What Controls Glycolysis in Bloodstream Form Trypanosoma
brucei?*
Barbara M.
Bakker
§¶,
Paul A. M.
Michels
,
Fred
R.
Opperdoes
, and
Hans V.
Westerhoff
§**
From
Molecular Cell Physiology, BioCentrum Amsterdam,
Vrije Universiteit De Boelelaan 1087, NL-1081 HV Amsterdam, The
Netherlands, § E. C. Slater Institute, BioCentrum
Amsterdam, University of Amsterdam Plantage Muidergracht 12, NL-1018 TV
Amsterdam, The Netherlands, and
Research Unit for Tropical
Diseases, Christian de Duve Institute of Cellular Pathology and
Laboratory of Biochemistry, Catholic University of Louvain, Avenue
Hippocrate 74, B-1200 Brussels, Belgium
 |
ABSTRACT |
On the basis of the experimentally determined
kinetic properties of the trypanosomal enzymes, the question is
addressed of which step limits the glycolytic flux in bloodstream form
Trypanosoma brucei. There appeared to be no single answer;
in the physiological range, control shifted between the glucose
transporter on the one hand and aldolase (ALD),
glyceraldehyde-3-phosphate dehydrogenase (GAPDH), phosphoglycerate
kinase (PGK), and glycerol-3-phosphate dehydrogenase (GDH) on the other
hand. The other kinases, which are often thought to control glycolysis,
exerted little control; so did the utilization of ATP.
We identified potential targets for anti-trypanosomal drugs by
calculating which steps need the least inhibition to achieve a certain
inhibition of the glycolytic flux in these parasites. The glucose
transporter appeared to be the most promising target, followed by ALD,
GDH, GAPDH, and PGK. By contrast, in erythrocytes more than 95%
deficiencies of PGK, GAPDH, or ALD did not cause any clinical symptoms
(Schuster, R. and Holzhütter, H.-G. (1995) Eur. J. Biochem. 229, 403-418). Therefore, the selectivity of drugs
inhibiting these enzymes may be much higher than expected from their
molecular effects alone. Quite unexpectedly, trypanosomes seem to
possess a substantial overcapacity of hexokinase, phosphofructokinase, and pyruvate kinase, making these "irreversible" enzymes mediocre drug targets.
 |
INTRODUCTION |
Trypanosoma brucei is a unicellular, eukaryotic
parasite. It causes the African sleeping sickness in humans and a
related disease, nagana, in livestock. When this organism lives in the mammalian bloodstream, it depends completely on glycolysis for its
supply of ATP. It possesses neither a functional Krebs cycle nor
oxidative phosphorylation, nor does it store any carbohydrate. Glycolysis in trypanosomes and in other members of the Kinetoplastida family differs substantially from the corresponding pathway in other
organisms (for reviews see Refs. 1-4). First, the conversion of
glucose to 3-phosphoglycerate
(3-PGA)1 takes place in
specialized organelles, related to peroxisomes. Since 90% of the
protein content of these organelles consists of glycolytic enzymes,
they have been called glycosomes (5). The glycosomal membrane is hardly
permeable to metabolites (6). Second, under aerobic conditions, the
NADH produced in glycolysis is reoxidized by molecular oxygen via a
mitochondrial glycerol 3-phosphate:DHAP (Gly-3-P:DHAP) shuttle (Fig.
1). Since there is neither a cytosolic glycerol kinase (GK) nor any
significant activity of glycerol 3-phosphatase (5, 7), all Gly-3-P is shuttled back via DHAP to the mitochondria and converted to pyruvate, leading to the production of two molecules of pyruvate per molecule of
glucose consumed. Under anaerobic conditions, equimolar amounts of
pyruvate and glycerol are produced due to requirements of glycosomal redox and ATP balance (1, 5, 7-10). This decreases the ATP production to one molecule of ATP per glucose. Third, the glycosomal enzymes are
hardly regulated by any of the compounds that strongly affect the
corresponding enzymes in other organisms. Most notably, in trypanosomes, fructose 2,6-bisphosphate activates the cytosolic enzyme
PYK (11-13) rather than the glycosomal PFK (14, 15). The
physiological function of this activation is elusive, since the
fructose 2,6-bisphosphate concentration in the bloodstream form
substantially exceeds its activation constant for PYK (12, 16).
It has been suggested that the transport of glucose into the cells is
the rate-limiting step of glycolysis in bloodstream form trypanosomes
(17). Yet, our present day knowledge of control of metabolism led us to
re-evaluate the evidence for this statement (4). Since the development
of metabolic control analysis (18, 19) (for reviews, see Refs. 20 and
21), it has been known that in general there is no single rate-limiting
step in a metabolic pathway, but control can be shared among several
steps. The quantitative measure of the strength of the control of the
steady-state flux J through a pathway by an enzyme
i in this pathway is given by its flux control coefficient,
CiJ. This coefficient is defined
as the percentage increase of the flux caused by a 1% activation of
enzyme i (for a more precise definition see Refs. 22 and
23). Flux control coefficients can have any value between 0 (not
limiting) and 1 (completely rate-limiting) (e.g. Refs.
24-28), but the sum of the flux control coefficients of all enzymes in
the pathway should be 1 (18).
To measure a flux control coefficient, it is necessary to modulate the
activity of the enzyme of interest with small steps around the normal
wild type level. For the trypanosome glucose transporter, this has not
been done. Consequently, the evidence presented for the glucose
transporter being rate-limiting is only indirect and qualitative. In
the first place, glucose, fructose, and mannose were metabolized at
different rates (17). However, the comparison of different substrates
alone did not correspond to the small modulation required for metabolic
control analysis. In addition, the modulation of the transport activity
was not quantified, nor did this experiment exclude control by
phosphorylation. Also the low intracellular glucose concentration (0.4 mM) has been taken as evidence that glucose transport was
rate-limiting (29). However, a theoretical analysis, based on the
kinetics of the glucose transporter and of HK, showed that an
intracellular glucose concentration of 0.4 mM may be
consistent with any flux control coefficient between 0 and 50%, but
not 100% (4). This suggests that, if at all important, glucose
transport is not the only step controlling trypanosome glycolysis.
Because bloodstream form trypanosomes depend completely on glycolysis
for their supply of ATP and because the organization of glycolysis in
the parasite is very different from that in the host cells, this
pathway has been selected as a target for drugs against the African
sleeping sickness (30). The selectivity of drugs might be enhanced by
choosing a target enzyme that has a high control in the parasite and a
low control in the host.
Despite the great interest, it is not yet known completely for any
organism how the control of the glycolytic flux is distributed. In
yeast, for example, many genes encoding glycolytic enzymes (HK,
phosphoglucose isomerase, PGK, PYK, pyruvate decarboxylase, alcohol
dehydrogenase) have been overexpressed manifold, but in none of the
mutants did the glycolytic flux differ substantially from the wild type
flux (31, 32). This may be due to several reasons. First, glycolysis in
yeast (and many other organisms) is part of a much wider metabolic
network. Consequently, the glycolytic flux may be controlled by steps
outside glycolysis, such as the utilization of ATP, the respiratory
branch, the synthesis of storage carbohydrates, and/or the glucose
transporter proteins (33). Second, the effects of overexpression are
necessarily investigated at time scales at which the cells may adjust
the expression of other genes. For example, the PFK-overproducing cells
contained decreased levels of 6-phosphofructo-2-kinase. Thus, they
compensated for the increased amount of PFK by decreasing the
concentration of its activator fructose 2,6-bisphosphate (32). Finally,
when the activity of an enzyme is increased, it often (but not always) loses control (34). By using overexpression mutants, one therefore runs
the risk of underestimating the control coefficients.
Several studies dealt with the control of glucose utilization in
mammalian cells. Measurements indicated that the rate of glycogen
synthesis was controlled by glucose transport and hexokinase (35). The
control of mammalian glycolysis has been measured by the so-called
matrix inversion method (36). In the absence of insulin, most control
was shared by glucose transport and hexokinase. This method, however,
requires that all relevant enzymes be included, but important steps
such as PFK and GAPDH were missing.
The above mentioned problems with the determination of control
coefficients should not apply, or should apply to a lesser extent, to
bloodstream form T. brucei. First, except for the
utilization of ATP, there are no branches with a substantial flux under
aerobic conditions. Second, the kinetics of glycolytic enzymes from
T. brucei have been investigated thoroughly in a limited
number of laboratories under standard conditions. This has enabled us
to develop a detailed kinetic model of trypanosome glycolysis
containing most glycolytic enzymes. The model calculations of the flux
and the metabolite concentrations corresponded unexpectedly well with experimental information (37). We here use the kinetic data to
calculate what controls trypanosome glycolysis under physiological conditions. It will be shown that there is a distribution of control of
trypanosome glycolysis, which depends strongly on glucose supply.
 |
MATERIALS AND METHODS |
Cultivation of Trypanosomes
All experiments were performed with the bloodstream form of
T. brucei stock 427. Male, 300-g Wistar rats were infected
with T. brucei, and the parasites were isolated from the
blood by DEAE-cellulose chromatography (DE52, Whatman) (38). The cells
were washed by centrifugation; resuspended in a 90 mM
Tris/HCl buffer containing 2.5 mM KCl, 77.5 mM
NaCl, 5 mM MgCl2, 2 mM
Na2HPO4, and 50 mM glucose at pH
7.5 (modified from Ref. 39); and stored on ice. In this buffer, the
cells maintained a constant motility and oxygen consumption capacity
for at least 7 h after isolation.
Flux and Metabolite Measurements
An aliquot of cells was washed three times by centrifugation at
4 °C and resuspended in the assay buffer at 37 °C. The
measurements were performed in a 90 mM Tris/HCl buffer (pH
7.5), containing 3.1 mM KCl, 96.9 mM NaCl, 5 mM MgCl2, 2 mM
Na2HPO4, and the indicated concentration of
glucose. The protein concentration was measured in each aliquot of
cells, according to Lowry (40) with bovine serum albumin as a standard.
Since the buffer weakly disturbed the assay, the same amount of buffer
as present in the samples was added to the bovine serum albumin standards.
The rate of oxygen consumption was monitored in a closed and
thermostated vessel with a Clark electrode. For determination of the
concentrations of other metabolites, the cells were kept in an open,
thermostated vessel and aerated with water-saturated pressurized air.
To check that the cell suspensions remained aerobic, the oxygen
concentration was monitored with a Clark electrode throughout the
experiment. Samples were taken by injecting 75 µl of the cell
suspension into 37.5 µl of 15% perchloric acid. Samples were
vortexed, centrifuged (5 min, Eppendorf table centrifuge, full speed),
neutralized by mixing 80 µl of supernatant with 45 µl of 1
M K2CO3, and centrifuged again. The
pH of the supernatants was checked with pH paper (pH was between 7 and
8). Supernatants were stored at
20 °C and analyzed further within
1 week. Glucose, pyruvate, and glycerol were measured by NADH-linked
analysis (41) in an automatic analyzer (COBAS FARA, Roche Molecular Biochemicals).
Chemicals
Phloretin was from Sigma. A phloretin stock was made up in 70%
ethanol. The ethanol concentration in cell suspensions was always kept
below 1%.
Modeling
The kinetic model of trypanosome glycolysis that was used in
this study has been described and validated previously, its predictions being compared with experimental results (37). It contained enzyme
kinetics, measured with purified trypanosome enzymes, for most
reactions depicted in Fig. 1. The reactions catalyzed by phosphoglucose
isomerase, triosephosphate isomerase (TIM), phosphoglycerate mutase,
enolase, and adenylate kinase were taken to be at equilibrium. The
rationale was that their measured ratios of substrate and product
concentrations were close to equilibrium (phosphoglycerate mutase and
enolase) (42), that they catalyze a dead-end branch (adenylate kinase),
or that they were close to equilibrium in initial model calculations
with explicit kinetics for these reactions (phosphoglucose isomerase
and TIM). The glycosomal membrane was assumed to be impermeable to
metabolites (6), except to those that need to be transported to allow
glycolysis to proceed. Because of a lack of kinetic information, the
latter transport steps were assumed to be at equilibrium. The transport
of glucose across the cytoplasmic and subsequently the glycosomal
membranes was lumped into one kinetic equation, because no distinction
could be made so far (29, 43). This is equivalent to assuming the glycosomal glucose transporter to be at equilibrium. The glycosomal concentration of inorganic phosphate was assumed to be saturating. This
assumption has been validated partially. At the normal blood concentration of inorganic phosphate (0.4-0.5 mM (44)),
the measured rate of oxygen consumption by intact trypanosomes,
i.e. the glycolytic flux, was fully saturated with phosphate
(result not shown).
The concentrations of both the adenine nucleotides (ATP, ADP, AMP) and
the nicotinamide adenine nucleotides (NAD, NADH) were treated as free
(although interdependent) variables, rather than fixed parameters of
the system. Due to the compartmentalization of the pathway, the model
contained distinct pools of cytosolic and glycosomal adenine
nucleotides. In principle, the model allowed both dynamic and
steady-state calculations, but the present study is limited to steady
states only. Below, only the changes that were made to the model
described in Ref. 37 are described.
Kinetics--
The kinetics of GDH have been determined more
accurately2:
Km, DHAP = 0.1 mM;
Km, Gly-3-P = 2 mM;
Km, NADH = 0.01 mM;
Km, NAD+ = 0.4 mM; and the ratio of the reverse and forward Vmax
(V
/V+) = 0.28. The
specific activity of the purified enzyme in the forward direction was
213 µmol min
1 (mg of enzyme)
1. The amount
of GDH in the cell is 0.25% of the total cell protein (45). Expressed
per total cell protein, V+ is then 533 nmol
min
1 mg of protein
1.
Bakker et al. (37) took the hexose kinases to be insensitive
to their products. Originally only an indirect and weak effect of
glucose 6-phosphate (Glc-6-P) on HK and of fructose 1,6-bisphosphate (Fru-1,6-BP) on PFK was included in the model via the conservation relation of bound phosphates. Under some conditions, this might cause
the set of equations defining the steady state to be underdetermined. This would be the case, for instance, if ALD were saturated with Fru-1,6-BP. Then none of the enzymes would sense the concentration of
Fru-1,6-BP, and consequently the latter could assume any value, only
restricted by the conserved sum. It has been reported that Fru-1,6-BP
does inhibit PFK, by acting both on the Vmax and
the Km for Fru-6-P (14). In the present study the
following rate equation was used,
|
(Eq. 1)
|
in which Ki1 = 15.8 mM and Ki2 = 10.7 mM (14). All other parameters held the same values as
described previously (37). HK was reported to be insensitive to Glc-6-P (46). Due to salt effects and a high affinity of the enzyme for glucose
(Km = 0.1 mM), a competitive inhibition
by Glc-6-P with a Km above 10 mM would
not be measurable.3 Under
some conditions, such a weak inhibition was relevant to prevent
unrestrained accumulation of Glc-6-P in the model, and therefore the
rate equation was modified to the following equation.
|
(Eq. 2)
|
Km,Glc-6-P was taken to be 12 mM, which does not contradict the measurements. The other parameters were not changed (37).
The rate of PYK was assumed to be independent of the concentrations of
its products, ADP and pyruvate, unless otherwise mentioned. If the rate
depended on the ATP concentration, the following rate equation was
used.
|
(Eq. 3)
|
Km,ATP was taken to be 0.1
mM (equal to Km,ADP (47)),
and the other parameter values were not changed (37).
Non-competitive inhibition of glucose transport was simulated by
multiplying the rate equation for glucose transport by a factor
Ki/(Ki + [I]), in which [I]
represents the inhibitor concentration and Ki is the
inhibition constant. Competitive inhibition of glucose transport was
simulated by multiplying the Km values for both
extracellular and intracellular glucose by a factor 1 + [I]/Ki.
The Transport of Gly-3-P and DHAP--
Under anaerobic
conditions, bloodstream form T. brucei maintains its
glycosomal redox and ATP balance by producing equimolar amounts of
pyruvate and glycerol (Fig. 1). The
G0' of GK does not favor the production of
glycerol. An inhibition of glycolysis by glycerol has indeed been
measured under anaerobic conditions (48). In the original kinetic model
(37), the concentration of glycerol required to inhibit the flux was
much lower than had been found experimentally. The model assumed the
transport of Gly-3-P and DHAP across the glycosomal membrane to be
independent of each other and at equilibrium. Consequently, any
increase of the glycosomal concentration of Gly-3-P was accompanied by
an identical increase of the cytosolic concentration of Gly-3-P. Both
the cytosolic and the glycosomal concentration of Gly-3-P participated
in a conserved sum of organic phosphate groups that are not exchanged
with inorganic phosphate as follows,
|
(Eq. 4)
|
in which Vg is the glycosomal volume and
Vc is the cytosolic volume. Since the cytosolic
volume was more than 20 times the glycosomal volume, any increase of
the cytosolic Gly-3-P concentration led to an enormous drain of the
glycosomal metabolites. This effect enhanced the inhibition of the
anaerobic glycolytic flux by glycerol.

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Fig. 1.
The stoichiometric scheme of the model of
glycolysis in bloodstream form T. brucei. The
reactions 3, 6, 9, 13,
16, 18, and 19 were treated as
equilibrium reactions. 1, transport of glucose across the
plasma membrane and the glycosomal membrane; 2, HK;
3, phosphoglucose isomerase; 4, PFK;
5, ALD; 6, TIM; 7, GAPDH;
8, PGK; 9, transport of 3-PGA across the
glycosomal membrane, phosphoglycerate mutase, and enolase;
10, PYK; 11, pyruvate transport across the plasma
membrane; 12, GDH; 13, transport of Gly-3-P and
DHAP across the glycosomal membrane; 14,
glycerol-3-phosphate oxidase; 15, GK; 16,
transport of glycerol across the glycosomal membrane and the plasma
membrane; 17, ATP utilization; 18, glycosomal
adenylate kinase; 19, cytosolic adenylate kinase.
PEP, P-enolpyruvate.
|
|
If the transport of Gly-3-P and DHAP would occur via an antiport
mechanism, as proposed by Opperdoes and Borst (5), the conserved sum of
bound phosphates would split in distinct glycosomal and cytosolic
conserved sums.
|
(Eq. 5)
|
and
|
(Eq. 6)
|
Consequently, an increase of the glycosomal Gly-3-P
concentration would not be automatically coupled to an equal increase of the cytosolic Gly-3-P concentration. Therefore, it was expected that
the inhibition of anaerobic glycolysis by glycerol would be much
weaker. This hypothesis was tested by implementing a Gly-3-P:DHAP antiporter in the model.
It was assumed that the antiporter was in equilibrium. Also, TIM was
taken to be in equilibrium, as previously. Therefore, the
triosephosphates were considered to behave as a single metabolite pool.
|
(Eq. 7)
|
The time derivative of [triose-P] remained exactly the same as
in the model with the two independent transporters (37). The
implementation of the antiporter entailed the solving of a set of five
equations with five unknowns, i.e. Equations 5-7 and the
equilibrium constraints for TIM and the exchanger itself.
|
(Eq. 8)
|
|
(Eq. 9)
|
It follows that the cytosolic DHAP concentration is as
follows,
|
(Eq. 10)
|
in which
|
(Eq. 11)
|
|
(Eq. 12)
|
|
(Eq. 13)
|
and
|
(Eq. 14)
|
When [DHAP]c was known, [DHAP]g followed
from equations 5, 6, 8, and 9.
|
(Eq. 15)
|
Subsequently, [Gly-3-P]c, [GA-3-P]g, and
[Gly-3-P]g were calculated from Equations 6, 8, and 9, respectively. All other equations in the model were as specified in
Ref. 37. The values of C4,antiporter and the sum
of the glycosomal adenine nucleotides (C1) have
not been determined experimentally. They were chosen as follows:
C1 = 6 mM, and
C4,antiporter = 45 mM.
C5,antiporter (5 mM) was based on
measurements of average concentrations of Gly-3-P and DHAP in the cell
(42). To allow comparison of the model with and without the antiport
mechanism, the total amount of metabolites contained in
C4 on the one hand and
C4,antiporter and
C5,antiporter on the other hand was kept the
same, as follows.
|
(Eq. 16)
|
Indeed, the coupling of the transport of Gly-3-P and DHAP
transport made the anaerobic flux less sensitive to glycerol (Fig. 2). The K0.5 of
glycerol increased 7.5-fold from 10 µM (independent transport) to 75 µM (antiporter). Nevertheless, the
calculated K0.5 was still lower than the
measured K0.5 (800 µM) (48). Table I shows that the implementation of the
antiporter did not cause a substantial deviation of the model from the
experiments with regard to the flux and the metabolite concentrations
as far as they could be measured in cell extracts (42). Only the
modeled concentration of DHAP deviated more than 3-fold from the
experiments due to the antiporter, while it was correctly predicted if
the transport was uncoupled. The results that will be shown have been obtained with a Gly-3-P:DHAP antiporter. It was confirmed that these
results were virtually independent of the mechanism of transport.

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Fig. 2.
The inhibition of the glycolytic flux by
glycerol under anaerobic conditions depends on the stoichiometry of the
transport of Gly-3-P and DHAP. The solid
line represents the inhibition curve that was calculated, if
it was assumed that these metabolites were transported independently
across the glycosomal membrane. The dashed line
is the corresponding curve if their transport was coupled by an
antiporter. Details of the model can be found under "Materials and
Methods."
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|
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Table I
The measured and calculated glycolytic flux and metabolite
concentrations
The steady-state glycolytic flux and metabolite concentrations, as they
were calculated with independent transport of Gly-3-P and DHAP or with
an antiporter, are compared with experimental values (42). The ratios
of aerobic to anaerobic concentrations were taken to avoid inaccuracy
due to the conversion of amounts measured in nmol/mg wet weight to
intracellular concentrations in mM. Since the measured
concentrations represent a weighted average of glycosomal and cytosolic
concentrations, this average was also used for the [DHAP] and
[Gly-3-P] calculated by the model. The ratio of cytosolic and
glycosomal volume was 22.3. Rates are expressed in nmol min 1
mg of protein 1, and concentrations are in mM.
When experimental data are available for comparison, boldface numbers
are used.
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|
Quantifying Control--
The control of an enzyme i
on a steady-state flux J was defined by its flux control
coefficient,
|
(Eq. 17)
|
in which
is the rate of enzyme i, p is
a parameter that only affects enzyme i, and
(
/
p) is the effect of the parameter change on
if the enzyme were isolated from the rest of the metabolic pathway,
i.e. at constant concentrations of all metabolites. The flux
control coefficient of an enzyme or transporter was calculated numerically by increasing its forward (V+) and
reverse (V
) maximal rate in proportion by
0.01% and calculating the steady-state flux J both prior to
and after this change. CiJ was
evaluated as follows.
|
(Eq. 18)
|
It has always been verified that the results obeyed the
summation theorem,
|
(Eq. 19)
|
in which the summation is over all enzymes i in the pathway.
The sensitivity of an enzyme to a metabolite concentration was
evaluated in terms of its elasticity coefficient, defined by the
equation,
|
(Eq. 20)
|
in which Xj is the concentration of
metabolite j. Partial derivatives were taken at constant
concentrations of the other metabolites at their steady-state values.
Numerically, elasticity coefficients were determined by calculating
i and Xj in the steady state, increasing
Xj by 0.01%, and calculating the change of
i.
Control coefficients and elasticity coefficients are related by
connectivity theorems. The connectivity theorem for intracellular glucose is, for example, the following.
|
(Eq. 21)
|
This means that the process that is the more sensitive to
intracellular glucose has the lower control. This can be understood intuitively, because the more sensitive process tends to adapt to a
change elsewhere in the system.
If specific conditions are fulfilled (49), a group of enzymes may be
treated as a single module. Under "The Distribution of Control
between the Supply and Demand for ATP" below, this principle was
applied. The glycolytic pathway was simplified to two modules: one
producing cytosolic ATP (supply) and one consuming it (demand) (20, 50,
51). For this system, the following modular connectivity theorem
holds,
|
(Eq. 22)
|
in which the asterisk emphasizes that these elasticities apply
to the whole module rather than to a single reaction. The summation
theorem for the flux control coefficients remains as follows.
|
(Eq. 23)
|
Together, Equations 22 and 23 yield the following.
|
(Eq. 24)
|
Usually,
*
[ATP]
c/[ADP]
c
supply is negative (product inhibition),
and
*
[ATP]
c/[ADP]
c
demand is positive, so that
CdemandJ is between 0 and 100%. To calculate the control of PYK on the flux through the
supply module (CPYKJ
supply), the cytosolic [ATP]/[ADP] ratio was
fixed.
Substrate and Product Concentrations--
The extracellular
concentrations of glucose, pyruvate, and glycerol were kept constant at
5, 0, and 0 mM, respectively, unless mentioned otherwise.
Software--
Conserved sums were analyzed with the program
SCAMP (52). The simulations were performed with MLAB (Civilized
Software, Bethesda, MD).
 |
RESULTS |
The Control of the Glycolytic Flux under Physiological
Conditions--
The first question we addressed was which reactions or
transport steps control the glycolytic flux of trypanosomes in the mammalian bloodstream. Although the mammalian bloodstream is a very
constant environment in many respects, the cells may encounter extracellular glucose concentrations varying between 4 and 8 mM (53, 54). The oxygen concentration is saturating
throughout the vascular system (4). Under aerobic conditions, only a
very small rate of glycerol production was measured (Table
II); therefore, the branch to glycerol
was neglected in all aerobic simulations reported here (see also Ref.
37). It was calculated to which extent glucose transport limits
glycolysis under these conditions. Whereas glucose transport controlled
the flux at low extracellular glucose concentrations, control gradually
eluded the transporter at the higher glucose concentrations, to be
taken over by ALD, GAPDH, PGK, and GDH together (Fig.
3). In accordance with the concepts of
metabolic control analysis, the control was
condition-dependent and was shared by several steps at high
glucose concentrations. Furthermore, there was no relationship
whatsoever between the extent to which any of the enzymes controlled
the glycolytic flux and its distance from equilibrium (Table
III). At 5 mM glucose, the
glucose transporter controlled the flux for more than 90%, but the
irreversible enzymes HK, PFK, and PYK were much further displaced from
equilibrium than the transporter.
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Table II
The fluxes as measured under aerobic conditions at 37 °C
Note that the measured fluxes were higher than the calculated fluxes
(Table I), since the model refers to 25 °C (37).
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Fig. 3.
The flux control coefficient of the glucose
transporter depends on the extracellular glucose concentration.
This result was obtained under aerobic conditions. The inset
shows the flux control coefficients of those enzymes that take over
control, when the transporter loses control at 10 mM
glucose.
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Table III
The control of the glycolytic flux (CiJ) and the
displacement from equilibrium ( /Keq) under aerobic
conditions
Flux control coefficients were calculated according to Equation 18. The
displacement from equilibrium was quantified as the actual ratio of
product to substrate concentrations ( ) divided by the equilibrium
constant (Keq). The extracellular glucose
concentration was varied between its physiological boundaries. The most
common blood glucose concentration is 5 mM. Control
coefficients above 5% have been set in boldface.
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The Control by Glucose Transport Is Highly Variable--
The above
calculations depend on many kinetic parameters, all of which have been
measured with finite accuracy and some of which may be subject to
biological variation or regulation. Therefore, the sensitivity of the
results to inaccuracies in the parameter values has been investigated
by varying the Vmax values of all enzymes around
their default values at 5 mM glucose. It turned out that
most flux control coefficients depended weakly on the enzyme activities
around their measured values. A most surprising exception was the flux
control by the glucose transporter, which depended strongly on the
activities of various processes. Under aerobic conditions, a relatively
small increase of the activity of the transporter above the measured
value already caused its flux control coefficient to drop to 0 (Fig.
4). Also, reduction of the
Vmax of ALD, GAPDH, or PGK shifted the control
from the transporter to other enzymes.

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Fig. 4.
The flux control coefficient of the glucose
transporter sharply decreases with increasing transport activity.
These results were obtained at 5 mM extracellular glucose.
The solid lines represent aerobic conditions, and
the dashed lines anaerobic conditions. The
markers indicate the default forward Vmax (106.2 nmol min 1 (mg of protein) 1) at which all of
the above results were obtained. The forward and reverse
Vmax were varied proportionally to avoid
violation of the equilibrium constant.
|
|
In view of the uncertainty of the exact Vmax of
the glucose transporter and possible variation between trypanosome
populations or between individual cells within populations, it is hard
to predict where in the curve of Fig. 4 a trypanosome will be.
What can be predicted is which enzymes do control the flux
at increased transport activities. To this end, the transport activity
was increased by 35%, and the flux control distribution was calculated again. Under aerobic conditions, ALD, GAPDH, PGK, and GDH assumed most
of the control, and again there was no relationship between the flux
control coefficients and the displacement from equilibrium (Table
IV). Under anaerobic conditions, the
Vmax of the glucose had to be doubled before the
transporter lost all control (Fig. 4). Then ALD, GAPDH, PGK, GDH, and
GK together took over control (result not shown).
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Table IV
The control of the glycolytic flux (CiJ) and the
displacement from equilibrium ( /Keq) at increased glucose
transport activity
Both the forward and the reverse Vmax were increased
by 35% so that the forward Vmax became 143.4 nmol
min 1 mg of protein 1. The extracellular glucose
concentration was 5 mM. All other parameters were the same
as for Table I. Control coefficients above 5% are given in boldface.
|
|
Experimental Determination of the Sensitivity of the Glycolytic
Flux to Inhibition of Glucose Transport--
Since modeling alone was
not sufficient to decide whether or not glucose transport controlled
the glycolytic flux, additional experiments were carried out. Glucose
transport was inhibited by increasing concentrations of phloretin, and
the rate of oxygen consumption was measured at 0.5 and 5 mM
glucose (Fig. 5, circles). The
rate of oxygen consumption is a measure of the glycolytic flux, since
bloodstream form trypanosomes consume one molecule of oxygen per
molecule of glucose under aerobic conditions (Table II).

View larger version (17K):
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|
Fig. 5.
Inhibition of glucose transport by
phloretin. The rate of oxygen consumption was measured
(circles) and simulated (lines) at various
concentrations of the glucose transport inhibitor phloretin and both at
0.5 mM (A and C) and 5 mM
glucose (B and D). Open and
closed symbols represent independent experiments
with trypanosomes isolated from different rats. In A and
B, it was assumed in the simulations that the inhibition was
non-competitive, with a Ki of 13 µM,
and at the default Vmax of glucose transport
(106.2 nmol min 1 mg of protein 1). In
C and D, competitive inhibition with a
Ki of 18 µM was simulated, and the
Vmax of glucose transport was, respectively, 160 (highest line in D), 170, 180, and
190% (lowest line in D) of the
default value of 106.2 nmol min 1 mg of
protein 1. At 0.5 mM glucose (C),
the inhibition curves at different Vmax values
overlapped.
|
|
Phloretin is a competitive inhibitor of glucose transport into
erythrocytes (55). One report claims that it is a non-competitive inhibitor of trypanosome glucose transport (56). However, this conclusion was based on measurements of the glycolytic flux, rather than of initial transport, and no data were given. Therefore, the
phloretin titrations were simulated, either assuming non-competitive (Fig. 5, A and B, or competitive inhibition (Fig.
5, C and D). When non-competitive inhibition was
assumed, it was impossible to simulate the data at a low and at a high
glucose concentration with the same inhibition constant (Fig. 5,
A and B). With a competitive inhibitor, the model
results approached the measurements, with a single inhibition constant
(Fig. 5, C and D). However, to obtain a
satisfactory agreement between model and measurements, it was necessary
to increase the Vmax of the glucose transporter
above the measured value. This may indicate that the real flux control coefficient of glucose transport at 5 mM glucose is
substantially lower than 1, implying that other steps also exert
control. The flux control coefficient of the glucose transporter is
higher than 0, since the lowest concentration of phloretin already
inhibited the flux. All in all, these experiments confirmed the
conclusion of the kinetic calculations that the glucose transporter
carries significant but not all control.
The Distribution of Control between the Supply and Demand for
ATP--
A main function of glycolysis is to supply the cell with the
ATP necessary for all free energy-requiring processes. This is especially true for bloodstream form trypanosomes in which glycolysis is the only source of ATP. Therefore, it was surprising that the utilization of ATP had no control of the glycolytic flux in the model
(Tables III and IV). What caused this lack of control by ATP utilization?
Zooming away from the details, we considered the glycolytic pathway as
consisting of two modules: one producing cytosolic ATP (supply) and one
consuming it (demand) (20, 50, 51). The only common intermediate
connecting these modules is the cytosolic [ATP]/[ADP] ratio. The
distribution of control between the supply and demand modules should
depend on their relative sensitivity to the common intermediate. The
more sensitively a module responds to a changing cytosolic
[ATP]/[ADP] ratio, the less control over the flux it should have
(see "Materials and Methods" for mathematical details). Therefore,
the low control by the demand for ATP can be due to two reasons; either
the demand is extremely sensitive to changes of the [ATP]/[ADP]
ratio or the supply is hardly sensitive to this ratio. These
sensitivities were quantified in terms of elasticity coefficients
(Equation 20). When we compared the sensitivities of the supply and the
demand module, it turned out that the control by ATP utilization was so
low because the supply rate of ATP was held totally insensitive to the
[ATP]/[ADP] ratio. The elasticity coefficient of the latter was
lower than 10
3 at [ATP]/[ADP] ratios between 1 and 8. Thus, the supply module could not respond to changes of ATP
utilization. Due to the compartmentalization of glycolysis, the
cytosolic [ATP]/[ADP] ratio is only sensed by PYK. Not only was PYK
itself only weakly sensitive to the [ATP]/[ADP] ratio (its
elasticity coefficient was
0.24 at 5 mM extracellular glucose), but it also had little control on the flux through the supply
module (less than 0.2%). Even if PYK was made more sensitive to the
[ATP]/[ADP] ratio (an elasticity coefficient of
0.9) by including
product inhibition by ATP (Equation 3), this was not transmitted to the
rest of the supply module due to the low control by this enzyme (still
less than 2%). One way to increase the control of the supply flux by
PYK and concomitantly to increase the flux control by the demand
reaction was to decrease the Vmax of PYK to
below 156 nmol min
1 mg of protein
1 in the
absence of product inhibition or below 780 nmol min
1 mg
of protein
1 with product inhibition. However, this is
only 6 or 30%, respectively, of the activity measured by two
independent groups (7, 47). It seems more likely that our calculation
that there resides little control in PYK and ATP utilization is realistic.
How Can Trypanosome Glycolysis Be Inhibited Effectively?--
One
intended application of this study is the identification of the best
drug targets of trypanosome glycolysis. Table
V reports the extent to which each enzyme
had to be inhibited for the glycolytic flux to drop by 50%. The
glucose transporter appeared to be the most promising candidate target,
since only 51% inhibition of the transporter sufficed to inhibit the
flux by 50%. ALD, GDH, GAPDH, and PGK, enzymes that under some
conditions shared control, were intermediate candidates. Surprisingly,
HK, PFK, and PYK, enzymes that are often thought to control glycolysis,
were the poorest candidates from this perspective. They had to be
inhibited by 93% or more to reduce the flux by 50%. To investigate
whether these enzymes were present in excess, it was also calculated
which enzyme inhibition was required for a 10% inhibition of the flux (Table V). Again, glucose transport was the most effective drug target,
followed by ALD, GAPDH, GDH, and PGK. Indeed HK, PFK, and PYK appeared
to have a huge overcapacity.
View this table:
[in this window]
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|
Table V
The inhibition of each individual enzyme required to inhibit the flux
by 10 and 50%
These results were obtained at 5 mM glucose under aerobic
conditions and at constant values of all other enzyme activities. The
forward and reverse Vmax were varied simultaneously
by the same percentage.
|
|
 |
DISCUSSION |
This study has addressed the question of which steps control the
glycolytic flux in bloodstream form T. brucei. The unique situation that a sufficiently complete set of kinetic data is available
for a single condition made it possible to calculate an answer to this
question. The model that was used in this study was based on this data
set and had been validated experimentally (37). The pertinence of our
calculations is limited mainly by lack of kinetic information on the
metabolite transporters across the glycosomal membrane. If these steps
do not operate at equilibrium, as was assumed in this study, the
current model overestimates the other flux control coefficients.
However, since the glycosome can be considered as a monofunctional unit
(49), the ratios of the flux control coefficients of the glycosomal
enzymes are not compromised by this uncertainty.
The results presented in this study are at variance with the deceptive
consensus in the literature that glucose transport is the
rate-limiting step of trypanosome glycolysis (17, 29, 43, 56), for the
control of glycolysis by the glucose transporter was less than
complete, and it depended considerably on both the extracellular
glucose concentration and the enzyme activities. A steep shift of
control was calculated upon varying the activity of the glucose
transporter itself (Fig. 4). Further calculations revealed that this
sudden drop of control resulted from the large difference between the
Km values of the glucose transporter (2 mM) and HK (0.1 mM) for intracellular glucose
in this model (57). Also an increase of the "apparent"
Km of HK for glucose by a decrease of its
Km for the product Glc-6-P weakened the dependence
of the control by the transporter on transporter activity (result not
shown). However, the Km of 12 mM for
Glc-6-P that was used here is the lowest Km that could be reconciled with all kinetic studies reported so far. This
suggests that the strong shift of control may well occur in living
trypanosomes. Would it also occur in the host cells? In mammalian
cells, the difference between the Km values of
glucose transport and HK is similar to that in trypanosomes or even
more extreme (58-60). Indeed, a shift of control has been observed in
perfused rat heart upon stimulation of the transporter by insulin (36).
Insulin may, however, cause a large change of the transport activity,
and it is not known whether a small change of the transport activity is
sufficient to cause the decrease of control, as it did in the
trypanosome model. It may be expected that the shift of control is less
abrupt in mammalian cells than in trypanosomes, since the affinity of
mammalian hexokinase I, II, and III toward Glc-6-P is very high
(59).
Our calculations used a single kinetic equation for the utilization of
ATP, obscuring the variety of processes in which ATP is consumed.
Ideally, if one of these processes is activated due to a change of the
extracellular conditions, the others should not slow down, but the
supply of ATP, i.e. the glycolytic flux, should adjust to
the altered demand (20, 21). The cell can achieve this either by making
the supply very sensitive to the cytosolic [ATP]/[ADP] ratio or by
making the demand reactions very insensitive to this ratio. The former
strategy ensures at the same time homeostasis of the cytosolic
[ATP]/[ADP] ratio. Hofmeyr and Cornish-Bowden (51) argued that
"the regulatory performance of the system can be judged in terms of
how sensitive the fluxes respond to the external stimulus and to what
degree homeostasis in the concentrations of the internal regulators is maintained." In the case discussed here, this external stimulus could
be anything changing the demand for ATP, and the internal regulator is
the cytosolic [ATP]/[ADP] ratio. By this criterion, trypanosome
glycolysis worked as a poor regulatory performer; the control by demand
was very low because the supply module hardly sensed the cytosolic
[ATP]/[ADP] ratio.
This result raises the question of whether homeostasis of the
[ATP]/[ADP] ratio is unimportant for bloodstream form trypanosomes. Alternatively, if homeostasis is important, are these cells unable to
cope with changes of their environment that affect the demand for ATP?
Trypanosomes living in the bloodstream enjoy a relatively constant
environment. Probably the most dramatic event these trypanosomes experience is the transfer from the mammalian bloodstream to the midgut
of the tsetse fly. The "long slender" bloodstream form, which is
dominant in the blood, does not survive this sudden transfer. Only the
intermediate "short stumpy" bloodstream form is able to adapt to
the new environment (61). Our calculations predicted that a 90%
decrease of the activity of PYK was required to shift the control to
the demand for ATP. Perhaps fructose 2,6-bisphosphate, a potent
activator of PYK, plays an important role in the transition from the
long slender to the intermediate form of T. brucei. In bloodstream form trypanosomes, PYK is saturated with fructose 2,6-bisphosphate (12, 16). An interesting test of this hypothesis is to
measure whether the intermediate "short stumpy" form of T. brucei has a strongly reduced concentration of fructose
2,6-bisphosphate and, consequently, a higher control by the demand for ATP.
The present study has strong implications for the design of
anti-trypanosomal drugs; inhibition of the transport of glucose into
the cells should be much more effective than inhibition of any of the
other steps. Until now the design and synthesis of inhibitors of
trypanosome glycolysis has been focused on the enzymes GAPDH (62-67),
PGK (68), and ALD (63). According to our model calculations, inhibition
of these steps should be less effective than inhibition of glucose
transport but far more effective than inhibition of HK, PFK, or PYK.
Does this imply that all effort should be shifted to the synthesis of
inhibitors of glucose transport? No, some certainly, but not all; the
difference of effectiveness between inhibition of GAPDH and inhibition
of the glucose transporter may be overcome by the design of an
inhibitor of GAPDH or PGK that is 2-fold more effective at the level of
the single protein. The real gain of our method may not be an increase
of effectiveness but rather an increase of selectivity. If one
optimizes the selectivity of the inhibitor at the enzyme level, the
inhibition of the host enzyme may be only weak. If, on top of this, the
enzyme of interest has a much lower flux control in the host than in
the parasite, the compound should inhibit the flux manifold more
selectively than it inhibits the single enzyme. From an elaborate model
of erythrocyte glycolysis, it was concluded that a 95% deficiency of
ALD, GAPDH, or PGK should not cause any clinical symptoms (69). Since
these enzymes exerted flux control in trypanosomes, drugs directed
against these enzymes have a high probability of being selective
against trypanosome glycolysis.
 |
ACKNOWLEDGEMENTS |
We thank S. Marché and J. van Roy for
the sharing of unpublished results and B. Teusink and K. van Dam for
careful reading of the manuscript and fruitful discussions.
 |
FOOTNOTES |
*
This study was supported by the Netherlands Organization for
Scientific Research and the Netherlands Association of Biotechnology Research Schools.The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement" in
accordance with 18 U.S.C. Section
1734 solely to indicate this fact.
¶
Present address: Kluyver Laboratory for Biotechnology, Delft
University of Technology, Julianalaan 67, NL-2628 BC Delft, The Netherlands.
**
To whom correspondence should be addressed: Molecular Cell
Physiology, BioCentrum Amsterdam, Vrije Universiteit De Boelelaan 1087, NL-1081 HV Amsterdam, The Netherlands. Tel.: 31 20 4447228; Fax: 31 20 4447229; E-mail:
hw{at}bio.vu.nl.
2
S. Marché, F. R. Opperdoes, and
P. A. M. Michels, unpublished results.
3
J. van Roy and F. R. Opperdoes, unpublished results.
 |
ABBREVIATIONS |
The abbreviations used are:
PGA, phosphoglycerate;
ALD, fructose-1,6-bisphosphate aldolase;
1, 3-BPGA,
1,3-bisphosphoglycerate;
subscript c and g, cytosolic and glycosomal, respectively;
CiJ, flux control coefficient of
enzyme i;
DHAP, dihydroxyacetone phosphate;
Xji, elasticity coefficient of enzyme i for metabolite
j;
Fru-1, 6-BP, fructose 1,6-bisphosphate;
Fru-6-P, fructose
6-phosphate;
, ratio of product and substrate concentrations;
GA-3-P, glyceraldehyde 3-phosphate;
GAPDH, glyceraldehyde-3-phosphate
dehydrogenase;
GDH, glycerol-3-phosphate dehydrogenase;
GK, glycerol
kinase;
Gly-3-P, glycerol 3-phosphate;
Glc-6-P, glucose 6-phosphate;
HK, hexokinase;
J, steady-state flux;
Keq, equilibrium constant;
P-enolpyruvate, phosphoenolpyruvate;
PFK, phosphofructokinase;
PGK, phosphoglycerate
kinase;
PYK, pyruvate kinase;
TIM, triosephosphate isomerase;
V, volume.
 |
REFERENCES |
-
Opperdoes, F. R.
(1987)
Annu. Rev. Microbiol.
41,
127-151[CrossRef][Medline]
[Order article via Infotrieve]
-
Michels, P. A. M.,
and Hannaert, V.
(1994)
J. Bioenerg. Biomembr.
26,
213-219[Medline]
[Order article via Infotrieve]
-
Hannaert, V.,
and Michels, P. A. M.
(1994)
J. Bioenerg. Biomembr.
26,
205-212[Medline]
[Order article via Infotrieve]
-
Bakker, B. M.,
Westerhoff, H. V.,
and Michels, P. A. M.
(1995)
J. Bioenerg. Biomembr.
27,
513-525[Medline]
[Order article via Infotrieve]
-
Opperdoes, F. R.,
and Borst, P.
(1977)
FEBS Lett.
80,
360-364[CrossRef][Medline]
[Order article via Infotrieve]
-
Visser, N.,
Opperdoes, F. R.,
and Borst, P.
(1981)
Eur. J. Biochem.
118,
521-526[Abstract]
-
Hammond, D. J.,
Aman, R. A.,
and Wang, C. C.
(1985)
J. Biol. Chem.
260,
15646-15654[Abstract/Free Full Text]
-
Hammond, D. J.,
and Bowman, I. B. R.
(1980)
Mol. Biochem. Parasitol.
2,
77-91[Medline]
[Order article via Infotrieve]
-
Hammond, D. J.,
and Bowman, I. B. R.
(1980)
Mol. Biochem. Parasitol.
2,
63-75[Medline]
[Order article via Infotrieve]
-
Eisenthal, R.,
and Panes, A.
(1985)
FEBS Lett.
181,
23-27[CrossRef][Medline]
[Order article via Infotrieve]
-
Van Schaftingen, E.,
Opperdoes, F. R.,
and Hers, H.-G.
(1985)
Eur. J. Biochem.
153,
403-406[Abstract]
-
Callens, M.,
Kuntz, D. A.,
and Opperdoes, F. R.
(1991)
Mol. Biochem. Parasitol.
47,
19-30[CrossRef][Medline]
[Order article via Infotrieve]
-
Callens, M.,
and Opperdoes, F. R.
(1992)
Mol. Biochem. Parasitol.
50,
235-244[CrossRef][Medline]
[Order article via Infotrieve]
-
Cronin, C. N.,
and Tipton, K. F.
(1987)
Biochem. J.
245,
13-18[Medline]
[Order article via Infotrieve]
-
Cronin, C. N.,
and Tipton, K. F.
(1985)
Biochem. J.
227,
113-124[Medline]
[Order article via Infotrieve]
-
Van Schaftingen, E.,
Opperdoes, F. R.,
and Hers, H.-G.
(1987)
Eur. J. Biochem.
166,
653-661[Abstract]
-
Gruenberg, J.,
Sharma, P. R.,
and Deshusses, J.
(1978)
Eur. J. Biochem.
89,
461-469[Abstract]
-
Kacser, H.,
and Burns, J. A.
(1973)
Symp. Soc. Exp. Biol.
27,
65-104[Medline]
[Order article via Infotrieve]
-
Heinrich, R.,
and Rapoport, T. A.
(1974)
Eur. J. Biochem.
42,
89-95[Medline]
[Order article via Infotrieve]
-
Westerhoff, H. V.,
and Van Dam, K.
(1987)
Thermodynamics and Control of Biological Free-energy Transduction, Elsevier, Amsterdam
-
Fell, D. A.
(1997)
in
Understanding the Control of Metabolism (Snell, K., ed), Portland Press, London
-
Kholodenko, B. N.,
Molenaar, D.,
Schuster, S.,
Heinrich, R.,
and Westerhoff, H. V.
(1995)
Biophys. Chem.
56,
215-226[CrossRef]
-
Burns, J. A.,
Cornish-Bowden, A.,
Groen, A. K.,
Heinrich, R.,
Kacser, H.,
Porteous, J. W.,
Rapoport, S. M.,
Rapoport, T. A.,
Stucki, J. W.,
Tager, J. M.,
Wanders, R. J. A.,
and Westerhoff, H. V.
(1985)
Trends Biochem. Sci.
10,
16
-
Groen, A. K.,
Wanders, R. J. A.,
Westerhoff, H. V.,
Van der Meer, R.,
and Tager, J. M.
(1982)
J. Biol. Chem.
257,
2754-2757[Abstract/Free Full Text]
-
Poolman, B.,
Bosman, B.,
Kiers, J.,
and Konings, W.
(1987)
J. Bacteriol.
169,
5887-5890[Medline]
[Order article via Infotrieve]
-
Ruijter, G. J. G.,
Postma, P. W.,
and Van Dam, K.
(1991)
J. Bacteriol.
173,
6184-6191[Medline]
[Order article via Infotrieve]
-
Jensen, P. R.,
Westerhoff, H. V.,
and Michelsen, O.
(1993)
EMBO J.
12,
1277-1282[Abstract]
-
Snoep, J. L.,
Arfman, N.,
Yomano, L. P.,
Westerhoff, H. V.,
Conway, T.,
and Ingram, L. O.
(1996)
Biotechnol. Bioeng.
51,
190-197[CrossRef]
-
Ter Kuile, B. H.,
and Opperdoes, F. R.
(1991)
J. Biol. Chem.
266,
857-862[Abstract/Free Full Text]
-
Michels, P. A. M.
(1988)
Biol. Cell
64,
157-164[CrossRef][Medline]
[Order article via Infotrieve]
-
Schaaff, I.,
Heinisch, J.,
and Zimmermann, F.
(1989)
Yeast
5,
285-290[Medline]
[Order article via Infotrieve]
-
Davies, S. E. C.,
and Brindle, K. M.
(1992)
Biochemistry
31,
4729-4735[Medline]
[Order article via Infotrieve]
-
Kruckeberg, A. L.
(1996)
Arch. Microbiol.
166,
283-292[CrossRef][Medline]
[Order article via Infotrieve]
-
Kholodenko, B. N.,
and Brown, G. C.
(1996)
Biochem. J.
314,
753-760[Medline]
[Order article via Infotrieve]
-
Shulman, R. G.,
Bloch, G.,
and Rothman, D. L.
(1995)
Proc. Natl. Acad. Sci. U. S. A.
92,
8535-8542[Abstract]
-
Kashiwaya, Y.,
Sato, K.,
Tsuchiya, N.,
Thomas, S.,
Fell, D. A.,
Veech, R. L.,
and Passonneau, J. V.
(1994)
J. Biol. Chem.
269,
25502-25514[Abstract/Free Full Text]
-
Bakker, B. M.,
Michels, P. A. M.,
Opperdoes, F. R.,
and Westerhoff, H. V.
(1997)
J. Biol. Chem.
272,
3207-3215[Abstract/Free Full Text]
-
Lanham, S. M.
(1968)
Nature
218,
1273-1274[Medline]
[Order article via Infotrieve]
-
Kiaira, J. K.,
and Njogu, M. R.
(1994)
Biotechnol. Appl. Biochem.
20,
347-356[Medline]
[Order article via Infotrieve]
-
Lowry, O. H.,
Rosebrough, N. J.,
Farr, A. L.,
and Randall, R. J.
(1951)
J. Biol. Chem.
193,
265-275[Free Full Text]
-
Bergmeyer, H. U.
(1974)
Methods of Enzymatic Analysis, Verlag Chemie, Weinheim
-
Visser, N.,
and Opperdoes, F. R.
(1980)
Eur. J. Biochem.
103,
623-632[Abstract]
-
Eisenthal, R.,
Game, S.,
and Holman, G. D.
(1989)
Biochim. Biophys. Acta
985,
81-89[Medline]
[Order article via Infotrieve]
-
Stanbury, J. B.,
Wyngaarden, J. B.,
Frederickson, D. F.,
Goldstein, J. L.,
and Brown, M. S.
(1993)
The Metabolic Basis of Inherited Disease, 5th Ed., McGraw-Hill Book Co., New York
-
Misset, O.,
Bos, O. J. M.,
and Opperdoes, F. R.
(1986)
Eur. J. Biochem.
157,
441-453[Abstract]
-
Nwagwu, M.,
and Opperdoes, F. R.
(1982)
Acta Trop.
39,
61-72[Medline]
[Order article via Infotrieve]
-
Barnard, J. P.,
and Pedersen, P. L.
(1988)
Mol. Biochem. Parasitol.
31,
141-148[Medline]
[Order article via Infotrieve]
-
Fairlamb, A. H.,
Opperdoes, F. R.,
and Borst, P.
(1977)
Nature
265,
270-271[Medline]
[Order article via Infotrieve]
-
Rohwer, J. M.,
Schuster, S.,
and Westerhoff, H. V.
(1996)
J. Theor. Biol.
179,
213-228[CrossRef][Medline]
[Order article via Infotrieve]
-
Schuster, S.,
Kahn, D.,
and Westerhoff, H. V.
(1993)
Biophys. Chem.
48,
1-17[CrossRef][Medline]
[Order article via Infotrieve]
-
Hofmeyr, J.-H. S.,
and Cornish-Bowden, A.
(1991)
Eur. J. Biochem.
200,
223-236[Abstract]
-
Sauro, H. M.,
and Fell, D. A.
(1991)
Math. Comp. Modelling
15,
15-28
-
Frankel, S., and Reitman, S.
(eds)
(1963)
Gradwohl's Clinical Laboratory Methods and Diagnosis, 6th Ed., Vol. 1, C.V. Mosby Co., St. Louis
-
Henry, R. J., Cannon, D. C., and Winkelman, J. W.
(eds)
(1974)
Clinical Chemistry Principles and Techniques, 2nd Ed., Harper & Row Publishers
-
Krupka, R. M.,
and Devés, R.
(1980)
Biochim. Biophys. Acta
598,
134-144[Medline]
[Order article via Infotrieve]
-
Seyfang, A.,
and Duszenko, M.
(1991)
Eur. J. Biochem.
202,
191-196[Abstract]
-
Bakker, B. M.,
Michels, P. A. M.,
and Westerhoff, H. V.
(1996)
in
BioThermoKinetics of the Living Cell (Westerhoff, H. V., Snoep, J. L., Sluse, F. E., Wijker, J. E., and Kholodenko, B. N., eds), pp. 136-142, BioThermoKinetics Press, Amsterdam
-
Gould, G. W.,
Thomas, H. M.,
Jess, T. J.,
and Bell, G. I.
(1991)
Biochemistry
30,
5139-5145[Medline]
[Order article via Infotrieve]
-
Colowick, S. P.
(1973)
in
The Enzymes (Boyer, P. D., ed), Vol. 9, pp. 1-48, Academic Press, Inc., New York
-
Mueckler, M.
(1994)
Eur. J. Biochem.
219,
713-725[Abstract]
-
Giffin, B. F.,
and McCann, P. P.
(1989)
Am. J. Trop. Med. Hyg.
40,
487-493[Medline]
[Order article via Infotrieve]
-
Vellieux, F. M. D.,
Hajdu, J.,
Verlinde, C. L. M. J.,
Groendijk, H.,
Read, R. J.,
Greenhough, T. J.,
Campbell, J. W.,
Kalk, K. H.,
Littlechild, J. A.,
Watson, H. C.,
and Hol, W. G. J.
(1993)
Proc. Natl. Acad. Sci. U. S. A.
90,
2355-2359[Abstract]
-
Perié, J.,
Riviere-Alric, I.,
Blonski, C.,
Gefflaud, T.,
Lauth de Viguerie, N.,
Trinquier, M.,
Willson, M.,
Opperdoes, F. R.,
and Callens, M.
(1993)
Pharmacol. Ther.
60,
347-365[Medline]
[Order article via Infotrieve]
-
Willson, M.,
Lauth, N.,
Perié, J.,
Callens, M.,
and Opperdoes, F. R.
(1994)
Biochemistry
33,
214-220[Medline]
[Order article via Infotrieve]
-
Verlinde, C. L. M. J.,
Callens, M.,
Van Calenbergh, S.,
Van Aerschot, A.,
Herdewijn, P.,
Hannaert, V.,
Michels, P. A. M.,
Opperdoes, F. R.,
and Hol, W. G. J.
(1994)
J. Med. Chem.
37,
3605-3613[Medline]
[Order article via Infotrieve]
-
Van Calenbergh, S.,
Verlinde, C. L.,
Soenens, J.,
De Bruyn, A.,
Callens, M.,
Blaton, N. M.,
Peeters, O. M.,
Rozenski, J.,
Hol, W. G.,
and Herdewijn, P.
(1995)
J. Med. Chem.
38,
3838-3849[Medline]
[Order article via Infotrieve]
-
Kim, H.,
Feil, I. K.,
Verlinde, C. L. M. J.,
Petra, P. H.,
and Hol, W. G. J.
(1995)
Biochemistry
34,
14975-14986[Medline]
[Order article via Infotrieve]
-
Bernstein, B. E.,
Michels, P. A. M.,
and Hol, W. G.
(1997)
Nature
385,
275-278[CrossRef][Medline]
[Order article via Infotrieve]
-
Schuster, R.,
and Holzhütter, H.-G.
(1995)
Eur. J. Biochem.
229,
403-418[Abstract]
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