PRL 95, 048101 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending22 JULY 2005

Electrostatically Driven Spatial Patterns in Lipid Membrane Composition

Raghuveer Parthasarathy, Paul A. Cripe, and Jay T. GrovesDepartment of Chemistry, University of California, Berkeley, California 94720, USA

(Received 24 November 2004; published 22 July 2005)

0031-9007=

To explore the physical mechanisms that can guide spatial organization at biological membranes, wehave constructed simple, cell-free intermembrane junctions. We find that the mechanically drivenpatterning of proteins uncovered in our earlier work can electrostatically generate spatial patterns inthe distribution of charged membrane lipids. Tuning the magnitude of the interaction as a function ofcomposition and ionic strength, and analyzing the interplay between thermodynamics and electrostaticsvia a Poisson-Boltzmann approach, we are able to determine the charge density and surface potential ofthe junction components. Surprisingly, the electrostatic potential of the proteins is a minor factor in thelipid reorganization; the protein size and its modulation of the junction topography play the dominant rolein driving the electrostatic patterns.

DOI: 10.1103/PhysRevLett.95.048101 PACS numbers: 87.16.Dg, 41.20.Cv, 87.14.Cc, 87.15.Kg

FIG. 1. (below) An intermembrane junction (schematic, not toscale). Two lipid membranes, one of which is supported on aglass substrate, adhere. Adhesion drives mobile proteins (anti-bodies) into patterns of high and low density zones. (above)Fluorescence image of proteins (20 �m� 5 �m; top viewrelative to the side view of the schematic).

The tremendous scientific interest in the self-organization of nanometer-scale objects is motivated notonly by its potential impact on the creation of new mate-rials, but also by its importance in understanding biologicalmembranes. Cellular membranes are complex, two-dimen-sional fluids that are spatially nonuniform in composition.A major goal of present research is to unravel physicalmechanisms by which nonuniformity is maintained—mechanisms that may include phase separation [1], cou-pling between membrane topography and protein motions[2,3], and electrostatic interactions between proteins andlipids [4]. In living cells, a host of active biological pro-cesses contribute to membrane behavior. To isolate thephysical forces behind spatial organization, we have de-signed a simple cell-free intermembrane junction (Fig. 1)that consists of mobile, membrane-bound proteins sand-wiched between lipid bilayers. The adhesive mechanicsgive rise to spatial patterns in the protein distribution, asdescribed in Ref. [5]. Here, we report that these mechani-cally formed protein patterns can induce correspondingpatterns of distributed charge in the upper membrane byan electrostatic mechanism. A quantitative analysis yieldsthe charge densities and surface potentials of the junctioncomponents—properties that are difficult or impossible tomeasure by other techniques [6].

The assembly and structure of the junctions are de-scribed in Ref. [5]. In brief: Anti-biotin antibodies arebound to the lower bilayer, which contains 1 mol % bio-tinylated lipids. Adhesion of a second bilayer rapidlydrives the mobile proteins into dense and sparse zoneshundreds to thousands of nm in lateral size. The uppermembrane is draped over protein plateaus 14� 2 nm inheight (measured via interferometry [5,7]). The bilayerscontain mostly zwitterionic phosphatidylcholine lipids;compositions are given in Ref. [8]. All data shown arefrom experiments conducted at room temperature(296 K) [9]. The upper membrane is spatially uniform inappearance at ionic strengths above a few mM.

05=95(4)=048101(4)$23.00 04810

At low ionic strengths, however, the upper membraneoften shows spatial patterns in the distribution of charged,fluorescent lipid probes, patterns that are in registry withthe underlying protein distribution. For the junctionsshown in Figs. 2(a)–2(f), for example: in distilled, deion-ized water [10] there is an enhanced concentration of thenegatively charged fluorescent probe Texas Red DHPE in‘‘region 2’’ (the upper membrane areas above the denseprotein zones; see Fig. 1) [Figs. 2(a)–2(c)]. Adding a fewmM NaCl leaves the protein patterns intact, but homoge-nizes the lipid probe distribution [Figs. 2(d)–2(f)]. Asystem with positively charged lipid probes (DiD) in theupper membrane shows inverted patterns: an enhancedprobe concentration in region 1 [Figs. 2(g)–2(i)]. The ionicstrength and probe charge dependence indicate an electro-static mechanism for the lipid pattern formation.

We characterize the strength of the lipid patterns bydefining a partitioning ratio f equal to the ratio of theupper membrane probe fluorescence intensities (and there-fore probe concentrations [11]) in region 2 versus region 1[12]. At equilibrium, an unequal concentration in the tworegions (f � 1) must be maintained by an energetic dif-ference, which we ascribe to a difference in the electro-

1-1 2005 The American Physical Society

FIG. 3. The partitioning ratio f is a function of the net mol %of cationic ionizable lipids in the lower bilayer. The fluorescenceimages (width 5 �m) at the left and right come from experi-ments in which the lower membrane has 2 and 10 net mol %cationic lipids, respectively, and show colocalization and anti-localization, respectively, of the anionic upper membrane probeswith the dense protein zones. The experiments are conducted in a0.1 mM NaCl solution. The solid line is a fit to a Poisson-Boltzmann model (see text). Error bars here and in Fig. 4indicate standard deviation among multiple samples.

FIG. 4. The partitioning ratio of upper membrane probes for aseries of junctions of identical compositions decreases as afunction of ionic strength (NaCl concentration). Gray curve: asimple model in which the electrostatic potential decays expo-nentially with distance; black curve: a Poisson-Boltzmann model(see text); the two curves are largely indistinguishable.

FIG. 2. Electrostatic patterns. Fluorescence images ofproteins (a),(d),(g) and upper bilayer probes (b),(e),(h), all5 �m wide; schematic ‘‘side views’’ (c),(f),(i) relative to the‘‘top views’’ of the fluorescence data. The black circles in (c),(f )indicate anionic membrane probes; the black circles in (i) in-dicate cationic membrane probes. (a)–(c) At low ionic strength(in deionized water), the negatively charged lipid probe TexasRed DHPE is preferentially colocalized with the dense proteinzones. (d)–(f) At higher ionic strength (3 mM NaCl) the probesare uniformly distributed. (g)–(i) At low ionic strength, thepositively charged upper membrane probe DiD is preferentiallyantilocalized with the dense protein zones.

PRL 95, 048101 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending22 JULY 2005

static potential, �. The partitioning ratio is given by theBoltzmann-weighted difference in the electrostatic energyof a probe in each of the two regions:

f � exp��ze��2 ��1�=�kBT��; (1)

where kB is Boltzmann’s constant, T is the absolute tem-perature, e is the magnitude of the electron charge, and zeis the probe charge. (See Refs. [13,14] for theoreticalstudies of the thermodynamics of electrostatically inducedlipid reorganization.) All experiments described belowmake use of Texas Red DHPE (z � �1) as the uppermembrane probe [15].

The data demonstrate a clear spatial modulation of theelectrostatic potential experienced by the upper membrane.For the data of Fig. 2, for example, Eq. (1) reveals �2 ��1 5 mV.

One might conclude, incorrectly, that the upper face ofthe proteins has a surface potential of �p 5 mV thatgenerates the lipid patterns. Several lines of enquiry showthat the proteins are not the key factor driving the electro-static reorganization. First, computational estimates of �p

in the 0.1 to 10 mM ionic strength range spanned by ourexperiments, calculated with both the commonly usedGRASP and DELPHI [16] programs, reveal �p �1 mV,small in magnitude and negative in sign. Second, thecharge density of the supported bilayer has a profoundinfluence on the upper bilayer lipid pattern (Fig. 3)—ca-pable of transforming it from preferential colocalization ofnegative probes and high protein density regions (f > 1) toantilocalization (f < 1). Third, the ionic strength (I) de-

04810

pendence of f points to a more distant field source than theupper protein surface. The lipid patterns decay sharplywith I [17], becoming uniform by a few mM NaCl(Fig. 4). (Physiological ionic strengths are much higher;see the end of the Letter for a discussion.) A rigorousanalysis is presented below; for now we note that theelectric potential (�) produced by a charged plate in asolution of monovalent ions, in the regime of small �(compared to kBT=e), decays with distance (x) as � ��0 exp�2�x�, where �0 is the surface potential and �, theinverse Debye length, is a function of I. If the proteins werethe dominant source of the electric potential (and �1 weretherefore negligible), this linearized Poisson-Boltzmannapproach gives

f � exp��ze�p exp���xc�=kBT�; (2)

1-2

PRL 95, 048101 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending22 JULY 2005

where xc is the distance between the electric field sourceand the upper membrane’s lipid probes. Fitting the data toEq. (2) gives e�p��0:40�0:02�kBT and xc�13:3�0:9 nm—far from the 1–2 nm distance between the uppersurface of the proteins and the upper lipid membrane [5].

We therefore conclude that the fields driving the lipidpattern formation come mainly from the supported mem-brane and its underlying substrate. The proteins act pri-marily to modulate the topography—changing the dis-tance between the field sources and the upper membrane.

For a more quantitative analysis, we apply a (nonlinear)Poisson-Boltzmann framework. The lateral dimensions ofthe junctions are much larger than the vertical, so we treatthe glass, supported bilayer, and upper protein surface asplates with charge density �g and �b, and surface potential�p, respectively. We ascribe to the aqueous regions adielectric constant equal to that of bulk water (� � 80).Since the spatial decay of the potentials is dominated bythe ions in solution, we neglect the volume and the interiordielectric constant of the lipid bilayers and the proteins. Wemodel the glass and supported bilayer as a composite plate,neglecting the 1–3 nm hydration layer [18] separating thetwo. This plate gives rise to an electrostatic potential, �,whose dependence on the distance from the plate (x), theionic strength (I) of the monovalent salt solution, and thedielectric constant (�) of the medium is given by [19]

��x� �2kBTe

log�1 � exp���x�1� � exp���x�

�; (3)

with

� � �2e2I=��0kBT�1=2; (4)

� � tanh�e�0=4kBT�; (5)

and

�0 � �2kBT=e� asinh��=

���������������������8��0IkBT

p �(6)

�0 is the surface potential, �0 is the permittivity of freespace, and � is the charge density ��g �b�. The electro-static potential experienced by the upper membrane probesis created by the glass, the supported bilayer, and, inregion 2, the proteins [20]. Calculations (via GRASP andDELPHI) provide the dependence of �p on I, leaving un-determined a scale factor �0

p, the effective surface poten-tial of the proteins, modeled as a superimposed effectiveplate, in the limit of I � 0. The key physical differencebetween regions 1 and 2 is that in region 1, the lower andupper membranes are separated by a thin aqueous layer(h � 1:5� 0:5 nm [5,21]), while in region 2, the separa-tion is increased by an additional hprotein � 14� 2 nm[5,7]. We calculate the electrostatic potential and the re-sulting f [(Eq. (1)] as a function of parameters �g, �b, and�0

p, and compare to the measured data.

04810

First, we examine f as a function of the supportedbilayer charge density (Fig. 3), tuned via the concentration(CD) of the cationic molecule DOTAP. We assume �b ��eCD, where � is the degree of DOTAP dissociation. Thedata are well fit, with � � 0:008� 0:001, and any valuesof �g and �p that satisfy the constraint

�0p=�mV� � 2:6 1:6�g=�10�4 Cm�2�: (7)

The nonunique determination of �g and �p is not surpris-ing: in the model, an increased �g raises the potential inregion 1, which can be compensated by an increased �0

g inregion 2. The value of � reveals a large degree of chargeregulation—i.e., the vast majority of ionizable DOTAPmolecules are uncharged; the high chemical potential ofdissociated counterions in the thin hydration layers favorsmore neutral DOTAP at equilibrium than would be the casein bulk solution [19]. A similar conclusion was reached byLeckband et al. for phosphatidylglycerol lipids at 0.3 mMNaCl, for which � � 0:022 was measured in a muchdifferent context [22].

Next, we examine f as a function of I (Fig. 4). We find�0

p � �3:3� 1:2 mV, �g���4:2�1:6��10�4 Cm�2,and �b � ��2:2� 1:7� � 10�4 Cm�2 [23]. The valuesof �0

p and �g agree with the independently determinedrelation of Eq. (7). The uncertainties are due both to theuncertainties in h and hprotein, and to the quality of the fit.The glass charge density is much smaller than that of bareglass [24], most likely due to charge regulation.

The exact parameter values are, of course, model depen-dent. While more complicated treatments are possible, thekey limitations of the model are found in the poorly under-stood dielectric character of the protein-rich regions, thethin hydration layers, and the bilayer interiors. Our datashould motivate more detailed investigations of electro-static environments at membranes.

These experiments reveal a simple route for hierarchicalpattern formation in membrane systems: mechanicallygenerated nonequilibrium protein patterns [5] electrostati-cally drive equilibrium reorganization of charged lipids. APoisson-Boltzmann approach successfully describes thedata—perhaps surprisingly given the nm-scale spaces in-volved [19], but understandably given the low chargedensity induced by charge regulation. The mean distancebetween charges (a) for the data of Fig. 3, for example,spans a 30–90 nm, slightly greater than the Debyelength (��1 � 32 nm), and much greater than theBjerrum length of water (lB � 0:7 nm). Theoretically(for monovalent salts), a � lB characterizes the regimeof expected validity for the Poisson-Boltzmann equation.We note that a is larger than the intermembrane spacing(1.5 nm and 15.5 nm in regions 1 and 2, respectively).Electrostatic patterns should be of interest for generatingnew classes of self-assembled materials, and for studyingbiomolecular interactions. The monovalent lipids in ourmembranes adopt spatial patterns at ionic strengths that arelow compared to physiological values (150 mM), but the

1-3

PRL 95, 048101 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending22 JULY 2005

mechanisms they illustrate should provide a springboardfor experiments on highly charged lipids, such as thephosphotidylinositol PIP2, whose electrostatic interactionswith proteins are believed to be important in a variety ofbiological contexts [4,13,25].

The authors thank Nir Ben-Tal, Haim Diamant, andSven Behrens for useful discussions, and HolgerSondermann for assistance with GRASP and DELPHI. Thiswork was supported by the Miller Institute for BasicResearch in Science, the National Institutes of Health(Grant No. 1 R01 GM64900-01), and the BeckmannFoundation Young Investigator Program (J. T. G.).

[1] K. Simons and D. Toome, Nat. Rev. Mol. Cell Biol. 1, 31(2000); C. Zurzolo, G. van Meer, and S. Mayor, EMBORep. 4, 1117 (2003).

[2] A. Grakoui et al., Science 285, 221 (1999).[3] S. Y. Qi, J. T. Groves, and A. K. Chakraborty, Proc. Natl.

Acad. Sci. U.S.A. 98, 6548 (2001).[4] S. McLaughlin et al., Annu. Rev. Biophys. Biomol. Struct.

31, 151 (2002); J. Wang et al., J. Biol. Chem. 277, 34401(2002).

[5] R. Parthasarathy and J. T. Groves, Proc. Natl. Acad. Sci.U.S.A. 101, 12 798 (2004).

[6] Methods including titration, zeta potential measurements,and surface force apparatus studies can probe surfaceelectrostatics without spatial resolution. Spatially resolvedtechniques are limited to potentiometric probes, easilyapplicable only to large (100 mV) potentials, and electricforce microscopy, quite difficult in implementation and inextraction of absolute charge density values: W. F. Heinzand J. H. Hoh, Biophys. J. 76, 528 (1999); A. S. Johnsonet al., Langmuir 19, 10 007 (2003).

[7] R. Parthasarathy and J. T. Groves, Cell Biochemistry andBiophysics 41, 391 (2004).

[8] Lipids were purchased from Avanti Polar Lipids: dimyr-istoylphosphatidylcholine (DMPC), 1,2-dioleoyl-sn-glyc-ero-3-phosphocholine (DOPC), 1,2-dioleoyl-sn-glycero-3-[phospho-L-serine] (DOPS), 1,2-dioleoyl-3-trimethy-lammonium-propane (DOTAP), and 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(Cap Biotinyl) (bPE).The lipids 1,2-dihexadecanoyl-sn-glycero-3-phospho-ethanolamine labeled with Texas Red (TR-DHPE) andMarina Blue (MB-DHPE), and the fluorescent probe1,1’-dioctadecyl-3,3,3’,3’- tetramethylindodicarbocyanine(DiD) were purchased from Molecular Probes. FITC-labeled mouse monoclonal anti-biotin (IgG1) was pur-chased from Sigma. The compositions (mole % lipid) ofthe supported (SB) and upper (UB) bilayers of the junc-tions described in the figures are as follows. Figures. 1 and4: SB 72 DMPC, 20 DOPC, 4 DOTAP, 3 MB-DHPE, 1bPE; UB 80 DMPC, 18 DOPC, 1.5 DOTAP, 0.5 TR-DHPE. Figure. 2: SB 92 DMPC, 4 DOTAP, 3 MB-DHPE, 1 bPE; UB 98 DMPC, 1.5 DOTAP, 0.5 TR-DHPE, and 99 DOPC, 1 DiD-C18. Figure 3: SB 70� xDMPC, 20 DOPC, 6 x DOTAP, 3 MB-DHPE, 1 bPE,where 0< x< 10; UB 80 DMPC, 18 DOPC, 1.5 DOPS,0.5 TR-DHPE (for SB with x � 2) or 80 DMPC, 18DOPC, 1.5 DOTAP, 0.5 TR-DHPE (for x 2). The com-

04810

positions used have no known tendency to phase separateat the temperatures examined.

[9] Experiments at 296< T < 313 K show no measurabledifference in the electrostatic pattern formation, consistentwith the model presented. Experiments outside this narrowtemperature range are prohibited for reasons of membranefluidity and protein denaturing.

[10] Ionic strength 20–30 �M, estimated by tracking themotions of charged colloidal particles (N. Clack, privatecommunication). The contribution to the ionic strengthfrom the lipid counterions is at most 0:01 �M.

[11] The concentration of Texas Red DHPE (cTR) in is alwaysless than 0.7 mol %. For cTR < several mole%, fluores-cence intensity is linearly proportional to cTR, as verifiedby electrophoretic experiments of the sort discussed in:J. T. Groves, S. G. Boxer, and H. M. McConnell, Proc.Natl. Acad. Sci. U.S.A. 94, 13 390 (1997).

[12] The edges of the pattern features are blurred by the finiteoptical resolution; to extract a precise, single f value fromeach image, we assume a binary distribution of probeintensities (as is evident for large features that are notdiffraction limited), and calculate the f of the binaryimage that, when convolved with the microscope pointspread function, best matches the observed image.

[13] E. Haleva et al., Biophys. J. 86, 2165 (2004).[14] J. T. Groves, S. G. Boxer, and H. M. McConnell, J. Phys.

Chem. B 104, 11 409 (2000).[15] We verified that another z � �1 probe, tail labeled NBD-

PS (1-oleoyl-2- [12- [(7-nitro-2- 1,3-benzoxadiazol-4-yl)amino]dodecanoyl]-sn-glycero-3-phospho-L-serine),gives the same f values as Texas Red DHPE.

[16] A. Nicholls, K. A. Sharp, and B. Honig, Proteins: Struct.,Funct., Genet. 11, 281 (1991); A. Nicholls and B. Honig,J. Comput. Chem. 12, 435 (1991); B. Honig and A.Nicholls, Science 268, 1144 (1995).

[17] The junctions are formed in an aqueous solution of fixedNaCl concentration. Subsequently altering I leads tohistory-dependent f values, as equilibration in the junction(especially by salt permeation) is slow.

[18] T. M. Bayerl and M. Bloom, Biophys. J. 58, 357 (1990);B. W. Koenig et al., Langmuir 12, 1343 (1996); A.Lambacher and P. Fromherz, J. Opt. Soc. Am. B 19,1435 (2002).

[19] J. N. Israelachvili, Intermolecular and Surface Forces(Academic, San Francisco, 1992), 2nd ed.

[20] We also include the potential due to the charged uppermembrane itself. Since the charge density is small, andf 1, the difference in the potentials of the two mem-brane regions contributes negligibly (i.e., altering fit pa-rameters by amounts smaller than their uncertainties).

[21] A. P. Wong and J. T. Groves, Proc. Natl. Acad. Sci. U.S.A.99, 14 147 (2002).

[22] D. E. Leckband, C. A. Helm, and J. Israelachvili,Biochemistry 32, 1127 (1993).

[23] Treating the protein surface as a simple charged plate incontact with the aqueous solution—i.e., applyingEq. (3)—does not self consistently fit the data of Figs. 3and 4.

[24] S. H. Behrens and D. G. Grier, J. Chem. Phys. 115, 6716(2001).

[25] J. Zimmerberg and S. McLaughlin, Curr. Biol. 14, R250(2004).

1-4