1

Bending Elasticity of Bio-MembranesStudied by Neutron Spin-Echo

Dobrin P. Bossev1 & Nicholas Rosov2

1Indiana UniversityBloomington, IN 47405

E-mail: dbossev@indiana.edu

2NIST, Center for Neutron ResearchGaithersburg, MD 20899

Summer School on Methods and Applications of Neutron SpectroscopyJune 20-24, 2005

NIST Center for Neutron Research, Gaithersburg, MD 20899

• Thermal undulations of cell membrane

• Neutron Spin Echo (NSE)- Why NSE is ideal for this study. Energy resolution- How NSE works. Principles

• Experimental system. Results & Discussion

• Summary

In this presentation …

2

The Cell Membrane

Polar

Polar

Non-polar

Water

Water

DMPC:

(1,2-Dimyristoyl-sn-Glycero-3-Phosphocholine)

Cholesterol

Thermal undulations: • Biosensing – contact time• Cell adherence – undulation• Cell mobility

↓↓↓↓Bending elasticity

Topologies of the lipid bilayers

Bicelles(~ 20 nm)

Lamellae (large)

Unilamellar vesicles(~ 50 nm - 10 µm)

Multilamellar vesicles(~ 50 nm - 10 µm)

Micelles(~ 2 nm)

~ 5 nm

Lipid bilayers• thermodynamically stable

• Not always thermodynamically stable• Mechanically stable

DMPC:

3

Factors that may affect the bending elasticityTemperature: liquid to crystallinetransition (Tc = 24 ºC for DMPC)

R. R. Gabdoulline, J. Phys. Chem., 100:15942, 1996

T < Tc T > Tc

R. R. Gabdoulline, J. Phys. Chem., 100:15942, 1996

T < Tc T > Tc

Presence of cholesterol

How to measure bending elasticity

Bending elasticity����

Thermal undulations(highly localized)

Properties:• Interfacial tension• Lateral elasticity• Bending elasticity

NSE:T scale ~ 0.01 - 100 ns

L scale ~ 1 - 10 nm

• Videomicroscopy: large T & L scales• NMR transverse relaxation times: wide T scale, relaxation model?• Dynamic light scattering: T scale > 100 ns• Computer simulations: not fast enough

Hofsäß, E. Lindahl, O. Edholm, Biophysical Journal, 84: 2192, 2003

DPPC + 10% cholesterol

Lipid bilayer

4

Small Angle Neutron Scattering (SANS)

neutron beam θ

sample

detector

I

q

2sin

4 θλπ=Q

Elastic scattering � static structure

Dynamics?

NSE basics• NSE is a quasielastic method: small deviation from the elastic scattering

• Energy transfer: ωωωω = 10-5 – 10-2 meV

• Goals: - Micellar systems in solution- Undulations of lipid membranes and thin films- Intra-molecular diffusion of proteins and polymers- Dynamics of polymer melts and glasses - Other thermal fluctuations of the soft matter

S(ω)

ωωωω0

• Principle: Precession in magnetic field. Each neutron has a personal stopwatch. Yields the intermediate scattering function in the time domain I(Q,t):

• Fourier time range: 0.01 to 200 ns

( ) ( )�∞

∞−

= ωωω dtQStQI cos),(,

S(ω)

ωωωω0

I(t)

t0

S(ω)

ωωωω0

I(t)

t0

5

NSE walkthrough

vv

vvgBL

vvgBL

∆=∆=��

���

−=∆ ϕϕ 2'11

vL

gB=ϕ

n

B Bsample

• elastic scattering• inelastic scattering

Angle 0 ϕϕϕϕ ϕϕϕϕϕϕϕϕ

0±∆∆∆∆ϕϕϕϕ

Analyzer:<cos(±∆∆∆∆ϕϕϕϕ)>

Neutrons posses spin and magnetic moment. Larmor frequency of precession in magnetic fields depends on B only (g =1.83×108 s-1T-1) gBL =ω

BSN ×=BωωωωL

SN n

5102 −≈≈∆ϕπ

vvB = 0.5 T, L = 2 m

ϕ ~ 1×106 rad( ) ( )�

∞

∞−

= ωωω dtQStQI cos),(,

±∆∆∆∆ϕϕϕϕ

Ingredients• 1,2-Dimyristoyl-sn-Glycero-3-Phosphocholine (DMPC), ttrans= 24 ºC• 1,2-Dimyristoyl-sn-Glycero-3-[Phospho-rac-(1-glycerol)] (Sodium

Salt) (DMPG)• Cholesterol• NaCl, CaCl2

DMPC

Cholesterol

DMPG

6

Vesicles compositions & preparation

- carbopack (elastic scatterer)Resolution- D2OBackground- Extrusion through a filter (200 - 400 nm pores)Method- CaCl2 added to L at 30 mMLCaCl2

- NaCl added to L at 50 mMLNaCl- cholesterol/total lipids = 50 mol.%LC50- cholesterol/total lipids = 33 mol.%LC33- DMPC and DMPG in D2OL- total lipids = 2 wt.%, DMPG/DMPC = 5 mol.% For all samples

Small Angle Neutron Scattering (SANS)

SANS from DMPC vesicles in D2O

R/Å 1002polydisp (0,1) 0.32shell/Å 42SLD core/Å-2 6.4×10-6

SLD shell/Å-2 1.0×10-6

SLD solvent/Å-2 6.4×10-6

Bkg/cm-1 0.07

0.1

1

10

100

I/cm

-1

7 8 90.01

2 3 4 5 6 7 8 90.1

Q/Å-1

L at 22 ºC L at 45 ºC LC33 at 22 ºC LC33 at 45 ºC

7

Dynamic Light Scattering (DLS)

R ≈≈≈≈ 100 nm

14

12

10

8

6

4

2

0

wei

ght f

ract

ion

(%)

102 4 6 8

1002 4 6 8

1000

R/nm

L LC3320 ºC

40

30

20

10

0

wei

ght f

ract

ion

(%)

102 4 6 8

1002 4 6 8

1000

R/nm

LNaCl (20 ºC) LNaCl (35 ºC)

The decay of I(Q,t) measured by NSE

( ) ( )�∞

∞−

= ωωω dtQStQI cos),(,

( )( ) ( ) �

� �

� Γ−= 32

exp0,,

tQI

tQI

L at 35 ºC

5

6

7

8

9

1

I(Q,t)

/I(Q

,0)

4035302520151050

Fourier time/ns

Q/Å-1

--------------- 0.043 0.071 0.095 0.121

8

Zilman-Granek theory for thermal undulations

Membrane plaquette

ξ ( ) ( ) ( )[ ]�

−=ji

RtRQi jietQS,

0,���

�

Dynamic structure factor

( ) ( ) ( )tztrtR iii += ��

lateral

perpendicular

( )[ ]222

21

rhrdH�∇= �κ

Helfrich bending Hamiltonian(small deformations, ∇h << 1) ( ) ( )( )ttrhtz ii ,

�=amplitude

( ) ( ) ( ) ( )[ ]22

||0,',

2'224 '

1,

rhtrhQ

rrQiz

eerdrda

tQS��

��

�

� −−−��=

( ) ( )[ ] ( ) ( )trrrrrhtrh ,''0,', 002 ������ −Φ+−Φ=−

static dynamic

A. G. Zilman, R. Granek, Phys. Rev. Lett., 77:4788, 1996A. G. Zilman, R. Granek, Chemical Physics, 284:195, 2002

( ) ( ) ( ) 3BB32

025.0,exp0,, QTkTk

tQItQI k ηκγ=Γ�

� �

� Γ−=

Relaxation rate of I(Q,t) as a function of Q

3BB QTkTk

ηκ∝Γ

4

68

0.001

2

4

68

0.01

2

4

68

0.1

Γ /n

s-1

5 6 7 8 90.1

Q/Å-1

L at 45 ºC LC33 at 45 ºC L at 20 ºC CPyCl at 35 ºC

3

38

BB QTkTk

ηκ∝Γ

9

Bending elasticity

13 – 31 (30 °C)13.2 ± 0.200.87135

88 (40 °C)96.7 ± 5.30.71445VM

146 (30 °C)94.9 ± 3.20.87135LC50

73 (40 °C)42.4 ± 0.910.7144596 - 98 (30 °C)48.1 ± 1.30.87135 VM

150 (20 °C)129.7 ± 5.31.2520LC33

13 – 31 (40 °C)12.9 ± 0.180.71445

NMR,VM

13 – 31 (30 °C)15.3 ± 0.310.87135L

methodκ/kBTref.

κ/kBTthis work

ηD2O×103

/N s m-2t/°CSample

Temperature

Tc

Cryst. Liq.

Phasetransition

6

1

2

3

456

10

2

3

4

κ /re

l.

6055504540353025201510

T/ºC

L

10

Cholesterol

Tc

50%

33%

0%

Presence ofcholesterol

6

1

2

3

456

10

2

3

4

κ /re

l.

6055504540353025201510

T/ºC

L LC33 LC50

NaCl

Tc

Addition of NaCl

78

1

2

3

4

5678

10

2

κ /re

l.

6055504540353025201510

T/ºC

L LNaCl

11

CaCl2

Tc

Addition of CaCl2

NaCl

Ca2+

+ +

81

2

4

6

810

2

4

6

8100

κ /re

l.

6055504540353025201510

T/ºC

L LNaCl LCaCl2

Summary• NSE probes short time and length scales:- Convenient for studies on thermal fluctuations of bio-membranes

• Temperature:- Liquid-to-crystalline transition increases κ by an order of magnitude- At T > Tc temperature effect is weak

• Cholesterol:- At T < Tc cholesterol has negligible effect on κ- At T > Tc κ increases proportionally to the cholesterol concentration- Cholesterol smears the sharp liquid-to-crystalline phase transition

• Electrolytes:- Presence of 50 mM NaCl increases κ by a factor of 1.5- Presence of 30 mM CaCl2 increases κ by a factor of 4 and shifts Tc to lower

values

• Suggestions for future studies:- Other electrolytes, pH etc.- Effect of other constituents in the lipid bilayers (e.g proteins, other lipids)

Acknowledgements: Dr. Dan Neumann @ NCNR, NIST