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THE OURNALF BIOLOGICALHEMISTRY0 992by Th e American Societyfor Biochemistryand Molecular Biology, Inc. Vol. 267,No. 5, ssue of February 15,pp. 3101-3105,1992Printed in U.S.A.

Systems Analysis of the Tricarboxylic Acid Cycle inDictyostelium discoideumI. THE BASIS FOR MODEL CONSTRUCTION*

(Received for publication, November 5 , 1990)

BarbaraE. Wright, MargaretH. Butler, and KathyR . AlbeFrom th e Division of Biological Sciences, U niversity of Montana, Missoulu, Montana 59812

A steady-state model of the tricarboxylic acid cyclewas constructed using a dynamicystems analysis com-puter program, METASIM. The model was based onradioactive tracer analyses which provided flux rela-tionshipsandcompartmentedmetaboliteconcentra-tions. Ten of the enzymes modeled were purified andcharacterizedrom Dictyosteliumdiscoideum. Al-thoughexperimentallydeterminedenzymemecha-nisms and constantswere used in the model, Vmax al-ues were found to be unreliable,.e. they did noteflectenzyme activity in vivo.This value was therefore cal-culated as the only unknown in each enzyme kineticequation and called Vvivo, o distinguish it from Vmaxdetermined in vitro.

An intriguing question for biochemists is the extent owhich enzyme activities, metabolite concentrations, kineticmechanisms and constantsdetermined in vitro apply in vivo.One approach to this roblem is to construct metabolic modelsthat incorporate such in vitro data and theno determine howwell the behavior of the model describes metabolism in theliving organism. This in turn can only be judged by thepredictive value of the model. Making a model match a givendata set does not necessarily indicate that it reflects reality;the model must be sufficiently realistic to have predictivevalue. When predictive value has been demonstrated, it isreasonable to conclude that the model parameters may ap-proximate these operative in vivo.In 1967 a simple metabolic model was constructed simulat-ing the glycogen cycle and saccharide end-product synthesisin Dictyostelium discoideum. Five assumptions (predictions)in thismodel were later demonstrated to be correct (1). Overthe years, about 40 predictions based on increasingly complexmodels of metabolism in this ystem have been substantiated,three unknowingly in other aboratories (1-17). The programused in the construction of these realistic models is calledMETASIM (18),which contains 27 different enzyme mecha-nisms; the user indicates he appropriate one or each reactionand supplies the kinetic constants. Other input data are theflux relationships and compartmented metabolite concentra-tions in the metabolic network. Most of the enzymes depictedin the models were isolated from Dictyostelium, purified andcharacterized using standard in vitro methods.In these models with demonstrated predictive value, Vmaxvalues could not be used, as theywere frequently found to be

*This work was upported by National Institutes of Health PublicHealth Service Grant AG03884.The costs of publication of this articlewere defrayed in part by the payment of page charges. This articlemust therefore be hereby marked advertisement in accordance with18U.S.C. Section 1734 solely to indicate th is fact.

artifacts (19-22) and to e incompatible with the other aram-eters in theenzyme kinetic expressions, namely, the rates ofthe reactions, metabolite concentrations, and kinetic con-stants. The values to replace Vmaxwere therefore calculatedfor each equation as the only unknown, assuming the otherparameters to be correct. These calculated values are calledVvivo.Reaction rates in vivo were determined in a number ofways and were very reliable. The ratesof individual reactionswere based on the rate f accumulation of counts in a roductknowing the specific radioactivity of the immediate precursor(5, 23, 24). These values were substantiated using a specificradioactivity curve-matching program (TFLUX (25)) t o sim-ulate data in which the specific radioactivity of many inter-mediates in the network was followed as a function of timeafter exposure to tracer (13, 14) or perturbing (2 ) levels of[4C]glucose. As hese analyses nvolved many interdependentmetabolites and reactions, they also provided informationregarding compartmented pools. For example, a difference inthe labeling patterns of UDP-glucose and glucose 1-phosphaterequired the existence of two pools of glucose 1-phosphate (2)(it hadlready been established tha t UDP-glucose was a singlepool (14)). Other studies directly demonstrated the locationof the two pools of hexose phosphates (13). Knowing totalsubst rate concentrations, these analyses gave the concentra-tions of the metabolite compartments. As most metabolitesare relatively stable, their total concentration can be deter-mined quite accurately. In comparing metabolite and enzymeconcentrations in seven different organisms, metabolite con-centrations were found to be more consistent, as might beexpected (26). K,,,and Ki alues are also relatively consistentand areoften similar for a given enzyme isolated from differ-ent organisms. For example, for the pyruvate dehydrogenasecomplex in Dictyostelium (27), Ascaris (28), and cauliflower(29), respectively, the K,,, values (mM) for pyruvate were 0.14,0.18, and 0.20; for CoA,0.008,0.005, and 0.007; for NAD,0.11, 0.01, and 0.12; the Ki values (mM) for NADH were 0.049,0.025, and 0.034; for CoA, 0.024, 0.062, and 0.013. For malatedehydrogenase in Dictyostelium (30), pig heart (31), mito-chondrial bovine heart (32), soluble bovine heart (32), andBacil lus sdti l is (32), respectively, the K , values (mM) formalate were 1.33,0.8,0.99,0.54, and 0.90; for NAD, 0.10,0.20,0.54, 0.20, and 0.4; for oxaloacetate 0.27, 0.04, 0.04, 0.05, and0.06; for NADH, 0.04, 0.02, 0.02, 0.04, and 0.03. The relativeconsistency of metabolite concentrations and kinetic con-stant s among different organisms suggested tha t these valueswere reliable as input data or metabolic models.In contrast to eaction rates, kinetic constants, metaboliteconcentrations and compartments, there are a number ofreasons to question the relevance of Vmax alues to enzymeactivity in intact cells. Cellular organization is destroyed inthe preparation of extracts, membrane-bound enzyme com-

3101


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3102 Model of Tricarboxylic Acid Cycle in Dictyostelium

FIG.1. A steady-state model ofthe citric acidcycle n D. discoi-deum. Encircled reactions are those forwhich the enzyme from D. iscoideumhas been kinetically characterized. Allmetabolite pools are intramitochondrial,as defined by Kelly et al. (37). See Ex-perimental Procedures for further de-tails. Glu, glutamate; 2KG, 2-ketoglutar-ate; SUC, uccinate; FUM, fumarate;MAL, malate; OAA, oxaloacetate; CZT,citrate; ASP, aspartate; ALA, alanine;PROT, protein; PYR, pyruvate; ACO,acetyl-coA.

plexes are disrupted; enzymesites bouna by product or inhib-itor in vivo (33, 34) maybecome reedandavailable tosubstrate on dilution in extracts; unknown inhibitors or ac-tivators maybe diluted,destroyed, orcreated; proteolyticinactivation may be initiated by extract preparation(19, 20);and inally,enzymeactivity is frequentlymeasuredunderoptimal rather than physiological conditions of pH , temper-ature, cofactor and protein concentration. As proteins, en-zymesmayplayrolesother than being catalysts. Proteinsmay be used as an energy source, especially under nutritionalstress. Because of the general vulnerability of most proteinsto proteolytic attack,excessive enzyme protein concentrationmay beessential to ensure adequate catalytic activityn timesof stress. Catalytically active enzymes have also been foundto serve structural roles 35). Regardless ofthe specific eventsoccurring in uiuo, treating VmaX s the unknown neachenzyme kinetic expression and calculating Vvivoresulted nmodels with predictive value. This approach was thereforeused to construct the model of the tricarboxylic acid cycle.

EXPERIMENTAL PROCEDURESIn this model (Fig. l ) , flux through the cycle was consistent with

O2 onsumption, net protein degradation (the energy source in thissystem), and NH, production (36, 37). Flux into the cycle (reactions21-26, Fig. 1)was based on an amino acid analysis of Dictyosteliurnprotein at three stages of differentiation (3). The percent concentra-tion of each amino acid in average protein was the same at each stage,indicating an even use of available protein, i.e. comparable oxida-tion rates of individual amino acids over the course of development.Knowing the pathways by which each amino acid is converted to oneor more cycle intermediates (3, 38), the flux of each amino acid intospecific intermediates could be calculated (37) and must sum to theflux through the cycle (reactions 21-26, Fig. 1).In a system using only amino acids as the source of cycle inter-mediates, more amino acids are converted to four- and five-carbonintermediates than to acetyl-coA. For the citrate synthase reactionTables 1, 3, 4, 5, and 6 are presented in miniprint at the end ofthis paper. Miniprint is easily read with the aid of astandard

magnifying glass. Full size photocopies are included in the microfilmedition of the Journal tha t is available from Waverly Press.

TABLE1A comparison of calculated enzyme activity in vivo, Vuiuo,nd V,,values fo r seven enzvmes of the tricarbonvlic acid cvcle

Enzvme V;. Ref.~ ~

Isocitrate DHb2-Ketoglutarate DCMalate DHMalic enzymeSuccinate DHCitrate synthasePvruvate DC

mM/min mM/min271.0 1.8 40

7,608.0 4.8 4177.8 196.003.08 8.6 393.15 45.028.23 1,071.03258.0 2.1 27

Converted to mM mitochondrial volume, using the conversionrelationships: 1mg of protein =1.4 mg of dry weight; pmol/min/mgdry weight X 150=mM packed cell volume n amoebae (44), and cell/mitochondrial volume is 1/5.DH, dehydrogenase.e DC, dehydrogenase complex.

to operate and maintain steady-state levels of cycle intermediates,the flux of acetyl-coA into the cycle must equal tha t of oxaloacetate.Therefore a pathway is required which converts excess four- orfive-carbon intermediates to acetyl-coA. The pathway for convertingtricarboxylic acid cycle intermediates to acetyl-coA involves malicenzyme. In this reaction, malate is decarboxylated to yield pyruvatewhich is in turn decarboxylated to form acetyl-coA via the pyruvatedehydrogenase complex. This pathway has been shown to occur inDictyostelium, and both of these enzymes have been purified andkinetically characterized (27, 39).essential to the cycle (Fig. 1 and Table I): 2-ketoglutarate dehydro-

We have purified and characterized seven of the nine enzymesgenase complex, succinate dehydrogenase, malate dehydrogenase,malic enzyme, pyruvate dehydrogenase complex, citrate synthase,and isocitrate dehydrogenase. These enzymes are listed in Table 2,together with their V,,, values and their calculated V,i, values. Twoof the most striking discrepancies between the V,i, and VmaXaluesare for the enzyme complexes, 2-ketoglutarate dehydrogenase com-plex and pyruvate dehydrogenase complex. As these complexes aremembrane bound, they dissociate during extract preparation, andhigher Vvivo ompared with VmaXalues might have been anticipated.deactivated form of the enzyme bound tightly to oxaloacetate (34),Most isolated preparations of succinate dehydrogenase containapreventing succinate from binding. As purification procedures can


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Model of Tricarboxylic Acid Cycle in Dictyostelium 3103activate the inactive form, V value 10-foldhigher than the V,,,value isno t surprising. The V,, and Vvivovalues for malate dehydro-genaseand malic enzyme are reasonably close, but there iso obviousexplanation for the differences in these valuesor isocitrate dehydro-genase or citrate synthase. It is of course possible that unknownactivators or inhibitors are present in uiuo. Calculated Vvivovaluescould include correction factorsor kinetic constants as well as forV, . However, evidence exists that kinetic constants used in thecarbohydrate models approximate those operative in vivo (see Dis-cussion).

RESULTSThe METASIM model shown in Fig. 1 was constructedbased on an original TFLUX analysis of the tricarboxylic acidcycle in D. discoideum (36, 37). This model is highly con-strained since many related intermediates were isolated andtheir interdependent specific radioactivities determined. Allsingle pools ncluded in the original TFLUX modelwereassumed to exist entirely within the mitochondrion. For thosemetabolites that existed in two or more pools, uch as malate,the pool external to the cycle was considered to be cytosolicand was eliminated from the present analyses. In these cases,the mitochondrial pool concentration predicted by the

TFLUX model was used ather than otal metabolite concen-tration. Theenzyme mechanisms and kinetic constants usedin the model are given in Tables 3 and 4.To consider intramitochondrial concentrations and fluxes,mitochondrial volume wasassumed to be 20%of the totalcellvolume (46). Cycle flux, determined from net protein degra-dation, or oxygen consumption (36, 37) was approximately0.4 mM/min based on total cell volume. Therefore, based onmitochondrial volume, cycle flux is 2 mM/min. Amino acidsserve asan energy source in his organism (3), and heconstant influx of carbon is balanced by the efflux of carbonthrough the generation of COz.A number of structural constraints exist on the fluxes in ametabolic pathway in steady state when metabolite concen-trations and fluxes are constant over time (3, 37). For eachmetabolite, the requirement tha t the input flux equals theoutput flux imposescertain constraints on the relative valuesof the fluxes (namely that the vector of steady-state fluxesmust lie in the null space of the stoichiometric matrix of themetabolic system). In this case, there are 23 net fluxes (de-scribed by26 reactions) and 13 variable metabolites; rankanalysis of the stoichiometry matrix confirms that there areno moiety conservation relationships among the metabolites,so the dimension of the null space is 10 (23 fluxes - 13metabolites); that is, there are only 10 independent fluxes,and the remaining 13 can be determined from these. Six ofthe independent fluxes are the input reactions from proteindegradation and were determined directly from experimentalmeasurements (3). That the reaction pairs 9 and 10, 14 and19, and 18 and 20 have zero net flux at the observed steadysta te accounts for a further three degrees of freedom. Thus,of the total 26 reactions, 13 can be specified. The 13 inde-pendent fluxes wereconsidered to be 9,10,14,16,18-26 (Fig.1).Table 5 shows the net reaction rates used in the steady-state tricarboxylic acid model compared with similar ratesfrom the TFLUXanalysis. The metabolite concentrations areshown in Table 6 and ere the same as thevalues determinedfrom the TFLUX analysis adjusted for mitochondrial volume(36, 37).Table 1gives the enzyme mechanisms and kinetic constantsdetermined in vitro for enzymes purified from D. discoideum.These data were used in the model (Table 3), supplemented(as required by the mechanisms) bysome assumed values

* D. Fell,personal communication.

whichcould not be obtained experimentally. A dead-endcompetitive inhibition mechanism (Table 4) rather than arapid equilibrium-ordered BiBi mechanism (Table 1) wasused for three enzymes (glutamate dehydrogenase, isocitratedehydrogenase, and citrate synthase) to include product in-hibitions which were physiologically significant (40, 43, 48).As discussed earlier, experimentally determined Vmax alueswere not used, but rather a calculated value called Vvivo Vl,V2 in Table 3) was used for maximal enzymatic activity inthese models. Flux and metabolite concentrations over thetime course of the simulation are shown in Table 6. Theconcentrations of NAD, NADH, and CoA were fixed timeconstants, taken from experimental measurements (45), andthe fixed input rates (reactions 21-26)were based on theconstant rate of net protein degradation and calculated ratesof conversion of individual amino acids to specific cycle nter-mediates (3,37).Over a 10-min simulation period the flux and metaboliteconcentrations vary less than 0.04%, indicating steady-stateconditions. The definition of steady state is discussed in thecompanion paper.

DISCUSSIONIn the model of the tricarboxylic acid cycle, flux was basedon 0 consumption, a TFLUX nalysis, the net rateof proteindegradation, and the rate of conversion of amino acids tospecific cyclentermediates. I n terms of mitochondrial volumethe rate of conversion of malate to pyruvate (reaction 6) was1.09 mM/min, and the ate of pyruvate formation from aminoacids (reaction 25) was 0.45 mM/min, giving a combined rateof 1.54 mM/min for reaction 8,which is catalyzed by pyruvatedehydrogenase. This rate was also checked independently invivo. The pyruvate dehydrogenase reaction in the slime mold,assayed in vitro using [l-4C]pyruvate and quantitating theevolution of 14C02, an be examined with virtually no inter-ference from other enzymatic reactions (49). Pyruvate car-boxylase, known o interfere with the pyruvate dehydrogenaseassay (38), has not been detected in D.discoideum, andglycolysis has been shown to play only a minor role. Signifi-cantly, the pyruvate dehydrogenase reaction assayed with[l-14C]pyruvate n crude extracts was completely dependentupon NAD, coenzyme A, and thiamine pyrophosphate, sug-gesting that pyruvate was converted to 14C02only via thereaction catalyzed by pyruvate dehydrogenase (27). In alllikelihood this is also true of the reaction measured in vivo.The in uivo rate of the reaction catalyzed by pyruvate dehy-drogenase was measured by exposing cells to [l-C]alanineand relating the rate of 14C0, evolution to thespecific radio-activity of the isolated [l-4C]pyruvate (49). The rate ob-tained, 1.65 mM/min, is in excellent agreement with the rateobtained using the other ypes of analyses summarized above.In he METASIM models of carbohydrate metabolismthere is evidence that many of the K,,,values used do reflectK , values operative in vivo. Perturbation studies have beencarried out in which Dictyostelium was exposed o glucose, Pi,uracil, or uridine, for example, and compared with the modelsperturbed by these same metabolites (1, 10, 11).These per-turbations resulted in changes in the levels of other metabo-lites, such as glucose 6-phosphate, UDP-glucose, glycogen andtrehalose, in both he models and Dictyostelium. The similar-ity of these effects indicate similar substrate-K,,,relationshipsin themodels and the organism. For example, glucose pertur-bation results in approximate 3-fold increases in glucose 6-phosphate and trehalose levels and less than a 2-fold increasein UDP-glucose levels (1, 11).The increased trehalose levelresults from the relationships between the K , values of tre-


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3104 Model of Tricarboxylic Acid Cycle inictyosteliumhalose-6-phosphate synthase for glucose 6-phosphate and 20. Wright, B. E., and Dahlberg, D. (1968) J . Bucteriol. 95,983-985the cell and in themodel.Ylic acid cyclemodel and the organism to tes t the many 23. Pannbacker, R. G. (1967) Biochemistry 6,1287-1293assumptions and predictions inherent in the model. Con- 24. Marshall, R., Sargent, D., and Wright, B. E. (1970) Biochemistrystraints on the modelwill also be examined, to determine if 9,3087-3094configuration, kinetic constants, and o on.

UDP-glucose and the concentrations of these substrates in 21. Gustafson, G.L., and Wright, 3- E. (1972) Crit Rev. Microbial.22. Gezelius, K., and Wright, B. E. (1965)J. Gen. Microbiol. 38,309-1,453-478Perturbation studies will be carried out with the tricarbox- 327

model behavior is affected by changes in enzyme mechanisms, 25. Sherwood, p., Kelly, p. J.9 Kelleher, J. K.9 and Wright, B. E.(1979) Comp. Prog. Biomed. 10 , 66-7426. Albe, K. R., Butler, M. H., and Wright, B. E. (1989) J . Theor.Acknowledgments-We would like to thank Dr. David Fell for hisconsiderations of our problems in meeting the requirements for thesteady state in these models and kindly analyzing our pathway forus. We would also extend thanks to the rganizers of the symposiumon metabolic control held in El Ciocco, Italy, in 1989 for providingus with a forum for presenting these ideas and interacting with otherresearchers in the field.

1.2.3.

4.5.6.7.8.9.

10.11.12.

REFERENCESWright, B. E., and Kelly, P. J. (1981) Curr. Top. Cell. Regul. 1 9 ,Wright, B. E., and Reimers, J. M. (1988) J. Biol. Chem. 2 6 3 ,Wright, B. E., and Butler, M. H. (1987) in Evolution and Longeu-

ity in Animals (Woodhead, A. D., and Thomson, K. H. , eds)pp. 111-122, Plenum Publishing Corp., New YorkWright, B. E., and Park, D. J. M. (1975) J . Biol. Chem. 2 5 0 ,Sargent, D., and Wright, B . E. (1971) J . Biol. Chem. 246,5340-Wilson, J. B., and Rutherford, C. L. (1978) J.Cell Physiol. 9 4 ,Wright, B. E. (1968)J. Cell Physiol. 7 2 , (Suppl. l ), 145-160Wright, B. E., and Dahlberg, D. (1967) Biochemistry 6 , 2074-Wright, B. E., and Marshall, R. (1971)J . Biol. Chem. 246,5335-Wright, B. E., Tai, A., and Killick, K. A. (1977) Eur. J . Biochem.Wright, B. E., Tai, A., Killick, K. A. , and Thomas, D. A. (1979)Wright, B. E. (1984)J. Theor. Biol. 110, 445-460

103-15814906-14912

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2079533974,217-225Arch. Biochem. Biophys. 192,489-499

13. Chiew, Y. Y., Reimers, J. M., and Wright, B. E. (1985) J. Biol.14. Wright, B . E., Thomas, D. A., and Ingalls, D. A. (1982) J. Biol.15. Emyanitoff, R. G., and Wright, B. E. (1979) J. Bucteriol. 140,16. Dimond, R. L., nd Loomis, W. F. (1976) J. Biol. Chem. 261 ,17. Dimond, R. L., arnsworth, P. A. , and Loomis, W. F. 1976) Deu.18. Park, D. J. M., and Wright, B. E. (1973) Comp. Prog. Biomed. 3 ,19. Wright, B. E. (1960) Proc. Natl. Acud. Sci. U . S. A . 4 6 , 798-803

Chem. 260,15352-15331Chem. 267,7587-75941008-10122680-2687Biol. 50,169-18110-26

27.28.29.30.

Biol. 143, 163-195Butler, M. H., Mell, G. P., and Wright, B. E. (1985) Curr. Top.Komuniecki, R., Komuniecki, P. R., and Saz, H. . (1979)Randall, D.D., Rubin, P. M., and Fenko, M. (1977) Biochim.Emyanitoff, R. G., and Kelly, P. J. (1982) J . Gen. M icrobiol. 128 ,

Cell. Regul. 26, 337-346Biochim. Biophys. Acta57 1, 1-11Biophys. Acta 48 6 , 336-3491767-177i31. Raval, D. N., and Wolfe, R. G. (1962) Biochemistry 1,263-26932. Thomas E. Barman (ed) (1969) Enzyme Handbook Springer-

33. Bloch, W., MacQuarrie, R. A., and Bernhard, S. A. (1971)J. Biol.34. Ackrell, B. A. C., Kearny, E. B., and Singer, T. P. (1978) Methods35. Wistow, G. J., Mulders, J. W. M., and de Jong, W. W. (1987)36. Kelly, P. J., Kelleher, J. K., and Wright, B. E. (1979) Biochem.37. Kelly, P . J., Kelleher, J. K., and Wright, B. E. (1979) Biochem.38. Palmer, T. N., and Sugden, M. C. (1983) Trends Biochem. Sci. 8,39. Kelleher, J. K., Kelly, P. J., and Wright, B. E. (1979)J . Bucteriol.40. Emyanitoff, R. G. (1982) Exp. Mycol. 6 , 274-28241. Heckert, L. L., Butler, M. H., Reimers, J. M., Albe, K. R., and42. Butler, M. H. (1989) Exp. Mycol. 13 , 294-29843. Porter, J. S., and Wright, B. E. (1977) Arch. Biochem. Biophys.44. Walsh, J. W., and Wright, B. E. (1978) J. Gen. M icrobiol. 108,45. Owen, T. G., and Hochachka, P. W. (1974) Biochem. J. 143 ,46. Srere, P. A. (1967) Science 158,936-93747. Wright, B. E., and Wasserman, M. E. (1964) Biochim. Biophys.48. Komuniecki, P. R., Detoma, F. J., and Wright, B. E. (1979)Abstracts of the Annual Meeting of the American Society ofMicrobiology, p. 10349. Butler, H.M., and Wright, B. E. (1989) Biochim. Biophys. Acta991,337-33950. Landridge, W. H. R., Komuniecki, P., and DeToma, F. J. (1977)Arch. Biochem. Biophys. 178,581-587

Verlag, New YorkChem. 246,780-790Enzymol. 5 3 , 466-483Nature 326,622-624J. 184,581-588J . 184,589-597161-162138,467

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Model of Tricarboxylic Acid Cycle in Dictyostelium 3105SUPPLEMENTAL MATERIAL TO: SYSTEMS ANALYSIS OF THE TRICARBOXYLIC ACID C YC LE

INDlrlYO SlE LIUM DlSCOlDEUM I . THE BASIS FOR HOOEL CONSTRUCTIONBarbara E. Wight,Margaret H. Butl er and Kathy R. Albe

TABLE 1ENZYMEMECHANISMS ND KIN ET IC CONSTANTSDETERWINED LH KLEQREACTIONNZYME K. (nM) K, (mnl ENZYMEECHANISHEFERENCE

1 GluDH G l u - 2 . 0 N H , = 3 . 0NAD = 0.2 NAOH - 0.025 Bii Rapid Equil lbriumrdered 502 2-KGDCKG - 1.0 NAOH - 0.018 Mul t i r i tein g Pong 41NAD - 0.07 SucCoA - 0.004 withP I - 0

CoA - 0.0023 SOH Suc - 0.22' Fum = 0.4 U" l un i 42

OM - 0.0035 MDH Hal = 1.33 NAD - 0.31NAD = 0.10 NADH - 0 04 Ir o Ordered BI Bi 30

OM - 0.276 ME Mal - 0 . 3 7NADP - 0.01 A l los te r icichae l l r -Menten 398 PDC P yr - 0.14 NADH = 0.049 M u l t i r i t ein g Pong w i t h 21CoA - 0.OOB ACO - 0.024P I - 0NAD = 0.11I 1 CS O M = 0.007apid Equilibrium Ordered 43ACO = 0 01 CoA = 0.11ii13 IracDH lrac - 0 13 I s m = 0.13 Rapi dqmllbrlumrdered 40NADH = 0 34 NAD - 0.34 BiiNAOH = 0.02I 5 AlpTA Asp = 0.46ZKG - 0.33 Ping Pong 48'81 Bi16 AlaTAla - 0.43 Ping Pang

2K G = 0.19 48'B1 81' O r l g i n l les t imate o f K was 0.1 mf Which w as used in heanalyzedmadel.' S e e also: Komrnunlecki. P R (1977) Ph.0. Dlrrertatian,U n i v e l s l t y o f MdslaChuIe tts tAmherrt.LEGEND: Ab bre via tla nr GluDH glutamateehydrogenase, Z~KGDC: 2-k etog luta ratedehydrogenase complex; SOH: succi nate ehydrogena se; ME: m11 c enzyme; MOH: malatedehydrogenase; PDC. pyruvateehydrogenase complex ; CS:cltrateynthase; IrocOH:1lOCltrdteehydrogenase, laTA: a l a n ~ n e rms ml na ie : ArpTA. asp artat e tranpamnse.

TABLE 4RATE' QUATIONSUSED IN TCA MIDEL

Unino lecula r Mars Act ionENZYMESODELED: C It ra te 1 -> Iso c? trate (12)': spartate,Oxaloacetate I (18):Oxaloacetate 1 -> Aspartate (20); Alanine -> Pyruvate ( 7 ) : Glutamate ~> succinate 1 ( 1 4 ) ;Succinate 1 -> Glutamate ( 1 9 ) : Oxaloacetate 1 -> Oxaloacetate 2 (17):Aspartate ->Oxaloacetate2 ( I O ) ; Oxaloacetate2 -> Aspartate (9).

Rate - K[A]

Dead-end C ornpetltlve nhi bltlonPlng Pong B i B iENZYMES MODELED: GlutamateDehydrogenase ( I ) ; Cl tr s te Synthase (11); I POCi t la teDehydrogenase13).

Rate - VI[A][B)/(KB[A]+WI(l.O+[~NHl/K~)[B~+[A][B])A l lo r tencMichae l l r -MentenENZYMESODELED: M al ic Enzyme (6).un iuo iENZYHESOOELED: Succinate Oehydrogenare (3); Fumarase ( 4 ) .Rate -Vx V2([Al-[Pl/KEP)/(KP x V2 + V 2[A I + VI[PI/KEP)

Rate - V l [ A l [ E ] / ( W I + [ A l ) ( K E P i [ E ] )

ENZYMESODELED: Malate ehydrogenase (5 )KP x KIP)P i " " D""" n, C...,Rate = V I X vZ([A][B] - [PI[PI/KEP)/DENOM

where OENOM - KB x V2[A1 + WI x VZ IB ) + V2[Al[B] + KP x VI[PI/KEQ + KP xVI[PI/KEP + VI[PI[PI/KEP + KP x VI IA I [P I / (K IA x KEPI + WI x V2[BI[Pl/KIPENZYHES OOELED: As partate rans aminare ( I S ) ; Alanine ransa ninare 16).

and rtea dy~rt ate nzyme ryitemr. John Yl l ey 8 Sans, New Yor k .' Taken from Segel, I.H. (1975) Enzyme Kl neti cr:Behav io r and analysis o f raprd quil ibrium

' KZ = K I B x KI C x KP/(KR x KIP)' Numbers ~n parentheses refer t o e a c t i o n s n Flgure I .

TABLE 5: NETEACTIONATESETERMINEDROMRACERXPERIMENTSCOHPAREO TO STEADY-STATE METASIH MODELREACTION'LUXES TFLUX Model ' METAS IM MOOEL

2.402.852.601.901.40I 902.10

InH/Mi"l0.152.412.772.851.761.092.002.000 04 + 19I8 + 20 0 0sp - > 0111' Hetabo l l te p o o lder rgnat lonrar eC o n l i f t e n twt h F l g u r e 1.' see reference 37; va lue r bared on iSIvmedmltochondrlal vo lume.

TABLE 6: FLUXND METABOLITEONCENTRATIONSIN STEADY-STATE MODEL T FIV E MINUTES

poolrarruming a m..ochandria to ce ll volume ra tlo of 1 5'Metaballte oncentratlonr ar e thosedstermnedb y K e l l y .et a1 . (36, 37 ) fa r mltochondrlal

wright_etal_systems analysis of TCA cycle1.pdf

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