1. Long Range Interactions beyond first neighbour
Intermolecular forces organizing complex fluids
…Laboratory experiments for challenging predictive theories.
3- Osmotic pressure and phase diagram of uncharged lipids

2. Self-assembly of a bilayer (packing…)
- Aggregated lipids feel a non-uniform lateral stress.
- Stress distributions generate bending moments.

3. Force (solution stress) vs. separation (from x-ray)
mw, Posm T mi D
x-ray

4. Liposomes of DMPC as responsive colloid
locally flat, multilayer stacks
D (repeat spacing)
Small-angle x-ray scattering
D=2p/q ~ 60Å

5. Posmotic
P. Rand (1982 – 96)

6. Plot as biochemist AND phys. chem.:
Lipid
PEG
DM Le Neveu, P. Rand and VA Parsegian . (1976) Nature:
« Measurement of forces between lecithin bilayers »

7. Lattice spacing D from “force balance”
D = DB + DW
van der Waals attraction with strength H (Hamaker parameter)
hydration repulsion with decay length l ~ 2-3 Å
Helfrich
shape-fluctuation repulsion, KC=bending modulus, s= fluctuation amplitude
Free energy
Per area
Spacing can be modified/controlled by osmotic stress (i.e. via water chemical potential).

8. Osmotic pressure vs. bilayer separation
Egg PC
PEG
due to fluctuations
Lipid
DW ( Å )
Zero pressure
Petrache, Tristram-Nagle, Nagle, 1998

9. Neutral bilayer free energy versus separation

10. In presence of excess water (or osmotically stressed)
Area per lipid, A
Deformation work
PEG and Lipids compete for water
DW (water spacing)
Separation work
Obtain the equation of state Posmotic vs. Dw.
P. Rand and VA Parsegian

11. Equation of state Posm vs. spacing DW. has Three(?) terms :
hydration repulsion with decaylength l ~ 2-3 Å
van der Waals attraction with strength H (Hamaker parameter)
fluctuation repulsion KC=bending modulus s = fluctuation amplitude

12. What is this strange “fluctuation” pressure ?

13. What is this strange “fluctuation” pressureS ?
“undulation”
“protrusion”
Israelachvili, JN and Wennerström H,
Entropic forces between amphiphilic surfaces in liquid (1992)

14. Measure fluctuations through shape of Bragg peaks
de Gennes-Caille’
smectic model
The (dis)order parameter h1 gives the amplitude of fluctuation s which gives the interlamellar fluctuation repulsion.
Safinya, CR“: Universality in interacting membranes : the effect of cosurfactants on the interfacial rigidity (1989)

15. Operational full expression in the MLV, La “onion”…

16. Perpendicular EOS set by Adrian works well for neutral lipids :

17. perpendicular EoS
P = 0 D dl dw
P ≠ ou = 0

18. Robust EOS for DPPC in water
Parameters
DPPC on water
H - Hamaker constant (kT)
1.0 ± 0.2
P0 - Hydration cœfficient (Pa)
108.95
λ - hydration decay length (Å)
2.55 ± 0.05
κc – bending rigidity (kT)
9 to 30
Predicts phase diagramm (effect of solutes ?)

19. Core reference :Life as matter of fat
Force balance predicts « maximum swelling » of liposomes… but « in-plane » soiology of mixed lipids opên field
Adding electrolytes, osmolytes, cholesterol, drugs….
Ole G Mouritsen (2005)

20. What we have learnt ?
Measuring EOS is a way to test force balance for bilayers .. But lateral equation of state is needed in anisotropic systems… Then effect of solutes : stiffening, bending, permeation…. … closed reservoir
O. G. Mouritsen : Life as a matter of fat