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Pietro Cicuta Mechanics, Dynamics and Thermodynamics of phospholipid membranes Cavendish Laboratory, University of Cambridge Lorentz Institute, Leiden. 26 - 30 September 2011

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Prof Sarah Veatch, Michigan Univ. and Prof Sarah Keller, Univ. Washington, Seattle. Background: Phase behavior of phospholipid membranes Lipid rafts, signalling and transport in cells

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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.

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Image analysis and feature tracking through a movie 1:1 DOPC:DPPC + 30% cholesterol 10 m

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Image analysis and feature tracking through a movie 1:1 DOPC:DPPC + 30% cholesterol 10C 20C 40 m 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 r). =2 D(r) t P. Cicuta, S.L. Keller and S.L. Veatch, J. Phys. Chem. B 111 (2007) 3328-3331

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3D sphere: D(r)= kT/(6 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. x y z h membrane above and below there is water w Saffman and Delbruck in 1975 calculated the flow for this case: Note the very weak dependence on r

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D(r) dependence on size large r (or low viscosity) Hughes limit D0D0

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D 0 dependence on temperature P. Cicuta, S.L. Keller and S.L. Veatch, J. Phys. Chem. B 111 (2007) 3328-3331

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Line tension of domains near critical point

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Capillary spectrum of fluctuations = 0 [ (T c -T) / T ] With =1 as in the 2d Ising model

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Ising critical behavior also from above T c Biophysical Journal 95, 236 (2008)

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Ising critical behavior also from above T c TcTc T Rafts ?? Biophysical Journal 95, 236 (2008)

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Same critical behavior also in cell blebs ACS CHEMICAL BIOLOGY 3, 287 (2008) Vesicles isolated from the plasma membranes of living rat basophilic leukemia (RBL-2H3) mast cells and other cell types also display critical behavior.

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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 2C8C 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 membranes proximity to a miscibility critical point. Relevance to Biology

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Julicher and Lipowsky (1992, 1996) = 0 is a sphere. For x 0.5: formation of bud around = 3.1, and budding off at = 4.4 Reduced line tension Area fraction The (strange) vesicle shape This calculation is with the assumption of free volume. + 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)

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Optical Tweezers (1/3) choice of fast CMOS or sensitive CCD camera mirror tube lens dichroic X and Y axis AOD beamsplitter monitor power 1064nm Yitterbium fiber laser fiber white light lamp condenser Sample cell Motorised sample stage Motorised z-focus Bright LED Custom electronics Custom software 60x water immersion objective mirror U(x)=1/2 k trap x 2 x U Typical k trap = 5 pN/ m

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Acousto Optical Deflectors Inverted microscope (x63 Water immersion) CCD Camera CMOS Camera 1064nm 1.1W Laser Tweezers controller Optical Tweezers (2/3)

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Optical Tweezers (3/3)

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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, 16061615 (2009) Physical Biology 5, 036007 (2008)

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Actively deforming a giant vesicle Driving mode 2, and observing its amplitude Active rheology of phospholipid vesicles Phys. Rev. E 84, 021930 (2011)

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What are the fits ? First the parameters and are tted to the phase, and then the stiffness is determined from the amplitude. Fitting gives: = 1.2 10 8 N m 1 = 19 k B T. The value of varies with mode number High frequency 1/f asymptotic modes 2,3,4 mode 2 Response, and mechanical properties

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Theoretical framework of membrane mechanics Helfrich (1972): For small deviations around a sphere: Where U lm is the displacement, decomposed onto spherical harmonics Y l m Applying equipartition theorem, and projecting on equator plane, gives the mean amplitude of fluctuations for each equatorial mode: Where h m is the F.T. of the equatorial displacement h( )

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Extending the theory to actively driven modes 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 M. A. Peterson, Mol. Cryst. Liq. Cryst. 127, 257 (1985)

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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)

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Thank you 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. Acknowledgements