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.

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.

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. V_c is the cytosolic volume and V_g 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 V_c/V_g 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 + V_c/V_g. 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).

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 I. The Vmax values in the catabolic direction (V+) for all enzymes included in the model The Vmax values of the glycosomal enzymes were derived from the reported glycosomal enzyme concentrations and from the turnover rates (kcat) reported after in vitro measurements. Other Vmax values were based on reported transport and activity assays. The Vmax of pyruvate transport was estimated as described in the text. Enzyme Concentration (% of cell protein) (46) kcat (µmol min1 (mg enzyme)1) Vmax (nmol min1 (mg cell protein)1) Glucose transport 106.2 (23) HK 0.25 250a 625 PFK 0.39 200 (10) 780 ALD 1.23 15 (35) 184.5 GAPDH 0.50 294 (48) 1470 PGK 0.16 400 (49) 640 PYK 2.6·103 (7) GDH 0.25 170b 425 GPO 368 or 0c,d (50) GK 0 or 200c Pyruvate transport 160 a  A.-M. Loiseau, unpublished results. b  M. Callens, D. Kuntz, O. Bos, and F. Opperdoes, unpublished results. c  To simulate aerobic conditions GK was switched off (Vmax = 0) and to simulate anaerobic conditions GPO was switched off (see "Substrate and Product Concentrations"). d  The Vmax of GPO was expressed as nmol Gly-3-P min1 (mg cell protein)1. Two molecules of Gly-3-P are converted per molecule of O2.

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 V_max 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 V_max measured for efflux is lower than that for influx, whereas the K_M 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 K_Glc is 2 mM (23). From the assumed symmetry of the carrier and from the finding that the V_max for equilibrium exchange was twice as high as the V_max 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 K_M, Fru6P = 0.82 mM, K_M, ATP = 2.6·10² mM, and n = 1.2 (9, 10).

The rate of PYK depends cooperatively on the concentration of PEP:

(Eq. 13)

in which K_M, PEP = 0.34·(1 + [ATP]_c/0.57 mM + [ADP]_c/0.64 mM) mM, K_M, ADP = 0.114 mM and n = 2.5 (12, 13). The equation for K_M, 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, K_M, F16BP = 9·10³ (1 + [ATP]_g/0.68 mM + [ADP]_g/1.51 mM + [AMP]_g/3.65 mM) mM, K_M, GA3P = 6.7·10² mM, K_M, DHAP = 1.5·10² mM, and K_i, GA3P = 9.8·10² 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 min¹ mg protein¹, 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.

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 V_max 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.

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 P_g and P_c, 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 V_tot 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 min¹ (mg cell protein)¹. In order to obtain the time derivatives of the concentrations in mM min¹, a correction was made for the volume of the compartment in which a metabolite pool resides. As the K_M 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.

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-P_g  Fru-6-P_g

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, DHAP_c  DHAP_g  GA-3-P_g

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-PGA_g  3-PGA_c  2-PGA_c  PEP_c

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, 2ADP_g  ATP_g + AMP_g

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 P_c was substituted for P_g.

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

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 V_max 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 IV. The calculated steady-state glycolytic fluxes under aerobic and anaerobic conditions Flux Consumption rate Aerobic Anaerobic nmol min1(mg cell protein)1 Glucose 73 71 O2 73 0 Pyruvate  147  71 Glycerol 0  71

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 /K_eq, 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 /K_eq 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.

Table VI. Steady-state /Kcq for the reversible glycosomal enzymes that were not assumed to be in equilibrium These were calculated with the equilibrium constants as they were implicitly used in the kinetic equations. The values given in brackets are the /Keq ratios in cell extracts (27). Enzyme  /Kcq Aerobic Anaerobic Glucose transport 1.1·102 2.1·102 ALD 1.8·101 (4.3) 2.4·101 GAPDH 3.1·101 (8.9·101) 3.2·101 PGK 3.6·103 (1.6·102) 4.2·103 (1.6·103) GDH 4.4·103 (1.0, assumed) 4.0·102 (1.0, assumed)

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 V_max 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 K_M 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 K_M of GK for glycerol, and thus the equilibrium constant of GK, further improved the glycerol resistance. A combination of both (C₄ = 360 mM and K_M, glycerol^GK = 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.

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 V_max of GPO was decreased by 40% from 368 to 220 nmol Gly-3-P min¹ (mg protein)¹. Then the rate of pyruvate production at 10 mM of glucose was 134 nmol min¹ (mg protein)¹ compared with 79 nmol min¹ (mg protein)¹ (59%) at 10 mM of glycerol. Actually a GPO activity as low as 171 nmol Glc-3-P min¹ (mg protein)¹ has also been reported for bloodstream form T. brucei at 25 °C (41).

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.