Different Mechanisms of Free Fatty Acid Flip-Flop and Dissociation Revealed by Temperature and Molecular Species Dependence of Transport across Lipid Vesicles*

The mechanism of free fatty acid (FFA) transport across membranes is a subject of intense investigation. We have demonstrated recently that flip-flop is the rate-limiting step for transport of oleic acid across phospholipid vesicles (Cupp, D., Kampf, J. P., and Kleinfeld, A. M. (2004) Biochemistry 43, 4473-4481). To better understand the nature of the flip-flop barrier, we measured the temperature dependence of a series of saturated and monounsaturated FFA. We determined the rate constants for flip-flop and dissociation for small (SUV), large (LUV), and giant (GUV) unilamellar vesicles composed of egg phosphatidylcholine. For all FFA and vesicle types, dissociation was faster than flip-flop, and for all FFA, flip-flop and dissociation were faster in SUV than in LUV or GUV. Rate constants for both flip-flop and dissociation decreased exponentially with increasing FFA size. However, only the flip-flop rate constants increased significantly with temperature; the barrier to flip-flop was virtually entirely due to an enthalpic activation free energy. The barrier to dissociation was primarily entropic. Analysis in terms of a simple free volume (Vf) model revealed Vf values for flip-flop that ranged between ∼12 and 15Å3, with larger values for SUV than for LUV or GUV. Vf values increased with temperature, and this temperature dependence generated the enthalpic barrier to flip-flop. The barrier for dissociation and its size dependence primarily reflect the aqueous solubility of FFA. These are the first results to distinguish the energetics of flipflop and dissociation. This should lead to a better understanding of the mechanisms governing FFA transport across biological membranes.

Transport of long chain free fatty acids (FFA) 2 across cell membranes is a necessary step for FFA utilization. Although considerable effort has been devoted to understanding the mechanism of cellular transport, there remains substantial disagreement as to whether transport is facilitated by membrane proteins or occurs by diffusion through the lipid phase (1)(2)(3)(4). A protein-mediated mechanism would necessitate slow diffusion across the lipid phase, and therefore, understanding the mechanism of transport across simple lipid membranes has received considerable attention (5)(6)(7)(8)(9)(10)(11)(12)(13).
We have recently re-examined this issue and found that flipflop is the rate-limiting step for transport of oleate across small (SUV), large (LUV), and giant (GUV) unilamellar vesicles and that dissociation is 5-10-fold faster than flip-flop (13). Previous conclusions (7,11) that flip-flop was rapid and that dissociation was rate-limiting were based on incorrect interpretations of the results, primarily measurements of oleate influx into vesicles using oleate that was not complexed with serum albumin. We demonstrated previously that such measurements provide information about vesicle binding rather than flip-flop because the lipid bilayer is perturbed by exposure to high concentrations of unbound oleate when using uncomplexed oleate (13). In contrast, accurate information about flip-flop can be obtained by measuring influx using oleate complexed with bovine serum albumin (BSA) and/or measuring oleate efflux and dissociation from the vesicles (13).
The studies of Cupp et al. (13) revealed that flip-flop represents a major barrier to transport of oleate across the lipid bilayer and that this barrier increases with increasing vesicle diameter from SUV (ϳ250 Å) to LUV and GUV (Ͼ1000 Å). Thus, the lipid phase barrier to FFA flip-flop, at least in certain cell membranes, might be large enough so that the cell's FFA metabolic requirements would necessitate a membrane protein transporter. In fact, we found a highly refractory lipid phase in our recent studies of FFA transport in adipocytes, where FFA transport was best described as mediated by an ATP-dependent transport pump (14,15).
How the lipid phase can generate such large barriers is not known. The expectation of rapid flip-flop is based on the notion that flip-flop occurs by "Stokesian" diffusion through the hydrocarbon interior of the bilayer, a process equivalent to diffusion through an isotropic organic fluid. An isotropic solvent model is unlikely to provide an accurate representation of FFA flip-flop because of the anisotropic nature of the bilayer and the requirement for reorientation of the FFA within the bilayer. Moreover, diffusion of a solute through an isotropic solvent exhibits a relatively weak dependence (V Ϫ1 ⁄ 3 ) on solute size, whereas studies of non-electrolyte solute permeation through lipid and red cell membranes reveal exponential dependences on solute size (16,17). Lieb and Stein (16) have proposed that this steep size dependence reflects the polymer-like characteristics of the bilayer, in which diffusion proceeds by a "non-Stokesian" mechanism. In addition, the temperature dependence of diffusion through a Stokesian fluid should also be smaller than the dependence through a polymer (18). Thus, if the polymer-like nature of the bilayer affects FFA flip-flop, both the FFA size and temperature dependence of transport should be significantly different from those expected for a simple organic fluid.
A systematic investigation of the FFA size and temperature dependence of transport across lipid vesicles in which the flipflop and dissociation steps were resolved has not been carried out previously. Previous results with selected FFA and temperatures need to be reconsidered because influx measurements were performed with uncomplexed FFA and because dissociation was not accurately separated from flip-flop (5,7,19). To develop a better understanding of the molecular basis for the steps involved in FFA transport across lipid membranes, we have, in this study, measured the temperature dependence for transport of a series of saturated and monounsaturated FFA of increasing size. Measurements were carried out in SUV, LUV, and GUV composed of egg phosphatidylcholine. The measurements allowed us to separate the FFA size and temperature dependence of the flip-flop and dissociation steps. The results indicate an exponential dependence of flip-flop and dissociation on FFA size. The barrier for flip-flop was dominated by large (15-20 kcal/mol) activation enthalpies and little or no entropy, whereas the barrier for dissociation was predominantly entropic. These results are inconsistent with a representation of the bilayer as a simple hydrocarbon fluid but suggest a more complex mechanism.

EXPERIMENTAL PROCEDURES
Materials-Egg phosphatidylcholine was purchased from Avanti Polar Lipids, Inc. (Alabaster, AL), and L-␣-dipalmitoyl-[choline,methyl-3 H]phosphatidylcholine was from American Radiolabeled Chemicals, Inc. (St. Louis, MO). Sodium salts of the FFA were purchased from NuChek Prep (Elysian, MN), and stock solutions were prepared in water containing 4 mM NaOH (pH 11) and 50 M butylated hydroxytoluene. Pyranine (8-hydroxypyrene-1,3,6-trisulfonic acid) was purchased from Molecular Probes (Eugene, OR). Acrylodan-labeled rat intestinal fatty acid-binding protein (ADIFAB) was prepared as described (20) and is available from FFA Sciences LLC (San Diego, CA). Fatty acid-free BSA was purchased from Sigma. The buffer used in FFA transport experiments contained 20 mM Hepes, 140 mM NaCl, and 5 mM KCl at pH 7.4 (buffer A), and both the FFA⅐BSA complexes and the vesicles were prepared in this buffer.
Vesicle Preparation-Vesicles were prepared as described recently (13). SUV, which are ϳ250 Å in diameter (21), were composed of egg phosphatidylcholine and sonicated in the presence of 0.5 or 2 mM pyranine in buffer A. LUV composed of egg phosphatidylcholine with 2 mM trapped pyranine or ADI-FAB were prepared by extrusion and are ϳ1000 Å in diameter (22). GUV were prepared by dialysis of octyl ␤-glucopyranoside-solubilized egg phosphatidylcholine in which either 400 M ADIFAB or 20 mM pyranine was also present and have diameters Ն2000 Å (23). The last step for all three vesicle types was chromatography through Sephacryl S-1000 to separate free and trapped pyranine and/or ADIFAB. Vesicle phospholipid concentration was determined using the Elon method for total inorganic phosphate (24). Vesicle concentrations used in the stopped-flow experiments were between 5 and 200 M. All stopped-flow concentrations refer to values in the mixing chamber, not in the syringe.
FFA⅐BSA Complexes and Buffering of Unbound FFA-Complexes of FFA and BSA were prepared so that unbound FFA were buffered at defined values (13). Complexes of the unsaturated FFA were prepared by mixing aliquots of the sodium salt of the FFA from a 5 mM stock solution in water plus 4 mM NaOH at 37°C with a 600 M BSA solution in buffer A, also at 37°C. For saturated FFA, the stock sodium salt solution was heated to between 55 and 70°C, higher temperatures for longer chain FFA, before addition to the BSA solution at 37°C. The concentration of free or unbound FFA was monitored several times during this titration using ADIFAB (25), and the final unbound FFA concentration ranged from 5 nM to 1.5 M. A critical feature of the FFA⅐BSA complexes is that, at sufficiently high BSA concentrations, the unbound FFA concentration will not change upon addition of vesicles. The conditions for a well buffered system depend upon unbound FFA, BSA, and vesicle concentrations and are determined by ensuring equal concentrations of unbound FFA in the complex and complex plus vesicles through direct measurement with ADIFAB. For a well buffered system and sufficiently low unbound FFA concentrations, the influx time courses are well described by a single exponential. However, for a poorly buffered system, the influx time course reveals additional temporal components, both faster and slower than observed with the well buffered system.
To measure FFA transfer between vesicles and BSA, SUV, LUV, and GUV were loaded with FFA by titrating a rapidly stirring solution of vesicles with aliquots of the sodium salt of the FFA. Titrating the vesicles with FFA was done by diluting a 50 mM sodium FFA solution in 4 mM NaOH (pH 11); raising the temperature to 37°C; and distributing equal aliquots, waiting 2 min between aliquots, into a rapidly stirring solution. For efflux and transfer experiments, vesicle concentrations were between 25 and 100 M, and the fraction of loaded FFA was between 10 and 20 mol %. Acceptor BSA was used at between 2 and 10 M.
Stopped-flow Fluorescence-The kinetics of FFA movement were monitored by stopped-flow mixing with temporal resolution of Ͻ2 ms. Stopped-flow fluorescence was performed using a KinTek instrument, which allows two emission wavelengths to be detected simultaneously and in which equal volumes of 0.1-ml reactants were mixed at flow rates of Ն6 ml/s as described previously (13). All concentrations refer to the value in the mixing chamber. Tryptophan and pyranine fluorescence intensities were monitored by excitation at 290 and 445 nm, respectively, and observation of emission through 20-nm bandwidth filters at 343 or 505 nm, respectively. ADIFAB fluorescence was excited at 386 nm, and simultaneous emissions were measured at 432 and 505 nm. At least two separate preparations and Ͼ20 kinetic traces were generated for most experimental conditions.
Analysis of FFA Kinetics-Three different time courses were measured: 1) influx measurements in which the time course of FFA movement from the BSA donor to the vesicles was monitored by the change in fluorescence intensity of pyranine and/or ADIFAB trapped within the vesicle, 2) efflux measurements in which the time course of FFA movement from the vesicles to BSA in the extra-vesicle aqueous phase was monitored by trapped pyranine and/or ADIFAB fluorescence, and 3) transfer measurements in which FFA movement from the vesicles to extra-vesicle BSA was monitored by the change in BSA tryptophan fluorescence. The kinetic traces were fitted with multi-exponential functions to determine empirical rate constants for influx (k in ), efflux (k out ), and vesicle-to-protein transfer (k trns ). For the transfer measurements, we observed two rates: the k trns value is the faster (generally ϳ5-10-fold) of the two rate constants. We analyzed the transfer time course either allowing both components to vary or fixing the slow component to equal k out . Both fits yielded virtually indistinguishable 2 values and generally similar rate constants. We therefore used in most of our analyses k trns obtained with the slow component fixed as k out .
To determine the intrinsic rate constants for flip-flop (k ff ) and dissociation (k off ) that govern the time courses and to better understand their dependence on kinetic parameters, we used the analysis and simulation facilities of the programs MLAB (Civilized Software, Silver Spring, MD) and MACSYMA as described (13). This analysis accounts for the movement of FFA between BSA and vesicles and the movement of FFA across the bilayer as discussed by Cupp et al. (13). Back-transfer from BSA to the vesicles could contribute to the transfer kinetics, and therefore, the k trns values we report may be less than the k off values; however, in all cases, k trns Ͼ k out . We did not detect any significant change in k trns at 5-50 M BSA for oleate (13) and in the selected cases examined in the present study (data not shown). We therefore conclude that, to a good approximation, k in and k out Ϸ k ff and k trns Ϸ k off .
As discussed by Cupp et al. (13), under conditions in which the FFA⅐BSA complexes buffer the unbound FFA, so that the unbound FFA concentration is the same in the presence or absence of vesicles, the determination of the inward flip-flop rate constant from the measured k in values is virtually independent of the BSA-bound FFA dissociation rate constant (k off (BSA)). Our simulations (13) of the transport time courses demonstrated that this lack of dependence on k off (BSA) results because, under buffered conditions, the fraction of BSA bound FFA that is transferred to the vesicles is small (typically Ͻ2%), and therefore, the time needed to transfer is Ͻ2% of the k off (BSA). Values for k off (BSA) were obtained from our measurements of the dissociation of palmitate (C16:0), stearate (C18:0), oleate, and linoleate (C18:2⌬9⌬12) at 22 and 37°C (26) and indicate that, in addition to oleate, k in should also be virtually independent of k off (BSA) for these other FFA. Dissociation rate constants for the additional FFA used in the present study are not available, nor are values available for any of the FFA at all temperatures studied in this investigation. We have assumed, however, that because the unbound FFA was buffered for all FFA, binding and therefore k in are independent of k off (BSA) for all FFA investigated.
Two features of our results provide experimental support for the accuracy of the flip-flop rates obtained from k in . First, for all FFA and temperatures, k in and k out are quite similar, given the caveats concerning k in discussed under "Results." Second, for the same FFA⅐BSA complexes, the k in values for SUV are ϳ10 times faster than for LUV or GUV. Because k off (BSA) is independent of the vesicle type and k in does not involve BSA-vesicle collisions (13), the results indicate that k in is independent of k off (BSA), at least for LUV and GUV.
Eyring Transition State Theory-The activation free energy (⌬G ‡0 ), activation entropy (⌬S ‡0 ), and activation enthalpy (⌬H ‡0 ) were calculated using the Eyring rate theory as described previously (27). This analysis assumes that the thermodynamic model provides a reliable representation of the formation of the transition state and that the activation enthalpies and entropies are temperature-independent.
Free Volume Model-We have used the approach of Lieb and Stein (16) to extract free volume parameters that capture the FFA size dependence of our results. At each temperature, we analyzed the FFA molecular species dependence by expressing the rate constants for transport as in Equation 1, where V f is the average free volume for a given vesicle and temperature and k o is a pre-exponential factor. The molecular volume V (Å 3 ) was estimated as M r ⅐10 27 /(N o ⅐d⅐1000), in which M r is the molecular weight of the FFA, N o is Avogadro's number, and d is the density of neat FFA and was adjusted (d ϭ 1.3) to yield volumes consistent with those of Xiang and Anderson (18). At each temperature, the values of k in and k out as a function of the molecular volume for the saturated and monounsaturated series of FFA were used to determine k o and V f by leastsquares fitting with Equation 1. Because the k o values generally showed little or no temperature dependence, we then repeated the analysis with the pre-exponential factor fixed to the value averaged over temperature and vesicle type, and the V f values from this analysis are reported here (see Fig. 6).

RESULTS
Stopped-flow measurements were carried out to determine the three rate constants that define FFA transport across lipid vesicles: 1) transfer of FFA from BSA to the vesicle while monitoring trapped pyranine or ADIFAB (k in ), 2) transfer of FFA from the vesicle to BSA while monitoring trapped pyranine or ADIFAB (k out ), and 3) transfer of FFA from the vesicle to BSA while monitoring BSA tryptophan fluorescence (k trns and k out ). This approach was used in our previous study of oleate at 22°C (13) and has now been extended to determine rate constants for 13 FFA using SUV, LUV, and GUV at temperatures between 15 and 37°C.
A representative example of the measured time courses from which the three rate constants were determined (in this case, for the series of saturated FFA transported across LUV at 20°C) is shown in Fig. 1. The results reveal a monotonic increase in all three rate constants with decreasing FFA chain length. These results also illustrate a feature common to all FFA studied and to the three types of lipid vesicles. The time course for the change in BSA tryptophan fluorescence resulting from transfer of FFA from the vesicles to BSA is composed of two components (k trns and k out ), and in all cases, k trns Ͼ k out . This indicates that the rate constant for transfer from the vesicle surface to BSA (k trns ) is faster than k out , and therefore, as found previously for oleate (13), flipflop is the rate-limiting step for FFA transport across lipid vesicles.
The rate constants determined from the time courses in Fig.  1 as well as from the corresponding time courses for SUV and GUV at 20°C are shown in Fig. 2 and Tables 1-3. For all three vesicle types, the three rate constants decreased exponentially with increasing chain length. The rate constants for SUV were larger by ϳ10-fold compared with those for LUV and GUV, whereas LUV and GUV revealed similar rate constants. The results emphasize that k trns Ͼ k out and, in most cases, k trns Ͼ k in for the saturated FFA and all three vesicle types. Therefore, for all saturated FFA, dissociation from the vesicles is faster than flip-flop (k in or k out ).
A similar variation of rate constants was observed for the series of monounsaturated FFA in SUV and LUV, except that the rate constants were ϳ10-fold larger for the monounsaturated FFA compared with the saturated FFA of the same chain length ( Fig. 3 and Tables 1 and 2). Furthermore, for the same chain length (18 carbons), the rate constants increased exponentially with double bond number, from zero for stearate to 2 for linoleate (data not shown). Notably, k out and, in most cases, k in for these unsaturated FFA were significantly slower than dissociation. Taken together with the similar behavior of saturated FFA, these results confirm that flip-flop is the rate-limiting step for all long chain FFA and vesicles investigated in this study.
Transport rate constants were measured as a function of temperature and analyzed in terms of the Eyring theory to determine the activation free energies (⌬G ‡0 ), enthalpies (⌬H ‡0 ), and entropies (T⌬S ‡0 ) for the saturated FFA in the three vesicle types (Fig. 4). The ⌬G ‡0 increased linearly with chain length, consistent with a transport barrier that increases by ϳ4 kcal/mol with chain length from 14 to 19 carbons. The barriers for the three rate constants were ϳ1 kcal/mol larger in LUV and GUV compared with SUV; the larger vesicles revealed slower rate constants than SUV. Although the ⌬G ‡0 barriers increased uniformly for all three rate constants, the barrier for dissociation (⌬G ‡0 trns ) was smaller than the flip-flop barriers for all chain lengths.
The linear behavior of ⌬G ‡0 with FFA and its dependence on vesicle type are similar for the three transport steps, yet the mechanisms underlying flip-flop and dissociation are quite different. This is apparent from the differences in the ⌬H ‡0 and T⌬S ‡0 contributions to the barriers for flip-flop and dissociation (Fig. 4). For the influx and efflux steps, the enthalpic portion of the barrier dominated the free energy. In contrast, the free energy activation barrier for transfer was dominated by entropic factors.
Activation thermodynamic potentials for the monounsaturated series of FFA in SUV and LUV reveal a roughly similar behavior compared with the saturated FFA series (Fig. 5). However, there were significant differences between saturated and monounsaturated FFA. For influx and efflux, ⌬G ‡0 values were ϳ1.4 kcal/mol smaller than for the corresponding saturated FFA; this reflects the ϳ10-fold faster rate constants for the unsaturated FFA. On average, the smaller ⌬G ‡0 values for unsaturated FFA reflect smaller (ϳ1 kcal/mol) enthalpic contributions. For transfer, the differences between saturated and monounsaturated ⌬G ‡0 values were smaller (ϳ1 kcal/mol), and on average, the smaller ⌬G ‡0 for the monounsaturated FFA was due to a more favorable entropic contribution.
Because dissociation is virtually temperature-independent, whereas flip-flop increases exponentially with temperature, resolving the rate constants for dissociation from efflux becomes  Table 2) were determine by fitting exponential functions (not shown) to these measured traces. The time courses shown here are averages of at least three individual stopped-flow traces. The total number of traces acquired for all conditions was Ͼ7000, and the estimated average uncertainty of the measured rate constants was Ͻ30%. increasingly difficult with increasing temperatures, and at sufficiently high temperatures, the rate of flip-flop may exceed that of dissociation. This does not occur at temperatures Յ37°C, although, as discussed below, k in was occasionally Նk trns for the shorter chain FFA probably because unbound FFA levels were too high.
We would expect rate constants for influx and efflux to be equal if flip-flop were symmetric. However, for all FFA and vesicles studied, k in Ն k out . This may reflect, in part, vesicle asymmetry because the k in Ϫ k out difference for SUV (ϳ2-fold) was larger than for LUV and GUV (ϳ60%). An additional contribution to this k in Ϫ k out difference is the FFA-induced perturbation of lipid vesicles as described previously for oleate transport (13). In the previous study, we showed that k in increases with increasing unbound oleate concentrations, whereas k out is much less sensitive to vesicle loading with FFA. Significant increases in k out were observed only for [FFA]/[vesicle phospholipid] Ͼ 0.2, and in the present study, all efflux measurements were performed with [FFA]/[vesicle phospho-lipid] Յ 0.2. We investigated the effect of increasing unbound FFA concentrations on k in for selected FFA and found increases in k in (data not shown), consistent with our previous oleate study. These effects were FFA type-dependent and appeared to be correlated with vesicle-water partition coefficients (K p ); for the same unbound FFA concentration, shorter chain and more unsaturated FFA were less perturbing. Because the pyranine response decreased with decreasing partition coefficient, higher unbound FFA concentrations were generally used for influx measurements for FFA with shorter chains and/or larger double bond numbers than for longer chain saturated FFA. For example, for myristate (C14:0), the unbound FFA concentration was 723 nM, whereas for nonadecanoate (C19:0), the unbound FFA concentration was 6 nM, but both generated similar equilibrium pH i decreases.

DISCUSSION
The results of this study demonstrate that flip-flop is the ratelimiting step for FFA transport across lipid vesicles. Transport    (13,28), previous studies of long chain FFA have reported flip-flop rate constants that were faster than stopped-flow resolution and concluded that flip-flop was virtually independent of the molecular species of FFA (7,11). As we demonstrated for oleate (13), the reports of extremely rapid flip-flop were incorrect because influx cannot be measured using FFA that is not complexed with albumin, as was done previously (7,11). We also found that studies of FFA transfer from donor vesicle to acceptor BSA or acceptor vesicles in which changes inside the vesicles were measured determined efflux rather than dissociation (13), as assumed previously (5,19). Indeed, the k out value for oleate we reported (13) and the "dissociation rate constant" of Zhang et al. (19) are in excellent agreement. For the five additional FFA (myristate, palmitate, margarate (C17:0), stearate, and linoleate) in the present study for which Zhang et al. (19) also reported values, our efflux rate constants are, on average, virtually identical to the dissociation rate constants of Zhang et al. (19), and both studies show similar trends with FFA molecular species. Massey et al. (29) determined rate constants for the dissociation of a number of long chain FFA from SUV by monitoring albumin fluorescence as FFA transferred from donor vesicles, similar to the methods used in the present study. We noted previously in the case of oleate that our k trns and the k off of Massey et al. (29) were in good agreement (13), and we have found here that our dissociation rate constants for the three additional FFA (palmitate, stearate, and eicosenate (C20:1⌬13) for which Massey et al. (29) also reported values agree, on average, to within a factor of 2 and display similar trends with FFA molecular species.
Membrane Permeability and Free Volume-In this study, we found that FFA flip-flop and dissociation are profoundly sensitive to the FFA type. Evidence of a size dependence for transport of molecules across membranes has been obtained previously in a number of studies of the permeability of non-electrolytes through lipid bilayers and membranes (16 -18, 30, 31). These previous studies of small non-electro-  lytes, including short chain FFA, reported significant discrepancies from Overton's rule, in which membrane permeability (P) is related simply to the partition coefficient (K p ) between an isotropic hydrocarbon solvent and water. In particular, the results demonstrated substantial decreases in permeability that were independent of the solute K p (16 -18, 30, 31). Within the context of the solubility-diffusion model, permeability can be considered as partition of the solute into the membrane, followed by diffusion through the membrane, so that P ϭ K p ⅐D/d, where D is the diffusion coefficient through a membrane of thickness d (32).
Most studies have suggested that the size dependence results in slower diffusion through a bilayer compared with isotropic organic solvents (30,31). The much steeper size dependence has led to the proposal that diffusion across membranes is non-Stokesian and is better described as diffusion through a polymer (16,30). Analyzing non-electrolyte permeability within the framework of a soft polymer, Stein (30) suggested that D should be modeled as D ϰ exp(ϪV/V f ), where V f is the average hole size or free volume within the membrane. Diffusion of the solute through the membrane would require the formation of a hole of volume V equal to the volume of the solute (30). A V f of 13 Å 3 yields an excellent fit to non-electrolyte permeability through human red cells (30). More recently, in a study of short chain FFA permeability, Xiang and Anderson (17,18) suggested that a free surface area model might better reflect the effect on FFA transport of phospholipid chain ordering and partition into and diffusion across the bilayer.
Separating the Mechanisms of FFA Flip-Flop and Dissociation-Permeability measurements do not directly distinguish partition and diffusion and therefore cannot determine whether partition or diffusion is the rate-limiting step for transport. In contrast, the methods used in this study enabled us to distinguish the translocation and binding/dissociation steps. This allowed determination of the rate-limiting step and the mechanisms of the individual steps in FFA transport across lipid membranes.
Our transport results revealed exponential dependences on molecular size and temperature, suggesting that FFA transport may be better represented as diffusion through a polymer-like structure rather than through a Stokesian fluid. Diffusion across such a membrane would involve the creation of free volume (16) or free area (17,18) and would reveal high activation energies. As discussed by Falck et al. (33), specific forms of free volume or free area models, at least for lateral diffusion in the bilayer, may be premature, and we therefore used the simple approach of Lieb and Stein (16) (see "Experimental Procedures") to analyze our results.
The results of the free volume analysis of influx (k in ) and efflux (k out ) for the saturated and monounsaturated FFA series revealed monotonic increases in V f with temperature for all vesicle types (Fig. 6). Free volumes for influx and efflux averaged over all vesicles and temperatures yielded 13.5 Ϯ 1 Å 3 , remarkably similar to the value reported for red cells (16). In all cases, V f values for SUV were larger than for LUV or GUV. The increase with temperature in V f values obtained from the flipflop rate constants is consistent with the enthalpic character of the Eyring activation free energy for flip-flop. By equating the Eyring and free volume equations for the rate constants, ⌬H ‡0  can be expressed as a function of the FFA molecular volume. 3 The slope of the V f temperature dependence and these calculated ⌬H ‡0 values are in good agreement with those obtained from the measured activation energies (Figs. 4 and 5). These results suggest that the rate-limiting enthalpic barrier reflects the energy needed to create free volume sufficient to allow FFA flip-flop between the outer and inner hemileaflets of the bilayer.
Although primarily entropic, the dissociation barrier includes a small enthalpic contribution (on average, 4 kcal/ mol). This enthalpic contribution may be involved in the creation of free area needed to allow the FFA to dissociate from or insert into a hemileaflet of the bilayer. The origin of the entropic contribution to the dissociation barrier and its molecular size dependence are probably related to solvation of the FFA as discussed in more detail below.
Vesicle Size Dependence-Our results indicate that, for all FFA, both flip-flop and dissociation decrease with increasing vesicle size. Similar results were obtained in previous studies of cholesterol, anthroyloxystearate, and bilirubin dissociation and anthroyloxystearate and bilirubin flip-flop (27, 34 -36). The similar LUV and GUV results we obtained are consistent with the detailed investigation of size dependence for bilirubin transfer, which revealed an asymptotic value for the transfer rate constant for vesicle diameters Ͼ1000 Å (36). The suggested origin of the size dependence of dissociation is a decrease in solute hydration or an increase in phospholipid packing with increasing vesicle size (36). Within the context of the free volume model, the vesicle size dependence can be accounted for by the larger V f for SUV compared with LUV or GUV. Whether free volume or some other characteristic of the different phospholipid order of SUV and LUV is an accurate description of how the bilayer affects flip-flop will require molecular models that are more refined than Equation 1.
Model of FFA Transport through Lipid Bilayers-The steps involved in FFA transport across the bilayer can be described with reference to Fig. 7B. We suggest that, from the aqueous phase (Step A), the FFA inserts tail first into the bilayer because Ͼ98% of the FFA is ionized at pH 7.4, and a carboxylate-first insertion would require an enthalpic activation energy of ϳ26 kcal/mol (37). However, dissociation (Figs. 4 and 5) and membrane partition (38) are largely entropic, and therefore, k on must also be largely entropic because K p ϭ k on /k off . Once in the bilayer, half of the membrane-bound FFA become protonated (39,40).
As suggested by Xiang and Anderson (18), insertion of the FFA into the bilayer (Fig. 7B, Steps A to B) involves the creation of free area. We suggest that the energy (⌬H ‡0 ) needed to generate this free area is small (ϳ4 kcal/mol) because this area has to accommodate only the cross-section of the short axis of the FFA. Because this area is similar for all FFA, this step is probably not involved in the FFA size dependence of dissociation.
To flip across the bilayer, the FFA must, in addition to a translocation, undergo a 180°reorientation in which the polar carboxyl group reorients between the lipid-water interfaces on the two sides of the bilayer. (Flip-flop of the anionic form of the FFA is between 4 and 6 orders of magnitude slower than that of the protonated form (37,41).) We speculate that, by slipping farther into the bilayer and rotating in a folded conformation (Fig. 7B, Steps C, D, and E), the FFA will undergo reorientation near the interface between the bilayer hemileaflets, where the membrane has substantially more disorder than near the head groups (42). The formation of the free volume and folding of the FFA may occur by torsional rotations along the acyl chains of the phospholipid and FFA. The ϳ10-fold larger flip-flop rates for monounsaturated FFA compared with saturated FFA 3 The derivative of ln(k) with respect to temperature using Equation 1 yields V/V f 2 (dV f /dT ). In the Eyring model, the derivative of ln(k) equals 1/T ϩ ⌬H ‡0 /R⅐T 2 , and therefore, ⌬H ‡0 ϭ R⅐T 2 (V/V f 2 (dV f /dT ) Ϫ 1/T ). Typical ⌬H ‡0 values for efflux and influx calculated using the values of Fig. 6 ranged between 15 and 18 kcal/mol. may result because the cis-double bond itself provides a partial fold. The final step in the flip-flop process is the movement of the FFA from Steps E to F, the reverse of the Step B-to-D sequence.
Dissociation from the vesicle presumably occurs by creation of free area and ionization of the FFA, which likely dissociates as the anion. The FFA then becomes solvated in the aqueous phase, where it is at equilibrium (Fig. 7B, Steps B to A). Free energies for partition of oleate and palmitate are 10 kcal/mol and virtually entirely entropic (38), which, together with the ⌬H ‡0 of 4 kcal/mol, accounts for most of the ⌬G ‡0 of 15-17 kcal/mol for oleate and palmitate (Fig. 7A). That FFA solvation accounts for most of the dissociation barrier is consistent with findings based on short chain fluorescent FFA (43).
The observed size dependence of the dissociation rate constants reflects the size dependence of solvation. This conclusion is supported by comparing ⌬G ‡0 for dissociation with the equilibrium free energy change (⌬G 0 ) for partitioning of FFA between water and heptane (44). The increase in ⌬G 0 with FFA carbon number (0.825 kcal/mol/carbon) is virtually identical to the value for ⌬G ‡0 (0.820) (Fig. 8). Furthermore, subtracting ⌬G 0 from ⌬G ‡0 yields a size-independent barrier of ϳ7 kcal/mol. Although larger than the 4 kcal/ mol attributed to free area formation, some of this disparity may be related to differences between heptane and the lipid bilayer. The faster dissociation of the monounsaturated FFA compared with the saturated FFA is also consistent with solubility because unsaturation increases the aqueous solubility of hydrocarbon chains (45).
Conclusion-Our results indicate that flip-flop is the ratelimiting step for FFA transport across lipid bilayer membranes and that the major barrier to flip-flop may be creation of a free volume large enough to accommodate the reorientation of an extended or partially folded FFA. The larger barrier for LUV and GUV and the correspondingly smaller V f compared with those for SUV suggest that interactions between the bilayer lipid components affect the barrier to flip-flop. Lipid components present in biological membranes may generate different barriers; our results in erythrocytes are consistent with a lipid phase and V f value similar to those of LUV (28), but our results in adipocytes suggest that the lipid phase is virtually impenetrable to flip-flop (14). This implies that at least certain biological membranes may require protein-mediated transporters to catalyze the flip-flop step. If V f formation is the barrier to flip-flop, vesicles with lipid compositions corresponding to those of erythrocytes and adipocytes may reveal different V f values. Studies to clarify this are now in progress.