1
Bending Elasticity of Bio-MembranesStudied by Neutron Spin-Echo
Dobrin P. Bossev1 & Nicholas Rosov2
1Indiana UniversityBloomington, IN 47405
E-mail: [email protected]
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