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

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:
Note
The mathematical model described here
has been submitted to the Online Cellular
Systems Modelling Database and can be
accessed at />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

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-

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

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

; 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

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

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

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

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

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

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

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.

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

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

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

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

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-

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

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

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

A kinetic model of E. histolytica glycolysis was con-
structed based on the kinetic properties of amoebal
glycolytic purified enzymes previously determined by
our research group [21]; enzyme activities in amoebal
extracts were measured under the same experimental
conditions of buffer and physiological pH value (6.0)
and temperature (37 °C). When determining the V
m
values for the forward and reverse reactions (Table 1),
care was taken to calculate the enzyme activities under
true V
m
conditions (i.e. in the presence of saturating
substrate concentrations, at least ten-fold the K
m
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 parame-
ters 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 AldDH reactions and those of the
branching reactions were indeed adjusted because they
have not been thoroughly studied as yet. In all the
conditions tested, the model simulations reached an
asymptotically steady-state condition, as long as the
PPi concentration was kept constant. When the PPi
level was variable, the model was unable to maintain

m
values for some prod-
ucts were only adjusted because they were not experi-
mentally determined. In the kinetic model described in
the present work, the influence of using K
eq
in the rate
equations was eliminated by introducing the actual V
m
0
0 20 40 60 80 100
20
40
60
80
100
PPDK
PGAM
PPi-PFK
HK
HK + PGAM
flux (%)
enzyme activity (%)
Fig. 4. Dependence of glycolytic flux on enzyme activity. In this
plot, 100% enzyme is the corresponding V
m
value determined in
amoebal extracts at pH 6.0 (Table 1); 100% flux is 37 nmol EtOH ⁄
(minÆmg cellular protein
)1

property of having one of the highest flux-control coef-
ficients as predicted by models with either reversible or
irreversible HK rate equation.
Feedback inhibition in metabolic pathways is an
efficient mechanism of metabolite homeostasis, partic-
ularly in pathways that have reactions with large K
eq
[46,47]. In this regulatory mechanism, the K
i
value of
the sensing enzyme determines the steady-state con-
centration of its product, and consequently that of
the subsequent metabolites, but it does not signifi-
cantly affect the pathway flux [48]. Glycolysis in
E. histolytica apparently lacks mechanisms of feed-
back inhibition, although it still has one reaction
(HK) with a large K
eq
. Because G6P (or ADP) does
not exert significant product inhibition on HK, there
should be an alternative regulatory mechanism that
transfers information from the ending to the initial
part of the pathway, under which conditions a stable
steady state may be reached [47]. As transfer informa-
tion between pathway reactions was ensured in the
model by introducing all reactions as reversible [47],
a stable steady state was reached, even when the HK
reaction was assumed irreversible (but with AMP
inhibition).
AMP potently inhibits HK activity by a mixed-type

bas may have time to find ways of eliminating the
HK (and glucose transporter) inhibitors. Therefore, a
better 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 concen-
tration 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 behavior under 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 synthesis and
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 sit-
uation in which the parasites are colonizing the intes-
tine because of the impossibility of reproducing the
intestine’s microenvironment in the laboratory and
because very little is known about the metabolism
under this condition.
There has been accumulating experimental evidence

concentrations that may be achieved when one or
more pathway enzymes are inhibited. The results of
the simulations indicate that HK and PGAM inhibi-
tion might have larger negative effects on glycolytic
flux and metabolite concentrations than inhibition of
the PPi-dependent enzymes PPi-PFK and PPDK.
Although the latter two enzymes are still appropriate
drug targets because of their divergence with respect
to the ATP-PFK and PYK enzymes present in
humans [22,23,55–57], their negligible flux-control
coefficients demand the design of highly potent and
very specific inhibitors for the parasite’s enzymes or
the full blockade of their gene transcription or trans-
lation. These two PPi-dependent enzymes exhibited
activity thresholds above 70% of total active enzyme,
thus making it difficult to apply specific drugs to
effectively kill the parasite. Moreover, the response
of these enzymes to inhibitors such as bisphospho-
nates [57], which are nonhydrolyzable analogs of PPi,
may depend on the concentration of this metabolite
within the cell if the inhibition mechanism is compet-
itive. In this regard, with the amoebal kinetic model,
the type of inhibitor that is best for each amoebal
enzyme and transporter can be evaluated not only to
inhibit the enzyme in the test tube, but also to exam-
ine whether the inhibition has significant effects on
the pathway flux and metabolite concentrations in
the parasite.
Experimental procedures
Chemicals

xico).
Glycolytic enzymes activities in amoebal
trophozoites
E. histolytica trophozoites strain HM1:IMSS were isolated
from experimentally induced amoebic liver abscess in ham-
sters and cultured in TYI-S-33 medium as previously
described [18]. Amoebas (1–2 · 10
8
) were harvested by
chilling on ice, centrifuging at 450 g (IEC Centra CL3R;
Needham Heights, MA, USA) and washing twice with
NaCl ⁄ Pi at pH 7.4. Clarified extracts to measure glycolytic
enzyme activities were prepared by freezing–thawing and
centrifugation as previously described [18]. Aliquots of the
soluble fraction were stored at )20 °C in the presence of
10% (v ⁄ v) glycerol. Cellular protein was determined by the
Lowry method. Protein in the soluble fraction corresponded
to 1.25 ± 0.5 mg protein per 10
6
cells (n ¼ 5). Total cellu-
lar protein was 2 ± 0.8 mg protein per 10
6
cells (n ¼ 4).
Enzyme activities from HK to PPDK in the forward and
reverse reaction (Table 1) were measured at 37 °C and physi-
ological pH values of 6.0 and 7.0 because the actual cytosolic
pH in amoebas has not been directly determined, and only
indirect evidence [58] suggests that it may be similar to the pH
of the medium, which varied along the time of culture (6.3–
6.7). The pH buffer mixture was 50 mm imidazole, 10 mm

phate buffer with 2 mm NAD
+
,10mm cysteine and 340 mm
EtOH. AldDH activity was measured in the ADH assay buf-
fer in the presence of 40 mm pyrazole to inhibit the ADH
activity. The activity of 3PGDH in the direction of 3PG con-
sumption was measured under several conditions at pH val-
ues of 6, 7 and 8 with 1–3 mm 3PG; however, in all trials, the
activity was below the limit of detection of the method.
The activity of AK in clarified extracts was measured
with two coupled assays: (a) production of ADP from ATP
and AMP using PEP and PYK ⁄ LDH as coupling system
and (b) production of ATP and AMP from ADP and cou-
pling to PEP, amoebal PPDK and LDH. However, the
specificity of both assays could not be directly ascribed to
AK because of the presence of contaminating activities (sig-
nificant basal activity in the absence of AMP in the first
case and presence of an ADP-consuming activity in the sec-
ond case). The activity of ATPases was monitored as ADP
production in a reaction containing pH buffer mixture,
5mm MgCl
2
, 1.2 mm PEP, 0.13 mm NADH and 5 U
PYK ⁄ LDH with 3 mm ATP as substrate. The reaction was
started by adding an aliquot of the soluble fraction of the
cellular extract, thus discarding the effect of contaminating
ADP from the ATP stock solution.
NAD(P)H consumption activities (DHases) were mea-
sured in buffer mixture in the presence of 0.13 mm NADH
or NADPH and following the oxidation of the coenzymes

described above, were re-suspended in NaCl ⁄ Pi buffer of
pH 7.4 to a density of 2–4 · 10
7
cellsÆmL
)1
. The cells
were incubated at 35 °C for 1 h in the presence of
10 mm glucose in a closed 50 mL plastic tube with gentle
agitation to avoid clogging. The tube was opened every
15 min to favor gas exchange. After this time, approxi-
mately 98% of the cells were viable as determined by
trypan-blue exclusion. The cell samples were treated with
3% (v ⁄ v) ice cold-perchloric acid in the presence of
1mm EDTA and centrifuged; the supernatant was neu-
tralized with different volumes of a solution of 3 m
KOH ⁄ 0.1 m Tris and stored at )70 °C. Metabolite con-
centrations were determined by similar assays to those
used to measure the enzymatic activities with the recom-
binant enzymes [21], except that aliquots (5–300 lL) of
the neutralized amoebal extracts were added instead of
the specific substrate and the reactions were initiated with
specific enzyme. All determinations were carried out in
2 mL of reaction mixture in fluorimetric cuvettes in a
spectrofluorometer (Shimadzu, Kyoto, Japan) or in quartz
cuvettes in a spectrophotometer, depending on the metab-
olite content. Concentrations of metabolites listed in
Table 2 were calculated by assuming that amoebal troph-
ozoites have a volume of 20 lL per 10
7
cells.

calibration curves of standard nucleotides.
Divalent metal concentration for cobalt, zinc and copper
were determined in amoebal acidic extracts by atomic
absorption spectrometry as previously described [59].
E. Saavedra et al. Modeling Entamoeba glycolysis
FEBS Journal 274 (2007) 4922–4940 ª 2007 The Authors Journal compilation ª 2007 FEBS 4935
Kinetics of EtOH production
Amoebas were incubated as described above for the determi-
nation of metabolites, except that at several time points, an
aliquot of 500 lL equivalent to 2 · 10
6
cells was withdrawn
for perchloric acid extraction and neutralization. EtOH was
determined enzymatically by measuring NAD
+
reduction
with commercial ADH in an assay mixture containing
50 mm bis-Tris-propane pH 9.0, 2 mm NAD
+
and 20 mm
cysteine. The reaction mixture was incubated in the absence
of extract to achieve full exhaustion of contaminating EtOH;
then, an aliquot (5–10 lL) of the cellular extract was added.
Description of the model
The glycolytic pathway in E. histolytica was simulated by
using the software gepasi[43] (available at http://www.
gepasi.org). Reactions were represented in the program as
described in Table S1A of the Supplementary Material. The
model was based on the K
m

i
for ADP
previously reported [21] was used as the K
m
for the
product. The values assigned to the constants a, b and c
were one.
HK kinetics was also considered as irreversible with
mixed inhibition by AMP and competitive inhibition by
ADP (Eqn 2) [60,61] as previously demonstrated with the
recombinant enzyme [21]:
The a, b, c and d constants were fixed to a value of 1.0;
when they were ten-fold varied, no change in the flux-con-
trol distribution was attained.
Simulations of these HK rate-equations in the computer
software origin mimicked the diminution in the enzyme
activity using the irreversible equation (data not shown).
These results validated the HK rate equations used in the
model.
When HK was represented as a reversible reaction with-
out AMP inhibition, the equation was Eqn (3) [60,61]:
Amoebal HPI, TPI, PGAM and ENO kinetics were
described as monoreactant reversible Michaelis–Menten
reactions (Haldane’s equation):
v ¼
V
m
f
S
Ks

v ¼
V
m
f
aK
gluc
K
ATP
½Gluc½ATPÀ
½G6P½ADP
Keq

1 þ
½gluc
K
gluc
þ
½ATP
K
ATP
þ
½gluc½ATP
aK
gluc
K
ATP
þ
½AMP
K
AMP

aK
gluc
K
ATP
1 þ
½gluc
K
gluc
þ
½ATP
K
ATP
þ
½AMP
K
AMP
þ
½ADP
K
ADP
þ
½gluc½ATP
aK
gluc
K
ATP
þ
½gluc½AMP
bK
gluc

½G6P½ADP
Keq

1 þ
½gluc
K
gluc
þ
½ATP
K
ATP
þ
½gluc½ATP
K
gluc
K
ATP
þ
½G6P
K
G6P
þ
½ADP
K
ADP
þ
½G6P½ADP
K
G6P
K

þ
½B
Kb
þ
½A½B
aKaKb
þ
½P
Kp
þ
½Q
Kq
þ
½P½Q
bKpKq
where A and B (for substrates) and P and Q (for products)
correspond to the substrates and products in the sequence
described in the reactions displayed in Table S1A. Strictly,
GAPDH is a ter-reactant enzyme; to simplify its rate equa-
tion, in the model the Pi concentration was fixed at a satu-
rating concentration (5 mm).
Amoebal PGK displays one order of magnitude higher
affinity for GDP over ADP [21]. The total GDP concentra-
tion found in amoebas (Table 2) was 2.4–17.5-fold the K
m
value of the enzyme for GDP (0.04 and 0.29 mm at pH 6.0
and 7.0, respectively) [21]; therefore, PGK should be satu-
rated with GDP at pH 6.0. In the model, the PGK reaction
was made dependent on ADP because of the lack of data
regarding the balance in the guanine nucleotide pool. More-

m
r
½DHAP½G3P
K
DHAP
K
G3P
1 þ
½F1;6P2
K
F1;6P2
þ
½DHAP
K
DHAP
þ
½G3P
K
G3P
þ
½DHAP½G3P
K
DHAP
K
G3P
PPDK transforms PEP, AMP and PPi into pyruvate, ATP
and Pi and displays a uni-uni-bi-bi ping-pong ordered
mechanism, for which the reported rate equation is extre-
mely complex [63]. The rate equation used in the present
model was simplified as follows:

nisms [60,61]:
v ¼
Vm½A½B
KaKb þ Kb½Aþ½A½B
For ADH, the K
m
values for NADH (0.05 mm) and acetal-
dehyde (0.15 mm) were those previously described for the
amoebal enzyme determined at pH 6.5 [44]. The V
m
was
the sum of the NAD(P)H-ADH activities displayed in
Table 1. The 3PGDH K
m
values were 0.2 mm and
0.087 mm for 3PG and NAD
+
, respectively, as described
by Ali et al. [38]. However, the V
m
f was adjusted to values
of 1.3–10 mUÆmg
)1
to fit the 3PG concentration.
The glycogen synthesis and glycogen degradation reac-
tions were defined as mass-action irreversible reactions
v ¼ k
Q
i
S

j
is the concentration of prod-
uct(s). For each reaction, the rate constants used are shown
in Table S1B.
Acknowledgements
This work received financial support from CONACyT-
Me
´
xico (grants numbers 46719-Q to ES and 43811-Q
to RMS). We thank Dr David Mendoza-Co
´
zatl for his
help in the preliminary stages of the modeling and
Mario Nequiz for help with the amoebal culture. We
also grateful recognize the insightful comments and
observations made by the three reviewers, which signif-
icantly improved the manuscript.
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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.
Doc S1. Variations to the kinetic model.
Table S2. Flux-control coefficients and metabolite
concentrations of the model with the HXT reversible
rate equation.
This material is available as part of the online article
from
Please note: Blackwell Publishing is 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.