Polyelectrolyte Molecular Weight and Electrostatically-Induced

Biomacromolecules 2000, 1, 365-376

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Polyelectrolyte Molecular Weight and Electrostatically-Induced Domains in Lipid Bilayer Membranes Peter Mitrakos and Peter M. Macdonald* Department of Chemistry, University of Toronto at Mississauga, 3359 Mississauga Road, Mississauga, Ontario, Canada, L5L 1A2 Received April 14, 2000; Revised Manuscript Received May 22, 2000

Polyelectrolyte-induced domain formation in charged lipid bilayer membranes was investigated as a function of polyelectrolyte molecular weight using 2H nuclear magnetic resonance (NMR) spectroscopy. Lipid bilayers consisting of mixtures of R- or β-choline-deuterated 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC-R-d2 or POPC-β-d2) plus the cationic amphiphile 1,2-dioleoyl-3-(dimethylamino)propane (DODAP) were exposed to the anionic polyelectrolyte poly(sodium 4-styrenesulfonate) (PSSS) of various molecular weights. Regardless of molecular weight, PSSS produced dual component 2H NMR spectra, indicating two distinct POPC populations, corresponding to PSSS-bound and PSSS-free lipid, in slow exchange with one another. Analysis of the 2H NMR subspectra quadrupolar splittings and intensities showed the PSSS-bound domain to be enriched in DODAP, with the PSSS-free domain correspondingly depleted. At polyelectrolyte loadings below global charge equivalence, PSSS bound DODAP stoichiometrically for all PSSS molecular weights, indicating that the polyelectrolyte chain lies flat upon the membrane surface. At higher PSSS loadings the domains dissipated, leading to single component 2H NMR spectra. At high NaCl concentrations PSSS dissociated from the bilayer surface. Domain size on a per PSSS chain basis increased while the degree of enrichment with DODAP decreased progressively as the PSSS chain length decreased. Such molecular weightdependent domain characteristics have not been predicted theoretically and need to be taken into account in future refinements of domain models. Introduction Membrane domains are regions enriched with respect to a particular membrane component, either lipid or protein. Domains influence various membrane functions, as reviewed in a recent series of articles.1-7 In particular, membrane physical properties, such as transbilayer permeability, may be altered by domains, or domains may act to sequester enzyme substrates or activators/inhibitors, thereby controlling enzymatic activity and/or cell signaling. Domains are also widely involved in cell adhesion and cell-cell contact. A primary means by which domains are induced to form is through electrostatic interactions between charged biopolymers and oppositely charged membrane lipids. Broadly, two electrostatic situations are of relevance. First, electrostatic interactions can occur between cationically charged membrane proteins and anionic membrane lipids such as phosphatidylglyerol, phosphatidylserine, phosphatidylinositol, and phosphatidic acid.8,9 Such interactions are relevant to the functional mechanism of the proteins involved. Second, anionically charged polynucleotides can interact electrostatically with cationic lipids such as DC-CHOL (3β[N-(N′,N′dimethylaminoethane) carbamoyl] cholesterol), DOTAP (dioleoyltrimethylaminopropane), or DOTMA (dioleoyloxypropyltrimethylammonium bromide).10-12 Such interactions are relevant to the mechanism of gene transfection in certain gene therapy strategies. * To whom correspondence should be addressed. Telephone: 905 828 3805. Fax: 905 828 5425. E-mail: [email protected].

A thermodynamic model of polyelectrolyte-induced domain formation in lipid bilayer membranes has been proposed recently by Denisov and co-workers.13 Domains are predicted to form when the decrease in the system’s free energy due to electrostatic interactions between polyelectrolyte and oppositely charged amphiphiles outweighs the increase in the system’s free energy due to the negative entropy of demixing charged amphiphiles into domains. Specific predictions extracted from the model include the following: (i) a sigmoidal increase in polyelectrolyte binding with increasing mole fraction of oppositely charged amphiphile, (ii) dissipation of domains at high polyelectrolyte or (iii) salt concentration, and (iv) a decrease in the degree of enrichment of the domain with oppositely charged amphiphile upon increased polyelectrolyte binding. Domains are a challenge to examine experimentally. Recently, the technique of fluorescence digital imaging microscopy has been shown to be capable of visualizing electrostatically induced domains in both cell and model membranes,1,13 and to reveal macroscopic properties of the domains, such as dimensions and duration. Even more recently, the technique of 2H NMR has been shown to be capable of revealing microscopic domain properties, such as composition and molecular dynamics within domains.14-17 Together, these techniques have confirmed the major predictions of the Denisov model.13 The effects of polyelectrolyte size on domain properties were not explicitly considered by Denisov et al.,13 although

10.1021/bm000029v CCC: $19.00 © 2000 American Chemical Society Published on Web 06/27/2000

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their model contains a term accounting for the valence charge per chain. Nevertheless, polyelectrolyte size is a parameter of some consequence, since naturally occurring polyelectrolytes vary considerably in length and total charge. Membrane-associated proteins, for example, range in size from small peptides such as pentalysine, to intermediatesized peptides such as mellitin and cardiotoxin, to large proteins such as myelin basic protein or spectrin (recently reviewed by Watts18). In gene transfection, one is interested in polynucleotides ranging in size from oligonucleotides (≈20 bases), to small plasmids (≈102 bases), to long DNA strands (≈106 base pairs).19 The important question is whether, and to what degree, polyelectrolyte size influences domain properties such as size and composition. Composition is important because the degree of enrichment of particular lipids within a domain can influence the activity of membrane-bound enzymes.20,21 Moreover, the efficiencies of DNA entrapment22 and transfection23 depend on the cationic lipid composition, the size of the DNA fragment, and the size of the DNA-cationic lipid “package”. In this report we employ 2H NMR to examine the influence of polyelectrolyte molecular weight on the size and the composition of electrostatically induced domains in lipid bilayer membranes containing oppositely charged amphiphiles. The polyelectrolyte examined here is the synthetic polyanion poly(sodium 4-styrenesulfonate) (PSSS). Synthetic polyelectrolytes, like PSSS, are useful proxies for biological polyelectrolytes, such as DNA, RNA, proteins, peptides, and glycosaminoglycans. Specifically, they display electrostatic interactions and domain induction similar to those exhibited by their biological counterparts, while permitting the facile manipulation of pivotal structural variables such as molecular weight, linear charge density, and hydrophilic/lipophilic balance (HLB). Additionally, synthetic polyelectrolytes are themselves directly of interest by virtue of their utility as environmentally sensitive liposome coatings in liposomal drug delivery systems.24,25 Furthermore, synthetic polyelectrolytes electrostatically coupled onto the surface of lipid selfassemblies enhance mechanical stability, a fact useful in the fabrication of devices such as chemical sensors.26-29 The charged amphiphile examined here is the cationic species 1,2-dioleoyl-3-(dimethylamino) propane (DODAP), introduced by Leventis and Silvius 11 for use in “packaging” DNA for gene transfection purposes. When incorporated into lipid bilayer membranes and upon exposure to an anionic polyelectrolyte, DODAP becomes sequestered into DODAPenriched domains, readily observable via 2H NMR.16 2H NMR of R- or β-choline-deuterated 1-palmitoyl-2oleoyl-phosphatidylcholine (POPC-R-d2 or POPC-β-d2) is ideally suited to study electrostatic interactions and domain formation in lipid bilayer membranes. The choline headgroup of phosphatidylcholine behaves like a “molecular voltmeter” in that it responds to and, via 2H NMR, reports on local surface charge.30 A domain, by definition, possesses a unique composition and, hence, a unique surface charge. Thus, 2H NMR may be exploited to examine domain formation, whether induced by cationic14,15 or anionic polyelectro-

Mitrakos and Macdonald

lytes.16,17 The 2H NMR spectra provide detailed information regarding domain composition and size, and molecular dynamics within the domain. In this report we examine, first, whether domains induction by PSSS in DODAP + POPC lipid bilayer membranes obey the predictions of the Denisov model,13 and, second, whether PSSS molecular weight decisively influences the domain size and composition. Materials and Methods Materials. PSSS (MW ) 780 000, 100 000, 35 000, and 4600, corresponding to degrees of polymerization N ) 3790, 485, 170, and 22 respectively, and Mw/Mn ) 1.10 in all cases) was purchased from Polysciences Inc. (Warrington, PA). Lipid Synthesis. POPC selectively deuterated at either the R or β position of the choline headgroup was prepared and purified as described previously.31 DODAP was synthesized and purified as described by Leventis and Silvius11 with slight modifications as described previously.16 Preparation of Multilamellar Vesicles (MLVs). Lipid mixtures of composition 40/60 (all ratios are mol/mol) DODAP/POPC were prepared by combining the appropriate volumes of chloroform stock solutions of DODAP and either POPC-R-d2 or POPC-β-d2. Typically, the lipid mixtures consisted of 10 mg of the desired deuterium labeled POPC along with the appropriate amount of DODAP required to achieve the desired lipid molar ratio. The solvent was removed under a stream of argon and the mixture was dried overnight under vacuum. The lipids were rehydrated in 160 µL of deuterium-depleted water, then gently warmed, vortexed, and finally freeze-thawed five times in order to ensure homogeneous lipid mixing. Preparation of MLVs Containing PSSS. The dried lipid mixtures were prepared as described above, but were hydrated using the desired volume of a stock solution of PSSS dissolved in deuterium-depleted water to which was added sufficient deuteriumdepleted water to bring the total volume of hydrating solution to 160 µL. To ensure homogeneous lipid and polyelectrolyte mixing the solution was gently warmed and vortexed, and subjected to five cycles of freeze-thaw. Titration of PSSS-Containing MLVs with NaCl. MLVs containing PSSS were prepared as described above, and the volume was adjusted to 200 µL. Sufficient NaCl was added thereafter from a 1.0 M stock solution to achieve the desired salt concentration upon adjusting the volume to 400 µL with deuterium-depleted water. The sample was subjected to four cycles of freeze-thaw in order to equilibrate the salt into all the interstices of the MLVs and then centrifuged for 10 min at 13 000 rpm. Then, 200 µL of the supernatant was removed, and the remaining volume was transferred for NMR measurement. The same procedure was used for subsequent salt additions to the same sample. NMR Measurements. 2H NMR spectra were recorded on a Chemagnetics CMX300 NMR spectrometer operating at 45.98 MHz, using a Chemagnetics wide-line deuterium probe. The quadrupolar echo sequence32 was employed using quadrature detection with complete phase cycling of the pulse pairs, a 90° pulse length of 1.9 µs, an interpulse delay of 40 µs, a recycle delay of 100 ms, a spectral width of 50 kHz, and a 2K data size. Pake Pattern Spectral Line Shape Simulations. 2H NMR Pake pattern line shapes were simulated using a computer program, written in our laboratory, based on the tiling method.33 The simulation variables include the quadrupolar splitting, ∆ν, the intensity of a given Pake pattern, and the line width parameter, T2.

Polyelectrolyte MW and Domain Properties

Figure 1. 2H NMR spectra of mixed DODAP + POPC-R-d2 (40/60) cationically charged lipid bilayers with added PSSS (N ) 3790) in amounts corresponding to, from top to bottom, 0, 0.50, and 0.75 equiv of anionic charge from PSSS to cationic charge from DODAP. The left column corresponds to the experimental spectra, the middle column to the corresponding de-Paked spectra, and the right column to simulated spectra obtained using parameters determined from dePake-ing.

The program does not include provisions for T2 asymmetry effects. This can lead to less-than-perfect simulations, particularly evident in the spectral shoulders. De-Pake-ing of 2H NMR Spectra. 2H NMR spectra were “dePaked” as per Sternin et al.34

Results 2H NMR Evidence for Domain Induction by PSSS. It is well established that 2H NMR of choline deuterated phosphatidylcholine provides a means for monitoring local surface charge within a lipid bilayer membrane.30,35 The fundamental observation is illustrated by the 2H NMR spectra of POPC-R-d2 and POPC-β-d2 at the top left in Figures 1 and 2, respectively. Here, 40% DODAP was added to POPC in the absence of polyelectrolyte. The spectral line shape consists of a motionally narrowed, axially symmetric Pake pattern, indicative of deuterons attached to a lipid contained within a liquid-crystalline lipid bilayer. The quantity which is measured from such spectra is the quadrupolar splitting, ∆ν, corresponding to the separation, in hertz, between the two maxima in the Pake doublet. The narrow resonance at 0 Hz arises from the natural abundance deuterium in water. Although not shown, lipid bilayer membranes composed of 100% POPC-R-d2 or POPC-β-d2 yield quadrupolar splittings of 6.4 and 5.5 kHz, respectively. Adding 40% DODAP alters the quadrupolar splittings for POPC-R-d2 and POPC-β-d2 to -3.0 and +11.0 kHz, respectively.

Biomacromolecules, Vol. 1, No. 3, 2000 367

Figure 2. 2H NMR spectra of mixed DODAP + POPC-β-d2 (40/60) cationically charged lipid bilayers with added PSSS (N ) 3790) in amounts corresponding to, from top to bottom, 0, 0.50, and 0.75 equiv of anionic charge from PSSS to cationic charge from DODAP. The left column corresponds to the experimental spectra, the middle column to the corresponding de-Paked spectra, and the right column to simulated spectra obtained using parameters determined from dePake-ing.

This inverse response of the quadrupolar splittings from POPC-R-d2 vs POPC-β-d2, relative to the control values for 100% POPC, is the characteristic behavior of these quadrupolar splittings in the presence of surface charge. The reduction of the quadrupolar splitting in the case of POPCR-d2 and the increase for POPC-β-d2 is diagnostic of the presence of cationic surface charge. It has been shown previously that the quadrupolar splitting of either POPC-Rd2 or POPC-β-d2 is linearly related to the amount of DODAP surface charge.16 Note that in this binary mixture of lipids one obtains a single quadrupolar splitting. This indicates that DODAP mixes homogeneously with POPC so that all POPC molecules experience the same surface charge. The sign of the quadrupolar splitting cannot be determined in these experiments, only its absolute value. The assignment of a value of -3.2 kHz to the quadrupolar splitting of POPCR-d2 in the presence of 40% DODAP arises from the fact that the calibration curve relating the quadrupolar splitting to the DODAP concentration passes through a value of 0 Hz at roughly 25% DODAP.16 If one assumes a positive sign for the control quadrupolar splitting of 100% POPC-R-d2, then the negative sign for the quadrupolar splitting with 40% DODAP follows. The consequences of adding the anionic polyelectrolyte PSSS are illustrated by the middle and the bottom spectra in the left column of Figures 1 and 2, for POPC-R-d2 and POPC-β-d2, respectively. One observes the emergence of a second overlapping Pake pattern which increases in intensity

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as a function of the amount of added PSSS. All PSSS molecular weights produced qualitatively the same results. The presence of two overlapping Pake patterns means that there are two distinct and separate environments for POPC molecules in these mixtures, with only slow exchange between the two, on the 2H NMR time scale. For both POPCR-d2 and POPC-β-d2, one spectral component has a quadrupolar splitting greater than, while the second spectral component has a quadrupolar splitting less than, the value measured in the absence of PSSS. For both POPC-R-d2 and POPC-β-d2, the spectral component with the larger absolute quadrupolar splitting grows in intensity as PSSS is added, thereby unequivocally identifying which signal corresponds to POPC associated with PSSS. Qualitatively, these changes indicate that the PSSS-free POPC population experiences an environment depleted with respect to DODAP, while, conversely, the PSSS-bound POPC population experiences an environment enriched with respect to DODAP. The quantitative analysis will be presented below. Although not shown here, adding PSSS in a large excess relative to DODAP produces a spectrum consisting of a single Pake pattern. Thus, at high PSSS concentrations, the domains dissipate, in conformity with the predictions of the Denisov model.13 In certain cases of overlapping Pake pattern subspectra, it can be exceedingly difficult to extract the desired quadrupolar splittings and spectral intensities by simple examination, particularly when one intensity is much lower than another or the quadrupolar splittings are poorly resolved. A useful approach is to “de-Pake” the Pake powder patterns.34 This mathematical manipulation removes the spectral broadening due to the powder distribution of orientations of the lipid long axes in the lipid bilayers, while leaving intact the desired conformational and ordering information from which one extracts the surface charge. Examples of de-Paked spectra are shown in the middle columns of Figures 1 and 2. The enhanced resolution of the two POPC populations so produced is evident, as is the ease with which one may measure the quadrupolar splittings and signal intensities. The right-hand columns of spectra in Figures 1 and 2 are computer simulations of the experimental spectra in the lefthand columns. The simulations were produced by assuming a superposition of two Pake pattern subspectra, with quadrupolar splittings and relative intensities as derived from the de-Paked experimental spectra. The success of this approach in reproducing the experimental spectra is obvious, even for cases with low intensity of one component or poorly resolved quadrupolar splittings. Ionic Strength Effects on PSSS-Induced Domains. If polyelectrolyte-induced domain formation is largely electrostatic in origin, then increasing ionic strength should eventually screen the electrostatic attraction between the lipid bilayer surface and the polyelectrolyte, thereby eliminating polyelectrolyte binding. It may be shown, for example, that oligonucleotide adsorption to cationic lipid bilayers decreases above 100 mM NaCl and complete desorption occurs above approximately 500 mM NaCl,36,37 in agreement with theory and experiment.13 The 2H NMR spectra in Figure 3 illustrate the effects of increasing NaCl concentration on PSSS-induced


Figure 3. 2H NMR spectra of mixed DODAP + POPC-R-d2 (40/60) cationically charged lipid bilayers with 0.75 equiv of anionic charge from added PSSS (N ) 3790) plus the indicated concentration of NaCl. Salt was added progressively to preassembled lipid + PSSS MLVs. For the control sample (absence of salt) the quadrupolar splittings (spectral intensities) are -7.0 kHz (57%) for the PSSSbound domain and -2.2 kHz (43%) for the PSSS-free domain. In the presence of 50 mM NaCl, these change to -6.4 kHz (69%) and -2.7 kHz (31%), respectively. Upon adding 100 mM NaCl these alter to -6.1 kHz (74%) and -3.4 kHz (26%), respectively. At 500 mM NaCl the quadrupolar splitting equals -4.5 kHz.

domains. In the absence of NaCl (upper spectrum), two subspectra are superimposed, corresponding to PSSS-bound and PSSS-free domains. At high ionic strength (500 mM NaCl), as shown in the lower spectrum, only a single quadrupolar splitting is evident, and its value corresponds to that of the control measured in the absence of PSSS. Since NaCl itself has little or no influence on the quadrupolar splitting, this result indicates desorption of bound PSSS at high ionic strength accompanied by dissipation of domains. At intermediate ionic strengths (middle two spectra) the two 2H NMR subspectra gradually coalesce with increasing NaCl concentration, as the quadrupolar splitting of each subspectrum progressively reverts toward the control value. Experiments with other polyelectrolytes such as polyadenylic acid, polyacrylate,36 or polynucleotides37 demonstrate that, even at 100 mM NaCl, little, if any, free polyelectrolyte is to be found in solution. Therefore, polyelectrolyte-induced domains continue to exist at physiological ionic strengths, but the domain size and composition are altered. Qualita-


Figure 4. 2H NMR quadrupolar splittings from POPC-R-d2 (panel A) and POPC-β-d2 (panel B) of the PSSS-bound and PSSS-free subspectra in the 2H NMR spectra of mixed (40/60) DODAP + POPC cationic bilayers as a function of the amount of added PSSS: N ) 3790 (circles), 485 (squares), 170 (triangles), and 22 (diamonds). Open symbols refer to the PSSS-free domain, while solid symbols refer to the PSSS-bound domain. The quadrupolar splittings are plotted as the difference vs the values measured in the absence of PSSS.

tively, the quadrupolar splittings and spectral intensities indicate that a higher ionic strength produces a lesser degree of enrichment with respect to the oppositely charged amphiphile and a less compact polyelectrolyte-bound domain. This, too, is consistent with the theoretical description of electrostatically induced domain formation proposed by Denisov et al.13 Variables in PSSS-Bound and PSSS-Free 2H NMR Subspectra. The two readily measured quantities in 2H NMR spectra of the type shown in Figures 1-3 are the quadrupolar splittings and the relative spectral intensities of the two subspectra. Figure 4 shows the quadrupolar splittings of the PSSS-bound and PSSS-free populations of POPC-R-d2 (panel A) and POPC-β-d2 (panel B) as a function of the global PSSS anion/DODAP cation charge ratio for the case of the four different PSSS molecular weights tested. Clearly, the quadrupolar splittings from the different deutero-labeling positions change in opposite directions relative to the control values as PSSS is added. Furthermore, at a given PSSS/ DODAP charge ratio, for a given population, the quadrupolar splitting of POPC-R-d2 changes in a direction opposite to that of POPC-β-d2. These facts indicate that the PSSS-bound


and PSSS-free populations differ with respect to surface charge. The direction of the change in quadrupolar splittings seen here indicates a PSSS-free environment depleted with respect to cationic DODAP, and a concomitant enrichment of DODAP in the PSSS-bound environment. In all cases, with increasing amounts of added PSSS the quadrupolar splitting of the PSSS-bound domain tends to return toward the control value measured in the absence of PSSS. Simultaneously, the quadrupolar splitting of the PSSSfree domain deviates further and further from that of the control value. Qualitatively, this indicates that the PSSSfree domain becomes ever more depleted with respect to DODAP while the PSSS-bound domain becomes less enriched with respect to DODAP as the polyelectrolyte concentration increases. This is another phenomenon predicted by the Denisov domain model.13 The various size PSSS do not behave identically. The greatest effect on the quadrupolar splittings is caused by the highest molecular weight PSSS, while the least change is induced by the lowest molecular weight PSSS. Clearly, an effect additional to the electrostatic energy and mixing entropy of the system considered by Denisov et al.13 is influencing the details of the domain composition and size when polyelectrolyte molecular weight becomes a variable. Figure 5 shows the fraction of bound POPC (Xzb/Xzt) as a function of the PSSS/DODAP ratio, for the four different molecular weight PSSS tested here. The ratio Xzb/Xzt is simply the fraction of the total POPC spectral intensity ascribed to the PSSS-bound population. Data from POPC-R-d2 are shown in Figure 5A, and data from POPC-β-d2 are shown in Figure 5B. Figure 5 also shows the fraction of bound DODAP, but since this is a quantity derived from calculation, as opposed to direct measurement, the DODAP data will be discussed later. It is evident from Figure 5 that the fraction of bound POPC increases with increasing PSSS/DODAP ratio in a fashion which is independent of the choline deuterolabeling position, as expected. The fraction of POPC trapped within the PSSS-bound domain does not vary linearly with the amount of added PSSS. In fact, at low levels of PSSS separate PSSS-bound and PSSS-free spectral components cannot be resolved. Only when the PSSS/DODAP charge ratio approaches 0.5 can two POPC populations be differentiated in the 2H NMR spectrum. This is another point of accord between experiment and theory. The Denisov model13 predicts that the domains formed at lower levels of bound polyelectrolyte will be less highly enriched with charged amphiphile. Such domains could easily be invisible in the 2H NMR spectrum. The different molecular weight PSSS display different behavior in trapping POPC. Lower molecular weight PSSS traps more POPC within a domain at a given PSSS/DODAP charge ratio than does higher molecular weight PSSS. For example, the N ) 22 PSSS chain traps all the POPC into PSSS-bound domains at a lower PSSS/DODAP ratio than any other PSSS chain. Nevertheless, at higher PSSS/DODAP ratios, 100% of the POPC is trapped eventually regardless of the PSSS chain length (not shown). In summary, the 2H NMR spectra demonstrate that adding PSSS to cationic lipid bilayer membranes induces a separa-

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(∆νf ) and the mole fraction of POPC-R-d2 or POPC-β-d2 in the PSSS-free domain (Xzf), one obtains the mole fraction of DODAP in the PSSS-free domain (X+f), according to eq 2, X+f )

Figure 5. Fraction of PSSS-bound lipid as a function of the PSSS/ DODAP anion/cation equivalence ratio: N ) 3790 (circles), 485 (squares), 170 (triangles), and 22 (diamonds). A: POPC-R-d2. B: POPC-β-d2. The fraction of PSSS-bound POPC, Xzb/Xzt (open symbols), was obtained from the relative intensities of the corresponding 2H NMR subspectra. The fraction of PSSS-bound DODAP, X+b/X+t (closed symbols), was obtained using eqs 1 and 2 as described in the text. The solid line shows the result expected for a 1:1 PSSS/DODAP complex.

tion into PSSS-bound domains enriched with the cationic amphiphile and PSSS-free domains depleted of the cationic amphiphile. The results confirm major predictions of a recent theoretical model13 of domain formation in lipid bilayers. However, differences exist between domains formed by different molecular weights of PSSS, a feature not explicitly considered by the model. We describe next how the 2H NMR data are analyzed to obtain quantitative information regarding domain composition and size, as a function of PSSS molecular weight. Quantifying Domain Composition from 2H NMR. The means by which domain composition and size are extracted from 2H NMR spectra has been described in detail elsewhere15,16 and will be presented here only in outline. The distribution of the cationic or zwitterionic amphiphiles (subscript “+” or “z”, respectively) between PSSS-bound and PSSS-free domains (superscript “b” or “f”, respectively) is conveniently expressed in terms of mole fractions according to eq 1. 1 ) X+f + X+b + Xzf + Xzb

(1)

From the quadrupolar splitting of the PSSS-free domain

Xzf(∆νf - ∆ν0) (m - ∆νf + ∆ν0)

(2)

where ∆ν0 is the quadrupolar splitting in the absence of DODAP, and m is the calibration constant relating the quadrupolar splitting of either POPC-R-d2 or POPC-β-d2 to the mole fraction of DODAP. Equation 2 assumes a linear relationship between ∆ν and X+/(X+ + Xz) within a given domain. For the case of a quadratic relationship see Crowell and Macdonald.15 Note that Xzf is simply the product of the global mole fraction of POPC in the lipid bilayers (i.e., Xzt ) Xzf + Xzb ) 0.6 in this case) and the fractional spectral intensity of the PSSS-free 2H NMR signal, as determined either by de-Pake-ing or by spectral simulation. If X+f, Xzf, and Xzb are known, then the fraction of DODAP contained within the PSSS-bound domains (X+b) is obtained by subtraction as per eq 1. All relevant quantities can be determined, therefore, independent of the quadrupolar splitting from the PSSSbound domain. In the ternary mixture of PSSS + DODAP + POPC (water constitutes a fourth component) found in the PSSS-bound domain one expects the net quadrupolar splittings to be the sum of perturbations due to both the cationic and the anionic species.38 However, as noted previously,16,17 PSSS and other polyelectrolytes appear not to be sensed directly by POPC, but only indirectly through their effects on the distribution of cationic amphiphiles. Thus, the quadrupolar splittings of the PSSS-bound domain provide directly an independent determination of X+b via an expression analogous to eq 2. The compositions derived from either set of quadrupolar splittings generally agree quite closely with one another. Turning to the results of such an analysis, consider first the charge stoichiometry within the PSSS-bound domains. Figure 5 (parts A and B) illustrates the fraction of PSSSbound DODAP (X+b/X+t) as a function of the global ratio of added PSSS anionic to DODAP cationic charges, for POPCR-d2 and POPC-β-d2, respectively. The solid line in the figure corresponds to the results expected for a 1:1 DODAP: PSSS stoichiometry within the PSSS-bound domain. Evidently, the PSSS-bound domains contain a near stoichiometric cation: anion charge ratio even at high surface loadings. Similarly, near stoichiometric binding of DODAP by PSSS was found previously for the case of DODAP + POPC (20/80) lipid bilayers.17 This implies that PSSS binding to the lipid bilayer surface is virtually quantitative until saturation is approached. Moreover, it suggests that the polyelectrolyte lies flat upon the membrane surface such that each sulfonate anionic charge is paired with a quaternary amine cationic charge. All molecular weights of PSSS produced the same result. Identical conclusions are reached with either POPC-R-d2 or POPC-β-d2. Consider next the proportion of DODAP to POPC within the domains. Figure 6 (A and B) illustrates the manner in



domain on a per chain basis. Such an effect was not specifically predicted by Denisov et al.13 Quantifying Domain Size from 2H NMR. The surface area occupied by polyelectrolyte-induced domains (Ab) is obtained from the summation rule for partial molar quantities as per eq 3, Ab )

Figure 6. Lipid composition of the PSSS-free and PSSS-bound domains in mixed (40/60) DODAP + POPC bilayers as a function of the PSSS/DODAP anion/cation ratio: N ) 3790 (circles), 485 (squares), 170 (triangles), and 22 (diamonds). Open symbols: PSSSfree domains. Closed solid symbols: PSSS-bound domains. Key: A, DODAP + POPC-R-d2; B, DODAP + POPC-β-d2.

which the mole fraction of DODAP depends on the global ratio of added PSSS anions to DODAP cations, for POPCR-d2 and POPC-β-d2, respectively. Plainly, the PSSS-bound domains are enriched with respect to DODAP, at the expense of depletion from the PSSS-free domains. Similar results are obtained whether one uses POPC-R-d2 or POPC-β-d2 2H NMR data. With increasing PSSS levels the degree of enrichment of the PSSS-bound domains decreases as the remaining available free DODAP diminishes. Concurrently, the degree of depletion of the remaining PSSS-free domains increases as the last DODAP are swept into PSSS-bound domains. At excess PSSS levels there is essentially a single domain, since the entire bilayer surface is coated with PSSS, and the lipid composition of that single domain is identical to the original in the absence of PSSS. The findings illustrated in Figure 6 agree with the predictions of the thermodynamic model of electrostatic domain formation propounded by Denisov et al.13 It is clear from Figure 6 that the higher molecular weight PSSS chains produce a higher degree of enrichment of DODAP in the PSSS-bound domain (and correspondingly greater depletion of the PSSS-free domain). This means that the higher molecular weight PSSS produce a more compact

∑i niAi*

(3)

where ni is the number of species “i” within the domain, each with a partial molar surface area Ai*. As a first approximation we will assume that the partial molar surface areas of POPC and DODAP equal one another and are not changed by the presence/absence of the polyelectrolyte. We will further assume that the partial molar surface area of the polyelectrolyte is simply NPSSS × ASEG* where NPSSS is the degree of polymerization of the PSSS chain and ASEG* is the partial molar surface area of one styrenesulfonate monomer segment of PSSS. The latter quantity will depend on the degree of penetration by PSSS into the bilayer proper and the average monomer orientation relative to the bilayer normal. These are unknown. However, the size of the PSSS monomer relative to an amphiphile’s partial molar surface area may be estimated as follows. The length of the styrene monomer is about 6.7 Å39 and the monomer-monomer spacing in PSSS is 2.55 Å,40 yielding a surface area per monomer of roughly 17 Å2. This is about a quarter of the surface area occupied by POPC (68 Å2). There is some discussion in the literature regarding the correct choice for the monomer-monomer spacing in PSSS.40,41 However, the calculation shows that the area occupied by the PSSS chain amounts to about 10% of the total domain area, so the monomer-monomer spacing is a moot point. Thus, the essential features of the domain size, calculated on a per chain basis, may be apprehended simply by examining the numbers of DODAP and/or POPC per PSSS chain. The number of DODAP bound per single PSSS chain equals NDODAP )

X+b NPSSS X t Q

(4)

+

where Q is the PSSS anion to DODAP cation equivalence ratio, assuming 100% sulfonation of PSSS and 100% dissociation of its styrenesulfonate groups, X+t ) X+f + X+b is the global DODAP mole fraction (i.e., equal to 0.4 in this case), and NPSSS is the degree of PSSS polymerization. One may express the number of POPC bound per single PSSS chain in a similar fashion, as per eq 5. Xzb NPSSS NPOPC ) t Q X

(5)

+

Table 1 lists values of NDODAP and NPOPC calculated according to eqs 4 and 5 as a function of Q for the different molecular weight PSSS. Generally, NDODAP is close to the degree of polymerization of the particular PSSS chain (NPSSS) and is constant with changing Q, as expected for stoichiometric electrostatic binding. The exception is the largest PSSS chain

372



Table 1. Number of Amphiphiles Per Polyelectrolyte in Polyelectrolyte-Bound Domain anion/cation

a

DODAP

POPC

total

0.5 0.75 1

PSSS (3790)a 4140 ( 320 4040 ( 400 3800 ( 140 4280 ( 220 3420 ( 60 4320 ( 110

8180 ( 720 8080 ( 360 7740 ( 170

0.5 0.75 1

PSSS (485) 460 ( 5 420 ( 5 460 ( 10 510 ( 5 445 ( 5 605 ( 5

880 ( 10 970 ( 15 1050 ( 10

0.5 0.75 1

PSSS (170) 150 ( 5 150 ( 5 150 ( 5 180 ( 5 155 ( 5 220 ( 5

300 ( 10 330 ( 10 375 ( 10

0.5 0.75 1

PSSS (22) 20 ( 1 23 ( 1 22 ( 1 29 ( 1 22 ( 1 33 ( 1

43 ( 2 51 ( 1 55 ( 1

Number in parentheses equals the degree of polymerization of PSSS.

the NPOPC/NDODAP ratio decreases by about 40% from low to high molecular weight, consistent with increased enrichment of the PSSS-induced domain with respect to DODAP at high PSSS molecular weights. In the cases described above the surface loading with PSSS is generally quite high and the possibility of perturbations introduced by polyelectrolyte-polyelectrolyte interactions is considerable. To reduce chain-chain interactions we conducted experiments with 10/90 DODAP/POPC membranes and Q ∼ 0.75. Since PSSS binding is proportional to the amount of cationic surface charge, under the latter conditions the overall surface concentration of PSSS will be a factor of 5.33 lower than in the case of 40/60 DODAP/POPC membranes with Q ∼ 1.0. As shown in Figure 7, the number of amphiphiles per PSSS chain nevertheless increases in a linear fashion with the size of the PSSS chain. However, the total number of amphiphiles per PSSS chain is now far greater than in the 40/60 DODAP/POPC membranes. Since the DODAP cation/PSSS anion ratio is still stoichiometric in the PSSS-induced domains, the additional amphiphiles are POPC, as may be ascertained from the high POPC/DODAP ratio within the domains, likewise illustrated in Figure 7. This general effect, in which a higher (lower) initial surface charge leads to more compact (diffuse) polyelectrolyteinduced domains, was first described by Crowell and Macdonald15 and can be attributed to the influence of entropy of mixing on the thermodynamics of domain formation. Overall, we conclude that the effects of PSSS molecular weight on domain properties are similar at both high and low PSSS loadings. Discussion

Figure 7. Number of domain-entrapped amphiphiles (NPOPC + NDODAP) (open symbols) and the proportion of zwitterionic to cationic amphiphiles within a domain (NPOPC/NDODAP) (closed symbols) as a function of the polyelectrolyte’s degree of polymerization (NPSSS). Squares: DODAP/POPC, 40/60, Q ) 1.0, where Q is the PSSS/ DODAP anion/cation equivalence. Triangles: DODAP/POPC, 10/90, Q ) 0.75.

(N ) 3790) where the average number of bound DODAP amphiphiles decreases at higher PSSS loadings. This may reflect entanglement, or finite size effects, or even bridging between lamellae. In contrast, there is a progressive increase in NPOPC with progressive addition of PSSS. One may understand this as arising from the dependence of the degree of enrichment/depletion of the bound/free domains on the statistical availability of DODAP/POPC and how this changes as PSSS is titrated in.15 Overall, Table 1 demonstrates that, for a given initial DODAP/POPC ratio, by far the single most important determinant of either NDODAP or NPOPC is the PSSS molecular weight. Figure 7 demonstrates graphically that the number of amphiphiles per polyelectrolyte chain increases linearly with increasing PSSS molecular weight. For the particular case of Q ) 1.0, across this range of PSSS molecular weights,

General Features of PSSS-Induced Domains. The 2H NMR results described above demonstrate that PSSS binding to mixed DODAP/POPC lipid bilayers induces a segregation of DODAP into DODAP-rich domains. These domains contain a stoichiometric ratio of PSSS anionic to DODAP cationic charges, so that the polyelectrolyte must lie flat upon the lipid bilayer surface provided that there remains an excess of cationic charge. These appear to be general properties of polyelectrolyte-induced domains in lipid bilayers in that they are common to a number of cationic or anionic polyelectrolytes interacting with oppositely charged lipid bilayer surfaces.14-17 The novel findings reported here are that domains are observable with both small and large polyelectrolytes, that the domain composition varies with the polyelectrolyte molecular weight, and that the domain size, on a per chain basis, is linearly proportional to the molecular weight of the polyelectrolyte. Prior to discussing the basis for these results in detail, certain more general features of PSSS-induced domains which may be extracted from such spectra are worthy of specific mention. First, both the PSSS-bound and the PSSS-free domains remain in a lamellar bilayer phase, as demonstrated via 31P NMR spectroscopy (data not shown). The same is true for DODAP/POPC mixtures exposed to polynucleotides.37 Others have reported similar findings, i.e., electron microscopy studies of DNA-cationic liposome complexes reveal lamel-


lar structures.42,43 Polyelectrolyte binding does cause a conversion to nonbilayer phases, e.g., hexagonal HII and/or isotropic/cubic macroscopic phases, if the constituent lipids are predisposed to such nonbilayer architectures.37,44 DODAP/ POPC mixtures, however, prefer to maintain a lamellar bilayer architecture. This is beneficial for our purposes since nonbilayer phases, however induced, obscure the 2H NMR “molecular voltmeter” response we wish to monitor. Second, PSSS-bound amphiphiles remain highly flexible. For all polyelectrolytes investigated to date, 31P and 2H NMR measurements consistently indicate that polyelectrolytebound lipids have mobilities comparable to lipids in the liquid-crystalline LR phase. This statement holds for both zwitterionic and oppositely charged lipids, whether one evaluates T1 or T2 relaxation times, or quadrupolar splittings, or chemical shift anisotropies.14-17,35,36 The 2H NMR spectra in Figures 1 and 2 confirm this conclusion for the case at hand. Evidently, the polyelectrolyte binds to the oppositely charged lipid bilayer surface in a fashion which permits the lipid polar regions to remain hydrated and, thus, mobile. Third, PSSS, in contrast, is likely to be virtually immobilized upon binding to the DODAP/POPC bilayer surface, at least below the global charge equivalence point. Several groups have reported evidence supporting the notion that electrostatically surface bound polyelectrolytes are immobile,45,46 including our 31P NMR measurements of bound polynucleic acids.37 Although it may seem contradictory to juxtapose mobile lipids with immobile polyelectrolytes, it should be borne in mind that the lipids associate with the polyelectrolyte at but a single juncture, while the polyelectrolyte associates with the bilayer surface at multiple sites. This would tend to eliminate all but local small amplitude librations of individual polyelectrolyte monomer segments. Fourth, lipid exchange between domains is slow on the time scale of the difference in quadrupolar splittings between domains, as indicated by the slow exchange NMR spectra seen in Figure 1 and 2. This admits of several possible explanations. One is that the polyelectrolyte-bound and -free domains occupy separate bilayer lamellae. As discussed below, the ionic strength experiments displayed in Figure 3 argue against this possibility, as do certain statistical considerations. A second possibility is that the polyelectrolyte-bound domains are so large that normal rates of lipid lateral diffusion cannot produce effective exchange averaging even between bound and free domains coexisting on the same bilayer lamella. Certainly, macroscopic domains approaching micron dimensions are observed by fluorescence digital imaging microscopy when cation proteins are added to anionic lipid bilayers.8 A third possibility is that lipid lateral diffusion within a polyelectrolyte-bound is slower than normal, to the extent that lipid exchange between polyelectrolyte-bound and -free domain becomes slow even if domains are small. Experimental values of lipid lateral diffusion coefficients within polyelectrolyte-bound domains are not available.47,48 However, one effect of slower lipid lateral diffusion is to increase the lipid’s 2H NMR T2 relaxation time,49 and the T2 relaxation times of polyelectrolyte-bound lipids show exactly such effects.14,15,36 While


slower lipid lateral diffusion might indeed explain our observation of slow exchange spectra, the effective T2 is influenced, in addition, by the radius of curvature of the lamellae, and by local undulations. Polyelectrolyte binding to the lipid bilayer can be expected to influence both these properties, so the T2 effects alone cannot be interpreted as definitive proof of slower lateral diffusion within a polyelectrolyte-bound domain. Fifth, lipid lateral diffusion within the polyelectrolytebound domain must be fast enough to average local compositional fluctuations. This follows from the fact that the 2H NMR subspectra from both the PSSS-bound and the PSSS-free POPC populations each display a single welldefined quadrupolar splitting. Hence, an individual POPC molecule samples a range of local charge environments sufficiently wide such that, on the time scale of the NMR experiment, its time average charge environment becomes identical to the ensemble average charge environment for that population. This will occur only if POPC remains free to diffuse laterally within a given domain. Were this not the case, the result would be a distribution of quadrupolar splittings, manifest as a broadening of the 2H NMR subspectra, an effect we do not observe. Sixth, there is a distinct thermodynamic optimum lipid composition at equilibrium for the PSSS-bound domains, and each such domain in the sample has nearly an identical composition. This follows when one recognizes that any significant compositional heterogeneity would be manifest as a distribution of quadrupolar splittings, which is most patently not the case here. This conclusion conforms with the predictions of the thermodynamic model proposed by Denisov et al.13 The Issue of Interlamellar vs Intralamellar Domains. An important conclusion arising from the ionic strength effects on the 2H NMR spectra in Figure 3 concerns the issue of whether the two lipid populations observed in the spectra originate with domains existing on separate bilayer lamellae or coexisting on the same lamella. The gradual coalescence of the 2H NMR subspectra from the PSSS-bound and PSSSfree populations upon titration with NaCl suggests that the PSSS-bound and PSSS-free domains coexist on the same lamella, as opposed to occupying separate lamellae. Such a coalescence can only occur if there is a complete reequilibration between the two populations, mediated by a lipid exchange mechanism. If the two populations occupy separate lamellae, then any such exchange would involve interlamellar lipid transport, an energetically unfavorable event with a time scale measured in days when not enzymatically catalyzed. If the two populations occupy identical lamellae, then such an exchange would involve only intralamellar lipid transport, i.e., lateral diffusion, a process which is fast relative to the time required for salt addition and sample equilibration in these titration experiments (several hours). Thus, one concludes that the PSSS-bound and PSSS-free domains coexist on the same lamella. Lasic and co-workers42 emphasize that the details of polyelectrolyte-induced domain size, composition, and distribution among lamellae will be influenced by kinetic, as well as thermodynamic, considerations. These researchers

374


observed a broad heterogeneity of particle size and composition when DNA was added rapidly to preformed cationic liposomes. On the other hand, Battersby et al.43 obtained a uniform distribution of DNA among cationic liposomes within 24 h of DNA addition. In our hands, polyelectrolytes added to preformed liposomes likewise produce 2H NMR spectra with broad quadrupolar splittings, indicative of heterogeneous complexes due to kinetic trapping, provided the samples are not subjected to freeze-thaw (Franzin and Macdonald, unpublished data). In contrast, the complexes examined in this study were formed slowly by assembly of the amphiphiles onto the polyelectrolyte during the hydration process, followed by extensive freeze-thaw cycling prior to measurement. As far as possible, this ensures an equilibrium distribution of polyelectrolytes across all lamellae in the sample. There is a further, statistical, argument favoring the view that the PSSS-bound and PSSS-free domains occupy common lamellae. The DNA-cationic liposome complexes investigated by Lasic et al.42 consisted of small DODAB/ cholesterol 1:1 liposomes (130 nm average diameter) to which were added DNA chains of 4.7 kilobases in size in a 0.5:1 charge ratio. Assuming an approximate cross-sectional area of 68 Å2 per lipid, this amounts to about 16 DNA chains per liposome. The probability of significant number density fluctuations away from the global average is, therefore, considerable, and a heterogeneous distribution of DNA chains per liposome is to be expected. On the other hand, for MLVs with an average diameter of 1 µm consisting of 40/60 DODAP/POPC mixtures such as employed here, adding PSSS in a 0.5:1 anion: cation ratio produces a global polyelectrolyte chain/liposome ratio of 80 000 for the case of the PSSS 22-mer. The probability of number density fluctuations so large as to produce distinct liposome populations containing all vs none of the polyelectrolytes, thereby giving rise to the observed 2H NMR spectra, seems remotely small. Further experimental proof that the PSSS-bound and PSSSfree domains occupy the same lamellae could be obtained using two-dimensional exchange NMR, provided the exchange rate between free and bound domains is fast relative to the T1 of the NMR nucleus used for observation. Polyelectrolyte-Induced Domain Formation: Theory and Experiment. Polymer adsorption at interfaces can be modeled using a self-consistent field (SCF) lattice approach as developed by Scheutjens and Fleer.50,51 The conformational statistics of adsorbed trains and nonadsorbed loops and tails of the polymer chain segments are examined in the presence of a specified potential field which defines the adsorption energy. The model permits predictions regarding, among other features, the volume fraction density profile of chain segments as a function of distance from the surface. Extending this approach to the case of polyelectrolyte adsorption to surfaces involves introducing an additional electrostatic term to the chemical affinity adsorption energy, as discussed by Van de Steeg et al.52 For the case of a strong polyelectrolyte in low salt adsorbing to an oppositely charged surface of high surface charge density, the system lies in the “charge-compensation” limit. In this situation individual


surface charges are entirely compensated (i.e., paired) with individual polyelectrolyte charges. The adsorbed polyelectrolyte chains are predicted to form stoichiometric charge complexes with the oppositely charged surface, independent of the molecular weight of the polyelectrolyte chain. Moreover, the chain conformational statistics predict that the adsorbed polyelectrolyte lies flat on the surface. Experimental verifications that stoichiometric complexes form between polyelectrolytes and oppositely charged single chain amphiphiles, in either monomeric or micellar states, are numerous.53,54 Stoichiometric complexes likewise form between polyelectrolytes and oppositely charged double chain amphiphiles in either monolayer45,55 or bilayer states.26,56 Studies of polyelectrolyte conformation at surfaces are far fewer. One example is the small-angle neutron scattering (SANS) study of PSSS adsorbed on positively charged polystyrene latex, which indicated that under such conditions the polyelectrolyte chain segments are confined entirely to the immediate surface layer.57 We conclude that both theory and experiment support the notion derived from 2H NMR measurements that polyelectrolytes bound at oppositely charged lipid bilayer surfaces form stoichiometric charge complexes and adopt a flat conformation at the surface, provided there is little salt screening, a high initial surface charge density, and a global excess of initial surface charges over added polyelectrolyte charges. At high salt concentrations and/or low surface charge densities polyelectrolytes simply fail to adsorb. However, between the “charge compensation” and the “desorption” regimes, theory indicates that under certain conditions of higher ionic strength and lower surface charge density there lies a “charge reversal” regime.58 Here, the amount of adsorbed polyelectrolyte more than compensates the initial surface charge and thus reverses the charge of the substrate. Attaining the charge reversal regime is a precondition for the success of layer-by-layer growth of polyelectrolyte multilayer composites on solid supports for use in nanodevice applications.59 The additional feature of lipid bilayers, not taken into account in SCF lattice models, is that the surface charges are mobile, in that individual charge-carrying amphiphiles are able to diffuse laterally within the plane of the twodimensional lipid bilayer. This permits domain formation upon polyelectrolyte adsorption when Coulombic attraction draws the relatively mobile amphiphiles toward the relatively immobile polyelectrolyte. Models of domain formation induced upon peptide or protein binding to oppositely charged mixed neutral and charged lipid bilayer membranes account for domain formation by considering the Gibbs free energy of the system to be the sum of contributions from the favorable electrostatic free energy and the unfavorable free energy of demixing the charged from the neutral amphiphiles.13 The latter term is dominated by the negative entropy of demixing the two amphiphiles into separate domains. The results reported here, and elsewhere,14-17 regarding synthetic polyelectrolyte-induced domain formation in lipid bilayers confirm the predictions of the Denisov model.13 First, the 1:1 cation:anion stoichiometry within the domain as



assumed by these researchers is verified. Second, the neutral amphiphile content of the domains is found to vary statistically with the initial neutral amphiphile content of the lipid bilayers, as shown in Figure 7 and elsewhere.15 This is the behavior expected for the case in which entropy of mixing plays a significant role in domain thermodynamics. Third, the degree of enrichment of the polyelectrolyte-bound domain with oppositely charged amphiphile is found to decrease with increasing polyelectrolyte loading. A fourth point of agreement with the Denisov model13 is that at excess added polyelectrolyte charge the domains dissipate. In the 2H NMR spectra this is manifest in the fact that at high PSSS concentrations one observes only a single Pake doublet, and its quadrupolar splitting corresponds to that measured initially in the absence of added polyelectrolyte. Note that this also explains why domain formation was not reported in studies of polyelectrolyte coupling to mixed lipid monolayers.45,55 Although many aspects of the polyelectrolyte coupling are similar in monolayers and bilayers, for example, the flat conformation of the stoichiometrically bound high charge-density polyelectrolyte, in the monolayer studies the polyelectrolyte was present in excess in the subphase, a circumstance now recognizable as being unfavorable to domain formation. Domain formation has been reported to be induced by coupling of a polyelectrolyte to a monolayer of an ionic amphiphile.60,61 However, one is dealing here not with a demixing phenomenon but with a polyelectrolyte-induced condensation of a liquid-condensed phase from a liquid-expanded phase. Polyelectrolyte-Induced Domains Contain Multiple Chains. The fact that domains are observed via 2H NMR even with a polyelectrolyte chain as short as 22 monomers in length suggests that the observed domains must contain multiple polyelectrolyte chains. The reasoning is as follows. The ability to observe domains via 2H NMR relies on a slow exchange of lipids between polyelectrolyte-poor and polyelectrolyte-rich phases. The time scale for exchange must be slower than the inverse of the difference in quadrupolar splitting between the two environments. Typical values are in the range 1-10 kHz for the difference in quadrupolar splittings between the two phases, as seen in Figure 4. Thus, a lipid residence time shorter than between approximately 0.1 and 1.0 ms within a domain will correspond to fast exchange. This allows one to place a lower limit on the domain size observable via 2H NMR. Assuming that the lipid two-dimensional lateral diffusion coefficient is the same in both phases and equal to a typical bulk value for liquidcrystalline phosphatidylcholine, e.g. D0 ) 5 × 10-12 m2 s-1,47,48,62 then the mean-square diffusion distance in a given time is calculated via the Einstein equation in two dimensions. 〈x2〉 ) 4D0t

(6)

The root-mean-square diffusion distance so calculated is between 45 and 140 nm for diffusion times (t) between 0.1 and 1.0 ms, which means that domains with radial dimensions smaller than the diffusion distance will not produce slow exchange 2H NMR spectra. This corresponds to a

domain containing between roughly 10 000 and 100 000 lipids, if each lipid occupies a surface area of 68 Å2. These dimensions are huge compared to the single chain dimensions in Table 1 and Figure 7. Such conclusions force us to modify our earlier conceptions regarding the origin of the separate Pake subspectra observed in our 2H NMR spectra. Previous studies used only large polyelectrolytes,14-17 and it could be supposed reasonably that a two-dimensional random coil conformation of the polyelectrolyte at the bilayer surface might cover a sufficient surface area such that POPC trapped within the polyelectrolyte’s folds would be incapable of diffusing out of the domain so formed on a time scale sufficiently rapid as to lead to fast exchange spectra. This supposition no longer seems tenable in light of the present results with very short polyelectrolytes. Instead, it appears that slow exchange 2H NMR spectra are only to be expected if a domain contains multiple polyelectrolyte chains. This conclusion must be considered tentative until lipid lateral diffusion coefficients within the domains can be determined, as it is entirely possible that lipid lateral diffusion within a polyelectrolyte domain is slower than in the bulk lipid bilayer. Employing eq 6 permits an estimate of the lipid lateral diffusion coefficient necessary to produce slowexchange 2H NMR spectra for the case of domains formed by the lowest molecular weight PSSS. For domains containing 55 lipids, each lipid having a cross-sectional areas of 68 Å2, the diffusion coefficient would have to lie between 3 × 10-14 and 3 × 10-15 m2 s-1 to produce slow exchange, i.e., a decrease of between 2 and 3 orders of magnitude relative to the bulk diffusion coefficient. It is difficult to conceive how this decrease might be accomplished by so small a polyelectrolyte when there is no direct Coulombic attraction to POPC. It would also seem inconsistent with the nature of the 2H NMR spectra of the domain-entrapped POPC, which indicate a highly fluid environment. Finally, we note that the fluorescence digital imaging techniques of Glaser1,8 indicate that electrostatically induced domain formation in lipid bilayers can produce macroscopic domains with dimensions approaching the micron scale. Polyelectrolyte Molecular Weight Effects. The origin of the molecular weight specific differences in polyelectrolyteinduced domain properties is a subtle point. Denisov et al.13 included size effects via the chain valency which enters the Boltzmann-like equation relating the bulk chain concentration to the chain concentration in the aqueous phase immediately adjacent to the membrane surface. The greater the valence the greater the membrane surface concentration, and the greater the level of binding as accounted for by a Langmuir isotherm. However, so strong is the electrostatic attraction in the case of PSSS coupling to 40/60 DODAP/POPC membranes that binding is virtually quantitative for all molecular weights until the charge equivalence point is approached. Therefore, rather than examining the binding equilibrium, consider instead the nature of the bound state. Several studies suggest that polyelectrolytes coupled to amphiphilic surfaces assume a rigid rodlike close-packed conformation. Examples include a copolymer of diallyldimethylammonium chloride and acrylamide bound to dipalmi-

376


toylphosphatidic acid monolayers45 and bacteriophage M13 coat protein in phosphatidylcholine bilayers.46 Recent 31P NMR measurements on polynucleotides electrostatically coupled to cationic lipid bilayers demonstrate a virtually static bound state, consistent with a rigid-rod conformation.37 If domains contain multiple chains in a rigid rod conformation, then polyelectrolyte chain-chain interactions will be considerable. Since chain-chain interactions scale according to molecular weight, longer polyelectrolyte chains should tend to pack more effectively. Favorable packing interactions between longer chains might ameliorate the unfavorable negative entropy of lipid mixing term in the thermodynamics of domain formation, leading to domains containing less POPC. The biological implications of the findings reported here relate to the ability of naturally occurring polyelectrolytes to segregate oppositely charged amphiphiles into lateral domains and to resist domain-dissipative forces such as physiological salt or high polyelectrolyte concentrations. Evidently, lateral segregation into domains can occur via a nonspecific electrostatic attraction between polyelectrolyte and amphiphile. Evidently, greater numbers of charges per chain equate to more compact, more thermodynamically stable domains. Evidently, as few as 22 charges per chain are sufficient to produce domains resistant to physiological salt concentrations. Denisov et al.13 report domain formation with pentalysine added to phosphatidylserine-containing membranes, but such domains were not stable at physiological salt concentrations. Thus, the question arises as to how many charges are sufficient to produce thermodynamically stable domains under physiological conditions. Acknowledgment. This work was supported by a grant from the Natural Science and Engineering Research Council (NSERC) of Canada. References and Notes (1) Glaser, M. Comments Mol. Cell. Biophys. 1992, 8, 37. (2) Thompson, T.; Sankaram, M. B.; Biltonen, R. L. Comments Mol. Cell. Biophys. 1992, 8, 1. (3) Vaz, W. L. C. Comments Mol. Cell. Biophys. 1992, 8, 17. (4) Tocanne, J. F. Comments Mol. Cell. Biophys. 1992, 8, 53. (5) Edidin, M.. Comments Mol. Cell. Biophys. 1992, 8, 73. (6) Wolf, D. E. Comments Mol. Cell. Biophys. 1992, 8, 83. (7) Jesaitis, A. J. Comments Mol. Cell. Biophys. 1992, 8, 97. (8) Yang, L.; Glaser, M. Biochemistry 1996, 35, 13966. (9) Buser, C. A.; Kim, J.; McLaughlin, S.; Peitzsch, R. M. Mol. Membr. Biol. 1995, 12, 69. (10) Gao, X.; Huang, L. Biochem. Biophys. Res. Commun. 1991, 179, 280. (11) Leventis, R.; Silvius, J. R. Biochim. Biophys. Acta 1990, 1023, 124. (12) Felgner, P. L.; Gadek, T. R.; Holm, M.; Roman, R.; Chan, H. W.; Wenz, M.; Northrop, J. P.; Ringold, G. M.; Danielsen. M. Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 7413. (13) Denisov, G.; Wanaski, S.; Luan, P.; Glaser, M.; McLaughlin, S. Biophys. J. 1998, 74, 731. (14) Crowell, K. J.; Macdonald, P. M. J. Phys. Chem. B 1997, 101, 1105. (15) Crowell, K. J.; Macdonald, P. M. J. Phys. Chem. B 1998, 102, 9091. (16) Mitrakos, P.; Macdonald, P. M. Biochemistry 1996, 35, 16714. (17) Mitrakos, P.; Macdonald, P. M. Biochemistry 1997, 36, 13647. (18) Watts, A. Biochim. Biophys. Acta 1998, 1376, 297. (19) Felgner, P. L., Heller, M., Lehn, P., Behr, J. P., Szoka, F. C., Jr., Eds. Artificial self-assembling systems for gene transfer; ACS Conference Proceedings Series; American Chemical Society: Washington, DC, 1996.

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Polyelectrolyte Molecular Weight and Electrostatically-Induced

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