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Journal of Lipid Research, Vol. 47, 561-570, March 2006
Copyright © 2006 by American Society for Biochemistry and Molecular Biology
* Department of Medical Biochemistry and Genetics, Laboratory B, University of Copenhagen, Panum Institute, DK-2200 Copenhagen N, Denmark
Department of Pharmacology and Pharmacotherapy, Danish University of Pharmaceutical Sciences, DK-2100 Copenhagen Ø, Denmark
Published, JLR Papers in Press, December 19, 2005.
1 To whom correspondence should be addressed. e-mail: norby{at}imbg.ku.dk
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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Supplementary key words red blood cell membranes • erythrocyte ghosts • membrane binding • exchange efflux • rate constant of anandamide dissociation from albumin • diffusion coefficient of anandamide
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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Hydrophilic molecules such as amino acids need membrane transporters/channels to pass through the lipophilic plasma membrane (7). Although anandamide is a neutral lipophilic molecule with low monomeric solubility in water (8), the uptake of anandamide into cells has also been suggested to be mediated by a membrane transporter (9–14). The permeation of cellular membranes has been studied in several cell types (9, 11, 12). The existence of such an anandamide transporter is an important but controversial subject that divides researchers into two groups of apparently incompatible opinions (15–20). The evidence for the existence of an anandamide transporter in the plasma membrane comes from saturable uptake kinetics in cells and from the use of inhibitors, but to date no carrier proteins have been isolated.
Studies have reported both saturable and nonsaturable uptake kinetics using total anandamide concentration as a variable (17, 20–22). However, according to conventional theory for the cellular uptake of protein-bound lipophilic compounds, only the free monomer lipophilic compound participates in the uptake process. When studying the transport of lipophilic compounds whose membrane translocation is rapid, it is important to consider the effect of an unstirred layer (UL) around cells, because it may also be a rate-limiting barrier for transport (23, 24). Therefore, finding saturable kinetics may not be a definitive proof for a carrier-mediated process.
Furthermore, intracellular metabolism by fatty acid amide hydrolase, binding to cellular proteins and binding to plastic tools in the absence of albumin, may complicate the measurement of the true membrane passage of anandamide (10, 11, 18, 25, 26). We have used red blood cell ghosts, which classically have been used for transport studies of chloride, bromide, iodide, thiocyanate, salicylate, and glucose (27–29). All of these water-soluble compounds pass the membrane by facilitated diffusion, and the studies are carried out from 0°C to 37°C. These studies show that protein-mediated transport can be studied at low temperatures, and because the translocation of anandamide is extremely rapid, we have chosen 0°C to get reliable results. Furthermore, it is possible to study the transport process without metabolism and the involvement of ATP and by using exchange efflux without a substrate gradient.
Diffusional barriers are important when transport processes are studied. Diffusional resistance in a UL will be the dominant factor if transmembrane movement is fast, as is the case for lipophilic compounds such as anandamide. Failure to consider the effect of a UL may result in erroneous estimation of uptake rates. One of the effects of a UL is that the clearance of unbound lipophilic compound is enhanced when albumin concentration is increased. This phenomenon led to different theories, such as the existence of albumin receptors on cell surfaces and conformational changes and/or local factors at the cell surface, which cause an enhancement of the dissociation of ligand-albumin complexes (surface-mediated dissociations) (30). However, receptors for albumin have never been found, and these speculations ended, especially after the elegant study of Weisiger, Pond, and Bass (30). They studied the effect of albumin concentration on oleate fluxes in a system of decane (lipid phase) separated from a stirred water phase by an unstirred planar interface and found that a decrease in the effective diffusion barrier with increasing albumin concentration resulted in an enhancement of the flux.
Cellular uptake of anandamide occurs only when it is in the monomeric form in a sequence of at least three steps: release from its binding protein, membrane transfer, and binding by intracellular binding proteins or by enzymes (19). The release of anandamide from cells occurs by the same three steps in reverse order. It is important to understand the mechanism by which anandamide passes membranes to elucidate whether a putative membrane transporter is a pharmacological target (12, 31) or whether cellular uptake is governed only by diffusion. One strong argument for the involvement of a protein is the apparent evidence of "saturable uptake." The aim of this study was to find an alternative interpretation of the apparent saturable uptake.
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MATERIALS AND METHODS |
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Preparation of erythrocyte ghosts
The preparation of a uniform population of BSA-free and BSA-filled resealed "pink" ghosts from freshly drawn human blood was carried out as described previously (19, 32). The pink ghosts, which still contain 
3% hemoglobin, are very robust and qualified for transport studies. After preparation, the ghosts were stored at 0°C in 165 mM KCl, 2 mM phosphate buffer, pH 7.3, containing 0.02 mM EDTA/EGTA (1:1) (buffer I) containing BSA of appropriate concentrations and used for experiments within 2 days. The density of ghosts was 1.02 g/ml; for calculations, we use 1 g of packed ghosts, which is equal to 1 ml. Eight donors, both men and women (age 21–64 years), were used.
Preparation of incubation buffers
[3H]anandamide and unlabeled anandamide was dissolved in 50 µl of benzene, just enough to moisten 200 mg small glass beads (diameter, 0.1 mm). The benzene was sublimated at low pressure, and incubation buffers were prepared by shaking the anandamide-loaded beads with a solution of BSA in buffer I for 15 min at room temperature.
Efflux experiments with ghosts
One volume of packed ghosts (with or without internal BSA) was equilibrated with 1.5 volume of incubation buffer at 0°C for 50 min. Radioactive ghosts were separated from buffer I containing labeled as well as unlabeled anandamide by centrifugation for 7 min at 30,100 g and washed with 10 volumes of buffer I, pH 7.3, at 0°C. These washed suspensions of ghosts were distributed onto 80 mm plastic tubes (inner diameter, 3 mm) and packed by centrifugation for 10 min at 17,000 g at 0°C. The supernatant was removed by cutting the plastic tube just below the interface, and 100–200 mg of packed ghosts was injected into 35 ml of vigorously stirred isotope-free buffer I containing BSA and unlabeled anandamide corresponding to the cellular 
value. Serial sampling of cell-free extracellular medium was done with the Millipore-Swinnex filtration technique. Ten to 15 samples were taken at appropriate intervals for the determination of the extracellular accumulation of radioactivity as a function of time. The activity of filtrates was measured by counting 400 µl in 3.9 ml of scintillation fluid. The efflux experiments were all carried out at 0°C as with the fast efflux of anandamide from ghosts our manual sampling technique does not allow higher temperatures.
In control efflux experiments at low (0.065) as well as at higher (0.4) with no albumin in the outer medium, we found <3.2% of the dpm in the medium. Furthermore, no increase in dpm by time was found.
Calculation of the unknown diffusion coefficient of anandamide
To our knowledge, the diffusion coefficient of anandamide has never been measured. An approximate value can be calculated on the basis of the theory of diffusion in liquids. With the assumption that anandamide is spherical and much larger than the water molecules, we can use the Sutherland-Einstein equation
 | (Eq. 1) |
is the viscosity of water at 0°C (1.798 centipoise = 1.798/100 g s–1 cm–1), r is the radius of the spherical particle, and N is Avogadro's number (6.02 x 1023 molecules per mol).
Furthermore, if anandamide consists of spherical particles of radius r and density d, its molecular weight (MW) should be
 | (Eq. 2) |
 | (Eq. 3) |
Theory of efflux
Efflux from BSA-free ghosts
We use the same models used in our studies of efflux of long-chain fatty acids from human red blood cell ghosts (19, 33, 34). The exchange kinetics follows a biexponential time course according to compartment model I shown in Fig. 1. The solution of the second order differential equation, which describes the kinetics, is according to a previous publication (19)
 | (Eq. 4) |
 | (Eq. 5) |
 | (Eq. 6) |
 | (Eq. 7) |
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Again, the exchange kinetics follows a biexponential time course. The solution of the second order differential equation, which describes the kinetics, is in this case
 | (Eq. 8) |
 | (Eq. 9) |
 | (Eq. 10) |
 | (Eq. 11) |
Calculation of the rate constant for anandamide dissociation from BSA
Previously, in our studies on arachidonic acid and oleic acid, it was possible to present an expression for the determination of the dissociation rate constant from BSA (33, 34). All details are given in those two publications in Appendix A and Appendix 2, respectively. The analogous equation for anandamide becomes
 | (Eq. 12) |
From the definition of the two dissociation constants Kd and Kdm, we get
 | (Eq. 13) |
 | (Eq. 14) |
Substitution of C into the equation for k1 gives
 | (Eq. 15) |
, the equilibrium dissociation constant of the anandamide-BSA complex (Kd), the diffusion resistance (RD), the area of ghosts (S), and the diffusion coefficient of anandamide (D) all are known.
Scintillation counting
We used a Tri-Carb 2200CA liquid scintillation analyzer from Packard. The efficiency is 67% for 3H in unquenched samples using 3.9 ml of Ultima Gold scintillation fluid. Counting rates were determined to a probable error of <1%.
Statistics and data analyses
The linear and nonlinear regression procedures given by Origin 6 were used to determine the best fit of the data to the exponentials of the model. The formula to calculate the variations of terms is the general formula
 | (Eq. 16) |
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RESULTS |
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values. The results are given in Table 1.
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and ß are determined. The model parameters km, k3, and B/E (see Fig. 1 and Notations) are determined by equations 5, 6, and 7, respectively. The most important information is that the ratio of anandamide bound to the inner leaflet to anandamide bound to the outer leaflet of ghost cell membranes (B/E) and the rate constant of unidirectional flow through the membrane from B to E (k3) are both constant at all concentrations of BSA in the medium ([BSA]o). The values are 0.27 and 0.36 s–1 (19), respectively. However, the rate constant (km) of the unidirectional flow of anandamide from the ghost membrane to BSA in the medium is dependent on [BSA]o (Table 1). This was not expected from the true exchange kinetics. This dependence, however, is understood when the effect of the UL around ghosts is taken into consideration. We have to consider the tracer uptake by BSA in unstirred volume Vu as well as in stirred volume Vs (see Appendix). For the parameters, see Notations.
As outlined in the Appendix, equation A12 is used to fit three constants (1, 2, and 3) to determine the rate constant (k5) of anandamide dissociation from membrane binding sites to the adjacent water phase and to demonstrate the validity of the model. Figure 2A shows the 1/km dependence of ([BSA]o)
according to equation A12 with the three constants 1, 2, and 3 (eq. A13). Constant 2 is the most reliable of the three constant. It can be calculated from values of M, , RD, and Kd using M = 5.25 nmol g–1, = 0.198, RD = 0.022 s ml–1, and Kd = 6.87 10–12 mol ml–1 (see Notations), so we fixed it at the calculated value of 67.55 .The fitting procedure gives a rate constant k5 equal to 4.2 ± 0.4 s–1 and a constant 3 of 410,374 ± 27,230, which is to be compared with the calculated value of constant 3 (256,985) using = 0.198, k1 = 3.33 s–1, and the values of RD, S, D, and Kd given in Notations. Figure 2B shows the 1/km dependence of 1/([BSA]o). Here, linear regression analysis according to equation A14 gives a fit with an R value of 0.995 and a Chi-square value of <0.002, indicating the validity of the model.
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= 0.2, S = 144 x 9 x 109 x 10–12 cm2, k1 = 3.33 s–1, Kd = 6.87 x 10–12 mol ml–1, and D = 209.5 µm2 s–1 turns out to be 2.6 x 10–4 ± 0.4 x 10–4. It can only be a try, because to our knowledge the diffusion coefficient of anandamide is not available, but with the calculated D = 209.5 µm2 s–1 and in view of the heterogeneous population of red blood cells from very different donors (see Materials and Methods), the agreement is remarkable and thereby demonstrates the validity of our model. It is noteworthy that the rate constants of anandamide dissociation from BSA (k1 = 3.33 ± 0.27 s–1) and from the ghost membranes (k5 = 4.2 ± 0.4 s–1) are very much alike.
According to the theory, km should not be dependent on . This can be seen from equation A14. If we rewrite equation A14 as
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)/)] are constant, and calculation of [M ((1 – )/)] shows that the expression is virtually constant. For a variation in with a factor of >7 from 0.102 to 0.784, M varies from 2.53 to 38.34 nmol g–1, to give a nearly constant value of the term [M ((1 – )/)] as it varies from 23.50 and 22.73.
Direct experimental verification of this constancy is obtained by efflux experiments at low and high values. At [BSA]o = 15 µM, we get km = 0.649 ± 0.074 s–1 at low value (0.06) and 0.622 ± 0.066 s–1 at high value (0.4). When [BSA]o = 30 µM, km = 0.712 ± 0.093 s–1 at low value (0.05) and 0.815 ± 0.062 s–1 at high value (0.4). These results are again weighty evidence for the validity of the model.
Exchange efflux of anandamide from BSA-filled ghosts
These kinds of experiments show that anandamide effluxes are much slower than from BSA-free ghosts (19). The experimental values for the rate constant of anandamide transfer from intracellular BSA complexes to the membrane outer leaflet (ki) (Fig. 1) were found to vary with the [BSA]i such that ki decreased with increasing [BSA]i (19). Because the rate constant of translocation (k3) is constant for all [BSA], it is apparent that the dissociation rate constant k1 of anandamide-BSA complexes does not account for the fractional anandamide release to the water phase inside ghosts. This is because the ghost volume is unstirred; therefore, it is the effective mean dissociation constant, k1*, that is responsible for the anandamide release from BSA inside ghosts. In previous publications, a detailed account of the effects of an unstirred intracellular compartment is given (33, 34). The effective mean dissociation rate constant k1* is calculated from k1 according to the equation k1* = k1 3 (r
ctnh(r) – 1)/(r)2 [Appendix 3 equation A12 in Bojesen and Bojesen (34)], where r (3 µm) is the radius of ghost (see Notations for ). The calculated values of k1* are 0.92 ± 0.19, 0.60 ± 0.10, 0.44 ± 0.06, and 0.29 ± 0.04 s–1 for [BSA]i of 7.5, 15, 30, and 60 µM, respectively.
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DISCUSSION |
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In the present system, the effect of the medium on the efflux kinetics of fatty acids was investigated previously (33–35). The data obtained could not be explained if the volume surrounding the ghosts was regarded as homogeneous with regard to tracer water phase concentration. Furthermore, we found that BSA of a limited volume was important (35). Likewise, a direct proportionality between the reciprocal constant 1/km (Fig. 1) (km, previously called k5*) and the reciprocal square root of BSA concentration outside the ghost cells ([BSA]o) was found; in other words, km divided by the square root of [BSA]o was constant [(33) (Table 1)]. The same was found in the present study (Figs. 2B, 3), and this is a predicted effect if a UL is present (see Appendix for the theory).
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In experiments with BSA-filled ghosts, the efflux kinetics is much slower than that in experiments with BSA-free ghosts. We found a decreasing effective mean dissociation rate constant of anandamide-BSA complexes (k1*) with increasing [BSA]i. This effect of [BSA]i can be explained by a UL inside the ghosts. With an intracellular UL, we have a situation in which although BSA makes larger diffusional fluxes possible, it reduces the availability of unbound anandamide for uptake into the membrane phase.
Application of the results
In exchange efflux experiments, the net flux of radioactive anandamide is balanced by an equal and opposite movement of nonradioactive anandamide. This means that the km dependence of [BSA]o (Fig. 3) is also valid for uptake. Such dependence was previously observed in studies of fatty acid uptake into cells, in which fatty acids were offered to the cells bound to albumin (36, 37). The phenomenon shown in Fig. 3 was referred to as a "pseudofacilitation mechanism" and explained by Weisiger, Pond, and Bass (30) as the existence of a disequilibrium layer within a UL. The concentration of unbound anandamide is so low that a concentration gradient easily arises within the UL. This study, as well as our previous study on oleic acid (34), adds to an understanding of such dependence. The concentration of unbound anandamide is 7,000 times lower than that of anandamide bound to BSA. Therefore, the release of unbound anandamide from the membrane disturbs the local equilibrium between ligand and BSA. When [BSA] is low, the possibility that an anandamide molecule can return to the membrane phase is highly likely, whereas this possibility becomes increasingly unlikely as the [BSA] increases. In the situation of nonlimiting membrane permeability and with free anandamide concentration adjacent to the membrane lesser than the equilibrium concentration (P), the efflux rate [J (nmol s–1); equal to the uptake rate] normalized to 1 ml (1 g) of ghosts can be calculated according to the equation
 | (Eq. 17) |
The values of Kd, S, and D are given in the Notations, k1 = 3.33 s–1, 60 µM (0.4%) is used for [BSA]o, and values are varied. Figure 4 shows such uptake rate versus the water phase concentration of the free unbound anandamide [P = Kd /(1 – ); see Notations]. This plot obviously shows "saturation kinetics," and if saturation kinetics is observed, it is not possible to distinguish between true saturation kinetics and a situation in which the membrane permeation is nonlimiting, and the uptake is determined by the clearance of unbound anandamide in the UL. The same form of curve is seen in studies of fatty acid efflux (34, 38) and in several studies of the short-term initial oleic acid uptake by metabolizing cells (39). Thus, taking the apparent saturation kinetics obtained for anandamide [for a critical review, see Glaser, Kaczocha, and Deutsch (20)] as a function of the total concentration, or even of the water phase concentration, as evidence for a membrane transporter may not be the correct interpretation of the data, because such data could equally indicate a barrier function of the UL around the cells followed by a much faster membrane translocation.
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According to our previous study (19), anandamide membrane transport is extremely rapid. With 60 µM binding protein inside as well as outside the red blood cell ghosts, the half-life for transport through the membrane at 0°C to extracellular binding protein is 16 s (19), so at 37°C, it is probably <1 s. Therefore, the data obtained for uptake lasting for minutes are probably not valid for studying the pure transport process.
More serious is the fact already mentioned that experiments that form the basis for the postulate of a carrier protein mostly are carried out without albumin in the medium. In our experiments, no anandamide is released from the cells without protein in the medium. The molar ratio of anandamide to albumin in body fluid is very low. With a plasma concentration of 4 nM, >99% is bound to albumin (8). This means that anandamide in such experiments is offered to the cells in concentrations that exceed the monomer water phase concentration (8) by a factor of >106. Anandamide is a hydrophobic compound and it adheres to glass tubes and plastic wells if not bound to albumin, so added to buffer directly or dissolved in alcohol, the actual concentration is unknown (18, 25).
As mentioned above, the membrane binding (M) has been used together with the inside/outside distribution (B/E) and the equilibrium dissociation constant (Kd) (19) to calculate the dissociation rate constant k1 according to equation 8 at different corresponding km values and [BSA]o (Table 1). The calculation requires that the model is correct, but from the above discussion it seems reasonable to believe this. The value 3.33 s–1 is high compared with the dissociation rate constant for the long-chain fatty acids. The corresponding rate constant for arachidonic acid is 0.21 s–1 (45), and according to Demant, Richieri, and Kleinfeld (46), extrapolation of the arachidonic acid values to 0°C gives a constant of 0.67 s–1. This means that the anandamide constant is 1 order of magnitude higher. This is surprising, but perhaps an explanation can be found by comparison with all of the fatty acids studied, with the exception of palmitic acid, that display diverging membrane binding characteristics (B/E = 4–5) (45, 47). Apparently, we have a linear relationship between changes in 
G* (activation free energy) and changes in G0 (reaction free energy). Thus, oleic acid as the most hydrophobic of the fatty acids has the highest binding constant Ka (0.83 x 109 M–1) and the lowest dissociation rate constant k1 (0.006 s–1). The group of fatty acids with similar and lower hydrophobicity, arachidonic acid, linoleic acid, and docosahexaenoic acid (47), have lower binding constants (Ka values of 0.20, 0.28, and 0.24 x 109 M–1, respectively) and k1 values 1 order of magnitude higher (0.21, 0.14, and 0.47 s–1). Anandamide as the least hydrophobic compound has the lowest binding constant (Ka = 0.14 x 109 M–1) and a k1 of 3.33 s–1, a value again 1 order of magnitude higher. This comparison makes sense, because we have shown that the carboxyl group does not contribute significantly to the free energy of binding of fatty acids to the hydrophobic channel in BSA by van der Waals-London dispersion interactions (48).
In conclusion, when highly hydrophobic compounds with fast transport across membranes are in question, the saturation kinetics seen in Fig. 4 may be understood as a [BSA] dependence (i.e., as an effect of a rate-limiting delivery of anandamide from BSA in the UL).
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APPENDIX |
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is the half length, where the concentration in the UL is half of the feeding concentration). It is defined as (k1 A/(P D)) = [k1 [BSA]i(1 – )/(Kd D)] (35). is calculated to 3.73, 5.27, 7.45, and 10.54 µm–1 for [BSA]i = 7.5, 15, 30, and 60 µM, respectively. –1 represents a disequilibrium layer near the membrane surface, which decreases with increasing [BSA] (30).
x S = 6 x 144 x 9 x 10 9 x 10–12 ml = 7.8 ml.
/(S D) = 6/(144 x 9 x 10 9 x 10–12 x D). Calculated to 0.022 s ml–1.
/(1 – ) (8).
) [[BSA] D (1 – ) k1/Kd].
– aP/A) by binding to BSA in Vs, equal to Vs k1 [BSA] (1 – )/Kd.
Significance of the UL around ghosts
To understand the effect of [BSA] on the rate constant, we have to consider the tracer uptake by BSA in the unstirred volume (Vu) as well as in the stirred volume (Vs). Anandamide is poorly soluble in water; therefore, it is impossible to dissolve anandamide in pure buffer and produce solutions with a well-defined monomer concentration of anandamide. However, in equilibrium with albumin-bound anandamide, a well-defined concentration can be obtained in buffer solutions at low ratios of anandamide to albumin. The water phase concentration of anandamide is low. With a high rate of uptake or release, small gradients can occur, which in the presence of a UL around the ghosts will influence the maximum uptake or release considerably. Thus, it is the binding to albumin that results in the efflux. For terms, see Notations.
The quasistationary efflux of tracer is based upon the principle of independent diffusion streams advocated by Jacobs (49). As described by Bojesen and Bojesen (35), the total flow of anandamide [(F1 + F2), corresponding to the net uptake of tracer in Vu and Vs, respectively] can be expressed in terms of clearance. Thus
 | (Eq. A1) |
 | (Eq. A2) |
 | (Eq. A3a) |
 | (Eq. A3b) |
from equations A3a and A3b gives
 | (Eq. A4) |
 | (Eq. A5) |
= Clu + 1/((1/Cls) + RD).
Furthermore, the flux between the membrane and medium space adjacent to the membrane is
 | (Eq. A6) |
Elimination of co from equations A5 and A5 gives
 | (Eq. A7) |
and the tracer dose T = m + y, we get
 | (Eq. A8) |
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A >> M, we obtain the differential equation
 | (Eq. A9) |
)/(PCl + k5M).
For t = 0, y = 0, which means that C = –T, and for t = , y = y = T. The solution is now 1 – y/y = e–km t and
 | (Eq. A10) |
/(1 – ), Cl = Clu + 1/((1/Cls) + RD) and Clu = S (1 – e–) (D (1 – ) (k1/Kd) [BSA]) (35) in equation A10 yields
 | (Eq. A11) |
) 
1 as is (k1 [BSA] (1 – )/(Kd D), which means that for = 6 µm, e– = 2 x 10–10 for [BSA] = 7.5 µM and 3.5 x 10–28 for [BSA] = 60 µM.
We focus on the term 1/((1/Cls) + RD). Cls is dependent on [BSA], but the following considerations show that 1/Cls is negligible compared with RD: i) Cls = Vs k1 [BSA] (1 – )/Kd; ii) Vs = V – Vu = 35 – 7.8 = 27.2 ml [see Notations and (35)].
With the values of the constant k1 equal to 3.33 s–1 and Kd (6.87 x 10–12 mol ml–1) published previously (8) and the experimental = 0.2, 1/Cls varies from 1.3 x 10–5 s ml–1 at [BSA] = 7.5 x 10–9 mol ml–1 to 1.6 x 10–6 s ml–1 at [BSA] = 60 x 10–9 mol ml–1. These values are to be compared with RD values of 2.2 x 10–2 s ml–1 (see Notations).
 | (Eq. A12) |
 | (Eq. A13) |
)RD/(Kd ), and constant 3 = RD S (D k1 (1 – )/Kd). This equation has been used to fit the three constants and show the km dependence of [BSA].
If we choose to ignore completely the term 1/((1/Cls) + RD) in Cl and the term (1 – e–), equation A10 reduces to
 | (Eq. A14) |
 | (Eq. A15) |
 | (Eq. A16) |
. At [BSA] = 7.5 µM, we make an error of 4.5%, and at the higher [BSA] of 60 µM, the error is 1.6%. |
ACKNOWLEDGMENTS |
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Manuscript received September 16, 2005 and in revised form December 9, 2005.
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