Dynamics of Nano-Meter-Sized Domains on a Vesiclen S. Komura% and M. Imai
Y. Sakuma, N. Urakami , Y. Ogata , M. Nagao'",
Department of Physics, Ochanomizu University, Bunkyo, Tokyo 112-8610, Japan*Department of Physics and Information Sciences, Yamaguchi University,
Yoshida, Yamaguchi 753-8512, Japan^Cyclotron Facility, Indiana University, Bloomington, IN47408-1398, USA"^Center for Neutron Research, National Institute of Standards and Technology,
Gaithersburg, MD 20899-6102, USA^Department of Chemistry, Tokyo Metropolitan University,
Minami Osawa, Tokyo 192-0397, Japan
Abstract. We have investigated the dynamics of nano-meter-sized domains on a vesicle composed of saturated
phospholipids, unsaturated phospholipids and cholesterols by means of a neutron spin echo technique. The diffiisioncoeffisient of the domains obtained from the intermediate scattering fimction is about two orders of magnitude larger
than that calculated by Saffman and Delbriick law. From molecular dynamics simulations we found another type of thedomain dynamics where the domains are agitated by thermal fluctuation and repeats coalescence and rupture. The
relaxation rate of the new mode is about two orders of magnitude larger than that of the diffusion mode. The coalescenceand rupture mode of domains may be responsible for the observed domain dynamics.
Keywords: Domain dynamics, Lipid raft, Nano-meter-sized domain. Neutron spin echo. Small unilamellar vesicle
PACS: 87.14.Cc, 87.14.dt, 87.16.drbeen shown that the model vesicles composed ofsaturated phospholipids, unsaturated phospholipids
and cholesterols exhibit lateral phase separation
between L„ (liquid-ordered) phase and La (liquiddisordered) phase below a miscibility temperature T^^,
which is observed as micro-meter-sized liquid domain
structure by a fluorescence microscopy. The diffiasionof micro-meter-sized domains on a giant vesicle wasvisited by Keller and our groups. The former group
showed that the diffusion of domains follows the
Saffman and Delbriick law [9]INTRODUCTION
In cell membranes, the constituents formcharacteristic lateral heterogeneities arising from theimmiscibility of the lipid components such as
sphingomyelin, unsaturated phospholipids, andcholesterol (Choi). The heterogeneitis coupled with thespecific protein distribution are responsible for theimportantbiological
functionalities
such asendocytosis, adhesion, signaling, protein transport andapoptosis and caUed lipid rafts [1,2]. Due to the wealthof biological significance of the lipid raft model, thestructure of lipid rafts in cell membranes has been
investigated using many techniques, which haveshown that the size of lipid raft is nano-meter lengthscale. On the other hand, the dynamical nature of theraft is still controversial [3-5]. One of the important
points of the raft is whether the raft is stable entity inthe cell membranes or dynamically fluctuating
platform, which is closely related to the mechanism of
the biological functionalities.

k„T„ / '7<5 X

4 7r?]STj^r

D(r)- —^—[ln(-^)n(1)

where D is the diffiasion coefficient, 77 and 77^ are theviscosities of the membrane and water, respectively, dis the membrane thickness, ]^0.5112 and r is theradius of domain [10], whereas we claimed that thehydrodynamic flow in the membrane affects the
diffusion of domains [11]. The behavior of the micrometer-sized liquid domains on the model
biomembranes is well understood by the direct
observations, while that of the nano-meter-length scale

In order to understand the statical and dynamical
nature of the lipid raft, the model biomembrane
systems consisting of phospholipids and cholesterol
have also been investigated [6-8]. For example, it has

CP982, Complex Systems, 5^ International Workshop on Complex Systems
edited by M. Tokuyama, I. Oppenheim, and H. Nishiyama©2008 American Institute of Physics 978-0-7354-0501-l/08/$23.00

717

domains is poorly understood due to the opticalresolution hmit of the microscopy.
In this study we prepare small unilamellar vesicles(SUVs) with nano-meter length scale for spatialconfinement, which makes it possible to focus ourattention on the nano-meter-sized domains. In order toreveal the dynamical structure we adopt the small
angle neutron scattering (SANS) and the neutron spinecho (NSE) techniques. A unique feature of theneutron scattering is that a hydrogen atom and a
deuterium atom have different scattering lengths. We
prepare SUVs using deuterated saturated lipid,
protonated unsaturated lipid and protonated cholesterol
and obtain the information on the deutrated domains in
the SUV. In addition we perform molecular dynamics
simulations with a coarse grained model to reproduce
the phase separation on a SUV. By comparing the
SANS, NSE and the simulation results we elucidate
the statical and dynamical nature of nano-meter-sizeddomains in the SUV.

After the sonication we obtained SUVs with radius of«1OOA and the suspension became transparent.

Small Angle Neutron Scattering
Measurements
In this study we performed SANS experiments
under two experimental conditions, one is a film
contrast condition where we can obtain whole shape of
the SUVs and the other is a contrast matchingcondition where we can estimate the lateralheterogeneity in the SUVs. In the film contrast
condition, we used /i-DPPC/DOPC/Chol ternary
vesicles in D2O solvent, whereas in the contrast
matching experiment, we substituted fif-DPPC for hDPPC to extract the domain structure on the vesicle.
At this matching condition (the H2O volume fractionof the matching solvent; /H2O=0.548) we observed no
scattering from SUVs in the homogeneous one-phaseregion. Decreasing temperature from the one-phaseregion to two-phase region, the lateral phaseseparation takes place at the miscibility temperature,
where of-DPPC rich L„ phase coexists with DOPC rich
Ld phase. Then the scattering length densities (SLDs)of the domain p^ and the matrix /?„ do not match withSLD of the solvent AOIV These SLD differences bringa characteristic scattering function.
The SANS measurements were performed using the
SANS-U instrument of the Institute for Solid State
Physics, The University of Tokyo at JRR-3M of theJapan Atomic Energy Agency [13,14].

EXPERIMENTS
Commercial Reagents
1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC)(> 99 % purity), l,2-dipalmitoyl-sn-glycero-3phosphocholine (/i-DPPC) (> 99 % purity) and 1,2dipalmitoyl-d62-sn-glycero-3-phosphocholine{dDPPC) (> 99 % purity) were obtained in a powder
form from Avanti Polar Lipid, Inc. (Birmingham, AL)[12]. Cholesterol (Choi)(> 99 % purity) was
purchased from Sigma-Aldrich Co. (St. Louis, MO)[12]. In this study we fixed the vesicle composition of
fif-DPPC/DOPC/cholesterol = 4/4/2 (mole ratio) having
Tni = 29°C, because it shows a nucleation-growth typephase separation in observed temperature region.

Neutron Spin Echo Experiments
In order to reveal the dynamics of nano-metersized domains we performed NSE experiments under
two experimental conditions, one is the film contrast
condition where we can obtain the dynamics of wholeshape of the SUVs and the other is the contrast
matching condition where we can estimate thedynamics of nano-meter-sized heterogeneity in the
SUVs.
The NSE experiments were performed using NG5NSE spectrometer at the NIST Center for Neutron
Research [15,16]. Incident neutron wavelength of 6 A
was selected by a mechanical neutron velocity selector
with a wavelength resolution of about 20 %. The
measured momentum transfer, q, covered the range(0.047 to 0.09) A"^ and the time range was (0.05 to 15)
ns. The DAVE software package was used forelements of the data reduction and analysis [17].

Sample Preparation
We prepared SUVs by the following procedure.
First we dissolved the lipids (DPPC, DOPC and Choi)in chloroform (5mM) and then the solutions weremixed at the prescribed ratio of DOPC, DPPC andChoi in a vial. The chloroform was evaporated in a
stream of nitrogen gas and then the obtained lipid film
was kept under vacuum for one night to remove theremaining organic solvent completely. The dried lipid
film was dispersed in 1 ml of pure water at 60 °C,
which results in the formation of micro-meter-sized
vesicles (giant vesicles). The suspension of vesicles
with milky appearance was sonicated using aultrasonic homogenizer with 20kHz frequency(Yamato, Powersonic Model 50 [12]) for 30 min.

718

given by

RESULTS AND DISCUSSIONSS{q,t)=<Y.e

Jq-[R,((hR/0)](2)

Domain Formation on SUVs
First, we checked the shape and the size of the
SUVs. We obtained the SANS profiles from SUVs atthe film contrast condition at 333.2 K (homogeneous
phase) which is well described by the model scatteringfunction for the spherical shell structure. From thefitting we extracted mean outer radius of vesicles Ro^t
= (112±11) A, the bilayer thickness <?= (42±6) A
and the size polydispersity {p"^ =<Rf„ >I<Ri„ >^ -1)
p= (0.32 ±0.02), and these values were independent of
the temperature.
Next, we investigated the nano-meter-sized domain
formation on the SUVs with R « 11OA using thecontrast matching technique of SANS experiments.
The SANS profiles of the SUV are shown in Fig. 1. At
333.2K where the SUVs are in one phasehomogeneous region, we observed no significant
scattering from the vesicles, indicating that the DOPC,
Choi and DPPC are mixed molecular level and each
SUV has almost uniform composition. When we
decreased temperature to the phase separation region(285.2 K), excess scattering intensity due to thedomain formation was observed as shown in Fig. 1.
The scattering intensity profile has a maximum in thevicinity of ^ = 0.03 A"\ which is a characteristic
scattering pattern from domains on a vesicle at thematching condition and the peak position depends onthe vesicle size or number of domains.

S{q,t)•-A(q) exp(-Z)„^^0 + (l-^(?))exp(-/l ) (3)Siq,0)
where DQ is the diffusion coefficient of the whole SUV,/"is the relaxation rate of the domain relaxation modeand A is the numerical constant. The value of DQ usedhere is obtained from the intermediate scatteringfunction of the SUV at the film contrast condition.
Under the assumption that the relaxation profile ofspherical vesicle is expressed by a sum of the wholevesicle diffusion mode and the vesicle deformationmode, we fitted the relaxation profile measured at thefilm contrast condition by a double exponentialfunction•B(q))exp(-rj)

S{q,0)In order to make clear the dynamical nature of thenano-meter-sized domains, we measured theintermediate scattering function of the ternary SUVs
with fif-DPPC/DOPC/Chol = 4/4/2 at the matchingcondition. The intermediate scattering function is

1.0-,

1

0.06A'

0.8-

0.8 -

a 0.6 . (

Wm
I m

(4)

where /"a is the relaxation rate of the shapedeformation mode [18]. The relaxation rate for thevesicle diffusion mode show linear relationship againstq^ and the slope gives the diffusion coefficient Do={lA±0.01) X 10"" mVs. The diffusion coefficient can be
estimated from the Stokes-Einstein equation

Dynamics of Nano-meter-sized Domainso 285.2 K
o 333.2 K

0.6-

u
^

where Ri(t) is the coordinates of individual lipid
molecules at time t. In Fig. 2 we show the obtainedintermediate scattering function for the ternary SUVs
at the contrast matching condition at 285.2 K. By
assuming that the intermediate scattering function
consists of two components, the whole vesicle
diffusion mode and the nano-meter-sized domain
relaxation mode, the intermediate scattering functions
were fitted by a double exponential function

3 0AA
0.4

•

I 0.2

0.2-

|||g}S»»&lif»***l|

0

0.0-

8

-0.2
0

0.02

0.04

0.06

0.08

0.1

10

12

14 16

t[ns]

0.12

FIGURE 1. SANS profiles from SUVs at the contrast
matching condition at 333.2 and 285.2 K [19]FIGURE 2. Intermediate scattering function for the ternary
SUVs at the contrast matching condition at 285.2 K [19]

719

£>„

kj
^^v„RoACKNOWLEDGMENTS(5)

This work utilized facilities supported in part by
the National Science Foundation under Agreement No.
DMR-0454672. This work was performed using
SANS-U of the Institute for Solid State Physics, theUniversity of Tokyo (Proposal No. 7606).

Using the values of r=285.2 K, T]^=\3 X 10 Pa-s and7?out=112A, the calculated DQ is 1.6 x 10"" m^/s, which
agrees well with the value estimated by the NSE
measurement. Then the eq. (3) contains only two
adjustable parameters, A and F, and the fitting results
are shown in Fig. 2 by solid lines. The relaxation rateof the nano-meter-sized domain mode obtained fromthe fitting are plotted against q^ in Fig. 3, which gives
good linear relationship although we have only threepoints. The q dependence of F indicates that thevesicle deformation mode does not affect the domain
relaxation mode significantly[18]. When we assume
that the domain relaxation mode corresponds to thedomain diffusion, the slope gives the diffusion
coefficient of the domains of (3.7 + 0.2) x 10"^'' m^/s.
The Saffman and Delbriick law (eq. (1)) gives the
diffusion coefficient of the domains of 2.7x10"^^ m^/s,
which is smaller than the experimental value by about
two orders of magnitude. Thus the domain diffusion
model may be inadequate to explain the observed
domain mode.
In order to interpret the domain dynamics on a
SUV, we performed the molecular dynamics
simulation. For a shallow quenched vesicle from thehomogeneous state, the mono-domain is agitated bythermal fluctuations and repeats coalescence andrupture, whereas for the deep quenched vesicle, themono-domain shows the Brownian motion on the SUV.
From the time resolved simulation data in theequilibrium state we calculated the intermediate
scattering function for two states. The obtained
relaxation rate for the domain diffusion mode is about
two orders of magnitude smaller than that of the
coalescence and rupture mode. Thus the coalescenceand rupture mode may correspond to the observed
relaxation mode of the nano-meter-sized domains.
Details of this issue will be reported in theforthcoming paper.

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0.003 0.004 O.OOS 0.006 0.007 0.008 0.009

FIGURE 3. The relaxation rate of the nano-meter-sizeddomain mode against q [19]720