Pietro Cicuta

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

2. 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.

3. 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.

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

5. 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

6. 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

7. D0 D(r) dependence on size large r (or low viscosity) Hughes limit

8. D0 dependence on temperature P. Cicuta, S.L. Keller and S.L. Veatch, J. Phys. Chem. B 111 (2007) 3328-3331

10. Line tension of domains near critical point

11. Capillary spectrum of fluctuations l=l0 [ (Tc-T) / T ]x With x=1 as in the 2d Ising model

12. Ising critical behavior also from above Tc Biophysical Journal 95, 236 (2008)

13. Ising critical behavior also from above Tc T Tc Rafts ?? Biophysical Journal 95, 236 (2008)

14. 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)

15. 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

17. 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)

18. 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

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

20. Optical Tweezers (3/3)

21. 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)

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

23. 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

24. 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 )

25. 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

26. 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…)

27. 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