Lorentz Institute, Leiden.
26 - 30 September 2011
Mechanics, Dynamics and Thermodynamics of
phospholipid membranes
Cavendish Laboratory, University of Cambridge
Pietro Cicuta
Background: Phase behavior of phospholipid membranes
Prof Sarah Veatch, Michigan Univ.
and Prof Sarah Keller, Univ. Washington, Seattle.
Lipid rafts,
signalling and transport in cells
Electro-Formation of Giant Uni-Lamellar Vesicles (GUV)
ITO Glass plates, 45℃ oven, AC field 1V, 10Hz
Two ITO coated slides form a capacitor. GUV grow over a few
hours when an AC electric field is applied.
Image analysis and feature tracking through a movie
1:1 DOPC:DPPC + 30% cholesterol
10 m m
Image analysis and feature tracking through a movie
1:1 DOPC:DPPC + 30% cholesterol
40 m m
10C
<x2>=2 D(r) t
20C
How can we relate the mean square displacement to the membrane (2D) viscostity ?
Stokes-Einstein makes it trivial in 3D, by D(r)= kT/(6 p h r)….
P. Cicuta, S.L. Keller and S.L. Veatch, J. Phys. Chem. B 111 (2007) 3328-3331
3D sphere:
D(r)= kT/(6 p h r)
z
…. But a 2D domain in a membrane is clearly not Stokes flow of a sphere.
…. Neither is it just membrane flow around a cylinder.
h
above and below there is
water
hw
membrane
h’’
x
y
Saffman and Delbruck in 1975 calculated the flow for this case:
Note the very weak
dependence on r
D(r) dependence on size
large r (or low viscosity) Hughes limit
D
D0 dependence on temperature
P. Cicuta, S.L. Keller and S.L. Veatch, J. Phys. Chem. B 111 (2007) 3328-3331
Line tension of domains near critical point
Capillary spectrum of fluctuations
l=l0 [ (Tc-T) / T ]x
With x=1 as in the 2d Ising model
Ising critical behavior also from above Tc
Biophysical Journal 95, 236 (2008)
Ising critical behavior also from above Tc
Tc
Biophysical Journal 95, 236 (2008)
T
Rafts ??
Same critical behavior also in cell blebs
Vesicles isolated from the plasma membranes of living rat basophilic leukemia (RBL-2H3) mast
cells and other cell types also display critical behavior.
ACS CHEMICAL BIOLOGY 3, 287 (2008)
Fundamental interest
In lipid vesicles, fluctuations are huge! Can be observed by light microscopy within 0.5C of Tc.
Relevance to Biology
Extrapolating from our data we expect fluctuations with correlation lengths of 50 nm to occur
between 2C–8C above their critical temperature.
In plasma membranes of unstimulated cells, no micrometer-scale domains are observed by
fluorescence microscopy at the cells’ growth temperature. Therefore, domains or
composition fluctuations must be submicrometer in dimension if they are present.
Submicrometer differences in membrane composition may confer advantages for cell processes.
Dynamic, small-scale membrane heterogeneities could result from critical fluctuations near a
critical temperature, rather than small domains far below Tc that are prevented from coalescing.
Here we have shown that it is possible to tune domain size (and line tension) by changing
the membrane’s proximity to a miscibility critical point.
The (strange) vesicle shape
Reduced line tension
Julicher and Lipowsky (1992, 1996)
Area
l = 0 is a sphere.
For x ≈ 0.5:
formation of bud around l = 3.1, and budding off at l = 4.4
This calculation is with the assumption of free volume.
fraction
+ line tension shown before
All vesicles would bud if volume could equilibrate.
J.Phys.Cond.Mat 22, 062101 (2010)
See also:Semrau S, Idema T, Holtzer L, Schmidt T and Storm C
Phys. Rev. Lett. 100 088101 (2008)
Optical Tweezers (1/3)
fiber
white light lamp
U
U(x)=1/2 ktrap Dx2
condenser
Sample cell
Motorised sample stage
60x water immersion objective
Motorised z-focus
mirror
x
dichroic
dichroic
Bright LED
X and Y axis AOD
tube lens
beamsplitter
monitor power
fiber
mirror
choice of fast
CMOS
or
1064nm
Yitterbium fiber
laser
sensitive CCD
camera
Typical ktrap= 5 pN/mm
Custom electronics
Custom software
Optical Tweezers (2/3)
Tweezers controller
Acousto
Optical Deflectors
1064nm 1.1W Laser
CCD Camera
Inverted microscope
(x63 Water immersion)
CMOS Camera
Optical Tweezers (3/3)
Mechanical Properties of Red Blood Cells
Soft Matter 7, 2042 (2011)
Medical and Biological Engineering and Computing 48, 1055-1063 (2010)
Optics Express 18, 7076 (2010)
Biophysical Journal 97, 1606–1615 (2009)
Physical Biology 5, 036007 (2008)
Actively deforming a giant vesicle
Driving mode 2, and
observing its amplitude
Active rheology of phospholipid vesicles
Phys. Rev. E 84, 021930 (2011)
Response, and mechanical properties
High frequency 1/f asymptotic
What are the fits ?
First the parameters κ and σ are fitted to
the phase, and then the stiffness β is
determined from the amplitude.
modes 2,3,4
Fitting gives:
σ = 1.2 × 10− 8 N m− 1
κ = 19 kBT .
mode 2
The value of β varies with mode number
Theoretical framework of membrane mechanics
Helfrich (1972):
For small deviations
around a sphere:
Where Ulm is the displacement, decomposed onto spherical harmonics Y lm
Applying equipartition theorem, and projecting on equator plane, gives the
mean amplitude of fluctuations for each equatorial mode:
Where hm is the F.T. of the equatorial displacement h(f )
Extending the theory to actively driven modes
M. A. Peterson, Mol. Cryst. Liq. Cryst. 127, 257 (1985)
Eq. of motion
of an
eigenmode:
Trap pos.:
Gives force:
Combining the above, and
in frequency domain:
The response function: a “fancy” driven damped harmonic oscillator
Why drive a system actively?
The intrinsic spectrum of fluctuations contains thermal and any nonthermal motion;
The response to external drive isolates the material properties.
Allows to verify presence of non-thermal sources of fluctuation (e.g. ion
pumps molecular motors, chemical energy in general…)
Acknowledgements
In Washington and Michigan Universities
Prof Sarah Veatch, Prof Sarah Keller and Dr Aurelia Honerkamp Smith
In Cambridge University
Experiments: Dr Aidan Brown and Dr Young Zoon Yoon
Optical Trap: Dr Jurij Kotar
Funding:
EPSRC, KAIST-Cavendish programmes (MoST and KICOS), Nanotechnology IRC,
Oppenheimer Fund, Royal Society, MRC, HFSP.
Thank you