/* * An integrated study of Threonine-pathway enzyme kinetics in * Escherichia coli * * Model Status * * This model runs in COR and OpenCell and the units are consistent * throughout. It is unknown whether it can recreate the published * results, as there are no figures containing output of the complete * model to compare it to. It is expected that if validation was * carried out the model would be unable to recreate the published * results, as some equations were missing from the paper and extrapolated * from the reaction scheme. * * Model Structure * * ABSTRACT: We have determined the kinetic parameters of the individual * steps of the threonine pathway from aspartate in Escherichia * coli under a single set of experimental conditions chosen to * be physiologically relevant. Our aim was to summarize the kinetic * behaviour of each enzyme in a single tractable equation that * takes into account the effect of the products as competitive * inhibitors of the substrates in the forward reaction and also, * when appropriate (e.g. near-equilibrium reactions), as substrates * of the reverse reactions. Co-operative feedback inhibition by * threonine and lysine was also included as necessary. We derived * the simplest rate equations that describe the salient features * of the enzymes in the physiological range of metabolite concentrations * in order to incorporate them ultimately into a complete model * of the threonine pathway, able to predict quantitatively the * behaviour of the pathway under natural or engineered conditions. * * The original paper reference is cited below: * * An integrated study of threonine-pathway enzyme kinetics in * Escherichia coli , Christophe Chassagnole, Badr Rais, Eric Quentin, * David A. Fell and Jean-Pierre Mazat, 2001, Biochemical Journal * , 356, 415-423. PubMed ID: 11368768 * * schematic diagram * * [[Image file: chassagnole_2001.png]] * * Threonine-synthesis pathway from aspartate in E. coli. The different * steps are catalysed by aspartate kinases I and III (AK I and * AK III), aspartate semialdehyde dehydrogenase (ASD), homoserine * dehydrogenase (HDH), homoserine kinase (HK) and threonine synthase * (TS). The abbreviations used are: asp, aspartate; aspp, beta-aspartyl * phosphate; ASA, aspartic beta-semialdehyde; hs, homoserine; * hsp, O-phospho-homoserine; thr, threonine and lys, lysine. Solid * black lines represent the individual reaction steps of the pathway * and the dashed red lines represent reaction inhibition by threonine * and lysine. */ import nsrunit; unit conversion on; unit minute=60 second^1; // unit molar predefined // unit millimolar predefined unit per_molar=.001 meter^3*mole^(-1); unit flux=.01666667 meter^(-3)*second^(-1)*mole^1; unit first_order_rate_constant=.01666667 second^(-1); unit second_order_rate_constant=.01666667 meter^3*second^(-1)*mole^(-1); math main { realDomain time minute; time.min=0; extern time.max; extern time.delta; real Asp(time) millimolar; when(time=time.min) Asp=10; real vAKI(time) flux; real vAKIII(time) flux; real aspp(time) millimolar; when(time=time.min) aspp=0; real vASD(time) flux; real ASA(time) millimolar; when(time=time.min) ASA=0; real vHDH(time) flux; real hs(time) millimolar; when(time=time.min) hs=0; real vHK(time) flux; real hsp(time) millimolar; when(time=time.min) hsp=0; real vTS(time) flux; real Thr(time) millimolar; when(time=time.min) Thr=0; real ATP(time) millimolar; when(time=time.min) ATP=30; real ADP(time) millimolar; when(time=time.min) ADP=0; real NADPH(time) millimolar; when(time=time.min) NADPH=0; real NADP(time) millimolar; when(time=time.min) NADP=0; real Pi(time) millimolar; when(time=time.min) Pi=0; real Lys(time) millimolar; when(time=time.min) Lys=0; real vAKI.K_asp millimolar; vAKI.K_asp=0.97; real vAKI.K_ATP millimolar; vAKI.K_ATP=0.98; real vAKI.K_aspp millimolar; vAKI.K_aspp=0.017; real vAKI.K_ADP millimolar; vAKI.K_ADP=0.25; real vAKI.K_iThr millimolar; vAKI.K_iThr=0.167; real vAKI.alpha dimensionless; vAKI.alpha=2.47; real h_Thr dimensionless; h_Thr=4.09; real vAKI.K_eq dimensionless; vAKI.K_eq=0.00064; real V_max_AK_I flux; V_max_AK_I=463; real vASD.K_aspp millimolar; vASD.K_aspp=0.022; real vASD.K_NADPH millimolar; vASD.K_NADPH=0.029; real vASD.K_ASA millimolar; vASD.K_ASA=0.11; real vASD.K_NADP millimolar; vASD.K_NADP=0.144; real K_Pi millimolar; K_Pi=10.2; real vASD.K_eq millimolar; vASD.K_eq=284000; real V_max_ASD flux; V_max_ASD=598; real vHDH.K_ASA millimolar; vHDH.K_ASA=0.24; real vHDH.K_NADPH millimolar; vHDH.K_NADPH=0.037; real vHDH.K_hs millimolar; vHDH.K_hs=3.39; real vHDH.K_NADP millimolar; vHDH.K_NADP=0.067; real vHDH.K_iThr millimolar; vHDH.K_iThr=0.097; real vHDH.alpha dimensionless; vHDH.alpha=3.93; real h dimensionless; h=1.41; real vHDH.K_eq dimensionless; vHDH.K_eq=100000000000; real V_max_HDH flux; V_max_HDH=2585; real vHK.K_hs millimolar; vHK.K_hs=0.11; real vHK.K_ATP millimolar; vHK.K_ATP=0.072; real vHK.K_iThr millimolar; vHK.K_iThr=1.09; real vHK.K_iLys millimolar; vHK.K_iLys=9.45; real K_ihs millimolar; K_ihs=4.7; real K_iATP millimolar; K_iATP=4.35; real V_max_HK flux; V_max_HK=483; real K_hsp millimolar; K_hsp=0.31; real V_max_TS flux; V_max_TS=208; real vAKIII.K_asp millimolar; vAKIII.K_asp=0.32; real vAKIII.K_ATP millimolar; vAKIII.K_ATP=0.22; real vAKIII.K_aspp millimolar; vAKIII.K_aspp=0.017; real vAKIII.K_ADP millimolar; vAKIII.K_ADP=0.25; real vAKIII.K_iLys millimolar; vAKIII.K_iLys=0.391; real h_Lys dimensionless; h_Lys=2.8; real vAKIII.K_eq dimensionless; vAKIII.K_eq=0.00064; real V_max_AK_III flux; V_max_AK_III=299; // // Asp:time=((-1)*vAKI-vAKIII); // aspp:time=(vAKI+vAKIII-vASD); // ASA:time=(vASD-vHDH); // hs:time=(vHDH-vHK); // hsp:time=(vHK+vTS); // Thr:time=vTS; // ATP:time=((-1)*vAKI-vAKIII-vHK); // ADP:time=(vAKI+vAKIII+vHK); // NADPH:time=((-1)*vASD-vHDH); // NADP:time=(vASD+vHDH); // Pi:time=(vASD+vTS); // Lys:time=(0 flux); // vAKI=(V_max_AK_I*(Asp*ATP-aspp*ADP/vAKI.K_eq)/((vAKI.K_asp*(1+(Thr/vAKI.K_iThr)^h_Thr)/(1+(Thr/(vAKI.K_iThr*vAKI.alpha))^h_Thr)+aspp*vAKI.K_asp/vAKI.K_aspp+Asp)*(vAKI.K_ATP*(1+ADP/vAKI.K_ADP)+ATP))); // vASD=(V_max_ASD*(aspp*NADPH-ASA*NADP*Pi/vASD.K_eq)/((vASD.K_aspp*(1+ASA/vASD.K_ASA)*(1+Pi/K_Pi)+aspp)*(vASD.K_NADPH*(1+NADP/vASD.K_NADP)+NADPH))); // vHDH=(V_max_HDH*(ASA*NADPH-hs*NADP/vHDH.K_eq)/((1+(Thr/vHDH.K_iThr)^h)/(1+(Thr/(vHDH.alpha*vHDH.K_iThr))^h)*(vHDH.K_ASA+hs*vHDH.K_ASA/vHDH.K_hs+ASA)*(vHDH.K_NADPH*(1+NADP/vHDH.K_NADP)+NADPH))); // vHK=(V_max_HK*hs*ATP/((vHK.K_hs*(1+ATP/K_iATP)/(1+Thr/vHK.K_iThr)+hs)*(vHK.K_ATP*(1+hs/K_ihs)+ATP)*(1+Lys/vHK.K_iLys))); // vTS=(V_max_TS*hsp/(K_hsp+hsp)); // vAKIII=(V_max_AK_III*(Asp*ATP-aspp*ADP/vAKIII.K_eq)/((1+(Lys/vAKIII.K_iLys)^h_Lys)*(vAKIII.K_asp*(1+aspp/vAKIII.K_aspp)+Asp)*(vAKIII.K_ATP*(1+ADP/vAKIII.K_ADP)+ATP))); }