J . Phys. Chem. 1993,97, 4479-4483
4479
Partial Molar Volume of Solutes in Bilayer Lipid Membranes J. J. Ramsden Department of Biophysical Chemistry, Biozentrum, CH-4056 Basel, Switzerland Received: April 27, 1992
Many biologically significant molecules interact with cell membranes. It is therefore important to study the mechanisms of interaction, preferably at the molecular level. A key parameter characterizing these interactions is partial molar volume. This article shows how the partial molar volumes of the membrane lipid and solutes partitioning into a lipid bilayer membrane can be determined from the membrane refractive index, which in turn is obtained from measuring the velocity of light guided along a planar optical waveguide on which the membrane has been deposited. The technique allows the optical parameters for a single bilayer to be measured. By arranging the supported membrane such that it forms one wall of a cuvette, changes in these parameters due to the incorporation into the membrane of solutes introduced into the cuvette can be determined. For the lecithin-dibucaine system, three regions of behavior were found. At low mole fractions x of incorporated solute (up to x 0.08),the dibucaine partial molar volume increases rather steeply, starting from a value only about half the estimated molecular volume, showing that the dibucaine is incorporated into preexisting voids in the bilayer membrane. In the second region (0.08 < x < 0.18), the dibucaine partial molar volume reaches a maximum, corresponding to its theoretical "vacuum" value, and then starts to decrease. Throughout these regions, the lipid partial molar volume changes by less than 1% but in the third region (x > 0.18),the lipid partial molar volume starts to increase, apparently as a result of extensive water penetration the bilayer due to the presence of the dibucaine, which is a prelude to the bilayer destruction and micellization observed at x > 0.3.
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Introduction Many biologically significant molecules are amphiphilic; in the absence of specificmembrane-bound receptors such molecules will partition into bilayer lipid membranes, a process equivalent to dissolution in the lipid phase. Characterization of amphiphile lipid membrane partitioning is an essential part of the study of the physical chemistry of membrane processes. Although partitioning in these systems has usually been characterized by of a single parameter, the partition coefficient, evidence for more complex partitioning processes is emerging from the nonideal partition isotherms found in several systems, e.g., alamethicin, which forms aggregates in the lipid bilayer phase,' and ionizable oligopeptides, which progressively repel successivearrivals at the surface of the bilayer as it charges up due to their incorporation.2 Presently, rather little is known about the interaction between lipid and solute at the molecular level and the complex interplay between solute and lipid water of hydration (for a lipid bilayer in contact with water, Le., fully hydrated, the mole fraction of water is about 0.9) in such partition processes. The basic parameters characterizing these intermolecular interactions are the partial molar volumes, D, of each component. It is impracticable, in the case of a single bilayer, to measure its actual volume, which is the usual route to D. In this paper, it is shown how D can be determined from the membrane refractive index, which is measured by a novel integrated-optics method: the bilayer lipid membrane is deposited on a planar optical waveguide, and measurementof the phase velocities of theguided light modes allows the refractive index of the membrane to be determined. A more complete physicochemical characterization of amphiphile-lipid membrane interaction has important applications. Many drugs are amphiphiles,whose absorption and distribution involve their passage across cell membranes. At present, the partition coefficient determined in the octanol/buffer system is a widely recognized parameter for drug design. In most cases, it is probably far too simplistic and in future one may expect a more sophisticated approach based on partition "functions", which
will explicitly take actual membrane structure and nonideal features into account, to be adopted.
Experimental Section The key to the refractive index measurement is the deposition of a bilayer lipid membrane as an overlayer on a high refractive index planar optical waveguide (Figure 1, layer F). Part of the guided wave propagates in the membrane (Figure 1, layer A), and the phase velocities of the waveguide modes therefore depend on the optical properties of the membrane.3 The phase velocity can be easily measured if the waveguide incorporates a grating coupler (Figure 1, G). By measuring the intensity of the guided modes as a function of the angle of incidence CY of light onto the grating, the effective refractive index N, i.e., the ratio of the vacuum velocity of light to the velocity in the waveguide, of the composite waveguide structure comprising support, waveguiding film, overlayer, and overlying medium, can be determined, according to the equation4
N = nairsin a + lA/A where nairis the refractive index of air, 1 is the diffraction order, X the wavelength of light, and A the period of the grating.
Planar optical waveguides made from a SiOz-Ti02 mixture (refractive index nF FZ: 1.8, thickness dp FZ: 170 nm) supported on glass (Figure 1, layer S) and incorporating a grating coupler (2400 lines/") were obtained from AS1 AG, Ziirich, Switzerland (type 2400). These waveguides have a thickness and refractive index sufficient for the zeroth transverse electric (TE) and zeroth transverse magnetic (TM) modes to be excited, such that the sensitivity of N to small changes in the overlaying membrane is 0ptima1.~Before use, the waveguides were stored in buffer solution (10 mM 2-(N-morpholino)ethanesulfonicacid (MES) 100mM NaCI, pH 6.0) for 24 h. The incoupling angle was measured by mounting the waveguide in an integrated optics scanner (10s-1, AS1 AG, Ziirich), in which the waveguide is rotated relative to the incoming light beam (He-Ne laser, X = 632.8nm) incident on thegrating coupler. Photodiodes positioned at the ends of the waveguide (Figure 1, D) enable the angle at
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0022-3654/93/2097-4479%04.00/0 0 1993 American Chemical Society
Ramsden
4480 The Journal of Physical Chemistry, Vol. 97, No. 17, I993
TABLE I: Parameters Used in the Solution of the Mode Equations (See Text)
I I
Darameter
value 1.525 781 1.332 620 1.809 105 178.23 nm
nc
n,
Figure 1. Schematic diagram of the waveguide and measuring cuvette (not to scale). S,glass support; F, SiOrTiOz waveguiding layer; A, phospholipid bilayer membrane; C,cuvette filled with aqueous buffer solution;G, diffraction grating; D, photodiode detector; L, incoming light beam. The n and the d are the refractive indices and thicknesses, respectively, of the various layers.
L
of 1.456 X 1014molecules/cm2,corresponding to an area of 68.7 A2/molecule. The waveguide was then slowly (at a speed of 0.04 mm/s) raised through the floating lipid monolayer, bringing the hydrophilichead groupsof the lipid in contact with the hydrophilic surface of the waveguide, to which they strongly adhere (Figure 2a). As the waveguide was withdrawn, the moving barrier was continuously repositioned to maintain the surface pressure u at 32 mN/m. u vs barrier position was plotted on a chart recorder, and from this plot the transfer ratio (the quotient of the areas of lipid removed from the floating monolayer (and hence deposited) and of the bare waveguide) was determined; it was always 100%. After a pause of ca. 2 min to allow surface water to evaporate, the waveguide was rotated 90' and lowered rapidly onto and through the monolayer (Figure 2b), into a watch glass standing on the bottom of the trough. After removing this receptacle, free water was carefully sucked away to prevent the waveguide from having to traverse an air/water interface again, and the bilayer-coated waveguide was quickly remounted in the integrated-optics scanner. In order to compute the refractive indices of the membrane, use is made of the mode equations for a four-layer waveguide (comprising glass support S, Si02-TiOz waveguiding film F, phospholipid bilayer membrane A, and buffer C), which give N as an implicit function of the various waveguide parameters ns, nF, dF, buffer refractive index nc, membrane thickness dA, and membrane refractive index n:499
(N/nc)2 ((N/nc)2
+ (N/n)2 - 1 + (N/nF)2 - 1
(b)
Figure 2. Deposition of a lipid bilayer on the waveguide, W. (a) Deposition of the first monolayer by slowly withdrawing the waveguide out of the subphase, while moving the barrier B to maintain the surface pressure of the floating monolayer at a constant value (Langmuir-Blodgett technique6.'). (b) Deposition of second monolayer by rapidly lowering the monolayer-coated waveguide prepared in (a) onto and through the floating monolayer into a waiting receptacle R in the subphase (LangmuirSchaefer technique).*
which the incoupled light is at a maximum to be determined, to a precision of k1.25 X 10-6 rad. A small flow-through cuvette (Figure 1, C) was sealed with an O-ring over the grating region, which thus formed one wall of the cuvette. The intrinsic waveguide parameters nF and dF were first determined with buffer solution only in the cuvette. The refractive index of the buffer solution, nc, was measured by using a Rayleigh interferometer (LI3, Carl Zeiss, Jena, Germany). Two successive monolayers of 1-palmitoyl-2-oleoyl-sn-glycero3-phosphocholine (POPC; Avanti Polar Lipids, Alabaster, AL) were then deposited on the waveguide as follows: a Langmuir trough, equipped with a Wilhelmy balance for measuring the surface pressure u and a moving barrier, was filled with buffer solution and a waveguide immersed in it. POPC was spread on the surface and compressed to a surface pressure of 32 mN/m by using the moving barrier. This pressure is considered to be the same as that in a bilayer (bilayer equivalence pre~sure).~ At this surface pressure, the lipid was found to have a surface density
where p = 0 and 1 for the TE and TM modes, respectively, and m is the mode number. (This equation is the corrected version of eq 2 on p 3389 of J . Phys. Chem. 1962,66,3388-3391.) The glassy layers S and F and the liquid C are isotropic and characterized by a single refractive index. The value of ns was supplied by the glass manufacturer, while nc, nF, and dF were measured separately as described above. These parameters are collected in Table I. The lipid bilayer, on the other hand, is anisotropic and is in principle characterized by three principal refractive indices, nl, n2, and n3. Since it is a (positive) uniaxial crystal,' two of the three principal refractive indices are equal, i.e., n2 = nl. Both nl and n3 may be determined from the measured NTEand NTM, respectively, provided all the other parameters in the mode equations are known. The remaining unknown parameter is the thickness of the membrane, dA. White and Kinglo have determined the thickness of a POPC bilayer (from an analysis of X-ray diffraction measurements on egg yolk phosphatidylcholine, of which POPC is the predominant component)at various hydration levels. For lipids in equilibrium with an atmosphere at 100% relative humidity (rH), there are 13.4 water molecules per lipid and the total thickness of the bilayer is 5.14 nm. This seems to be an appropriate value because, when a lipid is hydrated, the
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4481
Partial Molar Volume of Solutes
TABLE E Sample &E and h (Measured) and nl, RI,and n A Values (Calculated). condition bare waveguide waveguide coated with POPC 10 pM dibucaine ~~~
120 pM dibucaine ditto, with 1.0 mM dibucaine
Nm ~
Nru
nl
n7
~
nA ~~~
1.617682 1.618 038 1.618 042 1.618 064 1.618 139
~
~
1.572 484 1.572 947
1.377 542
1.372 644
1.375 909
1.572 954 1.572 977 1.573 076
1.378 038 1.380 767 1.390 03 1
1.373 269 1.375 324 1.384 242
1.376 448 1.378 953 1.388 101
Each N reading in the presence of dibucaine was averaged over 5-1 1 points, and the standard error of the sample ranged from 0.000 0006 to 0.000 002 1. The n were computed exactly from the N by using the mode equation 2 (see text for details), the parameters given in Table I, and the value d A = 5.14 nm.Io The effect of assuming that the value of d A does not change during dibucaine incorporation is unknown, and hence the real uncertainties in the computed values of n are likely to be larger than those given. ratio
Figure 3. Dibucaine.
first 10-14 water molecules mostly occupy void space between lipid head groups, and only in a second step do additional water molecules occupy and expand the volume between opposing head groups." The bilayer thickness barely changes from 23% rH (1.8 watersperlipid) to lOO%rH(l3.4watersperlipid),whereas in excess water it increases to 6.20 nm,Io indicating the presence of layers of ordinary water between bilayers of the multilayer structure used in the X-ray diffraction experiments. The question of the exact position of the hydrophobic/ hydrophilic boundary is discussed in detail by Scherer,12who gives 0.8 nm as the minimum distance between egg phosphatidylcholinebilayers. We have not subtracted thisvalue from 5.14 nm, however, because the position of the optical boundary between the membrane and the buffer is not known precisely. Furthermore, the X-ray data are for mixtures of lipid and pure water, whereas our lipid is in contact with aqueous buffer at pH 6.0, which may change the orientation of atoms in the head group. Further evidence in support of the 100%rH data being appropriate to the present experimentscomes from the closecorrespondencebetween the area per lipid at 100% rH (68.7 A2)IO and that found experimentally during compression of the lipid monolayers prior to their transfer to the waveguide. Measured NTEand NTMvalues for representative dicucaine concentrations are given in Table 11. The full four-layer mode equations4can be linearized if dA
