The Mechanism of Na'-dependent D-Glucose Transport*

The Mechanism of Na’-dependent D-Glucose Transport* (Received for publication, June 18, 1979)

Ulrich HopferS and Rhea Groseclose From the DeDartment of Anatomy, School of Medicine, and Developmental Biology Center, Case Western Reserve University, Cleueland, Ohio 44106

The mechanism of Na+-dependent D-glucose transport was investigated by kinetic means in rabbit small intestinal and renal brush border membranes. The rate of glucose transport was measured under equilibrium exchange conditions as a function of its own concentration and of the Na+ concentration. Likewise, the rate of Na+ transport was measured as a function of the D- glucose concentration. Noteworthy characteristics of the Na+-dependent glucose transport system are: 1) linear dependence of the glucose transport rate on Na+ concentration up to 0.1 M (at constant ionic strength), indicating a 1:l stoichiometry of Na+-D-glucose co- transport under net flux conditions; 2) virtual Na+ independence of the apparent affinity of the transport system fo r D-glucose; 3) a stimulation-inhibition pat- tern if the transport rate of either substrate (D-glucose, Na+) is measured as function of increasing concentrations of its co-substrate; 4) a varying flux ratio of D- glucose to Na+ which can be either above or below l, depending on the concentration ratio of the two substrates; 5 ) a rate constant fo r translocation of the loaded carrier which is fas te r than that for the dissociation of Na+. Treating Na+-D-glucose co-transport analogous to an enzyme reaction, these fea tures are consistent with an iso-ordered-bi-bi kinetic model, whereby the first solute that binds to the transport sys tem at one membrane interface is the one that is released f i r s t at the other interface (first-in-first-out characteristics). The kinetic model is explained by a gated pore mechanism, whereby the translocation of the transported solutes across the permeabili ty barrier is achieved b y a rocker-type conformational change of the transport system (presumed to be a protein) which moves the permeability barrier past the solutes.

Small intestinal and renal epithelial cells are capable of transporting D-glucose and related sugars against a concentration gradient from the luminal solution to the blood. This transport occurs without chemical modification of the transported sugars. The concentrative step is located at the luminal plasma membrane (l), and the energy is derived from an electrochemical Na’ gradient of about 5,800 J/eq across this membrane (lower potential on the cytoplasmic side) (2). The molecular basis for the stereospecific and concentrative sugar transport is thought to reside in a “carrier” that catalyzes the coupled translocation of sugars and Na+. The overall mecha-

* This research was supported by grants from the National Insti- tutes of Health (AM 18265) and from the National Science Founda- tion (PCM 78-07211). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “aduertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

$. Supported by Public Health Service Career Development Award 5 KO4 AM00199.

nism of Na’-coupled glucose transport has been investigated extensively in various intact epithelial preparations (see e.&. Refs. 1, 3, 4), isolated epithelial cells (5), and membrane vesicles from the brush border of the small intestine or the kidney (6, 7 ) . Results with intact rabbit intestine indicate a 1: 1 stoichiometry for Na’ and glucose under net influx conditions (8). Other ions besides Na’ do not appear to be directly involved in the glucose translocation. This conclusion is based on the observation that only in the presence of Na‘ can electrical potentials across the membrane energize glucose transport, whereby the direction of the glucose flux implies an electrogenic co-translocation of glucose and a positive charge (9).

The information on Na’-dependent glucose transport can be summarized by the following “transport reaction,” defined analogous to a chemical reaction: Na,,’ + Glc,, Na,+ + Glc,; whereby the subscripts o and i refer to the aqueous phases on either side of the separating membrane. Very little information is available at this time about the molecular identity of the carrier or how it accomplishes coupled Na’-glucose co- translocation. The aim of this study is to use a kinetic ap- proach to obtain insight into the mechanism. Vesicles of isolated brush border membranes constitute a convenient experimental system for this purpose because the composition of the intra- and extravesicular aqueous phases and, thereby, of the driving forces for Na’ and glucose flux can be controlled.

Experimental conditions that lend themselves to meaning- ful kinetic studies are those of equilibrium (isotope) exchange (10). Hereby, all solutes are in equilibrium across the membrane and solute flux is measured with labeled substrate added to one side only. Isotope exchange is an accepted method in enzyme kinetics and is particularly useful to eluci- date the mechanism of multireactant systems (11). Because of heterogeneity of isolated membrane vesicles with respect to size, cellular origin, or solute permeability, apparent rate constants for equilibrium exchange may vary with the prog- ress of the transport reaction. Therefore, when rate measurements are made as a function of experimental variables, such as substrate concentrations, temperature etc., it is important that they refer to the same fractional uptake or release of the isotope into or from the vesicles. A detailed discussion for the rationale of kinetic measurements in vesicles under equilibrium exchange conditions has been given previously (10).

The following questions are specifically relevant to the mechanism of Na’-coupled glucose transport and were investigated: 1) is Na’ obligatory for glucose transport via the carrier in the brush border membrane? 2) Is the ligand binding of Na” and glucose to the carrier an ordered or a random process? 3) If the binding is an ordered mechanism, what is the sequence of ligand binding and debinding?

MATERIALS AND METHODS

Isolation of Brush Border Membranes-The membranes were prepared from small intestinal scrapings or renal cortex of New

4453

4454 Na+-dependent Glucose Transport

Zealand white rabbits. The preparative procedure was a modification of the method developed by Schmitz et al. (12). This modification has recently been described (13). Briefly, the intestinal or renal material was thoroughly homogenized in 50 mM mannitol, 2 mM Tris- HCI, pH 7. The Ca" concentration of the homogenate was adjusted to 10 mM, and brush border membranes isolated by differential centrifugation. The brush border membranes sedimented between 1 X 105 and 6 X IO5 g per min. The membranes were rehomogenized in 100 mM mannitol, 1 mM Tris/Hepes' buffer, pH 7.4, and reisolated by differential centrifugation.

Enzyme Assays and Protein Analysis-Homogenate and final membranes were analyzed for sucrase (EC 3.2.1.48), alkaline phosphatase (EC 3.1.3.1), or K'-stimulated phosphatase (EC 3.1.3.) as described (14). Protein was assayed according to the method of Lowry et al. (15) with bovine serum albumin as standard.

Transport Experiments-Transport rates were estimated as inverse of the time for half-maximal isotope (~-["H]glucose, 'lNa+) uptake under equilibrium exchange conditions, i.e. as (t,,$'. The rates were measured as a function of the following variables: (i) phlorizin concentration, (ii) D-glucose concentration, (iiij NaSCN concentration, (iv) NaCl concentration a t constant ionic strength using mixtures of KC1 and NaCI. To estimate the rates as a function of one of the variables, membranes from one preparation were divided into aliquots (usually 80 pl) and preincubated in identical media (see legends of the figures), except for varying concentrations of one of the solutes (the variable). The preincubation was carried out for at least 30 min at room temperature. To start the rate determination, the solution containing the radioisotope (typically 10 PI) was added to the membranes. The composition of the added solution was identical with that of the preincubation medium, except for the presence of one of the transported solutes in radioactive form. The isotope concentration and amount was identical in each of the parallel incu- bations of an experiment. Equilibrium uptake of the radioisotope was determined after a t least 1 h of incubation at room temperature. Tracer uptake a t equilibrium was essentially identical for each experimental set, i.e. the experimental variable (e.g. unlabeled D-glucose concentration) did not influence the size of the intravesicular space which determines the equilibrium uptake.

Uptake of labeled solute by the membranes was measured by removing an aliquot from the incubation medium after predetermined periods, quenching of transport by dilution with 1 ml of ice-cold "quench" solution and collection of the membranes on nitrocellulose filters (pore size 0.6 pm). The filter was washed once with 3 ml of ice- cold "rinse" solution, and the amount of radioactive isotope determined by liquid scintillation techniques. T o improve the precision of time measurements a microswitch was activated at the time of the mixing of membranes with radioisotopes and of the quenching of uptake. The signals from the microswitch were recorded continuously with a strip-chart recorder.

The composition of the rinse solution was for the experiments with labeled D-glucose: 50 mM MgCI,, 150 mM NaCI, 1 mM D-ghcose, and 10 mM Tris-Hepes, pH 7.4. For those with labeled Na' it was: 100 mM MgCL, 150 mM mannitol, 1 mM D-glucose, 10 mM Tris-Hepes pH 7.4. One molar KC1 was added to either solution when required for osmotic stabilization of vesicles. The composition of the quench solution was identical with the rinse solution except for the additional presence of a radioactive solute that could be used to calculate the efficiency of the rinsing. Usually ~-[ '~C]glucose served as such marker in uptake experiments with ~-["H]glucose, and ~-['H]glucose in the uptake experiments with "Na+. Uptake of the tracer by the membranes was determined from the counts on the filter, after correction for insufficient rinsing.

tl,L values were estimated by interpolation on plots of In[l-(uptd upt,)] versus time, whereby upt, = tracer uptake at the indicated time point, and upt, = uptake a t equilibrium (>1 h of incubation at room temperature). The time points were taken around the actual half-time, determined in preliminary experiments. All measurements were carried out a t least in triplicates. Phlorizin, when present, was added to the membranes immediately before starting the glucose flux measurements. In experiments with Na' concentrations below 10 mM or with K', monactin was added to allow faster equilibration of Na' or K'. Monactin, when tested a t 10 mM Na+, had no effect on the K,, for glucose. Transport experiments with glucose were usually carried out a t 15°C in a constant temperature room, while Na+ transport

I The abbreviations used are: Hepes: 4-(2-hydroxyethylj-l-pipera- zineethanesulfonic acid.

measurements were made a t 25°C. Deviations from this protocol are specifically noted in the legends.

Calculations and Statistical Analysis-The theoretical basis for the kinetic analysis has been given previously (10) and only the essential features will be repeated here. Isotope exchange rates are expressed as the observed (t , ,z j - ' , In some experiments, the rate of carrier-mediated or of "leak' transport are calculated from the rela- tionship:

(tl/2);tkrued = (t1/2):drr~ev + (tl,2)'1;,8k'' (1)

(See Equation 13 of Ref. lo), whereby ( t1 r2 ) . ,~ea~ , . is either the observed (tlr.) in the presence of 0.1 mM phlorizin or a calculated value to give a "best fit" of the observed (tIr2) values for varying glucose concentrations to an equation of the form:

( ~ 1 , Q ) ~ I ~ ~ e r v e d fur ,\ C/(s + K ) + ( t l /2)qbnk" (2)

(modified Equation 12 of Ref. lo), whereby S = substrate concentration (i.e. D-gluCOSe), K = K,,, and C X V.,,,, terms defined analogous to parameters in enzyme kinetics. C, K, and (tl/2)..lmk.. are constants, and S and ( t1r2)< , t , -vwed are the independent and dependent variables, respectively. C, K, and ( t 1 , h e a k " were calculated using Equation 2 by weighted least square analysis according to the guidelines of Cleland (16). The standard deviation of the observed t lr l values was estimated to be proportional to the absolute value of tIr2, i.e. SD (tl,a) a t I l 2 . The leak-related tlrZ giving the best fit was found through an iterative procedure in which the leak-related tlr2 was systematically increased, starting with t 1 ,2 observed a t 100 mM D-glucose, until the correlation coefficient of the linear function of carrier-tlil on substrate concentration gave a maximum. Unless otherwise indicated, data are reported as mean & standard deviation and regression lines are calculated by the weighted least squares method. All calculations were carried out with a programmable desk calculator (Monroe 1860).

Materials-Phlorizin was obtained from ICN-Life Science group (Cleveland, 0.) and recrystallized twice from hot water before use. ""Na' and ~-[l-:~H(N)]glucose were bought from New England Nu- clear Corp. (Boston, Mass.), and D-[U-14C]ghCOSe was obtained from Schwartz-Mann (Orangeburg, N. Y.). Monactin was a gift of Ciba- Geigy, Basel, Switzerland. Other chemicals were of analytical grade and were obtained from common commercial sources.

RESULTS

To What Extent Is Glucose Transport under Equilibrium Exchange Conditions Mediated by the Nac-dependent Glu- cose Transport System?-Two main sources of errors have to be considered in the quantitation of glucose transport in vesicles of isolated brush border membranes: (i) Contarnina- tion of the brush border membrane fraction b y other cellular membranes known to contain Na'-independent glucose transport systems; (ii) glucose transport across the brush border membrane which does not involve the Na'-dependent carrier. Both types of glucose uptake together are designated here as leak relative to the Na'-dependent transport.

Contamination of the brush border membrane fract ion by other cellular membranes was assessed biochemically by the enrichment of the enzymes sucrase or alkaline phosphatase and the presence of K'-stimulated phosphatase, markers of the brush border and the basolateral plasma membrane, respectively (14, 17) (Table I). Sucrase was enr iched in the intestinal membranes 25-fold relative to the homogenate and 15-fold relative to the K'-stimulated phosphatase. Alkaline phosphatase was enriched 20-fold relative to the homogenate. The enrichment of brush border enzymes is similar to highly purified brush border membrane preparations which have been characterized more extensively (12, 18), thus suggesting only minor contamination by other cellular membranes (less than 10%).

A more quantitative assessment of the specificity of the observed transport is obtained from a comparison of leak and carrier-mediated rates in the membrane preparations used for this s tudy. Transport via leak pathways was operat ional ly defined as the fraction of tracer glucose flux that could not be suppressed by the specific inhibitor phlorizin or unlabeled D-

Na+-dependent Glucose Transport 4455

glucose. Under equilibrium conditions, the driving force for glucose flux along all pathways is the isotope concentration gradient. Since the same thermodynamic force is operating on leak and carrier-mediated glucose flux, it is possible to estimate relative permeabilities of each pathway. For example, the transport rates of tracer glucose in the absence and presence of 0.1 mM phlorizin or in the presence of low and high unlabeled D-glucose concentrations can provide information about this point. In the latter case, a leak rate can be calculated from the dependence of the observed rates on unlabeled D-glucose concentration. It is the rate necessary to explain the deviation of tracer flux at high glucose concentrations from the predictions based on carrier kinetics (for details see "Ma- terials and Methods" and legend of Fig. 3). Glucose transport rates, expressed as the inverse of the half-time for isotope equilibration, (tl,&', ranged for the leak pathway between 0.21 to 0.24 min" in the phlorizin inhibition experiments (Fig. l), and between 0.04 to 0.09 min" in the K, determinations of D-glucose in the intestine (Table 11). Moreover, the rate via leaks was always less than 30% of the observed transport rate in the absence of phlorizin or at low concentrations of D- glucose (see last two columns of Table 11). In many experiments, particularly in the presence of Na' above 10 mM, the leak rate accounted for less than 5% of the observed glucose transport rate at low glucose concentrations. Because most of the glucose transport proceeded through the carrier it was possible to quantitate the carrier-dependent rates under a variety of conditions without introducing unacceptably large errors in the rate measurements.

To test whether the carrier-mediated rates are a function of only the experimental variable and not additionally influenced by other factors, equilibrium glucose transport was measured in the presence of varying phlorizin concentrations and the inhibitory constant (K , ) for phlorizin calculated. As shown in Fig. 1, the K, for phlorizin at 0.1 M NaSCN was 6.0 & 0.1 PM, similar to the value observed in intact intestine (19).

I s There a n Obligatory Na' Requirement for Glucose Movement via the Transport System Specific for the Brush

TABLE I Enzyme activities of isolated brush border membranes

-~

Source Enzyme SpeciFc 1ty activ- f$hhO"m"o",'- enate

units/mg pro^ tein

Small intes- Sucrase 1.3 -+ 0.3 25 +. 6 12 tine Alkaline phos- 1.4 ? 0.2 2 0 f 3 4

K'-Pase" 0.10 f 0.03 1.6 f 0.4 4 Renal cortex Alkaline phos- 0.57 f 0.12 15.4 f 0.2 3

K+-Pase 0.02 f 0.03 0.5 f 0.8 3

phatase

phatase

I' K'-Pase, K+-stimulated phosphatase.

TABLE I1 Kinetic parameters of rabbit Nu+-dependent glucose carrier for D -

glucose

of mem- [Na+]" K,,, Source

branes K ( ; T X ( t , Y .,*"L.)" ( t , 2 (:I, = ,,, M) ' 10"

M mM M " min" mtn" Small in- 0.100 2.4 f 0.3 4.1 f 0.5 0.04 4.00

testine 0.050 2.2 f 0.2 4.5 f 0.2 0.05 1.76 0.010 5.7 +. 0.6 1.7 f 0.2 0.09 0.52 0.001 4.7 f 1.1 2.1 f 0.5 0.05 0.20

Renal 0.100 3.2 -c 0.4 3.1 f 0.4 0.17 1.94 cortex

'' AS NaSCN. The ionic strength was not fixed, but varied with NaSCN concentration.

Phlorulm Colornlrat~on lySl

FIG. 1. Phlorizin inhibition of tracer D-glucose transport by intestinal brush border membranes. The carrier-related t l is plotted as a function of phlorizin concentration. The carrier-related t l S r was calculated according to Equation 1 under "Materials and Methods," whereby ( t l , 2 j . , , t . a k , , = 250 s [observed ( t l i L ) at 0.1 mM phlorizin]. Buffer: 0.1 M mannitol, 0.1 M NaSCN, 1 mM Tris/Hepes, pH 7.4, 0.1 mM MgSO.,, and varying phlorizin concentrations. The glucose concentration was 0.1 mM and thereby negligible relative to the K,,, of 2.4 mM.

'i; 1

20 80 100

N a t Conccntrat ian ImYI

FIG. 2. Effect of Na+ on the rate of glucose transport. The rates are observed (tl.2j" values for isotope uptake. Buffer: 1 mM D- glucose, 0.1 M mannitol, l mM Tris/Hepes, pH 7.4, 0.1 mM MgSO,, and Na' and K' as thiocyanate salts at a combined concentration of 0.1 M. The line was calculated by regression analysis. The inset is a log-log replot of the same data (ordinate: multiplied by 1.85 X lo4; abscissa: by IO). The line in the inset is the theoretical one for a 1:l stoichiometry of glucose to Na' transport.

Border Membrane?-This question is fundamental to the transport mechanism. An alternative to an obligatory role of Na' is a facultative one, explained by a carrier that can also operate in the absence of Na', but whose affinity for the sugar or whose translocation rate are influenced by the presence of Na'. From an experimental point of view, the distinction between an obligatory and a facilitating role of Na+ is important because kinetic models and their analyses are simpler in the former case.

The problem was approached by evaluating the effect of Na' on (i) the rate of glucose transport at fixed glucose concentration, and (ii) the affinity of the carrier for glucose. Fig. 2 shows the effect of Na' at constant glucose concentration of about half the K,. The rate of glucose transport increased linearly with Na+ concentration up to 0.1 M, pro- vided the ionic strength was kept constant. Two features of this stimulation suggest an absolute Na' requirement. First, in the absence of Na+, the rate of glucose transport, measured as (t1,2)", was 0.04 min", and therewith similar to the leak rate calculated from the portion of the observed rates which


5-

3-

1-

20 60 100 1 100

Glucose Concentration I n " l FIG. 3. Dependence of tracer D-glucose transport on the con-

centration of D-g1UCOSe. Observed ( t 1 1 2 ) values (rate") are plotted as a function of unlabeled D-glucose. The line is calculated for carrier- mediated tracer flux according to Equation 2 under "Materials and Methods." The larger deviations of the observed ( t l r 2 ) values from the line at higher D-glUCOSe concentrations result from the contribu- tion of tracer o-glucose uptake via a leak pathway.

could not be suppressed by high unlabeled glucose concentrations (see Table I1 and Fig. 3 for glucose concentration dependence of glucose exchange rate). Second, the observed rates at all Na' concentrations can be accounted for by the sum of a Na'-independent rate and one that is proportional to the Na' concentration. This type of Na' dependence is consistent with a carrier imposing tight coupling between glucose and Na+ and a 1:l stoichiometry under net flux conditions. The latter point is demonstrated more clearly by the inset in Fig. 2, which is a log-log plot of the same data. The slope, which indicates the stoichiometry, is 1. Thus, the Na'- dependent carrier does not appear to be functional in the absence of Na'.

To evaluate whether Na' has an effect on the affinity of the carrier for glucose, rate measurements of tracer glucose flux as a function of varying unlabeled D-glucose concentrations were carried out. The K, determined under equilibrium exchange conditions corresponds to the unlabeled glucose concentration that decreases the rate of tracer flux by 2-fold. It directly measures the apparent2 dissociation constant of the carrier for glucose (see Appendix l), i.e. 1/K, indicates the apparent affinity (abbreviated as KC in the appendices). Fig. 3 illustrates the dependence of the transport rate of tracer glucose on unlabeled D-glucose concentration at 0.1 M Na'. The measured rates are graphed analogous to a Dixon plot (rate" uersus inhibitor concentration), whereby the unlabeled D-glucose corresponds to t,he inhibitor. The K, can be obtained directly from the graph, i.e. from the intersect with the abscissa.

Table I1 summarizes the affinity (KC a,,P) determinations over the experimental range of 1 to 100 mM Na'. The affinity for glucose does not change more than %fold as a function of Na'. Na' dependency of glucose binding can therefore be eliminated as explanation for the Na' stimulation of the

' The measured dissociation or association constants are apparent because in the case of a transport system the substrate binding site is potentially accessible from either membrane surface. The affinity for the substrate may differ depending on the surface at which the binding takes place. Therefore, the measured, apparent affinity depends on the equilibrium distribution of the binding site between the two surfaces and the respective affinity for the substrate at these surfaces, z.e. the observed affinity is some weighted mean of the affinities at either surface. The equilibrium distribution of the binding site in turn can be a function of experimental variables such as Na' concentration, ionic strength, pH, etc.

glucose transport rate and other possible explanations have to be considered. The results imply a strong Na' dependence of the V,,, of glucose transport (see Ref. lo), which is essentially identical with an obligatory Na' requirement. The molecular basis of Na' dependence of the V,,,, of the exchange can be either an inability of glucose to bind to the carrier in the absence of Na', or a very slow translocation movement of the carrier loaded only with glucose relative to one loaded with Na' and glucose.

Is Ligand Binding to the Carrier Ordered or Random?- The carrier-mediated co-transport of Na' and glucose can be perceived analogous to an enzymic reaction with two substrates and two products. Na' and glucose correspond to substrates when they are on one side of the membrane and to products when they are on the other side. Since there is an obligatory requirement for Na+, both substrates have to in- teract or bind to the carrier on the substrate face of the membrane before translocation and subsequent debinding on the product face can occur. This mechanism is analogous to an enzymic bi-bi reaction (20).

Two different general mechanisms of binding (or debinding) can theoretically be distinguished in the case of two substrates, namely an ordered and a random type. The possible ordered mechanisms are shown in Fig. 4; there is only one random type (Fig. 5 ) . Interestingly, the two types can be experimen- tally distinguished by their dependence of the transport rate of one substrate on the concentration of the other one when equilibrium exchange conditions are employed. For a random

I WRROR SYMMETRY

I GLnE SYMMETRY

FIG. 4. Iso-ordered-bi-bi mechanisms for Na+-dependent glucose transport. C,, = free carrier at the luminal interface; C, = free carrier at the cytoplasmic interface; the vertical double line represents the permeability barrier. The order of substrates and products is given by reading the diagram from left to right. Although the transport is written as net flux, all steps are freely reversible. Model C is given in detail in Appendix 1.

FIG. 5. Iso-random-bi-bi mechanism for Na+-dependent glucose transport. For abbreviations and explanations see legend of Fig. 4.


mechanism, in which either substrate can be the first to bind (or to &bind), a “typical” hyperbolic activation curve is expected. In contrast, for an ordered type of mechanism, the shape of the activation curve depends on the combination of the labeled substrate, whose flux is measured, and of the activating substrate. When the rate of the first ligand (substrate that binds first) is measured as a function of the second ligand (substrate that binds second), the activation curve is biphasic: Low concentrations of the second ligand stimulate the transport rate of the first one, while higher concentrations reduce it back to zero. The reduction is explained by the decreasing concentration of the free (unloaded) carrier with increasing concentration of the second ligand, so that the availability of the free carrier becomes rate-limiting for the isotope exchange of the first ligand. When, however, the rate of the second ligand is measured as a function of the first one, the resulting activation curve is hyperbolic because the isotope exchange rate of the second ligand depends on the concentration of the carrier loaded with the first substrate and because this concentration increases hyperbolically with the concentration of the first ligand. The same considerations apply in reverse to the debinding process, Le. a biphasic activation curve is expected when the transport rate of the product that is released last from the carrier, is measured as a function of the one that is released first. The reason for this phenomenon is that high concentrations of the product that is released first, prevent the formation of significant concentrations of the carrier loaded only with the second product (for a detailed discussion see Ref. 21).”

Figs. 6 and 7 present the results with intestinal brush borders when either glucose or Na+ transport rates are measured as function of the other substrate. The experiment in Fig. 6 is similar to the one in Fig. 2; in both experiments the rate of glucose transport is measured as a function of Na’ concentration. In Fig. 6, the range of Na+ concentration is extended to 1 M, and in this case, the activation curve is biphasic. The Na+ concentration of maximal stimulation was 0.2 M. At 1 M Na+, the glucose transport rate decreased to 42% of the maximum.

Fig. 7 demonstrates the reverse experiment in which the rate of tracer Na+ transport is measured as a function of increasing unlabeled D-glucose concentrations. Na’ transport across the brush border membrane occurs via several pathways (22) so that a substantial rate of Na+ isotope exchange in the absence of glucose is not surprising. Interestingly, glucose up to 5 mM stimulated Na’ transport above basal levels. Glucose concentrations above 10 mM had no effect. Na+ transport above the basal level must proceed via the Na’- dependent glucose carrier in this type of experiment. The rate via the glucose carrier can therefore be calculated as the difference between stimulated and basal rate.

The biphasic activation curves of glucose transport by Na’ and of Na’ transport via the glucose carrier by the presence of glucose eliminate a random transport mechanism and are consistent with an ordered mechanism of substrate binding and product debinding.4 As explained under “What Is the

’’ The biphasic behavior of transport velocity of the first substrate as a function of second substrate concentration (or velocity of the last product as a function of f m t product concentration) is particularly obvious when the reaction is not a rapid equilibrium reaction and the dissociation rate constant of the first-on substrate (or last-off product) is relatively slow. Here, rapid equilibrium refers to a rapid formation of the carrier .substrate complexes a t the membrane interfaces relative to the translocation across the membrane.

Since 1 M Na’ does not completely inhibit glucose exchange, a certain degree of randomness in the substrate release cannot be ruled out. However, 1 M Na’ is only about 3 times the apparent dissociation constant for Na’ (unpublished observation) so that complete inhibi-

I T

0 0.2 a4 as 0.8 10

N.+ ~oncontrat~on IYI

FIG. 6. Effect of Na’ on the rate of D-glUCOSe transport. The rates are observed ( t l l e ) - l values for isotope uptake. Buffer: 1 mM D- glucose. 0.1 M mannitol, l mM Tris/Hepes, pH 7.4, 0.1 mM MgSO?, and Na’ and K’ as chloride salts at a combined concentration of 1 M. Asterisks indicate significantly ( p < 0.05) different values from the maximal rate at 0.2 M Na’ (bars = +- 1 S.D.).

.O 8

.O?-

f .os-

a .os- d

0 - . c - .04-

L

I I l I /- 0 1 2 4 6 8 lo 100

0-Glucoaa Concmtratlon Wl

FIG. 7. Effect of glucose on the rate of Na’ transport. Ob- served ( t ) ,$’ values for tracer Na* uptake are plotted on the ordinate. The points are the weighted average of three experiments with different membrane preparations, each representing at least triplicate measurements. The weight of each experiment was inversely proportional to the variance of the data. Bars indicate & standard deviation. Asterisks indicate very significantly ( p < 0.001) different values from the basal transport rate without glucose.

Symmetry of Transport Reaction”, the ordered mechanism has to be of a special kind to explain the biphasic activation curves produced by both D-glucose and Na’.

Since substrate inhibition also results in biphasic activation curves, this explanation must be eliminated before the ordered mechanism can be accepted. Information relevant to this point comes from the experiments in which the affinity for D-glUCOSe was determined (Fig. 3 and Table 11). In these experiments, with essentially the same experimental conditions as in Fig. 7, and the same glucose concentration range, no substrate inhibition by glucose could be detected as indicated by the absence of sigmoid curves in graphs such as in Fig. 3. Therefore, an ordered mechanism of Na’ and glucose binding and debinding is likely for the Na+-dependent D- glucose carrier, and the transport mechanism can be characterized as an ordered-bi-bi reaction. Under net flux conditions, accessibility of the “active” site of the unloaded carrier must

tion of glucose exchange cannot be expected a t this Na’ concentration. Na+ concentrations higher than 1 M were not tested because extremes of ionic strength may affect membrane and protein struc- ture.

4458 Nu+-dependent Glucose Transport

change from one to the other membrane interface. This step is analogous to the isomerization of an enzyme. Therefore, the complete mechanism corresponds to an zso-ordered-bi-bi reaction.

What is the Symmetry of Transport Reaction?-Since we conclude that it is an ordered mechanism, then the actual order of substrate binding or product debinding becomes of great interest. Experiments carried out under equilibrium conditions cannot provide an absolute answer; however, it is possible to obtain information about the symmetry of the reaction. If one considers the translocation step for Na' and glucose across the permeability barrier as symmetry plane (axis) for the reaction, the binding and debinding process can be of two general types: (i) with mirror symmetry (Fig. 4, Models A and B), in which the substrate that binds first is the product that is released last (first-in-last-out or last-in-first- out); (ii) with glide symmetry (Fig. 4, Models C and D), in which the substrate that binds fiist is the product that is released fiist (first-in-first-out or last-in-last-out).

The experiments in Figs. 6 and 7 not only provide evidence for an ordered binding mechanism, but also for a glide symmetry of the transport reaction. The latter conclusion follows from a more detailed consideration of the dependence of transport inhibition on the site of substrate addition (product debinding) than given above in the context of the differences between random and ordered reactions. According to Segel (21), "total substrate inhibition is observed if either of the varied reactants (of a pair) adds between the point of combination of the exchange reactants." Thus, inhibition of Na' transport by high glucose concentrations (relative to the maximum at 1 mM) suggests that glucose adds to the carrier between the addition of Na' on one side and its release on the other. On the other hand, the inhibition of glucose transport by high concentrations of Na' (relative to the maximum at 0.2 M ) indicates that a t least one point of Na' binding or release lies between the addition of glucose on one membrane interface and its release on the other. Models C and D, but not A and B, fulfill this requirement.

To test the model with glide symmetry more directly, the ratio of the mass (in contrast to isotope) transport rates of glucose to those of Na' via the glucose carrier were measured at different concentration ratios of glucose to Na+. An ordered-bi-bi mechanism with mirror symmetry (Fig. 4, Models A and B) predicts that the ratio of transport rates under equilibrium exchange conditions be either 2 1 or 5 1, regard- less of the concentration ratio of the transported solutes. The ratio is z 1 for Model A, and 5 1 for Model B. In contrast, a model with glide symmetry predicts that the ratio of the transport rates of glucose to Na' be >1 at high glucose/Na+ concentration ratios and <1 at low ones. As shown in Table 111, the ratio of the transport rates varied with the ratio of the

TABLE I11 Carrier-mediated Na+ and D -glucose fluxes under equilibrium

exchange conditions (at 25OC)

[Na'] [D-Clc] ( t , 2 (.I, )" N a + ) - ~ , , Flux ratioh of Glc/Na' _~

IllM V I M ,%- ' s-

80 2 0.025 0.037 -C 0.004 0.023 f 0.013 0.04 f 0.02 80 10 0.125 0.013' t0.001 >1

'' (tl,2 N . , t ) - I = rate of Na+ transport via glucose carrier. The rate was calculated from the difference in rate of Na+ transport in presence and absence of glucose. The standard deviation was calculated from the sum of the variances of the rate measurements with and without glucose.

The flux ratio = ([~-Glc]/[Na']) X ( [ t l , r <;I,]- L' N ~ + ] ~ l ) .

' Calculated from t i ,2 a t 2 mM D-glucose and the K,,, of glucose transport at 80 mM Na' (i.e. 2.3 mM).

substrate concentration as predicted by the glide symmetry.5 Measurements of the ratio of mass transport rates are in effect another way of expressing the biphasic activation curves observed for glucose as well as for Na+ (Figs. 6 and 7 ) .

DISCUSSION

The kinetic model derived from the transport studies in vesicles differs in several respects from those previously considered for Na+-dependent glucose transport (1). Noteworthy characteristics of the suggested model are the ordered ligand addition to and debinding from the carrier and the presence of glide rather than mirror symmetry of ligand binding and debinding (Fig. 4, Models C and D). In addition, as will be shown below, the rate of translocation is faster than at least one of the ligand-debinding steps. Since this type of model for transport has not been discussed before, some of its features and implications for the physical mechanism of transport have to be examined.

In kinetic modeling, one usually tries to find a simple (or the "simplest") mechanism that is consistent with the experimental results and plausible in terms of t,he knowledge about the material that is investigated, in this case a biological membrane. The results with the vesicles have eliminated an iso-random-bi-bi reaction and mechanisms of the iso-ordered- bi-bi type with mirror symmetry (Fig. 5 and Fig. 4, Models A and B, respectively). On the other hand, the data are consistent with an iso-ordered-bi-bi reaction with first-in-first-out characteristics (Fig. 4, Models C and D). Unfortunately, experiments carried out under equilibrium exchange conditions do not allow any conclusions as to whether Na+ is the first ligand at the luminal surface (Fig. 4, Model C) or D-glUCOSe is the first one (Fig. 4, Model D). Information on this point must come from other types of experiments; for example, those in which ligands are asymmetrically distributed across the membrane. Binding of phlorizin, a competitive inhibitor of Na'- dependent glucose transport, could provide data relevant to the functional orientation of the transport system in the membrane. Phlorizin does not permeate the membrane (23) so that, when added to the medium, it will see only the outside of vesicles. Furthermore, since the vesicles are essentially all right-side-out (24); binding of phlorizin from the medium occurs to the luminal surface of isolated brush border membrane vesicles. If one assumes that phlorizin can bind to the glucose site of the carrier, then the predicted Na' dependence of phlorizin binding is different for Model C (Na' being the first ligand on the luminal surface) and Model D (glucose being the first ligand). Model C predicts that the apparent affinity for phlorizin increases in a hyperbolic manner with Na+ concentration, while it is independent of Na' at concentrations below the K, for Na+ in Model D (see Appendix 3). Recent results with renal (25) and intestinal (26, 27) brush border membranes have shown an increasing affinity for

" T h e conclusion that the ratio of o-glucose to Na' flux varies under equilibrium exchange conditions with the concentration ratio of the two substrates in the medium, is not incompatible with the earlier conclusion of a 1:l stoichiometry of o-glucose to Na' under net flux conditions. The I:1 ratio also applies to the translocation step

ligands have to be exchanged at either interface before the loaded under equilibrium exchange conditions. However, because not all

carrier can again cross the membrane and achieve isotope equilibration between intravesicular and extravesicular compartments, the 1:1 stoichiometry does not necessarily hold for substrate flux under equilibrium exchange conditions.

"The sidedness of isolated brush border membrane vesicles has been thoroughly investigated for rat intestine (24). The same right- side-out orientation appears to prevail also in rabbit brush border membranes as judged from the inability of Triton X-100 to stimulate the exo-enzyme sucrase (unpublished results).


phlorizin binding with increasing Na' concentration, consistent with Model C, but not Model D.

A more detailed mathematical treatment of Model C reveals that information about the translocation rate relative to one of the ligand dissociation rates can be obtained experimen- tally. In experiments in which the transport rate of one substrate is measured as a function of the concentration of the other substrate, the concentration being maximally stimulatory is dependent on the ratio of rate constants for translocation and debinding of the labeled substrate and the affinity for the stimulating substrate. In the case of stimulation of Na' transport by glucose, a lower limit for the rate constant of translocation of the loaded carrier, k3, is given by the following equation (see Appendix 2, Equation 12'):

hi > ~ - I / ( [ G ~ ] ' . K G nl,p,v.K~ app.v = I)

whereby k- , = dissociation rate constant for luminal Na', [G,] = glucose concentration that is maximally stimulatory for Na' transport, K(; a l l l l ~ = apparent affinity for glucose a t the same Na' concentration a t which [G,] is measured, and Kc; L,,,pN = = apparent affinity for glucose at infinite Na' concentration. The last three terms can be determined exper- imentally. From the experiment in Fig. 7, [G,] can be estimated as about M at a Na' concentration of 0.080 M. Both Ko and Ko al,,).\r = are about 4 X lo2 M", as judged by interpolation and extrapolation from the data in Table 11. Therefore, the rate constant for the translocation step is at least 6 times greater than the rate constant for Na' dissociation, k- , . In other words, the translocation step cannot be considered as the rate-limiting step for transport and the kinetic model cannot be treated by rapid equilibrium kinetics of association and dissociation of both ligands at either surface.

In principle, similar calculations can be made from the stimulation of glucose transport by Na'. However, experimental difficulties have so far prevented reliable measurements of the apparent K,,, of the glucose transport system for Na'. Preliminary experiments suggest a value of about 0.3 M. The Na' concentration which maximally stimulates glucose transport is about 0.2 M (Fig. 7) and thus, would fall below the K,. This result is consistent with a translocation rate constant of the loaded carrier which is faster than the dissociation rate constant for glucose.

If the kinetic model with an iso-ordered-bi-bi reaction, with rapid translocation of the loaded carrier, and with first-in- first-out characteristics of the co-transport can be accepted for Na'-dependent glucose transport, then the question arises what type of physical mechanism would correspond to the kinetic model. Two different classes have been distinguished for facilitated diffusion type of transport. Both exhibit carrier (and not pore-type) kinetics: 1) The classical mobile carrier mechanism in which the ligand binding site can become occupied a t one interface and physically move with the ligand across the permeability barrier of the membrane. 2) A gated channel or pore mechanism in which the ligand binding site is located within the membrane and is accessible from either membrane interface, although from only one at any given time. The translocation step for the transported ligands is envisioned as a conformational change in the transport system, presumably a protein, whereby a rocker-type movement shifts the permeability barrier around the stationary ligands. This type of transport is illustrate in Fig. 8.

TWO features of the gated pore mechanism make this model attractive to explain the kinetic data: (i) This model predicts the first-in-first-out characteristics that was observed for the Na'-dependent glucose transport system. (ii) Conformational changes within proteins can be fast and are consistent with a

v MODEL FOR No+-Glc COTRANSPORT

FIG. 8. Model for Na'-dependent glucose co-transport which is consistent with an iso-ordered-bi-bi reaction and first-in- first-out characteristics of the co-transport.

translocation rate constant that is faster than the dissociation rate constant of Na'.

In contrast, the classical mobile carrier explains more easily mirror symmetry of an ordered-hi-bi reaction. Furthermore, because the ligand binding site has to move with the ligand across the membrane, the mobile carrier is usually associated with a slow, rate-limiting translocation step.

The gated pore mechanism for Na'-dependent transport opens up interesting possibilities for the site(s) at which an electrical potential difference across the membrane could ex- ert its effect on the coupled Na'-glucose co-transport. An electric field across any membrane will also exist along a pore within the membrane. Thus, any ion moving onto or off a site within the membrane would experience the field, which would be reflected in a voltage dependence of the rate constants for the on and off movements. Applied to Na', this latter idea constitutes a new explanation for the observed voltage sensi- tivity of phlorizin binding to brush border membranes observed by Aronson (25) and Tannenbaum et al. (26). The original, and also possible, explanation was that the carrier itself is negatively charged and that this charge is neutralized through Na'.

The general mechanism of Na'-dependent glucose transport appears to be similar in rat and rabbit intestine. Results with brush border membrane vesicles show the same Na' dependence of the V,,,, and Na' independence of the K, for glucose (Ref. 10 and this report). For both species, the results were obtained under equilibrium exchange conditions and hence the calculated kinetic parameters express carrier prop- erties, rather than transport capacity constants for membrane vesicles which can differ with energization state. Interestingly, the K,, for glucose at the same Na' concentration is about 6- fold higher in the rat than the rabbit, while in the same species the values for renal and intestinal Na+-dependent glucose transport system are very similar (Table 111).

The kinetic data obtained with the rabbit vesicle preparation compare relatively well to those obtained by Goldner et al. (8) in intact rabbit ileum. The essential findings in intact rabbit ileum were a K, for D-glucose of 1.4 mM, Na' independence of the K,,,, Na' dependence of the V,,,.,, and a 1:l stoichiometry of Na' to glucose transport via the glucose carrier. The agreement is surprising because in the intact epithelium a net flux and not an exchange of glucose are measured, an electrical potential exists across the brush border membrane, and the measurements are complicated by unstirred layers and depolarization of the brush border membrane potential at high glucose fluxes (28, 29). Furthermore, it is conceivable that the thermodynamic driving force for glucose flux into the enterocytes can change when the luminal Na' concentration is varied in the experiments designed to determine the Na' dependence of the K, or V,,,,,. The agreement of the kinetic data from the intact epithelial preparation and the membrane vesicles is either fortuitous, or all the possible complications that can interfere with kinetics meas-

4460 Nu+-dependent Glucose Transport

urements in the intact tissue did not play a role in the experiments by Goldner et al. (8).

The kinetic data from the intact epithelial preparation were explained by a mobile carrier mechanism (1). It is now obvious that they also fit a different type of Inachanism, namely a gated pore with an iso-ordered-bi-bi reaction. The value of the isolated membrane preparation for kinetics has become evi- dent in the comparison of the results from both preparations. The membrane preparation allows the design of different types of kinetic experiments and experimental conditions can cover wider ranges of substrate concentrations or extreme conditions of, for example, Na' concentration compared with intact tissue. The additional information obtained with the isolated membranes was essential to make the distinction between a mobile carrier and a gated pore mechanism.

Acknowledgments-We thank Doctors K. Neet and P. Will for critically reading of the manuscript. The drawing of the carrier model (Fig. 8) was prepared by Ms. D. J. Castelic.

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6. Hopfer, U., Nelson, K., Perrotto, J., and Isselbacher, K. J. (1973)

7. Sacktor, B. (1977) Curr. Top. Bioenerg. 6, 39-82 8. Goldner, A. M., Schultz, S. G., and Curran, P. F. (1969) J . Gen.

9. Murer, H., and Hopfer, U. (1974) Proc. Natl. Acad. Sci. U. S. A .

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Physiol. 53,362-383

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10. Hopfer, U. (1977) J. Supramol. Struct. 7, 1-13 11. Segel, I. H. (1975) Enzyme Kinetics, pp, 846-883, John Wiley and

Sons, New York, N. Y. 12. Schmitz, J., Preiser, H., Maestracci, D., Ghosh, B. K., Cerda, J.

J., and Crane, R. K. (1973) Biochim. Biophys. Acta 323, 98- 112

13. Will, P. C. and Hopfer, U. (1979) J . Biol. Chem. 254, 3806-3811 14. Murer, H., Arnmann, E., Biber, J., and Hopfer, U. (1976) Biochim.

15. Lowry, 0. H., Rosebrough, N. J., Farr, A. L., and Randall, R. J.

16. Cleland, W. W. (1967) Adu. Enzymol. 29, 1-32 17. Crane, R. K. (1977) Znt. Reo. Physiol Gastrointest. Physiol. ZI.

18. Forstner, G . G . , Sabesin, S. M., and Isselbacher, K. J. (1968)

19. Diedrich, D. F. (1966) Arch. Biochem. Biophys. 117, 248-256 20. Cleland, W . W. (1963) Biochim. Biophys. Acta 67, 104-137, 173-

21. Segel, I. H. (1975) Enzyme Kinetics, pp. 847-852, John Wiley and

22. Schultz, S. G., Frizzell, R. A., and Nellans, H. N. (1974) Annu.

23. Stirling, C. E. (1967) J. Cell. Biol. 35, 605-618 24. Haase, W., Schafer, A,, Murer, H., and Kinne, R. 11978) Biochem.

25. Aronson, P. S. (1978) J. Membr. Biol. 42, 81-98 26. Tannenbaurn, C., Toggenburger, G., Kessler, M., Rothstein, A,,

and Semenza, G. (1977) J. Supramol. Struct. 6,519-533 27. Toggenburger, G., Kessler, M., Rothstein, A., Semenza, G., and

Tannenbaurn, C. (1978) J. Membr. Biol. 40,269-290 28. Thornson, A. B. R., and Dietschy, J. M. (1977) J. Theor. Biol. 64,

29. Hopfer, U. (1978) Am. J. Physiol. 234, F89-F96 30. Cleland, W . W. (1967) Annu. Rev. Biochern. 36, 77-112 31. Segel, I. H. (1975) Enzyme Kinetics, pp. 864-869, John Wiley and

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Appendix 1 'Ihe mechanism is Characterized by 4 association constants and 1

Equilibrium constants and rate equations for the iso-ordered-bi-bi- equilibrium distribution constant of the carrier across the membrane.

translocation reaction with glide syletry. The constants are defined for equilibrium exchange conditions (Go-Ci=C;

No=Ni=N) as follows:

Diagram 1 shows the kinetic model C with the translocation rates

of the loaded carrier expressedly specified because the rate equations so= ; K G O a ; KGi=& ; si=&$& ; and K 6 - H

from the extensive d e l contain infornation about this translocation

rate relative to the substrate dissociation rates. The other equilibrium distribution constant K3 is defined by the first 5

k6 constants, i.e.. K 3 W : E 1 2: x " . Additionally, apparent association constants for glucose and Na* are determined by the association

constants and the NB* and glucose concentrations. respectively: Gq-5 k-6 k - : b N

CiG CON

In order to kinetically characterize the nodel. 11 indepmdent +ate

constants are necessary. However, if the associatlon and dlstribution

constants are knom, only 6 rate constants are independent, since:

k3 k ' , k2 K =3; sis4 . '-' DIAORMI 1. Kinetic model of N a * - w g i u a eatnnsport via an isoordemd-bi-bi mech.- K6=<6 ' %O'+, ' x Ci k-s k-4' ' 3 = T

nien~ with first-in-fuatdut characterbtics. C = &r, C = glucose. N = Na'. aod the subsnipes o and i refer to the &r or the compleres on the o and i side of the membrane. The initlal rate of isotope equilibration of externally added


radioactive Na* or glucose can be derived from the King-Altman figures,

uslng the simpler schematic method of Cleland (30,31). With abbreviations

analogous to those used by Segel 1311, the rate of Isotopically labeled

Na' uptake into homgeneous vesicles is given by:

( 3 ) +vNas1 = k_,[ClG*N] .whereby the * in front of symbols indlcaces

the labeled form. The steady state concentratlon of CiG'N depends on the

number of ways that the complex c a n be formed, the total carrler concen-

tration Ct (Ct= Co + Ci + CaNG + C i a + CiG + CON), the isotope Concentration

['N] [ln dlsintegrations per unit time and per unit volwe), and the

unlabeled Sa+ and glucose concentratlons. The complete rate equation

reads:

k.4klk2k3K6[Cil I'NI [GI 14' '"No-rEi~ = k-lk_2k-3 + k-lk-2k_4 + k3k-1k-4 f k2k3k-4[G]

[CL] is determined by [C,]. the unlabeled glucose and Na* concentrations

In conlunctlon wlth the association constants:

( 5 ) IC11 = [Ctl - (1 + K6 + K6$,.,[Nl KCi[CI + K6~olN1KGoLGl + KNilNIKGilGl)

Two types of transport experiments can be carried out' 1) The rate

can be measured as a function of the unlabeled Na+ concentratlon.

In thls case. the glucose concentration is held constant. 2 ) The dependence

of the Na+ transport rate on the glucose concentration can be determined,

whereby the unlabeled Na' concentration 1 s fixed.

For the flrst type of experiment ( 1 . e . . [Gl,['N]=constants; [N]=varlable),

the rate equatlon 4 takes on the general form, after Ci 1 s replaced by

the Term on the rlght side of equatlon 5 :

(6) *vNaNI=+ , whereby ' A ' and ' 8 ' are constants with

,= 4 1 - 3 6 k - k L , L k I*N][I;]II~t)

( k . l k . , k . 3 + LLIk.2k.4 + k3k.lk.4 * k2k3h.41Cll x "

I n other words, ' A ' 1 5 the maximal veloclty of the Na+ t r a c e r tranrpart

for J g z v m glucoae concentration, and '8' corresponds IO the h l ~ c h d e l j . ;

con5tant for Na*. .The constant '8' can be easlly determined by one of

the tran\forms of equation 6 , for example:

( 7 1 l l ' v = B l h + j ~ l / A and on extrapolatlon t o I l ' v = O , IN]= - B ( s e e F I ~ 3 ) .

kor the second type of experiment vhlch determlne5 the dependence

of the rate of N=' transport ( v r a the glucose carrler~ on glucose ( , . e . ,

[N].[*N]=constants; [Glzvanable). one obtalns another equatlon ( ( : I I F agaln

replaced by t h e term on the rtght srde of equation 5 )

3t hlgh glucose concentratlons.

Slmllar equatlons can be derlved for glucose transport. They

have the same general form. The glucose Isotope transport rate a t

flxed Na' Concentration, but variable glucose concentratlon is given by:

In contrast, at flxed glucose, but varlable Na concentratlon one obtalns

(10) *vGo'Gi - - R I N 1 , , whereby K , S , T, and U are constants. S + TIN] + U [ N l -

APPENDIX 2

Relation between translocatlon and llgand dlssoclation rates

As shown In dppendlx 1, ~n an lso-ordered-bkbl translocatlon reactlon

wlth gllde symmetry of blndxng and debindlng of ligands ( s e e diagram tn

Appendix 1) the lsotope transport rate of one substrate depends in a blphaslc

manner on the concentration of the other substrate (equatlons R and IO of

Appendlx 1). This dependence can be used t o obtain mformatlon about the

relatlonshlp between the translocatlon rate and ligand dlssoclatlon rates.

Thls Appendlx 2 derlves t h e baslc equatlons of thls relatlonshlp.

From Appendlx 1, one obtalns f o r the veloclty of radio-labeled

Nat (*N) uptake as a fmctlon o f unlabeled glucose concentration

( [ G I ) and at flxed unlabeled Na+ concentratxon ( ( N ] ) :

(1 ' ) VINWN1 =

EH + (FH +EI)II ; I * 1 l I ( ; ] ' [from equ. 8 o f Appendlx 1)

whereby:

D = k"4klk2k3K6[Ct][*N] (see model In Appendlx 1 for the deslgnatlon

E = 1 f K6 + K6KNo[N] of rate constants)

r = KG, + KC,KNl[NI K6KGoKNo[NI

( 2 ' ) H = k.lk.2k-3 + k-I k.2k.4 + k3k.lk.4

(3') I = k2k3k-g

and ( 4 ' ) F I E = K (from equ. 1, Appendlx I ) G aPP

The glucose conCentrat1on that glves maximal stlmulatlon of Na+

transport ( [ G m ] ) can be calculated by taklng the first derlvatlve of the

VelOCIty equation wlth respect to glucose concentratlon and settrng it

equal to zero. After divldlng both sldes by 'D' and multlplvlng by the


Appendlx 3

Na' dependence of ph lo r i z in b lnd ing t o t he g lucose s i te

Glven t h e model i l l u s t r a t e d I n Appendix 1, t h e Na+ dependence

o f p h l o r l z l n b i n d l n g t o t h e g l u c o s e 5 i t e from t h e 0- and i - s i d e

of the membrane in te r face can he p red ic ted . Phlorizin can be

consldered a non-peneant analog of glucose. Therefore . it i s

reasonable to assume that i t can h ind to the same s i t e a s g l u c o s e

However, no t r a n s l o c a t i o n a c r o s s t h e membrane i s poss ib l e w i th

p h l o r l z i n on t h e s i t e . I n t h i s c a s e , a s s o c l a t i o n c o n s t a n t s f o r

p h l o r i z l n (Kp) on the 0- and i - s i d e o f t h e membrane can be de f ined :

(1") KPo = - and (2") Kpi = [CoNP] [CiP]

[CONI [PI t c i ] [ P I

whereby P = p h l o r i z l n and the complexes CoNP and C I P a r e formed

analogous to the glucose complexes In the model i n Appendlx 1.

On t h e o t h e r hand, t h e a p p a r e n t a f f l n l t i e s . ln the absence of glucose

( i . e . , [ClC], [CiGN], [CoNG] = O), a re g lven by:

(3") K [CoNP]

Po app ([Ci]+[Co]+[CoN]) [PI and

[Cip] + [ C i P N ]

( [Ci] + [Co] + [CON] 1 [PI . ( 4 " ) KPi app -

Replacement of [CoNP] and [CiP] in equa t ions 3" and 4" by the

co r re spond ing a s soc ia t lon cons t an t s and concen t r a t lons o f ph lo r l z ln

and Na+ (equa t lons 1" and 2" o f t h l s Appendix, and Appendlx 1) y i e l d s :

Kp0KN0K6[N1 Kpi(l + \ I IN l ) (5") KPo app-1 + K6+K6KNo[N] and 16") K P ~ app= 1 + K6 + K 6 K No[N1 '

I t i s obvlous from equat lon 5" t h a t t h e a p p a r e n t a f f i n l t y o f p h l o r l z l n

b ind ing t o t he ou t s ide l nc reases In a hyperhol lc manner wl th lncreas lng

Na' c o n c e n t r a t l o n . On t h e o t h e r h a n d , e q u a t i o n 6" p r e d i c t s t h a t

t h e a f f l n i t y f o r p h l o r i z i n on t h e 1 - s i d e I S independent of Na+

c o n c e n t r a t i o n o v e r B wide range below ( K N 1 ) - l and I n each

c a s e , t h e Na+ e f f e c t r e s u l t s from a s h i f t o f t h e e q u i l i b r i u m

d l s t r i b u t l o n o f t h e " a c t i v e " s l t e between the two membrane i n t e r -

f a c e s

The Mechanism of Na'-dependent D-Glucose Transport*

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