Ultracold neutron scattering study of local lipid mobility in bilayer membranes

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Ultracold neutron scattering study of local lipid mobility in bilayer membranes

W. Pfeiffer, G. Schlossbauer, W. Knoll, B. Farago, A. Steyer, E. Sackmann

To cite this version:

W. Pfeiffer, G. Schlossbauer, W. Knoll, B. Farago, A. Steyer, et al.. Ultracold neutron scattering study of local lipid mobility in bilayer membranes. Journal de Physique, 1988, 49 (7), pp.1077-1082.

�10.1051/jphys:019880049070107700�. �jpa-00210789�

1077

Short communication

Ultracold neutron scattering study ^{of local} lipid mobility ⁱⁿ bilayer ^membranes

W. Pfeiffer, ^G. Schlossbauer(*), ^W. Knoll(**), ^B. Farago (1), ^A. Steyer(***) and E. Sackmann

Physik-Department, Techn. Univ. München, ^D-8046 Garching, ^F.R.G.

(1) Institut Laue-Langevin, ¹⁵⁶ X, ^{Centre de} Tri, ^F-38042 Grenoble, ^France (Reçu ^{le 11 janvier 1988, accepti le 28 mars} 1988)

Résumé.2014 On présente ^la première ^étude par diffusion quasi élastique ^{des neutrons} ultrafroids de la

dynamique des bicouches lipidiques. ^{La variation en} température du transfert d’énergie ^des lipides ^aux

neutrons diffusés en fonction de la température, ^ainsi que la comparaison ^avec les résultats obtenus par échos de spins ^de neutrons montrent que ^ce transfert est déterminé _par la diffusion latérale des molécules lipidiques ^{dans la} gamme des microsecondes couverte par l’expérience. Pour les bicouches de dipalmitoyl-phosphatidyl-choline ^{à 45° on obtient un} coefficient de diffusion de 2, 6 10-7cm2/s,

un peu plus grand que les valeurs obtenues _par photoblanchiment. Cette méthode de diffusion des neutrons ultrafroids est complémentaire ^{de la} technique ^de photoblanchiment, ^{car elle mesure la}

diffusion latérale des lipides ^sur des distances de l’ordre de 20 Å, ^alors que ^cette dernière mesure les mouvements latéraux sur 10 03BCm.

Abstract.- The dynamics ^of lipid bilayers ^is studied for the first time by quasielastic scattering

of ultracold neutrons (UCN). Measurements of the _energy transfer from lipids ^{to the scattered}

UCN as a function of temperature and - in combination with spin ^echo experiments - ^{of the wave}

vector lead to the conclusion that it is determined, ^on the microsecond time scale investigated, by

lateral diffusion of lipid molecules. For dipalmitoyl-phosphatidyl-choline bilayers ^{at 45 °C a diffusion}

coefficient of D ⁼ 2.6 10-7 cm2/s ^{is obtained which is} slightly larger than the value obtained by ^the

conventional photobleaching technique. ^The present UCN-scattering ^{method is} complementary ^{to the} photobleaching technique ^{since it measures the local} lipid ^{diffusion over} short distances of some 20 Å

whereas the latter monitors the lateral motion ^{over some} _{10 03BCm.}

J. Phys. ^{France 49} (1988) ^{1077-1082 JUILLET} 1988,

Classification

Physics ^Abstracts

87.20 - 35.20

(*) ^{Present address : Kontron} Elektronik GmbH, ^D-8057 Eching, ^F.R.G.

(**) ^Present address : M ax- Planck- Institut f3r Polymerforschung, Jakob-Welder-Weg 11, ^D-6500 Mainz,

F.R.G.

(***) ^{Present address :} Dep. ^of Physics, ^{Univ. of Rhode} Island, Kingston, ^R.I. 02881, ^U.S.A.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019880049070107700

1078

1. Introduction.

The quasielastic ^neutron scattering belongs

to the most promising techniques ^to study

the dynamics ^of biological macromolecules and membranes on a molecular level. By ^combi- ning ^different techniques ^{such as} for instance the backscattering ^{and the} spin ^echo spectro-

scopy, the dynamic processes may be studied

over a wide frequency range (GHz ^to MHz) ^and

over molecular dimensions ranging ^{from a few}

Angstrom ^{to some 100 A} [1-3]. ^{A new promising} technique ^{is the} quasielactic scattering ^{of ultra-}

cold neutrons (UCN), by ^which energy transfers AE of some neV (N 106Hz) ^{and momentum}

transfers of _{q N 3} x 10-2 A -1 (corresponding

to spatial dimensions of 100 A) ^{can be measu-}

red. In the present ^{work we} report ^{the first stu-} dies of the molecular dynamics ^of lipid bilayers by ^a gravity spectrometer. ^It is shown that this

technique ^enables measurements of the lateral diffusion coefficients of lipid molecules in mem-

branes over short distances (20 A) and that it is thus complementary ^to the classical excimer

probe [4] ^and photobleaching technique [5] by

which the diffusion over some 10 A and some

pm, respectively, ^can be measured.

2. Materials and methods.

2.1 MATERIALS AND SAMPLE PREPARATION.-

The lipid dipalmitoyl-phosphatidyl-choline (DPPC) ^{is a} commercial product (Fluka) ^{and is}

used without further purification. ^The polyme-

rizable lipid, ^a phosphatidyl-choline containing polymerizable ^butadiene groups (cf. ^Ref. [7]) ^{is a} gift ^of Ringsdorf, ^Mainz. Dispersions ^{of 500} mg of lipid ^{in 10 ml of} D20 ^are prepared by ^the

usual technique [6]. ^{A thin} layer ^{of the} lipid ^is deposited ^on the wall of a glass ^flask by ^CHC13

solvent evaporation ^{which is} subsequently ^swol-

len by adding ^{the D20 and} annealing ^{at 50 °C}

for one hour.

The sample holder consists of an aluminium

ground plate (7 ^{x 17 x 1} cm3) into which a re- cess of 5 x 15 x 0.1 cm3 is milled and which is covered by ^a window made of 0.01 cm thick alu- minium foil. The lipid dispersion ^{is filled into the} sample ^holder through ^a tube fixed at one flat side of the holder. A second tube at the other side serves as air outlet. The thightness ^{of the} sample ^{holder is} carefully ^checked prior ^{to each}

measurement which lasted for about 4 weeks.

The structure of the lipid dispersion is checked

by ^{freeze fracture electron} microscopy ^{both be-}

fore and after each measurement.

2.2 UCN ^GRAVITY SPECTROMETER AND MEA- SURING PROCEDURE.- The experiments ^are performed ^{with the neutron} gravity spectrome-

ter NESSIE at the Munich reactor [8, 9]. ^The

ultracold neutrons are produced by ^decelera-

tion of cold neutrons of an average velocity ^of

v -- 50 m s-1 to v N 10 m s-1 by ^{means of a}

neutron turbine [10].

The spectrometer consists of a monochro- mator, focussing mirrors, ^an energy selective

analyser, ^{and a} (3He, Ar,C02) detector. The monochromator enables adjustment of the neu- tron energy from ⁼ 390 neV to E ⁼ 580 neV.

Monochromatic neutrons are produced by ^fo- cussing ^{at the} point ^of maximum reach of the

flight parabola ^{in the} gravity field. The ultracold

neutrons emanating ^{from the neutron conduc-}

tor move on strongly ^curved parabolas, ^{and the}

reach Ro is related to their kinetic _energy Eo by

where # ^{is the} angle formed between the ho- rizontal and the line joining ^the starting point

(virtual ^neutron source) ^{and the end} point [8, 9].

A high resolution is achieved by working ^{in the}

range of maximum reach where the _{energy is}

stationary ^with respect ^{to the} starting angle ^ao.

In order to optimize ^the intensity ^{at the} sample ^a pair ^of mirrors is placed ^{at the end}

of the monochromator in such a way that the neutron beam is focussed to an area of about

5xl5cm 2

The principle ^of focussing by range of flight ^is

also used for the determination of the _energy of the scattered neutrons. The scattered beam is focussed onto the detector by ^two cylindrical

mirrors with elliptical ^cross sections which are

arranged ^{one on} top of the other so that they

have one of their focal lines in common. The energy of the scattered neutrons can be varied

by moving the detector in a vertical direction.

The resolution of the spectrometer is determined

by ^the convolution of the resolution curves for the analyser ^{and the} monochromator, ^which

have been determined both theoreticaly ^and

experimentally [8, 9].

For the experimental determination of the re-

solution the scattering ^{of a} sample ^of beryl-

lium oxide (plate ^{of 5 x 15} cmZ) which is know to exhibit only ^elastic scattering ^{has been ana-} lysed. ^In figure ^{1 a} spectrum of the scattered neutrons is presented. ^A line width of DE ⁼ 16.4 ± 0.5 neV is found which _agrees well with the calculated resolution (G. Schlossbauer, ^Di- ploma Thesis, ^{TU Munich} 1985). ^{The UCN}

spectra ^are further corrected with respect ^{to the} background. ^{For that} purpose, ^a spectrum ^was

run with reference sample holders filled with a

H20/D20 ^{mixture or} cadmium, respectively.

Fig. ^{1.- Curve 1 :} spectrum of ultracold neu-

trons scattered by beryllium ^oxide. Energy ^at

maximum amplitude E ^{= 429.71} neV. A line width of ATE ⁼ 16.4 ± 0.5 neV is obtained by fitting ^a superposition ^{of a} Lorentzian line and

a Gaussian line to the experimental ^{data. The}

former represents ^the upper part between the maximum and the half height ^{of the curve and}

the latter is a model of the lower half of the ob- served spectrum. ^This shape ^is suggested by ^the

calculated resolution curve. Curve 2 : scattering spectrum of the reference cell (dummy).

3. Experimental ^results.

Figures ^{2 and 3} summarize the results of the quasielastic scattering ^{of UCN} by bilayers

of dipalmitoyl-phosphatidyl-choline (DPPC) ⁱⁿ

D20 ^solution.

Figure ^{2 exhibits a} typical spectrum ^of quasie- lastically scattered ultracold ^neutrons by ^DPPC

at a temperature (T ^{= 41} °C) ^{at which the}

bilayer ^{is in a} liquid crystalline ^state. Figure

3 shows the temperature dependence ^{of the}

line broadening ^{of UCN scattered} by ^DPPC bilayers. Although ^{the error} of the measured

broadening ^is very large, ^one clearly ^observes

a significant broadening ^{above 40 ° C but not}

at room temperature. ^The average values of AE increase slightly ^with increasing tempera-

ture from AE ⁼ 2.1 ± 1.0 neV at 41 °C to AE = 2.6 ± 1.4 neV at 45 °C.

Fig. ^2.- Spectrum of UCN scattered by ^bi- layer ^{of DPPC at 41° C.} By fitting ^{of the scat-} tering ^{curve to} the resolution curve broadened

by ^a Lorentzian one obtains a broadening ^of

AE ⁼ 2.1 f 1.0 neV. The dashed line corres-

ponds ^{to the} background.

The _energy transfer of the lipids ^{to the neu-}

trons was determined as a function of the scat-

tering vector q by measurement of the line broa-

dening ^{with the} spin-echo spectrometer ^{and the} gravity spectrometer. By using ^the former tech-

nique ^the range of scattering ^{vectors could be ex-}

tended. These scattering experiments ^were per- formed with bilayer dispersions ^{of a 1 : 1 mix-}

ture of DMPC and the butadiene phosphatidyl-

choline. The latter lipid ^was photopolymerized by ^UV light prior ^{to the} measurement and was

thus immobilized. The measurements were per- formed at a temperature well above the chain

melting transition of both lipids. ^{As can be seen}

from figure 4, ^the energy transfer AEis well des- cribed by ^a quadratic dependence ^{on momentum}

transfer _q.

4. Discussion.

The experiments presented ⁱⁿ figures ^{3 and}

4 show firstly ^{that a} significant energy trans- fer is only observed if the bilayer is in the li-

quid crystalline (smectic ^{A or} La ) ^state and, ^se- condly, ^{that the} broadening ^is proportional ^to

the _square of the momentum transfer _q.

In principle, ^three dynamic processes could

account for this broadening : firstly, ^{the late-}

ral diffusion of lipid molecules in the plane ^of

the membrane, secondly, the diffusion of small

1080

individual liposomes (or vesicles) within the dis-

persion, and, thirdly, the surface undulations of the lipid bilayers [11].

Fig. ^3.- Temperature dependence ^{of line broa-} dening ^{for DPPC as obtained} by gravity spec- trometer. The vertical bars indicate the relative

errors. The negative ^{fitted value at the lowest} temperature ^{is an artefact} of the convolution method used which admits of a linear extrapo- lation from positive ^to negative linewidths.

Fig. ^4.- Measurement of linewidth ^{as a} function of the _square of the scattering ^vector q. The

sample ^{is a} bilayer dispersion ^{of a 1 : 1 mixture of} dimyristoyl-phosphatidyl-choline (DMPC) ^and

the photopolymerized ^butadiene phospholipid ⁱⁿ

pure D20 (45% ^by weight). ^{The AE values for} q2 > 3 X 10-3 A-2 ^are measured with the

spin ^echo spectrometer and the value with the smallest momentum transfer with the gravity spectrometer. ^The measuring temperatures ^are given ^{in the} figure.

Consider first the case of the three- dimensional Brownian motion of the vesicles.

The dynamic ^{structure factor} corresponding ^to

this _process would be ^a broadened Lorentzian line of width

where D(3) is the vesicle diffusion coefficient.

A diffusion coefficient of D(3) ^{= 0.3 x} 10-6 cm2 S-1 (at ⁵⁰ °C) ^{would account for this}

broadening. According ^{to the} Stokes - Einstein

relation, ^{this would} correspond ^{to a vesicle ra-}

dius of

for a viscosity ^{of the} aqueous phase ^{of 17 -- 10-2}

g cm-1 s -1

As follows from separate ^freeze

fracture studies, ^{the number of vesicles of such a}

small size is extremely ^small (1% of lipid) ^{so that}

we neglect the Brownian motion of the vesicles.

The observed q dependence ^of the line broade-

ning ^{leads to} the conclusion that the third dy-

namic process, namely the surface undulations,

cannot account for the observed broadening. ^As

is well know, ^the thermally excited surface un-

dulations of liquid crystalline bilayers ^{are de-}

termined by ^two contributions to the bilayer elasticity : the membrane tension and the ben-

ding ^stiffness [11, 12]. The surface undulations

are completely overdamped. According ^{to the} theory ^of light scattering by membrane fluctua- tions [13] ^the dynamic ^{structure factors corres-} ponding ^{to these} overdamped ^{modes are Lorent-}

zian lines. The mean square amplitudes ^follow

the dispersion ^relation

where .Kc and q ^{are the} bending elastic modulus and the lateral tension, respectively.

For bilayers in the smectic A state K, 10-12 _ergs [11] and the maximum tension is -y ⁼ 10 dyn cm-1. _Moreover, the liposomes

are mostly non-spherical ^{and are} thus minimum

area surfaces with respect ^{to tension.} Therefore,

Kcq4 » "Iq2 and the surface undulations are do- minated by ^the bending stiffness. In this _case, the line width is

which is much larger than the observable line widths and exhibits a q3 - dependence ⁱⁿ

contrast to the observed q2 - dependence. ^We

thus conclude that the UCN line broadening ^is

determined by the lateral diffusion of the lipid

molecules.

Consider now the lateral diffusion of the lipid

molecules in the plane ^of the membrane. This process is equivalent ^to the two-dimensional dif- fusion of adsorbates on surfaces for which the

dynamic ^{structure factor has been} calculated by Stockmeyer [14]. The vibrational motion of the

lipid ^{molecules in the direction} perpendicular ^to

the membrane plane ^is expected ^{to be fast com-} pared ^to the lateral motion and the _{two pro-}

cesses are thus uncorrelated. The former _pro-

cess contributes only ^a Debye Waller factor to

the total dynamic ^{structure factor} [14] ^{which is}

determined by ^{the momentum transfer} parallel

to the membrane plane : _{qll = q} ^{sin3 where #}

is the angle between the membrane normal and the wave vector q. The length ^{of a} diffusional

jump ^{of the} lipid molecules is d 1.0 nm so

that _q d sino « 2 since _{q = 3} x 10-1 nm-1.

Under this condition the dynamic ^{structure fac-}

tor is a Lorentzian line of line width D(2)q2sin2{) (D(2) ⁼ lateral diffusion coefficient) ^{for a given}

value of the angle ^{3. The} contribution of the la- teral diffusion to the dynamic ^{structure factor is}

thus

In principle ^the integral ^{can be solved in closed}

form [14]. ^For the evaluation of the experimental data, ^the convolution of S(q, w) ^{with the instru-}

ment resolution curve has to be performed. ^Pro-

vided the latter can be represented ^{as a Lorent-}

zian line of width B, ^{the total} scattering ^curve

has the form

where tan

As pointed ^out by Stockmeyer, ^the dynamic

structure factors for the three - and two -

dimensional diffusion are distinguishable, ^{in line} shape, only ^for Dq 2IB > ^{50 whereas below this}

limit one sees essentially the resolution curve of the spectrometer. ^In spite of the large ^error bars,

a sharp increase in the broadening ^{of the scatte-} ring ^{curves at the} temperature ^{above the} gel ^to liquid crystalline transition of the lipid ^is sugges- ted by the data of figure ^{3. This} shows that the ultracold neutron scattering technique provides

a valuable tool to study ^{the membrane} dynamics

in the microsecond time scale. By analysing ^the broadening ^{of the measured} scattering ^{curves in}

terms of the two-dimensional diffusion model,

we arrive at the following diffusion coefficients :

These values are in good agreement ^{with the} diffusion coefficients of phospholipid ^molecules

measured with the excimer probe technique : D (2) = (2 =h 1) ^{x 10-7 cm2 s-1 at 45 °C} [4]. ^{It is}

by ^{about a factor of two} larger than the values measured for DPPC multilayers ^{with the} photo- bleaching (FRAP) technique : D (2) = (9 ± 1) ^x

10-8 cm2 s-1 ^{at 45 °C} [5].

This difference is interesting ^{for the} following

reason : the photobleaching technique ^measures

the difusion coefficient over distances of the or-

der of some pm whereas both the excimer tech-

nique ^{and the UCN} scattering technique ^moni-

tor the lateral motion of lipids ^{over some lat-}

tice spacings (= ¹⁰⁰ k). ^{The UCN} technique ^is

thus especially ^{suited to} determine the restric- ted lateral motion in heterogeneously organized

systems ^{such as} biological membranes. A com-

parative study of lateral motion by ^{the UCN and}

the photobleaching technique would thus help ^to

evaluate percolation processes in heterogeneous

two-dimensional layers [7, 15].

Further evidence for our conclusion that we measure the lipid lateral diffusion coefficient by

the UCN scattering ^{comes from} parallel experi-

ments on the local membrane dynamics by qua- sielastic neutron scattering ^at high scattering angles q > 10-1 k-l ) ^{A line} broadening ^of

the order of some 10 ueV ^at q m 0.5 A is ob- served in the La (= ^smectic A) ^{state. This} large broadening ^can be attributed to the rotational motion of the lipid molecules characterized by ^a

rotational correlation time of T N 10-1° s [16].

At present, ^{the UCN} technique suffers from the low beam intensities. However, ^{an increase} by ^{a factor 104 is} expected for NESSIE after installation at the new Turbine Source at ILL

[17].

Acknowledgements.

This work was supported by ^{the BMFT}

(03 - B01 - C03 2 and 03 - ST1 - TUM -

4) ^{and by the} Leonhard-Lorenz-Stiftung. ^For

excellent technical help ^{we are} very grateful

to H. Nagel ^{and F.-X.} Schreiber, ^{to the FRM}

reactor staff and to the workshops ^headed by

B. Schrocker and J. Schiller. We are grateful

to Prof. Ringsdorf ^{of the} Max-Planck Institut

fur Polymerforschung, Mainz, ^{for the} sample ^of

Phosphatidyl-choline.

1082

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