Lipid Bilayers and Membrane Dynamics:

Insight into Thickness Fluctuation

Andrea C. Woodka,1 Paul D. Butler,1 Lionel Porcar,2 Bela Farago,2 and

Michihiro Nagao,1,2,3

1 NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899-6102, USA, 2 Institut Laue Langevin, 6 rue Jules Horowitz, BP 156-38042, Grenoble Cedex 9, France,

3 Center for Exploration of Energy and Matter, Indiana University, Bloomington, IN 47408, USA

Motivation

Lipid membranes are self-assembled highly flexible structures that have the ability to undergo an array of conformational and dynamic transitions which are essential for many biological functions.

Spectroscopic length scale:

Intermediate length scale : Membrane thickness fluctuations have been proposed as a mechanism for pore formation.(3)

Microscopic length scale:

Membrane stiffness and fluidity have been shown to have a large impact on cellular uptake and release.(2)

Cell signal transduction is affected by molecular lateral diffusion within the lipid membrane.(1)

(1) D Marguet, et al. EMBO J, 25, 3446 (2006)

(2) P. Weber, et. al. Adv Med Eng, 114, 377(2006)

(3) L. Movilenu, et al. Bull Math Biol, 58, 1231 (2006)

Membrane Dynamics

observation length scale

molecular motion collective motion

incoherent-quasi-elastic scattering

nuclear magnetic resonance etc.

coherent-quasi-elastic scattering

photon correlation spectroscopy

Molecular movements (incoherent movements of molecules)

Lateral diffusion Vertical vibration

Coherent movements of molecular assemblies

Rotation

Stretching Compression

Bending Stretching

Compression

Protrusion Thickness fluctuations

The Dynamics in Lipid Bilayers

Techniques to Measure Dynamics

Neutron Spin Echo

Elastic Scattering

http://www.ill.eu/instruments-support/instruments-groups/groups/tof/home/spin-echo-video/

Farago et al, Physica B 213&214, 712 (1995).; Farago, Physica B 226, 51 (1996).

• NSE measured Q

dependence of Deff • showing an increase at

the membrane thickness

length scale

Nagao, Phys. Rev. E 80, 031606 (2009).; Nagao et al., Soft Matter 7, 6598 (2011).; Nagao, J. Chem. Phys. 135, 074704 (2011).

bending

thickness

Surfactant Membranes

Breathing model of a lipid bilayer by Miller Miller, Top. Bioelectrochem. Bioenerg. 4, 161 (1981).; Bach and Miller, Biophys. J. 29, 183 (1980).; Miller, Biophys. J. 45, 643 (1984).

Amplitude of the fluctuations reaches ≈ 15 Å or more from

the geometrical constraints (volume conservation)

Thickness fluctuations by Hladky and Gruen

Thickness fluctuations occur, but the amplitude is small.

Long wavelength fluctuation amplitude is negligible

Short wavelength fluctuations (< 30 Å) are severely limited

Intermediate wavelength fluctuation amplitude < 10 Å

Hladky and Gruen, Biophys. J. 38, 251 (1982).

Deformation free energy of bilayer membranes by Huang Huang, Biophys. J. 50, 1061 (1986).

Theoretically, thickness fluctuations exist, their amplitude is very small

Thickness fluctuations in lipid

bilayers (theoretical studies)

Bilayer Preparation

(D54)DMPC = C14

(D62)DPPC = C16

(D70)DSPC = C18

Phospholipid Melting Temperature

1.112

1.110

1.108

1.106

1.104S

pecific

Gra

vity

70605040302010

Temperature (ºC)

DMPC DPPC DSPC

20.5ºC

37.5ºC

50.5ºC

Gel phase, below Tm

Above Tm lipid tails highly fluid, disordered and in constant motion

Fluid phase above Tm

Below Tm transition to a gel state, tails are fully extended with highly ordered packing

0.1

1

10

100

I(q)

0.012 3 4 5 6

0.12 3 4 5

q (A-1

)

DMPC_35C_ABS_i DPPC_50C_ABS_i DSPC_65C_ABS_i

Small Angle Neutron Scattering

Peak shifts to higher Q with decreasing tail

length

q ~ 2π / length scale

*Scattering intensity is offset to highlight peak shift

SANS and NSE are complimentary techniques

q

SANS static “snapshot” elastic scattering

NSE dynamic “snapshot”

quasielastic scattering

dqSqI ),()(

dtqStqI )cos(),(),(

1.0

0.8

0.6

0.4

I(q

,t)

/ I(

q,0

)

14121086420t (ns)

q (Å-1

)

0.056

0.070

0.075

0.113

0.132

0.164

0.183

0.201

fits

NSE : I(q,t)

])(exp[)0,(

),( 32 /tqI

tqI

1.0

0.8

0.6

0.4

0.2

14121086420

IQT_0p0456 IQT_0p0556 IQT_0p0651 IQT_0p0697 IQT_0p0750 IQT_0p0792 IQT_0p0845 IQT_0p0889 IQT_0p0935 IQT_0p0988 IQT_0p1031 IQT_0p1083 IQT_0p1126 IQT_0p1221 IQT_0p1228 IQT_0p1312 IQT_0p1323 IQT_0p1418 IQT_0p1514 IQT_0p1606 IQT_0p1635 IQT_0p1730

IQT_0p1826 IQT_0p1921 IQT_0p2013

1.0

0.9

0.8

0.7

0.6

0.5

14121086420

IQT_0p0615 IQT_0p0714 IQT_0p0815 IQT_0p0898 IQT_0p0909 IQT_0p0994 IQT_0p1004 IQT_0p1089 IQT_0p1184 IQT_0p1240 IQT_0p1275 IQT_0p1336 IQT_0p1431 IQT_0p1527 IQT_0p1618

DPPC 50ºC

DMPC 25ºC

DSPC 55ºC

Helfrich bending energy

Assuming the membrane is thin enough sheet, which is undulating

Zilman-Granek theory

Dynamics of a planar non-interacting Helfrich sheet

h(r)

k: bending modulus

h: solvent viscosity

I(q,t)

I(q,0)= exp - Gt( )

2 / 3[ ]

G = 0.025gkBT

k

æ

è ç

ö

ø ÷

1/ 2kBT

hq3

Watson-Brown theory

Extension of ZG theory including slipping of each monolayer

Inter-monolayer friction plays a role, where lateral

compressibility km of membrane

appears in dynamical equation

Zilman and Granek, Phys. Rev. Lett. 77, 4788 (1996).

Zilman and Granek, Chem. Phys. 284, 195 (2002).

Helfrich, Z. Natureforsch. 28, 693 (1973).

Watson and Brown, Biophys, J. 98, L09 (2010).

Evans and Yeung, Chem. Phys. Lipids. 73, 39 (1994).; Seifert and Langer, Europhys. Lett. 23, 71 (1993).

Surfactant Membrane Dynamic (bending)

Considering slipping friction

: decay rate, b=2/3

Zilman and Granek, Phys. Rev. Lett. 77, 4788 (1996).; Zilman and Granke,

Chem. Phys. 184, 195 (2002).

k: effective bending modulus,

h: solvent viscosity, a ≈ 1

~

Watson and Brown, Biophys. J. 98, L9 (2010).

Rawicz et al., Biophys. J. 79, 328 (2000).

Lee et al., Phys. Rev. Lett. 105, 038101 (2010).

Bending motion is explained as a single membrane dynamics model

Fitting I(q,t)

NSE : Γ vs. q DPPC @ 50ºC

32/1

23

025.0 qTkTk

OD

BBBEND

hk

4

6

0.001

2

4

6

0.01

2

4

6

0.1

(n

s-1)

3 4 5 6 7 8 9

0.12 3

q (A-1

)

6

80.1

2

4

6

81

2

4

6

810

I(q) (cm

-1)

q3

I(q)Γ deviates from the

pure q3 dependence expected from bending motions

This peak occurs at the same q as the SANS dip position

Bending

Thickness

22

0

333 )(1

1

qqqqqTFBEND

M. Nagao Zilman-Granek

NSE : Bending Modulus

Z. Yi, et. al, J. Phys. : Cond. Mater, 21, 155104 (2009).

Literature

Experiment

10

2

4

6

8100

2

4

6

81000

2

k (

kBT

)

100-10

T-Tm (ºC)

DMPC

DPPC

DSPC

● ■ ▲

q dependence of the decay rate:

Below vs. Above Tm

Below Tm DMPC

T = 16 ˚C

Bending

no enhancement =

suppressed thickness fluctuations

Bending

Enhancement =

thickness fluctuations Above Tm

DMPC

T = 35 ˚C

q dependence of the decay rate:

Lipid Tail Length

22

0

333 )(1

1

qqqqqTFBEND

NSE : Thickness fluctuations (Γ / q3)

accounts for bending motions damping frequency of thickness fluctuations

Proportional to the amplitude of thickness fluctuations

SANS dip position (Lorentzian peak position)

ΓBEND / q3 :

ΓTF :

ξ-1 :

q0 :

M. Nagao

40

30

20

10

0

/q

3 (

Å3/n

s)

0.200.150.100.05

q (Å-1

)

40

30

20

10

0

/q

3 (

Å3/n

s)

40

30

20

10

0

/q

3 (

Å3/n

s)

DMPC T=15ºC (NG5) T=16ºC (IN15) T=25ºC (NG5) T=35ºC (NG5) T=35ºC (IN15)

DPPC T=30ºC T=40ºC T=50ºC

DSPC T=45ºC T=55ºC T=65ºC

(b)

(c)

(d)

0.1

1

10

100

1000

I(q)

2 4

0.012 4

0.12 4

q (A-1

)

DPPC 30ºC 40ºC 50ºC

6

80.1

2

4I(

q)

0.250.200.150.100.05q (A

-1)

0.01 0.1

40

30

20

10

0

/q

3 (

Å3/n

s)

0.200.150.100.05

q (Å-1

)

40

30

20

10

0

/q

3 (

Å3/n

s)

40

30

20

10

0

/q

3 (

Å3/n

s)

DMPC T=15ºC (NG5) T=16ºC (IN15) T=25ºC (NG5) T=35ºC (NG5) T=35ºC (IN15)

DPPC T=30ºC T=40ºC T=50ºC

DSPC T=45ºC T=55ºC T=65ºC

(b)

(c)

(d)

0.1 0.15 0.2

40

30

20

10

0

/q

3 (

Å3/n

s)

0.200.150.100.05

q (Å-1

)

40

30

20

10

0

/q

3 (

Å3/n

s)

40

30

20

10

0

/q

3 (

Å3/n

s)

DMPC T=15ºC (NG5) T=16ºC (IN15) T=25ºC (NG5) T=35ºC (NG5) T=35ºC (IN15)

DPPC T=30ºC T=40ºC T=50ºC

DSPC T=45ºC T=55ºC T=65ºC

(b)

(c)

(d)

30

20

10

0

1000

100

10

1

0.1 0.1

1

10

100

I(q

)

0.012 3 4 5 6

0.12 3 4 5

q (A-1

)

DMPC_35C_ABS_i DPPC_50C_ABS_i DSPC_65C_ABS_i

Above Tm: independent of either

temperature or tail length

Membrane Thickness Fluctuations

Time scale

22

0

333 )(1

1

qqqqqTFBEND

An order of magnitude

slower (than surfactant

membranes)

≈ 100 ns

Width of Lorentzian peak relates to the fluctuation amplitude(1)

(1) Nagao et al., Soft Matter 7, 6598 (2011). (2) Huang, Biophys. J. 50, 1061 (1986). (3) Lindahl and Edholm, Biophys. J. 79, 426 (2000).

Mean amplitude = 3.7 Å ± 0.7 Å

Huang’s mean amplitude ≈ 4.5 Å(2)

Lindahl & Edholm’s amplitude ≈ 5 Å(3)

Experiment:

Theory:

Simulation:

≈ 8 % of the membrane thickness;

close to the value seen in surfactant

membranes (≈ 12 %)

Suggests amplitude is defined by physical constraints, like volume conservation

Membrane Thickness Fluctuations

Amplitude

Thickness Fluctuation Theory

21

121

2

0

1

21

2 tan2

tan2

CCCCCaK

TkD B

11

2aKC

2/1

1

22

Ka

BC

mdK

k1

adm 2

+ from NSE measurements ٭from SANS measurements # from literature

a0

Although membrane thickness fluctuations have not been previously measured Huang(7) has proposed a theory for thickness fluctuations in a lipid bilayer under the consideration of deformation free energy:

D ≈ 4.5Å

D B#

dm* k #

= thickness fluctuation amplitude = membrane compressibility = wavelength cut off = membrane thickness = bending modulus = surface tension

Conclusions

NSE was used to successfully measure lipid membrane thickness fluctuations

From SANS it is clear that these fluctuations appear at the length scale of the membrane thickness.

The relaxation time ≈100 ns and is independent of temperature and tail length. An order slower than that observed in surfactant membranes

Amplitude is ≈ 8 % of the thickness, consistent with surfactant membranes (12 %). Volume conservation may define the fluctuation amplitude.

Below Tm, thickness fluctuations are not observed, suggesting total suppression of the mode or much slower relaxation times which are not accessible by the current setup.

The experimental amplitude agrees well with both theory and simulation

FUTURE DIRECTION: What kind of effects do membrane associated molecules have on membrane dynamics such as thickness fluctuations?

Preliminary Data w/ Protein

Gramicidin

Alamethicin

http://rsif.royalsocietypublishing.org/content/early/2009/12/09/rsif.2009.0443/F4.large.jpghttp://rsif.royalsocietypublishing.org/content/early/2009/12/09/rsif.2009.0443/F4.large.jpg

Preliminary Data w/ Protein

45

40

35

30

25

20

15

k (

kBT

)

2.52.01.51.00.50.0

[Protein] mol%

DMPC(ILL)Ala/DMPCGram/DPPCGram/DMPC

12

10

8

6

4

2

0

T

F(x

10

-3n

s-1

)

2.01.00.0

[Protein] mol%

DMPC(ILL) Ala/DMPC Gram/DPPC Gram/DMPC

20

15

10

5

0

-1

(x10

-3Å

-1)

2.01.00.0

[Protein] mol%

DMPC(ILL) Ala/DMPC Gram/DPPC Gram/DMPC