wright_etal_systems analysis of TCA cycle2.pdf

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THE OURNALF BIOLOGICALHEMISTRY8 1992by The American Society or Biochemistry and MolecularBiology,Inc. Vol. 267, No. 5, Issue of February 15, p. 31069114,1992Printed in U.S .A .

Systems Analysis of the Tricarboxylic Acid Cycle nDictyostelium discoideum11. CONTROLANALYSIS*

(Received for publication, April 16,1991)

Kathy R . Albe and Barbara .WrightFrom the Diuision of Biological Sciences,University of Montana, Missoula, Montana 59812

A steady-state computer model of the tricarboxyliccycle in Dictyostelium diecoideumwas analyzed usingmetabolic control theory. The steady state had varia -tions of less than 0.04% over the ast half of the simu-lation for both metabolite concentrations and fluxes.Metabolite and flux control coefficients were deter-mined by varying enzymatic activities within 2% oftheir initial values and simulating the responses ofmetabolite concentrations and fluxes to these changes.Under these conditions, summation properties weremet for most metabolite and all flux control coeffi-cients. Maximum flux control coefficients were foundfor succinate dehydrogenase (0.35), malic enzyme(0.24), and malate dehydrogenase (-0.18). Compa-rable control was found for he reaction supplyingpyruvate (0.14) and for the sum of the input aminoacids (0.43), which serve as an energy source for D.discoideum. The time-dependent processes bywhich anew steady state was stablished were examined afterincreasing malic enzymeor malate dehydrogenase ac-tivities. This provided a method for an analysis of themechanisms by whichhe observed control coefficientswere generated.In addition, the effects of increasing the stimuliwithin 5-20% of the original enzyme activity wereexamined. Under these conditions, more typical of ex-perimental stimuli and measurable responses, the met-abolic model failed to return to steady state, and thussummation properties were not met. Whether truesteady states ever ccur or whether metabolic controltheory can be applied in vivo s discussed.

Many theoretical and experimental techniques have beenused to examine the control and regulation ofmetabolicpathways in living cells.Recently, systematic approaches havebeen developed for the analysis of complex metabolic net-works. Metabolic control theory (1-5), flux-oriented theory(6), nd biochemical systems theory (7 ) all propose a mathe-matical analysis of metabolic pathways. Mathematically, theycan be interrelated (8); differences occur in terminology,emphases, and mathematical generality. Because of its appar-ent simplicity in description and application and its use offamiliar biochemical terminology, metabolic control theory(MCT) has been the most widely applied. For these reasons,MCT has been used to analyze a steady-state tricarboxylic

* This work was supported 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 aduertisernent in accordance with18U.S.C. Section 1734 solely o indicate this fact.The abbreviation used is: MCT, metabolic control theory.

acid model developedn our laboratory (see companion paper).The data used in thismodel were collected fromictyosteliumdiscoideum and included both flux relationships based on anextensive analysis of tricarboxylic acid cycle flux using radio-active tracers and theharacteristics of enzymes isolated fromthe same organism and analyzed using standard in uitrotechniques. After changing enzymatic activities, the responsesof metabolite concentrations and fluxes occurring over timewere determined using a computer simulating program calledMETASIM. METASIM models, constructed using these ex-perimentally determined data, have not only reproduced asingle data set butalso have predicted the organisms in uiuoresponses to perturbations by exogenous metabolites and tomutations in the pathways (see companion paper). Thisanalysis of the tricarboxylic acid model hould not only enableus to examine theoretical questions about MCT but also topredict the in uiuo distribution of control.Control analysis defines two control coefficients that quan-tify the response of metabolite concentration or pathway fluxto changes in enzymatic activity of one of the enzymes in thepathway (2-5). The mathematical descriptions of these coef-ficients are as follows.

CM--=-v,- 61nM (metabolite control coefficient)6 Vi/V, 61nViC J --=-v; - 6Vi/Vi 6lnV,

These control coefficients are normalized, and thus wo sum-mation properties can be defined (3-5). Simply stated, thesum of the normalized effects of individually changing allenzyme activities ( V , =1,2,...n) n any metabolite concen-tration ( M ) s 0, and on pathway flux ( J ) s 1, .e.n2 cc=o

i-1

c CJ, =1i=1In addition to control coefficients, MCT defines other rela-tionships, called elasticities, derived from the properties ofthe isolated pathway enzymes. Connectivity properties de-scribe the relationship of elasticities to systemic control coef-ficients (3). Connectivity and summation properties are nec-essary for the calculation of control coefficients in experimen-tal systems in which it is impossible either to change allenzymatic activities independently or to measure all responsesof the system.MCT states that this analysis is applicable to any experi-mental or theoretical system that has a stable steady stateand in which enzymatic activities can be changed and sys-temic responses measured. To increase enzymatic activity,

3106


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Control Analys is of Tricarboxylic Acid Cycle in D. iscoideum 3107experimental biologists have added enzymes to crude extracts(9, IO), analyzed mutants with increased activity (11),andused variably expressible plasmids (12-14). However, prepa-ration of crude extracts destroys both microcompartmenta-tion and protein interactions which are known to occur inuiuo (15-18).As there is a very poor correlation betweenenzymatic activity in uitro and in uiuo, such experiments areunlikely to provide information about the regulation of thepathway in vivo (19). To decrease enzymatic activity, inves-tigators have used inhibitors (12, 20-24), mutants with de-creased enzymatic activity (25, 26), and variably expressibleplasmids (14). Of necessity, most of these techniques resultin large changes in enzymatic activity. When enzymatic ac-tivity a t a step in a pathway is greatly increased, response ofpathway flux to that enzyme decreases; that is, the enzymebecomes less rate controlling, and its lux control coefficientdecreases. It is also true that asnzymatic activity is decreasedat a particular step, thatenzyme becomes more rate control-ling, and its lux control coefficient increases. Our analysis ofthe tricarboxylic acid cycle is compatible with these observa-tions; that is, when only decreased enzymatic activity wasused in the calculation of flux control coefficients, each coef-ficient was overestimated, and thus the sums were greatertha n one (see Table 5 ) .This observation is generally not madeor discussed in papers dealing with experimentally analyzedpathways, as only a few coefficients are measurable, and theremaining coefficients are calculated from connectivity andsummation properties (3 , 27). This would imply that fluxcontrol coefficients determined in these analyses are alwaysover- or underestimated. Although these phenomena are gen-erally not acknowledged in experiments designed to measurecontrol, these issues have been discussed (14, 26, 28). Exper-imental measurements of control also depend upon the inuitro measurement of enzymatic activity. This procedure can-not accurately measure in uiuo enzymatic activity, as intra-cellular organization is disrupted, inhibitors or activators arelost, and the measurements of activity are generally doneunder ideal, rather than physiological conditions. The use ofrelative enzymatic activities also has serious experimentalproblems such as differences in both extraction and in acti-vation of pathway enzymes. What may be ideal assay condi-tions for the referent enzyme may not be for other pathwayenzymes and will generally differ from physiological condi-tions. Although such analyses claim to quantify control, asedon the above inherent problems in experimental measure-ments, they can at best be a relative and qualitative descrip-tion of the distribution of control n the native pathway,regardless of the quantities assigned to particular s teps in theprocess.

Control analysis has also been applied to theoretical con-structs of linear and branched pathways, cycles, loops, andmoiety-conserved substrates (29-33). These types of analysespredict the distribution of control, i.e. where and how controlwould be distributed. Paper experiments have also been con-structed to examine the molecular basis of dominance (34,35). These typesof analyses may give insight into the eneralstructure of control distribution in pathways although theycannot give specific information about controlof a particularpathway. As the METASIM model is a mathematicaldescrip-tion of the tricarboxylic acid cycle consisting of independentequations which define individually catalyzed fluxes (see com-panionpaper) an analysis of control using MCTcan beperformed. To elucidate the problems in applying MCT toexperimental systems and o examine model constraints,changes were made in the pecified enzymatic activities (Vvivo;

see companion paper) of each enzyme in the pathway and theresponses of the model simulated.METHODS~RESULTS

There are three ajor advantages to using computer modelsfor MCT analysis: 1)much smaller changes can be made andsmaller responses measured; 2) all enzymatic activities can bechanged independently; 3) all system responses can be meas-ured. Control analysis is based on differential changes, thusthe smaller the changes, the closer to theory. MCT alsorequires a stable steady state, which can only be determinedif all variables can be measured. The structure of the mito-chondrial model used for these analyses is shown in Fig. 2.The companion paper discusses the development and use ofthis model.In the unperturbed, steady-state model input amino acidequaled output COP,and the variation between 5 and 10 minof simulation was 0.02% or less for metabolite concentrationsand 0.04% or less for fluxes. This variation occurred in thefourth place of the values reported by the METASIM simu-lation and was probably the result of computer round-off errorin he calculation of metabolite concentration and fluxesrather than inherentnstability of the steady state. Thus, orpurposes of this analysis, the model was n steady tate. When1 or 2% changes in enzyme activities were made, most simu-lated values returned to new steady-state values, i.e. less than1% ariation between values at 5and 10 min of the simulation.However, several responses had a variation of 1%or greaterfor some of the changes in enzymatic activities (data notshown). Because the control analysis was performed 10 minafter the application of the stimulus, hese more unstablemetabolite concentrations, and flux responses were examinedby comparing the values at 9 and 10 min to determine theextent towhich a new steady state had been reached (Tables1 and 2). Fewer time-dependent variations were seen in fluxvalues than in metabolite concentrations. The most unstablemetabolite concentration was pyruvate, which showed maxi-mal concentration variations in allhe simulations examined.Because it was unlikely that pyruvate or acetyl-coA concen-trat ions had obtained new steady-state values after 10 min ofstimulation, the control coefficients calculated for these me-tabolites would not quanti tate control accurately.

Metabolite control Coefficients and flux control coefficientsare shown in Tables 3 and 4, respectively. These coefficientswere determined from changes in stimuli of 1 or 2% aboveand below the original steady-state value for enzymatic ac-tivities. As noted previously, pyruvate and acetyl-coA con-centrations did not return to new steady-state values. This isreflected by the deviation from the theoretical summation of0, -0.5, and -0.19, respectively (see Table 3).The summationof 2-ketoglutarates metabolite control coefficients alsoshowed a deviation from theory (0.13 uersus 0), but the basisfor this variant behavior was not obvious from the observedpercent variation n metabolite concentration (Table1).How-ever, the concentration of 2-ketoglutarate is considerablylower than pyruvate (0.01uersus 0.3 mM), and smaller varia-tions from steady state may be more significant to its calcu-lated metabolite control coefficients. These metabolite controlcoefficients should qualitatively reflect the distribution of

* Methods,Figs. 1 and 3, and Tables 1, 2, 4, and 8 are presentedin miniprint at the end of this paper. Miniprint is easily read withthe aidof a standardmagnifying glass. Full size photocopies areincluded in the microfilm edition of the Journal that is available fromWaverly Press.


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3108 Control Analysis of Tricarboxylic Acid Cycle in D . discoideum

FIG. 2. Steady-state model of thetricarboxylic acid cyclen D. diecoi-deum. The encircled reaction numbersare catalyzed by enzymes, which wereisolated from D. discoideum and kinet-ically characterized. All metabolite poolsare intramitochondrial as defined byKelly et al. (43,44). Abbreviations are asshown in the legend to Table 3.

TABLE11Control coefficients (C,") of metabolite response o changes in enzymatic activities

Control coefficients were calculated from metabolite concentrations determined after 10-min simulations inwhich enzyme activities were changed ? 2% of the original steady-state value (see "Results"). The procedure forthe calculation of the control coefficient is described in Figure 1.Glu DH, glutamate dehydrogenase;2-KGDC, 2-ketoglutarate dehydrogenase complex; SDH, succinate dehydrogenase; MDH, malate dehydrogenase; ME, malicenzyme; PDC, pyruvate dehydrogenase complex; CS, citrate synthase; Isoc DH, isocitrate dehydrogenase; AspTA,aspartate transaminase; AlaTA, alanine transaminase; DH, dehydrogenase; PROT, protein; OAA, oxaloacetate;ACO, acetyl-coA; Isoc, isocitrate; Pyr, pyruvate; Glu, glutamate; Asp, aspartate; Ala, alanine; CIT, citrate; 2KG,2-ketoglutarate; SUC, succinate; FUM, fumarate; MAL, malate.

Stimulus" OAAl OAA2CO Isoc Pyr Glu Asp Ala C I T l 2KG1 S U C lU M lC,M*

1. Glu DH3. SDH4. Fumarase 0 0.008 -0.012.003 -0.0330.003.011 -0.006 0 -0.0200.0120.505. MDH6. ME7. Ala+Pyr 0.088 0.028.56 0.065 1.700.0330.300.36 0.060 0.65.44.0828. PDC 0 -0.11.99 0.003 -0.17.0170.0380.020 0 0 -0.004 0

2. 2-KGDC 0.020 0.020 -0.070 0.008 -0.15 -0.010 -0.054 -0.035 0.008 0.12 0.084 0.018-0.040 -0.028 0.21 -0.003 0.55 -0.17 0.36 0.11 0 -0.77 0.13 0.0180.45 0.97 -1.96 0.52 -3.35 -1.29 1.58 -0.62 0.50 -2.51 -2.79 0.880.16 0.72 -4.30 0.16 -10.91 0.77 0.70 -1.15 0.16 -0.85 -0.41 -0.62-0.21 -0.98 5.86 -0.22 14.80 -1.04 -0.94 1.56 -0.21 1.17 0.55 -0.23

9. OAA2+Asp 0.0400.072.430.010.070.12.36.120.020.0200.0190.00710. Asp+OAA2 -0.040.072 -0.43 0.011 -1.08.120.370.12.0200.020.019 0.00811. cs -0.0481.370.63.0151.59 0.18 -0.540.18.0200.024.029.01212. CITl* soc 0 0 -0.005 0 -0.010 0 0 -0.006 -1.00 0 0.004 013. Isoc DH 0 0 -0.0051.03 0 0 0 -0.004 0 0 0 014. Glu+S U C l 0.080 0.120.30.0630.590.100.140.16.060.39.48.08215. AspTA16. AlaTA 0.040 0.048 -0.37 0.003 -0.98 0.15 -0.35 -0.076 0 -0.19 -0.10 -0.0070.008 0.068 -0.53 0.003 -1.38 -0.017 -0.016 0.068 0 0.053 0.039 0.00817. OAAl+OAA2 -0.94 0.092 -0.56 0.013 -1.41 0.15 -0.35 -0.15 0.020 -0.051 -0.006 -0.00718. Asp+OAAl 0.048 0.068 -0.38 0.010 -0.95 0.11 -0.34 -0.11 0.020 0 0.019 0.00819. SUCl+Glu -0.080 -0.12 0.30 -0.061 0.60 0.10 0.14 0.15 -0.060 -0.38 -0.48 -0.08220. OAAl +ASP -0.048 -0.068 0.38 -0.010 0.94 -0.11 0.34 0.10 -0.020 0 -0.019 -0.00721. PROT +Asp 0.056 0.22 -0.67 0.10 -1.43 0.18 0.58 -0.12 0.096 0.052 0.079 0.00822. PROT-ACO 0.12 -0.052 1.69 0.10 3.99 -0.033 -0.31 0.46 0.092 0.81 0.54 0.09823. PROT- S U C l 0.12 0.21 -0.71 0.085 -1.56 0.58 -0.15 -0.089 0.094 0.68 0.71 0.1224. PROT+ FUMl 0.040 0.088 -0.24 0.043 -0.48 0.090 0.016 -0.045 0.040 0.076 0.066 0.05825. PROT+ALA 0.068 -0.028 1.07 0.065 3.08 -0.017 -0.14 0.61 0.060 0.48 0.31 0.05526. PROT+GLU 0.080 0.14 -0.51 0.063 -1.16 0.59 -0.070 -0.006 0.060 0.44 0.43 0.068

ma110.0140.0090.800-0.86-0.390.0770-0.0090.0090.014000.07700.009-0.014-0.009-0.077-0.00900.0910.120.0540.0540.068

Sum 0.012 0.0440.1920.0010.503.0940.0210.079 0 0.126.089.063.046Stimulus, enzyme changed in activity; numbers refer t o reactions in Fig. 2.CIM,Metabolite control coefficient calculated from the response, M, to the timulus, i, whereM is the metaboliteconcentration response and i is the enzyme changed in activity.


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Control Analys is of Tricarboxylic AcidCycle inD. discoideum 3109control even for metabolite concentrations which failed toestablish new steady-state values over the time of the simu-lation.

The effect of each enzyme variation on the individual fluxesis shown in Table4; the theoretical summationof 1.0 is foundin all cases. Obviously, his information is important to ssesscontrol for each individual enzyme flux, but it gives littleinformation about he effect of changing particular enzymaticactivities on the pathway flux. By defining pathway flux asthe production of COz,either by reactions within the tricar-boxylic acid cycle, or by total COz generation, a compositeflux control coefficient can be calculated (Table 5). Fromthese coefficients, malate dehydrogenase, succinate dehydro-genase, and malic enzyme share themajority of control overtricarboxylic acid cycle flux for enzymes within the cycle. Thesupply of two-carbon unit s is important in maintaining cycleflux, thus input from alanine to pyruvate (reaction 7) andfrom protein degradation to alanine (reaction 25) had signif-icant flux control ( C A ~ ~pyr =0.14; Cpmt- 1~ =0.25). Sum-mation propertieswere met for these composite values as wellas for the individual fluxes, indicating that he observedvariations n fluxes or concentrations from steady state(Tables 1 and 2) were not significant with respect to thisanalysis. Another observation, consistent with obtaining the

TABLEVEffect of changing enzymaticactivityon COSproduction

There is no net COS production when glutamate is converted tosuccinate since succinate is converted to glutamate at an equal rate(reaction 14 =reaction 19). Flux control coefficients were calculatedfrom fluxes determinedafter 10-minute simulations in which enzymeactivities were changed +2% of the original, steady-state value (seeResults). The procedure for the calculation of control coefficientsis described in Figure 1. Abbreviations are as in Table 3.Stimulus C : e Y c e C o ~ b C:co2c

1. Glu DH 0.027 0.0203. SDH 0.0430.35 0.454. Fumarase 0 05. MDH -0.18 -0.156. ME 0.24 0.217. Ala+Pyr 0.14 0.118. PDC 0 09. OAA24Asp 0.009 010.sp +OAA2 -0.009 011. cs -0.011 012. CITl + soc 0 013. Isoc DH 0 014.lu +SUCl -0.023 0.00715.AspTA16.AlaTA -0.054 -0.0370.011 0.00717. OAAl +OAA2 -0.02018. Asp+OAAl -0.01119. SUCl +Glu -0.0090.023 -0.00320. OAAl +Asp -0.0070.009 0.00321. PROT4 sp 0.034 0.05422. PROT+ACO 0.19 0.08923. PROT4 UCl 0.031 0.05724. PROT4FUMl 0.018 0.02825. PROT+Ala 0.12 0.094

2. 2-KGDC 0.063

26. PROT+Glu +0.034 +0.041Sum 0.993 1.006~. - .a Stimulus: enzyme changed in activity; numbers refer o reactionsin Fig. 2.

COS, o stimulus, i, where J cycle CO, is the sum of the responses offluxes 2 and 13, and i is the enzyme changed in activity.COS,to stimulus, i, where J total CO, is defined as the sum of theresponses of fluxes 2, 6, 8, and 13, and i is defined as enzyme changedin activity.

b c eyd eCq .. ontrol coefficient calculated from the response,J cyclec CJtOtalCO 2: control coefficient calculated from the response,J total

theoreticalsummation values, is that opposite and equalreactions (9 and 10, 14 and 19, 18 and 20) have opposite andequal flux control coefficients (Tables 4 and 5). Selectedmetabolite control coefficients (Table 6 ) and all the Co n luxcontrol coefficients (Table 7) were calculated after changes inenzymatic activity of 5-20%. These control coefficients didnot meet summation properties. These differences betweenthe summation of the calculated control coefficients andtheory probably result from the failure of the simulations toestablish a new steady sta te a fter these relatively large per-turbations n enzymatic activities. Obvious deviations be-tween flux control coefficients calculated from small pertur-bations versus those calculated from larger perturbation arethose reported for malate dehydrogenase and malic enzyme.If these enzymatic activities were decreased 5-20%, thenpositive flux control coefficients were observed. If these en-zymatic activities were increased 5-20%, then negative fluxcontrol coefficients were observed (see TimeEvents andMechanisms in the Re-establishment of Steady-state in theMiniprint).

DISCUSSIONThe application of MCT assumes the establishment of anew, stable steady s tate after changing enzymatic activities.

The definition of steady state is that mass in equals mass out.However, experimental measurements of mass in and/or outmaybe impossible. For the tricarboxylic acid cycle in D.discoideum, input is amino acid from protein degradation, andoutput is Con. ince there are many other reactions in vivousing amino acids as substrates and producing COz, neithermass in nor mass out is unique to the ricarboxylic acid cycle.Experimentally, it is therefore impossible to measure mass inor out for this model directly, and indirect methods must beemployed (see companion paper). Thus, determination ofsteady state in vivo will depend upon the variables which canbe measured, the sensitivity and specificity of the assays used,and upon the time at which the measurements are made. Toillustrate the problem in choosing the variables to be meas-ured, consider the METASIM model in which net mass inequaled net mass out before and after perturbation. If thestability of the steady state, after erturbation, were based onoxaloacetate concentrations, then all simulations resulted instable steady states. However, if the stability of the samesimulations were based on pyruvate concentrations, then noneof the simulations returned to a stable steadystate. By anal-ogy, in experimental systems in which mass in and/or outmay not be measurable and only a selected number of metab-olite concentrations can be determined, i t would be nearlyimpossible to establish clearly the existence of a stablesteadystate. In an explicit mathematical description of a pathway,such as this METASIM model, the stability of the steady-sta te depends on the precision of the estimation method, thenumber of significant figures reported for metabolite concen-trations and fluxes, and the buffering and feedback present.In experimental systems, variation n values of 0.1% aredifficult, if not impossible, to quantify but are reported by theMETASIM model. Most metabolite concentrations and fluxesin the METASIM model did establish new steady-state valuesas demonstrated by obtaining theoretical values for summa-tions properties. Although the model failed to return toteadystate after arge perturbations, the in vivo system may estab-lish a new quasi-steady sta te afteruch perturbations, as thereis considerably more buffering of metabolite concentrationsand more complexity of enzymatic reactions than can beusefully analyzed in the METASIM model.However, theinherent experimental difficulties both in changing parame-


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3110 Control Analysis of Tricarboxylic Acid Cycle in D. iscoideumTABLEVI

Selected m etabolite control coefficients Ci") using larger chnnges n enzymatic activityStimulus' Change intimulus (0.80-0.95)" Change intimulus (1.05-1.30)bOAAl Ism ASD CITl MALlAA l Isoc ASD CITl MALl

1. GluDH3. SDH4. Fumarase5. MDH6. ME8. PDC7. Ala +Pyr9. OAA2 +Asp10. Asp +OAA211. cs12 . CITl+soc13. Isoc DH14. Glu +SUCl15.AspTA16.AlaTA17. OAAl +OAA218. Asp -+ OAAl19. SUCl+ Glu20. OAAl +Asp21. PROT+Asp22. PROT+ACO23. PROT +SUCl24. PROT+FUMl25. PROT+Ala26. PROT+Glu

2. 2-KGDC 0.021-0.0271.000.0070.700.014-0.13-0.069

-3.19

0.068-1.410.00300.110.0420.0640.0980.064-0.11-0.0600.18-0.100.170.059-0.0540.14Sum -2.41

00.0100.650.0030.430.110.0660.002-0.0130.0200.0410-1.050.0580.0050.0050.0370.032-0.052-0.0110.0910.110.0820.0290.0730.0620.79

CzM-0.0470.411.64

0.0100.14-1.53-0.27-0.0480.34-0.34-0.6500-0.13-0.32-0.024-0.41-0.330.160.300.53-0.30-0.110.015-0.15-0.065

-1.18

0.009-0.0020.630.0040.410.110.0640.002-0.0140.0210.038-1.0000.0560.0030.0050.0370.033-0.053-0.0120.0870.100.0780.0280.0700.0580.76

0.0120.0100.950.003-0.65-0.220.0780.002-0.0110.0120.023000.075-0.0050.011-0.0070.024-0.072-0.01000.100.0970.0400.0580.0700.69

0.030-0.0260.790.0051.95-1.000.042-0.093-0.0820.081-1.34000.130.0520.0650.0940.072-0.12-0.0720.26-0.0260.190.079-0.0240.161.22

0.013-0.0030.300.004-0.026-0.670.0660-0.0240.0140.0200-1.040.06000.0040.0220.015-0.066-0.0210.100.0600.0750.0380.0420.060

-0.96

CZM-0.0680.331.25

0.0071.06-0.014-0.34-0.0310.41-0.40-0.49-0.0030-0.18-0.380-0.33-0.370.140.370.63-0.24-0.140.022-0.12-0.0681.04

0.013-0.0030.280.002-0.026-0.650.0610.002-0.0240.0150.017-1.0000.0570.0020.0020.0170.014-0.064-0.0200.100.0560.0740.0350.0410.057

-0.94

0.0180.0060.440.004-0.95-0.810.0740-0.0140.0110.019000.080-0.0060.004-0.0090.013-0.084-0.015-0.0030.0560.0920.0510.0360.070

-0.92a Enzyme activity is changed to (0.80,0.85,0.90, 0.93, or 0.95) X original steady-state value.*Enzyme activity is changed to (1.05, 1.07, 1.10, 1.15, 1.20, or 1.30) x original steady-state value.Stimulus: enzyme changed in activity; number refer to reactions in Fig. 2.

ters andmeasuring variables in uiuo make the application andsignificance of MCT analysis questionable.

Control analysis of realistic and predictive metabolicmodels may provide a useful tool for examining questionsabout applying MCT as well as for assessing control in uiuo.In a metabolicmodel all parameters are explicitly stated;independent and specific changes in these parameters canbemade; and very small changes in parameters, both increasingand decreasing around the operating point, can be made andsmall responses measured. In Dictyostelium major controlpoints within the tricarboxylic acid cycle were identified atreactions catalyzed by malate dehydrogenase, succinate de-hydrogenase, and malic enzyme (Table 5 ) . Citrate synthase,commonly thought to be a rate-controlling enzyme in thetricarboxylic acid cycle, was found to exert minor control inthis system. The rest of the control was distributed amongthe input fluxes from alanine to pyruvate and from proteindegradation. The sum (ZfZzl C of the input from proteinwas 0.43, with the majority from reaction 25 (CJ,Z5 =0.25).

The supply of C-2 fragments becomes important n D .discoideum as more four- and five-carbon tricarboxylic acidcycle intermediates are formed from amino acid degradation(reactions 21 + 23 + 24 + 26) = 1.09) than two-carbonfragments (reactions (22 + 25) = 0.91). To overcome thisimbalance in precursors, an anaplerotic pathway (providingacetate to thecycle) is formed by malic enzymeand pyruvatedehydrogenase complex. Malate, as the branchpoint metabo-lite, can serve either as aprecursor for oxaloacetate or can bedecarboxylated o form pyruvate. Since malate dehydrogenaseand malic enzyme re a t this key branchpoint, it is reasonableto expect, although not obvious that control a t this pointwould be a key feature in Dictyostelium.

Canela et al. (45) onstructed a model of the tricarboxylicacid cycle in muscle and used MCT to analyze control. Thismodelwas primarily theoretical and lacked the extensiveexperimental data used in our model of the tricarboxylic acidcycle in D. discoideum. However, they also found that varia-tions at their branchpoint metabolite, fumarate, resulted inchanges in he distribution of control and that succinatedehydrogenase had major control (0.19-0.39), depending uponthe conditions of analysis. Citrate synthase also had a largecontrol coefficient, but there was no anaplerotic pathway foracetate synthesis as found in D. iscoideum.

Although Dictyostelium is an unusual organism, other or-ganisms used as experimental systems do give support forsome of the results of our analysis. Succinate dehydrogenasewas identified as a major control site in tricarboxylic acidcycle flux in rat brain damaged by cold-induced edema; innormal brain this was not the case (46). Succinate dehydro-genasemay also play a role in respiratory control in themitochondrion since i t is a linkage point between the tricar-boxylic acid cycle and proton flux (23). The control exertedby citrate synthase was studied extensively using a variablyexpressible plasmid in Escherichia coli (14). Citrate synthasewas a major control point if the bacterium were grown onacetate whereas i t exerted only minor control if the bacteriumwere grown on glucose. This suggested that citrate synthaseserved as a ranchpoint regulator when twocarbon units weresupplied; basically the enzyme provided a shunt for acetateeither to degradation via the tricarboxylic acid cycle or tolipid synthesis (14).Predicting Flux Response fromEnzymeParameters-Ifthere were a simple way of predicting the relative size of thecontrol coefficients from familiar enzyme parameters rather


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Control Analysi s of Tricarboxyliccid Cycle in D. discoideum 3111TABLE I1

Flux control coefficients (C using larger changes in enzymaticactivityFlux control coefficients were calculated from fluxes determ inedafter ten min ute simulations, a s previously described (see Figure 1).Abbreviations are as in Table .

Chaneen timulusChaneen timulus

1. Glu DH3. S D H4. Fumarase5. M DH6. M E

2. 2-KGDC

7. Ala + yr8. PD C9. O AA2 + Asp10. As p3 OAA211. cs12. C I T l+soc13. Isoc DH14. Glu + U C l15. AspTA16. AlaTA17. OAAl +OAA218. Asp +OAAl19. S U C l +Glu20. OAAl +Asp21. P R O T +Asp22. P R O T +ACO23. P R O T ".*S U C l24. P R O T "*F U M l25. P R O T +Ala26. P R O T "*GluSu m

0.0230.0680.420.0020.280.530.14-0.0010.010-0.005-0.00500-0.012-0.0460.020-0.013

-0.0040.0200.0090.0360.210.0370.0160.130.0441.91

0.0170.0470.560.0030.230.480.1100.00400.005000.0150.01500.0030.0510.110.0540.0220.110.0511.84

-0.031-0.006-0.008

0.0340.0540.180.001-0.37-0.520.14-0.0020.006-0.014-0.01500-0.023-0.058

0.011-0.019-0.0130.0120.0050.0250.120.0120.0180.0780.028-0.31

0.0260.0360.240.002-0.32-0.420.11-0.0020-0.007-0.006000.009-0.0400.008-0.012-0.006-0.017-0.0010.0480.0290.0360.0260.0640.039

-0.16"Enzym e activitychanged to (0.80, 0.85, 0.90, 0.93, or 0.95) X'Enzym e activity changed to (1.05, 1.07, 1.10, 1.15, 1.20, or 1.30)

Stimulus: enzyme changed in activity; umbers refer to reactionsC;lcyc'eC02:lux control coefficient as defined in Ta ble 5.

e C?ta1C02: lux control coefficient as defined in Tab le 5.

original steady -state value.X original steady-s tate value.in Fig. 2.

th an having to calculate un famil iar e last ic i t ies, M CT wouldbe m ore widely used experimentally. Atkin son (47) attem ptedsuch an analysis, assuming mass act ionnzyme kinetics. Th istype of analysis was used for the tricarboxylic acid model,relating Vv,v,an d flux. However, it did not pred ict th e meas-ured control coefficients. In the prese nt study , an analy siss imi la r to tha tof A tkinson was done, assum ing that enzymekinetics followed the Michae lis-Menten equation. This ki-net ic equation is frequently sed as a fi rst s tep in the xperi-mental analysis of an enzyme to determine an apparentK,.From this analy sis th e following correlations were f ou nd 1)if S / K , 2 1, then 2 5 V/JI and 0.5 5 Cy 5 1.0; 2) if S /K , 2 a n d CU J


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3112 Control Analysis of Tricarboxylic Acid Cycle in D . discoideum14. Walsh, K., an d Koshland, D. E., r . (1985) roc. Natl. Acad. Sci.15. Albe, K.R., Butler, M. H., and Wright, B. E. (1989)J.Theor.16. Keleti, T., and Ovadi, J. (1988)Curr. Top. Cell. Regul. 29, 1-3317. Clarke, F. M., and Masters, C. J. (1975)Biochim. B ioplzys. Acta18. Welch, G. R. (ed) (1985)Organized Multienzyme Systems Cata-lytic Properties, Academic Press, Orland o, FL19.Wright, B. E., nd Albe, K. R. (1990) n Control of MetabolicProcesses (Cornish-Bo wden, A., an d Cardenas, M . L., eds)NATO AS1 Series, pp. 317-328,Plenu m Publishing Corp., NewYork20. Groen, A. D. , Wanders, R. J. A., Westerhoff, H. V. , Van derMeer, R., and T ager, J. M. (1982) . Biol. Chem. 257, 2754-275721. Kholondenko, B., Zilinskiene, V., Borutaik, V., Ivanoviene, L.,Toleikis, A., and Praskevicius, A. (1987) EB S Lett. 223,247-25022. Rigoulet, M., Guerin, B., a nd De nis, M. (1987) ur . J. Biochem.23. Brand, M. D., Hafne r, R. P., an d Brown, G. C. (1988) iochem.24. Petronilli, V., Azzone, G. F., an d Pietrobo n, D. (1988)Biochim.25. Middleton, R. J., and Kacser, H. (1983)Genetics 105,633-65026. Dykhuizen, D. E., ean, A. M., and Hartl , D. L. (1987)Genetics27. Kacser, H., and Porteous, J. W. (1987) rends Biol. Sci. 12, 5-28. Barrett, J. (1988) arasitology 97,355-36229. Hofmeyr, J. H. S.(1986) a b s 2,5-11

U.. . 82,3577-3581Biol. 143,163-195

381,37-46

168,275-279J.265,535-539Biophys. Acta 932,306-324

115,25-3114

30. Cascante, M., Franco, R., and Canela, E. . (1989)Math. Biosci.31. Cascante, M., Franco, R., and Canela, E. . (1989)Math. Biosci.94,271-28894,289-31032. Sauro, H. M., Small, J. R., and Fell, D. A. (1982) ur. J.Biochem.33. Hofmevr. J. H. S.. Kacser. H.. an d van der Merwe. K. J. (1986)166,215-221

94,289-31032. Sauro, H. M., Small, J. R., and Fell, D. A. (1982) ur. J.Biochem.33. Hofmevr. J. H. S.. Kacser. H.. an d van der Merwe. K. J. (1986)166,215-221Eur."J.'Biochem.156,631-641 . .34. Kacser, H., and B urns, J. A. (1981) enetics 97,639-66635. Keightley, P. D., and K acser, H. (1987) enetics 117,319-32936. Sherwoo d, P., Kelly, P., Kelleher, J. K., and W right, B. E. 1979)37. Wright, B. E., and Kelly, P. J. (1981)Curr. Top . Cell. Regul. 19,38. Wright, B. E. (1984) .Theor. Biol. 110,445-46039. Wright, B. E., nd Reimers, J. M. (1988) . Biol. Chern. 163,40. Park, D. J. M., and Wright, B. E. (1973) omp. Prog. Biomed.3,41. Wright, B. E., Ta i, A., an d Killick, K. A. (1977) ur . J. Biochem.42. Wright, B. E., and B utler, M. H. (1987) n Evolution and hngeu-i t y in Animals (Woodhead, A. D. , and Tom son, K. H., eds) pp.43. Kelly, P. J., Kelleher, J. K., and Wright, B. E. (1979)Biochem.111-122, lenum Publishing Corp., New York44. Kelly, P. J. , Kelleher, J. K., and W right, B. E. (1979) iochem.45. Canela, E. ., Ginesla, I., and Franco, R. (1987) rch. Biochem.46. Rigoulet, M., Averet, N., Mazed, J. P., Guerin, B., and CoLadon,F. (1988) iochim. Biophys. Acta932,116-12347. Atkinson, D. E. 1990)n Control of Metabolic Processes (Cornish-Bowden, A., and Cardenas, M. L., eds) NATO AS1 Series, pp.3-11,Plenum Publishing Corp., New York

Comp. Prog. Biomed. 10,66-74103-158

14906-1491210-2674,217-225

J. 184, 581-588J. 184,589-597Biophys.264, 42-155

SUPPLEMENT AL AT ERI AL TO SYST EMS ANALYSI S OF T HE RI CARBO XYLI C CI DC Y C L E I NOItTYOSTELIUnQlXQlRM: 11. CO NT RO L ANALYSI SKathy R. Albe and Barbara E. YrlghtTABLE I: PCRCt l l , ' "L R I IT IO H IN "LTLIBOLITI CONCINTWIIBN BETYttN T.9 Lho 1-11 "IWUTtl

values generated after a te n m i n u t e rlmulation.F I G URE 1: C A L C U L A T I O N OF CO NT RO L CO EF F I CI ENT S

I n stimulus. The slope of ihe line. fltted by-l i n e ~e g r e l s l o n , i s the control caefflcient.

0

0


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Control Analysis of Tricarboxylic Acid Cycle in D . discoideum 3113Since the P a t i o s determined rom he basic Michaelis -Menten equation were unambiguous andapparently predictive of C the more complex equations Used i n the nvldel were reduced to t h i sform. To develop hese educed quations, allmetabolites except S,md fl ux were considare4t o be constant, an d new va l u er fe r Km and V #ere calculated.Th isanalysis was app l ied to a11the enzymes r n Table 8 and the new ratlor, an d V"/Ji, were analyzed a s p r ed i c t ~ r ~ fcp and cF7'". As withAtkins on's approach, neitherof heseapploacheIpredicted he s i z e

af the cont ro l coeff ic ient


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3114 Control Analysisof Tricarboxylic AcidCycle in D. discoideumF I G U R E 3: PERCENT CHANGE I N CONCENTRATION OR FLUX IN RESPONSE TO IN C R EU SEDMALATE DEHYDROGENASE OR I U L I C ENZYME UCTIVITY'

3c 30

FIGUREC. Response t o MOH: PYR ( e ) : FIGURE 30: Response to HOH:K O (0); X16 (i).esponse to H i 2KGI (t): RX Z (0); XE (A). RerponrePYR ( A I ; ACO (A); RX16 (GI . to ME: ZKGI ( 4 : RX 2 (0); XE ( 0 ) .

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