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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. Lipid rafts, signalling and transport in cells.

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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

Lipid rafts,

signalling and transport in cells

Prof Sarah Veatch, Michigan Univ.

and Prof Sarah Keller, Univ. Washington, Seattle.


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)

…. But a 2D domain in a membrane is clearly not Stokes flow of a sphere.

…. Neither is it just membrane flow around a cylinder.

z

h

above and below there is

water hw

x

membrane h’’

y

Saffman and Delbruck in 1975 calculated the flow for this case:

Note the very weak dependence on r


D0

D(r) dependence on size

large r (or low viscosity) Hughes limit


D0 dependence on temperature

P. Cicuta, S.L. Keller and S.L. Veatch, J. Phys. Chem. B 111 (2007) 3328-3331



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

T

Tc

Rafts ??

Biophysical Journal 95, 236 (2008)


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.

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.

Relevance to Biology


The (strange) vesicle shape

Reduced line tension

Julicher and Lipowsky (1992, 1996)

l = 0 is a sphere.

For x ≈ 0.5:

formation of bud around l = 3.1, and budding off at l = 4.4

Area fraction

This calculation is with the assumption of free volume.

+ line tension shown before

All vesicles would bud if volume could equilibrate.

See also:SemrauS, Idema T, Holtzer L, Schmidt T and Storm C

Phys. Rev. Lett. 100 088101 (2008)

J.Phys.Cond.Mat22, 062101 (2010)


Optical Tweezers (1/3)

fiber

white light lamp

condenser

Sample cell

Motorised sample stage

60x water immersion objective

Motorised z-focus

mirror

dichroic

dichroic

Bright LED

X and Y axis AOD

tube lens

U

beamsplitter

U(x)=1/2 ktrapDx2

monitor power

mirror

Typical ktrap= 5 pN/mm

fiber

choice of fast CMOS

or

sensitive CCD camera

Custom electronics

Custom software

1064nm Yitterbium fiber laser

x


Acousto

Optical Deflectors

Tweezers controller

1064nm 1.1W Laser

CCD Camera

CMOS Camera

Inverted microscope(x63 Water immersion)

Optical Tweezers (2/3)



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.

Fitting gives:

σ = 1.2 × 10− 8 N m− 1

κ = 19 kBT.

The value of β varies with mode number

modes 2,3,4

mode 2


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 non-thermal 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 JurijKotar

Funding:

EPSRC, KAIST-Cavendish programmes (MoST and KICOS), Nanotechnology IRC, Oppenheimer Fund, Royal Society, MRC, HFSP.

Thank you


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