Glycolysis in Bloodstream Form Trypanosoma brucei Can
Be Understood in Terms of the Kinetics of the Glycolytic Enzymes*
(Received for publication, July 10, 1996, and in revised form, October 9, 1996)
Barbara M.
Bakker
§,
Paul A. M.
Michels
¶,
Fred R.
Opperdoes
¶ and
Hans V.
Westerhoff

From the
Microbial Physiology, BioCentrum Amsterdam,
Vrije Universiteit, De Boelelaan 1087, NL-1081 HV Amsterdam,
§ E. C. Slater Institute, BioCentrum Amsterdam, University
of Amsterdam, Plantage Muidergracht 12,
NL-1018 TV Amsterdam, The Netherlands, and the ¶ Research Unit
for Tropical Diseases, International Institute of Cellular and
Molecular Pathology and Laboratory of Biochemistry, Catholic
University of Louvain, Avenue Hippocrate 74, B-1200 Brussels, Belgium
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
FOOTNOTES
Acknowledgments
REFERENCES
ABSTRACT
In trypanosomes the first part of glycolysis
takes place in specialized microbodies, the glycosomes. Most glycolytic
enzymes of Trypanosoma brucei have been purified and
characterized kinetically. In this paper a mathematical model of
glycolysis in the bloodstream form of this organism is developed on the
basis of all available kinetic data. The fluxes and the cytosolic
metabolite concentrations as predicted by the model were in accordance
with available data as measured in non-growing trypanosomes, both under
aerobic and under anaerobic conditions. The model also reproduced the
inhibition of anaerobic glycolysis by glycerol, although the amount of
glycerol needed to inhibit glycolysis completely was lower than
experimentally determined. At low extracellular glucose concentrations
the intracellular glucose concentration remained very low, and only at
5 mM of extracellular glucose, free glucose started to
accumulate intracellularly, in close agreement with experimental
observations. This biphasic relation could be related to the large
difference between the affinities of the glucose transporter and
hexokinase for intracellular glucose. The calculated intraglycosomal
metabolite concentrations demonstrated that enzymes that have been
shown to be near-equilibrium in the cytosol must work far from
equilibrium in the glycosome in order to maintain the high glycolytic
flux in the latter.
INTRODUCTION
In several respects glycolysis in trypanosomes differs from
glycolysis in other eukaryotes. In these parasites most glycolytic enzymes occur sequestered in a specialized organelle closely related to
peroxisomes (1) (for reviews see Refs. 2-5). As in trypanosomes 90%
of the protein content of these microbodies consists of glycolytic enzymes; they are called glycosomes. In glycosomes glucose is converted
to 3-phosphoglycerate (3-PGA),1 which is
metabolized to pyruvate in the cytosol. The NADH produced in the
glycosomes by glyceraldehyde-3-phosphate dehydrogenase (GAPDH) is used
to reduce dihydroxyacetone phosphate (DHAP) to glycerol 3-phosphate
(Gly-3-P). Subsequently, Gly-3-P is reoxidized by molecular oxygen via
a glycerol-3-phosphate oxidase (GPO) in the mitochondria, and DHAP
returns to the glycosomes. In the organelles there is no net ATP
production or consumption by glycolysis, since the consumption of ATP
by hexokinase (HK) and phosphofructokinase (PFK) is balanced by
phosphoglycerate kinase (PGK). Only in the cytosol there is net
glycolytic ATP production by pyruvate kinase (PYK). Under anaerobic
conditions Gly-3-P is converted to glycerol with the concomitant
production of ATP via the reverse action of glycerol kinase (GK) (1, 2,
6, 7). Unlike the corresponding enzymes in most other organisms, the
glycosomal HK and PFK of trypanosomes are hardly subject to allosteric
regulation (8-10). In trypanosomes not PFK but PYK is activated by
fructose 2,6-bisphosphate (11-13), and consistently,
6-phosphofructo-2-kinase and fructose-2,6-bisphosphatase are found in
the cytosol (14).
Trypanosoma brucei, the parasite that causes African
sleeping disease in humans and nagana in livestock, is transmitted by the tse-tse fly. When living in the mammalian bloodstream T. brucei has neither a functional Krebs cycle nor oxidative
phosphorylation nor does it store any carbohydrates. Consequently,
complete inhibition of glycolysis kills the organism. Because of the
differences between mammalian and trypanosomal glycolysis, this pathway
is a major potential target for drugs against the African sleeping
disease (15). Many of the glycolytic enzymes of trypanosomes resemble, however, the corresponding enzymes of the hosts of the latter. A drug
that interferes strongly with trypanosome glycolysis may well
compromise this metabolic pathway in its host where glycolysis is also
essential. Consequently, it is important to design drugs that strongly
inhibit glycolysis in trypanosomes but only weakly that of their hosts.
This design task is complicated by the fact that the effect of
modulation of an enzyme activity on a metabolic flux also depends on
the properties of other enzymes in the metabolic pathway (16-18).
Nevertheless, recent developments may well bring such rational drug
design within reach. In the past decade most glycolytic enzymes of
T. brucei have been purified and characterized extensively,
both structurally and kinetically. Furthermore, fluxes and glycolytic
intermediates have been measured under various conditions. Although the
individual enzyme kinetic data are available, their implications for
the glycolytic pathway as a whole have not been evaluated nor has it
been attempted to predict the effect on glycolysis even for a drug for
which the effects on its target enzyme are known.
In this paper we relate the functioning of glycolysis in bloodstream
form T. brucei to the known kinetics of the individual trypanosome enzymes. To this end a detailed computer model of trypanosomal glycolysis has been constructed, including all available enzyme kinetics. The model distinguishes itself from other elaborate kinetic glycolysis models in the sense that the kinetic parameters are
not adjusted to fit the measured metabolite concentrations (19-21).
T. brucei is a very suitable organism for this type of modeling because its glycolysis lacks many branches (cf. in
other organisms (22)), the glycosomal enzymes lack allosteric
regulation, and because most trypanosomal enzymes have been
characterized under the same experimental conditions. The model
predicts how the steady-state glycolytic flux and metabolite
concentrations depend on the substrate and product concentrations and
the enzyme-kinetic parameters in non-growing cells. It explains certain
aspects of cell physiology, but it also makes us aware which data are
still lacking for a deeper understanding.
MATERIALS AND METHODS
This section describes how the model was constructed and what
equations were used.
Stoichiometry and Conserved Moieties
The model contains the
glycolytic pathway, including the branch to glycerol and the
utilization of ATP (Fig. 1). The two glucose transport steps,
i.e. across the plasma membrane and the glycosomal membrane,
were lumped into one, because in kinetic experiments no distinction
between them has been made so far (23). The glycosomal membrane was
taken to be impermeable to metabolites (24), except for those that need
to be transported across this membrane (Fig. 1). Nothing is known about
the kinetics of the transport of 3-PGA, Gly-3-P, and DHAP. These steps
were assumed to be in equilibrium and mutually independent. The
concentration of inorganic phosphate in the glycosome was assumed to be
saturating. At steady state adenylate kinase (AK) should be at
equilibrium. When the known kinetics of glucose-phosphate isomerase
(PGI) (25) and triose-phosphate isomerase (TIM) (26) were implemented
explicitly, these enzymes operated close to equilibrium (the ratio of
the steady-state product and substrate concentrations divided by the
equilibrium constant exceeded 0.8 for both reactions), and therefore,
they were further treated as equilibrium reactions. This facilitated
the calculations with hardly any effect on the outcome. Experimentally
it has been shown that the cytosolic enzymes phosphoglycerate mutase
(PGM) and enolase (ENO) operate near equilibrium (27). Accordingly, they were treated as if in equilibrium. Finally, the transport of
glycerol out of the cells was assumed to be in equilibrium. The
kinetics of all other enzymes and the transport of glucose and pyruvate
were implemented explicitly in the model.
Fig. 1.
The stoichiometric scheme of the model of
glycolysis in bloodstream form T. brucei. The
reactions 3, 6, 9, 13, 15 and 17, 19 and 20 were treated as equilibrium
reactions. 1, transport of glucose across the plasma
membrane and the glycosomal membrane; 2, HK; 3,
PGI; 4, PFK; 5, ALD; 6, TIM;
7, GAPDH; 8, PGK; 9, transport of
3-PGA across the glycosomal membrane, PGM, and ENO; 10, PYK; 11, pyruvate transport across the plasma membrane;
12, GDH; 13, transport of Gly-3-P
(G-3-P) across the glycosomal membrane; 14, GPO;
15, transport of DHAP across the glycosomal membrane;
16, GK; 17, transport of glycerol across the
glycosomal membrane and the plasma membrane; 18, ATP
utilization; 19, glycosomal AK; 20, cytosolic AK.
G-6-P, Glc-6-P; F-6-P, Fru-6-P; F-1, 6-BP, Fru-1, 6-BP.
[View Larger Version of this Image (76K GIF file)]
Four moiety conservation relations were derived from the stoichiometry
as depicted in Fig. 1 by using the metabolic modeling program SCAMP
(28). These correspond to the adenine nucleotides in the glycosome and
the cytosol, respectively, the nicotinamide adenine nucleotides in the
glycosome, and the organic phosphate that is not exchanged with
inorganic phosphate. None of the reactions modifies these sums:
|
(Eq. 1)
|
|
(Eq. 2)
|
|
(Eq. 3)
|
|
(Eq. 4)
|
The []c refers to the cytosolic concentration and
the []g to the glycosomal concentration.
Vc is the cytosolic volume and Vg the glycosomal volume in µl per mg of cell
protein. In Equation 4 the concentrations of Fru-1,6-BP and ATP are
multiplied by a factor of 2, because these metabolites contain two
phosphate groups that are transferred to other organic compounds. As
Gly-3-P and DHAP were assumed to equilibrate across the glycosomal
membrane, Equation 4 simplified to
|
(Eq. 5)
|
in which
|
(Eq. 6)
|
and
|
(Eq. 7)
|
The two distinct pools of adenine nucleotides occur as a
consequence of the assumed impermeability of the glycosomal membrane for these compounds. The fourth conserved moiety (Equations 4 and 5) is
also a consequence of the compartmentation. If glycolysis occurred in
one compartment, ATP utilization (Reaction R18 in Fig.
1), for example, would modify this sum. As the glycosomes occupy 4.3%
of the total cellular volume (29), the ratio
Vc/Vg amounts to 22.3. C2 and C4 were estimated from Ref. 27, by using that 1 g wet weight corresponds to 80 mg of protein and 1 ml of total
cellular volume corresponds to 175 mg of total cell protein (29).
C1 and C3 were chosen arbitrarily, but their
values hardly affected the results. The values were C1 = 3.9 mM, C2 = 3.9 mM, C3 = 4 mM, and C4 = 120 mM. This value
for C4 is just saturating; an increase does not affect the
flux. C4 is high, because [Gly-3-P] and [DHAP] are
multiplied by the factor 1 + Vc/Vg. Only when
[Gly-3-P] and [DHAP] become low, this high sum implies high
concentrations of the glycosomal metabolites. This did not occur in the
simulations reported in this paper (results not shown).
Kinetic Equations
All available literature data
(Tables I and II) on trypanosome enzyme
kinetics have been obtained at 25 °C, except for glucose transport
(37 °C) (23).
Table II.
Kinetic parameters of the enzymes described by Michaelis-Menten-type
kinetics
One-substrate reactions
|
Two-substrate
reactions
|
Enzyme |
KS |
Enzyme |
V /V+ |
KS1 |
KS2 |
KP1 |
KP2
|
|
|
mM |
|
|
mM |
mM |
mM |
mM
|
GPO |
1.7 (Gly-3-P) (50) |
HK
(8) |
|
0.116 (ATP) |
0.1 (Glci)a |
0.126 (ADP)
|
Pyruvate transport |
1.96 (PYRc)d (30) |
GAPDH
(48) |
0.67 |
0.15 (GA-3-P) |
0.45 (NAD+) |
0.1 (1,3-BPGA) |
0.02 (NADH)
|
|
|
PGK
(49) |
0.029b |
0.05 (1,3-BPGA)b |
0.1 (ADP)b |
1.62 (3-PGA) |
0.29 (ATP)
|
|
|
GDHc |
0.07 |
0.85 (DHAP) |
0.015 (NADH) |
6.4 (Gly-3-P) |
0.6 (NAD+)
|
|
|
GK
(6) |
167 |
5.1 (Gly-3-P) |
0.12 (ADP) |
0.12 (Gly) |
0.19 (ATP) |
|
a
A.-M. Loiseau, unpublished results.
|
b
Conjectured, in agreement with an equilibrium constant of
3.3·103 in the catabolic direction (51).
|
c
M. Callens, D. Kuntz, O. Bos, and F. Opperdoes, unpublished
results.
|
d
c, Cytosolic.
|
|
The kinetics of GPO and the transport of pyruvate across the plasma
membrane were described by irreversible Michaelis-Menten kinetics:
|
(Eq. 8)
|
in which S is the substrate concentration. The measured rate of
zero- trans pyruvate influx was well below the steady-state rate of pyruvate production (30). This may be due to asymmetry of the
transporter, but most probably the long time scale of the uptake assay
(30 s) (30) also led to an underestimation of the rate, because
pyruvate cannot be metabolized and accumulates. Therefore the
Vmax for efflux was adjusted so that the
pyruvate concentration in the model agreed with the measured
intracellular pyruvate concentration of 21 mM (31).
The kinetics of HK were described by a Michaelis-Menten type equation
for two substrates:
|
(Eq. 9)
|
in which S1 is ATP, S2 is intracellular
glucose, and P1 is ADP. Thus the competitive product
inhibition by ADP was included. Glucose 6-phosphate (Glc-6-P) had no
effect on the rate (8).
The kinetics of GAPDH, PGK, glycerol-3-phosphate dehydrogenase (GDH),
and GK were described by a reversible Michaelis-Menten equation for two
non-competing product-substrate couples:
|
(Eq. 10)
|
The transport of glucose was described according to a 4-state
model for a facilitated diffusion carrier (32). The experimental data
(33) may indicate that the carrier is slightly asymmetric. However, the
Vmax measured for efflux is lower than that for
influx, whereas the KM for efflux is higher. As this
would lead to a net flux in the absence of a glucose gradient, the
apparent asymmetry was neglected. Rewritten into a
Michaelis-Menten-like form the equations became:
|
(Eq. 11)
|
in which [Glc]o and [Glc]i are the
extracellular and intracellular glucose concentrations, respectively,
and KGlc is 2 mM (23). From the
assumed symmetry of the carrier and from the finding that the
Vmax for equilibrium exchange was twice as high as the Vmax for zero trans-influx,
the factor
was calculated to be 0.75.
The rate of PFK exhibits a slightly cooperative dependence on the
concentration of fructose 6-phosphate (Fru-6-P):
|
(Eq. 12)
|
in which KM, Fru6P = 0.82 mM, KM, ATP = 2.6·10
2 mM, and n = 1.2 (9, 10).
The rate of PYK depends cooperatively on the concentration of PEP:
|
(Eq. 13)
|
in which KM, PEP = 0.34·(1 + [ATP]c/0.57 mM + [ADP]c/0.64
mM) mM, KM, ADP = 0.114 mM and n = 2.5 (12, 13). The
equation for KM, PEP was fitted to the
measurements of this parameter at different concentrations of ATP and
ADP (12). Variable activation of PYK by fructose 2,6-bisphosphate (12)
was neglected, as the concentration of this compound was largely
saturating in bloodstream form trypanosomes in the presence of glucose
(14), and consequently it is unlikely that it plays a regulatory role
under these conditions.
Aldolase (ALD) works according to an ordered uni-bi mechanism.
Glyceraldehyde 3-phosphate (GA-3-P) dissociates from the enzyme before
DHAP does (34, 35). The rate equation reads:
|
(Eq. 14)
|
in which V
/V+ = 1.19, KM, F16BP = 9·10
3
(1 + [ATP]g/0.68 mM + [ADP]g/1.51 mM + [AMP]g/3.65 mM) mM,
KM, GA3P = 6.7·10
2
mM, KM, DHAP = 1.5·10
2 mM, and
Ki, GA3P = 9.8·10
2
mM (35).
The hydrolysis of ATP for free-energy-dissipating processes, such as
motion, biosynthesis, and the maintenance of the proton gradients
across the plasma membrane and the mitochondrial membrane (36, 37),
cannot be described by a simple and realistic equation based on the
mechanism of these processes. Therefore, a phenomenological equation
was constructed. Under steady-state conditions the flux through
pyruvate kinase should equal ATP hydrolysis. In the absence of ATP the
utilization rate should be zero. The ratios under anaerobic and aerobic
conditions were 1.2 and 2.9 (27), respectively, and the rate of
pyruvate production, and hence ATP utilization, under aerobic
conditions was twice the rate under anaerobic conditions (38). As the
relation between the rate of ATP utilization and the [ATP]/[ADP]
ratio seemed close to linear, we assumed
|
(Eq. 15)
|
This rate equation corresponds to a far-from-equilibrium
Michaelis-Menten reaction with dominant product inhibition. The value
of k was adjusted to 50 nmol min
1 mg
protein
1, so that the calculated steady-state
[ATP]/[ADP] ratio under aerobic conditions corresponded to the
measured ratio. Equation 15 should not be extrapolated to very high
[ATP]/[ADP] ratios.
Substrate and Product Concentrations
The extracellular
concentrations of glucose, O2, pyruvate, and glycerol were
treated as parameters of the system, which means that they were fixed
for each steady-state calculation. Glucose was 5 mM, which
is the concentration the trypanosomes encounter in the bloodstream
(23). O2 was taken to be saturating under aerobic
conditions, whereas the flux through GPO was completely blocked under
anaerobic conditions by setting the Vmax of GPO to zero. In the absence of glycerol, 10% of the total flux went to
glycerol under aerobic conditions in contradiction with the corresponding experimental finding that no glycerol was produced (38).
However, in the model only 0.5 µM of glycerol was
required to inhibit this flux, and at higher concentrations it was
reversed. If one were to allow free accumulation of glycerol, the GK
reaction should reach equilibrium. The aerobic steady state was
identical but easier to compute if the V+ of GK
was set to zero. The extracellular concentration of pyruvate and both
the extracellular and the intracellular concentrations of glycerol were
zero unless specified otherwise.
Differential Equations
If a reaction in the pathway was
considered to be in equilibrium, its products and substrates were
treated as a single metabolite pool. To this aim five pools were
defined.
The sum of hexose phosphates in the glycosome is
|
(Eq. 16)
|
The sum of triose phosphates is
|
(Eq. 17)
|
A pool [N] was defined by
|
(Eq. 18)
|
in which
|
(Eq. 19)
|
Consequently,
|
(Eq. 20)
|
Finally two variables Pg and Pc,
denoting the sums of high energy phosphates in the glycosome and the
cytosol, respectively, were defined:
|
(Eq. 21)
|
|
(Eq. 22)
|
The following set of differential equations described the
time-dependent behavior of glycolysis:
|
(Eq. 23)
|
|
(Eq. 24)
|
|
(Eq. 25)
|
|
(Eq. 26)
|
|
(Eq. 27)
|
|
(Eq. 28)
|
|
(Eq. 29)
|
|
(Eq. 30)
|
|
(Eq. 31)
|
|
(Eq. 32)
|
The total intracellular volume Vtot was
taken constant at 5.7 µl/mg total cellular protein (29). The time
t was expressed in minutes and the enzyme rates v
in nmol min
1 (mg cell protein)
1. In order
to obtain the time derivatives of the concentrations in mM
min
1, a correction was made for the volume of the
compartment in which a metabolite pool resides. As the
KM values were expressed in mM, the
metabolite concentrations were obtained in mM as well.
To calculate a steady state all above time derivatives of metabolite
concentrations were set to zero. The resulting system of nonlinear
equations was solved numerically for the metabolite concentrations. The
concentrations of NAD+ and Gly-3-P were calculated from the
conservation equations (Equations 3 and 5, respectively). The other
dependent concentrations were calculated from the equilibrium
conditions as described below.
Equilibrium Reactions
The equilibrium constants are found
in Table III. The transport of metabolites across the
glycosomal membrane was assumed to be driven only by concentration
gradients of these metabolites, and consequently, the corresponding
equilibrium constants were 1. The individual metabolite concentrations
were calculated from the equilibrium pools as follows.
Table III.
The equilibrium constants at 25 °C of the reactions treated as
equilibrium reactions (51)
Enzyme |
Kcq |
|
PGI |
0.29
|
TIM |
0.045 |
PGM |
0.187 |
ENO |
6.7
|
AK |
0.442 |
|
a, Glc-6-Pg
Fru-6-Pg
The
equilibrium equation reads
|
(Eq. 33)
|
It follows from Equations 16 and 33 that
|
(Eq. 34)
|
When [Glc-6-P]g was known
[Fru-6-P]g was calculated from Equation 16.
b, DHAPc
DHAPg
GA-3-Pg
The equilibrium equation of TIM is
|
(Eq. 35)
|
It follows from Equations 7, 17, and 35 that
|
(Eq. 36)
|
When [DHAP] was known [GA-3-P]g was calculated
from Equation 17.
c, 3-PGAg
3-PGAc
2-PGAc
PEPc
The equilibrium equations of PGM and ENO are
|
(Eq. 37)
|
|
(Eq. 38)
|
From Equations 19, 20, 37, and 38 it follows that
|
(Eq. 39)
|
When [3-PGA] was known, [2-PGA] and [PEP] were calculated
from Equations 37 and 38, respectively.
d, 2ADPg
ATPg + AMPg
The equilibrium equation is
|
(Eq. 40)
|
Solving the Equations 1, 21, and 40 gives a quadratic equation
and the relevant solution is
|
(Eq. 41)
|
in which
|
(Eq. 42)
|
|
(Eq. 43)
|
|
(Eq. 44)
|
The other solution of the quadratic equation gives negative
concentrations of ADP and was not considered. The concentrations of ADP
and AMP were calculated from Equations 21 and 1, respectively. To
obtain the cytosolic concentrations [ATP]c,
[ADP]c, and [AMP]c Pc was
substituted for Pg.
Numerical Methods
The simulations were performed with the
program MLAB (Civilized Software, Bethesda). First a
time-dependent simulation was performed by integrating
Equations 23, 24, 25, 26, 27, 28, 29, 30, 31, 32 with a Gear-Adams algorithm, until the system
approached a steady state. Usually the initial values of all
independent variables were arbitrarily chosen to be 1. Subsequently,
the system of nonlinear equations defining the steady state was solved
with a Marquardt-Levenberg algorithm, to which the final metabolite
concentrations of the time-dependent simulation were given
as initial values. An imposed constraint was that all concentrations
should be positive, and, if they were involved in a conserved moiety,
they should be smaller than the corresponding conserved sum. Finally,
starting from the obtained solution a second time integration was
performed to test the stability of the steady state. It was examined
whether the steady state was unique, by varying the initial metabolite
concentrations over a wide range. This never gave a different steady
state, but this cannot be considered definite proof of uniqueness.
RESULTS
Fluxes and Concentrations Under Aerobic and Anaerobic
Conditions
The first question we addressed was whether the
combination of all information on the in vitro kinetics of
the glycolytic enzymes leads to realistic fluxes and metabolite
concentrations. We therefore calculated the steady-state glycolytic
fluxes and metabolite concentrations using the model as described
above. The rate of glucose consumption hardly changed upon a shift from aerobic to anaerobic conditions (Table IV). This is in
agreement with measurements by Visser (38) who observed that the sum of pyruvate and glycerol production was the same under both conditions. Under aerobic conditions glucose was fully converted to pyruvate, while
under anaerobic conditions equimolar amounts of pyruvate and glycerol
were produced. The predicted cytosolic concentrations of DHAP, PEP,
pyruvate, Gly-3-P, and [ATP]/[ADP] differed by less than a factor 2 from the measured cellular concentrations (27, 31)
(Table V). The predicted concentrations of 3-PGA and
2-PGA deviated more from the concentrations obtained experimentally. The model-calculated ratios of the concentrations under aerobic and
anaerobic conditions corresponded more closely to the experimental ratios. The concentration of Gly-3-P increased by a factor of 4 upon
the shift from aerobic to anaerobic conditions, fully in agreement with
the measurements (27). For the cytosolic pyruvate concentration and
[ATP]/[ADP] ratio under aerobic conditions the correspondence
between the model and the experiments was imposed, because the
Vmax of the pyruvate transporter and the
equation for ATP utilization were adjusted to fit these concentrations. The [ATP]/[ADP] ratio and the flux under anaerobic conditions, however, were kept free. Only the relation between the two was set by
Equation 15.
Table V.
The steady-state metabolite concentrations under aerobic and anaerobic
conditions
The values shown in brackets are the concentrations measured by Visser
and Opperdoes (27). To express the latter concentrations in
mM, 1 g of wet weight corresponded to 80 mg of protein
and 1 ml of total cellular volume corresponded to 175 mg of total cell
protein (29). Pyruvate was measured by Wiemer et al. (31). The equations and parameter values are specified under "Materials and
Methods." To simulate aerobic conditions VGK was
set to zero, while under anaerobic conditions VGPO
was set to zero.
Metabolite |
Concentration
|
Ratio,
aerobic/anaerobic |
Aerobic |
Anaerobic
|
|
|
mM
|
Glucose
(c/g)a |
0.056 |
0.10 |
Glc-6-P
(g) |
0.44 |
0.44 |
Fru-6-P (g) |
0.13 |
0.13
|
Fru-1,6-bisphosphate (g) |
26 |
2.3 |
DHAP
(c/g) |
1.6 (2.6) |
0.61 (1.1) |
2.6 (2.3) |
GA-3-P
(g) |
0.074 |
0.027 |
1,3-BPGA (g) |
0.028 |
0.0097 |
3-PGA
(c/g) |
0.68 (4.8) |
0.46 (1.2) |
1.5 (4.1) |
2-PGA
(c) |
0.13 (0.59) |
0.085 (0.33) |
1.5 (1.8) |
PEP
(c) |
0.85 (0.74) |
0.57 (0.39) |
1.5 (1.9) |
pyruvate
(c) |
21 (21) |
1.6 |
Gly-3-P
(g) |
1.1 (2.0) |
4.2 (7.9) |
0.26 (0.25)
|
[NADH]/[NAD+] (g) |
0.036 |
0.040 |
[ATP]/[ADP]
(g) |
0.48 |
0.29 |
[ATP]/[ADP]
(c) |
2.9 (2.9) |
1.4 (1.2) |
2.1 (2.4) |
|
a
c, cytosolic; g, glycosomal.
|
|
Interestingly, the calculated [ATP]/[ADP] ratios in the cytosol and
the glycosome differed by up to a factor of 6, as a consequence of
compartmentation. The modeled displacement from equilibrium of
reversible reactions, expressed as
/Keq, was
compared with measurements in cell extracts (27) (Table
VI). These measurements were dominated by the cytosolic concentrations,
as the glycosomal volume is only 4.3% of the total cellular volume.
The measured log
/Keq of GAPDH corresponds
fairly well with the value predicted from the model. PGK and ALD were
in the model further displaced from equilibrium than they were
experimentally. GDH was assumed to work in equilibrium by Visser and
Opperdoes (27), but according to the model this enzyme was far
displaced from equilibrium. This demonstrates that enzymes that are
near equilibrium in the cytosol may work far from equilibrium in the
glycosome.
Glycerol Titration Under Anaerobic and Aerobic
Conditions
Under anaerobic conditions Gly-3-P is converted to
glycerol by GK (2). As the
G0
of this
reaction is strongly positive, glycerol effectively inhibits glycolysis
at low concentrations (50% inhibition at 0.8 mM) (39). In
the model, glycolysis was also inhibited by glycerol (Fig. 2), but 0.1 mM of glycerol reduced the glucose consumption already by
96.1%. Increasing the forward and reverse Vmax
of GK, i.e. the amount of the enzyme, did not increase the
resistance to glycerol (result not shown). The model concentration of
Gly-3-P in the presence of 0.1 mM glycerol was 5.1 mM which is equal to the KM of GK for
this metabolite. Gly-3-P is involved in one conserved moiety and, as it
equilibrates across the glycosomal membrane, it is weighted by a factor
23.3. Thus a large decrease of other concentrations in this sum is
required to compensate for an increase of Gly-3-P (Equation 5). It was conjectured that C4 became a limiting factor under
anaerobic conditions. Indeed, an increase of C4, from 120 to 360 mM, substantially increased the flux in the presence
of glycerol (Fig. 2) with a concomitant increase of
[Gly-3-P] (not shown). A 10-fold increase of the
KM of GK for glycerol, and thus the equilibrium
constant of GK, further improved the glycerol resistance. A combination
of both (C4 = 360 mM and
KM, glycerolGK = 1.2 mM) gave the maximum glycerol resistance. At a
C4 of 360 mM, however, under aerobic conditions
the glycosomal concentration of fructose 1,6-bisphosphate (Fru-1,6-BP)
increased to 136 mM. The concomitant increase of the
osmotic pressure in the glycosomes might then lead to swelling or even
bursting of the organelles. Obviously, simply increasing C4
is not a realistic option.
Fig. 2.
The steady-state glucose consumption rate
under anaerobic conditions as a function of the glycerol concentration
as modeled for various combinations of C4 and the
KM of GK for glycerol. 1, C4 = 120 mM and KM, glycerol = 0.12 mM; 2, C4 = 360 mM
and KM, glycerol = 0.12 mM;
3, C4 = 120 mM and
KM, glycerol = 1.2 mM;
4, C4 = 360 mM and
KM, glycerol = 1.2 mM. All
other equations and parameters can be found under "Materials and
Methods."
[View Larger Version of this Image (16K GIF file)]
Under aerobic conditions glycerol can be used as a substrate. This was
simulated by including both GK and GPO in the model and by substituting
glycerol for glucose. The modeled rate of pyruvate production from 10 mM of glycerol was 80% of the rate from 10 mM
of glucose, while experimentally only 50-60% was found (39, 40). This
discrepancy disappeared when the Vmax of GPO was
decreased by 40% from 368 to 220 nmol Gly-3-P min
1 (mg
protein)
1. Then the rate of pyruvate production at 10 mM of glucose was 134 nmol min
1 (mg
protein)
1 compared with 79 nmol min
1 (mg
protein)
1 (59%) at 10 mM of glycerol.
Actually a GPO activity as low as 171 nmol Glc-3-P min
1
(mg protein)
1 has also been reported for bloodstream form
T. brucei at 25 °C (41).
Variation of the Extracellular Glucose Concentration: the Model as
Interpreter
Using the silicone oil centrifugation technique Ter
Kuile et al. (23) demonstrated that the intracellular
glucose concentration [Glc]i remained very low when the
extracellular glucose concentration [Glc]o was kept below
5 mM. Above a [Glc]o of 5 mM a
drastic increase of [Glc]i was observed. The model
reproduced this (Fig. 3, full lines),
although the calculated [Glc]i remained lower than the measured [Glc]i. The difference between model and
experiment became most pronounced at the higher concentrations; at 10 mM of [Glc]o the measured
[Glc]i was 1.9 mM, whereas the calculated
[Glc]i was only 0.3. This difference was due to the fact
that the used assay does not distinguish between glucose and Glc-6-P
(23). The Glc-6-P concentration averaged over the whole cell was 1.6 mM (27). This concentration should not be confused with the calculated glycosomal concentration. Subtraction of Glc-6-P gives a
[Glc]i of 0.3 mM, which fits the value
calculated by the model.
Fig. 3.
The intracellular concentration of glucose,
the glycolytic flux, and the glycosomal [ATP]/[ADP] ratio as a
function of the extracellular concentration of glucose under aerobic
conditions. For the glycolytic flux the steady-state rate of
glucose transport was taken. The full lines were calculated with the
parameter set as described under "Materials and Methods." Only
above 5 mM glucose extracellularly the model showed an
accumulation of intracellular glucose. The biphasic increase of the
intracellular glucose concentration was lost when the
KM of HK for glucose was changed to 2 mM
(dashed lines).
[View Larger Version of this Image (13K GIF file)]
A mathematical model may serve to test the feasibility of proposed
mechanisms. Along this line it was investigated whether the biphasic
increase of intracellular glucose could be related to the fact that
glucose transport has a 20-fold higher KM for
intracellular glucose than HK. Indeed, when the model
KM of HK was increased from 0.1 to 2 mM
(Fig. 3, dashed lines) or when the KM of
the glucose transporter was decreased from 2 to 0.1 mM
(results not shown), the biphasic character of the curve
disappeared.
To understand this phenomenon, let us first examine the case in which
glucose uptake has a KM of 2 mM and HK
has a KM of 0.1 mM for intracellular
glucose. An increasing extracellular glucose concentration should cause
an increased influx of glucose. As the KM of HK is
relatively low, a small increase of [Glc]i should suffice
to increase the flux through HK so as to cope with the increased
influx. In the limit to an extracellular glucose concentration of zero,
the derivative of vglucose transport to
[Glc]i is zero, which means that initially the influx
rate is insensitive to [Glc]i. This is what happens
during the first phase when at low [Glc]o the
[Glc]i remains low. At increasing [Glc]o
the influx increases further, until [Glc]i saturates HK,
so that a further increase of [Glc]i does not lead to a
higher rate of phosphorylation. Consequently, [Glc]i starts accumulating until it inhibits the influx rate to the extent that a steady state is attained. This is what happens in the second phase where [Glc]i is accumulating. As the
KM values are so different there is only a very
small range of glucose concentrations at which both glucose transport
and HK are sensitive to [Glc]i and, therefore, the switch
between the two phases is very sudden.
If the KM of HK for [Glc]i were
increased to 2 mM, a higher [Glc]i should be
required to stimulate HK, and this should already lead to a
deceleration of glucose transport. In this case there should exist a
broad range of [Glc]i values at which both the
transporter and HK are sensitive to [Glc]i, so that no
sudden switch should be expected. Consistently, the calculated
[Glc]i was higher and the flux lower under these
conditions.
Under both conditions, i.e. low and high
KM of HK, the glycosomal [ATP]/[ADP] ratio
decreased drastically with increasing flux. This was required for the
PGK further downstream to be able to cope with the increased flux. A
side effect is, however, that a decreasing [ATP]/[ADP] ratio
inhibits the flux through HK. Thus, the increasing [Glc]i
serves partly to compensate for the decreased [ATP]/[ADP] ratio. If
one treats HK and the further metabolism of glucose as one block (42,
43), it has an even higher affinity for glucose than HK on its own.
This should make the biphasic shape of the [Glc]i curve
more pronounced, and, furthermore, it explains why the switch occurs
when [Glc]i is still below the KM of
hexokinase for [Glc]i.
Sensitivity Analysis
One cannot expect all kinetic constants
taken from the literature to be precisely correct. Therefore, we
examined whether the results of our calculations depended strongly on
the parameter values. All parameter values were varied independently by
plus and minus 50% (results not shown). The system always evolved to a
new steady state. Three types of responses were observed. Changes of
some parameters, such as the equilibrium constant of AK, hardly caused
any changes. In other cases only local effects were seen, e.g. variation of the KM of PGK for ATP
led to a small change of the glycosomal [ATP]/[ADP] ratio. Some
parameter changes led to global changes, mostly transmitted via the
coenzymes. For instance an increase of the KM of
GAPDH for GA-3-P led to a decrease of the flux, the [ATP]/[ADP]
ratio in both compartments, the [NADH]/[NAD+] ratio,
and the concentration of 1,3-bisphosphoglycerate (1,3-BPGA), and,
furthermore, to an increase of intracellular glucose
[Glc]i and triose phosphate. However, the effects on the
flux were rather small. The flux varied between 91 and 104% of the
unmodulated flux when all possible parameter changes were taken into
account. Only if the amounts of enzymes were decreased (i.e.
the Vmax), larger changes were observed but
always below 50%.
DISCUSSION
We constructed and tested an integral kinetic model that describes
the steady-state behavior of glycolysis in the bloodstream form of
T. brucei quantitatively. The model operates at the
metabolic level (44). Because transcription and translation have not
been included, the model may be limited to cells that do not grow or alter gene expression. Such conditions occur, for instance, in isolated
cells in the absence of any nitrogen source, but in the presence of
glucose. The model contains experimentally obtained kinetic expressions
for most glycolytic enzymes in T. brucei. Because no
information is available on the kinetics of transport of metabolites
across the glycosomal membrane, the transport of glucose across the
cytosolic and the glycosomal membrane was lumped, and the other
transport steps across the latter membrane were assumed to be at
equilibrium. Another limitation was the fact that the enzyme kinetics
had been measured at 25 °C, while physiological studies had been
performed at 37 °C. For this reason, relative changes of the flux
rather than absolute fluxes were considered when the model was compared
with experimental results. To the extent that the KM
values of the enzymes depend on the temperature and to the extent that
the Vmax values of different enzymes exhibit
different temperature dependences, one should expect the steady-state
metabolite concentrations to depend on the temperature.
As all parameter values included in the model are based on measurements
there may be experimental errors in them. Therefore, it was tested how
the model reacted to variations of its parameters. Both local and
global effects were observed. This was to be expected, because any
realistic model should represent the flexibility of the living cell.
However, the effects were relatively small, and particularly, none of
the parameter changes affected the stability of the steady state.
Therefore, we trust that minor adjustments of these parameters will not
overturn our conclusions.
The model constructed in this paper was virtually completely based on
in vitro determined enzyme kinetic data. It was not based on
a data fit. In view of this, the model predictions correspond remarkably well to experimental data. The relative changes of the flux
corresponded exactly, when aerobic and anaerobic conditions were
compared. Also most metabolite concentrations deviated less than a
factor 2 from the measured concentrations as far as these were
available. The available concentrations have been measured in cell
extracts, so if the glycosomal concentration is neglected because of
the small relative volume of the glycosomes, they represent the
cytosolic concentrations. As they were expressed on the basis of wet
weight, which is not very accurate, the ratios of concentrations under
aerobic and anaerobic conditions should be much more accurate than the
absolute concentrations. Indeed these ratios corresponded even better
between model and experiment. Only the ratio of the 3-PGA
concentrations did not correspond (1.5 calculated versus 4.1 mM measured). This may indicate that the assumption of
equilibrium of 3-PGA transport, PGM, and ENO is an
oversimplification.
The intracellular glucose concentration as a function of the
extracellular glucose concentration is an interesting example, where
the model not only mimics the experiments quantitatively but also
explains them. It was demonstrated that the biphasic relation between
the intracellular and extracellular glucose concentrations was caused
by the large difference of the KM values of glucose
transport and HK for intracellular glucose. As glucose is transported
via facilitated diffusion, i.e. down a concentration gradient, it is not unlikely that the second transport step has an
intermediate affinity. It remains to be investigated how this will
affect the intracellular glucose concentration in the model.
The main discrepancy between the model and the experiments, at least
quantitatively, concerned the anaerobic glycerol titration. Both in
real cells and in the model glycerol fully inhibited the glycolytic
flux under anaerobic conditions, the difference being that much less
glycerol was needed in the model. The glycerol tolerance in the model
could be improved by shifting the equilibrium of GK more toward
glycerol production and, more notably, by increasing the conserved sum
C4. A shift of the GK equilibrium is not realistic as the
enzyme kinetics have been determined in the presence of [Mg2+], so that the equilibrium was maximally shifted in
the direction of glycerol (6). An increase of C4 under
aerobic conditions led to an enormous accumulation of Fru-1,6-BP. The
cause of this is that Gly-3-P contributes enormously to C4,
because not only the glycosomal but also the cytosolic fraction is
included. Thus, an increase of the Gly-3-P concentration required to
drive the GK reaction leads to a relatively large decrease of other
metabolite concentrations and vice versa. This restriction may be
relieved when the transport of Gly-3-P is coupled to the transport of
DHAP. In that case the conservation equation of organic phosphate
groups that are not exchanged with inorganic phosphate (Equation 5), is
replaced by two equations:
|
(Eq. 45)
|
and
|
(Eq. 46)
|
Then a change of the Gly-3-P concentration in the glycosome should
have only small effects on the other metabolite concentrations. This
should also exclude the possibility of a high osmotic pressure in the
glycosomes in case of a drop of Gly-3-P and DHAP.
Glycosomal concentrations of Glc-6-P (4.4 mM), Fru-6-P (2.4 mM), Fru-1,6-BP (1.9 mM), DHAP (7.1 mM), GA-3-P (0.47 mM), and 1,3-BPGA (0.77 mM) have been estimated (45) on the basis of pulse-chase
experiments (24). Except for [Fru-1,6-BP], these concentrations are 1 order of magnitude higher than the concentrations predicted by the
model. One reason for the discrepancy may be the fact that the model
neglects sequestration of metabolites by the enzymes, which may
contribute substantially to the total metabolite concentrations due to
the high intraglycosomal enzyme concentrations (46). However, the
concentrations given by Misset and Opperdoes (45) were estimations.
According to the pulse-chase experiments (24) 20-30% of hexose
monophosphate (Glc-6-P plus Fru-6-P) and Fru-1,6-BP were labeled in the
first fast phase (15 s) and the remaining 70 to 80% in the second slow
phase (500 s and longer). The time constant of labeling is related to
the size of a metabolite pool divided by the flux through this pool
(47). Biphasic labeling kinetics imply that only part of a metabolite pool lies on the mainstream of metabolism but do not specify its location. The quickly labeled fraction was interpreted to be the glycosomal fraction and the slowly labeled fraction to be the cytosolic
fraction (24). The phosphoglycerates and PEP, however, were also
labeled in two phases. The authors themselves suggested that PGM, ENO,
and PYK might be attached to the glycosomes, but there is no direct
evidence for this. Even if the concentrations of the hexose
monophosphates and Fru-1,6-BP were correct, the estimated
concentrations of DHAP, GA-3-P, and 1,3-BPGA should be considered with
care. They were based on the total cellular concentrations, and the
assumption that also for these metabolites the glycosomal fraction was
20-30% of the total amount. We have shown, however, that at the
measured enzyme activities ALD, GAPDH, PGK, and GDH must work further
from equilibrium in the glycosome than in the cytosol to support the
high glycolytic flux. Therefore, one should perhaps refrain from
extrapolating average cellular concentrations to glycosomal
concentrations. Obviously it becomes important now to measure all
glycosomal metabolite concentrations unambiguously.
In conclusion, we may say that our model shows that most of the
available experimental data are consistent with each other, i.e. fluxes and concentrations are largely
predicted by the known kinetic properties of the enzymes. To optimize
the model, extra data on the transport of metabolites across the
glycosomal membrane and on the intraglycosomal metabolite
concentrations are required. In the light of the good correspondence
between the model and the experiments, we expect the model to serve as
a valuable heuristic tool. In particular we plan to use it to predict
how the glycolytic flux depends quantitatively on the different enzyme
activities. This then may prove to be very helpful in the search for
new drugs against sleeping sickness.
FOOTNOTES
*
This study was supported by the Netherlands Organization for
Scientific Research (NWO) and the Netherlands Association of Biotechnology Research Schools (ABON). 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.
To whom correspondence should be addressed: Microbial
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.
1
The abbreviations used are: 3-PGA,
3-phosphoglycerate; AK, adenylate kinase; ALD,
fructose-1,6-bisphosphate aldolase; 1,3-BPGA, 1,3-bisphosphoglycerate;
DHAP, dihydroxyacetone phosphate; ENO, enolase; Fru-1,6-BP, fructose
1,6-bisphosphate; Fru-6-P, fructose 6-phosphate; Glc, glucose;
,
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; GPO,
glycerol-3-phosphate oxidase; HK, hexokinase; [Glc]i,
intracellular glucose; Keq, equilibrium
constant; kcat, turnover rate;
KM, Michaelis constant; [Glc]o,
extracellular glucose; PEP, phosphoenolpyruvate; 2-PGA,
2-phosphoglycerate; PGI, glucose-phosphate isomerase; PFK, phosphofructokinase; PGK, phosphoglycerate kinase; PGM,
phosphoglycerate mutase; PYK, pyruvate kinase; TIM, triose-phosphate
isomerase.
Acknowledgments
We thank Drs. M. Callens, D. Kuntz, O. Bos,
and A.-M. Loiseau for the sharing of unpublished results and B. Teusink, M. C. Walsh, and K. van Dam for careful reading of the
manuscript and fruitful discussions.
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