many length scales surface fractality in monomolecular films of whole myelin lipids and proteins

$: Many length scales surface fractality in monomolecular films of whole myelin lipids and proteins$
Journal of Structural Biology 149 (2005) 158–169

www.elsevier.com/locate/yjsbi

Many length scales surface fractality in monomolecular Wlms of whole myelin lipids and proteins

Rafael G. Oliveiraa,b, Motomu Tanakab, Bruno Maggioa,¤

a Departamento de Química Biológica-CIQUIBIC, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, 5000 Córdoba, Argentinab Lehrstuhl für Biophysik E22, Physik Department, Technische Universität München, 85747, Garching, Germany

Received 10 March 2004, and in revised form 9 November 2004Available online 8 December 2004

Abstract

Monomolecular Wlms prepared with all the lipid and protein components of myelin were spread at the air/aqueous buVer interfacefrom isolated bovine spinal cord myelin fully dissolved in chloroform:methanol (2:1) or by surface free energy shock of myelin mem-brane microvesicles. These monolayers show indistinguishable surface behavior, with similar compositional phase coexistencethrough all the compression isotherm on several subphase conditions. The domains were observed through epiXuorescence andBrewster angle microscopy on the air/water interface and on Langmuir–Blodgett Wlms. Their thickness was measured ellipsometri-cally. Under molecular packing conditions resembling those found in the natural membrane, the morphology and size of thedomains are highly self-similar, displaying no characteristic length scale. These properties are the hallmark of fractal objects. Thefractality extends at least three orders of magnitudes, from the micrometer to the millimeter range, the fractal dimension being about1.7. A possible implication of fractality in membrane structure and/or function is demonstrated through the high Xuctuation of thepropagation of signals through constrained diVusion in corrals formed by domains in the plane of the monolayer, which restricts thediVusion of a Xuorescent probe over many length scale domains. 2004 Elsevier Inc. All rights reserved.

Keywords: Monolayers; Myelin; EpiXuorescence microscopy; Langmuir–Blodgett Wlms; Lipid–protein domains; Fractals

1. Introduction the diVerence in the perpendicular surface dipole

There is an increasing body of evidence regarding thelateral coexistence of phase domains formed by diVerentcomponents in biological membranes. However, themolecular base and underlying physico-chemical forcesleading to such microheterogeneity remain to be known(Maggio et al., 2004) and this impairs possibilities forprediction of the typical size of lipid domains in bio-membranes. In monolayers at the air/water interface theequilibrium lipid domain radii can be readily measured;moreover, they can be calculated and roughly predictedfrom the relation between the domain line tension and

* Corresponding author. Fax: +54 351 4334074.E-mail address: [email protected] (B. Maggio).

1047-8477/$ - see front matter 2004 Elsevier Inc. All rights reserved.doi:10.1016/j.jsb.2004.11.003

moment density between coexisting domains (Härtelet al., 2004; McConnell, 1991). Nevertheless, althoughthe last variable is relatively straightforward to measure,the Wrst one is rather complicated (Benvegnu andMcConnell, 1992; Würlitzer et al., 2000).

There is discrepancy about the typical size of domainsin membrane systems (Edidin, 2001; Yuan et al., 2002),ranging from some nanometers as calculated forphospholipid phase transitions and mixed systems withcholesterol (Mouritsen, 1990), to the order of microme-ters in giant unilamellar vesicles (Dietrich et al., 2001)and can be even larger in unrestricted size monolayersformed by complex natural membrane surfaces (Oliveiraand Maggio, 2002). Lipid domain sizes (in mixed mono-layer of dioleoylphosphatidyl choline, sphingomyelinGM1 and cholesterol, ceramide, and sphingomyelin) of

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R.G. Oliveira et al. / Journal of Structural Biology 149 (2005) 158–169 159

the order of micrometers and subdomains in the 100 nmrange have been reported (Härtel et al., 2004; Yuan et al.,2002). The root of the discrepancy could lie in the elec-tion of the compositional model for lipid domains repre-sentative of a canonical biological membrane.Additionally, interactions with the cytoskeleton, theextracellular matrix, and other membrane-associatedproteins complicate comparisons with natural systems.

In this paper, we report experiments with monomo-lecular layers formed with all the lipid and protein com-ponents of the isolated bovine spinal cord myelin(myelin monolayers). Since the structural asymmetry ofthe natural myelin membrane is lost in these Wlms theydo not correspond to, and we do not attempt to interprettheir behavior as, that of the natural myelin membrane.The advantage of their use, within the intention in thepresent work, is that they provide a complex system thatcontains all the compositional complexity of the naturalmembrane but that is amenable to be studied under pre-cisely known and controlled conditions of intermolecu-lar organization (Oliveira et al., 1998). In this way, thecritical problem of the (somewhat arbitrary) choice of arelevant compositional model for dynamic studies on acomplex biomembrane surface with all its natural com-ponents is avoided. The myelin membrane has severaladvantages as a preparation to prepare the Wlms com-pared to other cell membranes. (1) It is one of the mem-brane fractions that can be obtained in the purest form(Haley et al., 1981; Norton and Cammer, 1984). (2) It hasone of the highest lipid/protein ratio, with only twomajor protein components representing 80% of the pro-tein mass. Being soluble in organic solvents it allowsboth, full solubilization of the components (Folch et al.,1957; Gonzales-Sastre, 1970) and interfacial spreadingfrom this solvent as a monomolecular Wlm; moreover,this leads to the same physico-chemical features, thermo-dynamic behavior, domain topography, and composi-tion as that obtained for monomolecular Wlms formedby the spreading of microvesiculated myelin (Oliveiraet al., 1998). (3) Myelin structure is well known fromX-ray diVraction performed on intact nerve (Kirschneret al., 1984) and the combination of these studies withother techniques has allowed considerable insight aboutits structure and stability.

We have previously shown that myelin monolayersspread at the air/water interface show phase coexistenceunder a variety of conditions (Oliveira and Maggio,2000). We also characterized the preferential partition-ing of lipid and protein components of the monolayer intwo diVerent phase domains. One kind of phase domainis in the liquid expanded (LE) state, analogous to the liq-uid disordered (or liquid crystalline) state found inphospholipid bilayers (and in most biomembranes ingeneral) above the main phase transition temperature.This phase is Xuid, highly compressible, the mean areaper lipid is relatively large, the alkyl chains are disor-

dered, and as a consequence van der Walls interactionsare comparatively weak. Myelin proteins localize mainlyin this phase together with the Xuorescence labeling ofsome liquid-expanded lipids (like ganglioside GM1 andXuorescently labeled phosphatidylethanolamine). Theother phase, also Xuid, is particularly rich in cholesteroland galactocerebroside (the two major lipids of myelin)and phosphatidylserine (Oliveira and Maggio, 2002). Thehigh cholesterol content induces condensed and wellordered phospholipid fatty acyl chains but with a verylow viscosity (high Xuidity) packing arrangement of thelipids, this phase has been denominated as the liquid-ordered (LO) phase (Mouritsen, 1990). Work performedon isolated myelin (Arvanitis et al., 2002; Taylor et al.,2002) and intact nerve myelin (Kirschner et al., 1984)showed that myelin exhibits an equivalent phase behaviorwith a protein-rich phase coexisting with another, choles-terol-enriched, phase extending through both monolayerhalves of the myelin bilayer (Kirschner et al., 1984).

In the present work, we characterized the domainmorphology at two surface pressures over diVerent lengthscales, and obtained a fractal dimension corresponding tothe myelin monolayer at surface pressures within theaverage Xuctuating range corresponding to bilayer mem-branes (Marsh, 1996), well below the myelin monolayercollapse pressure which is equal to the equilibriumspreading pressure (Oliveira and Maggio, 2003); only ator above this surface pressure point can bilayer or multi-layered planes be formed (Gershfeld, 1989; Oliveira andMaggio, 2003). We Wnally present some evidence aboutthe possible eVects of fractal topography on the lateralpropagation of signals (lateral diVusion), restricted by thedomain phase coexistence, showing strong Xuctuationson the lateral propagation of a diVusing lipid probe.

2. Materials and methods

2.1. Myelin isolation and monolayer preparation

Highly puriWed myelin was prepared from bovine spi-nal cord (Haley et al., 1981). Myelin was vesiculated hyp-otonically in phosphate buVer 1 mM, pH 8, 2 mMdithiothreitol (Wüthrich and Steck, 1981), the vesicleswere resuspended in the same buVer to a Wnal proteinconcentration (Lowry et al., 1951) of 0.2–0.3 mg/ml, andmicrovesiculated by Wve passages through a 26G needleWtted to a syringe. Monolayers were obtained as previ-ously described by spreading a suspension of the myelinmicrovesicles in an analogous way to that described byother authors (Schürholz and Schindler, 1991; Vergerand Pattus, 1976) or by spreading a freshly preparedsolution of myelin fully dissolved (Gonzales-Sastre,1970) in 19 vol of chloroform–methanol (2:1) and imme-diately used for monolayer spreading (Oliveira et al.,1998). Both procedures allow formation of the monomo-

160 R.G. Oliveira et al. / Journal of Structural Biology 149 (2005) 158–169

lecular layer with indistinguishable behavior (Oliveiraand Maggio, 2002). In addition, in the method using sol-vent-solubilized myelin all the lipid and protein compo-nents are dissociated, a quantitative (100%) spreading ofall the components is obtained, and it further allowsdirect incorporation of Xuorescent lipid probes in thesolvent solution.

The myelin microvesicle suspensions, or the solvent-solubilized myelin were doped with 2 mol % of N-(7-nitro-2-1,3-benzoxadiazol-4-yl) diacyl phosphatidyletha-nolamine (NBD-PE) (McConnell et al., 1984; Peters andBeck, 1983) or 0.25–0.5 mol % of N-(lissamine rhodamineB sulfonyl) diacyl phosphatidylethanolamine (RHO-PE),both probes were from avanti polar lipids (Alabaster,AL). With the method of microvesicle spreading incor-poration of the probes was achieved by Xushing it, dis-solved in ethanol–methanol (1:1) solution, at a Wnalconcentration of 5%, in the aqueous suspension.

The monolayer subphase was 10 mM Tris[hydroxy-methyl aminomethane] buVer in 100mM NaCl, 20 mMCaCl2, adjusted to pH 7.4 with HCl. Equivalent results arefound on 145mM NaCl solution. The surface pressurereached in the initial spreading was usually below 0.3mN/m. The overall lipid and protein composition of monolay-ers (Oliveira et al., 1998) prepared from microvesiculated-or solvent-solubilized-myelin is very similar to that of thewhole myelin membrane fraction isolated by ultacentrifu-gation (Haley et al., 1981; Norton and Cammer, 1984).

2.2. Microscopy and imaging

Both RHO-PE and NBD-PE probes are head groupXuorescent labeled, with a 55% of acyl chain unsaturation,made from egg phosphatidylcholine; this favors parti-tioning in LE phases and their relative exclusion frommore ordered phases, such as the cholesterol-enrichedLO and condensed phases. Anti-proteolipid-DM20(anti-PLP) directed against CGRGTKF (C terminalregion) was from Serotec (Oxford, England). Anti-mouse IgG tetramethyl rhodamine isothiocyanatelabeled was from Jackson ImmunoResearch Laborato-ries (West Grove, PA).

After monolayer spreading, the Wlms were com-pressed at a rate of 3 Å2/mol/min; 5–15 min of equilibra-tion were allowed after each change of surface pressurebefore image capturing. The observations were carriedout after discontinuous isometric compression of themonolayers at room temperature using a KSV Minit-rough II (KSV, Helsinski, Finland) mounted on themicroscope stage. An open-end TeXon mask with a lat-eral vertical slit, extending through the Wlm into the sub-phase, was used in order to restrict lateral monolayerXow in the Weld being observed. Zeiss Axioplan or Axio-vert (Carl Zeiss, Oberkochem, Germany) epiXuorescencemicroscopes were used, equipped with a mercury lampHBO 50, and objectives of 10 and 20£. Exposure times

were typically 0.1 s. The pictures were registered by aCCD camera (Princeton Instruments, USA).

Brewster angle microscopy (BAM) does not requirethe use of probes to reveal surface domain coexistence(Rosetti et al., 2003) because diVerence in reXectance canoccur due to diVerence in the “optical thickness” (refrac-tive index, Wlm thickness) of the domains because ofvariations in composition or intermolecular organiza-tion (Henon and Meunier, 1991; Höning and Möbius,1991). A MiniBam microscope (NanoWlm Technologies,Gottingen, GE) was used and images were captured withthe software provided by the manufacturer under precisecontrol of the intermolecular packing as determined bythe surface pressure.

2.3. Film thickness measurement

Ellipsometry of the interfacial Wlms was performed atthe air/NaCl 145 mM interface. The Wlm was spread froma freshly prepared solution of myelin fully dissolved in 19vol. of chloroform:methanol 2:1 (Folch’s extractionphase), or from myelin microvesicles. The surface pres-sure was maintained at 40 mN/m. For better measure-ments we restricted the lateral Xow of the monolayerplacing a U-shaped piece of TeXon surrounding the laserspot and the through was cooled to 5 °C (Ducharmeet al., 2001). A refractive index of 1.42–1.46 was assumed(Lafont et al., 1998). The measurements were performedwith a Multiskop null imaging ellipsometer (Optrel, Ber-lin, GE) equipped with a 10£ objective. The angle of inci-dence for visualization of the heterogeneous Wlm wasnear the Brewster angle, in order to proper positioning ofthe measurement spot on the diVerent domains.

2.4. Myelin Langmuir–Blodgett Wlms

The myelin monolayer was coated onto alkylatedglass coverslips as previously described (Oliveira andMaggio, 2002). BrieXy, coverslips (12 mm diameter) wereWrst alkylated with octadecyltrichlorosilane to self-assemble a covalently linked monolayer of octadecylsi-lane (von Tscharner and McConnell, 1981). The qualityof the hydrophobic coverage of each coverslip waschecked before use on the basis of the contact angle andfree-running of double-distilled water droplets depositedon their surface. The alkylated coverslip, held horizon-tally above the monolayer set at the desired constantsurface pressure, were lowered until they gently touchedthe monolayers surface. The coverslip was left to restover the surface for 15 s at constant surface pressure, andthen pushed vertically through the monolayer at a con-stant speed that was synchronized with the servo-surfacepressure barostat to automatically keep the surface pres-sure constant during and after coating. When the mono-layer is successfully transferred to the alkylated coverslipa simultaneous decrease of the monolayer area occurs


that was automatically recorded in each case. The Lang-muir–Blodgett Wlms thus obtained were always handledunder aqueous solutions to avoid the collapse of themonolayers. These Wlms were labeled by incubating from1–12 h with speciWc ligands at room temperature. 10–63£ objectives were used with the same equipmentdescribed above. Filter sets were the standard for epi-Xuorescence microscopy.

2.5. Fractal dimension estimation

The commercial software Benoit 1.2 (Trusoft, USA)was employed. The methods eVectively used to deter-mine fractal dimension were box counting and informa-tion (entropy) dimensions.

The box dimension is deWned as the exponent Db in theequation N(d) t1/dDb where N(d) is the number of boxesof linear size d necessary to cover the data set of pointsdistributed in a 2D plane. In the deWnition of box dimen-sion, a box is counted as occupied and enters the calcula-tion of N(d) regardless of whether it contains one pointor a relatively large number of points. Information dimen-sion (Di) assign weights to the boxes according to theiroccupancy. Both dimensions generally diVer since the con-dition for equality is fulWlled only if the data set is uni-formly distributed over the plane. The mass dimensionmethod rendered non-consistent values, presumably dueto the non-centrally symmetric nature of the domains. Theperimeter–area dimension method results are not reportedbecause the LE clusters do not complete in a loop, never-theless taking oV the outermost points in the frame ren-ders a fractal dimension of 1.7. As a control, Db of Kochcurve and Sierpinski gasket Wgure (two classical fractalobjects) renders values of 1.268§0.006 and 1.579§0.002,very close the theoretical values of ln(4)/ln(3) and ln(3)/ln(2), respectively (Mandelbrot, 1983). The informationdimension method renders similar values.

2.6. Experiment of diVusion in corrals

Myelin monolayers were transferred from the air/water interface to solid supports as described above, andmanipulated under water. These Wlms contained NBD-PE in order to verify the quality of the coating process.These Langmuir–Blodgett Wlms were incubated for 24 hin the presence of myelin vesicles charged with RHO-PE.The microvesicles settle down on the Langmuir–Blodg-ett Wlm at random locations, which could be visuallyobserved in real time, releasing RHO-PE into the Wlm.The Wlms were observed by Xuorescence microscopy.

3. Results

Although the equilibration time before image captur-ing at the air/water interface is within the operational

period frequently employed and aVords reproducibility, itshould be emphasized that the surface patterns observedby microscopy in this type of studies correspond to rela-tively long-lived, but metastable, molecular distributions.These are usually not in true thermodynamic equilibrium.Similar to more simple lipid systems (McConnell, 1996),equilibration times of the order of days or weeks may berequired. This is increasingly noticeable at higher surfacepressures. In addition, myelin monolayers present coher-ent domains even at pressures of 0 mN/m. No homoge-neous gas phase is detected in our conditions; thisinhomogeneous starting condition probably renders themonolayer pattern less regular and reproducible thanthose of pure phospholipids. The condensed domains atlow surface pressures could be due to the strong lateralinteraction of myelin lipids with the major proteins ofmyelin, such as myelin basic protein and PLP (Demelet al., 1973; Fidelio et al., 1984; Maggio, 1997).

Myelin monolayers showed domain distributionssimilar to that described previously (Oliveira and Mag-gio, 2000, 2002). Fig. 1 shows the ordered domain mor-phology and distribution in myelin monolayers at lowsurface pressure (1.5–2.5 mN/m, mean molecular area ofabout 80 Å2/mol). A frequent characteristic length radiusfor LE domains (bright clusters) in the order of 100�mis easily recognized. The LO domains (dark) show phasepercolation, a topographic feature of dynamic biomem-brane surfaces characterized by merging of domains intoa continuous phase over the long range (Aharony andStauVer, 1994; Xia and Thorpe, 1988); neverthelessregions of large and elongated bright domains are alsofrequently observed within the percolating phase (notshown). According to McConnell (McConnell, 1991) cir-cular domains distort to ellipses when the radii exceedthe equilibrium radii by a factor e1/3. That is Req D Re1/3,where R is the radii at which distortion from circle is Wrstobserved. Fig. 1A shows total predominance of LE cir-cular domains, with some large bright domains distort-ing to elongated domains (arrows on Figs. 1B and C).Taking the radii from the domains, and the equationabove, the equilibrium radius is about 70�m. Also, thedomains smaller than Req/e are unstable against annihi-lation, then Req and “typical” domains are in the scaleobserved (McConnell, 1991). Annihilation could beimpaired by long range dipolar repulsion, eVective overscales of 10�m, that sets up an electrostatic kinetic bar-rier against domain merging. Dipolar repulsion can beinferred from the zone of exclusion of domains, this zoneis about 10 �m wide on average (circle in Fig. 1A).

Fig. 2 shows diVerent magniWcation scales of the samemonolayer at 40 mN/m (mean molecular area of about45 Å2/mol) labeled with anti-PLP, a LE domain marker(Oliveira and Maggio, 2002); the picture is shown for aLangmuir–Blodgett Wlm which produced a better imagebecause it is an immobile surface. The diVerent magniW-cations show that the general pattern of both the domain


distribution and shape is the same at any enlargement ofthe same Weld.

Fig. 3A shows a low resolution BAM overview of themyelin monolayer at the air/water interface at 40 mN/m.With this technique no probe or labeling is used. The LEphase is the more reXective at this surface pressure, prob-ably due to the high protein content in a lateral relativelycompact state (Oliveira and Maggio, 2002) and conse-quently of high optical thickness, still well within the val-ues of reXectance (R » 10¡5) corresponding to amonomolecular Wlm (Lheveder et al., 2000; Rosetti et al.,2003). Additionally, ellipsometry revealed an averagethickness of the phase-heterogeneous monolayer in therange of 35–45 Å. The general Gaussian distribution oflight with higher intensity in the middle of the frame isdue to the centered laser intensity proWle. As can be seen

Fig. 1. LE and LO domain distribution in myelin monolayers at low sur-face pressure. Round LE (bright) domains are observed in a backgroundof LO (dark) percolating phase. Excluded zone due to electrostaticrepulsion is highlighted in A (circular dashed line). Distortion from cir-cular shape is observed in some large LE domains in B and C (arrows).

the LE domains (bright) appear percolating with a fractalappearance, and LO domains (dark) display no charac-teristic length scale. Larger magniWcations are seen inFigs. 3B–D after Langmuir–Blodgett transfer and labeledwith anti-PLP (equivalent patterns are obtained usinglipid probes, Oliveira and Maggio, 2002). EpiXuorescencereveals new LO domains (whose size is below the BAMresolution) but with a similar general form and distribu-tion. For straightforward visual comparison the bar (rect-angle) on the three photographs represents the same size(100�m) and its successive enlargement. Figs. 3E–Gshows the actual Wltered and binarized images on whichthe fractal analysis was performed. Figs. 3H–J shows thelog–log plots (fractal analysis by the box counting algo-rithm) for the respective micrographs. The straight lines

Fig. 2. Self-similarity at diVerent enlargements in myelin Langmuir–Blodgett Wlms labeled with anti-PLP. Three diVerent magniWcations(10, 20, and 63£) show the same general pattern. As magniWcation isenhanced new details similar to the previous ones are found.


Fig. 3. Fractal analysis of myelin monolayers. (A) Brewster angle micrograph of a myelin monolayer at 40 mN/m, the bar represents 1 mm. Self-simi-larity is observed extending from low to high magniWcation. Three micrographs at diVerent enlargements, 10, 20, and 63£. The contrast was obtainedwith anti-PLP labeling the LE phase domains (Oliveira and Maggio, 2002). The bar represents a rectangle 100 �m long in the three micrographs. Thefollowing row (E–G) shows the pictures after Wltering and binarization (black and white transformation) needed for image processing in the fractalanalysis. The log–log plots (H–J) show the relation between the number boxes occupied by LE phase as a function of the box side length in which theimage is sectioned. From the slope of the lines, fractal dimensions of 1.71, 1.65, and 1.64 were obtained.


in the log–log plots clearly indicate the fractal nature ofthe LE domains, from the slope of this line the fractaldimensions of 1.71, 1.65, and 1.64 were obtained.

The method of information entropy which also takesinto account the heterogeneity of the micrograph typi-cally renders fractal dimensions about 0.06 points higherthan box counting. This could be an indication of thestochastic (non-deterministic) nature of the fractal for-mation that is characteristic of physical (non-mathemat-ical) fractals.

Fig. 4 shows the “metastable pseudo-equilibrium” dis-tribution of Xuorescent probe in diVerent domains. Thebright domains correspond to LE phase. Gray domains(diVerent intensities) are cholesterol-enriched LO domains(Oliveira and Maggio, 2002) with diVerent amounts ofXuorescent labeling by partition–diVusion incorporationtaken from probe-loaded microvesicles layered onto theLangmuir–Blodgett Wlm (seen as very bright dots at thisresolution). Homogeneity of the gray intensity level isobserved within each individual domain but a diVerence inthe gray-intensity level between the various LO choles-terol-enriched domains is evident, reXecting the non-homogeneous equilibration of the probe (RHO-PE) ineach of them due to corral-restricted diVusion.

4. Discussion

4.1. Monomolecular nature of the Wlm

Natural in vivo myelin is a multilamellar structureand even under osmotic shock it shows some degree ofself-association. In myelin from central nervous system

Fig. 4. Restricted diVusion in myelin monolayers transferred to solidsupport at 42 mN/m. After transfer, myelin vesicles loaded with Xuores-cent dye were added to the aqueous medium; on adsorption to the Lang-muir–Blodgett Wlm additional Xuorescent molecules are incorporatedinto the Wlm. The transfer occurs at random points on the surface of theWlm. The percolating LE phase is almost homogeneous in Xuorescenceintensity due to the unrestricted lateral diVusion of the probe. On theother hand, diVerent LO domains have incorporated variable amountsof Xuorescent label that is not equilibrated among them. This is reXectedby the diVerent gray levels of the various “dark” domains. It should betaken into account that although the probe is partitioned preferably intoLE phases (which thus appear more brilliant), it shows a small but Wnitepartition coeYcient into the LO phase domains. Homogeneous Xuores-cence due to diVusion equilibrium is observed within a particular LOdomain. However, because of the corral restricted diVusion broughtabout by the percolating LE phase that separates the LO domain, lateraldiVusion and probe equilibration between the latter is not possible.

membrane pairs, and pairs of pairs can be detected(McIntosh and Robertson, 1976). Thus, the possibilitywas considered that the Wlm formed at the aqueous/airinterface might consist of a multilayered structure andthat the domains observed could belong to diVerentstacked planes. We have ascertained that multilayerplanes, as those observed after the Wlm collapses (Olive-ira and Maggio, 2003) were not present in the conditionsused. The following reasons clearly show that the myelininterface discussed in this work is monomolecular andthat the domains belong to the same lateral plane at thesurface pressures studied:

(a) well demonstrated and standard interfacial ther-modynamic considerations indicate that if the surfacepressure rises on compression the interfacial Wlm ismonomolecular (Gaines, 1966). Multilayers are formedonly after the myelin monolayer collapses at the surfacepressure above the collapse point of 47 mN/m and, simi-lar to Wlms formed with other mixtures of lipids and pro-teins (Fidelio et al., 1984; Gaines, 1966), no furthervariation of surface pressure on compression takes place(Oliveira et al., 1998; Oliveira and Maggio, 2003). Byknowing the area on compression and the quantitativerecovery of the Wlm material (moles of spread molecules)the average molecular packing area and surface (dipole)potential is continuously determined and controlled. Thecompression can be carried out up to the limiting lateralcross-sectional areas before multilayers are formed atthe collapse pressure point. This is easily detected as aplateau of the compression isotherms relating both sur-face pressure and surface (dipole) potential as a functionof mean molecular area (Oliveira et al., 1998).

At the maximum surface pressure (47 mN/M) justbefore the collapse point the molecular area (42–44 Å2/mol) and surface potential/molecule 1.7 fV cm2 [this sur-face parameter is directly proportional to the meanresultant dipole moment perpendicular to the interface(Brockman, 1994)] correspond to the values expected fora lipid–protein monomolecular layer as that of the wholemyelin membrane Wlm (Oliveira et al., 1998). For com-parison, X-ray diVraction data of whole myelin lipidbilayers give a surface mean molecular area of 43.6 Å2/mol (Franks et al., 1982).

(b) A monomolecular Wlm with the compression–expansion thermodynamic surface behavior, indistin-guishable from that of the Wlm formed by spreadingmyelin microvesicles, is obtained by spreading themonolayer from an organic solvent solution of myelin inthe classical way employed in surfactant studies (Gaines,1966). In such manner, the 100% of the solvent-solubi-lized myelin membrane components can be spreadimmediately after solubilization. With this method allcomponents are dissociated before spreading and nomembrane apposition can occur. The Wlms can be com-pressed and decompressed reversibly at the interface in a


quantitatively reproducible way without loss of material,variation of composition nor formation of bulk (multi-layered) collapsed structures. The same reversible behav-ior reproducing the same compression isotherm isobtained when the monolayer is formed by spreadingmyelin microvesicles through the surface free energyshock at the air–aqueous interface. In both methods thelipid and protein myelin components of the original mul-tilayered membrane lose all asymmetry and becomeorganized as a monomolecular Wlm.

(c) The same topography and surface domainmorphology is obtained by spreading the Wlm from sol-vent-solubilized myelin and from myelin microvesicles(Oliveira and Maggio, 2002). This indicates that themyelin Wlm spontaneously adopt the same interfacialorganization. Similar equivalence in the behavior oflipid–protein monolayers formed from solvent solutionsand from vesicles has been previously reported, includ-ing the surface domain pattern formed by more simplesystems (Nag et al., 1996).

(d) The reXectance of p, polarized light; Rp D IR/I0(»10¡5) from the interfacial Wlm measured at the Brew-ster angle (Oliveira and Maggio, 2002) corresponds tothat of lipid–protein monomolecular Wlms (Lhevederet al., 2000; Rosetti et al., 2003); multilayers are opticallythicker and show much more reXectance because of itsquadratic dependence on thickness (De Mul and Mann,1998). Membrane pairs and pairs of pairs would increasethe intensity 16 and 64 times, respectively.

In addition, the thickness directly measured by ellips-ometry gave an average of 35–45 Å for the whole Wlm,the LO domains being in the range of 20–30 Å. Thesevalues can be compared with the reported 110–130 Åperiodicity (27–33 Å per monolayer, similar to ourmonomolecular Wlm) of the repeating unit of compactedmyelin, taking into account that the repeating unit hastwo bilayers due to the asymmetry of the membrane(Kirschner et al., 1984). This phase is free form intra-membranous particles and appears smooth (as seen byfreeze etching electron microscopy) and the spacing issimilar to that found by small angle X-ray diVraction forprotein free lipids, including myelin lipid extracts(Franks et al., 1982). The thickness of the LE domainswas in the range of 50–60 Å. This Wgure should be com-pared with the thickness of 180 Å for the non-compacted(protein-enriched) state of myelin, also with a repeatingunit of two bilayers rendering a thickness of 45 Å permonolayer [although some degree of superposition canhinder a larger thickness, (Kirschner et al., 1984)]. Theincreased thickness of the non-compacted (protein-enriched) state of myelin, in comparison to compactedmyelin, is due to the presence of intramembranous parti-cles in vivo which are supposed to be the natural spacersin myelin multilayered stacks (Kirschner et al., 1984).This correlates with the localization of proteolipid, mye-lin basic protein and CNPase in LE domains that

exclude galactocerebroside and cholesterol in myelinmonolayers (Oliveira and Maggio, 2002) and in moresimple systems (Marsh, 1995). This diVerential partitionis in full agreement with the solubilization of proteolipid,myelin basic protein and CNPase by Triton X-100, withcholesterol and galactocerebroside being excluded fromthis phase (Arvanitis et al., 2002), in analogy to our case.

(e) Using Xuorescence microscopy we have previouslyshowed that multilayers (bi- or trilayers) can only beformed by overcompressing the Wlm beyond the collapsepressure point (Oliveira and Maggio, 2003). The multi-layers can be clearly seen in real time under the micro-scope as a superposition of focal planes, each revealingthe same pattern found in successive monomolecularlayers; this proved that the collapsed phase of the myelinWlm consists of multilayers while the Wlm at all other sur-face pressures is a monolayer (Oliveira and Maggio,2003). In the conditions of surface pressure used in thepresent work the Wlm was monomolecular and no multi-ple focal planes due to multilayer formation occurred;this is also in full agreement with the results obtained bydirect exploration of the Wlm by ellipsometry.

4.2. Myelin multilayer–monolayer correspondence

We previously showed (Oliveira et al., 1998; Oliveiraand Maggio, 2002, 2003) that myelin monolayers can beformed either by spreading or by adsorption of microve-sicles to the air/water interface up to an equilibrium sur-face pressure that is equal to the collapse pressure(47 § 1 mN/m, mean molecular area of 42–44 Å2/mol);this is the maximum surface pressure at which the mono-layer can be compressed before multilayer formation.From a strict physico-chemical perspective the propercriterion for equilibrium between the interfacial Wlm andthe myelin vesicles is the equality of chemical potentials(and not of surface pressure and/or molecular area) foreach component in both, the bulk aqueous suspensionand the monolayer interface; nevertheless our results onequilibrium adsorption (Oliveira and Maggio, 2003)indicate that molecules in the myelin vesicles are in acompact state along the lateral plane. This is also sup-ported by X-ray measurements of packing on reconsti-tuted symmetrical myelin lipid bilayers, which show amean molecular area of 43.6 Å2 (Franks et al., 1982),very close to the limiting mean molecular area obtainedjust before the collapse point of the myelin lipid mono-layer (Oliveira et al., 1998).

4.3. Lateral heterogeneity in natural myelin and myelin monolayers

It should be mentioned that the literature concerningthe coexistence of lateral phases in the myelin membraneis conXictive. Existence of some specialized regions in themyelin membrane have been known for a long time from


electron microscopy, but compact myelin has beenshown to be rather homogeneous in freeze-etching andX-ray diVraction studies (Kirschner et al., 1984). On theother hand, some chemicals and other treatments wereshown to promote phase separation with the establish-ment in vivo of a phase enriched in cholesterol anddepleted of intramembranous particles. This is calledcompacted myelin that designates a myelin membranefraction with a decreased period of 110–130 Å; this com-pacted myelin should be diVerentiated from the normalcompact myelin phase with unaltered period (»180 Å)and very crowded with intramembranous particles (pro-teins), the normal spacers among myelin bilayers(Kirschner et al., 1984). Recent work based on solubili-zation techniques with detergents also points to a heter-ogeneous membrane, with the “raft” compositiondepending on the detergent used (Arvanitis et al., 2002;Taylor et al., 2002). The more likely situation may bethat the lateral surface structure formed by myelin com-ponents is highly dynamic and sensitive to physico-chemical conditions promoting protein segregation froma cholesterol-enriched phase. Regarding the fact that theprotein enriched phase percolates, being the cholesterolenriched domains immersed within the other phase, thesurface patterns that we observe coincide with thosereported for the myelin membrane (Kirschner et al.,1984). On compression, phase percolation is obtainedabove a surface pressure of 20 mN/m. This also suggestsan average surface pressure well above 20 mN/m possi-bly occurring in myelin membranes of intact nerve.

Previous work (Arvanitis et al., 2002; Kirschner et al.,1984) and our own observations (Oliveira and Maggio,2002) suggests some simple factors underlying the phaseseparation and partition of components at the surfaceformed by the myelin constituents. It is well-known thatcondensed cholesterol-enriched phases do not providedefects or voids for the insertion of membrane proteinsand tend to exclude them (Marsh, 1995). This fact isvalid for both nerve myelin multilayers and our wholemyelin component monolayers at the air/water interface.This is probably due to the fact that, although nervemyelin has an asymmetrical distribution of components,the main determinants for phase separation (cholesteroland proteins) distribute in both (intra- and extracellular)monolayers, buVering the asymmetry and coupling bothmonolayers. The mole fractions for cholesterol in themyelin cytoplasmic and extracellular monolayers werereported to be about 0.27 and 0.54, respectively (Kirsch-ner et al., 1984) and these proportions are known to pro-mote LO phases. Although, there is some diVerence inthe amount of cholesterol in both monolayers in the nat-ural myelin membrane, it appears that this diVerence isnot important for aVecting diVerentially the phase segre-gation in the normal compact myelin from compactedmyelin. This is deduced from the fact that both (intra-and extracellular) monolayers undergo this transition in

register, arranging up to 100 monolayers, which allowsfor X-ray diVraction (Kirschner et al., 1984). The result-ing average cholesterol mole fraction of 0.4 in our myelinmonolayer at the air/aqueous interface just represents anintermediate condition. Proteins are excluded from thecompacted myelin and are located at the normal periodmyelin, more crowded than normal as seen from freeze-fracture electron microscopy (Kirschner et al., 1984).Proteolipid is the more probable intramembranous par-ticle being the hallmark of this phase. This would pro-vide of a strong coupling between the extra andintracellular monolayers. The protein-rich normalperiod myelin is analogous to our LE phase and thecompositional phase separation reported in our previouswork (Oliveira and Maggio, 2002) is in full agreementwith studies that showed association of proteolipid, mye-lin basic protein and CNPase in a Triton X-100 solublefraction that exclude galactocerebroside and cholesterol(Arvanitis et al., 2002).

The complex morphology of the domains and thelack of a characteristic length scale are evident in theresults shown. Moreover, path-restricted propagation oflaterally diVusing signals at the surface should beexpected as a consequence of fractality, as shown in thiswork by the Xuorescent probe diVusion randomly depos-ited over the myelin Langmuir–Blodgett Wlm (Fig. 4).

4.4. Domain size and fractal dimension

Fractality has been invoked in the Weld of membranebiophysics in connection with a number of phenomenaranging from the geometry of self-aggregated vesicles(Lahiri et al., 1998), the folding of the membrane in 3Dspace (Paumgartner et al., 1981), the kinetics of channelconductance (Hoop and Peng, 2000), experimentallyobserved lipid domain topography (Miller et al., 1986)and its simulation (Fogedby et al., 1987), and lateral sur-face defects or diVusion (Nonnenmacher, 1989; Pinket al., 1991). In connection with lipid domains the focushas traditionally been on the determination of percola-tion thresholds of bilayer domains at thermotropic phasetransition points through Xuorescence recovery afterphotobleaching (FRAP) experiments (Almeida and Vaz,1995). These have implications on lateral diVusion(Dewey, 1998) and enzyme activity (Fanani et al., 2002)for which the concept of percoregulation has been previ-ously conceived (Muderhwa and Brockman, 1992) andfully supported later (Fanani et al., 2002). Also, work hasbeen devoted to liquid–liquid immiscible systems, a con-dition likely more applicable to biomembranes (Almeidaet al., 1992). Nevertheless, morphology is not accessiblefrom FRAP methodology. Although fractal dimension isaccessible from those measurements, more than one mor-phology can be ascribed to a given fractal dimension;thus, the problem of morphology cannot be resolved bydetermining only the fractal dimension or the percolation


thresholds. On the other hand, microscopy of monolay-ers allows direct inspection of lipid domain morphology(McConnell, 1991; Möhwald, 1990).

The above microscopic results show that the myelinmonolayer domains at high surface pressure [a relevantcondition for bilayers in general (Marsh, 1996) , and par-ticularly for myelin Wlms (Oliveira and Maggio, 2003)],have no characteristic length scale. Self-similarity alongorders of magnitude from millimeters to micrometers isevident from inspection of micrographs at diVerent mag-niWcations. These are relevant length scales for oligoden-drocytes, from which myelin multilayered structure isformed since the surface of an oligodendrocyte is in theorder of tens of square millimeters or more (see Kirsch-ner et al., 1984). The lower limit of this fractality is notamenable to be observed with the resolution employed inour optical measurements, but it is clear that if thedomains extend over the length scale described thiswould not represent “the characteristic length.” As statedabove, many length scales has been reported at the criti-cal point of phospholipid monolayers (Nielsen et al.,2000). This is an expected behavior analogous to the crit-ical opalescence of Xuids in equilibrium at the criticalpoint (Stanley, 1997) as a consequence of vanishing inter-facial tension (line tension in this case). We do not yetknow what is the molecular cause or driving force forestablishing fractality in the myelin monolayer but it islikely due to inhomogeneity of surface composition(Oliveira and Maggio, 2002) and lateral segregation ofcomponents in a dynamic out-of-equilibrium structurewhich characterizes membrane behavior (Edidin, 2001;Vereb et al., 2003). Even if equilibrium times of the orderof weeks have been suggested for composition-dependentdomain dynamics in lipid monolayers (McConnell, 1996),relatively fast non-equilibrium kinetic processes can beruled out since lowering the rate of compression, or wait-ing for several hours does not lead to relaxation of oursystem. In addition, proteins would further establishnon-relaxed inhomogeneities that should lengthen therelaxation time. The equilibrium condition might not beexperimentally attained, but this should also be the situa-tion in vivo, where mechanical perturbations of surfacepressure continuously Xuctuate due to metabolic changesor membrane recycling events.

Our work using the complex interface formed by themyelin monolayers points to a condition consisting oftwo immiscible liquids, one LE phase, and another cho-lesterol-enriched LO phase, which are believed to beanalogous to phases present in deWned regions of cellmembranes related to signal transduction events(Simons and Ikonen, 1997).

4.5. Comparison with fractal theory

Fractal dimension on 2D embedding simulated sys-tems of uncorrelated sites at percolation (random perco-

lation on lattices) is 91/48 (1.896), regardless of thelattice considered. That is an exact solution derived theo-retically (Aharony and StauVer, 1994). Our percolatedcluster dimension is diVerent from this value. This mightbe because the percolation threshold was exceeded oncompression; nevertheless, if this could be an explana-tion, then the fractal dimension should have convergedto two (Almeida and Vaz, 1995) and, instead, our fractaldimension is lower (1.7) thus ruling out that possibility.The fact that our clusters show a low fractal dimensioncould be due to correlations, that is the probability of apoint at the surface plane being occupied depending onthe occupancy of the neighboring sites. This can happendue to interaction energies between molecules, domainsand/or interfacial phenomena (Almeida and Vaz, 1995;Dewey, 1998). Alternatively, departure from the circularshape of the LE domains before, during and after perco-lation should also contribute to lower the fractal dimen-sion, by homology to what is observed with simulationof elliptical clusters, where increasing the anisotropyfrom circles to needles leads to a lower percolationthreshold (Xia and Thorpe, 1988) and, presumably, frac-tal dimension. In our system we could not determine thepercolation threshold because it is very variable andbecause of the uneven distribution of clusters as revealedby the diVerence between Db and Di.

5. Conclusions

Taking all the results together it appears that, underthe conditions of average surface pressures used, lipid–protein domains at the myelin monolayer surface showno characteristic length thus leading to a self-similartopography with large implications for strong Xuctua-tions and relay in lateral information transmission, as itis the case for corral-restricted diVusion. According toavailable literature, as far as we know, our observationsare the Wrst report on the direct visual indication of suchfractal microheterogeneity, spanning at least threeorders of magnitude, along the lateral plane of a surfaceformed with all the components of a natural membraneunder precisely controlled and known intermolecularorganization.

Acknowledgments

The authors thank Dr. SteVen Härtel for help withimage Wltering and segmentation routines applied to rawpictures. Dr. German Roth (Departamento de QuímicaBiológica, Universidad Nacional de Córdoba) kindlyprovided anti-PLP monoclonal antibody. This work wassupported by SECyT (UNC), CONICET, FONCyT andFundación Antorchas, Argentina. BM is a PrincipalInvestigator of CONICET and RGO is currently an


Alexander v. Humboldt Foundation Postdoctoral Fel-low at the Laboratory for Biophysics E22, PhysicsDepartment, Technical University of Munich, Germany.

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