Advantages and limitations of vesicles for the characterization and the kinetic analysis of transport systems.

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ADVANTAGES AND LIMITATIONS OF VESICLES

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[26] A d v a n t a g e s a n d L i m i t a t i o n s o f V e s i c l e s f o r t h e Characterization and the Kinetic Analysis of Transport Systems

By A. BERTELOOTand G. SEMENZA Following Kaback's pioneer work, ~ it has become more and more common to use closed and functional membrane vesicles for the study of membrane transport processes? In the particular case of intestinal and renal epithelia to which this chapter will be limited, there is no doubt that the successful development of transporting membrane vesicles3,4 was a decisive analytical methodological advance which has since been used in many laboratories and has resulted in a vast increase in our knowledge as to the characteristics of various transport systems. In this chapter we will first present the methodologies involved in both the preparation of functional brush border membrane vesicles and the determination of transport activities. We will next endeavor to discuss the advantages and limitations in the use of vesicles for investigating transport systems, as well as the special problems encountered in kinetic studies. The discussion will be limited to our own experience which is confined almost solely to vesicles from intestinal and renal brush border membranes. It should be emphasized, however, that many of the considerations to follow are likely to hold true for most, if not all, kinds of membrane vesicles. Finally, the interested~' reader is also referred to previous reviews on similar topics for broader coverage and/or different views of particular aspects?-~4

H. R. Kaback, Fed. Proc., Fed. Am. Soc. Exp. Biol. 19, 130 (1960). 2 j. E. Lever, Crit. Rev. Biochem. 7, 187 (1980). 3 U. Hopfer, K. Nelson, J. Perrotto, and K. J. Isselbacher, J. Biol. Chem. 248, 25 (1973). 4 A. G. Booth and A. J. Kenny, Biochem. J. 142, 575 (1974). 5 U. Hopfer, Am. J. Physiol. 233, E445 (1977). 6 B. Sacktor, Curr. Top. Bioenerg. 6, 39 (1977). 7 U. Hopfer, Am. J. Physiol. 234, F89 (1978). s H. Muter and R. Kinne, J. Membr. Biol. 55, 81 (1980). 9 p. S. Aronson, Am. J. Physiol. 240, F1 (1981). ~op. S. Aronson and J. L. Kinsella, Fed. Proc., Fed. Am. Soc. Exp. Biol. 40, 2213 (1981). l~ R. J. Turner, J. Membr. Biol. 76, 1 (1983). ~2G. Semenza, M. Kessler, M. Hosang, J. Weber, and U. Schmidt, Biochim. Biophys. Acta 779, 343 (1984). ~3H. Murer, J. Biber, P. Gmaj, and B. Stieger, Mol. Physiol. 6, 55 (1984). 14 H. Muter and P. Gmaj, Kidneylnt. 30, 171 (1986).

METHODS IN ENZYMOLOGY, VOL. 192

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Preparation of Functional Brush Border M e m b r a n e Vesicles The first procedure described was based on the use of EDTA, 3 as originally introduced by Eichholz and Crane, 15for the isolation of the total brush border. In "second generation" vesicles, advantage is taken of the differential precipitation of intracellular and basolateral membranes with Ca 2+ or Mg2+.16 Brush border membrane vesicles prepared via either Ca 2+ or Mg2+ precipitation have been compared by various authors./7-2° Using rabbit small intestine, Hauser et al. 2~ first reported that Mg 2+ is preferred to Ca 2+ due to the activation of brush border membrane phospholipase A, which degrades endogenous phosphoglyceddes to lysophosphoacylglycerols. However, as discussed by these authors, the possibility that phospholipase activation followed membrane disintegration during lipid extraction could not be ignored.2~ More recent studies suggest that phospholipase activation could occur during freezing and thawing of the intestinal tissue prior to membrane isolation and support the view that Ca2+-prepared membranes are less contaminated by basolateral membranes than are Mg2+-prepared membranes. 2° When assayed on rat intestinal scrapings, phospholipasc A activity was found to be higher as compared to isolated cells and higher in the presence of EGTA as compared to Ca2+.22 The source of enzyme activity was not identified in this study, but activity of both pancreatic and intestinal origin seemed compatible with the data. 22 In this context, it should also be mentioned that guinea pig intestinal phospholipasc was not found to be activated by Ca2+,23 and that lysosomal phospholipases do not require Ca 2+ for activity,u Morphological differences also exist between C~2+- versus Mg2+-pre pared vesicles. Freeze-fracture electron microscopy has shown that the distribution and area density of intramembrane particles on the P face of replicas of brush border vesicles prepared with Ca 2÷ resembled that seen in replicas of intact microvilli. ~9 However, when prepared with Mg2+ and either Ca 2+ or Mg2+ in the presence of KSCN, the P faces showed striking i~ A. Eichholz and R. K. Crane, J. CellBiol. 26, 687 (1965). ~6j. Schmitz, H. Preiser, D. Maestracci, B. K. Ghosh, J. J. Cerda, and R. K. Crane, Biochim. Biophys. Acta 323, 98 (1973). t7 K. Verner and A. Bretcher, Fur. J. CelIBiol. 29, 187 (1983). ta I. Sabolie and G. Burekhardt, Biochim. Biophys. Acta 772, 140 (1984). t9 D. J. Bjorkman, C. H. Allan, S. J. Hagen, and J. S. Trier, Gastroenterology91, 1401 (1986). 2o H. Aubry, A. R. Merrill, and P. Proulx, Biochim. Biophys. Acta 856, 610 (1986). 2~ H. Hauser, K. Howell, R. M. C. Dawson, and D. E. Bowyer, Biochim. Biophys. Acta 602, 567 (1980). 22 j. R. F. Waiters, P. J. Horvath, and M. M. Weiser, Gastroenterology 91, 34 (1986). 23 A. Diagne, S. Mitjavila, J. Fauvel, H. Chap, and L. Douste-Blazy, Lipids 22, 33 (1987). H. Van Den Bosch, Biochim. Biophys. Acta 604, 191 (1980).

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aggregation of intramembrane particles and large membrane domains devoid of intramembrane particles. ~9 Both clustering of membrane proteins induced by Mg2+ precipitation25 in addition to selective loss of membrane proteins and/or cytoskeletal core proteins ~9 in the presence of Mg2+ are compatible with these results, but the functional correlates of the morphological differences among various brush border preparations still need to be defined. Whether the reduced leak permeabilities of Mg2+- versus Ca 2+prepared vesicles as reported for kidney brush border membranes TM is a consequence of intramembrane particle aggregation would be interesting to consider. For transport studies, it would thus appear difficult at this time to recommend either one or the other of these precipitation methods since both, although still subject to considerable empiricism, have proved valuable in different laboratories. It would, however, seem more advisable, at a time when the biochemical characterization of membrane components is being attempted, to use Mg2+, rather than Ca 2+, as the precipitating cation. In fact, Mg2+ does not activate (1) brush border Ca2+-dependent proteases, (2) Ca2+-dependent transglutaminasc, or (3) Ca2+-dependent phospholipase A. The former two enzyme activities may produce artifactual bands in SDS-PAGE, the last one leads to vesicles containing an artifactually high percentage of lysophospholipids2~ (but see Refs. 20, 22, and 23). Most of the points to be considered in preparing brush border membrane vesicles have already been discussed in former reviews, n-~4 The procedure which we describe below is based on a version26 of the Schmitz et al. method? 6 In addition to using Mg2+, rather than Ca 2+, a number of minor modifications have been introduced which have proved of value in the laboratory of one of the authors (G.S.) for the 15 or so years that brush border membrane vesicles have been prepared for both research and teaching. Perhaps the most important addition has been the final gel filtration through Sepharose 4B, 2vwhich doubles the specific activity of brush border marker enzymes and vastly improves the stability of the vesicles. If vesicles are to be prepared from fresh material, small intestines are removed as soon as possible after sacrifice, rinsed with ice-cold saline, slit lengthwise, and freed of mucus by patting with gross paper towels (NOT with Kleenex!). The mucosa is collected by scraping the lumenal surface firmly with glass slides. The material is either used immediately, or collected and mixed well before freezing by dropping aliquots directly into 25M. W. Riglcr, G. C. Ferreira, and J. S. Patton, Biochim. Biophys. Acta 816, 131 (1985). 26M. Kessler, O. Acuto, C. Storelli, H. Murk, M. Muller, and G. Semenza, Biochim. Biophys. dcta 506, 136 (1978). 2~j. Carlsen, K. Cdstiansen, and B. Bro, Biochim. Biophys. Acta 727, 412 (1983).

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liquid nitrogen. The pea-sized bits are stored in tightly closed plastic bottles at - 8 0 ° for up to 2 months. On the day of use, aliquots are thawed in 300 m M mannitol, 5 m M EGTA, 10 m M T d s - H O , pH 7.1 buffer (30 ml/ g tissue). The total volume is increased t o 1 liter with the same buffer before homogenizing. The steps which follow are identical to those described for the preparation starting from frozen intestine (next paragraph). In fact, brush border vesicles of nearly equal quality can be prepared from frozen intestine, the only condition being that small intestine be collected, rinsed, and frozen as fast as possible. However, at least for one species, the rat, it has proved impossible to obtain transporting vesicles from frozen tissue. Small intestines are rinsed, slit, and freed of mucus as described in the previous paragraph. Instead of scraping, the entire intestine is frozen in dry ice and stored at - 8 0 o for up to a few months. At the day of use, aliquots of the frozen tissue are chopped into small pieces and thawed in 300 m M mannitol, 5 m M EGTA, l0 m M Tris-HCl, pH 7.1 buffer (3 ml/g tissue). During the thawing, the temperature of the mixture should not exceed 4 °. Mucosal cells are removed from the underlying connective tissue by the shearing forces of a vibrator (e.g., Vibromixer; Chemap AG, Mannedorf, Switzerland) and filtered through a Biichner funnel. The filtrate is diluted to a volume of 15 ml/g of original intestine with the same buffer and homogenized for 2 rain at full speed in a Waring blender (e.g., Ato-mix; MSE, Crawley, Great Britain). To the homogenate originating from either frozen or fresh tissue is added concentrated MgCI2 to reach a final concentration of l0 m M which precipitates nonbrush border membranes. After centrifugation at 3000 g for 15 min, the brush border membranes are pelleted from the superuatant at 27,000 g for 30 min. The pellet is resuspended in an appropriate amount of the buffer required for the experiment, thoroughly mixed to homogeneity by five passages with a Teflon Potter-Elvehjem homogenizer (e.g., Dyna-mix; Fisher Scientific Co., Ziirich, Switzerland), and can be used at once for transport measurement. Alternatively, the pellet is resuspended and homogenized in 150 m M KC1, 50 m M Tris-HC1 pH 7.4 buffer, or any other suitable high ionic strength buffer (approximately 1 ml butler/4.5 nag membrane protein). The resulting mixture is then chromatographed at 4 ° on Sepharose 4B2~ in the same buffer. The length of the column is always 15 cm but its diameter varies with the sample volume to maintain a constant ratio of 1 ml sample/30 ml settled gel (flow rate, 2.5 ml/hr/cm2 of cross-sectional area). The brush border membrane vesicles are recovered in the unretarded volume, are spun down at 30,000 g for 30 rain, and washed three times in 300 m M mannitol, l0 m M HEPES-Tris, pH 7.0, or TrisHC1, pH 7.4, or any other suitable buffer. The Sepharose column is regenerated by removing the retarded soluble proteins with l0 m M Tris-HC1, pH 7.4.

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The brush border membrane vesicles are stored in liquid nitrogen (1 ml of the mannitol-containing buffer described above/20-45 nag protein) for months without detectable decrease of transport activity. Shortly before use, the vesicles are carefully thawed, kept on ice, and washed with the buffer required for the planned experiment. The volumes indicated above have been optimized with the aim of allowing the preparation of as many vesicles as possible in one run, thereby saving both time and material, and providing vesicles from the same batch to be used on different days or even weeks with reproducible results. For preparing vesicles from renal brush border membranes, we use essentially Booth and Kenny's procedure,4 with a few minor modifications, as described above. If we wish to differentiate between proximal and distal parts of the renal proximal tubules, we follow Turner and Moran's method.2s Transport

Measurements

Both optical and radiotracer techniques are available for quantitation of solute transport in brush border membrane vesicles. 2,11-14 When compared, the optical methods would appear to present significant advantages: (1) fast and continuous recording of transport events, (2) high time resolution since slow mixing and separation methods are avoided, and (3) low running costs. Unfortunately, they are also associated with a number of disadvantages which have so far precluded general utilization: (1) available dyes are still rather limited and one must use indirect techniques based on membrane potential or volume determinations, which are thus limited to electrogenic and high flux transport systems; (2) mechanisms of dye responses are not always well understood and can be influenced by numerous factors such as membrane charges, pH, and ionic strength29-a2; (3) some of the fluorescent dyes must be loaded inside the vesicles and then extracellular probe removed before transport measurement33; (4) with intravesicularly loaded dyes, efllux over time will decrease signal-to-noise (S/N) ratios with time3a; and (5) for absolute activities to be measured, the dye response must be calibrated. 29 These should not discourage the reader from attempting to use such techniques and it is more than likely that

2s R. J. Turner and A. Moran, Am. J. Physiol. 242, F406 (1982). 29 A. S. Verkman, J. Bioenerg. Biomembr. 19, 481 (1987). 3o M. L. Graber, D. C. DiLillo, B. L. Friedman, and E. Pastoriza-Munoz, Anal. Biochem. 156, 202 (1986). 3x R. Krapf, N. P. Illsley, H. C. Tseng, and A. S. Verkman, Anal. Biochem. 169, 142 (1988). 32 S. Grzesiek and N. A. Dencher, Biochim. Biophys. Acta 938, 411 (1988). 33 A. S. Verkman and H. E. Ives, Biochemistry 25, 2876 (1986).

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current interest in the development of new fluorescent dyes may soon make optical methods more attractive. To date, tracer flux measurements according to the so-called "rapid filtration" technique3 have been most commonly used for transport studies using brush border membrane vesicles. The basic procedure is rather simple and involves three steps11: (1) vesicles are combined with an incubation medium containing radioactively labeled ligands or substrates and other constituents as required; (2) the uptake reaction is stopped at established time intervals by either aliquoting the previous mixture in a socalled "stop solution''3,1~ or by directly introducing the stop solution into the uptake medium; (3) the final mixture is collected on a filter which is rapidly washed with stop solution and then counted for radioactivity. Efliux studies can in principle be carried out in the same way using vesicles preloaded with labeled substrate. Obviously, each of the steps involved is associated with a number of problems which have been extensively discussed previously.2,~~-~4 Actually, the most critical limitations are time limitations associated with the mixing of the vesicles and the incubation medium (reliability of the zero time), the sampling over short periods of time (difficulty in measuring true initial rates for fast transport systems), and the duration of the stopping process (leak of accumulated substrates), all of which are related to the manual aspect of the technique. A semiautomatic mixing/diluting apparatus has proved very useful in improving the time resolution to fraction of seconds for both transport and binding measurements,a4 A rapid filtration technique for membrane fragments or immobilized enzymes has also been proposed which allows for time resolutions of the order of l0 to 20 msec at best, but has never been used with brush border membrane vesicles. 35 A further achievement has recently been introduced which overcomes the one-point approach of these two versions of the mechanical rapid filtration technique and allows both fast sampling and rapid filtration to be performed under fully automated conditions.~ Briefly, vesicles are rapidly injected (5 msec) and mixed (250 msec) with the incubation medium (0.2- 1 ml) in a chamber under controlled temperature (5-45°). At time intervals selected on the keyboard of a computer (any time combination from 0.25 to 9999 see), a maximum of 18 aliquots (20- 80 #l) can automatically be sampled (up to four/see) and injected into the upside chamber of a moving filter holder containing the stop solution. M. Kessler, V. Tannenbaum, and C. Tannenbaum, Biochim. Biophys. Acta 509, 348 (1978). 35 y. Dupont, Anal. Biochem. 142, 504 (1984). A. Berteloot, C. Malo, S. Breton, and M. Brunette, J. Membr. Biol., submitted (1990).

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While the process is going on, the sampled aliquots are automatically filteredand washed under conditions lastingjust a few seconds (I5- 20 scc for one filtrationand two washings). The whole sequence is under computer control and is triggered by a signal activated during the injection process. A photocell measures thc sampling time which was shown to bc directly proportional to the sampling volume (over the range 20-100 gl) and thus allows for standardization of thc sampling process. Automatic washing of the incubation chamber also allows runs to bc performed every I0 min. Finally,a delay sequence between sampling and triggeringof both filtrationand washings should permit fast efl]ux to bc measured as well. This version of the "fastsampling, rapid filtrationapparatus" (FSRFA) has so far proved very useful for kineticstudies using brush border membrane vesicles from both human 37 and rabbit intestines(see the section (Brush Border) Membrane Vesicles in Kinetic Studies). Advantages and Limitations in the Use of Vesicles for Investigating Transport Systems Most of the advantages generally associatedwith the use of membrane vesiclesin the characterizationof membrane transport systems have long bccn recognized and have led to almost universal acceptance of thispreparation for such studies. It must bc made equally clear, however, that vesicles do also have shortcomings and several limitationswhich arc not always as well appreciated. As compared to intact whole cells,intestinalrings, or evcrted sacs, brush border membrane vesiclesarc much simpler biologicalpreparations and, for this reason, present considerable advantages if trying to localize both transport systems and regulatory events in polarized cells such as those of the intestinaland renal epithelia,or if trying to characterizethe properties and kineticsof specifictransport systems as well as the possible interactionsbetween them. Some limitations,however, apply, and both the more specificadvantages and caveats associatedwith them can bc listedas follows. I. Vcsiclcs arc poor in intraceUular enzymes. As such, they cannot mctabolizc most of the naturally occurring substrates for the different transport systems and the transport of the physiologicallyrelevant substratcscan bc studied. This contrastswith the situationprevailingin intact tissues wherc the use of nonmctabolizable substratc analogs is the rule rather than the exception. One can also reasonably assume that the substratest~Lkenup by the vesiclesarc intactand in a frccform, and so vesicles 37C. Malo and A. Berteloot, J. Membr. Biol., submitted (1990).

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are in principle suitable biological preparations for determining energy conversion yields.It should not be forgotten, however, that brush border membranes do possess many membrane-bound enzyme activities,most of which arc hydrolascs implicated in the finaldigestion of sugars, proteins, and lipids.Studies on the transport of disaccharidcs,di- and tri-peptidcs, and phospholipids may thus prove impossible or inconclusive without furtherprocessing of the vesiclepreparation.In any case,both the extent of hydrolysis of the frec substrateand the amount of hydrolyzcd versus intact substratc found in the intravascularcompartment should be assessed as a function of incubation time. Ifeithertestwcrc to show unacceptable levels of hydrolyzcd substratc,alternativestrategiesincluding nonmetabolizable analogs, specificenzyme inhibitors,strippingof the membrane enzymes by protcase treatment,3s or use of animal species lacking the corresponding hydrolascs could bc tdcd and evaluated as to theirsuccess in reducing the extent of hydrolysis. 2. Vesicles are essentiallyfrcc of cellorgancllcs.Moreover, as low-molecular-weight substratcs are washed off during the preparation of the vcsiclcs,the remainders of other cellularcontaminants arc usually of no consequcnce in most experimental situations. However, even if brush border membrane vesiclesare perhaps among the cleanest organellcsthat can be prepared, the usual criteria of caution must be exerted when localizing one or another transport system in this membrane. A particularly disturbing contamination in this respect could be represented by vesicles from the basolateral membrane or by "chimeric" vesicles whose membrane derives from both brush border and basolateral domains or components. Also, reorganization of the normally polarized plasma membrane domains following the isolation procedure has been reported to occur when cells are isolated prior to membrane vesicle preparation, t9 In such cases, the Na+-independent D-glucose transport activity found in brush border membrane vesicles could actually represent the expression of the Na+-independent D-glucose transport activity normally associated with basolateral membranes. It may thus be necessary to use alternative substrates with specificities known to be selective for either the brush border~9 or the basolateral4° membranes and/or to use inhibitors specific for the apical4~ or contralumena142 glucose transport systems in order to assess this point. More difficult to resolve, however, might be to decide whether the 38A. Berteloot, R. W. Bennetts, and K. Ramaswamy,Biochim. Biophys. Acta ~01, 592 (1980). 39G. A. Kimmichand J. Randles,Am. J. Physiol. 241, C227 (1981). 4oG. A. Kimmichand J. Randles, J. Membr. Biol. 27, 363 (1976). 4~F. Alvaradoand R. K. Crane,Biochim. Biophys. Acta 56, 170 (1962). 42G. A. Kimmichand J. Randles,Membr. Biochem. 1, 221 (1978).

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Na+-independent D-glucose transport activity found in brush border membrane vesicles is the expression of the Na+-independent operation of the brush border Na+-dependent D-glUCOsetransport system(s) or belongs to a separate entity. This is so because phlorizin inhibition of the Na+/D-glucose cotransporter(s) has an absolute requirement for the presence of Na+. 43 An alternative and complementary strategy to check for this particular point could thus be to study efflux from the vesicles in the presence of Na + and saturating concentrations of this inhibitor after active loading of the vesicles in the presence of an Na + gradient. 3. Vesicles are not "alive." As such, they do not impose the restrictions typical of surviving tissues (02, pH, etc.). It is thus possible to study, for example, a transport system in the absence of 02 and in the presence of thiols, if the stability of the substrate so requires. A corollary limitation is, however, associated with this otherwise interesting property since the functional polarity of the two plasma membrane domains naturally found in intact epithelial cells is lost during the brush border membrane isolation. As a consequence, only transient phenomena (overshoots3) can be observed in the case of Na+-dependent, secondary active transport systems due to the absence in the brush border membrane vesicles of the Na+,K+ATPase necessary for continuous Na + extrusion in intact cells. Also, since the intravesicular concentrations of Na + and substrate are always changing with time, integrated Michaelis-Menten equations cannot be used to describe the full time course of the uptake process due to the mathematical limitations in finding analytical expressions of the integrated rate laws. 4. Vesicles have small, negligible unstirred layers. Because the active transport of a substance depends on the concentration of that substance immediately adjacent to the membrane, and because the concentration is affected by both the active transport rate and the presence of unstirred water layers, any measurement of apparent kinetic constants are themselves affected by unstirred water layers. 44 This problem is further complicated in vivo by the presence of a membrane surface mucous coaP 5 which artificially increases the thickness of the unstirred layer. Since the effect of an unstirred water layer surrounding a spherical membrane decreases as the sphere radius decreases,46 and since the membrane surface mucous coat is removed during vesicle preparation, unstirred water layer effects can in general be neglected in vesicle studies (the situation might, however, 43 G. Toggenburger, M. Kessler, A. Rothstein, G. Semenza, and C. Tannenbaum, J. Membr. Biol. 40, 269 (1978). 44 p. H. Barry and J. M. Diamond, Physiol. Rev. 64, 763 (1984). 45 K. W. Smithson, D. B. MiUar, L. R. Jacobs, andG. M. Gray, Science214, 1241 (1981). 46 A. S. Verkman and J. A. Dix, Anal. Biochem. 142, 109 (1984).

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be different in highly viscous media). This is shown by the much smaller Km for D-glucose uptake in rabbit brush border membrane vesicles (0.1 m M ) 43 as compared to those in everted sacs (5.0 raM), 47 disks (14100 mM), 4s or biopsies (20 raM). 47 Only when subjected to very high shaking rates do these last preparations show a decreased Km with values of 1.3 mM, 47 1.9-5.0 raM, 4s and l0 m M 47 for sacs, disks, and biopsies, respectively. However, under comparable conditions, essentially the same K i values for phlorizin inhibition are found in vesicles and everted rings. 5. Magnesium ion-precipitated brush border membrane vesicles are essentially completely right side out. 13,26This is probably due to the connections between the membrane and the cytoskeleton and/or to the presence of an external glycocalyx, both of which would decrease the probability of inversion for mechanical as well as steric reasons. More difficult to evaluate, however, is the ratio of intact versus opened or leaky vesicles,49 the latter would underestimate the true transport capacity. It should not be forgotten either that brush border membrane vesicles are heterogeneous in both form and size, which can be due to the extent of homogenization, but may well reflect a genuine heterogeneity of the original brush borders. 25,5° For this reason, the kinetics of ettlux and of tracer exchange are not described by a single exponential, sin,52and criteria to recognize homogeneity or inhomogeneity of vesicle preparations have been proposed by Hopfer. 52 6. Brush border membrane vesicles can be stored for months in liquid nitrogen without detectable loss of transport activity while no other preparation can (see the section Preparation of Functional Brush Border Membrane Vesicles). This advantage is highly significant in kinetic work, allowing comparisons in both Vm~ and Km to be made from a large pool of prepared vesicles. However, it is advisable to check if this also applies to transport systems which have not yet been tested for stability on freezing and thawing. 7. Vesicle studies only need reduced volumes (down to a few microliters) of incubation. Minute amounts of expensive substrates or effectors can thus be used. This advantage may, however, be limited by the specific radioactivity of the available substrates which, in turn, will affect the sensitivity of the assay. 8. Vesicles allow substrate uptake to be measured at far shorter incu47 A. B. R. Thomson and J. M. Dietschy, Am. J. PhysioL239, G372 (1980). 4s A. B. R. Thomson and J. M. Dietschy, J. Membr. Biol. 54, 221 (1980). 49 N. Gains and H. Hauser, Biochim. Biophys. Acta 772, 161 (1984). so G. Perevucmk, P. Schurtenberger, D. D. Lasic, and H. Hauser, Biochim. Biophys..4cta 821, 169 (1985). 5~ U. Hopfer, J. Supramol. Struct. 7, 1 (1977). 52 U. Hopfer, Fed. Proc., Fed. Am. Soc. Exp. Biol. 40, 2480 (1981).

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bation times than with rings. This is especially true when a semi- or fully automated apparatus is used for kinetic work) 4-36 It is thus possible to investigate unstable substrates and effectors under appropriate conditions. 9. Brush border membrane vesicles can in general be considered as "tight." This applies to vesicles prepared as described previously but should be assessed in each case since both the preparation procedure and the nature of the substrate may have to be considered in certain cases. It is thus recommended that one tests each reagent and each vesicle preparation to determine how permeant the vesicles are. With appropriate precautions, it is thus possible to draw conclusions as to the sideness of membrane components? 2 10. In general, the composition of the media at both sides of the membrane can be fixed by the experimenter much more easily with membrane vesicles than can be done with intact, surviving tissues. This freedom is not unlimited, though, as Mg2+-precipitated vesicles are so stable that it may be difficult to introduce high-molecular-weight compounds into the intravesicular space. 26,53,54For kinetic work, where the conclusions of the studies rely on precise loading of the vesicles, it is advisable to ascertain whether or not vesicles are fully equilibrated with the appropriate reagents at the start of the experiment. That failure to do so can result in possible artifacts has been reported. 55 In general, most low-molecular-weight substrates, effectors, etc., are assumed to equilibrate completely with the intracellular volume during preincubations of reasonable length (e.g., 1 - 2 hr at room temperature). This may not be the case actually, even for ions, as recently reported for KC1. 56 Similar results have been observed in the laboratory of one of the authors when comparing vesicle loading with KI and choline iodide. While the former would equilibrate within the time period required for resuspension, the latter required a m i n i m u m of 6 hr. 92 Such effects can easily be followed by taking advantage of the membrane potential dependency of Na+-dependent glucose transport 57 and following transport activity for some time after preparing the vesicles.92 Failure to load the vesicles at the appropriate concentrations would, in the example given above and when vesicles are incubated with NaI, create an internal negative membrane potential because of the higher external concentration of the very permeant anion I-. This effect would decrease in time on further incubation of the vesicles in the resuspension medium until reaching stability. 53F. S. Van Dommelen, C. M. Hamer, and H. R. De Jonge, Biochem. J. 236, 771 (1986). 54M. Donowitz, E. Emmer, J. McCullen, L. Reinlib, M. E. Cohen, R. P. Rood, J. Madam, G. W. Sharp, H. Murer, and K. Malmstrom, Am. J. Physiol. 252, G723 (1987). 55F. C. Dorando and R. K. Crane, Biochim. Biophys. Acta 772, 273 (1984). 56M. S. Lipkowitz and R. G. Abramson, Am. J. Physiol. 252, F700 (1987). 57A. Berteloot, Biochim. Biophys. Acta 857, 180 (1986).

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11. Membrane vesicles allow effector studies to be performed with more confidence than with intact tissue preparations. For example, both Na+-free conditions and requirements for extra ions are easier to obtain with brush border membrane vesicles as clearly demonstrated, for example, in the particular case of glutamic acid transport in the rabbit small intestine? s However, the quantitative assessment as to the membrane potential dependency of transport systems may be more difficult in vesicle studies since direct recording of potential values by means of microelectrodes is impossible with vesicles because of their small size. Thus, the general principle underlying the generation of membrane potentials consists of the imposition of ion gradients that lead to the formation of diffusive potentials. Both cations in the presence of specific ionophores (K+/valinomycin, H+/FCCP) or anions with different lipophilicities have proved successful for this p u r p o s e . 2'10'13'57 It should be noted, however, that such techniques may serve well for qualitative assessments (i.e., electrogenicity of transport mechanisms), but that quantitative studies (i.e., membrane potential dependency of transport processes for kinetic arguments) involve two major problems related to the indirect determination of membrane potential values. The first deals with the generation of membrane potentials of known size and, in the absence of knowledge on the permeability coefficients for all ions present in the incubation medium, has been approached by using the Nernst equation as an approximation to the more general Goldman-Hodgkin-Katz equation, thus assuming that the permeability of one ion greatly exceeds the permeability of all other ions present. Such a situation has been approximated by Kaunitz and Wright, 59 who used variable intra- versus extracellular KCI concentrations in the presence Of valinomycin. This same approach was later used by BertelooP~ and compared to another one involving different intra- versus extravesicular concentrations of a highly permeant anion. It thus appeared that the last procedure offered significant advantages: (a) it is easier to handle than techniques using ionophores which are sparsely soluble in water and must be added as solutions in an organic solvent, thus limiting the concentration of ionophore that can be used; (b) it is insensitive to pH variation, a characteristic not shared by the K+-diffusion potentials induced by valinomycin,57 (c) it can be used with cotransport systems in which K + has been shown to participate in the transport mechanism;~° (d) it may be more accurate in estimating membrane potential differences since K + permeability in the presence of valinomycin was found to be lower than generally assumed, thus underestimating the true potential as calculated by the 58 A. Berteloot, Biochim. Biophys. Acta 775, 129 (1984). s9 j. D. Kaunitz and E. M. Wright, J. Membr. Biol. 79, 41 (1984). ~o A. Berteloot, Biochim. Biophys. Acta 861, 447 (1986).

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Nernst equation;57 (e) it may thus prove more insensitive to ionic replacement, at least for Na +, CI-, and K ÷, which are used very often in vesicle studies. It should be borne in mind, however, that these last two conclusions should be evaluated for each different vesicle preparation since they depend on both the success in finding a highly permeant anion in a particular system and the efficiency of valinomycin in inducing K + permeability in that system. The second problem in the quantitative evaluation of membrane potentials deals with the selection of an appropriate probe that would allow their measurements. Radioactive lipophilic cations or anions, 2 membrane potential-sensitive dyes, 13 and high-affinity glucose transport activity57have all been suggested and used for this purpose. None of these probes is actually perfect since the first ones bind heavily to brush border membrane vesicles (Berteloot, unpublished), the second ones also suffer from binding problems, are not very sensitive, and respond by unknown mechanisms, la while the last one is obviously restricted to vesicle systems having well-characterized, electrogenic, Na+-dependent glucose transport system(s).57 It should be stressed, however, that the best of the probes would not solve the main problem, which still consists in the assessment of the validity of using the Nernst equation under particular conditions. For this same reason, the range of membrane potentials that can actually be covered for meaningful quantitative purposes using that approach is rather limited. 12. Membrane vesicles fulfill the three R's (reduce, refine, replace) and thus represent a typical example of positive development at a time of animal protection movements. They reduce the number of experimental animals in inhibitor, drug, and kinetic studies since (a) very little biological material is needed in each experiment, (b) in general fewer and more clear-cut experiments are needed to answer a given question than when using surviving tissues or whole animals, and (c) vesicles prepared from a single animal may allow many tests to be performed and directly compared. Vesicles also lead to a refinement in the experimental design because of their much greater flexibility, as compared to surviving tissues or intact animals. Finally, they often lead to replacement of animals from the animal house with animals from the slaughterhouse. Moreover, membrane vesicles can also be prepared from cultured cells. 13. Membrane vesicles can be used as the starting preparation for a number of biochemical studies. Vesicle preparation is a first and important step toward the identification, purification, and isolation of membrane components, including membrane-bound hydrolases and transporters, n lipids,2°,2~ or membrane-bound cytoskeletal components.6~ Further negative purification of brush border vesicles can be achieved by removing 6~ M. S. Mooseker, Annu. Rev. Cell Biol. 1, 209 (1985).

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(most of) the cytoskeleton12,62 and membrane-anchored enzymes.3s The cleaner the membrane preparations, the easier it is to optimize the conditions for solubilizing a membrane component. It should be remembered, however, that the preparation procedure may affect the outcome of the conclusions (see the section, Preparation of Functional Brush Border Membrane Vesicles). Brush border membrane vesicles have also been used for direct determination of carrier molecular weights by radiation inactivation 63 and for the identification of carder molecules in SDS-PAGE ~2 and the determination of molecular mechanisms of different transport systems using chemical modifications by group-specific reagents.~2 (Brush Border) M e m b r a n e Vesicles in Kinetic Studies Many of the advantages listed in the previous section have indicated the (brush border) membrane vesicles as a "perfect" tool for kinetic studies in trying to understand some of the molecular mechanisms of (secondary active) transport systems. In doing so, most of the theoretical and experimental principles generally applied in classical enzymology have been used. Although justified in general, it should, however, be stressed that the extension of methods devised for enzyme reactions in a homogeneous and liquid phase to transport in membrane vesicles is not straightforward and that this approach also suffers from limitations associated with both the use of the membrane vesicles themselves and the nature of the transport processes as opposed to enzyme reactions. Since several reviewsT M have already dealt with different aspects and limitations of kinetic studies as applied to brush border membrane vesicles, it is not our intention to repeat all of these but rather to focus on more specific assumptions inherent in such studies, both theoretical and experimental, while referring the interested reader to previous reviews.

Initial Rate Assumption Even if obvious, it must first be remembered that kinetic studies are intrinsically model dependent since they aim at comparing the mathematical predictions of different models, as expressed by their rate laws, with a series of experimental results performed under different conditions in order to identify the most probable one. As such, one must be certain that the conditions placed on the mathematical derivations are satisfied in the experiment. So far, the conventional approach to the study of cotransport 62U. Hopfer, T. D. Crowe, and B. Tandler, Anal. Biochem. 131, 447 (1983). 63R. B61iveau,M. Demeule, H. Ibnoul-Khatib, M. Bergeron, G. Beauregard, and M. Potier, Biochem. J. 252, 807 (1988).

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kinetics has been to apply the steady state methods in the derivation of kinetic equations for (co)transport models with64 or without~5 the rapid equilibrium assumption which reduces the number of parameters in the rate equations by assuming that the reactions taking place at the membrane interfaces are faster than those perpendicular to the membrane plane. Also, when brush border membrane vesicles are used, it has been common practice to use the so-called "zero-trans conditions" for influx or effiux measurements, thus assuming that the substrate concentrations are zero on the trans side as compared to the ds side where the radioactive substrates are introduced. It should thus be clearly understood that the initial rate assumption must be satisfied under these specific conditions for both meaningful results and conclusions to be obtained. From a more practical point of view, this means that the initial rate determinations should be performed under conditions where linear uptake is observed. Although quite simple in appearance, this condition is rather difficult to satisfy when using membrane vesicles, mainly because of their large surface/volume ratio as compared, for example, to isolated cells or intact tissues. This leads very rapidly to significant substrate depletion from the intravesicular space during effiux experiments. Similarly, significant intravesicular accumulation of substrate(s) is rapidly achieved during influx measurements such as to allow trans effects and/or reversal of the reaction over a short incubation period. Hence, in both cases, significant deviations from linearity will be observed very soon after the start of the experiment due to the rapid violation of the initial rate assumption. The situation is still worse under the so-called "gradient conditions," in which gradients for both driving ion and driven substrate are present at the start of the experiment. Early collapses of the chemical gradients for ion and substrate occur in parallel and are accompanied by membrane potential changes. Four principal experimental approaches have been used in trying to deal with this problem. 1. Measure tracer exchange rates under equilibrium exchange conditions to circumvent the problem. 5~,52Although very sound on theoretical grounds, this approach should, however, be used cautiously for the following reasons: (a) The results depend heavily on the successful preloading of the vesicles at the appropriate substrate concentrations55; (b) because of the heterogeneity in both the form and size of the vesicles, of the possible scrambling or contamination of the brush border preparation by basolateral membranes, of the presence of multiple transport pathways for the R. J. Turner, J. Membr. Biol. 88, 77 (1985). 65D. Sanders, U.-P. Hansen, D. Gradmann, and C. L. Slayman, J. Membr. Biol. 77, 123 (1984).

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same substrate in otherwise homogeneous vesicles, the equilibrium exchange rates will not be described in general by a single exponential51.52;(c) the sensitivity of the measurements, in terms of significant differences in measurable radioactivities between different conditions, is fixed by the maximum in uptake differences that one can expect to measure and is limited, under equilibrium exchange conditions, by the size of the intravesicular volume. Thus, the description of multiexponential functions will be very imprecise; (d) in case of multiple transport pathways for the same substrate within the membrane, it may become difficult to analyze the results properly. For example, assuming both Na+-dependent and Na +independent pathways for glucose transport in brush border membranes, the "leak" pathway will not be constant when varying the substrate and/or Na + concentrations. One could even select conditions with high Na + and low substrate concentrations for which the contribution of the Na+-dependent pathway to the overall uptake rate would be negligible since trans inhibition by Na + of the Na+-dependent pathway(s) have now been demonstrated. 12,55A still worse situation may occur if brush border membranes were contaminated by basolateral membrane vesicles since the above conditions would favor expression of the Na+-independent glucose transport system present in the contaminating membranes; (e) as already discussed by others, the conclusions of such studies are ambiguous from a theoretical point of view since they do not allow distinguishing between random Bi-Bi and ordered Bi-Bi kinetic reaction mechanisms~2.66,67; (f) experimental conditions that can be used are rather restrictive since they allow only the isotope exchange rates of substrate and Na + to be determined. In actual fact, the latter are very imprecise due to the high leak permeability for Na + in brush border membrane vesicles?2 This is not to say that equilibrium exchange experiments cannot produce valuable information but, rather, that this approach should not be regarded as the sole correct experimental set-up for kinetic studies. 2. Estimate initial transport rates by measuring substrate uptake at one time point taken as soon as possible in order to approximate as closely as possible the true initial rate conditionsJ 2 Obviously, the validity of this approach is straightforward if two basic hypotheses are validated. First, the chosen time point is on the linear part of the uptake time curve and, next, this condition is fulfilled over the whole range of substrate concentrations and experimental variations within the same experiment. While very easy 66 j. W. L. Robinson and G. Van Melle, J. Physiol. (London) 344, 177 (1983). 67 D. A. Harrison, G. W. Rowe, C. J. Lumsden and M. Silverman, Biochim. Biophys. Acta 774, 1 (1984).

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to satisfy using a semiautomatic apparatus, 34 these conditions may, however, be more difficult to demonstrate with the manual filtration technique because of its poor time resolution. It should be noted, however, that misleading information as to the contribution of the leak pathway (diffusional component) to the overall transport activity may be obtained with this approach (see "Uptake" versus Transport). 3. Perform multiple uptake measurements over a limited time range and estimate the initial transport rates by polynomial regression of the uptake time course,55 as seems to be accepted by enzymologists.6s While having the advantage that no assumption as to the transport mechanism involved must be made, 55,6s it has, however, the disadvantage that the coefficients of the polynomial have no physical meaning.6s Actually, the only justification for this approach is to consider the polynomial as a limit series of an exponential function, and, as such, may only be valid over a limited time range, close to the origin. Accordingly, it is the experience of one of the authorssT,Ss,6°that the polynomial fitting approach is very dependent on the number of available data points, on the presence of outliers, and on the degree of curvature in the uptake time courses. In any case, polynomials of order higher than three should not be used.6s One may also have to decide, and quite arbitrarily, whether the regression should go through the origin. It is the point of view of these authors that this approach should be used (and very cautiously) only when no alternative is available. 4. Estimate the initial transport rates from the slopes of straight lines drawn by linear regression through the uptake time courses determined under the various conditions of an experiment at a very early time period (in the few seconds range).69 This last condition is actually rather restrictive and may be obtained in most cases only by using special pieces of equipment such as the semi- or fully automated rapid filtration apparatuses described above (see Transport Measurements) or a stopped-flow spectrophoto(fluoro)meter when using optical methods. Obviously, this "dynamic approach" has the advantage of justifying in each experimental condition whether the initial rate conditions are fulfilled. It also allows estimation of the standard errors on the initial rate measurements when using appropriate linear regression software. Finally, it allows the determination of whether the regression line goes through the origin, thus also permitting correction for this uptake component and precise assessment of its mean-

68 B. A. Orsi and K. F. Tipton, this series, Vol. 63, p. 159. 69 S. Breton and A. Berteloot, Physiologist 31, A142 (1988).

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ing (see further in the next section). Using this approach with the FSRFA, it has recently been shown that the linearity period lies within the first 10% of the time required to reach maximal overshoot values.69 This conclusion actually applies to both rabbit° and human 37 intestinal brush border membrane vesicles when the Na+-dependent transport of v-glucose is analyzed at a 50 # M concentration over the 5 - 35 ° range of temperatures. However, when D-aspartic acid uptake by rabbit vesicles was studied in the presence of an inward Na + gradient, the observation of an initial linearity period was dependent on both the temperature and the pH of the incubation medium (A. Berteloot, 1990, unpublished). Actually, upward deviations from linearity were observed at pH 6 and were more important when decreasing the temperature from 40 to 15 °. On the other hand, initial linearity over the same range of temperatures was observed at pH 8. Since the linear versus nonlinear behavior did not correlate with the time at which maximum overshoot values were recorded, it is tentatively conduded that these results are compatible with the observation of presteady state kinetics69 (actually lags) according to the conclusions of a recent theoretical study. 70'71 In any case, this last example clearly shows that initial linearities should not be taken for granted even over very short incubation periods. Clearly, the authors' preference is for true initial rate determinations under gradient conditions since, as compared to equilibrium exchange, they avoid the interference from trans effects which can be investigated separately. They also allow a broader choice of experimental conditions to be tested with, in most cases, an easy and direct control as to the determination of the leak pathway. Moreover, the steady state assumption should apply under gradient conditions whether the membrane potential and/or the ion and substrate gradients collapse with time provided that linearity in the uptake time courses, which represents in itself a sufficient warranty of the existence of a prevailing steady state, is demonstrated. However, since brush border membrane vesicles have been shown to possess Na+/H + exchange activity, it would be advisable to use amiloride and/or proton ionophores in order to slow down the collapse of the Na + gradient and/or build-up of proton gradients through this system. A few comments also need to be made on etflux measurements. Actually, they still represent a challenge since the amount of substrate that

ToW. Wiel-zbicki, A. Berteloot, and G. Roy, Fed., Proc., Fed. Am. Soc. Exp. Biol. 46, 368 (1987). 71 W. Wierzbicki, A. Bertdoot, and G. Roy, J. Membr. Biol. 117, I l (1990).

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can be trapped into the intravesicular space is small, at least in terms of measurable counts per minute, thus making these measurements very imprecise. The so-caUed "active loading process''72 may thus look very attractive since it allows this problem to be overcome but suffers from the impossibility of fixing the internal substrate concentrations at values chosen by the researcher. Also, since true zero-trans initial rate conditions would necessitate a complete separation of the vesicles from the loading incubation medium (and simple dilution is obviously imperfect in this respect), it can be expected that significant amounts of substrates may have already leaked out at the start of the etilux experiment, thus making it unlikely that true initial etflux rates can actually be measured. The only possibility for accurate measurements in eitlux experiments may be that of using one of the (semi)automated techniques described in a previous section, but these still have to be applied to brush border membrane vesicles and thus cannot be evaluated as yet. Two other complications should also be considered when dealing with efflux experiments. First, internal binding of the substrates, if important and rate limiting for the etilux process, may represent a major obstacle since the kinetics observed for efflux may actually describe the debinding process. In fact, should the debinding and eiflux processes proceed at comparable rates, the kinetic parameters for transport would still be considerably distorted. Next, etitux kinetics are again influenced by the heterogeneities in the vesicle preparation and will not in general be described by a single exponential?2 These difficulties in determining accurately the kinetics of eitlux do represent a very serious drawback for the ldneticist since they preclude a full kinetic analysis of the Cleland type to be performed. In fact, they add to other factors which, by themselves, already hamper seriously this type of analysis (multiple transport pathways, vesicle heterogeneity, and Na + stoichiometries greater than one, which immensely increase the number of kinetic reaction mechanisms to be considered). Although all of the above difficulties apply particularly to transport studies using (brush, border) membrane vesicles as opposed to enzyme kinetics, one should not forget that all of the experimental precautions that apply to the latter also apply to the former, if one wants to obtain meaningful kinetic studies. Accordingly, all kinetic experiments ideally should be performed under controlled temperature, pH, and ionic strength, and the linearity in initial rates versus protein concentrations should be such as to allow comparisons on a day-to-day basis to be meaningful. Also, since kinetic experiments usually require a few hours to be completed, one

72 y . Fukuhara and R. J. Turner, Am. J.

Physiol. 248, F869

(1985).

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should verify the stability with time and with the incubation temperature of the membrane preparation.

"Uptake" versus Transport When looking at substrate uptake into (brush border) membrane vesicles, one should realize that the measure so obtained is a composite of different components, both unspecific and specific, that occur, simultaneously during the incubation process. Obviously, their contributions to the overall uptake need to be evaluated and separated for meaningful transport kinetic analysis to be obtained. These include the following: 1. The background radioactivity, which is the result of nonspecific, nonsaturable trapping of radioactive substrate in a "dead space" represented by the amounts of radioactivity bound onto the filters and/or trapped in the water space surrounding the vesicles and in leaky vesicles, all of which may not be washed out during the rapid filtration step: "En bloc" correction for these uptake components is usually made by running a zero time point in the presence of vesicles when radioactive substrate and stop solution are added simultaneously. Such a practice cannot be recommended, however, since it assumes (a) "exact" reproducibility from sample to sample, which is essentially not verified, and (b) time independence of the above processes, which may or may not apply in the specific cases under study. The first assumption can be released by using a "quenched" stop solution3 which contains a differentially labeled space marker or substrate analog (usually an inactive stereoisomer). A better approach, however, which does not make any of the above assumptions, involves a double tracer incubation with these same molecules. For these two corrections to be valid, one should verify the equivalence between 3H- and ~4C-labeled spaces. Also, when coincubation with a substrate analog is performed, the simple diffusional component of transport [see point (2) below] may be simultaneously corrected. 2. The simple (passive) diffusion of substrate, which represents the intrinsic leak permeability of the membranes to different substrates, and should demonstrate the following properties: (a) independence, in terms of counts per minute, as to the cold substrate concentrations, or, equivalently, linearity in the v over S plot or absence of saturation; (b) insensitivity to inhibition by known transport inhibitors or substrate analogs. Accordingly, this transport component is usually determined by running a transport experiment at different substrate concentrations in the presence of saturating concentrations of specific inhibitors of the carrier-mediated process(es) and/or under nonenergized conditions in the case of secondary active transport system(s). The slope of the straight line usually obtained by

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constructing the corresponding v over S plot is then taken as evidence for the contribution of a diffusive component to total transport and its slope assimilated to the diffusion rate constant kd. As straightforward as it may seem, we think that such a simple analysis can easily lead to erroneous conclusions since simple diffusion cannot be dissociated from either uncorrected background [point (1) above] or nonspecific binding [point (3) below] based on these criteria alone. This conclusion is best illustrated by recent data using the FSRFA and the dynamic approach for the characterization of glucose transport by human intestinal brush border membrane vesicles.37 When the v over S plot was constructed from the slopes measured under Na + gradient conditions, saturation was obtained directly. It was unequivocally deduced that simple diffusion of glucose does not contribute significantly to total transport. Since this result contrasts with what is usually observed in kinetic studies, the same plot was constructed from initial rates determined according to the one time point approach. In this case, both saturating and diffusional transport components were observed, and it was shown that the latter is actually an artifact due to the noncorrection for the y intercepts. This example clearly demonstrates that the socalled diffusion should only be considered as an operational parameter since it may fail to give any meaningful information as to the real passive permeability of the membrane for a given substrate. It also allows one to seriously question previous negative views as to the leakiness of the membrane vesicles.° Moreover, since one is generally interested in analyzing the saturating processes, a detailed delineation of the nonspecific uptake components is usually not required, and the fastest and best way to deal with these components is suggested in a following section (Determination of Kinetic Parameters in Uptake Studies). 3. The unspecific and/or specific substrate binding to intra- and/or extravesicuiar membrane sites. For kinetic studies, internal binding is usually not a problem during initial rate determinations under true steady state conditions since enough substrate needs to get into the intravesicular space for this component to show a significant contribution. However, the external binding contribution to total uptake should not be assumed to be small a priori, and, actually, could be very important, particularly in special circumstances. For example, membrane vesicles have an excess of negative charges, 2t which may make it difficult or even impossible to differentiate between the transmembrane movement and binding of cations with two or more charges. In the case of positively or negatively charged substrates such as amino acids," folio a c i d , 74 and quaternary 73 B. Y. L. Hsu, P. D. McNamara, C. T. Rea, S. M. Corcoran, and S. Sepal, Biochim. Biophys. Acta 863, 332 (1986). 74 A. M. Reisenaucr, C. J. Chandler, and C. H. Halsted, Am. J. Physiol. 251, G481 (1986).

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ammonium bases, 75 binding to membrane components has also been reported. Moreover, since membrane vesicles have a large surface/volume ratio, it may often be impossible to differentiate between transmembrane transport and "uptake" into the lipid bilayer in the case of lipophilic substrates. Several methods are available which allow qualitative evaluation of a contribution of substrate binding to total uptake in (brush border) membrane vesicles; they have been discussed in previous reviews, n- ~4For example, experiments run under accelerated exchange conditions (high intravesicular substrate concentrations) may help in resolving binding from transport since only the latter should be sensitive to these conditions. Absence of binding can also be demonstrated by showing that substrate uptake occurs entirely into an osmotically sensitive intravesicular space) that the amount of substrate associated with the vesicles at equilibrium, i.e., after a long incubation period, is independent of the chemical nature of the substrate and is directly proportional to the extravesicular substrate concentration, z2 and that uptake is abolished in vesicles permeabilized by low concentrations of detergent. Although it is very important to assess whether one deals with transport, binding, or both when performing uptake studies in vesicles, the presence of binding components is not a major obstacle to the kinetic analysis of transport, particularly when using the dynamic approach. For example, a linear relationship between intercepts and substrate concentrations is strong evidence for the presence of a fast, nonspecific binding component and/or of incomplete correction for the background. If a Michaelian relationship is found, however, a fast and specific binding component can be inferred and its kinetic parameters extracted. If a saturable, higher order specific binding component is observed, such a result is compatible with the existence of cooperativity in the fast binding of substrate to the membrane. Alternatively, this binding component may actually represent the amplitude of a presteady state burst. 7°'71the time resolution of which might not have been achieved in the experiment. However, if this last case applies, one may expect that the burst component will disappear in permeabilized vesicles. Finally, it should be emphasized that substrate binding may be difficult to differentiate from transport on the basis of time dependency alone since the former is not necessarily rapid as compared to the latter, contrary to what is generally assumed when analyzing the y intercepts of the uptake time courses. Accordingly, the v over S plots may contain more than one saturable component. In such cases, it might be possible to attribute these sites to binding and/or to transport by further analyzing the kinetics of

~5 K.-I. Inui, H. Saito, and R. Hori, Biochem. J. 227, 199 (1985).

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substrate uptake in the absence of transport (permeabilized vesicles, equilibrium uptake, etc.). Obviously, when using the one time point approach, both the intercept and slope components will be included in the measured uptake values, a situation which can lead to rather complex results and may prevent complete evaluation of the data. However, it should work quite well in the simplest cases discussed above. 4. The carrier-mediated transport process(es) can be of either the facilitated or secondary active types and actually represent(s) the system(s) that one wants to study in most cases. The evidence for active transport is best obtained under ionic gradient conditions in which the driving ion (for example Na +) is replaced by an inactive one (for example K+). The presence of a transient accumulation of substrate over the equilibrium uptake values, or the so-called "overshoot" phenomenon,3,76 is usually taken as evidence for secondary active transport. However, for this conclusion to be valid, conditions should be chosen so as to eliminate other possible interpretations such as volume changes or membrane potential effects in the case of charged substrates. It should also be realized that the overshoot may not be observed under the following conditions: transporters with low turnover rates or with special combinations of rate constant values in their molecular mechanisms,76 high leakiness of the vesicles for the driving ion, too high concentrations of the driven substrate, and transport systems very sensitive to inhibition by trans substrates or requiring additional factors for full expression of activity (ions, cellular components which are removed during the purification, etc.). Still more ditficult to resolve and to interpret is the simultaneous presence of both active and facilitated transport pathways for the same substrate in the vesicle preparation, since scrambling of the vesicles and/or contamination of the preparation by other membranes fragments, different expressions of the same transport system under different ionic conditions, and multiple transport systems for a given substrate, either separately or in combination, are all conditions that can lead to rather complex situations.

Determination of Kinetic Parameters in Uptake Studies As should now be obvious from the above discussion, the interpretation and analysis of uptake kinetics are complicated by the occurrence of, in general, more than one component, usually including both nonspecitic and saturable processes. In practical terms, this means that the usual linear transformations of the Michaelis-Menten equation are in fact nonlinear. It is thus current practice to estimate the diffusional component (whether 76E. Heinz and A. M. Weinst¢in, Biochim. Biophys. Acta 776, 83 (1984).

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real or just operative) in a separate experiment and to subtract its contribution from the total uptake data so as to extract the saturating component(s) which can now be analyzed by linear regression over a linear transformation of the Michaelis-Menten equation. The Eadie-Hofstee plot is actually preferred for its higher sensitivity to deviations from.linearity than the double-reciprocal plot of Lineweaver and Burk and thus serves as a determinant test in assessing the presence of multiple transport pathways. Although justified on purely mathematical grounds in the case of errorfree data, such an analysis is, however, of little value when dealing with experimental determinations for the following reasons: (1) the experimental conditions are not identical when estimating total uptake and diffusion separately and it may be difficult to assess subtle changes in the diffusional component under these two conditions; (2) statistical information on the determination of the diffusional component is lost during the subtraction procedure for which it is implicitly assumed that the ka value is unique and error free. It is thus lost during the computation of the kinetic parameters for the saturating component(s); (3) even small errors in the estimation of the diffusional component will distort the linearization of a saturating process so as to induce upward (underestimation) or downward (overestimation) deviations from linearity in an Eadie-Hofstee plot. The resulting curves will thus mimic a heterogeneity in binding sites or a negative cooperativity in the first case and a positive cooperativity in the second. Obviously, a more accurate and easier way to deal with such data is to use nonlinear regression analysis and to directly fit the total uptake curve to the (apparently) more complex rate equation which includes both the saturating and the nonsaturating components. All parameters would thus be determined simultaneously from a curve that contains all necessary information. 37,ss,77This point is particularly relevant when considering the high number of second sites (and even third sites) which have been reported for different transport systems by Eadie-Hofstee plots, and one may wonder, in the absence of supporting proof on heterogeneity in transport sites, how many of these would survive a more rigorous analysis by nonlinear regression. There are also a few other reasons why nonlinear regression analysis of kinetic data should be preferred. These have been discussed in a few recent reviews7s-s1 and will only be summarized here: (1) Linear transformations 77 G. Van Melle and J. W. L. Robinson, J. Physiol. (Paris)77, 1011 (1981). 7s F. W. Maes, J. Theor. Biol. 111, 817 (1984). 79 D. Garfinkel and K. Fegley, Am. J. Physiol. 246, R641 (1984). 8o G. A. Sagnella, TIBS 100 (1985). 81 j. H. T. Bates, D. A. Bates, and W. Mackillop, J. Theor. Biol. 125, 237 (1987).

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may distort (usually magnify) the experimental variability, thus leading to biased estimates for the values of the parameters3 9,s° This is particularly important with the double-reciprocal plot of Lineweaver and Burk, in which the inverse transformation places undue emphasis on the most variable points3 9,s° Similarly, in the Eadie-Hofstee plot the dependent variable v appears on both axes, thus leading to an unavoidable distortion of the variability in the dataS°; (2) nonlinear regression is in general less sensitive to the spacing and number of data points than is linear regression and is a versatile and general curve-fitting procedure which can be used with a variety of functionsS°; (3) the assumptions underlying the linear regression model are in general not satisfied when using either the Lineweaver-Burk or the Eadie-Hofstee plots: s For this reason, it has even been claimed that "linear regression analysis should not be applied to linearizing plots in biochemistry and pharmacology"Ts; (4) in the particular case of transport studies, the nonlinear regression approach allows different models to be objectively evaluated without any manipulation of the original data.ss,77 For example, in the case of both saturating and diffusional components, different equations corresponding to diffusion alone, one carrier alone, one carder plus diffusion, two carders, two carriers plus diffusion (and more if necessary) could be fitted to the data and the best model chosen according to statistical criteria a l o n e 66,77 (see below). It should be easy for anyone to understand that this procedure is completely different from first trying to correct for a diffusional component before fitting the resulting points to either a one- or a two (or more) carrier model after linear transformation. Should an underestimation in the diffusion constant be introduced during the subtraction procedure, then any requirement for a two-site fitting could actually give the desired output. This is also true should nonlinear regression be used on the transformed data. This is not to say that linearizing plots should not be used anymore but, rather, that they should be considered only as a quick and useful way to visualize enzyme and transport kinetic data. s2 Although to most individuals linear regression may appear easier to do, this is no longer the case, since very interesting nonlinear regression software is now available which would fit most of the microcomputers currently used for linear regression analysis! For any serious kinetic study to be carded out, the data must also be subjected to statistical analysis so that the precision of the derived kinetic constants can be evaluated, s3,~ This is particularly important when trying to distinguish between concurrent models or to evaluate the existence of s2 F. B. Rudolph and H. J. Fromm, this series,Vol. 63, 13. 138. s3 W. W. Cleland, this series,VoL 63, p. 103. u B. Mannervik, this series,Vol. 87C, p. 370.

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more than one transport pathway. In general, the problem of goodness of fit or of which model best describes the observed data should involve analysis of the residuals and the estimated parameters. 7s,s3,u Ideally, a satisfactory model should give an error term with constant variance randomly distributed about zero and the residuals should not be correlated with the independent and dependent variables. A satisfactory fit must also provide biologically meaningful values for the parameters. For example, a negative value for any of these would obviously be unacceptable. Finally, in a good fit, the standard errors of the estimated parameters should be small in comparison to the parameter values. It has been suggested that when the standard errors are less than 25% of the values, one can consider the values to be accurately determined, and thus that the term containing this constant is definitely present, sa Can this type of analysis represent a major obstacle to those who regard statistics as "horrible monsters"? The answer is no, since most of the good software for nonlinear regression analysis also include the statistics mentioned above and allow them to be used in a (very) user friendly way. A final comment should be made on the presentation of transport kinetic data. In general, kinetic experiments using radiotracer techniques are done at a constant concentration of isotope, while substrate concentrations are adjusted by adding varying amounts of cold substrate. The actual output of such experiments thus consists in decreasing cpm values for increasing substrate concentrations. However, v over S plots are usually constructed after correction for the specific radioactivity calculated at each concentration, so that one shifts from a decreasing curve to an increasing one where the highest v values correspond to the lowest clam values. Although perfectly acceptable, we think that this approach can easily lead to erroneous interpretations and that a different presentation, closer to the original data, should be chosen. In this approach, which is analogous to the displacement curves used in binding studies, the specific radioactivity is considered as constant and corresponds to that determined at the lowest substrate concentration. The cold substrate is then considered a competitive inhibitor of the saturable process(es) and, accordingly, the v over "cold" S plot is similar to the original clam data by some scaling factor. The resulting curve can be fitted by nonlinear regression analysis to an equation accounting for the competitive inhibition) 7 It should be emphasized that this approach directly expresses the initial rates in terms of the parameters and so does not involve any transformation of the data as when trying to express the inhibited rates as a function of the rate under pure tracer conditions. These two representations were recently compared in one of the authors' laboratories a7 and the following conclusions were drawn: (1) Identical parameter values are obtained when fitting any of these curves under similar weighting conditions; (2) the second approach is better when

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trying to visually assess the final fit, particularly when dealing with both high-affinity, low-capacity and low-affinity, high-capacity systems, and in the presence of more than one transport pathway; (3) the overall structure of the data is altered in the classical representation, putting undue emphasis on the high S region while masking the other. This is particularly obvious in the presence of a nonspecific component in which the linear part takes over most of the carder-mediated transport system(s). However, in the other approach, the v over S plot decreases to a constant value, thus clearly showing the exact contribution of carrier-mediated uptake to the measured values (hence the sensitivity of the assay) and pointing out the impossibility of distinguishing between ditfusional and nonspeciiic binding components from such plots as discussed in a previous section. It can thus be concluded that the second approach could advantageously replace the former without any loss in terms of kinetic parameter estimation, saving time in the processing of the raw data for computational purpose and allowing a better appreciation of the real data.

Multiple Transport Pathways in Kinetic Data As should now be obvious from the above discussion, good transport kinetics are more difficult to obtain than good enzyme kinetics due to the difficulties associated with both the experimental limitations inherent in the transport measurement in vesicles and the analytical evaluation of the resulting uptake and kinetic data. For these reasons, we cannot conceal our skepticism for "unequivocal" demonstrations as to the existence of two or even three transport systems (plus diffusion!) operating in parallel on a given substrate when these are based solely on curvi."linear Eadie-Hofstee plots, and particularly so when the claimed deviation from a Michaelian behavior relies on a single, deviating experimental point! This is not to say that curvilinear Eadie-Hofstee plots can only be the result of poor handling or collection of the data points (see above) but rather that such plots are neither necessary nor sufficient proof for the existence of more than one transporter. First, it is not necessary proof since theoretical studies have shown, in the case of multiple sites, that significant deviations from linearity can only be expected when the Vm~ and K~ values of the individual sites are well separated. Accordingly, linear Eadie-Hofstee plots may actually mask the presence of more than one transport pathway. Nor is it sufficient proof since nonlinear Eadie-Hofstee plots may also be obtained under multiple site situations in which only one carrier is present, including positive cooperativity,85 hysteresis,~ and random, steady state addition 85 K. E. Neet, this series, Vol. 64, p. 139. 86 K. E. Neet and G. R. Ainslie, this series, Vol. 64, p. 192.

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of two substrates on an enzymes5 or carrier. ~2~55.s7This last situation has been very well known among enzymologists since 1966 as (if not earlier) but does not seem to have attracted the attention of many transport workers. Random Bi-Bi or Bi-Uni kinetic reaction mechanisms may produce apparent cooperativity of the kinetics ff the following conditions hold: s5 (1) the two pathways for ternary complex formation have approximately the same individual equilibrium constants so that neither pathway is thermodynamically favored; (2) the rate constant for ternary complex reofientafion is of the same order of magnitude or is larger than the other unimolecular rate constants so that rapid equilibrium binding of substrates does not occur; (3) one of the pathways for ternary complex formation is kinetically favored. The apparent cooperativity may thus be conceptually seen as follows. At a fixed concentration of substrate (S) and low concentrations of the other substrate (Na + in cotransport systems), the carrier (C) flux will be through the slower C --~ CS -* CSNa pathway because of the high proportion of CS. As the concentration of Na + is increased, the tendency will be for the flux to occur through the faster C ~ CNa ---, CNaS pathway as CNa becomes competitive in concentration. The substrate curve will therefore be nonhyperbolic, and a nonlinear Eadie-Hofstee plot will result. The curvature wiU depend on the concentration of Na + and disappear at saturating Na + concentrations. As recently demonstrated in the case of cotransport systems,s7 this simple test should thus allow differentiation between the random steady state and the two-carrier models. Another criterion that should help in differentiating these two models is ~hat increasing internal subst~te concentrations should cause uncompetitive inhibition of transport in the former model o n l y . s7 It can be anticipated that similarly misleading kinetic situations may occur for ter-ter or tetra-tetra mechanisms. In addition to these theoretical considerations, there are other sources of error which may mimic multiplicity of transport systems. For example, even "pure" membrane vesicles may be scrambled (those from basolateral much more so than those from brush border membranes). As there is every good reason to believe that the transport systems are asymmetric, ~2the Km values of a transport system are likely to be different at the two sides of the membrane. Thus, scrambling will render even otherwise "homogeneous" vesicles kinetically heterogeneous, because right-side-out and inside-out vesicles will expose to the medium faces of the transporter having different kinetic parameters. Curvilinear Eadie-Hofstee plots will be the result. Since v over S plots alone may fail to give the right answer, they should be complemented by other studies [pH, temperature, stoichiometry, and s7 D. Sanders, J. Membr. Biol. 90, 67 (1986). ss W. Ferdinand, Biochem. J. 98, 278 (1966).

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inhibition by either known inhibitors of the putative transporter(s) or substrate analogs, etc.] for a meaningful characterization of the transport pathway(s) to be obtained. Among these, the partial (competitive) inhibition by another substrate is the most often used criterion to assert multiplicity of transport systems acting on a given substrate. The reasoning is deceivingly simple: if the membrane is endowed by, say, two systems transporting amino acid A, and one of the systems transports amino acid B also, saturating concentrations of B will only partially inhibit the transport of A. Straightforward as it may seem, this approach also has limitations. First of all, if a sizeable percentage of vesicles is scrambled, since the substrate specificity of a transport system may be (and usually is) different at the two sides of the membrane,s9 the same transport system may look at the outer surfaces of the two subpopulations of vesicles with substrate binding sites of different specificities. For example, it may interact with both A and B in the right-side-out vesicles but with A alone in the insideout vesicles (or vice versa). But even if the vesicles are unscrambled, homogeneous, and pure, interactions among Na+-dependent systems occurring in the same membrane occur through more than fully competitive inhibition alone. In fact, the increase in Na + trans and the partial collapse of the Na + electrochemical gradient which are brought about by the entry ofNa + via one Na+-dependent substrate indirectly inhibits the operation of other, also Na+-dependent, but otherwise independent cotransporters. The kinetic result is a "partial noncompetitive" inhibition.9°,91 Thus, in the example above, if B, in addition to being another substrate of the Na+-dependent system for A, is transported by other, also Na+-dependent system(s), the partial inhibition of A transport by B is the sum of at least a "fully competitive" and of a "partially noncompetitive" inhibition. It thus does not correspond simply to the contributions of the two systems in the transport of A. This is not to say, of course, that kinetic analysis is useless in testing for multiplicity of transport systems. Rather, we want to remind the reader of pitfalls which are, unfortunately forgotten all too often, that kinetic analysis does not inherently "demonstrate" (it is "compatible with" at best) and that only the use of several, preferably independent, criteria (kinetic, physical separation, biological development, molecular biochemistry, genetics, reconstitution, etc.), can lead to conclusions not liable to fall under Occam's razor. s9 j. E. G. Barnett, W. T. S. Jarvis, and K. A. Munday, Biochem. J. 109, 61 (1968). 90 G. Semenza, Biochim. Biophys. Acta 241, 637 (1971). 91 H. Murer, K. Sigrist-Nelson, and U. Hopfer, J. Biol. Chem. 250, 7392 (1975). 92 D. D. Maenz, C. Chenu, F. Bellemare, and A. Berteloot, Biochim. Biophys. Acta, submitted (1990).

Stoichiometry of coupled transport systems in vesicles.

Investigation of the kinetic and mass transport limitations in thermoelectrochemical cells with different electrode materials.

Advantages and limitations in the use of porcelain veneer restorations.

Advantages, limitations, and opportunities in the use of national databases.

Advantages and limitations of common testing methods for antioxidants.

Thermodynamic and kinetic analysis of heterogeneous photocatalysis for semiconductor systems.

Advantages and limitations of national arthroplasty registries. The need for multicenter registries: the Rempro-SBQ.

Characterization of amino acid transport systems in human placental basal membrane vesicles.

Ultrasound-guided percutaneous nephrolithotomy: Advantages and limitations.

Laparoscopic bowel resection: advantages and limitations.

Thymidine transport in cultured mammalian cells. Kinetic analysis, temperature dependence and specificity of the transport system.

Rapid methods for the detection of foodborne bacterial pathogens: principles, applications, advantages and limitations.

Characterization of the transport of tri- and dicarboxylates by pig intestinal brush-border membrane vesicles.

Characterization of the glucose transport systems in Neurospora crassa sl.

Total hip arthroplasty: areview of advances, advantages and limitations.

Excess surface area in bioelectrochemical systems causes ion transport limitations.

Zebrafish models of human motor neuron diseases: advantages and limitations.

Bedside Doppler ultrasound for the assessment of renal perfusion in the ICU: advantages and limitations of the available techniques.

Functional Advantages of Porphyromonas gingivalis Vesicles.

Minimally Invasive Suturectomy and Postoperative Helmet Therapy : Advantages and Limitations.

Personality and health: advantages and limitations of the five-factor model.

[Immunohistochemistry and personalised medicine in lung oncology: advantages and limitations].

The Transmanubrial Approach for Cervicothoracic Junction Lesions : Feasibility, Limitations, and Advantages.

Advantages and limitations of the use of optogenetic approach in studying fast-scale spike encoding.