Kinetic modeling can describe in vivo glycolysis in Entamoeba histolytica Emma Saavedra 1 , Alvaro Marı ´n-Herna ´ ndez 1 , Rusely Encalada 1 , Alfonso Olivos 2 , Guillermo Mendoza-Herna ´ ndez 3 and Rafael Moreno-Sa ´ nchez 1 1 Departamento de Bioquı ´ mica, Instituto Nacional de Cardiologı ´ a, Me ´ xico DF, Me ´ xico 2 Departamento de Medicina Experimental, Facultad de Medicina, Universidad Nacional Auto ´ noma de Me ´ xico, Me ´ xico DF, Me ´ xico 3 Departamento de Bioquı ´ mica, Facultad de Medicina, Universidad Nacional Auto ´ noma de Me ´ xico, Me ´ xico DF, Me ´ xico Keywords ATPases; drug targeting; hexokinase; phosphoglycerate mutase Correspondence E. Saavedra, Departamento de Bioquı ´ mica, Instituto Nacional de Cardiologı ´ a, Juan Badiano no. 1 Col. Seccio ´ n XVI, CP 14080, Tlalpan, Me ´ xico DF, Me ´ xico Fax: +5255 5573 0926 Tel: +5255 5573 2911 ext. 1422 E-mail: emma_saavedra2002@yahoo.com Note The mathematical model described here has been submitted to the Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/ database/saavedra/index.html free of charge (Received 7 November 2006, revised 13 July 2007, accepted 27 July 2007) doi:10.1111/j.1742-4658.2007.06012.x Glycolysis in the human parasite Entamoeba histolytica is characterized by the absence of cooperative modulation and the prevalence of pyrophosphate- dependent (over ATP-dependent) enzymes. To determine the flux-control dis- tribution of glycolysis and understand its underlying control mechanisms, a kinetic model of the pathway was constructed by using the software gepasi. The model was based on the kinetic parameters determined in the purified recombinant enzymes, and the enzyme activities, and steady-state fluxes and metabolite concentrations determined in amoebal trophozoites. The model predicted, with a high degree of accuracy, the flux and metabolite concentra- tions found in trophozoites, but only when the pyrophosphate concentration was held constant; at variable pyrophosphate, the model was not able to completely account for the ATP production ⁄ consumption balance, indicating the importance of the pyrophosphate homeostasis for amoebal glycolysis. Control analysis by the model revealed that hexokinase exerted the highest flux control (73%), as a result of its low cellular activity and strong AMP inhibition. 3-Phosphoglycerate mutase also exhibited significant flux control (65%) whereas the other pathway enzymes showed little or no control. The control of the ATP concentration was also mainly exerted by ATP consum- ing processes and 3-phosphoglycerate mutase and hexokinase (in the produc- ing block). The model also indicated that, in order to diminish the amoebal glycolytic flux by 50%, it was required to decrease hexokinase or 3-phospho- glycerate mutase by 24% and 55%, respectively, or by 18% for both enzymes. By contrast, to attain the same reduction in flux by inhibiting the pyrophosphate-dependent enzymes pyrophosphate-phosphofructokinase and pyruvate phosphate dikinase, they should be decreased > 70%. On the basis of metabolic control analysis, steps whose inhibition would have stronger negative effects on the energy metabolism of this parasite were identified, thus becoming alternative targets for drug design. Abbreviations ADH, alcohol dehydrogenase; AK, adenylate kinase; ALDO, fructose 1,6-bisphosphate aldolase; AldDH, aldehyde dehydrogenase; ATP-PFK, ATP-dependent phosphofructokinase; DHAP, dihydroxyacetone phosphate; ENO, enolase; EtOH, ethanol; F6P, fructose 6-phosphate; F(1,6)P 2 , fructose 1,6-bisphosphate; G6P, glucose 6-phosphate; G6PDH, glucose 6-phosphate dehydrogenase; G3P, glyceraldehyde 3-phosphate; GAPDH, glyceraldehyde 3-phosphate dehydrogenase; Gly3PDH, glycerol 3-phosphate dehydrogenase; HK, hexokinase; HPI, hexose 6-phosphate isomerase; HXT, hexose transporter; LDH, lactate dehydrogenase; MCA, metabolic control analysis; PGAM, 3-phosphoglycerate mutase; PGK, phosphoglycerate kinase; PGM, phosphoglucomutase; 3PGDH, 3-phosphoglycerate dehydrogenase; PEP, phosphoenolpyruvate; 2PG, 2-phosphoglycerate; 3PG, 3-phosphoglycerate; PPi, pyrophosphate; PPi-PFK, pyrophosphate-dependent phosphofructokinase; PPP, pentose phosphate pathway; PFOR, pyruvate:ferredoxin oxidoreductase; PFOR-AldDH, lumped reaction of PFOR and AldDH; PPDK, pyruvate phosphate dikinase; PYK, pyruvate kinase; TPI, triosephosphate isomerase. 4922 FEBS Journal 274 (2007) 4922–4940 ª 2007 The Authors Journal compilation ª 2007 FEBS The protist parasite Entamoeba histolytica is the causa- tive agent of human amoebiasis. Approximately one billion people are currently at risk of acquiring the dis- ease; the parasite causes severe illness in 48 million people each year and the number of annual deaths is in the range 40 000–100 000 [1,2]. Metronidazole ther- apy to control the disease is relatively effective; how- ever, in 40–60% of treated patients, the microorganism persists in the intestinal lumen, generating parasite car- rier states [3]. Recent reports describe the induction in vitro of E. histolytica resistant strains to this drug [4,5]. If clinical resistance of E. histolytica to metroni- dazole becomes prevalent, there is no alternative drug still available. The search for better drugs is a continu- ous process and further scientific research to under- stand parasite biology and host–parasite interactions is required to develop more effective treatment. Trophozoites of E. histolytica lack functional mito- chondria and have neither Krebs cycle, nor oxidative phosphorylation enzyme activities; thus, glycolysis is the only pathway able to generate ATP for cellular work [6–8]. In terms of regulation of glycolysis, the amoebal pathway diverges in two important aspects from that of the human host: First, it has the enzymes pyrophosphate-dependent phosphofructokinase (PPi- PFK) [9,10] and pyruvate phosphate dikinase (PPDK) [11,12], which catalyze reversible reactions under physi- ological conditions and are not subjected to allosteric regulation as their mammalian counterparts ATP- dependent phosphofructokinase (ATP-PFK) and pyru- vate kinase (PYK), respectively. In mammalian cells, ATP-PFK and PYK catalyze irreversible reactions under physiological conditions; these enzymes also dis- play cooperative modulation by several physiological metabolites and, together with hexokinase (HK) and glucose transporter, have been identified as the main flux-controlling steps of glycolysis in some human cell types [13–16]. Although ATP-PFK and PYK activities have also been detected in E. histolytica [17,18], their activities in amoebal extracts are low in comparison to their PPi-dependent counterparts and probably do not significantly contribute to the total glycolytic flux. Sec- ond, like the human glucokinase (HK IV), amoebal HK is not inhibited by its product glucose 6-phosphate (G6P) [19]; instead, AMP and ADP are potent inhibitors of the amoebal HK at physiological concentrations [19,20]. Other relevant differences of the amoebal glucose catabolism are the presence of a metal-dependent class II fructose 1,6-bisphosphate aldolase (ALDO) and a 2,3-bisphosphoglycerate-independent 3-phospho- glycerate mutase (PGAM), which have no homologues with the enzymes present in human cells [21]. More- over, pyruvate is converted to acetyl-CoA by pyru- vate:ferredoxin oxidoreductase (PFOR) instead of a pyruvate dehydrogenase complex; and acetyl-CoA is further metabolized to ethanol (EtOH) and acetate [6,7]. The differences found in amoebal glycolytic enzymes in comparison to those of its host suggest that these enzymes might be appropriate drug targets for thera- peutic intervention of this energetically important pathway in the parasite [22,23]. However, it should be initially established whether the proposed target enzymes display high control on both the glycolytic flux and ATP concentration in amoebas and low con- trol in the host pathway. If a difference in the control distribution is found in the parasite versus host, then the specific inhibition of the parasite’s enzymes with the highest control may lead to a successful perturba- tion of the parasite energy metabolism and growth. Despite glycolysis being a pathway present in all cells, subtle differences in glycolytic enzymes in, for example, parasite versus host or tumor versus normal cells, have been the basis in the search for drugs that affect prin- cipally the pathologic cells with minor effects on the normal cells. Metabolic control analysis (MCA) [24] provides the tools to infer the prospects of decreasing a pathway flux by inhibiting any individual enzyme. MCA allows to quantitatively determining the degree of control that a given enzyme (Ei) exerts over the pathway flux (J), namely the flux-control coefficient (C J Ei ). C J Ei is a value that represents the impact on flux of infinitely small changes in an enzyme activity by factors such as exter- nal inhibition or decreased expression. An enzyme with a C J Ei ¼ 1 means that the enzyme might indeed be the only rate-limiting step of the pathway. To date, how- ever, MCA studies have shown that there are no rate- limiting steps; instead, the flux control of a given pathway is distributed among different enzymes [24]. The summation theorem of MCA states that the sum of the C J Ei of all pathway steps is equal to one. This may include steps from other pathways (such as branches or end-product consuming processes) as long as they are linked by a metabolite or enzyme. Conse- quently, some pathway steps may have C J Ei values greater than one whereas those of branching steps have negative values, but the summation of all C J Ei has to be unity [24]. Metabolic modeling (i.e. in silico biology) uses the kinetic parameters of the complete set of enzymes belonging to a pathway (preferentially measured from the same source and under the same experimental con- ditions) to build kinetic models that can predict the system behavior. In this sense, kinetic modeling is a E. Saavedra et al. Modeling Entamoeba glycolysis FEBS Journal 274 (2007) 4922–4940 ª 2007 The Authors Journal compilation ª 2007 FEBS 4923 useful tool to establish predictions about which, why, by how much and under what conditions one enzyme exerts control over the pathway flux. Kinetic models have been constructed for glycolysis from erythrocytes [25], rat heart [15], the slime-mold Dictyostelium discoideum [26], the parasite Hymenolepis diminuta [27], potato [28], the human parasite Trypano- soma brucei [29–31], and Saccharomyces cerevisiae [32,33]. Until 2004, the kinetic properties of most of the amoebal glycolytic enzymes were scarce; however, we recently reported the kinetic characterization of the ten recombinant E. histolytica glycolytic enzymes from internal glucose to pyruvate under conditions that resemble those of the amoebal trophozoites [21]. In the present study, a kinetic model of amoebal glycolysis was constructed by using the kinetic properties of these ten enzymes [21] and their V m values for the forward and reverse reactions determined in cellular extracts. By fixing the PPi concentration, the model was able to reach stable steady states under a variety of near phys- iological conditions, thus allowing the estimation of the flux-control, concentration-control and elasticity coefficients for each enzyme. With this strategy, it was possible to quantitatively identify the main flux-con- trolling enzymes of the amoebal glycolysis, as well as the underlying biochemical mechanisms determining why some enzymes exert high control and others do not. The mathematical model described here has been submitted to the Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem. sun.ac.za/database/saavedra/index.html free of charge. Results Glycolytic flux, enzyme activities and intermediary concentrations in vivo Glycolytic flux was measured as EtOH production in amoebas incubated in the presence of 10 mm glucose and a representative time-course is shown in Fig. 1. The experimentally determined rate of flux was calcu- lated by considering that 1 · 10 6 amoebal cells corre- spond to 2 ± 0.8 mg of total protein (n ¼ 4). This glycolytic flux value was six- to ten-fold higher than the recalculated value previously reported by Montalvo et al. [34] in bacteria-grown amoebas under anaerobic conditions at 37 °C after 1 h in the presence of 2.5 mm glucose (3–6 nmol EtOHÆmin )1 Æmg protein )1 ; for calcu- lations, see Experimental procedures). These two amoebal flux values were low in comparison with the reported glycolytic fluxes displayed under anaerobic conditions by yeast (500 nmol EtOHÆmin )1 Æmg pro- tein )1 ) [32] or T. brucei (71 nmol pyruvateÆmin )1 Æ mg protein )1 ) [29], but similar to the glycolytic flux determined in some tumor cell lines (21–32 nmol lactateÆmin )1 Æmg protein )1 ) [35]. The maximal activity values for the glycolytic enzymes (Table 1) were evaluated in at least three cel- lular extracts obtained from different cultures of amoe- bal cells. These activities were determined under the same experimental conditions of buffer, temperature (37 °C) and physiological pH values (pH 6.0 and 7.0) used for the characterization of the pure enzymes [21]. For the reactions from hexose 6-phosphate isomer- ase (HPI) to PPDK, the activities were determined in the forward and reverse reactions (Table 1). ATP-PFK and PYK activities (Table 1) were also evaluated; how- ever, their activities were less than 10% of those displayed by PPi-PFK and PPDK. Therefore, these parallel reactions were not included in the kinetic model. The steps following PPDK are PFOR, aldehyde (AldDH) and alcohol (ADH) dehydrogenases (Fig. 2). PFOR activity in the amoebal HM1:IMSS strain used in the present study has not yet been determined. In our hands, AldDH activity was difficult to detect with acetyl-CoA as substrate and could only be determined in the reverse reaction. Both, NADH- or NADPH- dependent ADHs displayed almost the same activity using acetaldehyde as substrate. Notably, the reported activities for these ADHs in 200:NIH strain (6.9 and 0.96 UÆmg )1 , respectively) [36] were one order of mag- nitude higher than those displayed in Table 1. 100806040200 120 0.0 0.5 1.0 1.5 2.0 2.5 3.0 µmoles etoh / 10 6 cells Incubation time (min) Fig. 1. Time-course of EtOH production by E. histolytica trophozo- ites. Amoebas were incubated at 35 °C in NaCl ⁄ P i buffer at pH 7.4 in the presence of 10 m M glucose. At the indicated times, aliquots were withdrawn and mixed with perchloric acid as described in the Experimental procedures. EtOH was determined enzymatically with ADH. The plot shown is a representative experiment with tripli- cates. The solid line represents the fitting of the experimental points to a Hill equation using MICROCAL ORIGIN, version 5.0; this fit- ting has no mechanistic meaning. Modeling Entamoeba glycolysis E. Saavedra et al. 4924 FEBS Journal 274 (2007) 4922–4940 ª 2007 The Authors Journal compilation ª 2007 FEBS The V m value for ATP-consuming processes (ATP- ases) was higher (Table 1) than the estimated rate of ATP production by glycolysis, suggesting kinetic modulation of ATPases by the products ADP and Pi. NAD(P)H-consuming activity (DHases) was mea- sured by following the oxidation of the coenzymes after adding the amoebal extract (Table 1); however, the actual activity was probably underestimated because most DHases require a second substrate for activity. The adenylate kinase (AK) activity was measured in both directions, ATP ⁄ AMP production or 2ADP production; however, the specificity of the assay using extract samples could not be directly ascribed to this reaction (see Experimental proce- dures). The activities of some branches of amoebal glycoly- sis were explored. It is well documented that amoebas contain large amounts of glycogen as the main carbo- hydrate storage (Table 2) [37]. Therefore, glycogen metabolism (synthesis and degradation) is an active branch of the first section of glycolysis at the level of G6P. Indeed, a high phosphoglucomutase (PGM) activity in the direction of G6P production (glycogen- olysis) was determined (Table 1). Recently, the activity of 3-phosphoglycerate dehy- drogenase (3PGDH) involved in the synthesis of serine was described in E. histolytica [38]. In the direction of 3PG oxidation under our assay conditions, this activity was below the limit of detection in amoebal extracts (Table 1). The oxidative section of pentose phosphate pathway (PPP) is probably absent in E. histolytica because no G6P dehydrogenase (G6PDH) activity has been detected [6,7]. Moreover, after exhaustive experimental retesting, we were unable to detect G6PDH activity in the soluble fraction of amoebal extracts (Table 1); in addition, a gene coding G6PDH could not be identi- fied in the genome sequence database [39]. In amoebas, ribose 5-phosphate is synthesized from the glycolytic intermediaries fructose 6-phosphate (F6P) and glycer- aldehyde 3-phosphate (G3P) in a series of reactions catalyzed by PPi-PFK, aldolase and transketolase [40]. However, the flux through this modified PPP has not been explored in the parasite. Table 1. Specific activity of glycolytic enzymes determined in amoebal clarified extracts [mU · (mg protein) )1 ]. Values in parenthesis indicate the number of individual clarified extracts assayed. NA, not applicable; ND, not detected; NM, not measured. Enzyme Forward reaction Reverse reaction pH 7.0 pH 6.0 pH 7.0 pH 6.0 HK 200 ± 32 (5) 95 ± 18 (4) NA NA HPI 489 (2) 233 (2) 451 ± 48 (4) 206 ± 26 (4) PPi-PFK 479 ± 165 (6) 213 ± 35 (5) 612 346 ATP-PFK 37 ± 22 (5) 1.4 ± 0.4 (3) NA NA ALDO (–Co 2+ ) 57 (2) 0 (3) NM NM ALDO (+Co 2+ ) a 591 ± 78 (3) 160 ± 24 (3) 804 284 TPI 7235 4366 21 780 ± 7400 (4) 6098 ± 3000 (6) GAPDH 576 ± 77 (6) 405 ± 46 (5) 3968 3680 PGK 12 107 ± 3500 (4) 3182 ± 1350 (4) 1675 1742 PGAM 115 ± 51 (3) 116 ± 37 (3) 49 104 ENO 672 ± 41 (5) 508 ± 93 (5) 108 103 PPDK 341 ± 119 (4) 304 ± 62 (5) 4.5 19 PYK [+F(1,6)P 2 ] 32 ± 16 (5) 28 ± 15 (5) NA NA AldDH NM NM 74 NM ADH (NADH) 176 171 14 7.6 ADH (NADPH) 199 202 NM NM ATPases 149 (2) 122 (2) NM NM DHases (NADH) 10 ± 2 (3 7 ± 2 (3) NM NM DHases (NADPH) 25 ± 5 (3) 26 ± 6 (3) NM NM 3PGDH ND ND NM 26.6 b AK – c – c – c – c PGM NM NM 867 312 G6PDH ND ND NA NA Gly3PDH ND ND ND ND Alanine transaminase NM NM ND ND a The concentration of CoCl 2 was 0.2 mM. b Values reported by Ali et al. [38] at pH 6.5 and 25 °C. c No reliable determination (see Experimen- tal procedures). E. Saavedra et al. Modeling Entamoeba glycolysis FEBS Journal 274 (2007) 4922–4940 ª 2007 The Authors Journal compilation ª 2007 FEBS 4925 In agreement with Reeves and Lobelle-Rich [41], NAD + -dependent glycerol 3-phosphate dehydrogenase (Gly3PDH) activity in the soluble fraction of amoebal clarified extracts tested under different experimental conditions was below the limit of detection (Table 1; see Experimental procedures). However, putative Gly3PDH and glycerol kinase genes have been identified in the E. histolytica genome sequence database [8], which sug- gests the presence of glycerol metabolism in the parasite. Alternatively, triglyceride synthesis might initiate from dihydroxyacetone phosphate (DHAP) instead of Gly3P as described for several mammalian cells [42]. Alanine transaminase activity in the direction of pyru- vate synthesis was below the limit of detection (Table 1). However, a putative gene codifying for this enzyme has also been identified in the amoebal genome [8]. Glycolytic intermediary concentrations (Table 2) were determined in perchloric acid extracts after incu- bating trophozoites for 1 h in the presence of 10 mm glucose. Although after 1 h the steady-state glycolytic flux was about to end (Fig. 1), it allowed the detection of metabolites whose concentration was low [fructose 1,6-biphosphate, F(1,6)P 2 , G3P, pyruvate]. Model properties The kinetic model of E. histolytica glycolysis was built by using the computer software gepasi, version 3.3, PA i PGAM + P F6P Gluc F1,6P 2 DHAP G3P HK ALDO PPi-PFK HPI TPI G6P 2ADP ATPAMP AK ATP ADP ATPases NADH NAD + DHases PAAT MP + PPi PPi synthesis ADP ATP i Pi PP glycogen synthesis 2PG 1,3BPG 3PG PEP PGK PPDK GAPDH ENO PGAM + NADH NAD PAT ADP ATP + Pi AMP + PPi etoh pyr PFOR-AldDH acald ADH NAD + NADH NAD + NADH 3POHpyr NAD + NADH 3PGDH glycogen ATP ADP + PPi glycogen degradation Pi Fig. 2. Pathway reactions included in the kinetic model of E. histolytica glycolysis. Dotted boxes represent the reactions that are branches of the main pathway. The PFOR and AldDH reactions were lumped into one reaction (PFOR-AldDH). 1,3 BPG, 1,3-bisphosphoglycerate; acald, acetalde- hyde; ATPases; ATP consuming activities; DHases; NAD(P)H consuming activities; PPi synthesis, ATP consuming activities that produce AMP and PPi; 3POHpyr, 3-phos- phohydroxypyruvate; pyr, pyruvate. Modeling Entamoeba glycolysis E. Saavedra et al. 4926 FEBS Journal 274 (2007) 4922–4940 ª 2007 The Authors Journal compilation ª 2007 FEBS for metabolic modeling [43]. A scheme of the pathway reactions considered is shown in Fig. 2. Table S1A in the Supplementary Material displays the model reac- tions as written in gepasi, whereas Table S1B summa- rizes the kinetic parameters values incorporated in the model. The detailed rate equations are described in the Experimental procedures. The model included the K m values for substrates and products for the reactions from HK to PPDK, which were previously reported by our group at pH 6.0 [21]. The V m values present in the parasite in the forward and reverse directions, also determined at pH 6.0 (Table 1), were used. These reactions, including that of HK, were considered as reversible. The activity used for ALDO was that determined in the presence of saturating Co 2+ , because, at the total concentration of the heavy metals Co 2+ ,Zn 2+ and Cu 2+ found in amoebas (Table 2), this enzyme is expected to be fully activated [21]. The last glycolytic steps from pyruvate to EtOH cat- alyzed by PFOR, AldDH and ADH involve the oxida- tion of NADH. Because there is little kinetic information on E. histolytica PFOR and AldDH, these reactions were lumped in a reversible bisubstrate reac- tion involving NADH oxidation, with its V m value adjusted around 1 UÆmg )1 as reported for PFOR activ- ity determined in amoebal 200:NIH strain [36]. Some kinetic data for amoebal NAD(P)H-ADHs has been described [44]. These reactions were included as an irreversible bisubstrate reaction, also involving NADH oxidation, and using as V m the sum of the determined NADH and NADPH-ADH activities (Table 2). In addition, the kinetic model required a reversible, gen- eral NADH consumption reaction (DHases) for bal- ancing the pool of oxidized and reduced pyridine nucleotides. Cellular ATP consuming (ADP generating) processes (e.g. cellular work, ion ATPases) were included in the model as ATPases reaction; its rate equation was irre- versible mass-action with a fitted rate constant. Entamoeba histolytica lacks cytosolic pyrophosphatases and relies on PPi as phosphate donor in several meta- bolic reactions [6,7]; therefore, the most probable PPi supply comes from biosynthetic processes that also consume ATP (e.g. DNA and protein synthesis). In the kinetic model, this PPi supply was explicitly repre- sented as an ATP-consuming reaction that produces AMP and PPi (PPi synthesis). The AK reaction was included to maintain the balance in the adenine-nucleo- tide pool; its rate equation was dependent on the equilibrium constant. To simulate a glycolytic pathway that closer resem- bles that occurring within the parasite, three glycolytic branches (glycogen synthesis, glycogen degradation and serine synthesis) were included in the model; in their absence, nonphysiological hexose- and triose- phosphate concentrations were attained. The glycogen synthesis branch was modeled as an irreversible mass-action reaction that consumes G6P and ATP to produce glycogen, ADP and PPi (an additional source of PPi to that of PPi synthesis); the glycogen degradation branch was also modeled as an irreversible mass-action reaction (Fig. 2). There is high PGM activity (Table 1) but the fluxes through these branches have not yet been studied in amoebas. By introducing the PGM V m values of 0.3 and 0.87 UÆmg )1 cellular protein determined at pH 6.0 and 7.0, respectively, as the glycogen synthe- sis rate constant (Table 1), severe diminution of all glycolytic intermediaries to micromolar levels and one order of magnitude lower glycolytic flux were observed. Therefore, the glycogen synthesis and gly- cogen degradation rate constants were fitted (1.5 and 0.1 nmol min )1 Æmg protein )1 , respectively) to attain the physiological metabolite concentrations. Table 2. Glycolytic metabolite concentrations. NM, not measured; NS, not simulated; 1,3BPG, 1,3-bisphosphoglycerate. Metabolite (m M) Amoebal extracts Model G6P 6.2 ± 4.1 (5) 1.33 F6P 1.1 ± 0.5 (5) 0.88 F(1,6)P 2 0.43 ± 0.16 (4) 0.12 DHAP 1.15 ± 0.4 (3) 0.42 G3P 0.36 ± 0.09 (3) 0.21 1,3BPG NM 0.09 3PG < 0.28 (6) 0.45 2PG < 0.28 (6) 0.005 PEP < 0.28 (6) 0.0005 Pyruvate 0.92 ± 0.4 (6) 0.7 Acetaldehyde NM 0.02 ATP 5 ± 2 (5) 5.1 ADP 3.3 ± 1.2 (5) 2.4 AMP 1.6 ± 0.2 (3) 2.5 PPi 0.45 ± 0.1 (3) 0.45 (fixed) Pi 5.4 a 5 (fixed) NADH NM 0.08 NAD + 1.5 (2) 1.47 Glycogen 3400 b 1 (fixed) G1P 0.42 ± 0.15 (3) NS GTP 1.8 (2) NS GDP 0.7 (2) NS Co 2+ 0.023 (2) NS Zn 2+ 1.6 (2) NS Cu 2+ 0.12 (2) NS EtOH flux [nmolÆmin )1 Æ(mg cellular protein) )1 ] 39 ± 12 (5) 37 a Recalculated from [63]. b Glucose equivalents. E. Saavedra et al. Modeling Entamoeba glycolysis FEBS Journal 274 (2007) 4922–4940 ª 2007 The Authors Journal compilation ª 2007 FEBS 4927 The V m value of the 3PGDH branch for serine syn- thesis was adjusted within the same order of magnitude of the activity value reported by Ali et al. [38] to obtain the closest physiological concentration of 3PG (< 0.28 mm ; Table 2). In the absence of this reaction, 3PG elevated to 0.6 mm, which indicated a relevant role for this branch in the control of metabolite concentra- tions in the final reactions of the parasite’s glycolysis. The effect of other amoebal glycolytic branches on glycolytic flux and intermediary concentrations were explored: PPP, triglyceride synthesis, alanine transami- nase and malic enzyme. Because experimental data on fluxes through these other branches are not available, their rate constants were fitted; however, their inclu- sion in the model showed negligible effects on the intermediary concentrations, glycolytic flux and flux- control distribution (data not shown). The metabolites were initialized at the physiological concentrations displayed in Table 2. Fixed metabolite concentrations were: 5 mm glucose; 10 mm EtOH; 1mm glycogen; 1 mm 3-phosphohydroxypyruvate; 5mm Pi and 0.45 mm PPi. The conserved moieties were ATP + ADP + AMP ¼ 9.9 mm and NADH+ NAD + ¼ 1.55 mm. It is worth noting that, when including PPi concentration as a dynamic variable of the model, it was not possible to attain a physiological stable steady state because the PPi consumption by PPi-PFK and PPDK (and glycolytic ATP synthesis) was exceeded by the PPi synthesis rate. Due to the variety of PPi-generating biosynthetic processes, a true PPi synthesis rate is difficult to determine; moreover, further adjustments of the PPi synthesis rate constant compromised the physiological values of metabolites and fluxes. Thus, these modeling results indicate the importance of defining the PPi metabolism in the para- site because only the absence of cytoplasmic pyrophos- phatases [6,7] has been characterized, but participating enzymes and their rate equations and kinetic parame- ters have not been described. The present central model does not include the hexose transport reaction because there are a lack of data regarding kinetic parameters and difficulties in deter- mining the actual activity in the absence of glucose phosphorylation. However, the inclusion of the glucose transport may have an impact on the control distribu- tion [30,32] and therefore the effects of its incorporation in the model were evaluated by using the few available data (for the model, see supplementary Doc S1). Steady-state properties of the kinetic model In most of the explored conditions the simulations reached an asymptotically stable steady state, indicat- ing that the kinetic simulation displays a hyperbolic pattern that is able to reach an asymptote. To validate the construction of the kinetic model described above, the metabolite concentrations and glycolytic flux, experimentally determined when the cells were under glycolytic steady-state conditions, were used as reference. The predicted glycolytic flux (37 nmol EtOHÆmin )1 Æmg protein )1 ) agreed with the values determined in amoebas (Table 2). Model simu- lations approached 0.2- to one-fold the level of the in vivo metabolite concentrations for G6P, F6P, F(1,6)P 2 , DHAP, G3P, 3PG, pyruvate, ATP, ADP and NAD + (Table 2). The model also predicted very low concentrations for 2-phosphoglycerate (2PG) and phosphoenolpyruvate (PEP), which are below the lim- its of detection of the experimental assays, but they were similar to the low values reported in other cells [35,45]. Significant deviation was attained for AMP, which was 1.6-fold higher than the physiological value (Table 2). Flux-control distribution Analysis of the enzyme activities at pH 6.0 as determined in amoebal clarified extracts (Table 1) and the modeled fluxes through the enzymes (Table 3) indicated that HK and PGAM were work- ing at 32–33% of their V m values and that these enzymes were working closer to saturation than the other pathway enzymes (see below). In consequence, the HK and PGAM elasticities were lower in com- parison with those of the other pathway enzymes (Table 3). The low elasticities determined their high flux-control coefficients (C J HK ¼ 0.73; C J PGAM ¼ 0.65; Table 3), indicating that HK and PGAM were indeed the main controlling steps of amoebal glyco- lysis. Other glycolytic enzymes displayed small but significant flux-control coefficients in the interval of 0.08–0.13 [PPi-PFK, ALDO, glyceraldehyde 3-phos- phate dehydrogenase (GAPDH), enolase (ENO), HPI; Table 3]. For reactions outside the pathway, the glycogen syn- thesis and 3PGDH reactions showed high control (C J glycogen synthesis ¼ –0.32; C J 3PGDH ¼ –0.18). Notoriously, glycogen synthesis mainly modulated the hexosephos- phate concentrations, with a stronger effect on the F(1,6)P 2 level. On the other hand, the flux through the 3PGDH reaction affected the 3PG and pyruvate con- centrations, and final EtOH flux. The glycogen degra- dation reaction displayed low flux control under these conditions; however, at low HK activities, this branch became important in supplying G6P for glycolysis. The model predictions indicated that the ATP demand for Modeling Entamoeba glycolysis E. Saavedra et al. 4928 FEBS Journal 274 (2007) 4922–4940 ª 2007 The Authors Journal compilation ª 2007 FEBS cellular processes (cellular function represented by ATPases and PPi synthesis) exhibited high flux control over glycolysis (C J ATPases þ PPi synt ¼ –0.32; Table 3). PPi provides a link between glycolysis and anabolic path- ways and hence, variation in its steady-state concentra- tion (by modulating the PPi synthesis reaction) may affect the control distribution of glycolysis. The model predicted that most enzymes displayed over-capacity for the glycolytic flux (Tables 1 and 3) and, in particular, the fluxes through PPi-PFK and PPDK were 10% their forward V m values in amoebas. The steady-state intracellular amoebal concentrations of their respective substrates and products for these two enzymes (Table 2) were all above or around the K m values (Table S1B). Under these conditions, their elasticity coefficients were still relatively high (Table 3) and then they were not significant flux-controlling steps. Why an enzyme controls flux? The elasticity coefficient (e Ei X ) is defined as the ratio of relative change in the local rate of a pathway enzyme (Ei) to the relative change in a ligand, denoted as X (the concentration of an effector, e.g. substrates, products, inhibitors or activators) [24]. The connectivity theorem states that the sum of the flux-control coefficients of all pathway enzymes (Ei) affected by a common metabolite X and multiplied by their respective elasticity coeffi- cients towards X, is zero ð P i C J Ei e Ei X ¼ 0Þ [24]. The phy- siological significance of the connectivity theorem is easily visualized when considering that an enzyme satu- rated by its substrate cannot further increase its rate (it is working at maximal capacity or under V m conditions, and its elasticity is near zero), thus establishing a con- straint to the pathway flux; therefore, such an enzyme displays high flux-control coefficient. Table 3. Fluxes, elasticity coefficients for substrates (e Ei S ) and products (e Ei P ) and flux-control coefficients (C J Ei ) of the kinetic model. Enzyme Flux (nmolÆmin )1 ) e Ei S e Ei P C J Ei HK 31.4 Gluc 0.12 G6P )0.0008 0.73 ATP 0.55 ADP )0.001 AMP )0.66 HPI 21.8 G6P 4.1 F6P )3.9 0.08 PPi-PFK 21.8 F6P 2.3 F(1,6)P 2 )1.9 0.13 PPi 2.3 Pi )2.0 ALDO 21.8 F(1,6)P 2 2.8 DHAP )2.6 0.09 G3P )2.4 TPI 21.8 DHAP 72 G3P )71 0.003 GAPDH 43.6 G3P 5.7 1,3BPG )5.5 0.08 NAD 5.6 NADH )5.5 PGK 43.6 1,3BPG 12.1 3PG )11.5 0.04 ADP 11.9 ATP )11.9 PGAM 37 3PG 0.74 2PG )0.11 0.65 ENO 37 2PG 0.94 PEP )0.01 0.08 PPDK 37 PEP 1.0 Pyruvate )0.65 0.0009 AMP 1.0 ATP )1.0 PPi 1.0 Pi )1.0 PFOR-AldDH 37 Pyruvate 0.62 Acetaldehyde )0.14 0.001 NADH 0.88 NAD )0.53 ADH 37 Acetaldehyde 0.91 0.0001 NADH 0.34 Glycogen synthesis 10 G6P 1.0 )0.32 ATP 1.0 Glycogen degradation 0.5 Glycogen 1.0 0.01 Pi 1.0 3PGDH 6.7 3PG 0.33 )0.18 NAD + 0.02 ATPases 10 ATP 1.0 )0.04 AK 4 ADP 6286 ATP )3142 0.0001 AMP )3142 PPi synthesis 33 ATP 1.0 )0.28 DHases 24 NAD+ 6.2 NADH )5.2 )0.08 E. Saavedra et al. Modeling Entamoeba glycolysis FEBS Journal 274 (2007) 4922–4940 ª 2007 The Authors Journal compilation ª 2007 FEBS 4929 The elasticity coefficients of the pathway enzymes for effectors are shown in Table 3. As expected for the high flux control displayed by HK, the values of its elasticity coefficients were the lowest among all the enzymes, with values of 0.12 and 0.55 for glucose and ATP, respectively. HK also exhibited low sensitivity towards its products G6P and ADP and modulator AMP. PGAM also showed relatively low elasticities towards 3PG and 2PG. As deducted from their low flux-control coefficients, the other pathway enzymes showed comparatively higher elasticity coefficients towards their substrates whereas their elasticities towards products displayed essentially similar values to those for the substrates but with a negative sign. Together, the results indicated that HK strongly flux-controlled amoebal glycolysis because of its low activity in amoebal extracts and because of the low sensitivity toward its substrates and AMP derived from saturation (Table 3). Due to the similar elasticity towards ATP and AMP, HK inhibition by AMP might have physiological significance because the enzyme is strongly inhibited by this metabolite with a K i value of 36 lm at pH 6.0 [21], a value three-fold lower than the K m for ATP (121 lm at pH 6.0) [21], and because the physiological AMP steady-state level (1.6 mm) is 44-fold higher than the K i AMP . Amoebal HK exhibits a mixed-type inhibition by AMP [21]; therefore, the influence of the competitive inhibitory component (effect on K m ATP ) might be not as determi- nant on the enzyme activity because physiological ATP concentration (5 mm; Table 2) might overcome this inhibition; however, the noncompetitive inhibitory component (effect on V m ) might still be relevant to modulate the HK activity. Concentration control coefficients Similarly to the flux-control distribution (Table 3), the control of the concentration of most glycolytic metab- olites mainly resided in HK, PGAM, glycogen synthe- sis, ATPases, PPi synthesis and 3PGDH reactions (Table 4). The pyruvate concentration was also signifi- cantly controlled by the lumped reaction of PFOR and AldDH (PFOR-AldDH) and DHases reactions. In turn, the controlling order for the ATP concentration was PPi synthesis > PGAM > glycogen synthe- sis % HK (Table 4). Variations to the HK rate expression The kinetic model was used to determine the effect of varying the HK activity on flux rate and flux-control distribution in an attempt to further understand the underlying mechanism by which this enzyme has high control on the flux. As described in the construction of the amoebal model, the HK equation was considered as a reversible Table 4. Concentration control coefficients obtained with the kinetic model. The values shown are the concentration control coefficients, for which the net sum gives approximately 0. TPI, PGK, glycogen degradation and AK reactions did not exert significant control on the metabo- lite concentrations and therefore they were not included. Enzyme Metabolite G6P F6P F(1,6)P 2 DHAP G3P 1,3BPG 3PG 2PG PEP Pyruvate Acetaldehyde ATP ADP AMP NADH NAD + HK 2.5 2.4 2.59 1.29 1.29 1.38 1.1 0.81 2.3 1.6 0.87 0.2 )0.07 )0.33 )0.17 – HPI 0.09 0.33 0.36 0.18 0.18 0.19 0.12 0.34 0.17 0.092 0.06 )0.098 – – PPi-PFK 0.15 0.13 0.61 0.3 0.3 0.33 0.2 0.15 0.58 0.29 0.16 0.1 )0.03 )0.17 – – ALDO 0.1 0.09 0.06 0.2 0.2 0.23 0.14 0.1 0.4 0.2 0.1 0.07 )0.02 )0.11 – – GAPDH 0.09 0.08 0.05 0.02 0.01 0.2 0.12 0.09 0.35 0.18 0.095 0.06 )0.02 )0.1 – – PGAM 0.79 0.69 0.55 0.2 0.2 0.31 )0.36 0.74 2.9 1.5 0.79 0.46 )0.16 )0.79 )0.2 0.01 ENO 0.09 0.08 0.06 0.02 0.02 0.04 – )0.98 0.33 0.17 0.09 0.05 )0.02 )0.09 – – PPDK – – – – – – – – )0.98 – – – – – – – PFOR-AldDH – – – – – – – – )1.0 )1.6 – – – – – – ADH – – – – – – – – – )0.25 )1.1 – – – – – Glycogen synthesis )1.36 )1.35 )1.5 )0.76 )0.8 )0.8 )0.49 )0.36 )1.4 )0.7 )0.38 )0.24 0.08 0.4 – – 3PGDH )0.3 )0.3 )0.37 )0.2 )0.2 )0.36 )0.27 )0.2 )0.7 )0.5 )0.25 )0.07 0.13 0.14 – ATPases )0.28 )0.29 )0.33 )0.17 )0.18 )0.18 – – )0.34 – – )0.09 0.03 0.15 – – PPi synthesis )1.8 )1.9 )2.14 )1.1 )1.1 )1.18 )0.42 )0.32 )2.2 )0.6 )0.33 )0.57 0.2 0.97 – – DHases )0.09 – – – – )0.2 )0.13 – )0.54 )0.46 )0.17 )0.06 – 0.1 0.2 )0.01 Modeling Entamoeba glycolysis E. Saavedra et al. 4930 FEBS Journal 274 (2007) 4922–4940 ª 2007 The Authors Journal compilation ª 2007 FEBS reaction because it has been previously documented that significant changes in the control structure of a pathway are attained by introducing reversibility in all pathway reactions, even in those with very large K eq values [46–48]. It should be remarked, however, that including reversibility in reactions with high K eq requires the fitting and some times the guessing of kinetic parameters that cannot be easily determined (K m for products, V m in the reverse reaction). Under near-physiological conditions, the HK reaction is quasi-irreversible due to its high K eq value (1.6– 3.9 · 10 2 ) [49]. Therefore, it was interesting to evaluate the effect of changing the rate equation of this step in the pathway behavior. The reversible HK rate equation with mixed inhibi- tion by AMP was replaced for an irreversible rate equation with mixed-type inhibition by AMP and competitive inhibition by ADP (which was previously demonstrated in studies with the purified enzyme) [21]. In comparison to the model with HK revers- ible reaction, this kinetic model predicted two orders of magnitude lower flux through HK, with a conco- mitant diminution in the glycolytic flux (1.1 nmol EtOHÆmin )1 Æmg cellular protein )1 ) and three orders of magnitude decrease in the intermediary con- centrations. Under these conditions, the glycogen deg- radation reaction was the main flux-control step (C J glycogen degradation ¼ 0.78). The cause for the drastic decreased in HK rate when using the irreversible equa- tion was that the AMP inhibition predominated because two orders of magnitude increase in the HK K i AMP value restored the flux and metabolite concen- trations values to those obtained when using the HK reversible equation. To further evaluate the contribu- tion of AMP inhibition to the HK flux-control coeffi- cient in the main model with HK reversible reaction, two conditions were explored. First, the inhibitory component of AMP was elimi- nated from the bireactant reversible reaction of HK (see Experimental procedures); in other words, K i AMP became very large. Under this condition, there was a 2.3-fold increase in the flux through HK, an increase in the glycolytic flux (58 nmol EtOHÆmin )1 ) and two- to four-fold increase in the intermediary concentra- tions. The HK reaction still retained the highest flux control. Second, using the HK reversible equation with mixed inhibition by AMP, the effect of varying the HK K i AMP value was examined (Fig. 3). The pathway flux was highly sensitive to variation in the HK K i AMP value. Under these conditions, the glycogen degrada- tion reaction gained flux control at the lowest HK K i AMP values. These results indicated that HK inhibition by AMP, in addition to modulating the activity of the enzyme, may also be a mechanism for regulating the pathway metabolite concentrations and flux-control distribution. Because no cooperative modulation has been detected in amoebal glycolytic enzymes, the AMP inhibition of HK appears to be the sole mechanism of direct trans- ference of information from outside (ATPases, PPi synthesis, glycogen synthesis) and the end (PPDK) to the initial part of the pathway. Consequently, the mod- ulation of the AMP concentration might be an addi- tional mechanism for controlling the glycolytic flux in this parasite. Enzyme titration for the identification of drug targets MCA of the kinetic model allows for the determina- tion of the flux-control coefficients of the pathway enzymes. In addition, the kinetic model is a helpful tool for predicting the pathway behavior when inhibi- tion of some enzymes is evaluated. If the model closely reproduces the in vivo behavior, then the metabolic modeling approach would be an adequate tool for iden- tifying the best drug targets in a metabolic pathway 0.016 0.020 0.024 0.028 0.032 0.036 0 20 40 60 80 100 % flux HK Ki AMP (mM) Fig. 3. Effect of varying the HK K i for AMP on glycolytic flux. An interval of 1–36 l M is reported for the K i AMP values of amoebal HKs, either native or recombinant, at the pH range of 6.0–8.5 [19– 21]. For these simulations, 100% glycolytic flux was 37 nmol EtOH ⁄ (minÆmg cellular protein )1 ). The b-values (i.e. the K m modifier in the interaction between glucose and AMP with the enzyme in the HK rate equation; see Experimental procedures) were 1 (line) and 1.5 (dashed). By contrast, changing the c-value (i.e. the K m modifier in the interaction between ATP and AMP with the enzyme) did not induce significant alteration of the K i AMP versus pathway flux plot (data not shown). E. Saavedra et al. Modeling Entamoeba glycolysis FEBS Journal 274 (2007) 4922–4940 ª 2007 The Authors Journal compilation ª 2007 FEBS 4931 [...]... Perez-Montfort R (2004) Kinetic mechanism and metabolic role of pyruvate phosphate dikinase from Entamoeba histolytica J Biol Chem 279, 54124– 54130 Supplementary material The following supplementary material is available online: Table S1 (A) E histolytica glycolysis model reactions as written in gepasi (B) Kinetic parameters used in the model 4940 Doc S1 Variations to the kinetic model Table S2 Flux-control... Determining and understanding the control of glycolysis in fastgrowth tumor cells Flux control by an over-expressed but strongly product-inhibited hexokinase FEBS J 273, 1975–1988 36 Lo H-S & Reeves RE (1978) Pyruvate to ethanol pathway in Entamoeba histolytica Biochem J 171, 225–230 37 Bakker-Grunwald T, Martin JB & Klein G (1995) Characterization of glycogen and amino acid pool of Entamoeba histolytica. .. values taken from the literature, which, in most cases, were determined under nonphysiological conditions In addition, the Km values for some products were only adjusted because they were not experimentally determined In the kinetic model described in the present work, the in uence of using Keq in the rate equations was eliminated by introducing the actual Vm FEBS Journal 274 (2007) 4922–4940 ª 2007 The... strategy for killing the parasites may be to simultaneously target the two main controlling enzymes, HK and PGAM With this strategy, the model predicted that glycolytic flux and ATP concentration can be drastically decreased by only inhibiting 18% these two enzymes (cf Fig 4) We conclude that the present kinetic model of E histolytica glycolysis, with a fixed PPi concentration, can describe the in vivo pathway... NADP+ and 3 U G6PDH The reaction was started by adding 4 mm G1P Modeling Entamoeba glycolysis Alanine transaminase was measured in buffer mixture in the presence of 0.15 mm NADH, 0.11 mm pyridoxal 5-phosphate, 15 mm 2-oxoglutarate and 3 U LDH The activity was not detected in the soluble fraction of amoebal extracts after adding up to 50 mm alanine Intermediary metabolite concentrations under steady-state... clearly indicated that the amoebal PPi metabolism should be experimentally evaluated for further refinement of the present kinetic glycolysis model Then, the available in vitro kinetics did not fully account for the in vivo observed behavior However, by fixing the PPi concentration, the model closely reproduced the pathway behavior under the experimental conditions tested in live parasites Several kinetic. .. degradation, serine synthesis and ATP consuming and PPi-generating reactions for further rigorous validation of the model In addition, it is difficult to extrapolate the modeled behavior of glycolysis, which was based on data from amoebal cultures, to a more realistic situation in which the parasites are colonizing the intestine because of the impossibility of reproducing the intestine’s microenvironment in the... experimental conditions in which the parasites were evaluated (using external glucose as carbon source) However, in addition to maintaining constant the PPi concentration, another deficiency of the present model rests on the adjusted steps necessary to achieve the metabolite concentrations found in vivo According to the modeling results, it is relevant to experimentally determine the fluxes through glycogen... been described for glycolysis in erythrocytes [25], tuber tissue potato [28], trypomastigote stage of the parasite T brucei [29–31] and S cerevisiae [32,33] An improvement introduced in the models of T brucei and yeast was that most of the kinetic parameters used were determined in enzymes from the same source and under similar experimental conditions This certainly circumvented the problem of combining... least ten-fold the Km value, and in the absence of products) In addition, glycolytic flux and metabolite concentrations were determined in trophozoites under steady-state conditions In the present model, adjusting the kinetic parameters of the glycolytic enzymes to achieve a better model fitting to the measured metabolite concentrations was kept to a minimum However, the kinetic properties of the PFOR and . Kinetic modeling can describe in vivo glycolysis in Entamoeba histolytica Emma Saavedra 1 , Alvaro Marı ´n-Herna ´ ndez 1 ,. that can predict the system behavior. In this sense, kinetic modeling is a E. Saavedra et al. Modeling Entamoeba glycolysis FEBS Journal 274 (2007) 4922–4940