Evidence for Two Asymmetric Conformational States in the Human Erythrocyte Sugar-Transport System by JOHN E

Biochem. J. (1975) 145, 417429 417 Printed in Great Britain

Evidence for Two Asymmetric Conformational States in the Human Erythrocyte Sugar-Transport System By JOHN E. G. BARNETT, GEOFFREY D. HOLMAN, R. ALAN CHALKLEY and KENNETH A. MUNDAY Department ofPhysiology and Biochlemistry, University ofSouthampton, Southampton S09 3TU, U.K. (Received 4 June 1974)

6-0-Methyl-, 6-0-propyl-, 6-0-pentyl- and 6-0-benzyl-D-galactose, and 6-0-methyl-, 6-0-propyl- and 6-0-pentyl-D-glucose inhibit the glucose-transport system of the human erythrocyte when added to the external medium. Penetration of 6-0-methyl-D-galactose is inhibited by D-glucose, suggesting that it is transported by the glucose-transport system, but the longer-chain 6-0-alkyl-D-galactoses penetrate by a slower D-glucose- insensitive route at rates proportional to their olive oil/water partition coefficients. 6-0-n-Propyl-D-glucose and 6-0-n-propyl-D-galactose do not significantly inhibit L-sorbose entry or D-glucose exit when present only on the inside of the cells whereas propyl-f6-D-glucopyranoside, which also penetrates the membrane slowly by a glucose- insensitive route, only inhibits L-sorbose entry or D-glucose exit when present inside the cells, and not when on the outside. The 6-0-alkyl-D-galactoses, like the other non- transported C4 and C-6 derivatives, maltose and 4,6-0-ethylidene-D-glucose, protect against fluorodinitrobenzene inactivation, whereas propyl ,B-D-glucopyranoside stimulates the inactivation. Of the transported sugars tested, those modified at C-1, C-2 and C-3 enhance fluorodinitrobenzene inactivation, where those modified at C-4 and C-6 do not, but are inert or protect against inactivation. An asymmetric mechanism is proposed with two conformational states in which the sugar binds to the transport system so that C4 and C-6 are in contact with the solvent on the outside and C-1 is in contact with the solvent on the inside of the cell. It is suggested that fluorodinitrobenzene reacts with the form of the transport system that binds sugars at the inner side of the membrane. An Appendix describes the theoretical basis of the experimental methods used for the determination of kinetic constants for non-permeating inhibitors.

The transport ofhexoses across the human erythro- process when present only on the inner surface of cyte membrane takes place by 'facilitated diffusion', the cells. We now report a group ofsimilar non-trans- a saturable process which does not consume energy ported hexoses with lipophilic groups either at C-1 but which involves combination of the sugar with a or C-6. Their behaviour suggests that the specificity specific site or sites on the membrane. Studies over for binding is different on the inner and outer surfaces many years have established the specificity require- of the membrane and that the transport system is ments of the process, and similar results have been asymmetric. We also report some observations on the obtained whether the measurement was of transport fluorodinitrobenzene inactivation of the glucose- (LeFevre, 1961; Sen & Widdas, 1962), or of the transport system, which extend the observations of ability to inhibit transport of another sugar, such as Bowyer & Widdas (1958), Krupka (1971, 1972), L-sorbose (Barnett et al., 1973a) or the ability Shimmin & Stein (1970) and Edwards (1973), and selectively to displace D-glucose from membrane which appear to confirm that the transport system fragments (Kahlenberg & Dolansky, 1972). In the can exist in different conformational states. Prelimin- more recent studies, which have implicated hydrogen ary reports of some of this work have been published bonds in sugar-transport-site binding, the inhibitory (Barnett et al., 1973b,c). sugar was present on both sides of the membrane. Baker & Widdas (1973a) have shown that 4,6-0- ethylidene-D-glucose inhibits sugar transport asym- Materials and Methods When added does not metrically. outside the cells it O-Alkyl derivatives ofsugars penetrate the membrane by the glucose-transport system, but inhibits the system competitively. 6-0-Propyl-D-glucose. 3,5-0-Benzylidene-1,2-0-iso- However, the sugar will slowly penetrate the cells by propylidene-a-D-glucofuranose (2.5g) was dissolved another route, and does not inhibit the transport in dry dioxan (15ml) containing freshly powdered

Vol. 145 0 418 J. E. G. BARNETT, G. D. HOLMAN, R. A. CHALKLEY AND K. A. MUNDAY

NaOH (3g). n-Propyl bromide (15 ml) was added and cose(2g, 500uCi) wasconvertedinto thepenta-acetate the mixture stirred at 70°C overnight. After cooling, by the action of HCl04 and acetic anhydride (Kruger the mixture was poured into ice-water and diethyl & Roman, 1936). Treatment of the penta-acetate ether mixture. The ether layer was washed with water with Sml of 45% (w/v) HBr in acetic acid gave and dried over Na2SO4. Removal of the solvent gave 2,3,4,6-tetra-0-acetyl-a-D-glucopyranosyl bromide, 3,5 - 0 - benzylidene - 1,2 - 0 - isopropylidene - 6 - 0 - which was dissolved in propan-1-ol (50ml) and stirred propyl-a-D-glucofuranose, which was recrystallized with Ag2O (6g) overnight in the dark. The silver salts from ethanol, m.p. 72°C, [a]"J 8.20 (c 0.56 in ethanol). werefiltered offand thepropan-1-ol was removed.The A portion (1.8g) was dissolved in ethanol (lOml) residue was dissolved in chloroform and washed with and water (lOmI) and Amberlite IR 120 (H+ form; 5 % (w/v) Na2S203 and water and dried over CaCI2. 5g) added. The mixture was stirred at 70°C for 5 h and Removal ofthe solvent gave n-propyl 2,3,4,6-tetra-0- filtered to remove the resin, which was washed with acetyl - fl-D-[ - 3H]glucopyranoside, recrystallized water. Filtrate and washings were combined and fromethanol,m.p. 84°C [Timmell(1964)gives 96°Cfor washed with diethyl ether and the aqueous solution the unlabelled compound]. Catalytic deacetylation was evaporated to dryness to give 6-0-propyl-D- by 0.01 M-sodium methoxide gave the product, glucose, recrystallized from ethanol, m.p. 122-123°C. recrystallized from ethanol-diethyl ether, m.p. 6-0-Pentyl-D-glucose, m.p. 72-75°C, was made by 96-970C [Timmell (1964) gives 101-103°C]. a similar procedure. By using 1,2: 3,4-di-0-isopropy- Unlabelled n-propyl fl-D-glucopyranoside and lidene-a-D-galactopyranose or 1,2:5,6-di-0-isopro- n-propyl 8-D-galactopyranoside, m.p. 97-99°C, [oiD2 pylidene-a-D-glucofuranose (Koch-Light Ltd., Coln- -90 (c 1.2 in water), were made in the same way. brook, Bucks., U.K.), syrupy 6-0-methyl-D-galac- 1,2: 3,4-Di-O- isopropylidene- a-D- [6-3H]galacto- tose, 6-0-propyl-D-galactose, m.p. 58-60°C, 6-0- pyranose. 1,2: 3,4-Di - 0 - isopropylidene - a - D - pentyl-D-galactose, m.p. 110-1120C, syrupy 6-0- galactodialdose (1g) (Godman et al., 1968) was benzyl-D-galactose, 3-0-propyl-D-glucose, m.p. 138- dissolved in ethanol (3nml). NaB3H4 (12mg, 12mCi/ 140°C, 3-0-pentyl-D-glucose, m.p. 133-135°C, and mmol) was added in water (0.5ml) at 0°C with mag- syrupy 3-0-benzyl-D-glucose were obtained by the netic stirring. The mixture was left at room tempera- same procedure. ture for 1 h, and unlabelled NaBH4 (200mg) added. After 30min the product was poured into water and extracted into chloroform. The aqueous layer was Sugars extracted with a further 50ml of chloroform con- Phenyl f6-D-glucopyranoside, 6-deoxy-D-glucose, taining unlabelled product (5g). The chloroform 6-deoxy-D-galactose, 4,6-0-ethylidene-D-glucose, layers were combined, washed with water and dried 1,2:5,6-di-0-isopropylidene-oc-glucofuranose, 1,2:3,4 over Na2SO4. Removal of the solvent gave the di-O-isopropylidene-ax-D-galactopyranose and phenyl product (5g; 6uCi/mmol), which was stored in dry a-D-glucoronide were obtained from Koch-Light dioxan at -15°C until required. Ltd. Other sugars were obtained from British Drug 6 - Deoxy - 6 - iodo - D - galactose (Raymond & Houses Ltd., Poole, Dorset, U.K., or were made by Schroeder, 1948) and 6-0-methyl-, 6-0-propyl-, the methods used by Barnett et al. (1973a). 6-0-pentyl- and 6-0-benzyl-D-[6-3H]galactose were L-[U-14C]Sorbose, D-[6-3H]glucose, 6-deoxy-D- made from 1,2: 3,4-di-0-isopropylidene-oc-D-[6-3H]- [1-3H]galactose, [1-3H]galactose and NaB3H4 were galactopyranose by the established methods (see obtained from The Radiochemical Centre, Amer- Corbett & McKay, 1961). sham, Bucks., U.K. Phenyl f-D-([6_3H]glucopyranoside. Phenyl /1-D- glucuronide (100mg) was dissolved in methanol Stopping solutions (0.3ml) and a solution of diazomethane inetheradded dropwise until a precipitate formed. The solvents Two stopping solutions were used: mercury were removed and the process repeated until the stopper, 1 % NaCl, 2mM-HgCI2, 1.25mM-KI; supernatant was a permanent yellow colour. Removal phloretin stopper; 1% NaCI, 10#uM-HgCl2, 1.25mM- of the solvent gave phenyl #-D-glucopyranoside KI, to which was added a solution of phloretin, methyl ester, m.p. 131-132°C. The ester (50mg) was to give a final concentration of 0.1 mM-phloretin dissolved in water (0.5ml) and NaB3H4 (2mg,4mCi) and 1 % (v/v) ethanol. added in water (0.5ml). The solution was left at room temperature for 1 h, deionized with Amberlite IR 120 (H+ form; I g) and evaporated to dryness. The Phosphate-saline residue was purified by paper chromatography to give buffer the product (yield 22mg; m.p. 167°C; 4mCi/mmol). This was 25mM-sodium phosphate buffer, pH7.4, n-Propyl I_-Dj[1-3Hlglucopyranoside. D-[1-3H]Glu- in 1 % (w/v) NaCl. 1975 HUMAN ERYTHROCYTE SUGAR-TRANSPORT SYSTEM 419

Chromatography phosphate-saline buffer was added to a solution of the inhibitor and ("4C]sorbose in 2.5ml of the phos- All sugars were tested forpurity bychromatography phate-saline buffer. For experiments in which the as described by Bamett et al. (1973a). Most of the inhibitor was predominantly inside the cells, these sugars were finally purified by preparative chroma- were preincubated at 25°C for 2h with the inhibitor tography on Whatman no. 3 paper in butan-l-ol- and then rapidly washed with 2 x 30ml of the ethanol-water (49:11:19, by vol.) and all those used phosphate-saline buffer. The pellets were rapidly were chromatographically pure. resuspended in 4ml of the buffer and L-[14C]sorbose was added to start the penetration. Both of these Human erythrocyte suspensions adaptations are only suitable for slowly penetrating inhibitors. A kinetic treatment of the inhibition for These were prepared as described (Bamett et al., non-penetrating inhibitors is given in Appendix (A). 1973a). (b) Inhibition ofthe net influx ofD-glucose at 15°C. Sugars were tested as inhibitors of net D-[3H]glucose Penetration rates of D-glucose and D-galactose entry into erythrocytes at 15°C under conditions in derivatives which the initial rate of entry could be measured. The radioactively labelled sugar (25 or 50mM, Fig. I shows the rate of entry of both 2 and 20mM-D- 1#GCi in lml) in NaCl-sodium phosphate buffer, glucose measured as the percentage filling after pH7.4 (25mM-phosphate and 1 % NaCI), was added various times. The rate ofentry was linear for at least to flasks containing washed erythrocyte suspensions 15s and the initial rate was taken as the concentration (4ml, 25 % packed-cell volume) in the same buffer at of sugar accumulating in this time. The inhibition 25°C. The final sugar concentration was 5 or 10mM. was then analysed by a conventional reciprocal plot. Penetration was stopped at various time-intervals by the addition of 30ml of ice-cold mercury stopping medium. Samples were centrifuged rapidly and the pellet was rapidly washed with a further 30ml of ice-cold stopping solution. Tubes were dried with tissue and the pellets extracted with 10% (w/v) trichloroacetic acid (4ml). At zero time stopping medium was added before sugar, and one flask was incubated for an 'infinite' time (3-4h) so that the 0 system attained equilibrium and the radioactivity of the cells corresponding to 5 or 10mM final concentration could be measured. Penetration could then be expressed as mmol/min per cell unit where I cell unit is that number of cells whose cell water volume is 1 litre at equilibrium. This represents effectively the intracellular concentration in mM. Penetration rates were also measured in the presence of D-glucose (50mM). D-Glucose was preincubated with the cell suspension for 10min before addition of the labelled sugar, which was also 50mM in D-glucose.

Inhibition constants Inhibition constants were measured by three methods. (a) Inhibition of L-sorbose penetration at 250C. 0 10 20 30 40 50 60 The method of Levine et al. (1971) was adapted as Time (s) previously described (Barnett et al., 1973a). The method was also adapted to measure the effect of Fig. 1. Rate ofentry ofD-glucose into human erythrocytes maintaining the inhibitory sugar predominantly on at 150C the inside or on the outside of the cells. For experi- Results are expressed as % filling of the cells by sugar. ments in which the inhibitor was predominantly *, 2mM-D-Glucose; *, 20mM-D-glucose. Entry was outside the cell, a zero preincubation time was used followed by using [3H]glucose, and equilibrium was and 2.5ml of the erythrocyte suspension in the obtained in 5min at each concentration. Vol. 145 420 J. E. G. BARNETT, G. D. HOLMAN, R. A. CHALKLEY AND K. A. MUNDAY

A kinetic treatment adapted from that of Stein (1967) (1 ml) with vigorous mixing. A sample (0.5ml) was is shown in Appendix (B). Constant concentrations added to 20% (w/v) trichloroacetic acid (0.5 ml) and of inhibitor and [3H]glucose (2-20mM, 0.4uCi/flask) the mixture centrifuged and 0.5ml of the supernatant were dissolved in one phosphate-saline buffer (4ml) was counted for radioactivity in 10ml of NE 250 at 15°C. Similarflasks contained no inhibitor. Washed scintillation fluid (Nuclear Enterprises, Edinburgh, erythrocyte suspensions in the same buffer (1 ml, 50 % U.K.). Each exit experiment was repeated at least packed volume) were added and the flasks shaken three times and the means of the points at each time turbulently for 15s. Ice-cold phloretin stopping were used to calculate Km and V values. medium was added and the cells were washed and The apparent Km for D-glucose was identical in the extracted with trichloroacetic acid as described above absence of malonamide (inositol is omitted from the for the penetration of D-glucose and D-galactose exit medium), and agreed with the literature value derivatives. A sample at zero time was obtained by (Karlish et al., 1972). adding stopper solution before erythrocytes to 2 and 20mM-glucose, and an equilibrated sample was obtained by leaving an incubation with 20mM-D- Fluorodinitrobenzene inactivation of L-sorbose trans- glucose for 30min at 25°C. It was found that more port in the presence ofsugars radioactivity appeared to equilibrate into the cells at 2mM-glucose, and this was ascribed to a small amount The sugar (10-100mM) was preincubated in of metabolism of the glucose. phosphate-saline buffer with the erythrocytes (25 % packed-cell volume) at 25°C for 10min (longer for After subtraction of the zero-time blank, which sugars known to penetrate slowly). Fluorodinitro- accounted for sugar trapped in the extracellular benzene in ethanol was then added to give a final space, the apparent molarity in the intracellular concentration of 2mr and 4% (w/v) ethanol. After space could be determined from the comparison of 1 h cells were washed twice with the phosphate-saline the radioactivity after 15s with that of the fully buffer (30ml) and then resuspended in phosphate- equilibrated 20mM-D-glucose sample. Initial rates saline buffer (4ml). L-['4C]Sorbose (25,umol, 1 ml) were expressed as mM/15 s. was added and the cells were shaken at 25°C for (c) Inhibition of the 'zero-trans' exit of D-glucose. 10min. Ice-cold mercury stopper solution (30ml) The method of Karlish et al. (1972) was modified was added and the cells were centrifuged, extracted to measure the inhibition of glucose exit by inhibitors with trichloroacetic acid and the supernatants after inside the cell. The kinetic treatment is given in centrifugation were counted for radioactivity. One Appendix (C). The exit of D-glucose is rapid and is flask was treated with stopping solution at zero time most conveniently measured under conditions which to give a measure of extracellular space. The control lead to the use of an integrated rate equation. Washed rate of inactivation in the absence of sugar was cells (50% packed-ell volume) were pre-loaded with measured in each experiment. This gave the base from 40mM-inhibitor or -malonamide and 80mM-D-glucose which stimulation or protection against inactivation in phosphate-saline buffer at 25°C for 2h. Solutions could be measured. To ensure that washing after were then centrifuged and resuspended in iso-osmotic fluorodinitrobenzene inactivation was complete, phosphate-saline buffer (24mM-sodium phosphate sorbose transport was measured in cells that had buffer, pH7.4, in 147mM-NaCI) containing the same been preincubated with the sugar but not with solutions at 25°C together with [3H]glucose (50 p1, fluorodinitrobenzene. In all cases except that of 5#Ci)for 10min. Thesolutionwas thenre-equilibrated propyl ,B-D-glucopyranoside, for which correction to 18°C. Efflux of glucose was measured by pipetting was made, washing was sufficient. 0.2ml of the pre-loaded cells with vigorous magnetic stirring into 100ml of exit medium (40mM-inositol, 190.5mM-NaCl, 20mM-Na2HPO4 adjusted to pH7.4 Olive oil/waterpartition coefficients with HCI) at 18°C. Then 10ml of the mixture was expelled into 30ml of ice-cold phloretin stopper at 3H-labelled sugars (about 20mg) were added to 20, 30, 40, 50, 60 and 70s and at 5min by using an centrifuge tubes containing 1 ml of water and 1 ml of automatic syringe. The amount of radioactivity at olive oil. The tubes were vigorously shaken for 2min zero.time was found by adding 20,u1 ofthe erythrocyte to form a suspension, and the suspension was suspension to 30ml ofphloretin stopper with 10ml of separated by centrifugation at 1000g, for 5min. exit medium. The 5min value gave an estimate of A portion (0.1ml) of the oil layer was carefully extracellular space. The apparatus used in this part removed and counted for radioactivity. The oil layer ofthe experiment was maintained at 18°C by working was removed and 0.1 ml of the water layer counted in a temperature-controlled room. for radioactivity. Counts were corrected for the The cell suspensions in phloretin stopper were different quenching characteristics of the two centrifuged and the pellets lysed by addition of water media. 1975 HUMAN ERYTHROCYTE SUGAR-TRANSPORT SYSTEM 421

Results dent of the presence of glucose. This sugar and the sugars with larger C-6 substituent groups do not Determination of the rate and mode ofpenetration of penetrate on the glucose carrier, but instead their substituted hexoses into erythrocytes penetration rates relate more to their lipophilicity as Sugars penetrated the membrane by two distinct measured by their oil/water partition coefficients. routes, which were respectively inhibited or not Both n-propyl fi-D-glucopyranoside and phenyl inhibited by 50mM-D-glucose. The time-course of ,8-D-glucopyranoside also penetrate the membrane penetration by some of the sugars tested in the by this alternative route. presence and absence of glucose is shown in Figs. 2(a) and 2(b), and the initial rates for all the sugars Inhibition of L-sorbose or D-glucose entry into, and tested are shown in Table 1. Penetration of 6-deoxy- D-glucose exit from, human erythrocytes by sugars D-galactose, 6-deoxy-6-iodo-D-galactose and 6-0- which do not penetrate the membrane on the glucose- methyl-D-galactose was inhibited by D-glucose, transport system indicating that they penetrate the membrane by the glucose-transport system. The rates of penetration Sugars were first tested for inhibition of L-sorbose of these sugars decrease with size of the substituent transport, in many cases under conditions in which at C-6 and it seems probable that the decrease in rate the inhibitor was predominantly on either the inside is due to steric hindrance. 6-O-n-Propyl-D-galactose or outside of the erythrocyte. The results are shown penetrates even more slowly and the rate is indepen- in Table 2. This method is incapable ofdistinguishing

100

80 00 80 to 60 -S S 60 ;~i40 11040

20 20

0 2 3 4 0 2 3 4 Time (min) Time (h)

Fig. 2. Penetration of[6-3H]galactose derivatives (a) and [3Hjgalactose derivatives (b) into human erythrocytes at 250C in the presence and absence of5OmM-D-glucose For details see the text (a) 5mM-D-fucose (6-deoxy-D-galactose) alone (0) and in the presence of D-glucose (0); 5mM-6- deoxy-6-iodo-D-galactose alone (A) and in the presence of D-glucose (A). (b) lOmM-6-0-methyl-D-galactose alone (o) and in the presence of D-glucose (0); 1OmM-6-O-propyl-D-galactose in the presence or absence of D-glucose (A); lOmM-6-0- pentyl-D-galactose in the presence or absence of D-glucose (O).

Table 1. Olive oil/waterpartition coefficients andpenetration rates ofseveral sugars into human erythrocytes at 250C For details see the text. Inhibition 103 x Partition Concn. Rate by 50mM-glucose Sugar coefficient (mM) (mM/min) (%) M 6-Deoxy-D-galactose 5 8 64 6-Deoxy-6iodo-D-galactose 5 3 59 6-0-Methyl-D-galactose 10 0.5 78 6-O-n-Propyl-D-galactose 1.6 10 0.1 0 6-O-n-Pentyl-D-galactose 5.4 10 0.6 0 6-0-Benzyl-D-galactose 2.9 10 0.4 0 n-Propyl fl-D-glucopyranoside 0.7 10 0.1 0 Phenyl fl-D-glucopyranoside 5.5 10 0.35 0 Vol. 145 422 J. E. G. BARNETT, G. D. HOLMAN, R. A. CHALKLEY AND K. A. MUNDAY

Table 2. Inhibition ofpenetration by D-glucose or L-sorbose of the human erythrocyte membrane by hexoses substituted at C-1 or C-6 which arepredominantly either inside or outside the cells For details see the text. The sugars used in these experiments penetrated the membrane relatively slowly and were predominantly on one side ofthe membrane. The modified kinetic derivation described in the Appendix has therefore been used for calculation where K. (inhibited) = Km (uninhibited) (1 +1/2K,). N.D., No detectable inhibition. Apparent inhibition constants (K,) (mM) L-Sorbose entry D-Glucose entry D-Glucose exit Sugar Outside cell Inside cell Outside cell Inside cell Inside cell 6-O-Propyl-D-glucose 17 90 N.D. 6-0-Pentyl-D-glucose* 1.1 6-0-Propyl-D-galactose 17 N.D. 24 N.D. 6-O-Pentyl-D-galactose* 1.5 5 6-0-Benzyl-D-galactose* 1.2 6 3 Propyl fl-D-glucopyranoside N.D. 9 N.D. Inhibited 20 Phenyl l-D-glucopyranoside* 6 0.5 N.D. Propyl ,8-D-galactopyranoside N.D. 90 Propan-l-ol co Pentan-I -ol 30 00 Benzyl alcohol 11 Non-competitive * These sugars penetrate the membrane significantly during the time-course of the L-sorbose entry measurement.

reciprocal plots. In this system pentan-l-ol no longer inhibited, although benzyl alcohol was still a non- competitive inhibitor. All the 6-0-alkylgalactoses were shown to be competive inhibitors (Fig. 3) when present on the outside of the cell, and their effective- ness as inhibitors increased with increasing chain length in the alkyl substituent, so that 6-0-benzyl- and 6-0-pentyl-D-galactose were very good inhibitors (Table 2). Because the rate of penetration of the 6-0-alkyl-D- galactoses is slow, particularly for 6-0-propyl-D- -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 galactose, it was possible to investigate the inhibition 1/[S] (mM-,) of transport when the inhibitor was predominantly on either the inside or the outside of the cell. It was Fig. 3. Double-reciprocalplotsfor the net entry of2-20mM- found that 6-0-benzyl- and 6-O-propyl-D-galactose D-glucose into human erythrocytes at 15°C in the presence and absence of6-O-alkyl-D-galactoses and 6-0-propyl-D-glucose were very poor inhibitors when predominantly on the inside of the cell (Fig. 4, Cells were incubated for 15s with D-glucose with or Table 2) when transport was measured by the without the inhibitor, and the entry was stopped by L-sorbose entry method. In contrast n-propyl and addition of'stopper'. D-Glucose alone, *; with lOmM-6-O- phenyl fl-D-glucopyranoside inhibited L-sorbose entry benzyl-D-galactose, o; l0mM-6-0-pentyl-D-galactose, A; when present on the inside of the very and 40mM-6-O-propyl-D-galactose, 0. cells but only poorly when present on the outside of the cells. It should be noted that whereas the propyl derivatives will remain on one side of the cell membrane during between competitive and non-competitive inhibition the course of these experiments (15min), the pene- and also uses a long preincubation time during which tration rate of the aromatic derivatives is comparable some of the more lipophilic sugars seemed to cause with the incubation time. By using 6-0-propyl-D- non-specific inhibition. Table 2 shows that both galactose and n-propyl 6-D-glucopyranoside these pentan-1-ol and benzyl alcohol, although not results were confirmed with the D-glucose net entry propan-1-ol, also inhibit this system. Therefore the method. sugars were also tested for inhibition of entry by a To confirm and quantify the inhibition at the inner rapid net D-glucose entry method in which the nature face, the D-glucose-exit method ofKarlish etal. (1972) of the inhibition could be deternined from double- was used. Fig. 5 shows the rates of exit of D-glucoSe 1975 HUMAN ERYTHROCYTE SUGAR-TRANSPORT SYSTEM 423

bo is ._g60 00 co~0.4- 00 ~0.3-

0.2- 0 10 20 30 40 50 60 70 Time (s) 0.1I Fig. 5. Exit of D-[3Hjglucose from human erythrocytes pre-loaded with 80mM-D-glucose into an 'infinite' volume of iso-osmotic saline in the presence ofsubstitutedglucoses or 0 2 4 6 8 10 malonamide Time (min) For details see the text. o, 40mM-Malonamide; A, 40mM- Fig. 4. Inhibition ofL-sorbose entry into human erythrocytes propyl f,-D-glucopyranoside; *, 40mM-6-0-propyl-D- at 250C in thepresence andabsence ofD-glucose derivatives glucose. predominantly inside or outside the cells For details see the text. Penetration of L-sorbose in the absence ofadded sugar, 0; in thepresence of 10mM-propyl fi-D-glucopyranoside outside the cells, 0; or on both sides (equilibrated), o; in the presence of l5mM-6-O-propyl-D- benzene for 1 hat 250C, gave an inactivation of23% in glucose outside the cells, A; or only inside the cells, L. the absence of glucose and 36% in its presence. The SO, Sorbose concentration outside the cell at time zero or stimulation phenomenon is saturable, so that by inside the cell at equilibrium; St sorbose concentration plotting the reciprocal oftheincrement in inactivation inside the cell at time t. against the reciprocal of the sugar concentration a straight line is obtained and an apparent K, value can be calculated. This was done only for D-glucose, when in the presence of propyl a value of 5mM was obtained. In all other cases a f,-D-glucopyranoside, concentration the was 6-O-propyl-D-glucose, or malonamide. Propyl 46-D- high (40mM) of sugar used and glucopyranoside was an effective inhibitor of glucose the percentage increase in the fluorodinitrobenzene- exit, whereas 6-O-propyl-D-glucose was not. In our inactivation measured. Many of the sugars protected hands, the derived Km value for D-glucose in the against inactivation, as shown by the negative sign. presence and absence of inhibitor was subject to a The results are shown in Table 3. large standard error primarily owing to the obligatory use of an integrated rate equation for the determina- Discussion tion of kinetic constants, but the inhibition appeared to be competitive in that Km rather than Vwas altered, The structural requirements of sugars for binding and the inhibition constant, KL, was about 20mM, to the human erythrocyte sugar-transport system which correlated well with that found by the L-sorbose have been given recently by two groups of workers. method. Kahlenberg & Dolansky (1972) measured the relative inhibition of the binding of D-glucose compared with inhibition of the binding of L-glucose to isolated Inactivation of the transport system by fluorodinitro- erythrocyte membrane fragments, whereas Barnett benzene in the presence ofsubstituted hexoses et al. (1973a) measured the inhibition of L-sorbose A preliminary experiment was carried out by using entry into intact cells. Both methods measure the different concentrations of fluorodinitrobenzene and sum of the binding at the two sides of the membrane different times of incubation in the presence and ab- and the models produced are in good agreement sence of 20mM-D-glucose in order to find conditions except for the suggestion of a lipophilic binding giving a good stimulation of inactivation. The region close to C-6 in the intact membrane not increment in inactivation in the presence of sugar present in the membrane fragments. The increase in appeared to be fairly constant with increasing per- affinity of the 6-O-alkyl-D-galactose derivatives with centage inhibition with concentrations between 1 the lipophilicity of the substituent group appears to and 4mm-fluorodinitrobenzene and times of 15min confirm the presence of such an area on the outside to 1 h. The conditions chosen, 2mM-fluorodinitro- surface of the cell (Table 2). Vol. 145 424 J. E. G. BARNETT, G. D. HOLMAN, R. A. CHALKLEY AND K. A. MUNDAY

Table 3. Effect ofthepresence ofsubstituted hexoses on the extent offluiorodinitrobenzene inactivation ofthe sugar-transport system in the human erythrocyte Cells were preincubated with 2mM-fluorodinitrobenzene in the presence and absence of40mM-sugar for 1 h at 25'C and the percentage inactivation was measured by the L-sorbose entry method. % inactivation in the presence of sugar minus Binds to transport sys- Sugar % inactivation in its absence Transported tem inside or outside cell D-Glucose 14.8 ±0.3 Yes Both 1-Deoxy-D-glucose 12.4±0.2 Yes Both 3-Deoxy-D-glucose 7.2±1.1 Yes Both D-Galactose -0.9±0.4 Yes Both 6-Deoxy-D-galactose -5.6±0.1 Yes Both 6-Deoxy-D-glucose -2.3±0.4 Yes Both 6-Deoxy-6-fluoro-D-galactose -8.5±0.2 4,6-0-Ethylidene-D-glucose -10.6±0.4 No Outside 6-0-Propyl-D-galactose -12.6±0.4 No Outside 6-O-Propyl-D-galactose (80mM) -23.0±0.6 No Outside Propyl f-D-glucopyranoside (20mM) 12.5±1.4 No Inside Phloretin* Protects Both Phlorrhizin* Activates No Inside Methyl a-D-glucopyranoside* Activates No Maltose Protects No Outside Cellobiose* Protects No Outside 2-Deoxy-D-glucose* Activates Yes Both * Data from Krupka (1972), concentration variable.

Further investigation of the O-alkylgalactoses some inhibition when present primarily on the inside showed that only 6-0-methyl-D-galactose penetrates ofthe cell (Table 2), but this is far less than that found the membrane by the glucose-transport system when the sugar is present on the outside. The binding (Table 1). The rates of transport of the higher homo- of inhibitors to the transport system is therefore logues were roughly proportional to their oil/water asymmetric, as indicated by Baker & Widdas partition coefficients and were uninhibited by (1973b). D-glucose, although the sugars were competitive Sugars substituted at C-1, the propyl and phenyl inhibitors ofD-glucose entry (Fig. 3). These sugars are f6-D-glucopyranosides, also penetrate the membrane thereforecomparablewith4,6-O-ethylidene-D-glucose by some route other than the sugar-transport system (Baker & Widdas, 1973a), which also penetrates the because their penetration is not inhibited by D- membrane by an alternative route, and maltose, glucose (Table 1). These sugars were also tested for which also inhibits the glucose-transport system, but inhibition on the two sides of the cell membrane. In does not penetrate the cell membrane (Chen & contrast with the 6-0-alkyl sugars, it was found that LeFevre, 1965; Lacko & Burger, 1962). they inhibit only when present at the inner face of the Baker & Widdas (1973b) have used the relatively cell. By using n-propyl fi-D-glucopyranoside it was slow penetration of 4,6-0-ethylidene-D-glucose to shown that the inhibition of D-glucose exit (Fig. 5) measure the apparent affinity of the sugar for the was probably competitive. transport system on the two sides of the cell. They It therefore appears that the asymmetry of the found that althoughthis sugar was a good inhibitor of sugar-transport system is such that hexose derivatives D-glucose exit when present on the outside ofthe cell, with large substituent groups at C4 or C-6 can bind it was not an effective inhibitor when present on the to the system on the outside of the cell, but not on the inside of the cell. The same behaviour is apparent with inside, whereas sugars with large substituents at C-1 the non-penetrating 6-0-alkyl-D-galactoses and 6-0- can bind only on the inside and not at the outer face. propyl-D-glucose. The 6-0-propylhexoses inhibit only Large substituents at either end of the sugar molecule when present on theoutside ofthecell. Thesesugarsdo will prevent transport. A model consistent with these not appear to interfere with the transport system non- observations is shown in Fig. 6. specifically and penetrate the membrane slowly. The When entering the cell the sugar first binds to a higher alkyl derivatives, which may exhibit some site on the outside of the membrane by using binding non-specific inhibition of the transport system, show groups in the C-1 region of the molecule. Then part 1975 HUMAN ERYTHROCYTE SUGAR-TRANSPORT SYSTEM 425

We sought further confirmation of the proposed model by studying the fluorodinitrobenzene inacti- vationofthetransportsysteminthepresenceofseveral substituted hexoses. Since the original observation that the presence of D-glucose stimulated rather than protected against inactivation (Bowyer & Widdas, 1958), the inactivation has been extensively studied (Shimmin & Stein, 1970; Krupka, t971, 1972; Edwards, 1973) and several authors have suggested that the behaviour is caused by the ability of the Fig. 6. Possible model for sugar transport in the human membrane to exist in more than one conformational erythrocyte state. 6O-Propyl-D-glucose (R = C3H7; R' = H) can bind to the Themost extensive studies ofthe phenomenon have transport system in conformation A, but cannot be trans- been by Krupka (1971, 1972). He showed that most ported for steric reasons. Similarly, propyl #-D-gluco- sugars stimulated the inactivation, although by pyranoside (R= H; R' = C3H7) can bind to conformation and B but cannot be transported. D-Glucose can bind to both different amounts. Maltose, cellobiose phloretin, conformations, and if the transport site changes con- all competitive inhibitors of the glucose-transport formation from form A to form B, iseffectively transported system, protected against inactivation by fluoro- from outside to inside. There is some evidence that a dinitrobenzene. The glucoside of phloretin, phlor- hydrogen bond is formed between the C4 hydroxyl group rhizin, which has been shown (Lepke & Passow, 1973) of D-glucose and the transport protein only in conform- to inhibit D-xylose transport in erythrocyte 'ghosts' ation B. Only some of the probable hydrogen bonds are more strongly when on the inside of the membrane, shown. was a stimulator. By studying the combined effects of maltose, a protector, and 2-deoxy-D-glucose, an activator, Krupka (1972) showed that both actions of the membrane protein rearranges to give a second were by formation of a 1:1 complex between the stable conformation around the binding site thus sugar and the sugar-transport system. Baker & exposing the sugar to the inner solution. In this Widdas (1973a) have shown that 4,6-0-ethylidene-D- conformation it is the C4 and C-6 regions ofthe sugar glucose also protects the sugar-transport system that are involved in binding. Rearrangement is against fluorodinitrobenzene inactivation. prevented by a bulky group. This model would Table 3 shows that the ability to potentiate or explain the observed apparent asymmetry of the protect against fluorodinitrobenzene inactivation transport system (cf. Baker & Widdas, 1973b) because does not correlate with the ability to transport the the hydrogen bonds between sugar and membrane sugar. Instead, if non-transported sugars alone are protein will probably be different in the two confor- considered there is a direct correlation of protection mations, as will other non-bonding interactions. It is with binding on the outside ofthe cell and activation in effect a case of the theoretical allosteric model of with binding on the inside. Under the conditions Vidaver (1966), who showed that a conformational used 80mM-6-O-propyl-D-galactose completely pro- alteration in the transport barrier could give the same tectedagainstinactivation.Theseobservations suggest kinetics as a mobile carrier. A similar conformational that the fluorodinitrobenzene, which rapidly pene- 'flip' between two hydrogen-bonded conformations trates the membrane and is therefore present on occurs between the two stable forms ofhaemoglobin. both sides, may act only on the 'inner facing' form The structural requirements for binding to the of the transport system (conformation B, Fig. 6) but sugar-transport system given by both Kahlenberg & not necessarily close to the sugar-binding site. Non- Dolansky (1972) and Barnett et al. (1973a) must be transported compounds which stabilize this form, reinterpreted if an asymmetric model similar to that such as propyl ,B-D-glucopyranoside, phlorrhizin and described here is correct. Both groups of workers possibly methyl x-D-glucopyranoside, cause the used methods that could not distinguish between reactive residue to be exposed and therefore poten- binding on the inner or outer surface of the cell. The tiate inactivation by fluorodinitrobenzene. In con- methyl a- and fl-D-glucopyranosides were inhibitors trast, non-transported sugars which bind to the form of D-glucose binding to membrane fragments of the membrane that binds sugars at the outer (Kahlenberg & Dolansky, 1972), although neither surface will stabilize this form of the transport sugar is transported or is an inhibitor on the outside system and decrease the rate of inactivation. It is of the erythrocyte. Therefore the significant amount difficult to predict which form of the carrier a of inhibition observed could be attributed to inhibi- transported sugar will expose, because this will tion of glucose binding at the inner surface of the depend on the relative dissociation constants on the fragments. two faces of the membrane, the ratios of the rate Vol. 145 426 J. E. G. BARNETT, G. D. HOLMAN, R. A. CHALKLEY AND K. A. MUNDAY for 'translocation' of the 'loaded carrier' to that of tially with the 'outer facing' form of the transport the 'unloaded carrier' (Levine & Stein, 1966), the system. ratio of the rate of association of the sugar with the Together with the inhibition data described above transport system to both of these rates, and the type the experiments with alkylating agents appear to of experiment used. However, in the experimental confirm the asymmetry of the human erythrocyte situation used here, in which the sugar is allowed to sugar-transport system. equilibrate across the membrane, and extending the principle that the conformation binding sugars at the inner face is reactive towards fluorodinitrobenzene, those sugars which potentiate the fluorodinitro- References benzene inactivation should have a relatively high Baker, G. F. & Widdas, W. F. (1973a) J. Physiol. (London) affinity for the inner face of the membrane, whereas 231, 129-142 those which protect should have a relatively high Baker, G. F. & Widdas, W. F. (1973b) J. Physiol. (London) affinity for the outer surface. Inspection of Table 3 231, 143-165 shows that this correlates very well with the model in Barnett, J. E. G., Holman, G. D. & Munday, K. A. (1973a) Fig. 6. Sugars with alterations from the D-glucose Biochem. J. 131, 211-221 Barnett, J. E. G., Holman, G. D. & Munday, K. A. (1973b) structure near to C4 and C-6 which project out into Biochem. J. 135, 537-541 the solution on the outside of the cell would be Bamett, J. E. G., Holman, G. D. & Munday, K. A. (1973c) expected to have little effect on binding to the outer Biochem. Soc. Trans. 1, 1314-1316 membrane, but a significant effect on binding to the Bloch, R. (1974) J. Biol. Chem. 249, 1814-1822 inner membrane, where they would be in contact Bowyer, F. & Widdas, W. F. (1958) J. Physiol. (London) with the transport-system protein. They should 141, 219-232 therefore stabilize the form of the system that binds Chen, L. & LeFevre, P. G. (1965) Fed. Proc. Fed. Amer. sugars at the outer face (conformation A, Fig. 6) and Soc. Exp. Biol. 24,465 converse true for modified Corbett, W. M. & McKay, J. E. (1961) J. Chem. Soc. protect. The is sugars London 2930-2935 near C-1, which would stabilize the form binding Edwards, P. A. W. (1973) Biochim. Biophys. Acta 307, sugars on the inner surface (conformation B, Fig. 6) 415-418 and therefore activate. Godman, J. C., Horton, D. & Nakadate, M. (1968) The apparently anomalous observation by Carbohyd. Res. 7, 56-65 Edwards (1973), that 120mM-glucose on the inside of Kahlenberg, A. & Dolansky, D. (1972) Can. J. Biochem. the cells protects the system against fluorodinitro- 50, 638-643 benzene inactivation whereas the same concentration Karlish, S. J. D., Lieb, W. R., Ram, D. & Stein, W. D. outside the cell potentiates inactivation, can be (1972) Biochim. Biophys. Acta 255, 126-132 Kruger, D. & Roman, W. (1936) Chem. Ber. 69, 1830- reconciled with this model if one considers the 1834 different experimental conditions used. The inactiva- Krupka, R. M. (1971) Biochemistry 10, 1143-1153 tion proceeded during transport of the glucose under Krupka, R. M. (1972) Biochim. Biophys. Acta 282, conditions which approximated to a 'zero-trans' exit 326-336 procedure and with a very rapid fluorodinitrobenzene Lacko, L. & Burger, M. (1962) Biochem. J. 83, 622-625 inactivation over a short time-course. Because the LeFevre, P. G. (1961) Pharmacol. Rev. 13, 39-70 rate of'translocation' ofthe 'loaded carrier' is greater Lepke, S. & Passow, H. (1973) Biochim. Biophys. Acta 298, than that of the 'unloaded carrier', glucose on the 529-533 inside of the may lead to an increase in Levine, M. & Stein, W. D. (1966) Biochim. Biophys. Acta cell actually 127, 179-193 the concentration of the form of the transport system Levine, M., Levine, S. & Jones, M. N. (1971) Biochim. (conformation A, Fig. 6) that binds sugars at the Biophys. Acta 225, 291-300 outer surface, that is, should lead to protection of the Raymond, A. L. & Schroeder, E. F. (1948)J. Amer. Chem. transport system againstfluorodinitrobenzene inactiv- Soc. 70, 2785-2791 ation. This explanation of this result was also sug- Sen, A. K. & Widdas, W. F. (1962) J. Physiol. (London) gested by Edwards (1973). 160, 392-403 Bloch (1974) has shown that sodium tetrathionate Shimmin, E. R. A. & Stein, W. D. (1970) Biochim. Biophys. inactivates sugar transport in the erythrocyte in a Acta 211, 308-312 Stein, W. D. (1967) The Movement of Molecules across rather similar way to fluorodinitrobenzene. However, Cell Membranes, pp. 152-158, Academic Press, London D-glucose protects against the inactivation, whereas and New York maltose potentiates theinactivation. It seems possible, Timmell, T. E. (1964) Can. J. Chem. 42, 1456-1472 therefore, that sodium tetrathionate reacts preferen- Vidaver, G. A. (1966) J. Theor. Biol. 10, 301-306

1975 HUMAN ERYTHROCYTE SUGAR-TRANSPORT SYSTEM 427

APPENDIX Derivation of the Kinetic Parameters for an Asymmetric Carrier with Non-penetrating Inhibitors

This Appendix describes the theoretical basis of inhibitor in mol/litre, S. and Si are the respective the methods used in the precedingpaper. The existing concentrations of L-sorbose outside and inside the theoretical treatments of the experimental methods cell at time t. It is assumed that the concentration of required adapting to take account of the asymmetry L-sorbose outside the cells does not alter with time of the transport system and the non-penetration of so that SO is constant. CO, C1 represent the concen- the inhibitors used. To relate to the theoretical treat- trations of free carrier and CSO, CS,, the concen- ments from which they have been adapted, the proofs trations of carrier loaded with L-sorbose. CI4 is assume a 'carrier' model for transport. The model the concentration of carrier loaded with inhibitor. used in the paper to explain the results, in which The rate constants are as shown in Scheme 1, and transport is effected by a conformational change in the ratio of the rate of translocation of loaded to the membrane protein, leads to identical kinetics (see unloaded carrier is r, k÷2/k+4, in the forward direc- Vidaver, 1966) and each concept has a direct analogy. tion and r', kL2/k_4, in the reverse direction. We For instance the ratio of the rates of translocation of therefore have the following dissociation constalnts loaded/unloaded carrier (r) becomes the ratio of the if it is assumed that k+1, k-, are much greater than rate of conformational change of the transport k+2, k+4 etc: protein in the loaded and unloaded states. C,*Si CO50c K o*I Ks = ; K CoSo; Ki = (1) (A) Measurement of inhibition constants by the Cs,1' cs0' a0ci penetration ofL-sorbose The total concentration of carrier is always: This treatment is closely adapted from the kinetic treatment of Levine et al. (1971), who assumed Total C= C1+Co+ CS,+CSo+ CIo (2) complete equilibration of the inhibitory sugar and that the affinity of the inhibitor for the transport site Substituting: was much greater than that of L-sorbose. They also assumed a symmetrical carrier. The present kinetics Total C = C, 1 + -]+ CO 1++K A I (3) will assume that the inhibitor is present only on the outside of the membrane, that the transport system is The rate of entry L-sorbose is: asymmetric, and that the affinity of the inhibitor for of the transport system is much greater than that of dt = k+2CSo-k2CSI L-sorbose. This is summarized symbolically in Scheme dt 1. The rate of entry of L-[14C]sorbose is determined in the presence and absence ofinhibitor. or substituting from eqn. (1): The subscripts o and i represent the outside and inside of the cells, t is the time in min, I. is the k+2Co*So k 2Ci*Si concentration ofthe strongly bindingnon-penetrating K* Ks (4)

k+j k+2 k+3 C S.+ C, 5 ' Cs, I CS, I C + S, L k-2 k-3 k-I I

k+4

k45 10+ Co CI, K,=k-s/k+s k-s Scheme 1. Rate ofentry ofL-sorbose in thepresence and absence ofinhibitors For details of subscripts and terminology see the text, Vol. 145 428 J. E. G. BARNETT, G. D. HOLMAN, R. A. CHALKLEY AND K. A. MUNDAY

At any steady state, the total carrier moving in each and substituting for D: direction must be equal, therefore: dS, Total C k S0- S] (13) kL2CSI +kL4C, = k+2CSO + k+4Co dt 2K*k+ Io or substituting from eqn. (1): [- 2K,_] When 10= 0: k-2- +k4Ci = k+2 , k+4Co (5) Ks K~~~~~~~sK dS, Total C (14) Dividing out: dt 2K *+(S-, Integrating and substituting Vfor Total C k+2/2: = Cl [1 +k-*R Co0 [1+k+42K*-4k4K (6) In so-=S_ + (15) or SO-Si K*(1+Iol2K,) An identical solution is obtained if the non-penetrat- C1 [1 +r']Si = Co[ +r *] (7) ing inhibitor is on the inside ofthe cell, or ifthe system is symmetrical. Solving eqns. (3) and (7) for CO or C,: (B) Measurement ofinhibition constants by D-glucose C= Total C [1+ r' Ss/D (8) entry under conditions in which the internal concentration ofglucose is effectively zero C, = Total C[1+ rS]/D (9) The theoretical treatment is based on that of Stein (1967). The symbols are identical with those used where above and the model used is shown in Scheme 1. The initial rates of entry of D-glucose into cells were D= 1+ S 1+r-so + 1+ -o+ Io 1 +r'-] measured under conditions in which the internal concentration of glucose could be neglected. It is Substituting for CO and C, in eqn. (4): assumed that the transport system is asymmetric and that the inhibitor is present only on the outside of the dS, cells. The general equation for entry of a sugar in the dt presence of a non-penetrating external inhibitor is Total C{[k+2 S (k+r' ) -2[L S (1s+r5)]} given by eqn. (10) above. dS, (10) dt Total C (1+r'5) This is a general equation for the entry of sugar into [k+2i o25 cells in the presence of an external, non-penetrating, competitive inhibitor. (10) But under the experimental conditions used K*, where D has the same value as above: KS > K, and Si/Ko and So/K*< Io/K, or 1. Therefore D simplifies to [2+IO/K,] neglecting all D= 1 Si so S! terms in S5/K, or So/KR. ) I+rK + (1s+K*KIo1 +r' Again neglecting terms in So/K* and SiIK,: Whentheinternal concentration ofsubstrateis zero, Total C k-2 Si = 0, this simplifies to: dS, k+2 (11) dt D *KSO-- S d-i = Total Ck+-2 So (16) But at equilibrium dSI/dt = 0 and S. = S,; therefore dt k* I +r so,°+1+ S.1*+ ° substituting in eqn. (11): K, KS K, k+2 =k2 Total Ck+2 SO KS* Ks (17) 2K* (1+ r)So I0 and so eqn. (11) simplifies to: \s 2K* 2K,, Total dSi = C.k+2 (12) Let dS, = and Total C k+2 =V 1975 HUMAN ERYTHROCYTE SUGAR-TRANSPORT SYSTEM 429

1 lK* Io (1+r)S0 (18) (B) and eqn. (19) holds in which K' is replaced by K. u VS [ 2K1 2 Ks ] and r by r' and v by -dSIfdt. However, the integrated form of the equation must be used experimentally. ( I 2(1+r)l (19) This is: =*V 2KJIo So 2 V -V (1 IO S°+ ) (20) The solution is identical in a symmetrical system, t=Ks 2Kg) InnS 2 (SO-St) and in both cases when IO =0. where SO is the internal concentration at time 0 and St' 1 K1 (l+r)l the internal concentration at time t. Corrections have V V SO 2V to be made for volume changes in the cell and these Plotting 1/v against 1/s the x intercepts for the inhibi- were identical with those ofKarlish etal. (1972). In the ted and uninhibited systems are respectively: absence of inhibitor, I. = 0 and eqn. (20) simplifies to the equation used by these authors. 1+r 1 1+r 2Ks* /I S \-and -___2K, \ 2K,/ References Karlish, S. J. D., Lieb, W. R., Ram, D. & Stein, W. D. (C) Measurement ofinhibition constants by D-glucose (1972) Biochim. Biophys. Acta 255, 126-132 exit under conditions in which the external concentra- Levine, M., Levine, S. & Jones, M. N. (1971) Biochim. is zero Biophys. Acta 225, 291-300 tion ofglucose effectively Stein, W. D. (1967) The Movement ofMolecules across Cell In this method the non-penetrating inhibitor is on Membranes, pp. 152-158, Academic Press, London and the inside of the cell, as is the substrate, and so the New York assumptions and equations are identical with those in Vidaver, G. A. (1966) J. Theor. Biol. 10, 301-306

Vol. 145