Description of glucose transport in isolated bovine mammary epithelial cells by a three-compartment model

Changting Xiao, V. Margaret Quinton, and John P. Cant

Department of Animal and Poultry Science, University of Guelph, Guelph, Ontario, Canada, N1G 2W1

Submitted 22 August 2003 ; accepted in final form 21 November 2003


    ABSTRACT
 TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Initial rates of glucose entry into isolated bovine mammary epithelial cells display moderate degrees of asymmetry and cooperative interactions between export and import sites. The present study examined the hypothesis that these kinetic features are due to compartmentalization of intracellular glucose. Net uptake of 3-O-methyl-D-[1-3H]glucose (3-OMG) by isolated bovine mammary epithelial cells was measured at 37°C. The time course of 3-OMG net uptake was better fitted by a double-exponential equation than by a single- or triple-exponential equation. Compartmental analysis of the time course curve suggested that translocated 3-OMG is distributed into two compartments with fractional volumes of 32.6 ± 5.7% and 67.4 ± 5.7%, respectively. The results support the view that glucose transport in bovine mammary epithelial cells is a multistep process consisting of two serial steps: fast, carrier-mediated, symmetric translocation of sugar across the cell plasma membrane into a small compartment and subsequent slow exchange of posttranslocated sugar between two intracellular compartments. A three-compartment model of this system successfully simulated the observed time course of 3-OMG net uptake and the observed dependence of unidirectional entry rates on intra- and extracellular 3-OMG concentrations. Simulations indicated that backflux of radiolabeled sugar from the small compartment to extracellular space during 15 s of incubation gives rise to the apparent asymmetry, trans-stimulation, and cooperativity of mammary glucose transport kinetics. The fixed-site carrier model overestimated the rate of glucose accumulation in cells, and its features can be accounted for by the compartmentalization of intracellular sugar.

compartmentalization; milk synthesis


GLUCOSE TRANSPORT ACROSS the plasma membrane of mammary epithelial cells is mediated by transporter protein GLUT-1 (35, 17, 22, 25). Extensive studies of GLUT-1 function in human erythrocytes have revealed an apparent asymmetry of transport in which Michaelis-Menten parameters for efflux from cells are greater than for influx (2), a stimulation of influx by sugar on the trans, intracellular side (23), and cooperativity between simultaneously presented export and import sites (9, 21). Sugar entry into bovine mammary epithelial cells also exhibits asymmetry, trans-stimulation, and cooperativity (24), although only to a 2-fold extent, not 10- to 60-fold as in human erythrocytes (6).

The mechanism of sugar binding and transport by GLUT-1 that results in the features of asymmetry, trans-stimulation, and cooperativity is under investigation. The fixed-site carrier model (12) can accommodate these features. However, because the Vmax and Km for zero-trans glucose efflux from human erythrocytes predicted from effects of intracellular sugar on glucose entry were different from those observed, it was suggested that some sort of unstirred glucose layer on the intracellular aspect of the plasma membrane confounded initial rate measurements, causing an artifactual apparent asymmetry (16). It has been recently proposed that the glucose transporter in human erythrocytes is a homotetramer of GLUT-1 molecules. Although each GLUT-1 monomer functions as a simple carrier, cooperative interactions between GLUT-1 dimers cause the carrier to present two export and import sites simultaneously at any instant (6, 9, 11, 21). On allosteric regulation by intracellular ATP binding, the GLUT-1 cytosolic domains form a cage. Sugar is translocated across the cell membrane and into the cage, where the sugar molecules can be recycled back to the extracellular space, bound to binding sites within the cage, or released into the cytosol (10).

Heard et al. (10), using a mathematical model of glucose translocation, occlusion, binding, and release, were able to simulate the 60-fold asymmetry of glucose transport into human erythrocytes. Our objective in this study was to examine possible compartmentalization of intracellular sugar and to determine whether this compartmentalization results in the observed kinetic characteristics of glucose transport by isolated bovine mammary epithelial cells. Typically, kinetics of transport are described by a Michaelis-Menten equation, such as that for the fixed-site carrier, which is parametized from transmembrane fluxes measured at various initial sugar concentrations. Here, we have combined time course and concentration dependence data to fit a three-compartment model that accounts for the apparent asymmetry, trans-stimulation, and cooperativity of mammary glucose transport.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Materials. All chemicals and enzymes were purchased from Sigma-Aldrich unless otherwise stated. 3-O-methyl-D-[1-3H]glucose (3-OMG; 99.8% purity, 167 GBq/mmol) was from Amersham Life Science (Little Chalfont, UK). Hanks' balanced salt solution (HBSS) and Dulbecco's modified Eagle's medium (DMEM) base were from GIBCO-BRL (Life Technologies, Burlington, ON, Canada).

Cell isolation. Procedures involving animals were approved by the Animal Care Committee of the University of Guelph. Cells were prepared as a modification of the procedure described by Prosser and Topper (18). In brief, fresh tissue was obtained from lactating Holstein dairy cow (milk yield ~15 kg/day) mammary gland and digested with 0.1% (wt/vol) collagenase in HBSS. Cells were collected by centrifugation and washed in phosphate-buffered saline (PBS, pH 7.4). Washed cells were resuspended in glucose-deficient DMEM base at a protein content of 2–4 mg/ml and stored on ice for further experiments. Cell protein was analyzed by the Bio-Rad method with bovine serum albumin as the standard.

Net uptake of 3-OMG by isolated bovine mammary epithelial cells. Time course of glucose transport was measured at 37°C by incubating 100 µl of cell suspension with 100 µl of DMEM base medium containing 10 mM 3-OMG and 1 µCi of tracer. Uptake was terminated after a range of incubation times between 15 s and 20 min by addition of 3 ml of ice-cold PBS (pH 7.4) containing 20 µM cytochalasin B. Cells were then loaded onto Whatman GF/C filters (Fisher Scientific, Whitby, ON, Canada) premoistened in PBS and mounted on a Millipore vacuum filtration unit. Filters were immediately washed with 30 ml of ice-cold PBS. Filters were transferred into 20-ml scintillation vials and soaked with 0.5 ml of water for 30 min, and then 10 ml of scintillation fluid (ICN, Costa Mesa, CA) was added to each vial. Vials were counted in a Beckman 6000 scintillation counter. Blanks (time 0 uptake) were prepared by addition of stopping solution before addition of incubation medium containing 3-OMG and radiolabel followed by an immediate wash. Nonspecific binding of radiolabel to filters was obtained by filtration and washing of incubation medium alone. Uptakes for each time point were measured in triplicate.

Calculation of rate constants. The time course of intracellular radioactivity accumulation in disintegrations per min (DPMt) was fit to the following single-, double-, or triple-exponential equations, respectively

(1)

(2)

(3)
where DPM0 is the background radioactivity in disintegrations per minute. DPMi and rate constant ki (i = 1, 2, or 3) were estimated by nonlinear, least-squares regression of untransformed data with the Gauss-Newton method (19).

Derivation of three-compartment model. On the basis of curve-fitting results and the model of Heard et al. (10) for glucose transport in human erythrocytes, the model structure of Fig. 1 was adopted for interpretation of time course and kinetic data.



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Fig. 1. Model structure. GlE, extracellular glucose pool; GlO, occluded glucose pool; GlI, free intracellular glucose pool; kij, rate constants of unidirectional exchange (where i, j = E, O, or I). Box represents total cellular glucose.

 

According to this model, extracellular (E) glucose (GlE) is first translocated across the cell membrane and into an occlusion compartment by a symmetric carrier exhibiting a simple Vmax and Km. Exchange between the occlusion (O) and intracellular (I) compartments is a first-order process governed by rate constants kOI and kIO.

The differential equations describing sugar fluxes (U; nmol/min) in the system are

(4)

(5)

(6)
where

Concentrations of 3-OMG in each compartment are calculated from the integrals of Eqs. 4, 5, and 6 divided by their respective volumes of distribution (evol, ovol, and ivol).

For radiolabeled sugar (RA; dpm/min)

(7)

(8)

(9)
where specific activities (SA) in pools E, O, and I, respectively, are calculated from the integrals of Eqs. 7, 8, and 9 divided by their respective pool sizes from integrated Eqs. 4, 5, and 6. Equations 4–9 were written in Advanced Continuous Simulation Language (1) for solution and numerical integration with a fourth-order Runge-Kutta algorithm using a step size of 0.05 min.

Calculation of model parameters. Values for rate constants kOI and kIO and volumes evol, ivol, and ovol were derived from compartmental analysis of the time course of 3-OMG net uptake assuming a closed, sequential three-pool system and first-order interchanges between pools (20). Attempts to estimate Km and Vmax from the time course curve failed to yield unique parameter solutions because of the high correlation between Km and Vmax and the narrow range of extracellular 3-OMG concentration ([3-OMG]) manifest during 20 min of incubation. Hence, least-squares estimates of Km and Vmax were obtained by iteratively simulating, with Eqs. 4–9 and kOI, kIO, evol, ivol, and ovol from the compartmental analysis, the 15-s incubations of mammary epithelial cells with varied initial extracellular and intracellular concentrations of 3-OMG reported previously (24). In these simulations, initial [GlE] was set to the concentration in the incubation medium. In cases in which cells were preloaded with different concentrations of intracellular sugar, initial [GlO] and [GlI] were both set to the same loaded concentrations. Rates of 3-OMG entry for comparison with observed were obtained from the 15-s values of RAO and RAI as (RAO + RAI)/(iSAE x 0.25 min), where iSAE is the initial specific activity in incubation medium before initiation of uptake.


    RESULTS
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Net uptake of 3-OMG by isolated bovine mammary epithelial cells. 3-OMG accumulated in cells until reaching a plateau after ~10 min (Fig. 2A). The time course data were well described by the double-exponential equation (r2 = 0.98; Fig. 2). Residuals from Eq. 2 were evenly distributed around 0; the residuals (y, nmol/mg protein) plotted against time (x, min) yielded y = 0.77x 14.63 (r2 = 0.0007). Best fit of the single-exponential equation (Eq. 1) yielded a lower r2 (r2 = 0.91) and residuals that were systematically displaced from 0; the residuals (y, nmol/mg protein) plotted against time (x, min) yielded y = –7.75x 89.16 (r2 = 0.02), which indicated substantial underestimation of 3-OMG accumulation in the cells. When the number of exponential terms was raised to 3 (Eq. 3), the nonlinear regression failed to converge on unique parameter solutions. These results indicate that glucose uptake by bovine mammary epithelial cells involves distribution into two distinct compartments as displayed in human erythrocytes (8). The rate constants associated with DPM1 and DPM2 in bovine mammary epithelial cells were estimated to be, on average, k1 = 3.12 ± 0.81 min–1 and k2 = 0.13 ± 0.02 min–1 (n = 3), whereas in human erythrocytes at 4°C these were estimated to be k1 = 7.4 ± 1.7 min–1 and k2 = 0.56 ± 0.11 min–1, respectively (8).



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Fig. 2. Time course of 3-O-methyl-D-[1-3H]glucose (3-OMG) net uptake by isolated bovine mammary epithelial cells. Uptake was measured at 37°C with 5 mM 3-OMG [radiolabeled sugar (RA) = 1,485,918 dpm] in the incubation medium. A: time-dependent accumulation of radiolabeled 3-OMG in isolated bovine mammary epithelial cells from 1 cow. The lines represent various simulations as indicated. Simulations from compartment analysis were computed by nonlinear regression, assuming that the uptake is a biexponential process. Parameters used in the simulation are k1 = 3.24 min–1 DPM1 = 975.2, k2 = 0.12 min–1, DPM2 = 3,219, r2 = 0.98. Simulations from the 3-compartment model were computed by numerical integration with Km =7.88 mM, Vmax = 29.65 nmol·min–1·mg protein–1, kOI = 0.29 min–1, kOI = 0.16 min–1, and volumes of distribution for extracellular (E), occlusion (O), and intracellular (I) compartments (evol, ovol, and ivol, respectively) = 613.48, 0.59, and 1.12 µl/mg protein, respectively. Simulations from the fixed-site carrier model were computed by numerical integration with Michaelis-Menten constant (K) = 10.13 mM, forward Vmax = 20.03 nmol·min–1·mg protein–1, cooperativity between external and internal binding sites ({alpha}) = 0.56, degree of trans-stimulation ({beta}) = 1.59, and degree of symmetry in transport ({lambda}) = 5.69. B: rate of 3-OMG net uptake plotted as a function of time.

 

Compartmental analysis of time course of 3-OMG net uptake. First-order compartmental analysis of the time course curves yielded the parameter values summarized in Table 1. The rate constant for backflux of sugar from the occluded space, kOE, was an order of magnitude greater than kOI for entry into the inner compartment, as observed in erythrocytes (8). All estimated volumes were expressed per milligram of protein for purposes of simulation. Although evol merely represents the volume of incubation medium used, it was estimated that the occluded space accounted for 32.6 ± 5.7% of the total 3-OMG distribution volume, whereas the true intracellular space represented 67.4 ± 5.7%. These results are in close agreement with the 29% and 71% obtained in human erythrocytes for the relative distribution volume of these two compartments, respectively (8). In human erythrocytes, it was suggested that the small compartment is formed within the cytoplasmic domain of the glucose transporter protein, immediately under the plasma membrane, and that the multistep transport is sequential rather than parallel (8). Because zero-time binding was subtracted from the net uptake and cells were extensively washed in this study, the two compartments are not located on the exofacial aspect of the cell membrane, i.e., they may also be located on the cytoplasmic side.


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Table 1. Parameters derived from compartmental analysis of time course of 3-OMG net uptake

 

Parameters for three-compartment model. Sugar exchange rates between the two posttranslocation compartments were estimated from compartmental analysis to be kIO = 0.29 ± 0.03 min–1 and kOI = 0.16 ± 0.03 min–1 (Table 1). When these parameters were used in the model shown in Fig. 1, least-squares estimates of Km and Vmax from fits to an additional set of kinetic data were 7.88 mM and 29.65 nmol·min–1·mg protein–1, respectively. Parameter estimates for the three-compartment model were associated with low standard errors among cows (Table 2). The fully parameterized three-compartment model mimicked the time course of 3-OMG uptake (Fig. 2A) with an r2 of 0.98 and the kinetics of 15-s intracellular accumulation with an r2 of 0.99 (Figs. 3 and 4).


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Table 2. Estimated parameters of a three-compartment model of glucose transport in bovine mammary epithelial cell

 


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Fig. 3. Simulation of 3-OMG transport kinetics under various experimental conditions. x-Axis: intracellular glucose concentration ([Glc]) for high-cis entry, extracellular [Glc] for others (in mM). Lines indicate simulated rates of 3-OMG accumulation in 15-s incubations, and symbols indicate observed rates (24). Simulations were run with parameter values listed for Fig. 2.

 


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Fig. 4. Regression between 3-compartment model simulations and measured initial rates. Units are nanomoles per minute per milligram of protein. Simulations were run with parameter values listed for Fig. 2.

 


    DISCUSSION
 TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Compartmentalization of intracellular sugar. Analysis of sugar net uptake into bovine mammary epithelial cells suggests that accumulation of intracellular sugar is biphasic, involving rapid filling of a smaller compartment and slow filling of a larger compartment. Compartmentalization of intracellular sugar has been proposed in human erythrocytes. It has been postulated that there exists an unstirred layer of translocated 3-OMG under the plasma membrane (15). In the latest proposed glucose transport mechanism in human erythrocytes, Carruthers' group attributed intracellular sugar compartmentalization to allosteric regulation of the carrier by intracellular ATP (7, 10, 13, 14). It was suggested that the carrier is a homotetramer of GLUT-1 molecules (7, 9). Although each monomer represents one single transport pathway, cooperative interactions give rise to more complex transport behavior. When one GLUT-1 presents an export site, the adjacent subunit must present an import site and vice versa; therefore, the carrier presents two export sites and two import sites simultaneously (7, 9, 21). This represents a symmetric, carrier-mediated process of sugar translocation across the plasma membrane. When intracellular ATP binds to the cytoplasmic domain of the transporter monomers, adjacent dimers form a cage. Posttranslocated sugar first enters the cage, where it can be bound to the high-affinity sites within the cage, exported back to the extracellular space (substrate recycling), or released into the cytosol. Because of the presence of the slow release step or the presence of the small compartment, steady-state transport measurements represent more than just the translocation step and cannot be used to parametize a model of the carrier function directly (6). The biological significance of intracellular compartmentalization may be as a mechanism for regulation of glucose transport and/or metabolism by intracellular energy status through ATP binding to the carriers.

Three-compartment model. On the basis of similarities between erythrocytes and mammary cells in sugar distribution spaces and the ratio of exponents in the biexponential time course equation, we modeled glucose transport in bovine mammary epithelial cells according to the above cage hypothesis. In this model, two serial steps are considered: saturable, symmetric, carrier-mediated sugar translocation followed by slow, diffusive exchange with intracellular glucose.

The model was used to explore the origin of the asymmetry, trans-stimulation, and cooperativity exhibited in kinetics of sugar accumulation in mammary epithelial cells (Fig. 3). Intracellular radiolabeled sugar accumulation in 15-s incubations was simulated under zero-trans conditions where initial intracellular glucose concentration was 0 and initial extracellular glucose concentration ranged from 0 to 20 mM. The apparent Vmax of the simulated zero-trans curve (20.13 nmol·min–1·mg protein–1; Table 3) was 68% of the Vmax of the translocation step (29.65 nmol·min–1·mg protein–1; Table 2) because of rapid backflux of label from the occlusion compartment within 15 s (Fig. 5). The apparent Km of zero-trans-accumulation kinetics (10.18 mM) was elevated 30% above the Km of the translocation process (7.88 mM) because the proportion of incoming radiolabel that exits cells within 15 s declined as initial glucose concentration increased. Under high-trans conditions, where initial intracellular glucose concentration was maintained at 20 mM for all initial extracellular concentrations, the backflux of label was lessened by dilution in the occlusion compartment so that the apparent Vmax of sugar entry simulated over 15 s (24.50 nmol·min–1·mg protein–1; Table 3) was elevated to 83% of the translocation Vmax. The apparent Vmax of equilibrium exchange kinetics (30.80 nmol·min–1·mg protein–1), where initial extracellular and intracellular glucose concentrations are equal, was essentially equivalent to the Vmax of translocation because the apparent Vmax is an extrapolation to infinitely high intracellular glucose where backflux of radiolabel approaches zero. As glucose concentrations increased in the equilibrium-exchange experiment, dilution in the occlusion compartment also increased so that backflux as a proportion of influx declined, causing the apparent Km to be highest of all the three saturation curves.


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Table 3. Estimated kinetic parameters of 15-s 3-OMG accumulation from simulations of various experimental conditions with three-compartment model

 


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Fig. 5. Cumulative translocation of radioactive glucose simulated with the 3-compartment model. Each data point is the result of a 15-s simulation using Eqs. 4–9 in the text. A: zero trans. B: equilibrium exchange. C: high trans. For each condition, influx , backflux , and accumulation (middle line) = (RAO + RAI)/(iSAE x 0.25 min), where U is the glucose flux, SA is specific activity, and iSAE is initial SA in incubation medium. Simulations were run with parameter values listed for Fig. 2.

 

Parameters of the fixed-site carrier equation

where v is reaction velocity, [A] and [P] are extracellular and intracellular substrate concentrations, K is the Michaelis-Menten constant, {alpha} is cooperativity between external and internal binding sites, {beta} is degree of trans-stimulation, and {lambda} is degree of symmetry in transport, were estimated by least-squares fit to the set of all simulated 15-s accumulation values as previously described (24). Although the fitted equation describes the concentration dependence of 15-s sugar accumulation well (24), it greatly overestimated the rate of accumulation over 20 min (Fig. 2) because it is weighted toward rapid entry into the small intracellular compartment. The three-compartment model, on the other hand, described concentration dependence and time course curves equally well.

Kinetics of glucose transport by mammary epithelial cells are better represented by a three-compartment model with four parameters than a carrier model with five parameters. To study the effect of experimental treatments on mammary glucose transport, the parameters describing first-order exchange between the two intracellular compartments can be obtained from the time course of sugar accumulation. The Km and Vmax of transmembrane translocation are equivalent to those of short-term infinite-trans accumulation. Unfortunately, osmotic effects of high intracellular sugar concentrations make the infinite-trans experiment a practical impossibility. Instead, parameters of the translocation step of mammary glucose transport can be obtained from a combined set of time course and concentration dependence data.


    FOOTNOTES
 

Address for reprint requests and other correspondence: J. P. Cant, Dept. of Animal and Poultry Science, Univ. of Guelph, Guelph, ON, Canada, N1G 2W1 (E-mail: jcant{at}uoguelph.ca).

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.


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 DISCUSSION
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