The Influence of Domain Crowding on the Lateral Diffusion of

Aug 28, 2009 - Ciudad UniVersitaria, X5000HUA Córdoba, Argentina. ReceiVed: May 11, 2009; ReVised Manuscript ReceiVed: August 10, 2009. In this paper...
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J. Phys. Chem. B 2009, 113, 12844–12851

The Influence of Domain Crowding on the Lateral Diffusion of Ceramide-Enriched Domains in a Sphingomyelin Monolayer N. Wilke* and B. Maggio CIQUIBIC, Dpto. de Quı´mica Biolo´gica, Fac. de Cs. Quı´micas, UNC. Pabello´n Argentina, Ciudad UniVersitaria, X5000HUA Co´rdoba, Argentina ReceiVed: May 11, 2009; ReVised Manuscript ReceiVed: August 10, 2009

In this paper, we analyze the Brownian motion of ceramide-enriched condensed domains immersed in a fluid sphingomyelin-enriched monolayer at the air-water interface. The diffusion coefficient of the domains is determined under different molecular packings and domain arrays, and the monolayer viscosity is calculated. With this approach, the effect of domain crowding and of intrinsic monolayer viscosity can be split. We found that, for mixed monolayers of palmitoylated sphingomyelin and ceramide, the monolayer viscosity depends on the lateral pressure and on the domain-domain distance. In a 9:1 proportion of sphingomyelin: ceramide, the viscosity is about 4 × 10-9 N s m-1 below 15 mN m-1 (continuum sphingomyelin phase in a liquid expanded state) and increases at higher lateral pressures (continuum phase in a condensed state). The viscosity change with pressure is caused by both an increase of intrinsic viscosity and an increase in domain crowding. At very high domain crowding, the monolayer viscosity increases because the domains are held in place by steric hindrance generated by the other condensed domains of the array. These are short-range forces, effective when the domains are close together. As the domain array is relaxed and the domain-domain distance increases, these forces become negligible, and repulsive dipolar interactions appear to acquire importance. For the lipid mixture analyzed, the dipolar repulsion is more noticeable on subphases of 0.15 M NaCl than on pure water, revealing the influence of surface electrostatics. Introduction Most natural membranes show phase coexistence, characterized by solid domains in a more fluid environment. The presence of solid domains influences the diffusion of molecules residing either in the domains or in the continuum phase.1-5 In turn, the lateral diffusion of the components in membranes is a factor that determines, among others, the velocity of biochemical reaction-diffusion processes, and thus the function of cells.6 The understanding of the diffusion process in membranes, being complex two-dimensional fluids, is an active research area that has not yet been completely deciphered.7,8 The domains, which can reach to hundreds of nanometers, provide an inhomogeneous scenario, not only related to rheological properties but also to electrostatics. The electrostatic field generated by the domains can attract or repel the diffusing components, thus influencing its lateral motion.4,9 Lipid monomolecular layers at the air-water interface allow following the diffusing species over a relatively large area and for a long time. Besides, the environment of the diffusing species can be controlled and also varied in a controlled manner. All of this makes Langmuir lipid monolayers a convenient system for analyzing the influence of domains on the mechanical properties of membranes. In this paper, we directly measured the diffusion of micrometersize condensed domains in lipid monolayers, by analyzing their Brownian motion. We find a good agreement of the domain diffusion coefficient with the theoretical model of Hughes et al.,10 and propose an approach for the determination of monolayer viscosity at different domain arrays. Our experimental approach allows analyzing the effect of domain-domain * To whom correspondence should be addressed. E-mail: wilke@ mail.fcq.unc.edu.ar. Phone/Fax: +54-351-4334171.

proximity and of monolayer packing on the domain movement. This permits investigation of some of the possible reasons for the observed monolayer viscosity. Experimental Section Materials. Palmitoylated sphingomyelin (smC16), palmitoylated ceramide (cerC16), and the lipophilic fluorescent probe l-R-phosphatidylethanolamine-N-(lissamine rhodamine B sulfonyl)-ammonium salt were purchased from Avanti Polar Lipids (Alabaster, AL). Solvents and chemicals were of the highest commercial purity available. The water used for the subphase was from a Milli-Q system (Millipore), 18 MΩ. Lipid monolayers were prepared and characterized in a Langmuir balance using a glass through (microthrough, Kibron, Helsinki, Finland). Methods. The fluorescent probe was incorporated in the lipid solution before spreading (1 mol %). After spreading the lipid layer, the subphase level was reduced to a thickness of about 3 mm to minimize convection. Besides, a Teflon mask with lateral slits extending through the film into the subphase was used to restrict lateral monolayer flow under the field being observed. The Langmuir balance was placed on the stage of an inverted fluorescence microscope (Axiovert 200, Carl Zeiss, Oberkochen, Germany) with a 40× objective. Images were registered by a CCD video camera AxioCam HRc (Carl Zeiss, Oberkochen, Germany) commanded through the Axiovision 3.1 software of the Zeiss microscope. The observations were carried out at 23 ( 1 °C. The surface potential measurements were performed by a high impedance millivoltmeter connected to a surface ionizing 241Am electrode positioned 5 mm above the monolayer surface, and to a reference Ag/AgCl/Cl1- electrode submerged in the aqueous subphase.

10.1021/jp904378y CCC: $40.75  2009 American Chemical Society Published on Web 08/28/2009

Lateral Diffusion of Ceramide-Enriched Domains

J. Phys. Chem. B, Vol. 113, No. 38, 2009 12845

SCHEME 1: Schematic Representation of the Experimental Setup (Not to Scale)a

a A Langmuir monolayer is spread on an aqueous surface in a glass trough that is mounted on an inverted microscope: (1) Wilhelmy plate. (2) Upper electrode and qualitative electric field lines. The electrode can be displaced along the three orthogonal directions with a micromanipulator. (3) Pt electrode. (4) PTFE barriers. (5) Subphase: electrolytic solution. (6) Microscope objective.

The experimental setup for applying an electrostatic field was the same as that in ref 11. Briefly, a metal wire is held at 200 µm above the subphase. A second electrode is placed in the subphase, and a potential difference is applied between the electrodes (see Scheme 1). The upper electrode was charged by applying potentials of up to 300 V with respect to the subphase electrode. A positive potential leads to domain migration away from the zone under the electrode above the subphase, and a negative potential generates the opposite effect.12 When the desired domain array was achieved (recruited or dispersed domains), the field was turned off and images of the surface of the smC16:cerC16 monolayer were recorded for 200 s (1 frame/s). Then, the positions b X of selected domains were followed through the 200 frames. A number of domains were selected in pairs and the position of domain a relative to the position of domain b was calculated for each frame time: b Xa - b Xb. The mean square displacement of a relative to Xrel ) b b (MSDrel) was calculated for different time lapses between t+δt t 2 brel -b Xrel | 〉. MSDrel was plotted as frames (δt) as MSDrel ) 〈|X a function of δt for each experimental condition. If the domains in the selected pair are close together, the drift of each domain should be similar. Additionally, if they are of approximately the same size, the diffusion coefficient would be the same. In these conditions, MSDrel ) 8Dδt.13 Results and Discussion

Figure 1. (A) Representative photograph (200 µm × 200 µm) of a smC16:cerC16 (9:1) monolayer on 0.15 M NaCl at 5 mN m-1. The arrows show examples of domain pairs for the relative mean square displacement calculations (see text). The amplified zone is of 25 µm × 25 µm. (B) Relative mean square displacement of a domain pair as that shown in A as a function of the time lapse between frames. Domain sizes: 9 µm2 (squares), 14 µm2 (circles), 19 µm2 (up triangles), and 26 µm2 (down triangles). Inset: amplification of the linear range.

Many studies exist on the differences between the monolayer and bulk phase behavior of natural and synthetic ceramides and sphingomyelins.14 The bulk phase transition temperature of cerC16 is above 90 °C15 and forms monolayers in the condensed state; on the other hand, smC16 shows a bulk phase transition temperature at 40 °C16 and undergoes a surface pressure induced liquid expanded to condensed state transition in monolayers (see Figure 3B). Mixed monolayers of smC16 and cerC16, similar to sm:cer mixtures from bovine brain,17 show domain segregation at all lateral pressures with cer-enriched (dark) domains that exclude the fluorescent lipid probe (l-R-phosphatidylethanolamine-N-(lissamine rhodamine B sulfonyl)-ammonium salt) within a fluorescent continuum sm-enriched phase (bright) in which the probe preferentially partitions. The cer-enriched domains percolate at a proportion of cer of about 30-40%. Figure 1A shows a representative micrograph of a mixed monolayer of smC16:cer16 (9:1) on 0.15 M NaCl at 5 mN m-1. This monolayer was photographed for 200 s, at 1 frame/s (see recording 1 in the Supporting Information). Different domains of similar size and close to each other were picked in pairs;

Figure 1A shows two examples. If the domains are close, the drift of each domain is expected to be the same, and in that case, the relative MSD (MSDrel) will be proportional to the time lapse between frames, with the proportionality constant equal to 4(D1 + D2), where D1 and D2 are the diffusion coefficients of each domain. 13 Since the picked domains are approximately of the same size and can reasonably be assumed to be in the same environment, D1 ) D2 ) D, whereupon the slope of MSDrel versus δt is 8D. The domain positions were followed for 200 s and MSDrel was calculated, as explained in the Experimental Section, for different time lapses. Under all conditions, MSDrel increases linearly with time at least up to about 5 s (see Figure 1B); the latter was taken as the maximum time lapse for the linear fits under all of the experimental conditions analyzed. Since smC16 undergoes a liquid expanded to condensed state transition at a surface pressure between about 15 and 18 mN m-1 at 23 °C (see Figure 3B), the comparisons will be made at 5 mN m-1 and at 25 mN m-1 where the continuum phase is in

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Figure 2. Diffusion coefficients measured for different domains as a function of the domain radius in monolayers at 5 mN m-1 (circles) and 25 mN m-1 (triangles). The lines are theoretical calculations using eq 2 and the viscosity values shown in Figure 3A. Subphase: pure water (open symbols and solid lines) and 0.15 M NaCl (black symbols and dashed lines).

the liquid expanded or condensed states, respectively. Figure 2 shows the measured diffusion coefficient (symbols) as a function of domain radius on water (open symbols) and on 0.15 M NaCl (black symbols) at 5 (circles) and 25 mN m-1 (triangles). At low lateral pressures on both water and 0.15 M NaCl subphases, the diffusion coefficient decreases slightly with the domain size (Figure 2). This is not the case for lateral pressures above 20 mN m-1, where the diffusion coefficients are low and do not depend on (or depend slightly on) domain size. The dependence of the diffusion coefficient on the surface rheology has been studied by different authors and through different approaches; a valuable account on this topic was published.18 The dependence of D on the surface rheology can be expressed as follows:

D)

kT rdom4πηwΛT(ε)

(1)

In this equation, ΛT(ε) is the reduced translational drag coefficient, rdom is the domain radius, and ε ) rdomηw/ηm, where ηw is the subphase viscosity (0.001 N s m-2 for aqueous solutions at 23 °C) and ηm is the 2D membrane viscosity, ηm ≈ hη3D, with h being the membrane thickness and η3D being the three-dimensional viscosity.2 The dependence of ΛT(ε) with ε cannot be resolved analytically. Saffman19 proposed an asymptotic result for ε < 0.1. Afterward, Hughes et al.10 introduced a new analysis extending the asymptotic result to ε < 1 and provided an exact numerical calculation up to ε ) 10. In the present work, we were able to determine the diffusion coefficient of a domain of known size. Using eq 1, the value of ΛT(ε) can be calculated, and from the results of Hughes et al.,10 the ε value (and consequently the ηm value) can be obtained. From the data in Figure 2, the surface viscosity at 5 and 25 mN m-1 was calculated. The ε values determined vary from 0.04 to 0.90; in all cases, ε is less than 1. As stated before, Hughes et al.10 described an asymptotic result for this ε value range, which reads as follows:

D)

kTε[ln(2/ε) - γ + 4π-1ε - 0.5ε2 ln(2/ε)] rdom4πηw

(2)

Figure 3. (A) Monolayer viscosity as a function of the lateral pressure for mixed monolayers of smC16:cerC16 (9:1) on 0.15 M NaCl (black symbols) and water (open symbols). Inset: the viscosity is plotted as a function of the percent in area of condensed domains. (B) Compression isotherms for smC16 (solid line) and for cerC16 (dotted line). Both isotherms behave similar on water and on 0.15 M NaCl. Inset: domain-domain border distances as a function of the lateral pressure for films on water subphase (open symbols) and 0.15 M NaCl subphase (black symbols). (C) Domain diffusion coefficients for small domains (5-10 µm2) as a function of the cerC16 proportion in the mixture. The diffusion coefficient of domains at 50% cerC16 corresponds to domains in corrals, as shown in the photo. Inset: the domain diffusion is plotted as a function of the percentage of the condensed area.

In this equation, γ is Euler’s constant (0.5772). Using eq 2 and the obtained average monolayer viscosities at 5 and 25 mN m-1

Lateral Diffusion of Ceramide-Enriched Domains (Figure 3A), the theoretical D value was calculated as a function of the domain radius (lines in Figure 2). The diffusion coefficients for domains of different size were also determined at other lateral pressures (Figure 4C, triangles show the results for small domains), and from these data, the surface viscosity was calculated. Figure 3A shows the variation of ηm with the lateral pressure on pure water (open symbols) and on 0.15 M NaCl (black symbols). In the inset, ηm is plotted as a function of the fractional area occupied by the condensed domains. The surface viscosity is similar on both subphases at all lateral pressures. At low lateral pressures ( 1(see Figure 2 of Hughes et al.10); thus, the determination of the surface viscosity by this approach becomes less reliable as ε increases and we only show the ηm values for lateral pressures above 10 mN m-1. An unexpected result that emerges from comparing the data of Figure 4A and B at 5 mN m-1 (black symbols) is that the domain movement on the water subphase resembles that of isolated domains at small domain-domain distances, compared to the movement of domains on 0.15 M NaCl. Furthermore, at 5 mN m-1 on pure water, there is an abrupt increase of the domain diffusion coefficient at distances of 3 µm, while on 0.15 M NaCl D increases smoothly with the domain-domain distance, reaching a plateau at a separation distance of about 8 µm. At 25 mN m-1, the comparison is not clear because the relative dispersion of data is rather large. If the domain dipoles were in contact with the subphase, domain dipole-dipole interactions should be screened on 0.15 M NaCl compared to when the domain resultant dipoles are on an ion-free aqueous environment; however, if only the hydrocarbon chain dipoles (which are placed in a region that excludes the subphase molecules) are considered, the ionic strength should not influence the domain-domain repulsion.

Wilke and Maggio TABLE 1: Surface Potencial for smC16 and cerC16 Pure Monolayers at 5 mN m-1 on the Indicated Subphases ∆V on pure water/mV ∆V on 0.15 M NaCl/mV

cerC16

smC16

cerC16-smC16

470 ( 20 460 ( 20

260 ( 10 200 ( 10

210 ( 30 260 ( 30

SCHEME 2: Schematic Representation of the Effect of the Subphase on the Potential Surface (and the Dipole Density) at 5 mN m-1 a

a The surface potential (∆V) values for the cerC16-enriched domains and the smC16-enriched continuum phase are represented as solid lines (subphase: pure water) and dashed lines (subphase: 0.15 M NaCl). As shown in Figure 4D, the ∆V value for cerC16 monolayers is similar on 0.15 M NaCl and on pure water. On the contrary, ∆V decreases when salt is added to the subphase for smC16 monolayers.

To analyze the reason for the different behavior shown in Figure 4A and B, the surface potential (∆V) of smC16 and cerC16 monolayers was determined on both subphases as explained in the Experimental Section. Figure 4D shows the ∆V values for cerC16 (gray lines) and for smC16 (black lines) on pure water (solid lines) and on 0.15 M NaCl (dashed lines) as a function of the lateral pressure. For cerC16, the ∆V value is independent of the subphase ionic strength, as expected considering that cer is a molecule that forms densely packed monolayers with a relatively small dipole moment associated to the single hydroxyl in the polar headgroup. On the contrary, the ∆V value of films of the zwitterionic smC16, which contains a larger polar headgroup dipole moment oriented opposite to the hydrocarbon chain dipoles, decreases by 50-100 mV when NaCl is added to the subphase (see Table 1) and, consequently, the ∆V difference between cerC16 and smC16 (∆Vcer - ∆Vsm) is higher on 0.15 M NaCl than on pure water (see Scheme 2). The ∆V value generated by a homogeneous monolayer is proportional to the dipole density of the monolayer,22 and since the domain-domain repulsion is related to the difference in dipole moment density between each phase,20 a higher ∆Vcer ∆Vsm implies a higher domain-domain repulsion (see Scheme 2). The calculated ∆Vcer - ∆Vsm is a rather crude estimation of the dipole density difference because neither the condensed domains nor the liquid expanded phase are constituted by pure cerC16 or pure smC16, but the result obtained indicates that the salt addition in this system not only does not diminish the domain-domain repulsion but it causes its enhancement. Another observation pointing in the same direction is that the average domain size, at the same lipid proportion and lateral pressure, is smaller on 0.15 M NaCl than on pure water (about 1.5 times less at 5 mN m-1), which is expected considering the effect of dipole-dipole repulsion on the equilibrium domain size.20 The effect of a high dielectric subphase on the electrostatic interactions in the monolayer was theoretically studied by several authors.23-25 They all agree that the presence of a high dielectric surface under an array of dipoles enhances the electrostatic

Lateral Diffusion of Ceramide-Enriched Domains repulsion between the dipoles. The addition of salt to an aqueous subphase should not enhance this effect, since the dielectric constant of the subphase is already high. In our system, the addition of salt to the high dielectric subphase increases the dipolar repulsion between domains probably due to a change in the average molecular dipole density. Regarding the overall behavior at 5 mN m-1 shown in Figure 4A and B, the smooth increase of D as the domain-domain distance increases on NaCl is expected for long-range domaindomain repulsive interactions; on the other hand, the sharp increase of the D value observed on pure water is characteristic of a short-range steric hindrance interaction. We suggest that, on 0.15 M NaCl, the electrostatic repulsion between domains generated by the difference in dipole moment density of each phase in coexistence influences the observed apparent viscosity. On the contrary, for monolayers on pure water, the dipolar repulsion energy is lower than the thermal energy, and thus, domain crowding hinders domain movement only at very small interdomain distances, due to steric hindrances. A model estimating the dipole repulsion potential energy of a domain surrounded by other domains, supporting our idea is given in the Appendix. Conclusions In this paper, we determined the diffusion coefficient of domains (and estimated the membrane viscosity) at different molecular densities and for different domain-domain distances. With the employed approach, the effect of domain crowding and of intrinsic membrane viscosity can be split. We found that the apparent viscosity of monolayers of smC16:cerC16 (9:1) is about 4 × 10-9 N s m-1 below 15 mN m-1 (continuum smC16 phase in a liquid expanded state) and increases up to 5 × 10-8 N s m-1 at higher lateral pressures (continuum phase in a condensed state). On the other hand, the intrinsic monolayer viscosity, calculated from the Brownian motion of isolated domains, ranges from values below 1.5 × 10-10 N s m-1 (lower value that can be calculated through this approach) to 10-8 N s m-1. Similar studies on bilayers of phospholipids and cholesterol2 found ηm values for liquid ordered phases in the range 10-8-10-7 N s m-1, which is in agreement with our values for the continuous phase in a condensed state. Other studies using an interfacial stress rheometer for eicosanol26 monolayers report viscosity values of 10-6 N s m-1. This alcohol forms monolayers less compressible than smC16 at high lateral pressure, which is in agreement with a higher viscosity value. Using the Brownian movement of micrometer sized particles inserted in a dimiristoyl phosphatidylcholine monolayer and monolayers of other molecules at the air-water interfaces, Sickert et al.27 calculated ηm values from 10-10 to 10-9 N s m-1. Baoukina et al.28 found for monolayers in a homogeneous liquid expanded phase simulated viscosity values of about 10-10 N s m-1. For isolated domains in a liquid expanded smC16 continuous phase, we obtained viscosity values lower than 1.5 × 10-10 N s m-1, in agreement with the theoretical value of Baoukina et al. Regarding the variation of the rheological properties in the presence of domains, for different proportions of mixed monolayers that present phase coexistence, Ding et al.1 found that the surface viscosity can change as much as 100-fold when the condensed area fraction changes from 0 to 0.5-0.8. An abrupt change is seen when about 40% of the area corresponds to the condensed domains. In our case, the domain area fraction changes over a more narrow range (about 15-35%, see inset in Figure 3A), and the viscosity value changes about 10 times. With our approach, we could split the contribution to the surface

J. Phys. Chem. B, Vol. 113, No. 38, 2009 12849 viscosity due to the increase in the lipid packing from the contribution due to the domain crowding, and we found that the change in viscosity is caused by both effects and not only by the increase of the domain area fraction. In summary, we can conclude that the observed change of domain lateral diffusion with pressure is caused by both an increase of intrinsic viscosity and an increase of domain crowding. At relatively high domain crowding, the monolayer viscosity increases because the domains are held in place by hydrodynamic friction forces generated by the presence of the other condensed domains in the array.1 These are short-range forces that acquire importance when the domains are close together (in our case, at domain-domain distances smaller than 3 µm). When the domain array is relaxed and the domain-domain distance increases, these forces become negligible, and repulsive interactions due to the domain resultant dipoles become predominant. For the lipid monolayers analyzed, this is the case when the subphase is 0.15 M NaCl but not when it is pure water. The difference observed over each subphase can be explained on the basis of the measured ∆V values, considering that on NaCl solutions the dipole moment density difference between the condensed domains and the liquid expanded phase is greater than on pure water. Therefore, the domain-domain dipole repulsion would be higher on NaCl than on water. This conclusion is also supported by the observation that, on pure water subphases, the average domain size is 1.5 times larger than that on 0.15 M NaCl solutions. In that sense, an estimation of the potential energy of a dipole in a dipolar confinement (given in the Appendix) further supports this hypothesis. We also found in this work that both isolated and crowded domains move similarly on NaCl than on water. The isolated domain movement indicates that the intrinsic monolayer viscosity is independent of subphase ionic conditions and depends on the lateral pressure. Finally, the results found for the smC16:cerC16 mixture are in agreement with our previous results of electrostatic field induced domain migration in sm:cer mixtures. In those experiments, we found that domain migration under the effect of an external electric field was precluded at high lateral pressures.12 At that time, those results could not be simply explained on the basis of final state thermodynamic arguments. Now, we are confirming that at high lateral pressures the domain migration becomes so slow that it can no longer be observed under the experimental time scales used. Acknowledgment. This work was supported by SECyTUNC, CONICET, FONCYT (Program BID 1728/OC-AR PICT 1381, PAE 22642), Argentina. B.M. and N.W. are Career Investigators of CONICET. Appendix The electrostatic energy of a domain confined in an infinite array of domains is estimated considering a central dipole in a confinement of homogeneous dipolar density of radius R (see inset in Figure 5 for details). The central domain is considered as a point dipole of moment Pdom ) ∆µ Adom, where Adom is the domain area and ∆µ is the difference in dipole moment density between the condensed and expanded phases. The dipole is at a position defined by b x0 (0 e x0 e R, where R is the confinement radius). The other domains are approximated as homogeneously distributed dipoles of dipole moment F at a distance r from the central dipole, generating an electrostatic field:

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E)

1 4πεε0

∑ rF3

Wilke and Maggio

(A1)

s

The sum is carried over the entire surface s where the domains are present, that is, the entire surface excluding the circular confinement (see inset in Figure 5). This surface is partitioned in rings of width dr. Each ring is divided in M subintervals, and the sum is performed over a differential area element of size 2π(rdr + dr2)/M (lined area in inset of Figure 5). Since dr , r, the differential area element can be approximated as 2πrdr/ M. In 2πrdr/M, there are F0(2πrdr/M) domains,with F0 being the number of domains per m2. With these considerations, the dipole moment in eq A1 is F ) PdomF0(2πrdr/M). To generalize the results, the following reduced variables are defined: X0 ) x0/R, dr′ ) dr/R, r′ ) r/R. Thus, eq A1 reduces to

E)

PdomF0dr′ 2εε0MR

∑ (r′)1 2

(A2)

The sum is performed for all of the possible r values, in other words, from r′ ) (sin2 R + cos2 R)1/2 (0 < R e 2π, divided in M subintervals) to infinity for each X0 value (0 e X0 e 1). M is increased and dr is decreased until the resulting E values converge. Then, the potential energy U(X0) is calculated as

U(X0) ) PdomE(X0) )

(Pdom)2F0dr′ 2εε0MR

1 ∑ (r′)1 2 ) ξ dr′ ∑ M (r′)2

(A3) In eq A3, ξ ) (Pdom)2F0/2εε0R. For the system under study, Pdom ∼ 10-24 C m, F0 ∼ 1011 m-2, and 2 e ε e 7. Then, ξ ∼ 10-27 J m/R. In Figure 5, the three curves were calculated with ξ ) 3.8 × 10-21, 3.5 × 10-21, and 3.1 × 10-21 J. For R ) 3µm and rdom ) 1 µm, the vertical lines in Figure 5 indicate the X0 value where the central dipole and the walls of the confinement would contact. In that case, the lower curve corresponds to a central domain that would not be affected by electrostatics but by steric

Figure 5. Dipole repulsion energy for a dipole confined in a circle of radius R surrounded by a homogeneous dipole density as a function of X0 ) x0/R for ξ ) 3.8 10-21 J (straight lines), 3.5 10-21 J (dotted lines), and 3.1 10-21 J (dashed lines) (see the inset and the Appendix). The horizontal gray line shows the thermal energy at 23 °C. The vertical lines indicate the X0 value where the central dipole and the walls of the confinement would contact for R ) 3 µm and rdom ) 1 µm.

hindrance, because the thermal energy (horizontal gray line in Figure 5) is higher than the dipole repulsion energy for all of the possible X0 values before contact of domains. Notice that the fractional change in ∆Vcer - ∆Vsm on NaCl compared to water is about 1.2, and this is also the ratio between the ξ values for the middle and lower curves in Figure 5. In other words, the potential energy estimation indicates that it is possible that a change in dipole moment density similar to that observed in this work could lead to the change of domain movement shown in Figure 4A and B. When the domains are very crowded (domain-domain distances smaller than 3 µm), the domain movement is impaired by steric hindrance. As the domain density decreases, their movement will be affected by the dipole repulsion if the dipole moment density is large enough to exceed the thermal energy. This could be the case of cerC16-enriched domains in films on 0.15 M NaCl subphases but not on pure water. However, the potential energy calculated is only a crude estimation, because the central domain does not behave as a point dipole, and the surrounding domains are not a homogeneous array of dipoles. Nevertheless, it provides insight on the possible influence that the dipole repulsion may have on the domain movement. Supporting Information Available: (1) Brownian motion of domains in a mixed monolayer of smC16:cer16 (9:1) on 0.15 M NaCl at 5 mN m-1. Real time: 25 s, 1 frame/s. Real size: 325 µm × 258 µm. (2) Brownian motion of domains in corrals in a mixed monolayer of smC16:cer16 (1:1) on 0.15 M NaCl at 30 mN m-1. Real time: 25 s, 1 frame/s. Real size: 325 µm × 258 µm. (3) Electric field induced migration of domains for a mixed monolayer of smC16:cer16 (9:1) on 0.15 M NaCl at 5 mN m-1. Real time: 30 s, 1 frame/2 s. Real size: 650 µm × 515 µm. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Ding, J.; Warriner, H. E.; Zasadzinski, J. A. Viscosity of twodimensional suspensions. Phys. ReV. Lett. 2002, 88 (16), 168102. (2) Cicuta, P.; Keller, S. L.; Veatch, S. L. Diffusion of liquid domains in lipid bilayer membranes. J. Phys. Chem. B 2007, 111 (13), 3328–3331. (3) Saxton, M. J. Lateral diffusion in an archipelago. Dependence on tracer size. Biophys. J. 1993, 64 (4), 1053–1062. (4) Forstner, M. B.; Martin, D. S.; Ruckerl, F.; Kas, J. A.; Selle, C. Attractive membrane domains control lateral diffusion. Phys. ReV. E: Stat., Nonlinear, Soft Matter Phys. 2008, 77, 051906. (5) Selle, C.; Ruckerl, F.; Martin, D.; Forstner, M. B.; Kas, J. A. Measurement of diffusion in Langmuir monolayers by sinlge-particle tracking. Phys. Chem. Chem. Phys. 2004, 6, 5535–5542. (6) Bhalla, U. S.; Iyengar, R. Emergent properties of networks of biological signaling pathways. Science 1999, 283 (5400), 381–387. (7) Vereb, G.; Szollosi, J.; Matko, J.; Nagy, P.; Farkas, T.; Vigh, L.; Matyus, L.; Waldmann, T. A.; Damjanovich, S. Dynamic, yet structured: The cell membrane three decades after the Singer-Nicolson model. Proc. Natl. Acad. Sci. U.S.A. 2003, 100 (14), 8053–8058. (8) Jacobson, K.; Sheets, E. D.; Simson, R. Revisiting the fluid mosaic model of membranes. Science 1995, 268 (5216), 1441–1442. (9) Nassoy, P.; Birch, W. R.; Andelman, D.; Rondelez, F. Hydrodynamic mapping of two-dimensional electric fields in monolayers. Phys. ReV. Lett. 1996, 76 (3), 455–458. (10) Hughes, D.; Pailthorpe, B.; White, L. The translational and rotational drag on a cilinder moving in a membrane. J. Fluid Mech. 1981, 110, 349– 372. (11) Wilke, N.; Dassie, S. A.; Leiva, E. P.; Maggio, B. Externally applied electric fields on immiscible lipid monolayers: repulsion between condensed domains precludes domain migration. Langmuir 2006, 22 (23), 9664–9670. (12) Wilke, N.; Maggio, B. Effect of externally applied electrostatic fields on the surface topography of ceramide-enriched domains in mixed monolayers with sphingomyelin. Biophys. Chem. 2006, 122 (1), 36–42. (13) Forstner, M. B.; Ka¨s, J.; Martin, D. Single Lipid Diffusion in Langmuir Monolayers. Langmuir 2001, 17 (3), 567–570.

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