548061e+04 1.702547448e+04 1.8e-08 0.40 37 1.8e-04 2.1e-08 8.2e-07 1.00e+00 1.702548053e+04 1.702547441e+04 1.8e-08 0.41 38 1.7e-04 2.0e-08 7.9e-07 1.00e+00 1.702547900e+04 1.702547305e+04 1.7e-08 0.41 39 1.7e-04 2.0e-08 7.9e-07 1.00e+00 1.702547899e+04 1.702547303e+04 1.7e-08 0.42 40 1.7e-04 2.0e-08 7.9e-07 1.00e+00 1.702547899e+04 1.702547303e+04 1.7e-08 0.43 41 1.7e-04 2.0e-08 7.9e-07 1.00e+00 1.702547899e+04 1.702547303e+04 1.7e-08 0.44 42 3.8e-05 4.4e-09 7.9e-08 1.00e+00 1.702543493e+04 1.702543364e+04 3.8e-09 0.45 43 3.8e-05 4.4e-09 7.9e-08 1.00e+00 1.702543493e+04 1.702543364e+04 3.8e-09 0.47 44 3.8e-05 4.4e-09 7.9e-08 1.00e+00 1.702543493e+04 1.702543364e+04 3.8e-09 0.49 Optimizer terminated. Time: 0.51 Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 1.7025434927e+04 nrm: 5e+02 Viol. con: 3e-07 var: 2e-05 acc: 3e-08 Dual. obj: 1.7025433643e+04 nrm: 8e+03 Viol. con: 8e-08 var: 1e-07 acc: 0e+00 Optimizer summary Optimizer - time: 0.51 Interior-point - iterations : 45 time: 0.50 Basis identification - time: 0.00 Primal - iterations : 0 time: 0.00 Dual - iterations : 0 time: 0.00 Clean primal - iterations : 0 time: 0.00 Clean dual - iterations : 0 time: 0.00 Simplex - time: 0.00 Primal simplex - iterations : 0 time: 0.00 Dual simplex - iterations : 0 time: 0.00 Mixed integer - relaxations: 0 time: 0.00 > [mosek] Primal optimality condition in solveCobraEP satisfied. > [mosek] Dual optimality condition in solveCobraEP satisfied. Optimality conditions (biochemistry) 2.8e-07 || N*(vf - vr) + B*ve - b ||_inf Inf || C*(vf - vr) + s_C - d ||_inf, s_C = slack variable 8.8e-08 || cf + ci + N'*y_N + C'*y_C + y_vi + Qv*vf + k_vf + z_vf ||_inf 8.8e-08 || cr - ci - N'*y_N - C'*y_C - y_vi + Qv*vf + k_vr + z_vr ||_inf 7.4e-13 || ce + B'*y_N + z_ve ||_inf 0 || k_e_1 + z_e_1 ||_inf 1.5e-07 || -g + k_e_vf + z_e_vf||_inf 1.5e-07 || -g + k_e_vr + z_e_vr||_inf 2.1e-06 || e_vf + vf*log(vf) ||_inf 3.4e-06 || e_vr + vr*log(vr) ||_inf Derived optimality conditions (biochemistry) 18 || g.*log(vf) + g - k_vf ||_inf 0.0043 || g.*log(vr) + g - k_vr ||_inf 18 || cf + ci + N'*y_N + C'*y_C + y_vi + Qv*vf + g.*log(vf) + g + z_vf ||_inf 0.0043 || cr - ci - N'*y_N - C'*y_C - y_vi + Qv*vf + g.*log(vr) + g + z_vr ||_inf Thermo conditions 2.7e+02 || g.*log(vr/vf) - 2*N'*y_N - 2*C'*y_C ||_inf 53 || g.*log(vr/vf) + cr - cf - 2*ci - 2*N'*y_N - 2*C'*y_C - 2*y_vi ||_inf 88 || g.*log(vr/vf) + cr - cf - 2*ci - 2*N'*y_N - 2*C'*y_C - 2*y_vi - z_vr + z_vf ||_inf -1.5e+02 min(slack) Inf max(slack)
model=modelOut;
Extract the fields of the solution structure
if solution.stat ~=1
disp('No solution')
return
end
[v,vf,vr,vt,y_N,z_v,z_dx,z_vf,z_vr,stat]=...
deal(solution.v,solution.vf,solution.vr,solution.vt,solution.y_N,solution.z_v,solution.z_dx,solution.z_vf,solution.z_vr,solution.stat);
cf = model.cf;
cr = model.cr;
 
g=deal(model.g);
if isfield(solution,'x')
[x, x0, z_x, z_x0, z_dx] = deal(solution.x, solution.x0, solution.z_x, solution.z_x0, solution.z_dx);
[u0,f]=deal(model.u0,model.f);
dx = x - x0;
end
Extract the internal (N) and exchange (B) stoichiometric matrices
N = model.S(:,model.SConsistentRxnBool);
B = model.S(:,~model.SConsistentRxnBool);
Extract the matrix of coupling constraints, if present
if isfield(model,'C')
C = model.C(:,model.SConsistentRxnBool);
y_C = solution.y_C;
end
Extract the objective on the internal reaction rates
e = ones(length(vf),1);
ci = solution.osense*model.c(model.SConsistentRxnBool);
Extract the net internal reaction dual variable
z_vi = z_v(model.SConsistentRxnBool);
Compute the nullspace of the internal stoichiometric matrix
if 0
%get nullspace of N
[Z,rankS]=getNullSpace(N,0);
else
Z=[];
end

ANTICIPATED RESULTS

Optimality conditions should be satisfied approximately to the feasibility (or optimality) tolerances of the numerical optimisation solver, typically 1e-6.
if param.printLevel>2 || 1
v_detailed=1;
else
v_detailed=0;
end
Biochemical optimality conditions: steady state
if isfield(solution,'x')
fprintf('%8.2g %s\n',norm(N*(vf - vr) - x + x0 - model.b,inf), '|| N*(vf - vr) - x + x0 - b ||_inf');
else
fprintf('%8.2g %s\n',norm(model.S*v - model.b,inf), '|| S*v - b ||_inf');
end
2.8e-07 || S*v - b ||_inf
Optionally, display detailed properties of flux related solution vector
if v_detailed
fprintf('%8.2g %s\n',sum(vf)+sum(vr),'sum(vf)+sum(vr) >= 0');
fprintf('%8.2g %s\n',norm(g.*reallog(vf),inf),'|| g*log(vf) ||_inf');
fprintf('%8.2g %s\n',norm(g.*reallog(vr),inf),'|| g*log(vr) ||_inf');
fprintf('%8.2g %s\n',norm(cr,inf),'|| cr ||_inf');
fprintf('%8.2g %s\n',norm(cf,inf),'|| cf ||_inf');
fprintf('%8.2g %s\n',norm(ci,inf),'|| ci ||_inf');
fprintf('%8.2g %s\n',norm(N'*y_N,inf),'|| N''*y_N ||_inf');
fprintf('%8.2g %s\n',norm(z_v,inf),'|| z_v ||_inf');
fprintf('%8.2g %s\n',norm(z_vf,inf),'|| z_vf ||_inf');
fprintf('%8.2g %s\n',norm(z_vr,inf),'|| z_vr ||_inf');
if isfield(model,'C')
fprintf('%8.2g %s\n',norm(C'*y_C,inf),'|| C''*y_C ||_inf');
end
end
4.1e+03 sum(vf)+sum(vr) >= 0
31 || g*log(vf) ||_inf
13 || g*log(vr) ||_inf
0.1 || cr ||_inf
0.1 || cf ||_inf
0 || ci ||_inf
1.4e+02 || N'*y_N ||_inf
1.4e+02 || z_v ||_inf
2e-07 || z_vf ||_inf
35 || z_vr ||_inf
37 || C'*y_C ||_inf
if isfield(model,'C')
fprintf('%8.2g %s\n',norm(g.*reallog(vf) + ci + cf + N'*y_N + C'*y_C + z_vi + z_vf,inf), '|| g*log(vf) + ci + cf + N''*y_N + C''*y_C + z_vi + z_vf ||_inf');
fprintf('%8.2g %s\n',norm(g.*reallog(vr) - ci + cr - N'*y_N - C'*y_C - z_vi + z_vr,inf),'|| g*log(vr) - ci + cr - N''*y_N - C''*y_C - z_vi + z_vr ||_inf');
fprintf('%8.2g %s\n',norm( C'*y_C + z_vi + z_vf,inf), '|| + C''*y_C + z_vi + z_vf ||_inf');
fprintf('%8.2g %s\n',norm( - C'*y_C - z_vi + z_vr,inf),'|| - C''*y_C - z_vi + z_vr ||_inf');
else
fprintf('%8.2g %s\n',norm(g.*reallog(vf) + ci + cf + N'*y_N + z_vi - z_vf,inf), '|| g*log(vf) + ci + cf + N''*y_N + z_vi - z_vf ||_inf');
fprintf('%8.2g %s\n',norm(g.*reallog(vr) - ci + cr - N'*y_N - z_vi - z_vr,inf),'|| g*log(vr) - ci + cr - N''*y_N - z_vi - z_vr ||_inf');
end
16 || g*log(vf) + ci + cf + N'*y_N + C'*y_C + z_vi + z_vf ||_inf
2 || g*log(vr) - ci + cr - N'*y_N - C'*y_C - z_vi + z_vr ||_inf
1.4e+02 || + C'*y_C + z_vi + z_vf ||_inf
1.4e+02 || - C'*y_C - z_vi + z_vr ||_inf
Derived biochemical optimality conditions (fluxes)
if isfield(model,'C')
res = g.*reallog(vr./vf) + cr - cf - 2*ci - 2*N'*y_N - 2*C'*y_C - 2*z_vi - z_vr + z_vf;
fprintf('%8.2g %s\n',norm(res,inf),'|| g*log(vr/vf) + cr - cf - 2*ci - 2*N''*y_N - 2*C''*y_C - 2*z_vi - z_vr + z_vf ||_inf');
else
res = g.*reallog(vr./vf) + cr - cf - 2*ci - 2*N'*y_N - 2*z_vi - z_vr + z_vf;
fprintf('%8.2g %s\n',norm(res,inf),'|| g*log(vr/vf) + cr - cf - 2*ci - 2*N''*y_N - 2*z_vi - z_vr + z_vf ||_inf');
end
88 || g*log(vr/vf) + cr - cf - 2*ci - 2*N'*y_N - 2*C'*y_C - 2*z_vi - z_vr + z_vf ||_inf
Optionally, display detailed properties of concentration related solution vector
if isfield(solution,'x')
fprintf('\n%s\n','Optimality conditions (concentrations)')
if v_detailed
fprintf('%8.2g %s\n',norm(reallog(x),inf), '|| log(x)||_inf');
fprintf('%8.2g %s\n',norm(u0,inf), '|| u0 ||_inf');
fprintf('%8.2g %s\n',norm(y_N,inf), '|| y_N ||_inf');
fprintf('%8.2g %s\n',norm(z_dx,inf), '|| z_dx ||_inf');
fprintf('%8.2g %s\n',norm(z_x,inf), '|| z_x ||_inf');
fprintf('%8.2g %s\n',norm(z_x0,inf), '|| z_x0 ||_inf');
end
fprintf('%8.2g %s\n',norm(f.*reallog(x) + u0 - y_N + z_dx + z_x,inf), '|| f.*log(x) + u0 - y_N + z_dx + z_x ||_inf');
fprintf('%8.2g %s\n',norm(f.*reallog(x0) + u0 + y_N - z_dx + z_x0,inf),'|| f.*log(x0) + u0 + y_N - z_dx + z_x0 ||_inf');
 
fprintf('\n%s\n','Derived biochemical optimality conditions (concentrations)')
fprintf('%8.2g %s\n',norm(f.*reallog(x./x0) - 2*y_N + 2*z_dx + z_x - z_x0,inf),'|| f.*log(x/x0) - 2*y_N + 2*z_dx + z_x - z_x0 ||_inf');
fprintf('%8.2g %s\n',norm(f.*reallog(x.*x0) + 2*u0 + z_x + z_x0,inf),'|| f.*log(x.*x0) + 2*u0 + z_x + z_x0 ||_inf');
 
 
fprintf('\n%s\n','Derived biochemical optimality conditions (fluxes and concentrations)')
if isfield(model,'C')
fprintf('%8.2g %s\n',norm(g.*reallog(vf) + cf + ci + N'*(u0 + f.*reallog(x) + z_dx + z_x) + C'*y_C + z_v + z_vf,inf),'|| g*log(vf) + cf + ci + N''*(u0 + f*log(x) + z_dx + z_x) + C''*y_C + z_v + z_vf ||_inf');
fprintf('%8.2g %s\n',norm(g.*reallog(vr) + cr - ci - N'*(u0 + f.*reallog(x) + z_dx + z_x) - C'*y_C - z_v + z_vr,inf), '|| g*log(vr) + cr - ci - N''*(u0 + f*log(x) + z_dx + z_x) - C''*y_C - z_v + z_vr ||_inf');
else
fprintf('%8.2g %s\n',norm(g.*reallog(vf) + cf + ci + N'*(u0 + f.*reallog(x) + z_dx + z_x) + z_v + z_vf,inf),'|| g*log(vf) + cf + ci + N''*(u0 + f*log(x) + z_dx + z_x) + z_v + z_vf ||_inf');
fprintf('%8.2g %s\n',norm(g.*reallog(vr) + cr - ci - N'*(u0 + f.*reallog(x) + z_dx + z_x) - z_v + z_vr,inf),'|| g*log(vr) + cr - ci - N''*(u0 + f*log(x) + z_dx + z_x) - z_v + z_vr ||_inf');
end
 
fprintf('\n%s\n','Derived biochemical optimality conditions (fluxes and concentrations)')
if isfield(model,'C')
fprintf('%8.2g %s\n',norm(g.*reallog(vr./vf) + cr - cf - 2*ci - 2*N'*(u0 + f.*reallog(x) + z_dx + z_x) - 2*C'*y_C - 2*z_v - z_vf + z_vr,inf), '|| g.*reallog(vr./vf) + cr - cf - 2*(ci + N''*(u0 + f*log(x) + z_dx + z_x) + C''*y_C + z_v) - z_vf + z_vr ||_inf');
fprintf('%8.2g %s\n',norm(g.*reallog(vr./vf) + cr - cf - 2*ci + 2*N'*(u0 + f.*reallog(x0) - z_dx + z_x0) - 2*C'*y_C - 2*z_v - z_vf + z_vr,inf),'|| g.*reallog(vr./vf) + cr - cf - 2*(ci - N''*(u0 + f*log(x0) - z_dx + z_x0) + C''*y_C + z_v) - z_vf + z_vr ||_inf');
else
fprintf('%8.2g %s\n',norm(g.*reallog(vr./vf) + cr - cf - 2*ci - 2*N'*(u0 + f.*reallog(x) + z_dx + z_x) - 2*z_v - z_vf + z_vr,inf), '|| g.*reallog(vr./vf) + cr - cf - 2*(ci + N''*(u0 + f*log(x) + z_dx + z_x) + z_v) - z_vf + z_vr ||_inf');
fprintf('%8.2g %s\n',norm(g.*reallog(vr./vf) + cr - cf - 2*ci + 2*N'*(u0 + f.*reallog(x0) - z_dx + z_x0) - 2*z_v - z_vf + z_vr,inf),'|| g.*reallog(vr./vf) + cr - cf - 2*(ci - N''*(u0 + f*log(x0) - z_dx + z_x0) + z_v) - z_vf + z_vr ||_inf');
fprintf('%8.2g %s\n',norm(g.*reallog(vr.*vf) + cr + cf - N'*(u0 + f.*reallog(x) + z_dx + z_x) - 2*z_v - z_vf + z_vr,inf), '|| g.*reallog(vr./vf) + cr - cf - 2*(ci + N''*(u0 + f*log(x) + z_dx + z_x) + z_v) - z_vf + z_vr ||_inf');
fprintf('%8.2g %s\n',norm(g.*reallog(vr./vf) + cr - cf - 2*ci + 2*N'*(u0 + f.*reallog(x0) - z_dx + z_x0) - 2*z_v - z_vf + z_vr,inf),'|| g.*reallog(vr./vf) + cr - cf - 2*(ci - N''*(u0 + f*log(x0) - z_dx + z_x0) + z_v) - z_vf + z_vr ||_inf');
end
end
fprintf('\n')
if isfield(solution,'v')
vfpad = NaN*ones(size(model.S,2),1);
vfpad(model.SConsistentRxnBool)=vf;
vrpad = NaN*ones(size(model.S,2),1);
vrpad(model.SConsistentRxnBool)=vr;
zvfpad = NaN*ones(size(model.S,2),1);
zvfpad(model.SConsistentRxnBool)=z_vr;
zvrpad = NaN*ones(size(model.S,2),1);
zvrpad(model.SConsistentRxnBool)=z_vr;
T1 = table(model.lb, v,model.ub,z_v,vfpad,zvfpad,vrpad,zvrpad,'VariableNames',{'vl','v','vu','z_v','vf','z_vf','vr','z_vr'});
if length(v)<=10
disp(T1)
end
end
 
if isfield(solution,'x')
T2 = table(model.xl,solution.x,model.xu,z_x,model.x0l,x0,model.x0u,z_x0,model.dxl,dx,model.dxu,z_dx,...
'VariableNames',{'xl' 'x' 'xu' 'z_x' 'x0l' 'x0' 'x0u' 'z_x0' 'dxl' 'dx' 'dxu' 'z_dx'});
if length(solution.x)<=10
disp(T2)
end
end

TROUBLESHOOTING

Debugging satisfaction of constraints

Entropic Flux Balance Analysis will find a thermodynamically feasible steady state, provided one exists. That is, bounds on net fluxes, for example those causing net flux around a stoichiometrically balanced cycle, can preclude the existince of a thermodynamically feasible steady state. The following plots can be used to investigate deviation from thermodynamic feasibility for certain reactions, indicated by numerical tolerances beyond that considered satifactory (typically 1e-6 for a double precision solver). Setting the bounds on reaction direction is important, because certain bounds may be incompatible with the existence of a thermodynamically feasible steady state
param.internalNetFluxBounds = 'original' maintains direction and magnitude of internal net flux from model.lb & model.ub
param.internalNetFluxBounds = 'directional' maintains direction of internal net flux from model.lb & model.ub but not magnitude
param.internalNetFluxBounds = 'none' removes lower and upper bounds on internal net flux
param.internalNetFluxBounds = 'random' random internal net flux direction, replacing constraints from model.lb & model.ub
l = model.lb(model.SConsistentRxnBool);
u = model.ub(model.SConsistentRxnBool);
vi = vf - vr;
logvrvf = reallog(vr./vf);
 
figure
histogram(log10(abs(z_v)))
title('distribution of abs( $z_v$)')
 
zBool = abs(z_vi)>0.1;
if any(l(zBool)~=0)
figure
histogram(l(zBool))
title('distribution of internal lower bound when $z_v$ substantial')
end
if any(u(zBool)~=inf)
figure
histogram(u(zBool))
title('distribution of internal upper bound when $z_v$ substantial')
end
 
if any(zBool)
figure
histogram(log10(abs(res(zBool))))
title('distribution of thermodynamic residual when $z_v$ is substantial')
end
if any(zBool)
figure
plot(vi(zBool),logvrvf(zBool),'.')
xlabel('Small net flux')
ylabel('Change in chemical potential')
end
 
if any(~zBool)
%thermo residual is large even when z_v is small
figure
histogram(log10(abs(res(~zBool))))
title('distribution of thermodynamic residual when $z_v$ is small')
end
if any(~zBool)
figure
plot(vi(~zBool),logvrvf(~zBool),'.')
xlabel('Large net flux')
ylabel('Change in chemical potential')
end
rBool = abs(res)>0.001;
fwdBool = vi>0;
if any(rBool)
ab = z_vf - z_vr;
figure
histogram(ab(rBool))
title('distribution of $z_v$f - $z_v$r when residual is large')
end
if any(rBool)
%deviation from thermodynamic constraint occuring when net flux is
%substantial
figure
res1 = g.*reallog(vr./vf) + cr - cf - 2*ci - 2*N'*y_N;
histogram(res1(rBool))
title('distribution of log(vr/vf) - 2*N''*y\_N when residual is large')
end
if any(rBool)
figure
plot(vi(rBool),res(rBool),'.')
xlabel('Net flux')
ylabel('Large thermo residual')
end
if any(rBool)
figure
plot(vi(rBool & fwdBool),res(rBool & fwdBool),'.')
xlabel('Net flux')
ylabel('Large thermo residual')
end
if any(rBool)
figure
if isfield(model,'C')
res5 = g.*reallog(vr./vf) + cr - cf - 2*ci - 2*N'*y_N - 2*C'*y_C - 2*z_vi;
histogram(res5(rBool))
title('distribution of g.*log(vr/vf) + cr - cf - 2*ci - 2*N''*y\_N - 2*C''*y\_C - 2*z\_vi when residual is large')
else
res5 = g.*reallog(vr./vf) + cr - cf - 2*ci - 2*N'*y_N - 2*z_vi;
histogram(res5(rBool))
title('distribution of g.*log(vr/vf) + cr - cf - 2*ci - 2*N''*y\_N - 2*z\_vi when residual is large')
end
end
if any(~rBool)
figure
plot(res(~rBool),vi(~rBool),'.')
xlabel('Net flux')
ylabel('Small thermo residual')
end
if any(rBool)
figure
plot(vi(~rBool & fwdBool),res(~rBool & fwdBool),'.')
xlabel('Net flux')
ylabel('Small thermo residual')
end
if isequal(modelToUse,'single') && isfield(solution,'x')
fprintf('%8.2g %s\n',norm(vf - exp(-(cf + cr - u0(1) - u0(2))/2)*x(1)), '|| vf - exp(-(cr + cf - u0 - u0)/2)*x1 ||')
end

Quadratically constrained entropic flux balance analysis - all external reactions

Generate a random external flux vector that is a perturbation of the previously obtained external flux vector and then quadratically penalise any deviation from it.
model.h = (solution.v).*(rand(length(solution.v),1)+0.5)*2;
Do not optimise toward any internal net flux
model.h(model.SConsistentRxnBool)=NaN;
Compare the original external flux vector, with the external flux vector to peanlise deviation from
figure
hold on
fplot(@(x) x, 'LineWidth', 1.5,'Color','r')
plot(solution.v(~model.SConsistentRxnBool),model.h(~model.SConsistentRxnBool),'o','Color','b')
xlabel('EntropicFBA flux')
ylabel('h')
title('External flux values')
axis equal
Set the penaltiy
HH = ones(length(solution.v),1);
HH(model.SConsistentRxnBool)=0;
model.H = spdiags(HH,0,length(solution.v),length(solution.v));
Run the optimisation
[solutionQEFBA,modelOut] = entropicFluxBalanceAnalysis(model,param);
Using directional internal net flux bounds only. Using existing external net flux bounds without modification. MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 Problem Name : Objective sense : minimize Type : LO (linear optimization problem) Constraints : 3170 Affine conic cons. : 0 Disjunctive cons. : 0 Cones : 0 Scalar variables : 3830 Matrix variables : 0 Integer variables : 0 Optimizer started. Presolve started. Eliminator started. Freed constraints in eliminator : 1219 Eliminator terminated. Linear dependency checker started. Linear dependency checker terminated. Eliminator started. Freed constraints in eliminator : 141 Eliminator terminated. Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 9 dual deps. : 0 Presolve terminated. Time: 0.02 GP based matrix reordering started. GP based matrix reordering terminated. Optimizer - threads : 18 Optimizer - solved problem : the primal Optimizer - Constraints : 514 Optimizer - Cones : 0 Optimizer - Scalar variables : 1704 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.01 Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 4991 after factor : 1.23e+04 Factor - dense dim. : 5 flops : 5.75e+05 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 8.1e+03 1.2e+03 2.6e+04 0.00e+00 2.566112318e+04 -8.236241217e+01 1.3e+02 0.04 1 4.0e+03 6.3e-01 1.3e+04 8.50e-01 9.850126937e+03 2.790977534e+03 6.2e+01 0.05 2 1.8e+03 2.8e-01 5.6e+03 1.00e+00 5.514031979e+03 2.486949549e+03 2.8e+01 0.05 3 3.7e+02 5.8e-02 1.2e+03 1.04e+00 1.582358312e+03 9.674172343e+02 5.8e+00 0.06 4 1.4e+02 2.2e-02 4.5e+02 1.02e+00 7.750755310e+02 5.407839174e+02 2.2e+00 0.06 5 2.4e+01 3.8e-03 7.7e+01 1.01e+00 3.840553962e+02 3.438656965e+02 3.8e-01 0.06 6 7.1e+00 1.1e-03 2.3e+01 1.01e+00 3.179179905e+02 3.061918973e+02 1.1e-01 0.06 7 2.5e+00 3.9e-04 7.8e+00 1.01e+00 2.995918221e+02 2.955633008e+02 3.8e-02 0.07 8 2.1e-01 3.3e-05 6.7e-01 1.00e+00 2.907815335e+02 2.904374570e+02 3.3e-03 0.07 9 3.1e-02 4.8e-06 9.8e-02 1.00e+00 2.900770246e+02 2.900267589e+02 4.8e-04 0.07 10 9.2e-03 1.4e-06 2.9e-02 9.99e-01 2.899745013e+02 2.899594753e+02 1.4e-04 0.07 11 1.3e-03 2.1e-07 4.3e-03 1.00e+00 2.899369219e+02 2.899347208e+02 2.1e-05 0.08 12 2.3e-05 3.7e-09 7.4e-05 1.00e+00 2.899307232e+02 2.899306850e+02 3.6e-07 0.08 13 5.3e-08 8.3e-12 1.7e-07 1.00e+00 2.899306170e+02 2.899306169e+02 8.2e-10 0.08 14 1.1e-09 2.2e-15 2.5e-10 1.00e+00 2.899306168e+02 2.899306168e+02 8.4e-14 0.08 Basis identification started. Primal basis identification phase started. Primal basis identification phase terminated. Time: 0.00 Dual basis identification phase started. Dual basis identification phase terminated. Time: 0.00 Basis identification terminated. Time: 0.01 Optimizer terminated. Time: 0.11 Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 2.8993061677e+02 nrm: 3e+02 Viol. con: 7e-10 var: 3e-11 Dual. obj: 2.8993061677e+02 nrm: 5e+00 Viol. con: 0e+00 var: 1e-15 Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 2.8993061677e+02 nrm: 3e+02 Viol. con: 1e-12 var: 6e-14 Dual. obj: 2.8993061677e+02 nrm: 7e+00 Viol. con: 1e-14 var: 1e-10 Optimizer summary Optimizer - time: 0.11 Interior-point - iterations : 14 time: 0.10 Basis identification - time: 0.01 Primal - iterations : 37 time: 0.00 Dual - iterations : 95 time: 0.00 Clean primal - iterations : 0 time: 0.00 Clean dual - iterations : 0 time: 0.00 Simplex - time: 0.00 Primal simplex - iterations : 0 time: 0.00 Dual simplex - iterations : 0 time: 0.00 Mixed integer - relaxations: 0 time: 0.00 solveCobraEP: LP part of EPproblem is feasible according to solveCobraLP with mosek. MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 Problem Name : Objective sense : minimize Type : CONIC (conic optimization problem) Constraints : 3170 Affine conic cons. : 3625 (10875 rows) Disjunctive cons. : 0 Cones : 0 Scalar variables : 7457 Matrix variables : 0 Integer variables : 0 Optimizer started. Presolve started. Linear dependency checker started. Linear dependency checker terminated. Eliminator started. Freed constraints in eliminator : 177 Eliminator terminated. Eliminator started. Freed constraints in eliminator : 0 Eliminator terminated. Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 25 dual deps. : 0 Presolve terminated. Time: 0.04 Optimizer - threads : 18 Optimizer - solved problem : the primal Optimizer - Constraints : 2001 Optimizer - Cones : 3625 Optimizer - Scalar variables : 11715 conic : 10875 Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.02 Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 1.21e+04 after factor : 2.08e+04 Factor - dense dim. : 0 flops : 7.99e+05 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 3.5e+02 1.2e+00 1.1e+04 0.00e+00 6.142759534e+03 -4.414972768e+03 1.0e+00 0.07 1 2.1e+02 7.1e-01 8.1e+03 -9.69e-01 1.293676978e+04 2.486468134e+03 6.1e-01 0.10 2 8.4e+01 2.8e-01 4.9e+03 -9.48e-01 3.821773325e+04 2.819119065e+04 2.4e-01 0.11 3 3.5e+01 1.2e-01 2.8e+03 -8.52e-01 7.716914143e+04 6.825818530e+04 9.9e-02 0.12 4 2.4e+01 8.1e-02 2.0e+03 -5.23e-01 7.314062084e+04 6.533922498e+04 6.9e-02 0.12 5 1.8e+01 6.0e-02 1.4e+03 -2.41e-01 6.246633604e+04 5.578403824e+04 5.1e-02 0.13 6 1.4e+01 4.6e-02 1.0e+03 -8.27e-03 5.393114255e+04 4.825307503e+04 3.9e-02 0.14 7 5.7e+00 1.9e-02 3.4e+02 1.81e-01 3.383569036e+04 3.081079831e+04 1.6e-02 0.15 8 2.3e+00 7.8e-03 9.6e+01 6.23e-01 2.508943839e+04 2.371772103e+04 6.7e-03 0.16 9 1.3e+00 4.5e-03 4.4e+01 8.51e-01 2.236402705e+04 2.154830688e+04 3.9e-03 0.17 10 4.7e-01 1.6e-03 9.5e+00 9.18e-01 1.966955885e+04 1.937963274e+04 1.3e-03 0.18 11 1.5e-01 4.9e-04 1.7e+00 9.76e-01 1.861852162e+04 1.852707961e+04 4.2e-04 0.19 12 2.4e-02 8.0e-05 1.2e-01 9.94e-01 1.822719660e+04 1.821223790e+04 6.8e-05 0.20 13 5.6e-03 1.9e-05 1.3e-02 1.00e+00 1.817800220e+04 1.817447205e+04 1.6e-05 0.21 14 3.8e-03 1.3e-05 7.2e-03 9.92e-01 1.817193446e+04 1.816961635e+04 1.1e-05 0.22 15 4.5e-04 1.5e-06 3.0e-04 1.00e+00 1.816384080e+04 1.816356651e+04 1.3e-06 0.23 16 6.8e-05 2.3e-07 1.7e-05 1.00e+00 1.816291739e+04 1.816287632e+04 2.0e-07 0.25 17 3.9e-05 1.3e-07 7.5e-06 1.00e+00 1.816284866e+04 1.816282527e+04 1.1e-07 0.26 18 3.8e-05 1.3e-07 7.4e-06 1.00e+00 1.816284837e+04 1.816282506e+04 1.1e-07 0.27 19 9.6e-06 3.2e-08 9.7e-07 1.00e+00 1.816277947e+04 1.816277366e+04 2.8e-08 0.29 20 9.6e-06 3.2e-08 9.7e-07 1.00e+00 1.816277946e+04 1.816277366e+04 2.8e-08 0.30 21 9.5e-06 3.2e-08 9.7e-07 1.00e+00 1.816277943e+04 1.816277364e+04 2.8e-08 0.31 22 9.5e-06 3.2e-08 9.7e-07 1.00e+00 1.816277943e+04 1.816277363e+04 2.8e-08 0.32 23 9.5e-06 5.8e-08 9.6e-07 1.00e+00 1.816277929e+04 1.816277353e+04 2.8e-08 0.33 24 9.3e-06 1.5e-07 9.3e-07 1.00e+00 1.816277877e+04 1.816277312e+04 2.8e-08 0.34 25 9.3e-06 1.6e-07 9.3e-07 1.00e+00 1.816277874e+04 1.816277310e+04 2.8e-08 0.35 26 9.3e-06 1.7e-07 9.3e-07 1.00e+00 1.816277864e+04 1.816277302e+04 2.7e-08 0.36 27 9.3e-06 1.7e-07 9.3e-07 1.00e+00 1.816277864e+04 1.816277302e+04 2.7e-08 0.37 28 9.3e-06 1.8e-07 9.2e-07 1.00e+00 1.816277861e+04 1.816277300e+04 2.7e-08 0.38 29 9.2e-06 1.8e-07 9.2e-07 1.00e+00 1.816277857e+04 1.816277296e+04 2.7e-08 0.39 30 9.2e-06 1.8e-07 9.2e-07 1.00e+00 1.816277857e+04 1.816277296e+04 2.7e-08 0.39 31 9.2e-06 1.8e-07 9.2e-07 1.00e+00 1.816277856e+04 1.816277296e+04 2.7e-08 0.41 32 9.2e-06 1.9e-07 9.2e-07 1.00e+00 1.816277852e+04 1.816277293e+04 2.7e-08 0.42 33 2.3e-06 4.1e-08 1.1e-07 1.00e+00 1.816275925e+04 1.816275788e+04 6.7e-09 0.44 34 2.3e-06 4.4e-08 1.1e-07 1.00e+00 1.816275925e+04 1.816275788e+04 6.7e-09 0.45 35 2.3e-06 1.2e-07 1.1e-07 1.00e+00 1.816275923e+04 1.816275786e+04 6.7e-09 0.46 36 2.3e-06 1.2e-07 1.1e-07 1.00e+00 1.816275923e+04 1.816275786e+04 6.7e-09 0.47 37 2.3e-06 1.3e-07 1.1e-07 1.00e+00 1.816275923e+04 1.816275786e+04 6.7e-09 0.48 38 2.3e-06 1.3e-07 1.1e-07 1.00e+00 1.816275923e+04 1.816275786e+04 6.7e-09 0.49 39 2.3e-06 1.3e-07 1.1e-07 1.00e+00 1.816275923e+04 1.816275786e+04 6.7e-09 0.50 40 2.3e-06 1.3e-07 1.1e-07 1.00e+00 1.816275922e+04 1.816275785e+04 6.7e-09 0.53 41 2.3e-06 1.3e-07 1.1e-07 1.00e+00 1.816275922e+04 1.816275785e+04 6.7e-09 0.53 42 2.3e-06 1.3e-07 1.1e-07 1.00e+00 1.816275922e+04 1.816275785e+04 6.7e-09 0.54 43 2.3e-06 1.3e-07 1.1e-07 1.00e+00 1.816275922e+04 1.816275785e+04 6.7e-09 0.56 44 2.3e-06 1.3e-07 1.1e-07 1.00e+00 1.816275922e+04 1.816275785e+04 6.7e-09 0.56 45 2.3e-06 1.4e-07 1.1e-07 1.00e+00 1.816275922e+04 1.816275785e+04 6.7e-09 0.57 46 2.2e-06 1.4e-07 1.1e-07 1.00e+00 1.816275901e+04 1.816275769e+04 6.5e-09 0.59 47 2.2e-06 1.4e-07 1.1e-07 1.00e+00 1.816275901e+04 1.816275769e+04 6.5e-09 0.60 48 2.2e-06 1.6e-07 1.1e-07 1.00e+00 1.816275901e+04 1.816275768e+04 6.5e-09 0.61 49 2.2e-06 1.6e-07 1.1e-07 1.00e+00 1.816275901e+04 1.816275768e+04 6.5e-09 0.62 50 2.2e-06 1.6e-07 1.1e-07 1.00e+00 1.816275901e+04 1.816275768e+04 6.5e-09 0.63 51 2.2e-06 1.8e-07 1.1e-07 1.00e+00 1.816275900e+04 1.816275768e+04 6.5e-09 0.65 52 2.2e-06 1.5e-07 1.1e-07 1.00e+00 1.816275899e+04 1.816275767e+04 6.5e-09 0.67 53 2.2e-06 1.5e-07 1.1e-07 1.00e+00 1.816275899e+04 1.816275767e+04 6.5e-09 0.68 54 2.2e-06 1.5e-07 1.1e-07 1.00e+00 1.816275899e+04 1.816275767e+04 6.5e-09 0.70 Optimizer terminated. Time: 0.73 Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 1.8162758994e+04 nrm: 5e+02 Viol. con: 4e-05 var: 1e-06 acc: 3e-08 Dual. obj: 1.8162757675e+04 nrm: 8e+03 Viol. con: 9e-08 var: 3e-06 acc: 0e+00 Optimizer summary Optimizer - time: 0.73 Interior-point - iterations : 55 time: 0.72 Basis identification - time: 0.00 Primal - iterations : 0 time: 0.00 Dual - iterations : 0 time: 0.00 Clean primal - iterations : 0 time: 0.00 Clean dual - iterations : 0 time: 0.00 Simplex - time: 0.00 Primal simplex - iterations : 0 time: 0.00 Dual simplex - iterations : 0 time: 0.00 Mixed integer - relaxations: 0 time: 0.00 > [mosek] Dual optimality condition in solveCobraEP satisfied. Optimality conditions (biochemistry) 4.4e-05 || N*(vf - vr) + B*ve - b ||_inf Inf || C*(vf - vr) + s_C - d ||_inf, s_C = slack variable 8.8e-08 || cf + ci + N'*y_N + C'*y_C + y_vi + Qv*vf + k_vf + z_vf ||_inf 8.8e-08 || cr - ci - N'*y_N - C'*y_C - y_vi + Qv*vf + k_vr + z_vr ||_inf 1 || ce + B'*y_N + z_ve ||_inf 8.2e+03 || k_e_1 + z_e_1 ||_inf 8.2e+03 || -g + k_e_vf + z_e_vf||_inf 1.5e-07 || -g + k_e_vr + z_e_vr||_inf 1.8e-06 || e_vf + vf*log(vf) ||_inf 3e-06 || e_vr + vr*log(vr) ||_inf 1.6e+02 || k_q_1 + z_q_1 ||_inf Derived optimality conditions (biochemistry) 17 || g.*log(vf) + g - k_vf ||_inf 0.005 || g.*log(vr) + g - k_vr ||_inf 17 || cf + ci + N'*y_N + C'*y_C + y_vi + Qv*vf + g.*log(vf) + g + z_vf ||_inf 0.005 || cr - ci - N'*y_N - C'*y_C - y_vi + Qv*vf + g.*log(vr) + g + z_vr ||_inf Thermo conditions 2.6e+02 || g.*log(vr/vf) - 2*N'*y_N - 2*C'*y_C ||_inf 52 || g.*log(vr/vf) + cr - cf - 2*ci - 2*N'*y_N - 2*C'*y_C - 2*y_vi ||_inf 87 || g.*log(vr/vf) + cr - cf - 2*ci - 2*N'*y_N - 2*C'*y_C - 2*y_vi - z_vr + z_vf ||_inf -1.5e+02 min(slack) Inf max(slack)
Compare the original external flux vector, with the quadratically constrained external flux vector. The values should be closer to the red line than above, but not exactly, because the quadratic penalty is trading off against entropy maximisation of internal reactions. Change H(j,j) to adjust this trade off.
figure
hold on
fplot(@(x) x, 'LineWidth', 1.5,'Color','r')
plot(solution.v(~model.SConsistentRxnBool),solutionQEFBA.v(~model.SConsistentRxnBool),'o','Color','b')
xlabel('EntropicFBA flux')
ylabel('Quadratically constrained EntropicFBA flux')
title('External flux values')
axis equal

Quadratically constrained entropic flux balance analysis - subset of external reactions

Generate a random given external flux vector that is a perturbation of the previously obtained external flux vector and then quadratically penalise any deviation from it.
model.h = (solution.v).*(rand(length(solution.v),1)+0.5)*2;
Do not optimise toward any internal net flux
model.h(model.SConsistentRxnBool)=NaN;
Only optimise toward the top 10 magnitude given external net flux
[sortedh,ind]=sort(abs(model.h),'descend','MissingPlacement','last');
if length(ind)>10
model.h(ind(11:end))=NaN;
end
Compare the original external flux vector, with the external flux vector to peanlise deviation from
figure
hold on
fplot(@(x) x, 'LineWidth', 1.5,'Color','r')
plot(solution.v(isfinite(model.h)),model.h(isfinite(model.h)),'o','Color','b')
xlabel('EntropicFBA flux')
ylabel('h')
title('External flux values')
axis equal
Set the penaltiy
HH = ones(length(solution.v),1);
HH(model.SConsistentRxnBool)=0;
model.H = spdiags(HH,0,length(solution.v),length(solution.v));
Run the optimisation
[solutionQEFBA,modelOut] = entropicFluxBalanceAnalysis(model,param);
Using directional internal net flux bounds only. Using existing external net flux bounds without modification. MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 Problem Name : Objective sense : minimize Type : LO (linear optimization problem) Constraints : 2975 Affine conic cons. : 0 Disjunctive cons. : 0 Cones : 0 Scalar variables : 3635 Matrix variables : 0 Integer variables : 0 Optimizer started. Presolve started. Eliminator started. Freed constraints in eliminator : 1219 Eliminator terminated. Linear dependency checker started. Linear dependency checker terminated. Eliminator started. Freed constraints in eliminator : 141 Eliminator terminated. Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 9 dual deps. : 0 Presolve terminated. Time: 0.02 Optimizer - threads : 18 Optimizer - solved problem : the primal Optimizer - Constraints : 512 Optimizer - Cones : 0 Optimizer - Scalar variables : 1700 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.01 Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 5040 after factor : 1.19e+04 Factor - dense dim. : 1 flops : 5.13e+05 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 8.0e+03 1.2e+03 2.7e+04 0.00e+00 2.536209125e+04 -1.137375866e+03 1.3e+02 0.04 1 4.3e+03 7.2e-01 1.4e+04 1.01e+00 1.109112427e+04 2.131423372e+03 6.8e+01 0.05 2 1.6e+03 2.7e-01 5.2e+03 1.30e+00 5.333642613e+03 2.475579900e+03 2.5e+01 0.05 3 3.7e+02 6.2e-02 1.2e+03 1.11e+00 1.677123434e+03 1.043181022e+03 5.9e+00 0.05 4 4.5e+01 7.6e-03 1.5e+02 1.04e+00 4.494526587e+02 3.734394760e+02 7.1e-01 0.05 5 2.3e+01 3.8e-03 7.5e+01 1.01e+00 3.721136544e+02 3.336327497e+02 3.6e-01 0.06 6 4.2e+00 7.1e-04 1.4e+01 1.01e+00 3.060528620e+02 2.990462288e+02 6.7e-02 0.06 7 1.3e+00 2.3e-04 4.4e+00 1.00e+00 2.951088773e+02 2.928706595e+02 2.1e-02 0.06 8 5.7e-01 9.6e-05 1.9e+00 1.00e+00 2.921571806e+02 2.912048430e+02 9.1e-03 0.06 9 9.0e-02 1.5e-05 3.0e-01 1.00e+00 2.902963878e+02 2.901452889e+02 1.4e-03 0.07 10 2.0e-02 3.4e-06 6.6e-02 9.99e-01 2.900126991e+02 2.899790785e+02 3.2e-04 0.07 11 6.9e-03 1.2e-06 2.3e-02 1.00e+00 2.899593316e+02 2.899477152e+02 1.1e-04 0.07 12 3.9e-04 6.5e-08 1.3e-03 1.00e+00 2.899323089e+02 2.899316648e+02 6.1e-06 0.07 13 1.5e-05 2.5e-09 4.9e-05 1.00e+00 2.899306835e+02 2.899306588e+02 2.4e-07 0.08 14 3.4e-07 3.7e-10 3.5e-07 1.00e+00 2.899306169e+02 2.899306167e+02 4.6e-10 0.08 Basis identification started. Primal basis identification phase started. Primal basis identification phase terminated. Time: 0.00 Dual basis identification phase started. Dual basis identification phase terminated. Time: 0.00 Basis identification terminated. Time: 0.01 Optimizer terminated. Time: 0.10 Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 2.8993061688e+02 nrm: 5e+02 Viol. con: 1e-06 var: 1e-07 Dual. obj: 2.8993061665e+02 nrm: 5e+00 Viol. con: 0e+00 var: 2e-10 Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 2.8993061677e+02 nrm: 5e+02 Viol. con: 8e-13 var: 3e-14 Dual. obj: 2.8993061672e+02 nrm: 6e+00 Viol. con: 6e-11 var: 4e-07 Optimizer summary Optimizer - time: 0.10 Interior-point - iterations : 14 time: 0.09 Basis identification - time: 0.01 Primal - iterations : 37 time: 0.00 Dual - iterations : 95 time: 0.00 Clean primal - iterations : 0 time: 0.00 Clean dual - iterations : 0 time: 0.00 Simplex - time: 0.00 Primal simplex - iterations : 0 time: 0.00 Dual simplex - iterations : 0 time: 0.00 Mixed integer - relaxations: 0 time: 0.00 solveCobraEP: LP part of EPproblem is feasible according to solveCobraLP with mosek. MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 Problem Name : Objective sense : minimize Type : CONIC (conic optimization problem) Constraints : 2975 Affine conic cons. : 3430 (10290 rows) Disjunctive cons. : 0 Cones : 0 Scalar variables : 7067 Matrix variables : 0 Integer variables : 0 Optimizer started. Presolve started. Linear dependency checker started. Linear dependency checker terminated. Eliminator started. Freed constraints in eliminator : 7 Eliminator terminated. Eliminator - tries : 1 time : 0.00 Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 25 dual deps. : 0 Presolve terminated. Time: 0.03 Optimizer - threads : 18 Optimizer - solved problem : the primal Optimizer - Constraints : 1960 Optimizer - Cones : 3430 Optimizer - Scalar variables : 11284 conic : 10290 Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.02 Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 1.19e+04 after factor : 2.06e+04 Factor - dense dim. : 0 flops : 7.95e+05 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 1.0e+04 1.2e+00 1.0e+04 0.00e+00 5.947759534e+03 -4.414972768e+03 1.0e+00 0.06 1 8.1e+03 9.5e-01 9.3e+03 -9.99e-01 8.037729882e+03 -2.321978061e+03 8.1e-01 0.08 2 7.3e+03 8.6e-01 8.8e+03 -9.96e-01 9.251313347e+03 -1.094838395e+03 7.3e-01 0.09 3 5.4e+03 6.3e-01 7.5e+03 -9.85e-01 1.411292582e+04 3.857496674e+03 5.4e-01 0.10 4 1.8e+03 2.1e-01 4.1e+03 -9.66e-01 5.104523733e+04 4.123658305e+04 1.8e-01 0.11 5 7.7e+02 9.1e-02 2.5e+03 -8.61e-01 9.839593865e+04 8.950761846e+04 7.7e-02 0.12 6 4.2e+02 4.9e-02 1.5e+03 -6.00e-01 1.025664394e+05 9.529333740e+04 4.2e-02 0.13 7 3.0e+02 3.5e-02 1.0e+03 -1.72e-01 8.505723708e+04 7.901253075e+04 3.0e-02 0.14 8 2.1e+02 2.5e-02 6.5e+02 8.13e-02 6.954940345e+04 6.468064026e+04 2.1e-02 0.14 9 1.2e+02 1.5e-02 3.3e+02 2.99e-01 5.111476715e+04 4.781160692e+04 1.2e-02 0.15 10 9.8e+01 1.2e-02 2.4e+02 5.63e-01 4.528535708e+04 4.256295185e+04 9.8e-03 0.16 11 3.6e+01 4.3e-03 5.9e+01 6.52e-01 2.920508427e+04 2.807972182e+04 3.6e-03 0.17 12 9.4e+00 1.1e-03 8.3e+00 8.79e-01 2.082004927e+04 2.051703883e+04 9.4e-04 0.18 13 4.4e+00 5.2e-04 2.8e+00 9.76e-01 1.924949650e+04 1.910574210e+04 4.4e-04 0.19 14 1.0e+00 1.2e-04 3.2e-01 9.90e-01 1.814985735e+04 1.811605395e+04 1.0e-04 0.20 15 2.1e-01 2.5e-05 3.0e-02 9.99e-01 1.792314815e+04 1.791624423e+04 2.1e-05 0.21 16 5.3e-02 6.2e-06 3.8e-03 1.00e+00 1.787841040e+04 1.787669859e+04 5.3e-06 0.22 17 7.0e-03 8.3e-07 1.9e-04 1.00e+00 1.786577541e+04 1.786554655e+04 7.0e-07 0.23 18 6.9e-03 8.1e-07 1.8e-04 1.00e+00 1.786575033e+04 1.786552448e+04 6.9e-07 0.24 19 6.0e-03 7.0e-07 1.5e-04 1.00e+00 1.786548486e+04 1.786529081e+04 6.0e-07 0.25 20 5.9e-03 6.9e-07 1.4e-04 1.00e+00 1.786545512e+04 1.786526463e+04 5.9e-07 0.26 21 5.8e-03 6.8e-07 1.4e-04 1.00e+00 1.786544992e+04 1.786526005e+04 5.8e-07 0.27 22 3.3e-03 3.9e-07 6.0e-05 1.00e+00 1.786475410e+04 1.786464697e+04 3.3e-07 0.28 23 3.2e-03 3.8e-07 5.8e-05 1.00e+00 1.786473323e+04 1.786462859e+04 3.2e-07 0.29 24 3.2e-03 3.8e-07 5.7e-05 1.00e+00 1.786472788e+04 1.786462387e+04 3.2e-07 0.30 25 3.2e-03 3.8e-07 5.7e-05 1.00e+00 1.786472784e+04 1.786462384e+04 3.2e-07 0.31 26 3.2e-03 3.8e-07 5.7e-05 1.00e+00 1.786472783e+04 1.786462383e+04 3.2e-07 0.32 27 2.9e-03 3.4e-07 4.9e-05 1.00e+00 1.786464169e+04 1.786454793e+04 2.9e-07 0.33 28 2.9e-03 3.4e-07 4.9e-05 1.00e+00 1.786463783e+04 1.786454452e+04 2.9e-07 0.34 29 2.9e-03 3.4e-07 4.9e-05 1.00e+00 1.786463779e+04 1.786454449e+04 2.9e-07 0.35 30 2.8e-03 3.3e-07 4.8e-05 1.00e+00 1.786462591e+04 1.786453402e+04 2.8e-07 0.36 31 2.8e-03 3.3e-07 4.8e-05 1.00e+00 1.786462415e+04 1.786453247e+04 2.8e-07 0.36 32 2.8e-03 3.3e-07 4.7e-05 1.00e+00 1.786462172e+04 1.786453033e+04 2.8e-07 0.37 33 2.8e-03 3.3e-07 4.7e-05 1.00e+00 1.786462156e+04 1.786453019e+04 2.8e-07 0.39 34 2.8e-03 3.3e-07 4.7e-05 1.00e+00 1.786462155e+04 1.786453017e+04 2.8e-07 0.40 35 2.8e-03 3.3e-07 4.7e-05 1.00e+00 1.786462154e+04 1.786453017e+04 2.8e-07 0.41 36 6.9e-04 8.1e-08 6.0e-06 1.00e+00 1.786404195e+04 1.786401940e+04 6.9e-08 0.43 37 6.9e-04 8.1e-08 6.0e-06 1.00e+00 1.786404189e+04 1.786401935e+04 6.9e-08 0.44 38 6.9e-04 8.1e-08 6.0e-06 1.00e+00 1.786404189e+04 1.786401935e+04 6.9e-08 0.45 39 6.9e-04 8.1e-08 5.9e-06 1.00e+00 1.786404177e+04 1.786401925e+04 6.9e-08 0.46 40 6.9e-04 8.1e-08 5.9e-06 1.00e+00 1.786404174e+04 1.786401922e+04 6.9e-08 0.47 41 6.9e-04 8.1e-08 5.9e-06 1.00e+00 1.786404168e+04 1.786401916e+04 6.9e-08 0.47 42 6.9e-04 8.1e-08 5.9e-06 1.00e+00 1.786404146e+04 1.786401897e+04 6.9e-08 0.48 43 6.9e-04 8.1e-08 5.9e-06 1.00e+00 1.786404146e+04 1.786401897e+04 6.9e-08 0.49 44 6.9e-04 8.1e-08 5.9e-06 1.00e+00 1.786404144e+04 1.786401895e+04 6.9e-08 0.50 45 6.3e-04 7.4e-08 5.1e-06 1.00e+00 1.786402303e+04 1.786400265e+04 6.3e-08 0.52 46 6.3e-04 7.4e-08 5.1e-06 1.00e+00 1.786402298e+04 1.786400261e+04 6.3e-08 0.53 47 6.3e-04 7.3e-08 5.1e-06 1.00e+00 1.786402288e+04 1.786400252e+04 6.3e-08 0.54 48 6.3e-04 7.3e-08 5.1e-06 1.00e+00 1.786402288e+04 1.786400251e+04 6.3e-08 0.54 49 6.1e-04 7.1e-08 4.9e-06 1.00e+00 1.786401709e+04 1.786399739e+04 6.1e-08 0.56 50 6.1e-04 7.1e-08 4.9e-06 1.00e+00 1.786401706e+04 1.786399736e+04 6.1e-08 0.57 51 6.1e-04 7.1e-08 4.9e-06 1.00e+00 1.786401704e+04 1.786399735e+04 6.1e-08 0.58 52 6.1e-04 7.1e-08 4.9e-06 1.00e+00 1.786401697e+04 1.786399728e+04 6.1e-08 0.59 53 6.0e-04 7.1e-08 4.8e-06 1.00e+00 1.786401648e+04 1.786399685e+04 6.0e-08 0.60 54 6.0e-04 7.1e-08 4.8e-06 1.00e+00 1.786401642e+04 1.786399680e+04 6.0e-08 0.61 55 6.0e-04 7.1e-08 4.8e-06 1.00e+00 1.786401641e+04 1.786399678e+04 6.0e-08 0.62 56 6.0e-04 7.1e-08 4.8e-06 1.00e+00 1.786401635e+04 1.786399673e+04 6.0e-08 0.63 57 6.0e-04 7.1e-08 4.8e-06 1.00e+00 1.786401627e+04 1.786399667e+04 6.0e-08 0.64 58 6.0e-04 7.1e-08 4.8e-06 1.00e+00 1.786401624e+04 1.786399664e+04 6.0e-08 0.65 59 6.0e-04 7.1e-08 4.8e-06 1.00e+00 1.786401613e+04 1.786399654e+04 6.0e-08 0.66 60 6.0e-04 7.1e-08 4.8e-06 1.00e+00 1.786401596e+04 1.786399639e+04 6.0e-08 0.67 61 6.0e-04 7.1e-08 4.8e-06 1.00e+00 1.786401596e+04 1.786399639e+04 6.0e-08 0.67 62 6.0e-04 7.1e-08 4.8e-06 1.00e+00 1.786401591e+04 1.786399635e+04 6.0e-08 0.68 63 6.0e-04 7.0e-08 4.8e-06 1.00e+00 1.786401513e+04 1.786399565e+04 6.0e-08 0.70 64 6.0e-04 7.0e-08 4.8e-06 1.00e+00 1.786401502e+04 1.786399556e+04 6.0e-08 0.71 65 6.0e-04 7.0e-08 4.8e-06 1.00e+00 1.786401502e+04 1.786399556e+04 6.0e-08 0.72 66 6.0e-04 7.0e-08 4.8e-06 1.00e+00 1.786401498e+04 1.786399552e+04 6.0e-08 0.73 67 6.0e-04 7.0e-08 4.8e-06 1.00e+00 1.786401498e+04 1.786399552e+04 6.0e-08 0.73 68 6.0e-04 7.0e-08 4.8e-06 1.00e+00 1.786401495e+04 1.786399550e+04 6.0e-08 0.74 69 6.0e-04 7.0e-08 4.8e-06 1.00e+00 1.786401495e+04 1.786399549e+04 6.0e-08 0.75 70 6.0e-04 7.0e-08 4.8e-06 1.00e+00 1.786401473e+04 1.786399530e+04 6.0e-08 0.77 71 5.9e-04 7.0e-08 4.7e-06 1.00e+00 1.786401388e+04 1.786399455e+04 5.9e-08 0.79 72 5.9e-04 6.9e-08 4.7e-06 1.00e+00 1.786401317e+04 1.786399392e+04 5.9e-08 0.81 73 5.9e-04 6.9e-08 4.6e-06 1.00e+00 1.786401117e+04 1.786399215e+04 5.9e-08 0.83 74 5.9e-04 6.9e-08 4.6e-06 1.00e+00 1.786401117e+04 1.786399215e+04 5.9e-08 0.84 75 5.9e-04 6.9e-08 4.6e-06 1.00e+00 1.786401115e+04 1.786399214e+04 5.9e-08 0.85 76 5.9e-04 6.9e-08 4.6e-06 1.00e+00 1.786401114e+04 1.786399212e+04 5.9e-08 0.86 77 5.9e-04 6.9e-08 4.6e-06 1.00e+00 1.786401114e+04 1.786399212e+04 5.9e-08 0.87 78 5.9e-04 6.9e-08 4.6e-06 1.00e+00 1.786401111e+04 1.786399210e+04 5.9e-08 0.88 79 5.9e-04 6.9e-08 4.6e-06 1.00e+00 1.786401109e+04 1.786399207e+04 5.9e-08 0.89 80 5.9e-04 6.9e-08 4.6e-06 1.00e+00 1.786401107e+04 1.786399206e+04 5.9e-08 0.89 81 5.8e-04 6.8e-08 4.6e-06 1.00e+00 1.786401041e+04 1.786399148e+04 5.8e-08 0.91 82 5.8e-04 6.8e-08 4.6e-06 1.00e+00 1.786401039e+04 1.786399146e+04 5.8e-08 0.93 83 5.8e-04 6.8e-08 4.6e-06 1.00e+00 1.786401037e+04 1.786399144e+04 5.8e-08 0.95 84 5.8e-04 6.8e-08 4.6e-06 1.00e+00 1.786401037e+04 1.786399144e+04 5.8e-08 0.96 85 5.8e-04 6.8e-08 4.6e-06 1.00e+00 1.786401036e+04 1.786399143e+04 5.8e-08 0.96 86 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400875e+04 1.786399001e+04 5.8e-08 0.98 87 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400874e+04 1.786399000e+04 5.8e-08 0.99 88 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400874e+04 1.786398999e+04 5.8e-08 1.00 89 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400874e+04 1.786398999e+04 5.8e-08 1.01 90 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400869e+04 1.786398996e+04 5.8e-08 1.03 91 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400869e+04 1.786398995e+04 5.8e-08 1.04 92 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400855e+04 1.786398983e+04 5.8e-08 1.06 93 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400854e+04 1.786398982e+04 5.8e-08 1.07 94 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400853e+04 1.786398981e+04 5.8e-08 1.08 95 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400852e+04 1.786398980e+04 5.8e-08 1.09 96 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400851e+04 1.786398980e+04 5.8e-08 1.10 97 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400849e+04 1.786398978e+04 5.8e-08 1.11 98 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400849e+04 1.786398978e+04 5.8e-08 1.14 99 5.8e-04 6.8e-08 4.5e-06 1.00e+00 1.786400849e+04 1.786398978e+04 5.8e-08 1.15 100 5.8e-04 6.7e-08 4.5e-06 1.00e+00 1.786400830e+04 1.786398960e+04 5.8e-08 1.15 101 5.8e-04 6.7e-08 4.5e-06 1.00e+00 1.786400824e+04 1.786398955e+04 5.8e-08 1.16 102 5.7e-04 6.7e-08 4.5e-06 1.00e+00 1.786400790e+04 1.786398925e+04 5.7e-08 1.17 103 5.7e-04 6.7e-08 4.5e-06 1.00e+00 1.786400770e+04 1.786398908e+04 5.7e-08 1.18 104 5.7e-04 6.7e-08 4.5e-06 1.00e+00 1.786400759e+04 1.786398898e+04 5.7e-08 1.19 105 5.7e-04 6.7e-08 4.5e-06 1.00e+00 1.786400759e+04 1.786398897e+04 5.7e-08 1.20 106 5.2e-04 6.1e-08 3.8e-06 1.00e+00 1.786399159e+04 1.786397481e+04 5.2e-08 1.23 107 5.2e-04 6.1e-08 3.8e-06 1.00e+00 1.786399156e+04 1.786397479e+04 5.2e-08 1.24 108 5.2e-04 6.1e-08 3.8e-06 1.00e+00 1.786399154e+04 1.786397477e+04 5.2e-08 1.24 109 5.1e-04 6.0e-08 3.8e-06 1.00e+00 1.786399031e+04 1.786397367e+04 5.1e-08 1.26 110 5.1e-04 6.0e-08 3.8e-06 1.00e+00 1.786399014e+04 1.786397353e+04 5.1e-08 1.28 111 5.1e-04 6.0e-08 3.8e-06 1.00e+00 1.786399012e+04 1.786397351e+04 5.1e-08 1.30 112 5.1e-04 6.0e-08 3.8e-06 1.00e+00 1.786399005e+04 1.786397344e+04 5.1e-08 1.31 113 5.1e-04 6.0e-08 3.8e-06 1.00e+00 1.786399004e+04 1.786397344e+04 5.1e-08 1.32 114 5.1e-04 6.0e-08 3.8e-06 1.00e+00 1.786399003e+04 1.786397343e+04 5.1e-08 1.33 115 5.1e-04 6.0e-08 3.8e-06 1.00e+00 1.786399003e+04 1.786397343e+04 5.1e-08 1.34 116 5.1e-04 6.0e-08 3.8e-06 1.00e+00 1.786399000e+04 1.786397340e+04 5.1e-08 1.36 117 3.0e-04 3.6e-08 1.7e-06 1.00e+00 1.786393151e+04 1.786392160e+04 3.0e-08 1.37 118 3.0e-04 3.5e-08 1.7e-06 1.00e+00 1.786393094e+04 1.786392111e+04 3.0e-08 1.39 119 3.0e-04 3.5e-08 1.7e-06 1.00e+00 1.786393094e+04 1.786392110e+04 3.0e-08 1.40 120 3.0e-04 3.5e-08 1.7e-06 1.00e+00 1.786393091e+04 1.786392108e+04 3.0e-08 1.41 121 2.9e-04 3.4e-08 1.6e-06 1.00e+00 1.786392763e+04 1.786391817e+04 2.9e-08 1.43 122 2.9e-04 3.4e-08 1.6e-06 1.00e+00 1.786392762e+04 1.786391816e+04 2.9e-08 1.45 123 2.9e-04 3.4e-08 1.6e-06 1.00e+00 1.786392762e+04 1.786391817e+04 2.9e-08 1.46 124 2.9e-04 3.4e-08 1.6e-06 1.00e+00 1.786392762e+04 1.786391817e+04 2.9e-08 1.46 125 2.9e-04 3.4e-08 1.6e-06 1.00e+00 1.786392753e+04 1.786391808e+04 2.9e-08 1.48 126 2.9e-04 3.4e-08 1.6e-06 1.00e+00 1.786392752e+04 1.786391807e+04 2.9e-08 1.50 127 2.9e-04 3.4e-08 1.6e-06 1.00e+00 1.786392752e+04 1.786391807e+04 2.9e-08 1.51 128 2.9e-04 3.4e-08 1.6e-06 1.00e+00 1.786392748e+04 1.786391804e+04 2.9e-08 1.53 129 2.9e-04 3.4e-08 1.6e-06 1.00e+00 1.786392748e+04 1.786391804e+04 2.9e-08 1.54 130 2.9e-04 3.4e-08 1.6e-06 1.00e+00 1.786392748e+04 1.786391804e+04 2.9e-08 1.55 Optimizer terminated. Time: 1.59 Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 1.7863927476e+04 nrm: 5e+02 Viol. con: 5e-04 var: 1e-05 acc: 1e-07 Dual. obj: 1.7863918037e+04 nrm: 8e+03 Viol. con: 6e-07 var: 1e-06 acc: 0e+00 Optimizer summary Optimizer - time: 1.59 Interior-point - iterations : 131 time: 1.57 Basis identification - time: 0.00 Primal - iterations : 0 time: 0.00 Dual - iterations : 0 time: 0.00 Clean primal - iterations : 0 time: 0.00 Clean dual - iterations : 0 time: 0.00 Simplex - time: 0.00 Primal simplex - iterations : 0 time: 0.00 Dual simplex - iterations : 0 time: 0.00 Mixed integer - relaxations: 0 time: 0.00 > [mosek] Dual optimality condition in solveCobraEP satisfied. Optimality conditions (biochemistry) 0.00049 || N*(vf - vr) + B*ve - b ||_inf Inf || C*(vf - vr) + s_C - d ||_inf, s_C = slack variable 6.4e-07 || cf + ci + N'*y_N + C'*y_C + y_vi + Qv*vf + k_vf + z_vf ||_inf 6.4e-07 || cr - ci - N'*y_N - C'*y_C - y_vi + Qv*vf + k_vr + z_vr ||_inf 1 || ce + B'*y_N + z_ve ||_inf 8.2e+03 || k_e_1 + z_e_1 ||_inf 8.2e+03 || -g + k_e_vf + z_e_vf||_inf 1.1e-06 || -g + k_e_vr + z_e_vr||_inf 1.5e-05 || e_vf + vf*log(vf) ||_inf 1.5e-05 || e_vr + vr*log(vr) ||_inf 1.7 || k_q_1 + z_q_1 ||_inf Derived optimality conditions (biochemistry) 21 || g.*log(vf) + g - k_vf ||_inf 0.022 || g.*log(vr) + g - k_vr ||_inf 21 || cf + ci + N'*y_N + C'*y_C + y_vi + Qv*vf + g.*log(vf) + g + z_vf ||_inf 0.022 || cr - ci - N'*y_N - C'*y_C - y_vi + Qv*vf + g.*log(vr) + g + z_vr ||_inf Thermo conditions 2.7e+02 || g.*log(vr/vf) - 2*N'*y_N - 2*C'*y_C ||_inf 56 || g.*log(vr/vf) + cr - cf - 2*ci - 2*N'*y_N - 2*C'*y_C - 2*y_vi ||_inf 91 || g.*log(vr/vf) + cr - cf - 2*ci - 2*N'*y_N - 2*C'*y_C - 2*y_vi - z_vr + z_vf ||_inf -1.5e+02 min(slack) Inf max(slack)
Compare the original external flux vector, with the quadratically constrained external flux vector. The values should be closer to the red line than above, but not exactly, because the quadratic penalty is trading off against entropy maximisation of internal reactions. Change H(j,j) to adjust this trade off.
figure
hold on
fplot(@(x) x, 'LineWidth', 1.5,'Color','r')
plot(solution.v(isfinite(model.h)),solutionQEFBA.v(isfinite(model.h)),'o','Color','b')
xlabel('EntropicFBA flux')
ylabel('Quadratically constrained EntropicFBA flux')
title('External flux values')
axis equal

Quadratically constrained entropic flux balance analysis - subset of external reactions and no coupling constraints

model = rmfield(model,{'C','d'});
Generate a random given external flux vector that is a perturbation of the previously obtained external flux vector and then quadratically penalise any deviation from it.
model.h = (solution.v).*(rand(length(solution.v),1)+0.5)*2;
Do not optimise toward any internal net flux
model.h(model.SConsistentRxnBool)=NaN;
Only optimise toward the top 10 magnitude given external net flux
[sortedh,ind]=sort(abs(model.h),'descend','MissingPlacement','last');
if length(ind)>10
model.h(ind(11:end))=NaN;
end
Compare the original external flux vector, with the external flux vector to peanlise deviation from
figure
hold on
fplot(@(x) x, 'LineWidth', 1.5,'Color','r')
plot(solution.v(isfinite(model.h)),model.h(isfinite(model.h)),'o','Color','b')
xlabel('EntropicFBA flux')
ylabel('h')
title('External flux values')
axis equal
Set the penaltiy
HH = ones(length(solution.v),1);
HH(model.SConsistentRxnBool)=0;
model.H = spdiags(HH,0,length(solution.v),length(solution.v));
Run the optimisation
[solutionQEFBA,modelOut] = entropicFluxBalanceAnalysis(model,param);
Using directional internal net flux bounds only. Using existing external net flux bounds without modification. MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 Problem Name : Objective sense : minimize Type : LO (linear optimization problem) Constraints : 2964 Affine conic cons. : 0 Disjunctive cons. : 0 Cones : 0 Scalar variables : 3635 Matrix variables : 0 Integer variables : 0 Optimizer started. Presolve started. Eliminator started. Freed constraints in eliminator : 1218 Eliminator terminated. Linear dependency checker started. Linear dependency checker terminated. Eliminator started. Freed constraints in eliminator : 141 Eliminator terminated. Eliminator - tries : 2 time : 0.00 Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 9 dual deps. : 0 Presolve terminated. Time: 0.02 GP based matrix reordering started. GP based matrix reordering terminated. Optimizer - threads : 18 Optimizer - solved problem : the primal Optimizer - Constraints : 502 Optimizer - Cones : 0 Optimizer - Scalar variables : 1690 conic : 0 Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.01 Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 4935 after factor : 1.17e+04 Factor - dense dim. : 2 flops : 5.02e+05 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 8.0e+03 1.2e+03 2.6e+04 0.00e+00 2.503116488e+04 -1.234172434e+03 1.3e+02 0.04 1 3.9e+03 6.4e-01 1.3e+04 9.99e-01 1.002253781e+04 2.316670551e+03 6.2e+01 0.05 2 1.7e+03 2.8e-01 5.6e+03 1.18e+00 5.545217022e+03 2.452230824e+03 2.7e+01 0.05 3 3.6e+02 5.9e-02 1.2e+03 1.09e+00 1.613658539e+03 9.982955221e+02 5.6e+00 0.06 4 1.5e+02 2.5e-02 4.9e+02 1.03e+00 8.264611299e+02 5.722855572e+02 2.4e+00 0.06 5 2.8e+01 4.5e-03 9.1e+01 1.01e+00 3.934480893e+02 3.467403504e+02 4.4e-01 0.06 6 5.5e+00 9.0e-04 1.8e+01 1.02e+00 3.052316807e+02 2.960376884e+02 8.6e-02 0.06 7 4.2e-01 6.9e-05 1.4e+00 1.01e+00 2.838759387e+02 2.831788041e+02 6.6e-03 0.07 8 2.4e-02 4.0e-06 7.9e-02 1.01e+00 2.820862755e+02 2.820463229e+02 3.8e-04 0.07 9 1.2e-03 1.9e-07 3.9e-03 1.01e+00 2.819644523e+02 2.819625049e+02 1.9e-05 0.07 10 2.7e-05 4.4e-09 8.8e-05 1.00e+00 2.819572914e+02 2.819572471e+02 4.2e-07 0.07 11 2.4e-06 1.9e-08 1.1e-08 1.01e+00 2.819571856e+02 2.819571856e+02 1.2e-08 0.08 12 2.4e-06 1.9e-08 1.1e-08 1.00e+00 2.819571856e+02 2.819571856e+02 1.2e-08 0.08 Basis identification started. Primal basis identification phase started. Primal basis identification phase terminated. Time: 0.00 Dual basis identification phase started. Dual basis identification phase terminated. Time: 0.00 Basis identification terminated. Time: 0.01 Optimizer terminated. Time: 0.10 Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 2.8195718558e+02 nrm: 5e+02 Viol. con: 7e-06 var: 3e-07 Dual. obj: 2.8195717596e+02 nrm: 5e+00 Viol. con: 0e+00 var: 9e-09 Basic solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 2.8195718114e+02 nrm: 5e+02 Viol. con: 8e-13 var: 1e-14 Dual. obj: 2.8195718114e+02 nrm: 8e+00 Viol. con: 0e+00 var: 8e-16 Optimizer summary Optimizer - time: 0.10 Interior-point - iterations : 12 time: 0.09 Basis identification - time: 0.01 Primal - iterations : 47 time: 0.00 Dual - iterations : 103 time: 0.00 Clean primal - iterations : 0 time: 0.00 Clean dual - iterations : 0 time: 0.00 Simplex - time: 0.00 Primal simplex - iterations : 0 time: 0.00 Dual simplex - iterations : 0 time: 0.00 Mixed integer - relaxations: 0 time: 0.00 solveCobraEP: LP part of EPproblem is feasible according to solveCobraLP with mosek. MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 MOSEK Version 10.2.5 (Build date: 2024-9-17 12:12:35) Copyright (c) MOSEK ApS, Denmark WWW: mosek.com Platform: Linux/64-X86 Problem Name : Objective sense : minimize Type : CONIC (conic optimization problem) Constraints : 2964 Affine conic cons. : 3430 (10290 rows) Disjunctive cons. : 0 Cones : 0 Scalar variables : 7067 Matrix variables : 0 Integer variables : 0 Optimizer started. Presolve started. Linear dependency checker started. Linear dependency checker terminated. Eliminator started. Freed constraints in eliminator : 8 Eliminator terminated. Eliminator - tries : 1 time : 0.00 Lin. dep. - tries : 1 time : 0.00 Lin. dep. - primal attempts : 1 successes : 1 Lin. dep. - dual attempts : 0 successes : 0 Lin. dep. - primal deps. : 25 dual deps. : 0 Presolve terminated. Time: 0.03 Optimizer - threads : 18 Optimizer - solved problem : the primal Optimizer - Constraints : 1949 Optimizer - Cones : 3430 Optimizer - Scalar variables : 11273 conic : 10290 Optimizer - Semi-definite variables: 0 scalarized : 0 Factor - setup time : 0.02 Factor - dense det. time : 0.00 GP order time : 0.00 Factor - nonzeros before factor : 1.17e+04 after factor : 2.01e+04 Factor - dense dim. : 0 flops : 7.52e+05 ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME 0 1.0e+04 1.2e+00 1.0e+04 0.00e+00 5.947759534e+03 -4.414972768e+03 1.0e+00 0.06 1 7.9e+03 9.3e-01 9.2e+03 -9.99e-01 8.232311490e+03 -2.127371810e+03 7.9e-01 0.09 2 7.2e+03 8.4e-01 8.8e+03 -9.96e-01 9.502069016e+03 -8.439738464e+02 7.2e-01 0.10 3 5.3e+03 6.2e-01 7.5e+03 -9.85e-01 1.447239244e+04 4.217526204e+03 5.3e-01 0.15 4 1.7e+03 2.0e-01 4.1e+03 -9.66e-01 5.230892004e+04 4.250374657e+04 1.7e-01 0.33 5 7.0e+02 8.2e-02 2.4e+03 -8.61e-01 1.067632391e+05 9.800078150e+04 7.0e-02 0.34 6 4.0e+02 4.7e-02 1.4e+03 -5.59e-01 1.049141326e+05 9.770526243e+04 4.0e-02 0.35 7 2.8e+02 3.3e-02 9.6e+02 -1.56e-01 8.608338702e+04 8.013144341e+04 2.8e-02 0.36 8 1.7e+02 2.0e-02 5.3e+02 1.01e-01 6.412938836e+04 5.978465784e+04 1.7e-02 0.37 9 1.2e+02 1.4e-02 3.2e+02 3.93e-01 5.168438193e+04 4.842911750e+04 1.2e-02 0.38 10 6.6e+01 7.7e-03 1.4e+02 5.72e-01 3.786764539e+04 3.590026862e+04 6.6e-03 0.39 11 4.6e+01 5.4e-03 8.3e+01 7.65e-01 3.225068439e+04 3.083571157e+04 4.6e-03 0.40 12 1.2e+01 1.4e-03 1.2e+01 8.40e-01 2.140669702e+04 2.101253429e+04 1.2e-03 0.41 13 3.7e+00 4.3e-04 2.1e+00 9.68e-01 1.845839483e+04 1.833657509e+04 3.7e-04 0.42 14 1.0e+00 1.2e-04 3.1e-01 9.93e-01 1.755884221e+04 1.752535817e+04 1.0e-04 0.43 15 2.7e-01 3.1e-05 4.4e-02 9.99e-01 1.733318360e+04 1.732430925e+04 2.7e-05 0.44 16 6.6e-02 7.7e-06 5.4e-03 1.00e+00 1.727034946e+04 1.726816170e+04 6.6e-06 0.45 17 1.4e-02 1.6e-06 5.2e-04 1.00e+00 1.725455691e+04 1.725410508e+04 1.4e-06 0.46 18 8.8e-03 1.0e-06 2.7e-04 1.00e+00 1.725310464e+04 1.725281349e+04 8.8e-07 0.46 19 5.6e-03 6.6e-07 1.4e-04 1.00e+00 1.725214547e+04 1.725196026e+04 5.6e-07 0.48 20 5.0e-03 5.8e-07 1.1e-04 1.00e+00 1.725196013e+04 1.725179540e+04 5.0e-07 0.49 21 4.9e-03 5.8e-07 1.1e-04 1.00e+00 1.725194216e+04 1.725177942e+04 4.9e-07 0.50 22 4.8e-03 5.7e-07 1.1e-04 1.00e+00 1.725192055e+04 1.725176019e+04 4.8e-07 0.51 23 4.7e-03 5.5e-07 1.1e-04 1.00e+00 1.725188600e+04 1.725172946e+04 4.7e-07 0.52 24 4.7e-03 5.5e-07 1.1e-04 1.00e+00 1.725188038e+04 1.725172446e+04 4.7e-07 0.53 25 4.5e-03 5.3e-07 9.8e-05 1.00e+00 1.725181785e+04 1.725166884e+04 4.5e-07 0.54 26 4.5e-03 5.3e-07 9.8e-05 1.00e+00 1.725181614e+04 1.725166732e+04 4.5e-07 0.55 27 4.5e-03 5.3e-07 9.8e-05 1.00e+00 1.725181610e+04 1.725166728e+04 4.5e-07 0.56 28 4.4e-03 5.2e-07 9.7e-05 1.00e+00 1.725180155e+04 1.725165434e+04 4.4e-07 0.56 29 4.4e-03 5.2e-07 9.6e-05 1.00e+00 1.725179983e+04 1.725165281e+04 4.4e-07 0.57 30 4.4e-03 5.2e-07 9.6e-05 1.00e+00 1.725179981e+04 1.725165279e+04 4.4e-07 0.58 31 4.2e-03 4.9e-07 8.8e-05 1.00e+00 1.725171945e+04 1.725158131e+04 4.2e-07 0.59 32 4.1e-03 4.8e-07 8.6e-05 1.00e+00 1.725170588e+04 1.725156924e+04 4.1e-07 0.60 33 4.0e-03 4.7e-07 8.2e-05 1.00e+00 1.725166415e+04 1.725153212e+04 4.0e-07 0.61 34 3.9e-03 4.6e-07 8.1e-05 1.00e+00 1.725165276e+04 1.725152199e+04 3.9e-07 0.62 35 3.9e-03 4.6e-07 8.1e-05 1.00e+00 1.725165262e+04 1.725152186e+04 3.9e-07 0.63 36 3.9e-03 4.6e-07 8.1e-05 1.00e+00 1.725165254e+04 1.725152179e+04 3.9e-07 0.64 37 3.9e-03 4.6e-07 7.9e-05 1.00e+00 1.725163673e+04 1.725150773e+04 3.9e-07 0.65 38 3.9e-03 4.5e-07 7.9e-05 1.00e+00 1.725163234e+04 1.725150382e+04 3.9e-07 0.65 39 3.8e-03 4.5e-07 7.8e-05 1.00e+00 1.725162216e+04 1.725149476e+04 3.8e-07 0.67 40 3.8e-03 4.5e-07 7.7e-05 1.00e+00 1.725161063e+04 1.725148450e+04 3.8e-07 0.67 41 3.8e-03 4.5e-07 7.7e-05 1.00e+00 1.725160908e+04 1.725148313e+04 3.8e-07 0.68 42 3.8e-03 4.5e-07 7.7e-05 1.00e+00 1.725160845e+04 1.725148257e+04 3.8e-07 0.69 43 3.8e-03 4.5e-07 7.7e-05 1.00e+00 1.725160838e+04 1.725148251e+04 3.8e-07 0.70 44 3.0e-03 3.6e-07 5.5e-05 1.00e+00 1.725137931e+04 1.725127873e+04 3.0e-07 0.71 45 3.0e-03 3.6e-07 5.5e-05 1.00e+00 1.725137837e+04 1.725127789e+04 3.0e-07 0.72 46 3.0e-03 3.5e-07 5.4e-05 1.00e+00 1.725137662e+04 1.725127634e+04 3.0e-07 0.73 47 3.0e-03 3.5e-07 5.4e-05 1.00e+00 1.725137360e+04 1.725127365e+04 3.0e-07 0.74 48 3.0e-03 3.5e-07 5.4e-05 1.00e+00 1.725137289e+04 1.725127302e+04 3.0e-07 0.75 49 3.0e-03 3.5e-07 5.3e-05 1.00e+00 1.725136541e+04 1.725126636e+04 3.0e-07 0.76 50 3.0e-03 3.5e-07 5.3e-05 1.00e+00 1.725136508e+04 1.725126607e+04 3.0e-07 0.77 51 3.0e-03 3.5e-07 5.3e-05 1.00e+00 1.725136501e+04 1.725126601e+04 3.0e-07 0.78 52 3.0e-03 3.5e-07 5.3e-05 1.00e+00 1.725136419e+04 1.725126528e+04 3.0e-07 0.79 53 3.0e-03 3.5e-07 5.3e-05 1.00e+00 1.725136416e+04 1.725126525e+04 3.0e-07 0.80 54 3.0e-03 3.5e-07 5.3e-05 1.00e+00 1.725136391e+04 1.725126503e+04 3.0e-07 0.81 55 3.0e-03 3.5e-07 5.3e-05 1.00e+00 1.725136324e+04 1.725126444e+04 3.0e-07 0.81 56 3.0e-03 3.5e-07 5.3e-05 1.00e+00 1.725136313e+04 1.725126433e+04 3.0e-07 0.82 57 7.2e-04 8.4e-08 6.4e-06 1.00e+00 1.725068311e+04 1.725065935e+04 7.2e-08 0.84 58 7.2e-04 8.4e-08 6.4e-06 1.00e+00 1.725068310e+04 1.725065934e+04 7.2e-08 0.85 59 7.2e-04 8.4e-08 6.4e-06 1.00e+00 1.725068301e+04 1.725065926e+04 7.2e-08 0.86 60 7.2e-04 8.4e-08 6.4e-06 1.00e+00 1.725068289e+04 1.725065915e+04 7.2e-08 0.86 61 7.2e-04 8.4e-08 6.4e-06 1.00e+00 1.725068288e+04 1.725065914e+04 7.2e-08 0.87 62 7.2e-04 8.4e-08 6.4e-06 1.00e+00 1.725068253e+04 1.725065883e+04 7.1e-08 0.89 63 7.1e-04 8.4e-08 6.4e-06 1.00e+00 1.725068252e+04 1.725065882e+04 7.1e-08 0.90 64 7.1e-04 8.4e-08 6.3e-06 1.00e+00 1.725068231e+04 1.725065863e+04 7.1e-08 0.91 65 7.1e-04 8.4e-08 6.3e-06 1.00e+00 1.725068227e+04 1.725065860e+04 7.1e-08 0.92 66 7.1e-04 8.4e-08 6.3e-06 1.00e+00 1.725068226e+04 1.725065859e+04 7.1e-08 0.93 67 7.1e-04 8.4e-08 6.3e-06 1.00e+00 1.725068225e+04 1.725065858e+04 7.1e-08 0.94 68 7.1e-04 8.4e-08 6.3e-06 1.00e+00 1.725068225e+04 1.725065858e+04 7.1e-08 0.95 69 7.1e-04 8.3e-08 6.2e-06 1.00e+00 1.725067970e+04 1.725065631e+04 7.1e-08 0.97 70 7.0e-04 8.3e-08 6.2e-06 1.00e+00 1.725067928e+04 1.725065594e+04 7.0e-08 0.98 71 7.0e-04 8.3e-08 6.2e-06 1.00e+00 1.725067923e+04 1.725065589e+04 7.0e-08 0.99 72 7.0e-04 8.3e-08 6.2e-06 1.00e+00 1.725067923e+04 1.725065589e+04 7.0e-08 1.00 73 7.0e-04 8.3e-08 6.2e-06 1.00e+00 1.725067921e+04 1.725065587e+04 7.0e-08 1.01 74 6.7e-04 7.8e-08 5.7e-06 1.00e+00 1.725066747e+04 1.725064542e+04 6.6e-08 1.03 75 6.7e-04 7.8e-08 5.7e-06 1.00e+00 1.725066746e+04 1.725064542e+04 6.6e-08 1.04 76 6.4e-04 7.5e-08 5.4e-06 1.00e+00 1.725066042e+04 1.725063915e+04 6.4e-08 1.05 77 6.4e-04 7.5e-08 5.4e-06 1.00e+00 1.725066041e+04 1.725063914e+04 6.4e-08 1.06 78 6.4e-04 7.5e-08 5.4e-06 1.00e+00 1.725066041e+04 1.725063914e+04 6.4e-08 1.07 79 1.5e-04 1.8e-08 6.3e-07 1.00e+00 1.725051265e+04 1.725050760e+04 1.5e-08 1.09 80 1.5e-04 1.8e-08 6.3e-07 1.00e+00 1.725051265e+04 1.725050760e+04 1.5e-08 1.09 81 1.5e-04 1.8e-08 6.3e-07 1.00e+00 1.725051265e+04 1.725050760e+04 1.5e-08 1.11 82 1.5e-04 1.8e-08 6.2e-07 1.00e+00 1.725051262e+04 1.725050757e+04 1.5e-08 1.11 83 1.5e-04 1.8e-08 6.2e-07 1.00e+00 1.725051262e+04 1.725050757e+04 1.5e-08 1.13 84 1.5e-04 1.8e-08 6.2e-07 1.00e+00 1.725051262e+04 1.725050757e+04 1.5e-08 1.15 85 1.5e-04 1.8e-08 6.2e-07 1.00e+00 1.725051262e+04 1.725050757e+04 1.5e-08 1.17 86 1.5e-04 1.8e-08 6.2e-07 1.00e+00 1.725051260e+04 1.725050756e+04 1.5e-08 1.18 87 1.5e-04 1.8e-08 6.2e-07 1.00e+00 1.725051260e+04 1.725050756e+04 1.5e-08 1.20 88 1.5e-04 1.8e-08 6.2e-07 1.00e+00 1.725051260e+04 1.725050756e+04 1.5e-08 1.22 Optimizer terminated. Time: 1.24 Interior-point solution summary Problem status : PRIMAL_AND_DUAL_FEASIBLE Solution status : OPTIMAL Primal. obj: 1.7250512601e+04 nrm: 5e+02 Viol. con: 2e-04 var: 7e-06 acc: 7e-08 Dual. obj: 1.7250507555e+04 nrm: 8e+03 Viol. con: 3e-07 var: 6e-07 acc: 0e+00 Optimizer summary Optimizer - time: 1.24 Interior-point - iterations : 89 time: 1.23 Basis identification - time: 0.00 Primal - iterations : 0 time: 0.00 Dual - iterations : 0 time: 0.00 Clean primal - iterations : 0 time: 0.00 Clean dual - iterations : 0 time: 0.00 Simplex - time: 0.00 Primal simplex - iterations : 0 time: 0.00 Dual simplex - iterations : 0 time: 0.00 Mixed integer - relaxations: 0 time: 0.00 > [mosek] Dual optimality condition in solveCobraEP satisfied. Optimality conditions (biochemistry) 0.00025 || N*(vf - vr) + B*ve - b ||_inf 3.4e-07 || cf + ci + N'*y_N + y_vi + Qv*vf + k_vf + z_vf ||_inf 3.4e-07 || cr - ci - N'*y_N - y_vi + Qv*vf + k_vr + z_vr ||_inf 1 || ce + B'*y_N + z_ve ||_inf 8e+03 || k_e_1 + z_e_1 ||_inf 8e+03 || -g + k_e_vf + z_e_vf||_inf 5.7e-07 || -g + k_e_vr + z_e_vr||_inf 8.2e-06 || e_vf + vf*log(vf) ||_inf 7.9e-06 || e_vr + vr*log(vr) ||_inf 1.3 || k_q_1 + z_q_1 ||_inf Derived optimality conditions (biochemistry) 20 || g.*log(vf) + g - k_vf ||_inf 0.0082 || g.*log(vr) + g - k_vr ||_inf 20 || cf + ci + N'*y_N + y_vi + Qv*vf + g.*log(vf) + g + z_vf ||_inf 0.0082 || cr - ci - N'*y_N - y_vi + Qv*vf + g.*log(vr) + g + z_vr ||_inf Thermo conditions 2.4e+02 || g.*log(vr/vf) - 2*N'*y_N ||_inf 54 || g.*log(vr/vf) + cr - cf - 2*ci - 2*N'*y_N - 2*y_vi ||_inf 88 || g.*log(vr/vf) + cr - cf - 2*ci - 2*N'*y_N - 2*y_vi - z_vr + z_vf ||_inf -1.5e+02 min(slack) 2e+02 max(slack)
Compare the original external flux vector, with the quadratically constrained external flux vector. The values should be closer to the red line than above, but not exactly, because the quadratic penalty is trading off against entropy maximisation of internal reactions. Change H(j,j) to adjust this trade off.
figure
hold on
fplot(@(x) x, 'LineWidth', 1.5,'Color','r')
plot(solution.v(isfinite(model.h)),solutionQEFBA.v(isfinite(model.h)),'o','Color','b')
xlabel('EntropicFBA flux')
ylabel('Quadratically constrained EntropicFBA flux')
title('External flux values')
axis equal

Acknowledgments

Co-funded by the European Union's Horizon Europe Framework Programme (101080997)

REFERENCES

[1] Fleming, R. M. T., Maes, C. M., Saunders, M. A., Ye, Y., and Palsson, B. O., "A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks", Journal of Theoretical Biology 292 (2012), pp. 71--77.
[2] Preciat, German and Moreno, Edinson Lucumi, "Mechanistic model-driven exometabolomic characterisation of human dopaminergic neuronal metabolism", bioRxiv (2022). https://www.biorxiv.org/content/10.1101/2021.11.08.467803v2
[3] Ronan M T Fleming, Hulda S Haraldsdottir, Le Hoai Minh, Phan Tu Vuong, Thomas Hankemeier, Ines Thiele, Cardinality optimization in constraint-based modelling: application to human metabolism, Bioinformatics, Volume 39, Issue 9, September 2023, btad450, https://doi.org/10.1093/bioinformatics/btad450
[4] Ronan M T Fleming, Subset of a model that admits a thermodynamically consistent flux https://opencobra.github.io/cobratoolbox/stable/tutorials/tutorial_findThermoConsistentFluxSubset.html
[5] German Preciat, Agnieszka B. Wegrzyn, Xi Luo, Ines Thiele,Thomas Hankemeier,Ronan M.T. Fleming, XomicsToModel: Omics data integration and generation of thermodynamically consistent metabolic models, Nature Protocols (to appear) Biorxiv v2 https://www.biorxiv.org/content/10.1101/2021.11.08.467803v2
[6] German Preciat, Extraction of context-specific models via XomicsToModel https://opencobra.github.io/cobratoolbox/stable/tutorials/tutorial_XomicsToModel.html