International Conference on Neutron Scattering 2009
Journal of Physics: Conference Series 251 (2010) 012036

IOP Publishingdoi:10.1088/1742-6596/251/1/012036

Diffusion of domains on nanometer sized vesicle
Y Sakuma, N Urakami1, Y Ogata1, M Nagao2,3, S Komura4, T Kawakatsu5 andM Imai
Dept. of Physics, Ochanomizu Univ., Tokyo112-8610, Japan
Dept. of Physics and Information Sciences, Yamaguchi Univ., Yamaguchi 753-8512,
Japan
2
Cyclotron Facility, Indiana Univ., Bloomington, IN 47408-1398, USA
3
Center for Neutron Research, National Institute of Standards and Technology,
Gaithersburg, MD 20899-6102, USA
4
Dept. of Chemistry, Tokyo Metropolitan Univ., Tokyo 192-0397, Japan
5
Dept. of Physics, Tohoku Univ., Sendai 980-8578, Japan1

sakuma@sweetcream.phys.ocha.ac.jp
Abstract. We have investigated the diffusion coefficient of nano-meter-sized domains on avesicle composed of saturated phospholipids, unsaturated phospholipids and cholesterols bymeans of neutron spin echo spectroscopy. The obtained diffusion coefficient was examinedfrom a viewpoint of the hydrodynamic model of Brownian objects in a fluid membrane.

1. Introduction
In recent years, a lateral phase separation in cell membranes so-called lipid raft has gathered muchattention in relation to biological functionalities [1]. Lipid rafts are liquid domains rich in cholesterol,sphingolipid and specific proteins, which might play important roles in the biological processes. Since
the biochemical functions may be diffusion controlled [2], the lateral diffusion of lipid rafts in bilayers
is of biological interest.
In order to understand the physiochemical nature of lipid rafts, the model giant unilamellar vesicles(GUVs) consisting of saturated lipids, unsaturated lipids and cholesterol have been investigated,because a lateral phase separation of the lipids into a liquid-ordered (Lo) phase and a liquid-disordered(Ld) phase might be responsible for the formation of rafts in cell membranes. One of the advantages ofthe model GUV systems is that the domains have the size in micrometer length scale, which makes it
possible to observe the phase separation directly by a fluorescence microscopy. Taking this advantage,
Cicuta et al. [3] estimated the diffusion coefficients of micrometer-sized liquid domains. They foundthat the liquid-ordered domains diffuse in the liquid-disordered matrix via Brownian motion and thediffusion coefficient, D, obeys a D ∝1/ r law in the micrometer length scale, where r denotes thedomain radius.
Based on the hydrodynamic continuum theory, Saffman and Delbrück [4] derived the size
dependence of the diffusion€ coefficient of an object undergoing Brownian motion in the membrane.
For the case of r < η′ / ηw ( η′ : 2D membrane viscosity and ηw: 3D bulk viscosity of surrounding
aqueous phase), the diffusion coefficient is expressed by [4]€€c 2010 IOP Publishing Ltd!

1

International Conference on Neutron Scattering 2009
Journal of Physics: Conference Series 251 (2010) 012036

k BT   η′ 1 1 ln− γ + ,4 πη′   ηw r 2

D(r) =IOP Publishingdoi:10.1088/1742-6596/251/1/012036(1)

where kB is the Boltzmann constant, T is the temperature and γ is the Euler constant, 0.5772. The 3D
membrane viscosity, η′3D , is given by η′3D ≅ η′ / h , where h is the bilayer thickness. Using typicalvalues
for the membranes immersed in water, ηw ≈ 10-3 Ns/m2, η′3D ≈ 10-1 Ns/m2 [5] and h ≈ 5 x 10-9 m,€we obtain η′ / ηw ≅ 500 nm. Thus this logarithmic scaling law is valid for diffusing objects withnanometer-lengthscale. On the€ other hand, for the diffusing domains with micrometer-length scale,€the diffusion coefficient is expressed by €[6]€€
k BT 1
D(r) =,(2)€16ηw rwhich well explains the experimental results reported by Cicuta et al.
Since the lipid rafts are believed to have the diameter of 10-100 nm [7], the nanometer-sizeddomainsshould obey the D ~ ln(1/ r) law. In order to confirm the scaling laws, it is desirable to€measure the diffusion coefficients of objects in the nanometer scale range. In this study weinvestigated the dynamics of nanometer-sized domains using a contrast matching technique forneutron spin echo (NSE) and small unilamellar vesicles (SUVs).
€

2. Experiments
2.1. Samples
1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) (> 99 % purity), 1,2-dipalmitoyl-sn-glycero-3phosphocholine (h-DPPC) (> 99 % purity) and 1,2-dipalmitoyl-d62-sn-glycero-3-phosphocholine (dDPPC) (> 99 % purity) were obtained in a powder form from Avanti Polar Lipid, Inc. Cholesterol(Chol) (> 99 % purity) was purchased from Sigma-Aldrich Co. All lipids were used without further
purification and stored 253 K until use [8].
2.2. Sample preparations
GUVs were prepared by a gentle hydration method [9]. The obtained GUV suspension was sonicatedusing an ultrasonic homogenizer with 23kHz frequency (Branson, Sonifire Model 150) for ~20 min.
After the sonication the suspension became transparent and we obtained the SUVs.
2.3. Measurements
In this study we performed small angle neutron scattering (SANS) experiments under two
experimental conditions, one is a film contrast condition where we can obtain whole SUV shape andthe other is a contrast matching condition where we can estimate the heterogeneity in the SUVs. TheSANS measurements were performed using the SANS-U instrument of ISSP, The University of Tokyoat JRR-3M of the JAEA [10]. In order to obtain the dynamical structure factor of nanometer-sizeddomains we performed NSE experiments. Since the scattering intensity is low for the matching
contrast samples, in this work we concentrated the NSE measurement at q = 0.07 Å-1 and 285 K inorder to maximize statistics. The NSE experiments were performed using the NG5-NSE spectrometerat the NIST Center for Neutron Research [11].
3. Results and Discussion
First, we characterized the ternary SUVs with the composition of DPPC/DOPC/Chol = 4/4/2 by SANS
profiles under the film contrast condition [12]. The obtained SANS profile is well described by themodel scattering function for the spherical shell structure. From the fitting we extracted mean outerradius of vesicles Rout = (11.2±0.1) nm, the bilayer thickness h = (4.2±0.6) nm and the size
polydispersity ( p 2 =< Rin2 > / < Rin > 2 −1) p = (0.32±0.02), and these values were independent of thetemperature.
€2

International Conference on Neutron Scattering 2009
Journal of Physics: Conference Series 251 (2010) 012036

IOP Publishingdoi:10.1088/1742-6596/251/1/012036

The static structure of the nanometer-sized domains on a SUV was examined by the contrast
matching technique for SANS. We adjusted the mean scattering length density (SLD) of thehomogeneous ternary membrane ρd-mix to that of the solvent ρsolv. The obtained SANS profiles for theSUV at the contrast matching condition are shown in figure 1(a). At 333 K in the homogeneous one
phase region, we observed no significant scattering from the vesicles, indicating that the lipids arehomogeneously mixed in the one phase region and each SUV has the same composition. When wedecreased the temperature to the coexisting two-phase region (below 303 K), a scattering maximum
due to the phase separation was observed in the vicinity of q ≅ 0.02 Å-1 [12, 13, 14]. With decreasing
temperature to 285 K, the scattering maximum increases its intensity with keeping the maximum
position. We analyzed the observed profiles using a multi-domain model (e.g. two domain model isshown in figure 1(b)). The model scattering function of the multi-domain model was calculated by a€Monte Carlo simulation technique [12], where we assumed that each domain has the same size andcomposition. The model scattering function with two domains was well described the observed
profile as shown in figure (a), which gave θc = 35° (corresponding to r ~ 8 nm).
We examined the dynamics of nanometer-sized domains on the SUV from the intermediate
scattering function S(q,t)/S(q,0) obtained by the NSE measurement. Since the diffusion of domains ona vesicle is composed of two modes, diffusion of the center of gravity of the SUV and that of domains
on the SUV, we assumed that the intermediate scattering function of the phase separated SUVs underthe matching contrast is expressed by(3)S(q, t) / S(q, 0) = A exp[−D0 q 2 t] + (1 − A) exp[−(D0 + Dd )q 2 t]
where D0 and Dd are the diffusion coefficients of the whole SUV and the nanometer-sized lipid
domain on a SUV, respectively, and A is a numerical constant. Here we estimated D0 from theS(q,t)/S(q,0)
of the ternary SUVs at the film contrast condition. The intermediate scattering functions€
were well described by single exponential functions S(q,t) / S(q,0) = exp(− Γt) . The obtained relaxation
rates, Γ , at various q has the relation Γ = D0 q 2 and gives the diffusion coefficient of whole SUV, D0 =(1.31±0.01) x 10-11 m2/s at 285 K. This value agrees with the diffusion coefficient DSE = 1.14 x 10-11
m2/s calculated by the Stokes-Einstein relation€ using R = 11.2 nm.
The S(q,t)/S(q,0) of the ternary€ SUV at the matching contrast condition is shown in figure 2 with thatat the film contrast condition. The difference between S(q,t)/S(q,0) of the film contrast and that of thematching contrast is attributed to the diffusion of domains in an SUV and the fitting using equation (3)gives the diffusion coefficient of the domains with r = 8 nm as Dd = 8.8 × 10-12 m2/s.

€(b)

(a)

Figure 1. (a)Temperature dependence of SANS profiles of binary SUVs at matching
contrast condition. Fitting result is shown by solid line. (b) Geometry of two-domain
model for Monte Carlo simulations.

3International Conference on Neutron Scattering 2009
Journal of Physics: Conference Series 251 (2010) 012036

IOP Publishingdoi:10.1088/1742-6596/251/1/012036

In figure 3 we plot the diffusion coefficients of liquid-ordered domains in the liquid-disordered matrix
obtained by the NSE measurements (nanometer-scale) and the microscope observation (micrometerscale) [3] as a function of the radius of the domains. The broken and the solid lines in figure 3 show
the 1/r (equation (2)) and the ln(1/r) (equation (1)) scaling laws, respectively, where we used ηw ≈ 10-3
Ns/m2 and η′3D ≈ 10-1 Ns/m2. The obtained diffusion coefficient was intermediate between the 1/r andln(1/r) scaling law, indicating the necessity of further experiments to examine the Saffman andDelbrück law quantitatively. On this issue we will address in the forthcoming paper. €€
1.00
0.95

10-11

film contrast

0.85

10-12

2

Dd / m /sS(q,t)/S(q,0)

0.90

10-13

0.80

10-14
0.75

matching contrast

10-15
10-90.70
01020304050t / ns

Figure 2. Intermediate scatteringfunctions at q = 0.07Å-1 obtained fromNSE experiments. Open circles andclosed circles represent the film and thematching
contrast
experiments,respectively.

10-810-7r/m

10-610-5

Figure 3. Diffusion coefficients ofdomains as a function of domain radiuswith 1/r (broken line) and the ln(1/r) (solidline) scaling laws. Closed circle and open
circles indicate the data from this work andCicuta et al. [3], respectively.

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[5] Peters R and Cherry R J 1982 Proc. Natl. Acad. Sci. 79 4317
[6] Hughes B D, Pailthorpe B A and White L R 1981 J. Fluid Mech. 110 349[7] Plowman S J, Muncke C, Parton R G and Hancock J F 2005 Proc. Natl. Acad. Sci. 102 15500[8] Certain commercial equipment or materials are identified in this paper to foster understanding.
Such identification does not imply recommendation by the National Institute of Standards andTechnology, nor does it imply that the materials or equipment identified are necessarily the bestavailable for the purpose.
[9] Reeves J P and Dowben R M 1969 J. Cell Physiol. 73 49[10] Ito Y, Imai M and Takahashi S 1995 Physica B 213&214 889[11] Monkenbusch M, Schätzler R and Richter D 1997 Nuclear Instruments and Methods in Physics
Research Section A 399 301[12] Masui T, Urakami N and Imai M, 2008 Eur. Phys. J. E 27 379[13] Pencer J, Mills T, Anghel V, Krueger S, Epand R M and Katsaras J 2005 Eur. Phys. J. E 18 447[14] Pencer J, Jackson A, Kucerka N, Nieh M-P and Katsaras J 2008 Eur. Biophys. J. 37 665

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