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
Trang 1Entamoeba histolytica
Emma Saavedra1, Alvaro Marı´n-Herna´ndez1, Rusely Encalada1, Alfonso Olivos2,
Guillermo Mendoza-Herna´ndez3and Rafael Moreno-Sa´nchez1
1 Departamento de Bioquı´mica, Instituto Nacional de Cardiologı´a, Me´xico DF, Me´xico
2 Departamento de Medicina Experimental, Facultad de Medicina, Universidad Nacional Auto´noma de Me´xico, Me´xico DF, Me´xico
3 Departamento de Bioquı´mica, Facultad de Medicina, Universidad Nacional Auto´noma de Me´xico, Me´xico DF, Me´xico
Keywords
ATPases; drug targeting; hexokinase;
phosphoglycerate mutase
Correspondence
E Saavedra, Departamento de Bioquı´mica,
Instituto Nacional de Cardiologı´a, Juan
Badiano no 1 Col Seccio´n XVI, CP 14080,
Tlalpan, Me´xico DF, Me´xico
Fax: +5255 5573 0926
Tel: +5255 5573 2911 ext 1422
E-mail: emma_saavedra2002@yahoo.com
Note
The mathematical model described here
has been submitted to the Online Cellular
Systems Modelling Database and can be
accessed at http://jjj.biochem.sun.ac.za/
database/saavedra/index.html free of charge
(Received 7 November 2006, revised
13 July 2007, accepted 27 July 2007)
doi:10.1111/j.1742-4658.2007.06012.x
Glycolysis in the human parasite Entamoeba histolytica is characterized by the absence of cooperative modulation and the prevalence of pyrophosphate-dependent (over ATP-pyrophosphate-dependent) enzymes To determine the flux-control dis-tribution of glycolysis and understand its underlying control mechanisms, a kinetic model of the pathway was constructed by using the software gepasi The model was based on the kinetic parameters determined in the purified recombinant enzymes, and the enzyme activities, and steady-state fluxes and metabolite concentrations determined in amoebal trophozoites The model predicted, with a high degree of accuracy, the flux and metabolite concentra-tions found in trophozoites, but only when the pyrophosphate concentration was held constant; at variable pyrophosphate, the model was not able to completely account for the ATP production⁄ consumption balance, indicating the importance of the pyrophosphate homeostasis for amoebal glycolysis Control analysis by the model revealed that hexokinase exerted the highest flux control (73%), as a result of its low cellular activity and strong AMP inhibition 3-Phosphoglycerate mutase also exhibited significant flux control (65%) whereas the other pathway enzymes showed little or no control The control of the ATP concentration was also mainly exerted by ATP consum-ing processes and 3-phosphoglycerate mutase and hexokinase (in the produc-ing block) The model also indicated that, in order to diminish the amoebal glycolytic flux by 50%, it was required to decrease hexokinase or 3-phospho-glycerate mutase by 24% and 55%, respectively, or by 18% for both enzymes By contrast, to attain the same reduction in flux by inhibiting the pyrophosphate-dependent enzymes pyrophosphate-phosphofructokinase and pyruvate phosphate dikinase, they should be decreased > 70% On the basis of metabolic control analysis, steps whose inhibition would have stronger negative effects on the energy metabolism of this parasite were identified, thus becoming alternative targets for drug design
Abbreviations
ADH, alcohol dehydrogenase; AK, adenylate kinase; ALDO, fructose 1,6-bisphosphate aldolase; AldDH, aldehyde dehydrogenase; ATP-PFK, ATP-dependent phosphofructokinase; DHAP, dihydroxyacetone phosphate; ENO, enolase; EtOH, ethanol; F6P, fructose 6-phosphate; F(1,6)P2, fructose 1,6-bisphosphate; G6P, glucose 6-phosphate; G6PDH, glucose 6-phosphate dehydrogenase; G3P, glyceraldehyde 3-phosphate; GAPDH, glyceraldehyde 3-phosphate dehydrogenase; Gly3PDH, glycerol 3-phosphate dehydrogenase; HK, hexokinase; HPI, hexose 6-phosphate isomerase; HXT, hexose transporter; LDH, lactate dehydrogenase; MCA, metabolic control analysis; PGAM, 3-phosphoglycerate mutase; PGK, phosphoglycerate kinase; PGM, phosphoglucomutase; 3PGDH, 3-phosphoglycerate dehydrogenase; PEP, phosphoenolpyruvate; 2PG, 2-phosphoglycerate; 3PG, 3-phosphoglycerate; PPi, pyrophosphate; PPi-PFK, pyrophosphate-dependent phosphofructokinase; PPP, pentose phosphate pathway; PFOR, pyruvate:ferredoxin oxidoreductase; PFOR-AldDH, lumped reaction of PFOR and AldDH; PPDK, pyruvate phosphate dikinase; PYK, pyruvate kinase; TPI, triosephosphate isomerase.
Trang 2The protist parasite Entamoeba histolytica is the
causa-tive agent of human amoebiasis Approximately one
billion people are currently at risk of acquiring the
dis-ease; the parasite causes severe illness in 48 million
people each year and the number of annual deaths is
in the range 40 000–100 000 [1,2] Metronidazole
ther-apy to control the disease is relatively effective;
how-ever, in 40–60% of treated patients, the microorganism
persists in the intestinal lumen, generating parasite
car-rier states [3] Recent reports describe the induction
in vitro of E histolytica resistant strains to this drug
[4,5] If clinical resistance of E histolytica to
metroni-dazole becomes prevalent, there is no alternative drug
still available The search for better drugs is a
continu-ous process and further scientific research to
under-stand parasite biology and host–parasite interactions is
required to develop more effective treatment
Trophozoites of E histolytica lack functional
mito-chondria and have neither Krebs cycle, nor oxidative
phosphorylation enzyme activities; thus, glycolysis is
the only pathway able to generate ATP for cellular
work [6–8] In terms of regulation of glycolysis, the
amoebal pathway diverges in two important aspects
from that of the human host: First, it has the enzymes
pyrophosphate-dependent phosphofructokinase
(PPi-PFK) [9,10] and pyruvate phosphate dikinase (PPDK)
[11,12], which catalyze reversible reactions under
physi-ological conditions and are not subjected to allosteric
regulation as their mammalian counterparts
ATP-dependent phosphofructokinase (ATP-PFK) and
pyru-vate kinase (PYK), respectively In mammalian cells,
ATP-PFK and PYK catalyze irreversible reactions
under physiological conditions; these enzymes also
dis-play cooperative modulation by several physiological
metabolites and, together with hexokinase (HK) and
glucose transporter, have been identified as the main
flux-controlling steps of glycolysis in some human cell
types [13–16] Although ATP-PFK and PYK activities
have also been detected in E histolytica [17,18], their
activities in amoebal extracts are low in comparison to
their PPi-dependent counterparts and probably do not
significantly contribute to the total glycolytic flux
Sec-ond, like the human glucokinase (HK IV), amoebal
HK is not inhibited by its product glucose 6-phosphate
(G6P) [19]; instead, AMP and ADP are potent
inhibitors of the amoebal HK at physiological
concentrations [19,20]
Other relevant differences of the amoebal glucose
catabolism are the presence of a metal-dependent
class II fructose 1,6-bisphosphate aldolase (ALDO)
and a 2,3-bisphosphoglycerate-independent
3-phospho-glycerate mutase (PGAM), which have no homologues
with the enzymes present in human cells [21]
More-over, pyruvate is converted to acetyl-CoA by pyru-vate:ferredoxin oxidoreductase (PFOR) instead of a pyruvate dehydrogenase complex; and acetyl-CoA is further metabolized to ethanol (EtOH) and acetate [6,7]
The differences found in amoebal glycolytic enzymes
in comparison to those of its host suggest that these enzymes might be appropriate drug targets for thera-peutic intervention of this energetically important pathway in the parasite [22,23] However, it should be initially established whether the proposed target enzymes display high control on both the glycolytic flux and ATP concentration in amoebas and low con-trol in the host pathway If a difference in the concon-trol 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 (CJEi) CJEi is a value that represents the impact on flux of infinitely small changes in an enzyme activity by factors such as exter-nal inhibition or decreased expression An enzyme with
a CJEi¼ 1 means that the enzyme might indeed be the only rate-limiting step of the pathway To date, how-ever, MCA studies have shown that there are no rate-limiting steps; instead, the flux control of a given pathway is distributed among different enzymes [24] The summation theorem of MCA states that the sum
of the CJEi of all pathway steps is equal to one This may include steps from other pathways (such as branches or end-product consuming processes) as long
as they are linked by a metabolite or enzyme Conse-quently, some pathway steps may have CJEi values greater than one whereas those of branching steps have negative values, but the summation of all CJEi has to be unity [24]
Metabolic modeling (i.e in silico biology) uses the kinetic parameters of the complete set of enzymes belonging to a pathway (preferentially measured from the same source and under the same experimental con-ditions) to build kinetic models that can predict the system behavior In this sense, kinetic modeling is a
Trang 3useful 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 Vm values for the forward
and reverse reactions determined in cellular extracts
By fixing the PPi concentration, the model was able to
reach stable steady states under a variety of near
phys-iological conditions, thus allowing the estimation of
the flux-control, concentration-control and elasticity
coefficients for each enzyme With this strategy, it was
possible to quantitatively identify the main
flux-con-trolling enzymes of the amoebal glycolysis, as well as
the underlying biochemical mechanisms determining
why some enzymes exert high control and others do
not
The mathematical model described here has been
submitted to the Online Cellular Systems Modelling
Database and can be accessed at http://jjj.biochem
sun.ac.za/database/saavedra/index.html free of charge
Results
Glycolytic flux, enzyme activities and
intermediary concentrations in vivo
Glycolytic flux was measured as EtOH production in
amoebas incubated in the presence of 10 mm glucose
and a representative time-course is shown in Fig 1
The experimentally determined rate of flux was
calcu-lated by considering that 1· 106 amoebal cells
corre-spond to 2 ± 0.8 mg of total protein (n¼ 4) This
glycolytic flux value was six- to ten-fold higher than
the recalculated value previously reported by Montalvo
et al [34] in bacteria-grown amoebas under anaerobic
conditions at 37C after 1 h in the presence of 2.5 mm
glucose (3–6 nmol EtOHÆmin)1Æmg protein)1; for
calcu-lations, see Experimental procedures) These two
amoebal flux values were low in comparison with the
reported glycolytic fluxes displayed under anaerobic
conditions by yeast (500 nmol EtOHÆmin)1Æmg pro-tein)1) [32] or T brucei (71 nmol pyruvateÆmin)1Æ
mg protein)1) [29], but similar to the glycolytic flux determined in some tumor cell lines (21–32 nmol lactateÆmin)1Æmg 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 (37C) and physiological pH values (pH 6.0 and 7.0) used for the characterization of the pure enzymes [21] For the reactions from hexose 6-phosphate isomer-ase (HPI) to PPDK, the activities were determined in the forward and reverse reactions (Table 1) ATP-PFK and PYK activities (Table 1) were also evaluated; how-ever, their activities were less than 10% of those displayed by PPi-PFK and PPDK Therefore, these parallel reactions were not included in the kinetic model
The steps following PPDK are PFOR, aldehyde (AldDH) and alcohol (ADH) dehydrogenases (Fig 2) PFOR activity in the amoebal HM1:IMSS strain used
in the present study has not yet been determined In our hands, AldDH activity was difficult to detect with acetyl-CoA as substrate and could only be determined
in the reverse reaction Both, NADH- or NADPH-dependent ADHs displayed almost the same activity using acetaldehyde as substrate Notably, the reported activities for these ADHs in 200:NIH strain (6.9 and 0.96 UÆmg)1, respectively) [36] were one order of mag-nitude higher than those displayed in Table 1
100 80 60 40 20
0.0 0.5 1.0 1.5 2.0 2.5 3.0
6 cells
Incubation time (min)
Fig 1 Time-course of EtOH production by E histolytica trophozo-ites Amoebas were incubated at 35 C in NaCl ⁄ P i buffer at pH 7.4
in the presence of 10 m M glucose At the indicated times, aliquots were withdrawn and mixed with perchloric acid as described in the Experimental procedures EtOH was determined enzymatically with ADH The plot shown is a representative experiment with tripli-cates The solid line represents the fitting of the experimental points to a Hill equation using MICROCAL ORIGIN , version 5.0; this fit-ting has no mechanistic meaning.
Trang 4The Vm value for ATP-consuming processes
(ATP-ases) was higher (Table 1) than the estimated rate of
ATP production by glycolysis, suggesting kinetic
modulation of ATPases by the products ADP and
Pi NAD(P)H-consuming activity (DHases) was
mea-sured by following the oxidation of the coenzymes
after adding the amoebal extract (Table 1); however,
the actual activity was probably underestimated
because most DHases require a second substrate for
activity The adenylate kinase (AK) activity was
measured in both directions, ATP⁄ AMP production
or 2ADP production; however, the specificity of the
assay using extract samples could not be directly
ascribed to this reaction (see Experimental
proce-dures)
The activities of some branches of amoebal
glycoly-sis were explored It is well documented that amoebas
contain large amounts of glycogen as the main
carbo-hydrate storage (Table 2) [37] Therefore, glycogen
metabolism (synthesis and degradation) is an active
branch of the first section of glycolysis at the level
of G6P Indeed, a high phosphoglucomutase (PGM)
activity in the direction of G6P production (glycogen-olysis) was determined (Table 1)
Recently, the activity of 3-phosphoglycerate dehy-drogenase (3PGDH) involved in the synthesis of serine was described in E histolytica [38] In the direction of 3PG oxidation under our assay conditions, this activity was below the limit of detection in amoebal extracts (Table 1)
The oxidative section of pentose phosphate pathway (PPP) is probably absent in E histolytica because no G6P dehydrogenase (G6PDH) activity has been detected [6,7] Moreover, after exhaustive experimental retesting, we were unable to detect G6PDH activity in the soluble fraction of amoebal extracts (Table 1); in addition, a gene coding G6PDH could not be identi-fied in the genome sequence database [39] In amoebas, ribose 5-phosphate is synthesized from the glycolytic intermediaries fructose 6-phosphate (F6P) and glycer-aldehyde 3-phosphate (G3P) in a series of reactions catalyzed by PPi-PFK, aldolase and transketolase [40] However, the flux through this modified PPP has not been explored in the parasite
Table 1 Specific activity of glycolytic enzymes determined in amoebal clarified extracts [mU · (mg protein))1] Values in parenthesis indicate the number of individual clarified extracts assayed NA, not applicable; ND, not detected; NM, not measured.
Enzyme
a The concentration of CoCl2was 0.2 m M b Values reported by Ali et al [38] at pH 6.5 and 25 C c No reliable determination (see Experimen-tal procedures).
Trang 5In 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 histolyticagenome 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)P2, G3P, pyruvate]
Model properties The kinetic model of E histolytica glycolysis was built
by using the computer software gepasi, version 3.3,
PGAM
+
P
F6P Gluc
F1,6P 2
DHAP G3P
HK
ALDO PPi-PFK HPI
TPI
G6P
2ADP
ATP AMP
AK
ATP ADP
ATPases
DHases
AT MP + PPi
PPi synthesis
ADP ATP
i Pi PP
glycogen synthesis
2PG
1,3BPG
3PG
PEP
PGK
PPDK
GAPDH
ENO PGAM
+
NADH NAD
P AT ADP
ATP + Pi AMP + PPi
etoh
pyr
PFOR-AldDH
acald
ADH
NAD +
NADH
NAD +
NADH
3POHpyr
NAD + NADH
3PGDH
glycogen
ATP ADP + PPi
glycogen degradation
Pi
Fig 2 Pathway reactions included in the kinetic model of E histolytica glycolysis Dotted boxes represent the reactions that are branches of the main pathway The PFOR and AldDH reactions were lumped into one reaction (PFOR-AldDH) 1,3 BPG, 1,3-bisphosphoglycerate; acald, acetalde-hyde; ATPases; ATP consuming activities; DHases; NAD(P)H consuming activities; PPi synthesis, ATP consuming activities that produce AMP and PPi; 3POHpyr, 3-phos-phohydroxypyruvate; pyr, pyruvate.
Trang 6for metabolic modeling [43] A scheme of the pathway
reactions considered is shown in Fig 2 Table S1A in
the Supplementary Material displays the model
reac-tions as written in gepasi, whereas Table S1B
summa-rizes the kinetic parameters values incorporated in the
model The detailed rate equations are described in the
Experimental procedures
The model included the Km 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 Vm 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 Co2+, because, at the total concentration of
the heavy metals Co2+, Zn2+ and Cu2+ found in
amoebas (Table 2), this enzyme is expected to be fully
activated [21]
The last glycolytic steps from pyruvate to EtOH
cat-alyzed by PFOR, AldDH and ADH involve the
oxida-tion of NADH Because there is little kinetic
information on E histolytica PFOR and AldDH, these reactions were lumped in a reversible bisubstrate reac-tion involving NADH oxidareac-tion, with its Vm value adjusted around 1 UÆmg)1as reported for PFOR activ-ity determined in amoebal 200:NIH strain [36] Some kinetic data for amoebal NAD(P)H-ADHs has been described [44] These reactions were included as an irreversible bisubstrate reaction, also involving NADH oxidation, and using as Vmthe sum of the determined NADH and NADPH-ADH activities (Table 2) In addition, the kinetic model required a reversible, gen-eral NADH consumption reaction (DHases) for bal-ancing the pool of oxidized and reduced pyridine nucleotides
Cellular ATP consuming (ADP generating) processes (e.g cellular work, ion ATPases) were included in the model as ATPases reaction; its rate equation was irre-versible mass-action with a fitted rate constant Entamoeba histolyticalacks cytosolic pyrophosphatases and relies on PPi as phosphate donor in several meta-bolic reactions [6,7]; therefore, the most probable PPi supply comes from biosynthetic processes that also consume ATP (e.g DNA and protein synthesis) In the kinetic model, this PPi supply was explicitly repre-sented as an ATP-consuming reaction that produces AMP and PPi (PPi synthesis) The AK reaction was included to maintain the balance in the adenine-nucleo-tide pool; its rate equation was dependent on the equilibrium constant
To simulate a glycolytic pathway that closer resem-bles that occurring within the parasite, three glycolytic branches (glycogen synthesis, glycogen degradation and serine synthesis) were included in the model; in their absence, nonphysiological hexose- and triose-phosphate concentrations were attained
The glycogen synthesis branch was modeled as an irreversible mass-action reaction that consumes G6P and ATP to produce glycogen, ADP and PPi (an additional source of PPi to that of PPi synthesis); the glycogen degradation branch was also modeled
as an irreversible mass-action reaction (Fig 2) There
is high PGM activity (Table 1) but the fluxes through these branches have not yet been studied in amoebas By introducing the PGM Vm values of 0.3 and 0.87 UÆmg)1 cellular protein determined at
pH 6.0 and 7.0, respectively, as the glycogen synthe-sis rate constant (Table 1), severe diminution of all glycolytic intermediaries to micromolar levels and one order of magnitude lower glycolytic flux were observed Therefore, the glycogen synthesis and gly-cogen degradation rate constants were fitted (1.5 and 0.1 nmol min)1Æmg protein)1, respectively) to attain the physiological metabolite concentrations
Table 2 Glycolytic metabolite concentrations NM, not measured;
NS, not simulated; 1,3BPG, 1,3-bisphosphoglycerate.
EtOH flux [nmolÆmin)1Æ(mg
cellular protein))1]
a Recalculated from [63] b Glucose equivalents.
Trang 7The Vm value of the 3PGDH branch for serine
syn-thesis was adjusted within the same order of magnitude
of the activity value reported by Ali et al [38] to obtain
the closest physiological concentration of 3PG
(< 0.28 mm; Table 2) In the absence of this reaction,
3PG elevated to 0.6 mm, which indicated a relevant role
for this branch in the control of metabolite
concentra-tions in the final reacconcentra-tions of the parasite’s glycolysis
The effect of other amoebal glycolytic branches on
glycolytic flux and intermediary concentrations were
explored: PPP, triglyceride synthesis, alanine
transami-nase and malic enzyme Because experimental data on
fluxes through these other branches are not available,
their rate constants were fitted; however, their
inclu-sion in the model showed negligible effects on the
intermediary concentrations, glycolytic flux and
flux-control distribution (data not shown)
The metabolites were initialized at the physiological
concentrations displayed in Table 2 Fixed metabolite
concentrations were: 5 mm glucose; 10 mm EtOH;
1 mm glycogen; 1 mm 3-phosphohydroxypyruvate;
5 mm Pi and 0.45 mm PPi The conserved moieties
were ATP + ADP + AMP¼ 9.9 mm and NADH+
NAD+¼ 1.55 mm It is worth noting that, when
including PPi concentration as a dynamic variable of
the model, it was not possible to attain a physiological
stable steady state because the PPi consumption by
PPi-PFK and PPDK (and glycolytic ATP synthesis)
was exceeded by the PPi synthesis rate Due to the
variety of PPi-generating biosynthetic processes, a true
PPi synthesis rate is difficult to determine; moreover,
further adjustments of the PPi synthesis rate constant
compromised the physiological values of metabolites
and fluxes Thus, these modeling results indicate the
importance of defining the PPi metabolism in the
para-site because only the absence of cytoplasmic
pyrophos-phatases [6,7] has been characterized, but participating
enzymes and their rate equations and kinetic
parame-ters have not been described
The present central model does not include the hexose
transport reaction because there are a lack of data
regarding kinetic parameters and difficulties in
deter-mining the actual activity in the absence of glucose
phosphorylation However, the inclusion of the glucose
transport may have an impact on the control
distribu-tion [30,32] and therefore the effects of its incorporadistribu-tion
in the model were evaluated by using the few available
data (for the model, see supplementary Doc S1)
Steady-state properties of the kinetic model
In most of the explored conditions the simulations
reached an asymptotically stable steady state,
indicat-ing that the kinetic simulation displays a hyperbolic pattern that is able to reach an asymptote
To validate the construction of the kinetic model described above, the metabolite concentrations and glycolytic flux, experimentally determined when the cells were under glycolytic steady-state conditions, were used as reference The predicted glycolytic flux (37 nmol EtOHÆmin)1Æmg protein)1) agreed with the values determined in amoebas (Table 2) Model simu-lations approached 0.2- to one-fold the level of the in vivo metabolite concentrations for G6P, F6P, F(1,6)P2, DHAP, G3P, 3PG, pyruvate, ATP, ADP and NAD+ (Table 2) The model also predicted very low concentrations for 2-phosphoglycerate (2PG) and phosphoenolpyruvate (PEP), which are below the lim-its of detection of the experimental assays, but they were similar to the low values reported in other cells [35,45] Significant deviation was attained for AMP, which was 1.6-fold higher than the physiological value (Table 2)
Flux-control distribution Analysis of the enzyme activities at pH 6.0 as determined in amoebal clarified extracts (Table 1) and the modeled fluxes through the enzymes (Table 3) indicated that HK and PGAM were work-ing at 32–33% of their Vm 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 (CJHK ¼ 0.73; CJ
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 (CJglycogen synthesis¼ –0.32; CJ3PGDH ¼ –0.18) Notoriously, glycogen synthesis mainly modulated the hexosephos-phate concentrations, with a stronger effect on the F(1,6)P2level On the other hand, the flux through the 3PGDH reaction affected the 3PG and pyruvate con-centrations, and final EtOH flux The glycogen degra-dation reaction displayed low flux control under these conditions; however, at low HK activities, this branch became important in supplying G6P for glycolysis The model predictions indicated that the ATP demand for
Trang 8cellular processes (cellular function represented by
ATPases and PPi synthesis) exhibited high flux control
over glycolysis (CJATPasesþ PPi synt ¼ –0.32; Table 3) PPi
provides a link between glycolysis and anabolic
path-ways and hence, variation in its steady-state
concentra-tion (by modulating the PPi synthesis reacconcentra-tion) may
affect the control distribution of glycolysis
The model predicted that most enzymes displayed
over-capacity for the glycolytic flux (Tables 1 and 3)
and, in particular, the fluxes through PPi-PFK and
PPDK were 10% their forward Vmvalues in amoebas
The steady-state intracellular amoebal concentrations
of their respective substrates and products for these
two enzymes (Table 2) were all above or around the
Km 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 (eEi
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 ðP
i
CJEieEi
X ¼ 0Þ [24] The phy-siological significance of the connectivity theorem is easily visualized when considering that an enzyme satu-rated by its substrate cannot further increase its rate (it
is working at maximal capacity or under Vmconditions, and its elasticity is near zero), thus establishing a con-straint to the pathway flux; therefore, such an enzyme displays high flux-control coefficient
Table 3 Fluxes, elasticity coefficients for substrates (e Ei
S ) and products (e Ei
P ) and flux-control coefficients (C J
Ei ) of the kinetic model.
Ei
Trang 9The elasticity coefficients of the pathway enzymes
for effectors are shown in Table 3 As expected for the
high flux control displayed by HK, the values of its
elasticity coefficients were the lowest among all the
enzymes, with values of 0.12 and 0.55 for glucose and
ATP, respectively HK also exhibited low sensitivity
towards its products G6P and ADP and modulator
AMP PGAM also showed relatively low elasticities
towards 3PG and 2PG
As deducted from their low flux-control coefficients,
the other pathway enzymes showed comparatively
higher elasticity coefficients towards their substrates
whereas their elasticities towards products displayed
essentially similar values to those for the substrates but
with a negative sign
Together, the results indicated that HK strongly
flux-controlled amoebal glycolysis because of its low
activity in amoebal extracts and because of the low
sensitivity toward its substrates and AMP derived from
saturation (Table 3) Due to the similar elasticity
towards ATP and AMP, HK inhibition by AMP
might have physiological significance because the
enzyme is strongly inhibited by this metabolite with a
Ki value of 36 lm at pH 6.0 [21], a value three-fold
lower than the Km 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 Ki AMP Amoebal
HK exhibits a mixed-type inhibition by AMP [21];
therefore, the influence of the competitive inhibitory
component (effect on Km 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 Vm) might still be relevant to modulate the HK activity
Concentration control coefficients Similarly to the flux-control distribution (Table 3), the control of the concentration of most glycolytic metab-olites mainly resided in HK, PGAM, glycogen synthe-sis, ATPases, PPi synthesis and 3PGDH reactions (Table 4) The pyruvate concentration was also signifi-cantly controlled by the lumped reaction of PFOR and AldDH (PFOR-AldDH) and DHases reactions In turn, the controlling order for the ATP concentration was PPi synthesis > PGAM > glycogen synthe-sis HK (Table 4)
Variations to the HK rate expression The kinetic model was used to determine the effect of varying the HK activity on flux rate and flux-control distribution in an attempt to further understand the underlying mechanism by which this enzyme has high control on the flux
As described in the construction of the amoebal model, the HK equation was considered as a reversible
Table 4 Concentration control coefficients obtained with the kinetic model The values shown are the concentration control coefficients, for which the net sum gives approximately 0 TPI, PGK, glycogen degradation and AK reactions did not exert significant control on the metabo-lite concentrations and therefore they were not included.
Enzyme
Metabolite
G6P F6P F(1,6)P2DHAP G3P 1,3BPG 3PG 2PG PEP Pyruvate Acetaldehyde ATP ADP AMP NADH NAD +
Glycogen
synthesis
PPi
synthesis
Trang 10reaction 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 Keq
values [46–48] It should be remarked, however, that
including reversibility in reactions with high Keq
requires the fitting and some times the guessing of
kinetic parameters that cannot be easily determined
(Km for products, Vm in the reverse reaction) Under
near-physiological conditions, the HK reaction is
quasi-irreversible due to its high Keq value (1.6–
3.9· 102) [49] Therefore, it was interesting to evaluate
the effect of changing the rate equation of this step in
the pathway behavior
The reversible HK rate equation with mixed
inhibi-tion by AMP was replaced for an irreversible rate
equation with mixed-type inhibition by AMP and
competitive inhibition by ADP (which was previously
demonstrated in studies with the purified enzyme)
[21] In comparison to the model with HK
revers-ible reaction, this kinetic model predicted two orders
of magnitude lower flux through HK, with a
conco-mitant diminution in the glycolytic flux
(1.1 nmol EtOHÆmin)1Æmg cellular protein)1) and three
orders of magnitude decrease in the intermediary
con-centrations Under these conditions, the glycogen
deg-radation reaction was the main flux-control step
(CJglycogen degradation¼ 0.78) The cause for the drastic
decreased in HK rate when using the irreversible
equa-tion was that the AMP inhibiequa-tion predominated
because two orders of magnitude increase in the HK
Ki 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 inhibicontribu-tion 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, Ki 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 Ki AMP value was examined (Fig 3) The pathway
flux was highly sensitive to variation in the HK Ki AMP
value Under these conditions, the glycogen
degrada-tion reacdegrada-tion gained flux control at the lowest HK
Ki AMPvalues
These results indicated that HK inhibition by AMP,
in addition to modulating the activity of the enzyme, may also be a mechanism for regulating the pathway metabolite concentrations and flux-control distribution Because no cooperative modulation has been detected
in amoebal glycolytic enzymes, the AMP inhibition of
HK appears to be the sole mechanism of direct trans-ference of information from outside (ATPases, PPi synthesis, glycogen synthesis) and the end (PPDK) to the initial part of the pathway Consequently, the mod-ulation of the AMP concentration might be an addi-tional mechanism for controlling the glycolytic flux in this parasite
Enzyme titration for the identification
of drug targets MCA of the kinetic model allows for the determina-tion of the flux-control coefficients of the pathway enzymes In addition, the kinetic model is a helpful tool for predicting the pathway behavior when inhibi-tion of some enzymes is evaluated If the model closely reproduces the in vivo behavior, then the metabolic modeling approach would be an adequate tool for iden-tifying the best drug targets in a metabolic pathway
0.016 0.020 0.024 0.028 0.032 0.036 0
20 40 60 80 100
HK Ki AMP (m M )
Fig 3 Effect of varying the HK K i for AMP on glycolytic flux An interval of 1–36 l M is reported for the K i AMP values of amoebal HKs, either native or recombinant, at the pH range of 6.0–8.5 [19– 21] For these simulations, 100% glycolytic flux was 37 nmol EtOH ⁄ (minÆmg cellular protein)1) The b-values (i.e the K m modifier
in the interaction between glucose and AMP with the enzyme in the HK rate equation; see Experimental procedures) were 1 (line) and 1.5 (dashed) By contrast, changing the c-value (i.e the K m modifier in the interaction between ATP and AMP with the enzyme) did not induce significant alteration of the Ki AMP versus pathway flux plot (data not shown).