To better define the role of soluble binding proteins in the cytoplasmic transport of amphipathic molecules, we measured the diffusional mobility of a fluorescent long-chain fatty acid, 12-N-methyl-(7-nitrobenz-2-oxa-1,3-diazol)aminostearate (NBD-stearate), through model cytoplasm as a function of soluble binding protein concentration. Diffusional mobilities were correlated with the partition of the fatty acid between membrane and protein binding sites. Cytoplasm was modeled as a dense suspension of liposomes, and albumin was used as a model binding protein. Albumin saturably increased NBD-stearate mobility through the membrane suspension approximately eightfold. Fatty acid mobility in the absence of albumin was identical to the mobility of the membrane vesicles (1.99 ± 0.33 × 10−8cm2/s), whereas the mobility at saturating concentrations was identical to the mobility of albumin (1.65 ± 0.12 × 10−7cm2/s). The protein concentration producing half-maximal stimulation of NBD-stearate diffusion (42.8 ± 0.3 μM) was unexpectedly greater than that required to solubilize half of the NBD-stearate (17.9 ± 3.0 μM). These results support a proposed mechanism for cytoplasmic transport of small amphipathic molecules in which aqueous diffusion of the protein-bound form of the molecule largely determines the transport rate. However, slow interchange of fatty acid between the binding protein and membranes also appears to influence the transport rate in this model system.
- cytoplasmic transport
- cytosolic fatty acid binding proteins
soluble intracellular binding proteins are found in high concentrations in mammalian cytoplasm, where they are thought to facilitate intracellular transport of their ligands by poorly defined mechanisms (40). Many such proteins are found in liver cell cytoplasm where they bind many ligands, including long-chain fatty acids (15), bilirubin (17), bile acids (34), and a host of other metabolites and xenobiotics (17). Although these proteins collectively make up more than 1% of total cellular protein in the hepatocyte, their physiological functions remain poorly understood despite extensive molecular characterization. Among the most studied is fatty acid binding protein, of which several different forms have been defined (15). Previous studies indicate a strong correlation between intracellular fatty acid binding protein concentrations and the intracellular mobility of fatty acids (23-25, 27). On the basis of these results, it was proposed that binding proteins stimulate cytoplasmic diffusion by reducing binding of their ligands to relatively immobile cytoplasmic membranes (27).
Efforts to test this proposal have been hampered by the substantial difficulty of measuring intracellular transport within living cells while also varying intracellular conditions. In particular, it is difficult to compare the functions of different types of binding proteins in the same cell or system. In contrast, model systems permit much greater experimental freedom for testing existing hypotheses. Concepts developed while studying model systems can often be extended to living cells through a process of experimentally confirming or refuting model predictions. Model systems using liposomes have been used by numerous investigators to study the role of soluble binding proteins in the transfer of amphipathic molecules between adjacent vesicles or vesicles and binding protein (6, 9, 18, 28, 30, 32, 35,49). However, none of these investigators has studied transport over distances comparable to the radius of living cells.
The experimental system described in this paper is suitable for studying the function of a variety of binding proteins available in milligram quantities. These include not only the fatty acid binding proteins but also the ligandins (cytosolic glutathioneS-transferases) (21) and bile acid binding proteins (34, 37). The current study used BSA, a well-characterized binding protein with a high affinity for long-chain fatty acids but no known intracellular transport function (8). Results indicate that stimulation of fatty acid diffusion by albumin is saturable in the albumin concentration. Saturation occurred in the absence of detectable binding of albumin to the model membranes, suggesting that it reflects partition of the fatty acid between immobile membranes and more mobile albumin molecules rather than binding of albumin to membrane binding sites. These results support the view that soluble intracellular binding proteins are genuine carrier-mediated transport systems that catalyze movement of hydrophobic molecules through aqueous cytoplasm (41). Multiple predictions of this model system can be tested in living cells using available methods.
MATERIALS AND METHODS
Sources of materials.
BSA (essentially fatty acid free, product A6003) and negative liposome kits were purchased from Sigma (Sigma Chemical, St. Louis, MO, no. L4145). [14C]stearate (specific activity 58 mCi/mmol) and [3H]dipalmitoyl phosphatidylcholine (specific activity 50 Ci/mmol) were purchased from NEN (Boston, MA). Sephacryl S-100 was purchased from Pharamacia (Piscataway, NJ). 12-N-methyl-(7-nitrobenz-2-oxa-1,3-diazol)aminostearate (NBD-stearate) and fluorescein-labeled albumin were purchased from Molecular Probes (Eugene, OR). All other reagents were of the highest grade commercially available.
Measurement of diffusional mobility.
Liposome suspensions containing defined concentrations of albumin were loaded by capillary action into microslide capillary tubes containing two optically flat glass surfaces 50 μm apart (no. 5002, Vitro Dynamics, Rockaway, NJ). Mobilities of NBD-stearate and fluorescein-albumin were measured by fluorescence repolarization after photobleaching (FRAP) as previously described (27), except that room temperature was used (∼22°C) and the microscope objective was ×10 instead of ×40. Five to 10 replicate bleach studies were performed on different areas within each tube, and results were averaged to provide a single data value for that particular day and concentration. This process was repeated on six different days, and the results for each protein concentration were averaged to provide the mean and standard error values.
Binding of NBD-stearate to liposomes and albumin was measured by centrifugation of liposome suspensions at 17,000g for 30 min, sufficient to pellet nearly all of the liposomes. Liposome suspensions were identical to those used for FRAP except that trace amounts of125I-labeled BSA and [3H]dipalmitoyl phosphatidylcholine were also included to permit correction for fluid trapped in the pellet. After centrifugation, supernatant was carefully aspirated and the pellet was resuspended in buffer. NBD-stearate in the supernatant and pellet were assayed using an excitation wavelength of 467 nm and an emission wavelength of 532 nm. The pellet fraction was then assayed by scintillation counting for trapped or unaspirated [14C]sucrose, and the distribution of NBD-stearate between the membrane and albumin was calculated after correcting for albumin in the pellet.
Binding was also assessed by chromatography. Column chromatography allows simultaneous measurement of the distribution of labeled fatty acid between membranes and albumin and the binding (if any) of albumin to liposomes. This additional information comes at the cost of replacing NBD-stearate with [14C]stearate, which may partition differently between liposomes and albumin. However, we were subsequently unable to find any difference in the behaviors of [14C]stearate and NBD-stearate (see results). Samples for chromatography were identical to those used for FRAP except that liposomes were labeled with trace amounts of [3H]dipalmitoyl phosphatidylcholine during preparation and trace amounts of [14C]stearate and125I-albumin were added. A somewhat lower range of albumin concentrations was studied because preliminary studies indicated that less albumin was required to solubilize the fatty acids than to stimulate diffusion. After incubation at room temperature for at least 1 h to ensure binding equilibrium, 25 μl of the suspension were eluted over a 8 × 40-mm column packed with 2 ml of Sephacryl S-100 using a bicarbonate-free Krebs-tricine buffer (46). Elution volume was ∼1.5 times the volume required to elute the lowest molecular weight peak. Samples consisting of three drops each were collected in 1.5-ml polypropylene tubes. Each tube with its effluent sample was added to a 20-ml glass scintillation vial and thoroughly mixed with 5 ml Optifluor (Packard Instrument, Meriden, CT). Vials were then counted for3H and14C activity using a dual-channel liquid scintillation counter and for125I activity using a Packard model 5000 gamma counter. Columns were used once only, after which the column medium was counted by scintillation and gamma counting to measure all radioactivity that had not yet eluted. Channel settings and relative amounts of each radioactive tracer were optimized for separation of 14C,3H, and125I counts. Pure standards of14C,3H, and125I prepared using the same perfusion medium were included to correct for counting efficiency and cross-channel spill.
For each individual column, effluent profiles for the liposomes were fit to the sum of two Gaussian peaks (Eq.1 ) by nonlinear least-squares curve fitting Equation 1where c(f) is the concentration infraction f,A andB are the fitted heights of the peaks,x andy are the fitted widths of the peaks, and f 0 andf 1 are the fractions on which each peak was centered. The two peaks represent the bimodal size distribution of the liposomes (seeresults). Control studies indicated that the liposome profile was unaffected by the presence of albumin or stearate. Albumin and stearate elution profiles were similarly fit to two or more Gaussian peaks. In the absence of liposomes,125I-albumin eluted as a single peak plus a small tail that we have previously shown to be inorganic125I contaminants (47). Thus any high-molecular-weight 125I in the effluent was interpreted as binding of albumin to liposomes, whereas any 125I activity with a molecular weight less than albumin was ignored. Because [14C]stearate plus albumin eluted as a single radioactive peak in the absence of liposomes, any high-molecular-weight14C in the effluent was assumed to reflect binding of [14C]stearate to the liposomes. This binding was assumed to consist of protein-free [14C]stearate plus a possible component of albumin-[14C]stearate complexes in proportion to the degree of binding of125I-albumin to the liposomes. The area under each peak was assessed as the product of peak height and peak width as defined in Eq. 1 . Results of curve fitting analysis for each column assay were averaged and used to calculate the soluble and membrane-bound fractions of [14C]stearate and125I-albumin.
All data are expressed as means ± SE unless otherwise specified. In Figs. 2, 3, 5, and 6, lack of visible error bars on any plotted point indicates that the SE values for that point are small enough that they are hidden by the symbol. Where appropriate, statistical comparison of mean values was used to test previously stated hypotheses only. Significance was assessed by the single-tailed Student’st-test method assuming a normal distribution of both population values.
Preparation of liposomes.
Liposomes were prepared daily from Sigma negative liposome kits (each of which contains 63 μmoll-α-phosphatidylcholine, 18 μmol dicetyl phosphate, and 9 μmol cholesterol) by a minor modification of the recommended procedure. Briefly, the contents of the liposome kit were added to 3 ml of chloroform containing 50 μl of [3H]methylcholine-l-α-dipalmitoyl phosphatidylcholine in 1:1 toluene-ethanol and the solution was dried uniformly onto the interior of a 250-ml round-bottomed flask under nitrogen. Nine milliliters of Krebs tricine buffer were added, and the flask was vigorously shaken to suspend the lipids. The suspension was then vortex mixed at maximum intensity for 90–120 min in a 20-ml glass tube using a Lab-Line desktop vortex tube mixer (no. 1290, Melrose Park, IL). Suspensions were warmed to 37°C for 30 min before use. Sonication was avoided because it was found to produce liposomes too small for our purposes. Liposomes were not size fractionated before use, but the size distribution was assessed. Multilamellar liposomes were not excluded.
Measurement of liposome size distribution.
Liposome sizes were assessed by light scattering using a Coulter N4 Plus photon correlation spectrometer (Coulter, Miami, FL). This device determines particle size by measuring the rate of diffusion of particles in aqueous suspension. A small volume of the liposome suspension was illuminated with a helium-neon laser beam, and the intensity of scattered light (90° to the incident beam) was measured vs. time. Analysis of this time-intensity curve using built-in autocorrelation algorithms gives the rate at which particles move into and out of the beam by Brownian motion. Because temperature and solvent viscosity are known, the diffusion constant and particle diameter can be calculated using the Stokes-Einstein equation. This approach provides the distribution of particle diameters (range of 0.003–3 μm), expressed either as the number or particles or the particle volume for each diameter. Total membrane surface area on the liposomes was assumed to be proportional to the square of the particle diameter. We note that this assumption is true whether or not the liposomes include multilamellar forms. We make no assumption regarding whether the fatty acid binds only the outer membrane of multilamellar liposomes or is evenly distributed throughout the particle.
Size of liposomes.
Liposome diameter exhibited a bimodal distribution with peaks at 0.26 and 2.70 μm (Fig. 1). Less than 2% of the particles were in the larger peak. However, the larger peak contained two-thirds of the liposome surface area due to the greater surface area per particle. Particles were not detected in the range 0.003–0.1 μm diameter (not shown).
Diffusion constant of liposomes.
The diffusion constants of particles with these two diameters estimated using the Stokes-Einstein diffusion equation (38) are 1.79 × 10−8cm2/s and 1.72 × 10−9cm2/s, respectively, both of which are substantially below the diffusion constant of BSA in free solution (∼9.35 × 10−7cm2/s) (45). Thus the diffusion rate of a fatty acid molecule should vary by more than an order of magnitude, depending on whether it is bound to liposomes or albumin. The relative contribution of each liposome fraction to diffusion of the bound NBD-stearate was assumed to be proportional to its diffusion rate constant times its surface area. The effective diffusion constant for the entire range of liposome diameters was calculated by numerically integrating the distribution in Fig. 1 using the Stokes-Einstein equation after weighting for surface area. The weighted mean thus calculated is 1.88 × 10−8cm2/s. This value is much faster than for particles in the large liposome peak and slightly faster than for particles in the center of the smaller peak, indicating that the smallest (and thus most rapidly diffusing) liposomes contribute disproportionately to the observed diffusional flux.
The predicted liposome diffusion rate was then compared with the measured value assessed by FRAP. Conditions were identical to those used in later studies except that no binding protein was added so that effectively all of the NBD-stearate was bound to the liposomes. Use of NBD-stearate to label liposomes is consistent with its prior use as a membrane probe (2). The apparent diffusion constant of the liposomes (assessed on 22 different days with >5 assays per day) was 1.99 ± 0.33 × 10−8 (SE) cm2/s (n = 22), in close agreement with the value predicted from the liposome size distribution.
Diffusion constant of BSA.
The diffusion constant of fluorescein-conjugated BSA (0.01% wt/vol, Sigma) in the liposome suspension was 1.76 ± 0.09 × 10−7 (SE) cm2/s (n = 28). This value is ∼20% of that previously reported for BSA in free solution (13). As will be discussed, slow diffusion of BSA may reflect transient interactions of BSA with the liposomes, increased tortuosity of the diffusional path, or other factors.
Fractionation of albumin-liposome mixtures.
Gel exclusion chromatography was used to characterize the binding of NBD-stearate and albumin to liposomes as a function of albumin concentration. In these studies, albumin was labeled with125I and [14C]stearate was used in place of NBD-stearate to facilitate effluent analysis.125I-albumin eluted as a single peak from the Sephacryl S-100 column (Fig.2). When [14C]stearate was added to the BSA solution, the two peaks coincided exactly, indicating avid binding of the stearate to BSA (not shown). [3H]liposomes eluted as two overlapping peaks, consistent with their bimodal size distribution. Relative size of the two liposome peaks was unaffected by the albumin concentration (range of 0.0–0.5%, correlation of −0.39, P > 0.5,n = 6). Both liposome peaks eluted before the albumin peak, although some overlap occurred.
Recovery of added materials.
Total recovery of added radioactivity averaged 100 ± 2% for125I-albumin, 84 ± 11% for [14C]stearate, and 97 ± 4% for [3H]liposomes (means ± SE). These values are not significantly different from 100%. Effluent radioactivity accounted for 96 ± 2%, 69 ± 10%, and 74 ± 7% of these amounts, respectively, whereas the remainder had not eluted from the column at the end of the experiment.
Fits to Gaussian curves.
As shown in Fig. 2, outflow curves for125I-albumin were adequately represented by a single Gaussian curve, whereas outflow curves for [3H]liposomes were adequately represented by the sum of two Gaussian curves (r = 0.996 ± 0.002 for liposomes, 0.983 ± 0.003 for albumin, means ± SD). The slight positive deviation of the albumin data from the Gaussian curve at later time points represents low-molecular-weight125I contaminants (47) and was not further analyzed. Attempting to fit two Gaussian profiles to the albumin curves failed to detect any liposome-bound albumin [bound fraction of 0.02 ± 0.03%, not significant (NS) vs. zero]. Thus any binding of albumin to liposomes is too small or too rapidly reversible to be detected by this assay.
Diffusional mobility of NBD-stearate in model cytoplasm.
In the absence of binding proteins, the diffusional mobility of NBD-stearate in the liposome suspension was 1.99 ± 0.33 × 10−8cm2/s (means ± SE,n = 22). This value is identical to the diffusion constant of the liposomes determined by light scattering, consistent with complete binding of NBD-stearate to liposomes in the absence of albumin. This value is <3% of the diffusion rate of either albumin or NBD-stearate in water (41) and corresponds to a half-time for diffusion of NBD-stearate back into the bleach site (radius of 5.2 μm) of ∼10 s.
Effect of added albumin on fatty acid mobility.
Addition of BSA stimulated diffusion of NBD-stearate approximately eightfold (Fig. 3). Stimulation of diffusion by albumin was saturable (r 2, correlation coefficient, > 0.999). Half-maximal stimulation was seen at 42.8 ± 0.3 μM albumin (0.287 ± 0.003 g/dl), whereas the maximum diffusion rate (D max) was 1.65 ± 0.12 × 10−7cm2/s.
This result is consistent with progressive transfer of the fatty acid from the relatively immobile liposomes to the more mobile albumin. However, it could also indicate a saturable interaction of albumin with binding sites on the liposome membrane as has been reported previously (36). To discriminate between these alternatives, we measured the soluble (i.e., albumin-bound) fatty acid fraction as a function of the albumin concentration.
Validation of column method for fatty acids.
[14C]stearate outflow curves from the Sephacryl column were adequately described as a weighted sum of the liposome and albumin curves (r = 0.988 ± 0.005), consistent with partition of the fatty acid between the liposomes and albumin. The weighting factor at each albumin concentration thus reflects the partition of the fatty acid between membrane and albumin. The amount of fatty acid bound to membranes and albumin is calculated as the area under the corresponding Gaussian curves.
Effect of albumin concentration on soluble fraction of NBD-stearate.
Added albumin caused a progressive shift of [14C]stearate from the high-molecular-weight liposome peak to the low-molecular-weight albumin peak (Fig. 4). The fraction of the stearate in the low-molecular-weight peak is shown as a function of albumin concentration in Fig. 5. Maximum solubilization was 99 ± 7% (NS vs. 100%). Half-maximal solubilization of [14C]albumin occurred at 17.9 ± 3.0 μM albumin (0.12 ± 0.02%), substantially below the albumin concentration required for half-maximal stimulation of cytoplasmic diffusion (42.8 ± 0.3 μM,P < 0.001). This difference could reflect differences in albumin binding between NBD-stearate and [14C]stearate but could also reflect failure of some of our assumptions (seediscussion). To further assess these possibilities, we repeated the study using NBD-stearate and a centrifugation assay in place of column chromatography.
Validation of column method using centrifugation assay.
Results were identical when a centrifugation assay was used to assess binding of NBD-stearate to the liposomes, indicating that partition of [14C]stearate between membranes and albumin is comparable to that of NBD-stearate and that elution across the column bed does not measurably alter the partition. As for [14C]stearate, the soluble NBD-stearate fraction was saturably related to the albumin concentration (Fig. 6). The albumin concentration producing half-maximal solubilization was 12.2 ± 3.7 μM (0.082 ± 0.025 g/dl), also substantially below the albumin concentration required for half-maximal stimulation of diffusion (P < 0.001) but not significantly different from the value obtained for [14C]stearate in the column assay. Maximum solubilization after correction for trapped solvent in the liposome pellet (using [3H]sucrose as an indicator) was 115 ± 12% (n = 6, NS vs. 100%). These data were corrected for the ∼3% of the NBD-stearate fluorescence that failed to sediment in the absence of albumin. This small amount of nonsedimenting fluorescence is thought to reflect binding of the NBD-stearate to liposomes too small to sediment or to liposomes that became resuspended after centrifugation. Thus we conclude that the concentration of albumin required to solubilize one-half of the NBD-stearate using the centrifugation assay was no different from that required to solubilize one-half of the [14C]stearate by the column assay. Unexpectedly, both values are well below the concentration required to produce half-maximal stimulation of cytoplasmic diffusion. This result, which is not predicted by theory, has important implications for the mechanism of cytoplasmic transport (see discussion).
We have proposed a detailed theory for how binding proteins stimulate intracellular diffusion of their ligands (27, 40-42). Briefly, fatty acids and other small amphipathic molecules are rarely found in the unbound form in cytoplasm. Instead, nearly all are bound to either mobile binding sites (e.g., soluble proteins) or to relatively immobile sites (e.g., membranes, cytoskeleton). The diffusional mobility of an amphipathic molecule is largely determined by its partition between these mobile and immobile pools. For long-chain fatty acids in liver cytoplasm, the mobile fraction is in the range of 18–35% (27).
The mobile fraction of an amphipathic molecule in cytoplasm reflects a balance between the concentration and affinity of soluble binding proteins on the one hand and the density and affinity of cytoplasmic membranes and other relatively immobile structures on the other. Although binding of amphipathic molecules to membranes and cytoskeletal filaments may be weak, the surface area available for binding in a parenchymal liver cell is enormous, ∼1.3 × 107cm2/g for membranes and 1.9 × 104cm2/g for cytoskeletal filaments (3, 14). Theory predicts that the diffusional mobility of the total cytoplasmic pool should be proportional to the concentration of the binding protein, provided that the mobile fraction is ≪1. This prediction has been amply demonstrated in both isolated hepatocytes and perfused rat liver using both native (24) and fluorescent fatty acids (23, 27) and was confirmed by the current data as well (Fig. 3).
Three additional predictions of the theory have not been previously tested. First, stimulation of diffusion should approach a maximum at higher binding protein concentrations as the mobile fraction approaches 100%. This follows because, once essentially all of the amphipathic molecule has been solubilized by the binding protein, further increases in binding protein concentration can no longer stimulate diffusion. Second, the maximum stimulated diffusion rate should be identical to the diffusion constant of the binding protein (because nearly all of the amphipath is bound to the protein). Finally, the concentration of binding protein producing half-maximal stimulation should be identical to that required to solubilize one-half of the fatty acid in the cytoplasm.
The first prediction was confirmed by the data in Fig. 1. Albumin saturably stimulated fatty acid diffusion by about eightfold in model cytoplasm. The second prediction was also confirmed. The maximally stimulated diffusion rate for NBD-stearate was identical to the diffusion constant of fluorescein-labeled albumin in the same system. However, the final prediction was not confirmed. The albumin concentration producing half-maximal stimulation of diffusion was less than half the value required to produce half-maximal solubilization of the fatty acid.
First, it was considered whether this discrepancy might be due to differences between NBD-stearate (used for FRAP) and [14C]stearate (used for column chromatography). However, control studies showed that the albumin concentration required to solubilize NBD-stearate was no different from that required to solubilize [14C]stearate (compare Figs. 5 and 6). Next, it was considered whether the discrepancy might reflect limitations of the column assay. Although chromatography has been used extensively to study binding interactions, it is a nonequilibrium method that might permit redistribution of the fatty acid while the bolus is passing through the column bed. However, repeating the study using an equilibrium method (differential centrifugation) gave similar results. Next, it was considered whether the discrepancy could be due to differences in processing of the liposome suspensions used for FRAP from those used for binding assays. However, both samples were prepared by identical methods and used within 4 h of preparation. Both studies were done using the same albumin and reagent lot numbers, buffers, and temperatures. The only difference was the inclusion of radioactive tracers in the solubilization assays. It was considered whether labeling the albumin with 125I could have caused a reduction in its binding affinity for fatty acids. However, radioiodinated albumin never constituted more than a minuscule fraction of the total albumin present. Finally, it was considered whether the discrepancy might be a statistical anomaly. However, the probability of this is P < 10−5.
Thus the conclusion that the theory of stimulated diffusion is either inaccurate or incomplete may need to be made. Because the theory is a logical extension of basic diffusion and mass action principles, I believe it is fundamentally correct. However, it may well oversimplify the process by assuming rapid exchange of the membrane- and protein-bound pools. Thus the higher concentration of albumin required to stimulate diffusion could reflect slow dissociation of the fatty acid from albumin, which has a half-time of 14 s at the temperature used here (43). Dissociation of NBD-stearate from the liposomes may also be slow, especially if dissociation requires diffusion across the interior of one or more membranes. Although slow dissociation would have no effect on the partition of fatty acids in the binding assays (because there is sufficient time for even slow processes to come to equilibrium), it could prevent rapid exchange of fatty acids between membranes and the binding protein in the FRAP system. The result would be slower diffusional transport of membrane-bound fatty acids, which constitute the bulk of the fatty acids in cytoplasm under physiological conditions (27).
Transfer of fatty acid from albumin to liposomes is analogous to transfer from albumin to the plasma membrane during uptake of fatty acids by cells. It was previously shown that this transfer rate is strongly influenced by a thin aqueous layer that exists at the membrane surface within which uptake of unbound ligand by the membrane exceeds the rate at which unbound ligand can be replenished by dissociation, resulting in binding disequilibrium (39, 45). This disequilibrium layer represents a substantial barrier to the overall transport process (1). The magnitude of this barrier is greater at higher transport rates (i.e., flux densities) but is reduced at higher albumin concentration (42, 44, 45). I propose that the higher concentration of albumin required to produce half-maximal stimulation of diffusion reflects failure of the assumption that equilibrium between membrane-bound and protein-bound fatty acid is very rapid. Because higher albumin concentrations favor binding equilibrium, higher albumin concentrations can overcome this effect. This interpretation can explain why higher albumin concentrations were needed to produce half-maximal stimulation of diffusion than were needed to produce half-maximal solubilization of the fatty acid.
The rate-limiting steps in intracellular transport of amphipathic molecules remain poorly defined. These could include dissociation of the amphipath from membranes or proteins, diffusion of the unbound or bound forms of the amphipath through the aqueous medium, lateral diffusion of the amphipath in the membrane, bulk convection of cytoplasm, and vectorial movement of membrane vesicles or other structures. We have shown that convection and vectorial movement are not detectable in cultured hepatocytes (at least for NBD-stearate) (27) and that lateral diffusion within cytoplasmic membranes is too slow to account for observed fluxes (42). Similar data have been reported in intestinal epithelial cells (B. A. Luxon and M. T. Milliano, unpublished observation). This leaves aqueous diffusion of bound or unbound forms of the fatty acid and ligand exchange between binding proteins and membranes as the most likely steps limiting cytoplasmic transport.
Which of these is actually limiting depends on the relative rates of these processes, including the diffusion constants of bound and unbound amphipath in cytoplasm, the distance across which diffusion must occur, the unidirectional association and dissociation rate constants of the amphipath with the membrane and binding protein, the equilibrium partition of the amphipath between binding protein and immobile binding sites, and the magnitude of the diffusional gradient. Although a full definition of the interactions of these steps is beyond the scope of the current study, certain generalizations are possible. First, rapid association and dissociation rate constants favor binding equilibrium and thus make it more likely that diffusion will limit the intracellular transport rate. Second, steep diffusional concentration gradients favor binding disequilibrium and make it more likely that binding and dissociation will be limiting. Finally, shorter diffusional distances permit a significant flux of unbound ligand between membranes, whereas longer diffusional paths require soluble binding proteins to obtain comparable fluxes. The final point will be discussed further in reference to existing literature data.
Comparison with data for cytoplasmic transport of bilirubin.
Zucker and co-workers (50, 51) have studied the exchange of bilirubin between donor and acceptor membrane vesicles in the presence and absence of cytosolic binding proteins and have concluded that dissociation of bilirubin from membranes is too rapid to limit transfer. Instead, transfer was limited by the rate of diffusion of unbound bilirubin monomer between the vesicle membranes (51). The rate of dissociation was modulated by the size and cholesterol content of the membrane vesicles (50). Addition of a soluble binding protein, glutathione-S-transferase B, did not stimulate the rate of bilirubin transfer between the vesicles but instead diminished it. The authors (50) concluded that cytoplasmic transport of bilirubin does not require binding proteins. Instead, they suggested that bilirubin may move through the cytoplasm by a series of small jumps of unbound bilirubin between adjacent membranes. These data are of high quality. A complete theory of cytoplasmic transport must therefore account for these data as well as the current observations.
Importance of distance on transport mechanism.
It is proposed that the differences between the results of this study and those of Zucker and co-workers (50, 51) reflect the different distance scales across which transport is being measured. The current study deals with transport across distances comparable to the size of cells. The photobleaching laser beam (radius of 5.2 μm) generated a diffusional gradient across many thousands of vesicles. In contrast, the bilirubin study measured transport between donor vesicles and their nearest neighbors in the absence of large-scale diffusional gradients. Although the mean distance between vesicles was not assessed in this study, it was many orders of magnitude smaller than the diffusional gradient in the current study. On the basis of this difference, a testable theory is offered for why the need for binding proteins depends on the distance across which the diffusion occurs.
Consider the fate of a single ligand molecule that has just dissociated from a membrane. In the absence of binding protein, only two outcomes are possible. It can rebind to the same membrane or it can bind to a different membrane located a distance (x) from the first. The probability that the molecule will bind to the second membrane is determined by the relative values of the rate constants for the alternate paths. If the rate constant for rebinding to the original membrane isk 1 and the rate constant for binding to the second membrane isk 2, then the probability of transfer to the second membrane isk 2/(k 1+ k 2). In general, k 2 <k 1 becausek 2 incorporates the rates of both diffusion and binding to the second membrane, whereask 1 includes only binding. However, for sufficiently low values ofx,k 2 ≅k 1 and the probability of transfer approaches 50% (Fig.7).
If the second membrane is more distant, however, the need to diffuse across the water layer separating the two membranes will reducek 2 until it is ≪k 1 and transfer is less likely. For simplicity, we assume rapid equilibrium between the protein-bound and unbound forms of the ligand and identical donor and acceptor membranes. From Fick’s law, the rate constant for diffusional transport isD/x 2(where D is the aqueous diffusion constant of the ligand). By analogy to sequential electrical conductances (11),k 2 is Equation 2Substituting this value for k 2and rearranging gives the probability of transfer (P) as Equation 3The condition that prevents efficient transfer of the ligand to the second vesicle is thusD/x 2≪ k 1. Because the distance term in this inequality is squared, increasing values ofx rapidly prevent efficient transfer of unbound ligand between vesicles. After rearrangement, the condition preventing efficient transfer becomes Equation 4In contrast, for distances much smaller than this, transfer to the second membrane is equally likely as rebinding to the first membrane.
Addition of a binding protein can greatly extend the distance that can be traveled in a single diffusional “jump.” Protein binding reduces the rate constant for rebinding of the ligand to the membranes,k 1, permitting a longer mean residence time in solution and thus a greater mean diffusional path. However, binding to a protein also reduces the diffusion constant of the ligand, which slows transfer. Thus whether protein binding increases or decreases the diffusional flux depends on the relative importance of these offsetting effects. The reduction in the diffusion constant of fatty acid after binding to albumin is ∼10-fold (44). In contrast, the reduction in the rate of rebinding of soluble fatty acid to the membrane is approximately equal to the decline in its unbound fraction in the aqueous phase caused by protein binding. In the case of long-chain fatty acids, a 1% albumin concentration should reduce the unbound fraction (and thusk 1) by a factor of ∼30,000 (8). Substituting these values in Eq.4 indicates that albumin increases the distance that the ligand can diffuse before rebinding by a factor of or more than 50-fold.
It may be argued that cytoplasmic transport could occur by a sequence of many such jumps, each covering a distance small enough to make binding proteins unnecessary. Such a mechanism is certainly possible, but it would be inefficient. If, for example, cytoplasmic transport from point A topoint B requires a sequence of 10 successful jumps, then the probability that all 10 will be successful is P 10. We noted previously that P cannot be >0.5 in a two-membrane system. With multiple sequential membranes, however,P is even smaller. This follows because a ligand molecule that jumps into the aqueous medium now has three possible fates: it may rebind to the original membrane, bind to the next membrane in the sequence (moving toward point B), or bind to the previous membrane in the sequence (moving back toward point A). ThusP cannot be greater than one-third even for closely spaced membranes; the probability of transfer fromA toB in the minimum 10 jumps cannot be greater than (1/3)10 (∼0.00002). Because P appears with a large positive exponent, the probability of transfer is extremely sensitive to the value of P.
Thus binding protein can increase P[by reducing the rate constant for rebinding to the membranes (k 1) by more than the reduction in the diffusion constant (D); see Eq.3 ]. Binding proteins increase not only the probability of successful transfer from one membrane to another after a single jump but also (to a much greater degree) the probability of transfer from point A topoint B after multiple jumps. A complete theoretical analysis of the effects of binding proteins on diffusional transfer of ligands through a membrane suspension is beyond the scope of this paper. However, the conclusion may be made that for sufficiently small intermembrane distances (as defined inEq. 4 ) binding proteins do not stimulate the diffusional transfer of ligands between membranes, whereas for sufficiently large distances diffusional transport is strongly dependent on binding protein concentration regardless of how many jumps occur.
Alternate interpretations of the data.
Although I interpret saturation at higher albumin concentrations as a reflection of ligand partition between mobile and immobile pools, it might alternatively reflect a transient interaction of albumin with a limited number of liposome binding sites. Several considerations support this possibility. Albumin is known to bind phospholipid membranes and many other surfaces (5, 10, 20, 29, 36). Albumin binding is saturable, presumably reflecting the limited surface area available for binding (5). Certain forms of cytosolic fatty acid binding protein have been shown to interact directly with membranes during transfer of fatty acids to and from their binding sites (16, 19), suggesting that albumin might act similarly. Several laboratories have suggested that a direct interaction of albumin with membranes may be involved in exchange of fatty acids with membranes (7, 12, 31). If the rate-limiting step in cytoplasmic transport were transfer of the fatty acid to and from the binding protein rather than diffusion, then saturation could reflect this interaction rather than progressive solubilization of the fatty acid by albumin.
The current data are most consistent with a mechanism in which both aqueous diffusion and exchange of fatty acids between the membrane and albumin are important factors in determining fatty acid mobility. At higher albumin concentrations, the rate-limiting step is strictly diffusional, with a fatty acid mobility identical to the diffusion rate of the binding protein. If exchange of fatty acids between membranes and albumin were rate limiting under these conditions, the maximum observed mobility would have been slower. However, at lower albumin concentrations, the observed mobility of the fatty acid appears also to be limited by slow exchange. This conclusion is supported by the fact that a significantly higher albumin concentration was required to stimulate diffusion than to produce desorption of the fatty acids from the membrane. It is interesting to note that transfer of fatty acids between albumin and a lipid surface shows similar features (4). At low albumin concentrations, the transfer rate is determined primarily by the rate of desorption from albumin or from the lipid surface. At higher albumin concentrations, the rate is determined primarily by diffusional processes. The current study cannot exclude a transient interaction of albumin with the membrane during fatty acid exchange. If this occurs, however, it must involve only a small fraction of the albumin molecules at any time, as no significant binding of albumin to the membranes was detected using either chromatography or centrifugation.
A second unexpected finding is that the diffusion constant of albumin in the model cytoplasm (1.76 ± 0.09 × 10−7cm2/s) was significantly slower than published aqueous diffusion constants of mammalian albumins (∼6 × 10−7cm2/s) (41). This could reflect tortuosity of the diffusional path (22), molecular crowding (22), reversible formation of soluble aggregates of albumin (48), changes in water structure near membranes (33), or other factors. Slow diffusion of albumin seems unlikely to reflect errors in calibration of our system, as the diffusion constant observed for the liposomes was exactly that predicted from their measured size distribution. It also seems unlikely to reflect changes in the albumin molecule caused by covalent modification with fluorescein, as the same value was obtained for NBD-stearate-albumin complexes at high albumin concentrations.
Limitations of the current approach.
To the degree that the suspension of liposomes, albumin, and NBD-stearate used in this study does not accurately reflect conditions in the cytoplasm, the model used in this study may give misleading results. For example, liposomes are small enough to have a significant diffusion constant, whereas endoplasmic reticulum and mitochondria would be expected to diffuse much more slowly in vivo. Cytosolic fatty acid binding proteins should also diffuse more rapidly than albumin due to their much smaller molecular weights. In both cases, the model system would be expected to underestimate the degree of stimulation of cytoplasmic diffusion provided by cytosolic binding proteins in vivo. Finally, the rate of exchange of fatty acids between soluble fatty acid binding proteins and cytoplasmic membranes in vivo may well be faster than between albumin and liposomal membranes in our model system, reflecting differences in binding constants, temperature, membrane properties, membrane density, and the potential for certain soluble fatty acid binding proteins to interact directly with membranes to facilitate fatty acid exchange. If so, the in vivo discrepancy between the concentration required to stimulate diffusion and the concentration required to solubilize the fatty acid may be different or absent.
In summary, binding proteins stimulate diffusional transport of amphipathic ligands within model cytoplasm by reducing ligand binding to relatively immobile membrane binding sites. These results confirm multiple predictions made on the basis of FRAP data in cultured hepatocytes (27) and multiple indicator dilution in perfused liver (24). Use of this model system to study other binding proteins and microsomal membrane vesicles should be straightforward.
I acknowledge the expert technical assistance of Wei-Lan Ma.
Address for reprint requests and other correspondence: R. A. Weisiger, Division of Gastroenterology and the Liver Center, S-357, Univ. of California, San Francisco, San Francisco, CA 94110-0538 (E-mail:).
This study was supported by National Institute of Diabetes and Digestive and Kidney Diseases Grant DK-32898 and Liver Core Center Grant DK-26743.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.
- Copyright © 1999 the American Physiological Society