Experimental validation of metabolic pathway modeling

Experimental validation of metabolic pathway modeling

An illustration with glycolytic segments fromEntamoeba histolytica

Rafael Moreno-Sanchez, Rusely Encalada, Alvaro Marın-Hernandez and Emma Saavedra

Departamento de Bioquımica, Instituto Nacional de Cardiologıa, Mexico

Keywords

pathway reconstitution; metabolic control

analysis; PPi inhibition; PPi activation; AMP

modulation

Correspondence

E. Saavedra, Departamento de Bioquımica,

Instituto Nacional de Cardiologıa, Juan

Badiano No. 1, Seccion XVI, Tlalpan,

Mexico, D.F. 14080, Mexico

Fax: +52 55 5573 0994

Tel: +52 55 5573 2911, ext. 1298, 1422

E-mail: [email protected]

Database

The mathematical models described here

have been submitted to the Online Cellular

Systems Modelling Database and can be

accessed at http://jjj.biochem.sun.ac.za/

database/moreno1/index.html and http://jjj.

biochem.sun.ac.za/database/moreno2/

index.html free of charge

(Received 27 November 2007, revised

1 April 2008, accepted 6 May 2008)

doi:10.1111/j.1742-4658.2008.06492.x

In the search for new drug targets in the human parasite Entamoeba

histolytica, metabolic control analysis was applied to determine, experimen-

tally, flux control distribution of amebal glycolysis. The first (hexokinase,

hexose-6-phosphate isomerase, pyrophosphate-dependent phosphofructo-

kinase (PPi-PFK), aldolase and triose-phosphate isomerase) and final

(3-phosphoglycerate mutase, enolase and pyruvate phosphate dikinase) gly-

colytic segments were reconstituted in vitro with recombinant enzymes

under near-physiological conditions of pH, temperature and enzyme pro-

portion. Flux control was determined by titrating flux with each enzyme

component. In parallel, both glycolytic segments were also modeled by

using the rate equations and kinetic parameters previously determined.

Because the flux control distribution predicted by modeling and that deter-

mined by reconstitution were not similar, kinetic interactions among all the

reconstituted components were experimentally revised to unravel the causes

of the discrepancy. For the final segment, it was found that 3-phosphoglyc-

erate was a weakly competitive inhibitor of enolase, whereas PPi was a

moderate inhibitor of 3-phosphoglycerate mutase and enolase. For the first

segment, PPi was both a strong inhibitor of aldolase and a nonessential

mixed-type activator of amebal hexokinase; in addition, lower Vmax values

for hexose-6-phosphate isomerase, PPi-PFK and aldolase were induced by

PPi or ATP inhibition. It should be noted that PPi and other metabolites

were absent from the 3-phosphoglycerate mutase and enolase or aldolase

and hexokinase kinetics experiments, but present in reconstitution experi-

ments. Only by incorporating these modifications in the rate equations,

modeling predicted values of flux control distribution, flux rate and metab-

olite concentrations similar to those experimentally determined. The experi-

mentally validated segment models allowed ‘in silico experimentation’ to be

carried out, which is not easy to achieve in in vivo or in vitro systems. The

results predicted a nonsignificant effect on flux rate and flux control distri-

bution by adding parallel routes (pyruvate kinase for the final segment and

ATP-dependent PFK for the first segment), because of the much lower

activity of these enzymes in the ameba. Furthermore, modeling predicted

Abbreviations

AK, adenylate kinase; ALDO, aldolase; CJEi , flux control coefficient; DHAP, dihydroxiacetone phosphate; ENO, enolase; Fru(1,6)P2, fructose-

1,6-bisphosphate; GAPDH, glyceraldehyde-3-phosphate dehydrogenase; Glc6P, glucose-6-phosphate; aGPDH, a-glycerophosphate

dehydrogenase; HK, hexokinase; HPI, hexose-6-phosphate isomerase; Lac, L-lactate; LDH, L-lactate dehydrogenase; 2PG,

2-phosphoglycerate; 3PG, 3-phosphoglycerate; PGAM, 3-phosphoglycerate mutase; PFK, phosphofructokinase,; PPDK, pyruvate phosphate

dikinase; Pi, phosphate; PPi, pyrophosphate; PYK, pyruvate kinase; Pyr, pyruvate; TPI, triose-phosphate isomerase.

3454 FEBS Journal 275 (2008) 3454–3469 ª 2008 The Authors Journal compilation ª 2008 FEBS

The parasite Entamoeba histolytica is the causal agent

of human amebiasis, for which metronidazole is the

drug of choice for treatment. As metronidazole resis-

tance has been observed in amebas [1], identification of

new drug targets is necessary. E. histolytica relies solely

on glycolysis for ATP supply; because several of its

glycolytic enzymes display important differences com-

pared with their human enzyme counterparts, E. his-

tolytica glycolytic enzymes have therefore become a

point of focus in the search for new drug targets [2,3].

Metabolic control analysis [4] is a theoretical frame-

work that can be applied to identify the main flux con-

trol steps in amebal glycolysis. Once identified, the

enzymes involved in these flux control steps become

potential targets for pharmaceutical intervention, thus

affecting the functioning of this energetically important

pathway in the parasite.

To determine and understand the flux control distri-

bution of a metabolic pathway through metabolic con-

trol analysis, several different experimental approaches

have been developed [4,5]. For instance, to evaluate

flux control of glycolysis experimentally, pathway

shortening to the first segment [from glucose to dihy-

droxiacetone phosphate (DHAP)] [6–8] and reconstitu-

tion of the final segment [from 3-phosphoglycerate

mutase (3PG) to pyruvate (Pyr)] [9], have been carried

out by using cellular extracts and commercial enzymes.

Modeling metabolic pathways is another powerful

tool to determine the flux control distribution of a

metabolic pathway. Kinetic modeling identifies the

properties of a given pathway that may not be deduced

by simple inspection of the kinetic parameters of the

individual enzymes and that might be relevant for

understanding the biochemical mechanisms involved in

the control of the pathway. Modeling involves quanti-

tative consideration of the vast array of reported data

and the interactions typical of a biological system, thus

permitting an integrative view of disperse data to be

made and irrelevant observations to be disregarded.

Although models are oversimplifications of complex

cellular processes, they are useful for the deduction of

essential relationships. Modeling helps to design exper-

imental strategies for testing hypotheses on pathway

control and may help in detecting incompatibilities on

the kinetic parameters of the participating enzymes,

prompting experimental revision of the most critical

enzyme uncertainties.

The recent kinetic modeling of E. histolytica glycoly-

sis revealed that the glucose transporter (GluT), hexo-

kinase (HK) and 3-phosphoglycerate mutase (PGAM)

were the main controlling steps [10]. It should be noted

that the glycolytic pathway in this human parasite is

unique in the sense that the cooperative enzymes ATP-

dependent PFK-1 and pyruvate kinase (PYK) are

rather scarce [11,12]. Instead, E. histolytica glycolysis

has a predominant flux through PPi-dependent PFK

(PPi-PFK) and pyruvate phosphate dikinase (PPDK),

which replace ATP-PFK and PYK, respectively, and

they catalyze fully reversible reactions under near-

physiological conditions and have a noncooperative

kinetic behavior [13–15]. Moreover, E. histolytica HK

is not product inhibited by glucose 6-phosphate

(Glc6P) or ADP, like the human HK-1, -2 and -3,

although it is potently blocked by AMP [10,16]. In

consequence, the glycolytic pathway in E. histolytica

from glucose to pyruvate (Pyr) is completely reversible,

perhaps with the exception of the HK reaction.

Another consequence of this particular pathway design

is that, in addition to the information transfer between

enzymes through the reversibility of the reactions,

there is an AMP-mediated link between the first (HK)

and the final (PPDK) segments, which is very likely to

be modulated by adenylate kinase (AK) activity [10].

Modeling of a complex pathway might overlook

hidden, but important, interactions among metabolites

and enzymes, particularly regarding noncontrolling

enzymes. Kinetic data are usually determined with the

known substrates, products and modulators of the

individual enzymes; however, other pathway meta-

bolites, which are included in the in vitro reconstitution

and in the model, but are not present in the kinetic

assays, might affect the enzyme activity and thus the

pathway flux-control distribution. Hence, to avoid

uncertainties in the model and its discrepancies with

the in vivo behavior, it is desirable to analyze experi-

mentally the complete range of interactions among the

system components. Once these hidden interactions

have been revealed, identified and quantitatively deter-

mined, their incorporation into the kinetic model

should reduce the number of discrepancies with the

full flux-control by 3-phosphoglycerate mutase and hexokinase, in the pres-

ence of low physiological substrate and product concentrations. It is con-

cluded that the combination of in vitro pathway reconstitution with

modeling and enzyme kinetics experimentation permits a more comprehen-

sive understanding of the pathway behavior and control properties.

R. Moreno-Sanchez et al. Metabolic modeling validation

FEBS Journal 275 (2008) 3454–3469 ª 2008 The Authors Journal compilation ª 2008 FEBS 3455

observed system behavior. In return, a strongly vali-

dated model may predict, with a higher degree of accu-

racy, the pathway response towards an extended set of

situations, thus facilitating a full understanding of the

regulatory mechanisms operating in the metabolic

pathway under investigation.

In the present work, to identify experimentally poten-

tial drug targets of E. histolytica glycolysis, the flux rate,

the flux control distribution and the metabolite concen-

trations were determined in both in vitro-reconstituted

systems (with recombinant enzymes) and in silico-mod-

eled pathway segments (using the known kinetic data) at

pH values of 6 and 7. It should be noted that each

reconstituted segment contained one of the main con-

trolling enzymes, namely HK and PGAM [10]. As no

agreement was initially found between the in vitro recon-

stitution and modeling results, re-evaluation of the

kinetics of the participating enzymes [PGAM, enolase

(ENO), and PPDK for the final segment; and HK, hex-

ose-6-phosphate isomerase (HPI), PPi-PFK, aldolase

(ALDO) and triose-phosphate isomerase (TPI) for the

first segment] was undertaken. Thus, novel interactions

between enzymes and metabolites were unveiled, which

led to a better correlation between reconstitution and

modeling results.

The mathematical models described here have been

submitted to the Online Cellular Systems Modelling

Database and can be accessed at http://jjj.biochem.

sun.ac.za/database/moreno1/index.html and http://jjj.

biochem.sun.ac.za/database/moreno2/index.html free

of charge

Results

3PG fi Pyr segment

Pathway reconstitution

To reconstitute a pathway segment under near-physio-

logical conditions, the correct proportion of participat-

ing enzymes has to be present. The enzyme proportion

previously used for reconstitution of the final segment of

E. histolytica glycolysis at pH 7.0 [16] was slightly dif-

ferent from the proportion found in live trophozoites

[10]. By using the Vmax values of the forward reaction

determined in amebal cells, it was established that the

appropriate enzyme activity ratios were 1 PGAM : 5.8

ENO : 2.9 PPDK at pH 7.0; and 1 PGAM : 4

ENO : 2.6 PPDK at pH 6.0 (see table 1 of Ref. [10]).

A quasi steady-state flux to l-lactate (Lac) was

established by coupling the reconstituted pathway with

excess commercial lactate dehydrogenase (LDH), by

following the rate of NADH oxidation and by starting

the reaction upon the addition of 3PG (Fig. 1). After a

lag period (transition time) that was dependent on the

concentration of PGAM, a stable pseudo steady-state

flux was reached. In the range of PGAM activities

tested (50–100 mU), while maintaining constant the

enzyme proportion for ENO and PPDK at both pH

values, a quasi linear relationship with the flux rate

was obtained (Fig. 1, inset). At a lower PGAM activity

(£ 25 mU), the system was extremely slow in reaching

a stable pseudo steady state (> 2.5 min), which

resulted in less reliable data owing to the surge of

enzyme instability in highly diluted solutions; in addi-

tion, the relationship between flux and enzyme propor-

tion lost proportionality, suggesting enzyme

inactivation at low concentrations, perhaps because of

a change in the enzyme oligomerization state. At

higher PGAM activities (> 100 mU), and the corre-

sponding correct proportions of ENO and PPDK, the

system rapidly consumed the added NADH, which did

not allow the establishment of a stable and reliable

pseudo steady state (data not shown).

We are aware that a true steady state cannot be estab-

lished under the conditions described in Fig. 1 because

the concentrations of the substrates 3PG, AMP, PPi and

NADH, and those of the products ATP, Lac and

NAD+, do not remain constant throughout the reac-

tion. However, a quasi steady state, regarding a constant

flux rate (i.e. of Lac formation) and constant inter-

mediate metabolite concentrations [i.e. of 2-phospho-

glycerate (2PG), phosphoenolpyruvate and Pyr)], may

be sufficient to analyze the control properties of the

system [4].

Titration of flux using different activities of each

enzyme, keeping the rest of the system constant, was

carried out to determine the flux control coefficients

(CJEivalues) of the participating enzymes, in which the

slope of the tangent at the reference point was taken

to calculate its value (Fig. 2). The experimental points

fitted well to hyperbolic patterns, but did not fit sig-

moidal or parabolic patterns. A summary of the esti-

mated CJEi value under three different experimental

conditions is shown in Table 1. The pathway flux rate

was slightly higher at pH 6 than at pH 7 because the

optimal pH values for PGAM and PPDK activities are

approximately 6 [16].

The main flux control was exerted by PGAM at

both pH values. ENO was the enzyme with the highest

activity in the reconstituted system and it is also the

most efficient [16]. However, as its optimal pH is

approximately 7, ENO exerted significant flux control

at pH 6, whereas PPDK exerted the lowest flux con-

trol, being negligible at pH 6. In the presence of the

pathway products ATP and phosphate (Pi), the flux

rate was significantly diminished, whereas the PPDK

Metabolic modeling validation R. Moreno-Sanchez et al.


flux control increased by sixfold (Table 1) and that of

ENO diminished by threefold. The sum of the flux

control coefficient mean values (Table 1), of slightly

greater than 1 (1.15–1.24), is explained by the intrinsic

experimental variability of the measured parameters.

The pseudo steady-state concentration of 2PG was

very similar in the reconstituted pathway at both pH

values, whereas in the presence of the products ATP +

Pi, at pH 6, the 2PG concentration was 21% lower, sug-

gesting a stimulatory effect on ENO (Table 1). The

pseudo steady-state concentration of phosphoenolpyru-

vate was very similar at pH 6 in the absence or presence

of ATP + Pi; at pH 7, the phosphoenolpyruvate con-

centration was 50% higher than at pH 6, probably

because PPDK is less active at pH 7.

Modeling

A kinetic model of the final glycolytic segment was built

by using the computer program gepasi (http://www.

gepasi.org). The equations and kinetic parameters used

are shown in the supplementary Table S1; they can also

be found in previous publications [10,16]. Some systemic

characteristics and the flux control coefficients calcu-

lated from this initial modeling can also be found in the

supplementary Table S2. The PGAM flux control coeffi-

cient value (CJPGAM ¼ 0:46� 0:76) estimated from the

model correlated relatively well with the experimentally

determined value (see Table 1). By contrast, the

ENO and PPDK control coefficient values

(CJENO ¼ 0:1� 0:13; CJ

PPDK ¼ 0:14� 0:41) estimated

from the model did not correlate with those determined

experimentally by enzyme titration at pH 6 or 7. More-

over, the predicted phosphoenolpyruvate steady-state

concentrations were 4–25 times higher than those exper-

imentally measured (Table 1). In turn, the flux rates and

the 2PG concentration predicted by the model were, at

both pH values, reasonably close (within 70–80% of

the experimental values) to the determinations from the

in vitro reconstituted pathway.

This lack of full correlation suggested that the

kinetic parameters used in the model did not

0 1 2 3 4 5

0

1

2

3

4

5

6

7

8

pH 7

pH 6Frac

tion

al fl

ux

r

Fig. 1. Flux rate of the reconstituted E. his-

tolytica final glycolytic segment at different

concentrations of PGAM. The recombinant

E. histolytica enzymes PGAM, ENO and

PPDK were incubated under the conditions

described in the Materials and methods, at

pH 6.0 and 37 �C. After 3.5 min, 4 mM 3PG

was added, as indicated, to initiate the reac-

tion. The PGAM activities used were 23.2,

37.1, 65, 85.8, 102 and 125.2 mU in traces

A, B, C, D, E and F, respectively. For clarity,

the traces with 51, 74.1 and 111.3 mU of

PGAM were omitted. The ENO and PPDK

activities used in all experiments (A–F) were

329 and 196.5 mU, respectively. Inset: the r

factor represents the simultaneous fold-vari-

ation in the three enzyme activities; with

r = 1, the PGAM activity was 25 mU at both

pH values, whereas the ENO and PPDK

activities were 109.5 and 65.5 mU at

pH 6.0; and 146 and 74 mU at pH 7.0.



completely represent the behavior of ENO and PPDK

in the reconstituted system, indicating that other,

not-so-apparent, factors and interactions may affect

the activity of these two enzymes. Moreover, in the ini-

tial model, a simplified rate equation for PPDK (Bi Bi

Ping Pong reversible mechanism) was used, in which

phosphoenolpyruvate and PPi transform to Pyr and Pi,

by considering that AMP and ATP are present in the

intracellular milieu at saturating concentrations [10].

The much more complex kinetic mechanism of PPDK

(Uni Uni Bi Bi Ping Pong-Ordered) yields a rate equa-

tion that is exceedingly complex [17].

To understand the lack of correlation between

enzyme titration and modeling results, the effects of

Pyr, Lac, AMP, 3PG and PPi were assayed on ENO

activity. According to the pathway model, the

steady-state Pyr concentration was below the limit of

detection (< 5 nmolÆmL)1) owing to the presence of

excess LDH. ENO activity was unaffected by the pres-

ence of 0.1–1 mm Pyr, 0.1–1 mm Lac, or 0.5 mm AMP.

However, PPi (Fig. 3B) and 3PG (data not shown)

behaved as competitive inhibitors of the ENO forward

reaction. Furthermore, PPi also competitively inhibited

the PGAM forward reaction (Fig. 3A); the addition of

0.05–2.5% glycerol (derived from the enzyme prepara-

tions) did not affect the PGAM activity. Moreover, the

presence of 10 mm Pi + 3 mm ATP diminished the

ENO Vmax value by 40% (pH 6; n = 3) and 26%

(pH 7; n = 4), whereas the ENO Km 2PG was increased

by threefold (data not shown); ATP alone inhibited

ENO activity by 16% (pH 6; n = 2) and 10% (pH 7;

n = 3). Ammonium (7–13 mm) did not affect the

reverse activities of PGAM, ENO or PPDK.

By introducing a double-competitive inhibition (PPi

and 3PG) in the ENO rate equation and a PPi compet-

itive inhibition in the PGAM rate equation (see

Scheme 1; see also the supplementary Doc. S1. for

equations), together with an empirical PPDK rate

equation with six ligands (three substrates, three prod-

ucts; see rate equations in supplementary Doc. S1),

a re-evaluation of the pathway model was carried out.

The PGAM and ENO flux control coefficients, now

estimated using the modified model, correlated better

(Table 2) with the experimentally determined values

(see Table 1), although the predicted flux control

0 20 40 60 80 10005

1015202530 *

Flu

x (n

mo

l·min

–1)

PGAM (mU)

0 50 100 150 20005

1015202530

*

PPDK (mU)

0 100 200 300 40005

10152025

*

ENO (mU)

Fig. 2. Enzyme titration of flux in the reconstituted final glycolytic

segment. The final pathway segment was reconstituted with

75 mU PGAM, 328.5 mU ENO and 196.5 mU PPDK

(1 PGAM : 4.38 ENO : 2.62 PPDK) at pH 6.0 and 37 �C and in the

presence of 3 mM ATP and 10 mM Pi. Only one enzyme activity

was varied, as indicated, maintaining constant the other enzyme

activities at the above-mentioned values. The solid lines represent

the fitting to the Michaelis–Menten equation, which was carried

out by using the computer program MICROCAL ORIGIN 5.0. The aster-

isks indicate the point at which the slope of the tangent to the

curve was calculated. The flux control coefficients estimated for

this particular experiment by using the expression [4] CJEi ¼ dJ

dEi� Eo

Jo

were 0.55, 0.15 and 0.22 for PGAM, ENO and PPDK, respectively.

The slope value is dJdEi

, whereas Eo and Jo are the reference, control

values of enzyme activity and flux rate, respectively.

Table 1. Flux control of the in vitro reconstituted final segment of

Entamoeba histolytica glycolysis. The enzyme activity proportions

were PGAM 1 (50 mU), ENO 4.75 ± 0.82 (n = 4) and PPDK

2.64 ± 0.17 (n = 4) at pH 6.0; PGAM 1 (75 mU), ENO 4.37 ± 0.02

(n = 3), PPDK 2.62 (n = 2) at pH 6.0 + 3 mM ATP + 10 mM Pi; and

PGAM 1 (50 mU), ENO 6.4 ± 1.5 (n = 5), PPDK 2.8 ± 0.38 (n = 5)

at pH 7.0. The values shown represent the mean ± standard devia-

tion of the flux control coefficients (CJEi ) calculated from experi-

ments similar to those shown in Fig. 1. The number of different

preparations assayed is included in parentheses. For determination

of the metabolite concentrations, aliquots were withdrawn from

the reconstituted system at two different time-points when the flux

rate achieved a constant value; because the two concentration val-

ues were within a 10% difference, they were averaged for each

preparation and experimental condition. PEP, phosphoenolpyruvate.

pH 6.0

pH 6.0 +

ATP + Pi pH 7.0

Flux rate,

(nmolÆmin)1)

43 ± 10 (5) 27 ± 7 (5) 31 ± 10 (6)

CJPGAM 0.75 ± 0.15 (5) 0.72 ± 0.24 (4) 0.62 ± 0.22 (6)

CJENO 0.37 ± 0.17 (4) 0.11 ± 0.03 (3) 0.33 ± 0.05 (5)

CJPPDK 0.03 ± 0.06 (4) 0.13 (2) 0.29 ± 0.12 (5)

2PG, lM 73 ± 27 (3) 58 ± 29 (4) 77 ± 7 (3)

PEP, lM 38.5 ± 5 (3) 37 ± 16 (4) 57 ± 26 (3)



exerted by PPDK still showed no correlation with the

experimental value. The predicted steady-state concen-

trations of 2PG and phosphoenolpyruvate, as well as

the predicted flux rate (Table 2), were now closer to

the experimental values (Table 1), particularly at pH 7.

Thus, incorporation of the PPi and 3PG inhibition on

ENO activity, and of the PPi inhibition on PGAM

activity, improved the predictive value of the model. In

turn, replacing the PPDK trireactant equation with the

Bi Bi Ping Pong equation, as in the initial model, the

predicted PPDK flux control approached the experi-

mentally determined values (CJPPDK ¼ 0:02 at pH 6.0;

and 0.37 at pH 7.0, although at the expense of PGAM

losing control, CJPGAM ¼ 0:46). Hence, further refine-

ment of the PPDK rate equation is required.

The elasticity coefficients for the substrates of the

three enzymes were similar (Table 2); however, lower

elasticity coefficients were obtained for products and

inhibitors of PGAM and ENO, explaining why these

enzymes have higher flux control coefficients. The

enzyme concentration control coefficients (Table 2) did

not vary at the two pH values.

The model predictions were not significantly modi-

fied by variations in either the PPDK Km values of

substrates and products or the Keq of the PPDK reac-

tion from 0.73 [17] to 36.5, probably because of the

low flux control exerted by this enzyme. The improved

model was also relatively insensitive to changes in the

ENO Km for phosphoenolpyruvate. However, the

model was slightly susceptible to diminution in the Km

for 3PG and 2PG and in the Ki for PPi of PGAM;

and moderately sensitive to changes in the ENO Km

for 2PG (see supplementary Fig. S1) and in the ENO

Ki for PPi (data not shown). This last observation

prompted experimental revision of the PGAM and

ENO Km values of the respective substrates (see sup-

plementary Table S1). For the PGAM Km value for

3PG, it was noted that the previously determined value

[16] was accompanied by high experimental dispersion,

which was, in part, related to the presence of contami-

nating 2PG (1–2%) in the 3PG stock solutions and to

the way the assay is performed, with the prior estab-

lishment of a baseline in the presence of coupling com-

mercial ENO (which is contaminated with PGAM)

and the subsequent addition of recombinant PGAM.

In the case of the ENO Km for 2PG, the value deter-

mined here was very similar to that previously

reported [16], although for the model, the Km 2PG with

the highest value improved fitting (supplementary

Table S1). For instance, increasing the ENO Km 2PG

from 86.4 to 130 lm induced a 6–13% diminution in

CJPGAM, rate flux and [phosphoenolpyruvate], and an

increase of 31–39% in CJENO and [2PG]; whereas

decreasing the ENO Km 2PG to 40 lm provoked an

increase of 12–13% in CJPGAM, rate flux and

[phosphoenolpyruvate], and a diminution of 40–47%

in CJENO and [2PG] (supplementary Fig. S1).

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50E

hP

GA

M a

ctiv

ity

mU

(m

g p

rote

in)–

1 ×

103

Eh

EN

O a

ctiv

ity

mU

(m

g p

rote

in)–

1 ×

103

3PG (mM)

0.0 0.1 0.2 0.3 0.40

25

50

75

100

125

2PG (mM)

A

B

Fig. 3. PPi inhibition of PGAM (A) and ENO (B) activities at pH 7.

The reaction at 37 �C was started by adding 0.55 lg of PGAM or

0.9 lg of ENO. The PPi concentration (mM) was: 0 (closed squares),

0.5 (open circles) or 2.0 (open triangles). The solid lines represent

the fitting to the Michaelis–Menten equation with simple competi-

tive inhibition calculated using the ORIGIN MICROCAL software. Eh,

E. histolytica.

Scheme 1. Metabolic-enzyme interactions in the E.histolytica (Eh)

final glycolytic segment.



Modeling experimentation

With this experimentally validated model (at pH 6

with competitive inhibition by PPi and 3PG), several

questions that are not easily resolved through ‘wet’

experimentation can be examined. For instance, to

reach a stable pseudo steady state, saturating concen-

trations of 3PG and PPi (4 and 2 mm, respectively)

were used in the in vitro experiments (Fig. 1; Table 1)

because lower, more physiological concentrations were

insufficient to establish a stable pseudo steady state.

Hence, to achieve a more physiological description of

the control structure in the final glycolytic segment,

the modeling was carried out at 0.45 mm PPi and

0.4 mm 3PG, together with physiological concentra-

tions of ATP, AMP and Pi [10] (Table 3). Under these

conditions, the model was highly robust to changes in

ATP, AMP and Pi: a 50% variation in these meta-

bolites brought about a change of only 10–20% in

CJPGAM, CJ

ENO, [2PG] and flux (data not shown); a

large variation in Pi concentration (2.5–10 mm) did not

alter the control coefficients, metabolites and flux.

Changes in 3PG (0.2–1 mm) drastically affected metab-

olite concentrations and flux, but did not affect the

control coefficient distribution. By contrast, the

improved model showed that all systemic characteris-

tics, including CJPPDK, were sensitive to PPi variation

(Fig. 4). At 0.45 mm PPi, PGAM was the main con-

trolling step (Table 3), but PPDK emerged as a con-

trolling step at PPi concentrations of 0.2 mm or lower.

In turn, the flux rate exhibited a biphasic pattern with

a maximum at about 0.1 mm PPi (Fig. 4). Modeling

also showed that a large AMP variation (0.8–3.2 mm)

promoted a negligible change in all systemic properties

(data not shown).

Another question that cannot be experimentally ana-

lyzed at present because of a lack of the recombinant

amebal enzyme, is the effect of the presence of PYK as

an alternative, parallel, route on flux control and rate.

Recently, in addition to the well-described role of

PPDK in synthesizing Pyr (and ATP) from

phosphoenolpyruvate, it was established that PYK

activity was also present in amebas [12]. The PYK

activity in amebal extracts was strongly stimulated by

Table 2. Control analysis in the modeled final segment of E. his-

tolytica glycolysis with 3PG and PPi inhibition on ENO and PGAM,

and a ter-reactant PPDK rate equation. PEP, phosphoenolpyruvate.

The following metabolites were fixed: 3PG (3.7 mM); AMP

(0.2 mM); PPi (1.7 mM); Lac (0.3 mM); ATP (0.3 mM); Pi (0.3 mM).

These values were reached in the reconstituted system around the

middle of the pseudo-steady state duration (see Fig. 1).

pH 6.0 pH 7.0

Flux rate, nmolÆmin)1

(50 mU PGAM)

16.6 24.7

2PG, lM 139.8 142

PEP, lM 6.1 24.5

CJPGAM 0.79 0.74

CJENO 0.21 0.24

CJPPDK 0.002 0.02

Elasticity (eEiM ) and concentration-control (CM

Ei ) coefficients

eEiM at pH 6.0 eEi

M at pH 7.0

PGAM ENO PPDK PGAM ENO PPDK

3PG 0.78 )0.29 0.58 )0.48

2PG )0.24 0.93 )0.31 0.96

PEP )0.01 0.87 )0.07 0.83

AMP 0.87 0.83

PPi )0.49 )0.58 0.87 )0.20 )0.36 0.83

ATP )0.63 )0.26

CMEi at pH 6.0 CM

Ei at pH 7.0

PGAM ENO PPDK PGAM ENO PPDK

2PG 0.86 )0.85 )0.01 0.84 )0.78 )0.06

PEP 0.90 0.24 )1.14 0.89 0.29 )1.18

Table 3. Control analysis in the modeled final segment of E. his-

tolytica glycolysis with 3PG and PPi inhibition at pH 6, physiological

metabolite concentrations, and the presence of PYK. The rate equa-

tion for the PYK reaction was assumed to be that describing a

steady-state Bi Bi ordered reversible mechanism (see the supple-

mentary material). For this equation, in addition to the Keq, it also

required a value for the maximal rate in the reverse reaction, Vr,

which was taken as 0.061 of the Vf value. The PPDK ⁄ PYK activity

ratio was set at 10. The Km values for PEP and ADP were 18 and

1050 lM [12], whereas the Km values for the products Pyr and ATP

were both assumed to be 1000 lM; this last value was also

assigned to KiA, KiP and KiQ. The ADP concentration was fixed at

3.3 mM. The systemic properties and the flux control distribution

were insensitive to changes in the Keq value for the PYK reaction

from 100 to 1000.

0.4 mM 3PG;

0.45 mM PPi;

5.4 mM Pi; 5 mM

ATP; 1.6 mM AMP

0.4 mM 3PG;

0.45 mM PPi;

5.4 mM Pi; 5 mM

ATP; 1.6 mM AMP + PYK

Flux rate,

nmolÆmin)1

7.4 7.4

2PG, lM 19.1 18.8

PEP, lM 20.2 18.9

CJPGAM 0.77 0.77

CJENO 0.18 0.18

CJPPDK 0.05 0.04

CJPYK 0.003



fructose 1,6-bisphosphate [Fru(1,6)P2]; the Fru(1,6)

P2-stimulated PYK activity was, however, 3-10-fold

lower than that of PPDK [12,16]. Therefore, with the

experimentally validated model at pH 6, the effect of

including and varying the PYK activity in the relevant

range, keeping the PPDK activity constant, was exam-

ined at physiological concentrations of 3PG, PPi,

AMP, ATP and Pi. Thus, the apparently simple

sequence of reactions for the E. histolytica glycolytic

segment from 3PG to Pyr became a more complex

structure (Scheme 1). By adding PYK to set a

PPDK ⁄PYK activity ratio of 10, the system properties

(flux, metabolites and control coefficients) did not

change significantly with respect to the pathway lack-

ing PYK (Table 3), except for the transfer of some

PPDK flux control to PYK. In turn, at a PPDK ⁄PYK

ratio of 2, under which the phosphoenolpyruvate

concentration decreased by 31.5% owing to a higher

phosphoenolpyruvate–Pyr flux, CJPPDKand CJ

PYK were

0.04 and 0.03, but other systemic properties remained

unchanged.

Glucose fi DHAP segment


A pseudo steady-state flux from glucose to a-glycero-phosphate was established by coupling amebal recom-

binant HK, HPI, PPi-PFK, ALDO and TPI with

excess commercial a-glycerophosphate dehydrogenase

(aGPDH), following the rate of NADH oxidation and

starting the reaction by adding glucose (data not

shown). Reconstitution of the first pathway segment

with an HK activity range from 25 to 100 mU, main-

taining constant the enzyme proportion for the other

four enzymes (supplementary Fig. S2A), yielded a

near-linear relationship with the flux rate. In the

absence of added TPI, the flux rate lost linearity after

a few seconds; it should be noted, however, that in the

reconstituted first segment coupled to aGPDH, the

TPI reaction functioned in the reverse glycolytic direc-

tion (see Scheme 2).

As expected from amebal ALDO class II proper-

ties [16], in the absence of added CoCl2, the flux

control of the reconstituted system resided entirely in

the ALDO step (supplementary Fig. S2B), as shown

by its extremely low Vmax values (57 mUÆmg)1 pro-

tein at pH 7 and zero at pH 6) [10]. However, an

intracellular concentration of 23 lm for total Co2+

was detected in amebal cells [10]. Moreover, other

heavy metals that also activate ALDO were detected

at significant concentrations (1.6 mm Zn2+, 120 lm

Cu2+; [10]). Therefore, titration of flux in the first

glycolytic segment with different enzyme activities

(Fig. 5) was carried out in the presence of saturating

Co2+; glucose, ATP, PPi and NADH concentrations

were also saturating. The titration curves for each

enzyme activity yielded hyperbolic curves (Fig. 5).

The calculated CJEi at two pH values is shown in

Table 4.

A higher pathway flux rate at pH 7 than at pH 6 is

related to the optimal pH values for HK and ALDO

activities (i.e. around pH 7 [16]), but also to the higher

enzyme proportion used (50 mU HK at pH 7 versus

30–40 mU HK at pH 6). There was no particular

5

10

50

100

150

200

[PPi] (µM)

[PEP]

[2PG]

Flux

Flu

x (n

mo

l·min

–1);

Met

abo

lite

(µM

)

0 200 400 600 800 1000

0 200 400 600 800 1000

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

PPDK

ENO

PGAM

Flu

x co

ntr

ol c

oef

fici

ent

Fig. 4. Effect of varying the PPi concentra-

tion on pathway parameters of the final gly-

colytic segment. See the legend to Table 3

for modeling details. The dotted line repre-

sents the PPi physiological concentration of

amebal cells.



reason for using different enzyme proportions between

pH 6 and 7; it was just a matter of enzyme availability

at the time when the experiments were performed. The

data are comparable because these enzyme proportions

are within the quasi linear relationship with flux (sup-

plementary Fig. S2A). The main flux control was

exerted by HK at both pH values but, somewhat sur-

prisingly, HPI, together with PPi-PFK, and ALDO,

also exerted significant flux control, whereas TPI was a

noncontrolling step (Table 4). The flux control exerted

by HK was enhanced by the addition of AMP, a con-

dition under which HK became the rate-limiting step

(data not shown). The effect of the strong mixed-type

inhibition of AMP (Ki AMP = 24 lm at pH 7 [16]) on

HK flux control was evident in the reconstituted

system only when a high AMP concentration was

used, because the assay normally contained 3 mm ATP

(Km ATP = 77 lm [16] or 89 lm, as redetermined in

the present work; supplementary Table S3). With the

addition of 1.5 mm AMP, and in the presence of 3 mm

ATP at pH 7, the flux of the reconstituted system

decreased by 55.4 ± 12% (n = 3) and the CJHKvalue

increased to 0.89 ± 0.18.

Reconstitution of the first glycolytic segment, includ-

ing amebal glyceraldehyde-3-phosphate dehydrogenase

(GAPDH) and 3-phosphoglycerate kinase was unsuc-

cessful, as recombinant GAPDH has not yet been

maintained in a satisfactorily stable way. Moreover,

reconstitution of the middle segment of glycolysis with

amebal ALDO, TPI, GAPDH and 3-phosphoglycerate

kinase yielded no hyperbolic patterns during enzyme

titrations, which made it difficult to evaluate path-

way behavior and calculate flux control coefficients.

Scheme 2. Metabolic-enzyme interactions in the E.histolytica (Eh)

first glycolytic segment.

0 10 20 30 40 50 60

0

5

10

15

20

25

30

*

Flu

x (n

mo

l·min

–1)

Flu

x (n

mo

l·min

–1)

HK (mU)0 20 40 60 80

0 20 40 60 80

100 120 140

0

5

10

15

20

25

30

*

HPI (mU)

0 20 40 60 80 100 120 140PFK (mU)

0

5

10

15

20

25

30

*

0

5

10

15

20

25

30

*

ALDO (mU)

Fig. 5. Enzyme titration of flux in the recon-

stituted first glycolytic segment The glyco-

lytic reactions from glucose to DHAP were

reconstituted with 40 mU HK, 98 mU HPI,

89.6 mU PPi-PFK, 67.2 mU ALDO, and

1836 mU TPI (1 HK : 2.45 HPI : 2.24 PPi-

PFK : 1.68 ALDO : 45.9 TPI) at pH 6.0 and

37 �C, and in the presence of 3 mM ATP,

1 mM PPi and 0.5 mM CoCl2. The solid lines

represent the fitting of the experimental

points to the irreversible Michaelis–Menten

equation. The calculated CJEi values for this

particular experiment were 0.37, 0.19, 0.28

and 0.08 for HK, HPI, PPi-PFK and ALDO,

respectively.



Negligible flux control of glycolysis by the middle-seg-

ment enzymes, as well as other NADH ⁄NAD+-utiliz-

ing steps, has been predicted by the entire pathway

model [10]; hence, the NADH ⁄NAD+ ratio does not

seem to have an important role in the control of ame-

bal glycolytic flux.

Modeling

The kinetic model of the first glycolytic segment was

also built. The equations and kinetic parameters used

are shown in the supplementary Table S3; they can

also be found in previous publications [10,16]. With

the kinetic parameters experimentally determined for

the five enzymes, including those of the reverse reac-

tions, the model predicted that flux was fully con-

trolled by HK (CJHK ¼ 0:99). Such a flux-control

distribution did not correlate with that experimentally

determined by enzyme titration at pH 6 and 7

(Table 4). In consequence, once again, there must be

interactions among the enzymes and metabolites in the

reconstituted pathway that were not apparent in the

enzyme kinetics studies.

Therefore, the effects of ATP, Mg2+, glucose, PPi, Pi

and Co2+ were assayed on the activities of the enzymes

that do not use these metabolites. Glucose (1–10 mm)

did not affect the activities of HPI, PPi-PFK, ALDO or

TPI; Mg2+ (5–10 mm) did not affect the activities of

HPI, ALDO or TPI; and Co2+ (0.5 mm) did not affect

the activities of HK, HPI, PPi-PFK or TPI. On the

other hand, PPi was a competitive inhibitor of ALDO,

with Ki values in the physiological concentration range

(Fig. 6) and, surprisingly, PPi was also a nonessential

mixed-type activator of HK (Fig. 6). The PPi-activating

effect on the recombinant amebal HK became evident

when either Glc6P phosphate dehydrogenase (Fig. 6)

or PYK ⁄LDH (data not shown) were used as coupling

enzymes. Furthermore, PPi also induced a potent acti-

vating effect on the native amebal HK and on the com-

mercially available yeast HK, but had no significant

effect on the HK of rat and human tumor cell (see sup-

plementary Table S4). As the PPi activating effect on

amebal HK was dependent on the protein concentra-

tion added to the assay (at lower protein concentrations

a greater PPi activation is attained) and on the time of

pre-incubation (the enzyme incubated without PPi

becomes inactivated in a time-dependent manner,

whereas the enzyme incubated with PPi maintains an

initial high activity for at least 10 min; data not shown),

the amount of protein added from each biological

source has to be indicated, as well as the specific HK

activity, to be able to make a more rigorous compari-

son (supplementary Table S4).

The HPI activity at pH 7 was not altered by 3 mm

ATP, 1 mm PPi or 1 mm Pi; however, at higher Pi

concentrations (5–10 mm), its activity decreased by

16–41%. Furthermore, the combination of 1 mm

Pi + 1 mm PPi lowered the HPI Vmax by 8–13%. The

presence of 3 mm ATP induced a diminution of 26%

in the PPi-PFK Vmax, whereas 10 mm Mg2+ + 1 mm

PPi decreased, by 19.4%, the ALDO Vmax. Ammo-

nium (7–13 mm) did not affect PPi-PFK activity.

A re-evaluation of the pathway modeling was carried

out by incorporating the PPi effect on ALDO and HK

(see the supplementary Doc. S1 for the rate equation)

activities (see Scheme 2), together with diminished Vmax

(and corresponding Vmax) values for HPI, PPi-PFK and

ALDO, and by using the metabolite concentrations

determined in the pseudo steady-state conditions of the

reconstitution experiments. Other adjustments to the

model are detailed in the legend to Table 5.

With the enhanced HK activity and lower HPI,

PPi-PFK and ALDO activities, the model flux control

distribution correlated better with the experimentally

determined values (Table 4). However, the model

metabolite concentrations were two to three orders of

magnitude higher than those determined experimentally,

indicating that something in the model was still missing,

perhaps a branching reaction as a contaminant of one of

the recombinant enzymes used for the pathway reconsti-

tution. Indeed, by adding a Glc6P branching reaction to

the modified model, it was possible to attain closer val-

ues for flux, metabolite concentrations and flux control

distribution to those directly measured (data not

shown); however, a contaminating Glc6P dehydroge-

nase activity was not detected.

Table 4. Flux control of the in vitro reconstituted first segment of

E. histolytica glycolysis. The Vmax values of the forward reaction

determined in amebal cells (see Table S3; see also table 1 of Ref.

[10]) were used to establish the correct enzyme activity ratios: HK

1 (50 mU): HPI 2.44 (122 mU): PPi-PFK 2.39 (119.5 mU): ALDO

2.95 (147.5 mU): TPI 36.1 (1805 mU) at pH 7.0; and HK 1 (30–

40 mU): HPI 2.45 (73.5–98 mU): PPi-PFK 2.24 (67.2–89.6 mU):

ALDO 1.68 (50.4–67.2 mU): TPI 45.9 (1377–1836 mU) at pH 6.0.

See legend to Table 1 for other experimental details. Fru6P, fruc-

tose 6-phosphate.

pH 6.0 pH 7.0

Flux rate,

nmolÆmin)1

20–25 (30–40 mU HK) 30–50 (50 mU HK)

Glc6P, mM 0.56 ± 0.08 (5) 0.28 ± 0.15 (5)

Fru6P, mM 0.08 ± 0.01 (5) 0.04 ± 0.01 (5)

CJHK 0.46 ± 0.16 (3) 0.48 ± 0.13 (6)

CJHPI 0.18 ± 0.08 (4) 0.23 ± 0.09 (5)

CJPPi�PFK 0.21 ± 0.06 (3) 0.13 ± 0.11 (5)

CJALDO 0.14 ± 0.05 (3) 0.12 ± 0.07 (5)

CJTPI 0 0



Modeling experimentation

With the experimentally validated model at pH 7

modified by the PPi effect, it became possible to

examine several questions not easily resolved through

experimentation. In particular, lower and physiologi-

cal glucose and PPi concentrations, which are insuffi-

cient for establishing an experimentally stable pseudo

steady state, could be evaluated. Thus, at 2 mm

glucose and 0.45 mm PPi, together with physiological

concentrations of ATP, ADP, AMP and Pi [10], the

improved model predicted, with high accuracy, the

flux rate and metabolite concentrations (Table 6)

found in live parasites [10], whereas the flux control

resided exclusively in the HK reaction. To explore

whether the high flux control exerted by HK was

caused by the potent inhibition of AMP, flux rate

was analyzed in the experimentally reconstituted first

glycolytic segment (Fig. 7A) and by modeling

(Fig. 7B) at different AMP concentrations. In both

systems, the AMP inhibition of flux was similar,

which added further validation to the glycolysis in

the improved model. The model permitted estimation

of variation in the flux control exerted by HK

(Fig. 7B); at AMP concentrations higher than

0.25 mm [and 2.5 mm ATP (i.e. at ATP ⁄AMP ratios

lower than 10)], HK reached full flux control. Model-

ing also showed that variation in the PPi concentra-

tion (0.1–2 mm) did not affect the HK flux control,

although large changes (9–910% of values at 0.45 mm

PPi) were attained for metabolite concentrations and

flux rate (data not shown).

Another question analyzed in silico was the effect on

flux control of the presence of the ATP-PFK as an

alternative, parallel route. In addition to the well-

described PPi-PFK role in generating Fru(1,6)P2 from

fructose 6-phosphate, the presence of a nontypical

ATP-PFK activity has been established in amebas [11].

The complete reaction sequence for the E. histolytica

glycolytic segment from glucose to DHAP is shown in

Scheme 2. The ATP-PFK activity in amebas corre-

sponds to approximately 7% of the PPi-PFK activity

[10]. Incorporation of this parallel route did not

modify any of the model properties (metabolite con-

centrations, flux or flux-control distribution; data not

shown) and hence HK was the only flux control step.

Discussion

Reconstitution of a pathway segment under

near-physiological conditions

In previous studies with the first glycolytic segment, it

was concluded that either liver HK or glucokinase

(CJHK ¼ 0:77� 0:83) and PFK-1 (CJ

PFK�1 ¼ 0:17� 0:24)

were the main flux control steps, whereas HPI, ALDO

0.0 0.2 0.4 0.6 0.8

0.0 0.2 0.4 0.6

0.0 0.2 0.4 0.6

0.8 1.0

0

100

200

300

400

500

[PPi] (mM)0.250.100.05

0.00

KA(PPi) = 0.05 mM

β = 1.63α = 1.20

HK

act

ivit

y, m

U (

mg

pro

tein

)–1

× 10

3

0

20

40

60

80

100

120pH 6.0

AL

DO

act

ivit

y, m

U (

mg

pro

tein

)–1

x 10

3

0

50

100

150

200 pH 7.0

FBP (mM)

[ATP] (mM)

Fig. 6. PPi activation of amebal HK and PPi inhibition of amebal ALDO. The reaction at 37 �C was started by adding 0.085 lg of HK or

0.36 lg of ALDO. For the HK plot (at pH 7) the solid lines represent the best fit to nonessential mixed-type activation (see the supplemen-

tary Doc. S1 for the rate equation); the values of a (the factor affecting ATP binding to the enzyme–PPi complex), b (the factor affecting

Vmax), and Kact PPi (the activation constant) refer only to this particular experiment. The mean values are shown in the legend to Table 5. For

ALDO experiments, the PPi concentrations (mM) were: closed squares, 0; open circles, 0.3; and open triangles, 1. The lines represent the

best fit to a competitive inhibition-type equation. The Vmax [mU · (mg protein)1)], Km (mM) and Ki (mM) values were: 118, 0.085 and 0.21 at

pH 6.0; and 213, 0.029 and 0.42 at pH 7.0, respectively.



and TPI exerted no control [6–8]. For the final reconsti-

tuted segment from 3PG to Pyr, Giersch [9] showed that

PYK (CJPYK ¼ 0:8� 1:0) and ENO (CJ

ENO ¼ 0:16� 0:18)

controlled flux, with PGAM having negligible control.

Unfortunately, these studies were carried out under

nonphysiological conditions regarding temperature, pH,

ammonium concentration (this cation is a potent activa-

tor of PFK-1 at millimolar concentrations) or, perhaps

more importantly, at enzyme proportions that did not

correspond with those found in the respective biological

systems.

It may not be biologically relevant to identify one

given enzyme as the main controlling step by pathway

reconstitution experiments if the amount of added

enzyme is below the physiological level, thus imposing a

flux limitation where there should have been none. The

addition of arbitrary proportions of enzymes affects all

the system properties: flux rate, steady-state concentra-

tion of metabolites and flux control distribution.

For instance, in a previous work [16], the E. histoly-

tica final glycolytic segment was reconstituted at pH 7

with an enzyme proportion similar (1 PGAM; 10.6

ENO; 1.6 PPDK), but not identical, to that deter-

mined in amebas (1 PGAM; 5.8 ENO; 3 PPDK) [10].

With such higher ENO activity and lower PPDK activ-

ity, the flux control resided mostly in the PPDK

(CJPPDK ¼ 0:52), whereas at a lower PPDK active con-

tent (PPDK ⁄PGAM = 0.1–0.25), PPDK became a

typical rate-limiting step (CJPPDK ¼ 1:0). In contrast,

Table 6. Control analysis in the modeled first segment of

E. histolytica glycolysis at pH 7 and at physiological concentrations

of glucose, PPi, ATP, ADP, AMP and Pi. Fru6P, fructose 6-phos-

phate.

2 mM glucose; 0.45 mM

PPi; 5 mM ATP; 3.3 mM

ADP; 1.6 mM AMP; 5.4 mM Pi

Flux rate, nmolÆmin)1 25.6

Glc6P, mM 4.7

Fru6P, mM 0.67

Fru(1,6)P2, mM 0.052

CJHK 0.997

CJHPI 0.0006

CJPPi�PFK 0.0009

CJALDO 0.0014

CJTPI 0.000005

0.00.51.020

40

60

80

100

IC50 = 480 µM

CJ

HK

Flu

x (n

mo

l·min

–1)

[AMP] (µM)

0 500 15001000 2000

0 500 15001000 2000

0

5

10

15

20

IC50 = 300 µM

A

B

Fig. 7. Effect of varying the AMP concentration on flux of the first

glycolytic segment. (A) Reconstituted pathway. The line represents

the fitting of the experimental points to the first-order exponential

decay rate equation. (B) Modeled pathway. IC50, AMP concentra-

tion required to reach half-maximal inhibition.

Table 5. Control analysis in the modeled first segment of E. histo-

lytica glycolysis with PPi activation of HK and PPi inhibition of

ALDO. The values of the kinetic parameters used in the model are

shown in Table S3. The concentrations of ATP (2.5 mM), PPi

(0.5 mM), ADP (0.5 mM), AMP (0.03 mM) and Pi (0.5 mM) were

fixed. These values were reached in the reconstituted system

around the middle of the pseudo steady-state duration (data not

shown). The PPi activation in the HK rate equation involves, at

pH 7, a b value (factor affecting Vmax) of 1.6 ± 0.09 (n = 4), an a

value (factor affecting ATP binding to the enzyme–PPi complex) of

1.38 ± 0.25 (n = 4), and a Kact PPi of 67.5 ± 57 lM (n = 4); at pH 6

the same constants were 1.45, 1.2 and 150 lM, respectively. The

Vmax and Vmax values for HPI, PPi-PFK and ALDO were diminished

by 40, 25 and 40%, respectively, at pH 7, and by 40, 15 and 20%

at pH 6. Other changes were: for HK, the c value (the factor affect-

ing substrate binding induced by AMP) was 2.5 at pH 7 and 1.3 at

pH 6; for PPi-PFK, the a (the factor affecting binding of the second

substrate to the enzyme–first substrate complex) and b (the factor

affecting binding of the second product to the enzyme–first product

complex) values were 1.2 and 0.5 at pH 7, and 1 and 1 at pH 6,

respectively: for ALDO, instead of using the Ki PPi value of 430 lM

obtained experimentally at pH 7, the model required the diminution

of this value to 43 lM (at pH 6, the Ki PPi was unaltered), whereas

variation of the a value (the factor affecting binding of the second

product to the first product–enzyme complex) from 0.1 to 5 did not

alter any system or control property. Fru6P, fructose 6-phosphate.

pH 6.0 pH 7.0

Flux rate, nmolÆmin)1 105 (50 mU HK) 125.5 (50 mU HK)

Glc6P, mM 351 585

Fru6P, mM 47 9.2

Fru(1,6)P2, mM 0.9 0.83

CJHK 0.68 0.54

CJHPI 0.06 0.21

CJPPi�PFK 0.18 0.17

CJALDO 0.08 0.08

CJTPI 0.0002 0.0004



with the correct enzyme proportion, PGAM was the

main controlling step (see Table 1). Giersch [9] recon-

stituted the final glycolytic segment of rabbit skeletal

muscle with an enzyme proportion of 1 PGAM; 1

ENO; 1 PYK, and at a pH of 7.6 and at room temper-

ature. Under such nonphysiological conditions, the

control of flux was exerted mainly by PYK. By using

the well-documented physiological enzyme proportion

found in skeletal muscle, of 1 PGAM; 1.6 ENO; and

3.8 PYK [18], it is expected that the PYK flux control

should diminish. Therefore, it is highly crucial in path-

way reconstitution analyses to use the correct, physio-

logical proportion of enzymes to draw biologically

meaningful conclusions about the pathway’s flux con-

trol distribution.

The physiological catalytic efficiency (Vmax ⁄Km)

sequence order for the final reconstituted segment is

PPDK>ENO�PGAM at both pH values of 6 and 7

(supplementary Table S1). However, a more rigorous

comparison of catalytic efficiencies was elaborated by

Heinrich & Rapoport [19], who considered the efficien-

cies for the forward as well as the reverse reactions in

their analysis of linear enzymatic chains. By using the

kinetic parameters reported in the previous publication

for the forward and reverse reactions of PGAM, ENO

and PPDK [16], it was possible to establish that the

net catalytic efficiency [(Vmax ⁄Km S) ) Vmax ⁄Km P)]

sequence order was identical to that described above

for the forward reaction. It should be noted that the

described expression for the net catalytic efficiency

only applies to enzymes with one substrate and one

product. For bireactant and ter-reactant enzymes, the

correct expression is: [Vmax ⁄ (Km S1 x Km S2 x ÆÆ) )Vmax ⁄ (Km P1 x Km P2 x ÆÆ)]. It should also be noted

that the catalytic efficiency is inversely related to the

flux control coefficient [20]. Both the experimentally

determined and the modeled flux control distribution

of the final glycolytic segment were in agreement with

the catalytic efficiency sequence (i.e. higher flux control

with lower catalytic efficiency) because the control

sequence was PGAM�ENO>PPDK. The higher flux

control exerted by ENO, in comparison to that exerted

by PPDK, is a result of the PPi (and 3PG) competitive

inhibition, which increases the Km value and hence

decreases the catalytic efficiency. Therefore, to have an

initial semiquantitative appreciation of flux control

distribution in a given pathway, it may be useful to

compare catalytic efficiencies.

Although the PPDK Km values for products were

determined in the present work, the rate equation for

this enzyme (Uni Uni Bi Bi Ping Pong-Ordered) [17],

contains several other kinetic constants (Ki A, Ki B,

Ki C, Ki P, Ki Q, Ki R), for which no experimental deter-

mination has been carried out. Simplifying the rate

equation for PPDK to Bi Bi Ping Pong might have

some validity under in vivo conditions because the total

concentrations of ATP and AMP are certainly present

at saturating conditions [10]; however, for the in vitro

reconstituted system, this logic does not apply because

the concentrations of ATP and AMP used were not

saturating. Therefore, an empirical rate equation that

included the six PPDK ligands substituted for the Uni

Uni Bi Bi Ping Pong-Ordered equation; however, the

six-ligands equation did not completely account for the

PPDK behavior in the reconstituted system. Moreover,

the refined model with PGAM and ENO inhibition by

PPi and with the PPDK simpler Bi Bi Ping Pong equa-

tion, simulated better the experimentally determined

flux control coefficient distribution. Therefore, further

refinement of the PPDK equation is still required.

Modeling of other pathways containing ter-reactant or

cooperative enzymes (e.g. GAPDH, ATP-PFK) has

also used simplified rate equations. It might be possible

to achieve better modeling results if not-so-simplified

rate equations are used.

The Vmax ⁄Km sequence order for the first glycolytic

reconstituted segment is ALDO>TPI�HK>>>PPi-

PFK>HPI (supplementary Table S3), whereas the

experimentally determined and modeled flux-control

distribution indicated the sequence HK>HPI,

PPi-PFK>ALDO�TPI (see Table 4). Hence, there

must be additional interactions of metabolites with HK

and ALDO that decrease their catalytic efficiencies. The

predominant HK flux-control is explained by the strong

AMP inhibition (see Fig. 7), under which even a small

contaminating concentration of AMP, derived from

added ATP, exerts a potent inhibition on HK, thus sur-

passing the PPi activation. In turn, ALDO was inhibited

by PPi. It might be of value to investigate the PPi modu-

lating effect on glycolytic enzymes in other organisms,

to identify relevant, but currently ignored, interactions

that might affect flux control.

The experimentally validated models of the final and

first glycolytic segments allowed simulation of the sys-

tem behavior under low, physiological concentrations

of metabolites and the incorporation of alternative,

parallel routes. The predictions from both models were

in agreement with the model of the complete pathway

[10]: HK and PGAM are the main controlling steps of

glycolysis.

Unveiling hidden interactions in a metabolic

pathway

The model for the final glycolytic segment at pH 6, with

PPi and 3PG inhibition on ENO activity, was robust



regarding changes in the ENO Km phosphoenolpyruvate

and Ki PPi values and all PPDK Km values (for

phosphoenolpyruvate, PPi, AMP, Pyr, ATP and Pi), but

was less robust for variations in the ENO Km 2PG.

Certainly, Km 2PG is the kinetic parameter most affected

by other metabolites distinct from the substrate (double-

competitive inhibition exerted by PPi and 3PG). Thus,

it was relevant to re-evaluate the determination of this

parameter (see supplementary Table S1 for values);

however, no significant difference from the previously

reported value was found, although the slightly higher

ENO Km 2PG favored the model robustness. A more

robust model may be expected with the incorporation

of a greater number of reactions, as demonstrated in

previous work on the complete glycolytic pathway [10].

HK activity in E. histolytica is strongly modulated

by AMP [10,16]. However, at a high physiological

ATP concentration of 5 mm, the AMP inhibition may

be attenuated if micromolar inhibitor concentrations

are used. Thus, to overcome the presence of high con-

centrations of ATP, AMP also has to be present at

millimolar concentrations. Determination of the AMP

concentration in amebas under steady-state conditions

revealed that this metabolite was indeed at an unusu-

ally high concentration of 1.6 mm [10]. Therefore, the

effect of millimolar concentrations of AMP on flux

rate and flux control distribution of the reconstituted

first glycolytic segment may have physiological rele-

vance because at this high AMP concentration it is

expected that HK could be the main flux control step,

as demonstrated by modeling the complete glycolytic

amebal pathway [10].

The activation of HK by PPi has not been previously

described for HK from other sources. For human HKs,

the product Gluc6P acts as a potent inhibitor. It has

been described that the HK-binding site for Gluc6P can

be blocked by PPi [21], thus inducing de-inhibition or

pseudo-activation. As Gluc6P does not affect amebal

HK [10,16], it is probable that the PPi activation is

exerted through a different mechanism. Such an activa-

ting PPi effect was observed when the amebal recom-

binant HK activity was coupled to either Gluc6P

dehydrogenase (for Gluc6P generation) or PYK ⁄LDH

(for ADP formation), discarding an unspecific effect of

PPi on the coupling enzymes. Moreover, PPi activation

was also shown on native amebal and yeast HK

enzymes (see supplementary Table S4), but not on

tumor HK enzymes that are inhibited by Gluc6P.

In conclusion, the combination of enzyme titration

of the in vitro reconstituted pathway flux with model-

ing and enzyme kinetics allows for a better under-

standing of the pathway behavior and control

properties. Thus, considering the absence of cytosolic

pyrophosphatases, the low PPi concentration in troph-

ozoites, as well as the presence of PPi-dependent

enzymes in amebal metabolism [13] and the PPi modu-

lation of HK, ALDO, PGAM and ENO (this work), it

is suggested that PPi has a central regulatory function

in the parasite (modeling predicted that a relatively

small variation in the PPi concentration affects flux-

control distribution). AMP also appears as another

important regulatory metabolite in amebal glycolysis

as a substrate of the last glycolytic enzyme (PPDK)

and an inhibitor of the first enzyme (HK). Modeling

of the entire amebal glycolysis predicted negligible reg-

ulatory roles for the ATP ⁄ADP and NADH ⁄NAD+

ratios [10]. Therefore, with the replacement of the typi-

cal highly exergonic reactions of cooperative ATP-

PFK and PYK by the noncooperative (hyperbolic)

PPi-PFK and PPDK, it seems that the information

transfer and regulatory mechanisms of amebal glycoly-

sis are mediated by AMP and PPi.

Amebal PPi-dependent enzymes (PPi-PFK and

PPDK) have been traditionally considered as appropri-

ate drug targets for therapeutic intervention in amebia-

sis, because these enzymes are not present in the

human host [2,3,13]. Furthermore, some PPi analogs

that inhibit these enzymes indeed decrease parasite

growth [22–24] (although in these studies no measure-

ment of glycolytic fluxes or in vivo enzyme inhibition

was made to determine the specificity of glycolysis

blockade). By describing the enzyme kinetics of amebal

glycolytic enzymes [16] and by applying metabolic con-

trol analysis to kinetic modeling [10] and pathway

reconstitution (the present work), we found that PPi-

dependent enzymes are not the main flux control steps

of amebal glycolysis and, in consequence, highly spe-

cific and very potent inhibitors for these enzymes have

to be used in order to affect the glycolytic flux and

ATP level. By contrast, other enzymes not considered

therapeutically relevant have been revealed as potential

drug targets because of their high flux control coeffi-

cient (HK, PGAM and perhaps the glucose trans-

porter) or their divergence from the human host

(ALDO and PGAM). The PPi modulation of HK,

ALDO, PGAM and ENO found in the present work

may open new venues for drug target evaluation.

Materials and methods

Chemicals

3PG, AMP, PPi, ATP, NADH, glucose, MgCl2, CoCl2,

PYK, LDH, ALDO, Glc6P dehydrogenase, TPI and

aGPDH were from Roche (Mannheim, Germany) or Sigma

(St Louis, MO, USA).



Enzyme preparation and storage

The over-expressed recombinant enzymes from E. histolytica

(i.e. PGAM, ENO, PPDK, HK, HPI, PPi-PFK, ALDO and

TPI) were prepared as previously described [16]. Thereafter,

the purified enzymes were concentrated by ultrafiltration and

centrifugation through Amicon filters (Millipore, Billerica,

MA, USA); glycerol was added to a final concentration of

50% and the concentrated enzymes were stored at )20 �C.The protein concentrations were 2–18 mgÆmL)1. Under these

storage conditions, the enzyme activities showed minimal loss

of activity for at least 6 months. In some enzymes, 50%

activity loss was observed only after 12 months.

Enzyme kinetics assays

To reconstitute the final and first glycolytic segments under

the correct enzyme proportions, the activities of PGAM,

ENO and PPDK (final segment) and of HK, HPI,

PPi-PFK, ALDO and TPI (first segment), were always

determined in the forward reaction prior to starting the

reconstitution experiment at both pH 6.0 and 7.0, and at

37 �C. The enzymatic assay conditions were as previously

described [16], using a buffer mixture of 50 mm imidazole,

10 mm acetate, 10 mm Mes and 10 mm Tris, adjusted to

pH 6.0 or 7.0. The stock solutions for enzymatic activities

and for reconstitution experiments (3PG, ATP, AMP,

glucose and PPi) were routinely calibrated.


Final segment

The reaction assay medium contained 10 mm MgCl2,

0.5 mm AMP, 0.15–0.2 mm NADH, 2 mm PPi, 10–15 units

(at pH 7) or 20–30 units (at pH 6) of LDH (suspension in

ammonium sulfate; activity as supplied by the manufac-

turer) and the E. histolytica recombinant enzymes PGAM,

ENO and PPDK at the indicated enzyme ratios and at

37 �C. When varying one enzyme concentration, the other

enzymes were kept at a constant ratio. Where indicated,

3 mm ATP + 10 mm Pi were included in the reaction med-

ium. To avoid precipitation, PPi, ATP and Pi were added

after mixing the reaction assay with the pH buffer mixture.

The reaction was initiated 3–4 min later by adding 4 mm

3PG. No NADH oxidation was attained in the absence of

either PPi or AMP in the presence of 3PG.

First segment

The reaction assay medium contained 10 mm MgCl2,

0.5 mm CoCl2, 0.15–0.2 mm NADH, 3 mm ATP, 1 mm PPi

and 7 (pH 7) or 10 (pH 6) units of aGPDH (ammonium

suspension; activity as supplied by the manufacturer) in the

pH buffer mixture at pH 6.0 or 7.0. The E. histolytica

recombinant enzymes HK, HPI, PPi-PFK, ALDO and TPI

were added at the indicated ratios and the reaction was

incubated at 37 �C. After a short pre-incubation of 3.5–

4 min, the reaction was started by adding 10 mm glucose.

With glucose added, no NADH oxidation was observed in

the absence of either ATP or PPi.

Determination of metabolites

The reconstituted final and first glycolytic segments were

allowed to reach a pseudo steady state. Then, aliquots were

withdrawn at two different time-points and mixed with 3%

(v ⁄ v) ice-cold perchloric acid in the presence of 1 mm

EDTA. The samples were centrifuged and the supernatant

was neutralized with a solution of 3 m KOH ⁄ 0.1 m Tris

and stored at )70 �C. The amounts of 2PG and

phosphoenolpyruvate (final segment) and of Glc6P and

fructose 6-phosphate (first segment) were determined by use

of standard enzymatic assays [16].

Acknowledgement

The present work was partially supported by grant

numbers 60517 and 46719-Q from CONACyT-Mexico.

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Supplementary material

The following supplementary material is available

online:

Doc. S1. Rate equations.

Fig. S1. Effect of varying the Km values on flux control

coefficient and, rate and metabolite concentrations at

pH 6.0.

Fig. S2. (A) Flux rate- enzyme proportion relationship

for the first glycolytic segment. (B) Flux control by

ALDO in the absence of added Co2+ in the reconsti-

tuted upper segment.

Table S1. Kinetic parameters of the enzymes in the

final E. histolytica glycolytic segment.

Table S2. Control analysis in the modeled final

segment of E. histolytica glycolysis.

Table S3. Kinetic parameters of the enzymes in the

first E. histolytica glycolytic segment.

Table S4. Effect of PPi on the HK activity from differ-

ent sources.

This material is available as part of the online article

from http://www.blackwell-synergy.com

Please note: Blackwell Publishing are not responsible

for the content or functionality of any supplementary

materials supplied by the authors. Any queries (other

than missing material) should be directed to the corre-

sponding author for the article.



Experimental validation of metabolic pathway modeling

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