1. Lecture 5 Interactions Introduction to Statistical Thermodynamics
of Soft and Biological Matter
Lecture 5
Interactions
Osmotic pressure.
Depletion force.
Hydrophobic interactions.
Hydration force.
Electrostatic interactions. Debye screening.
DNA condensation by multivalent ions.
van der Waals attraction.
Phase separation.

2. Diffusion coefficient
Number of random steps N corresponds to time t:
From dimensional analysis:

3. Diffusion coefficient and dissipation
Einstein relation:
Friction coefficient:
Viscosity
Particle size
- velocity
Force

4. Osmotic pressure Free energy of ideal gas: concentration:
N – number of particles
V - volume
Pressure:
Osmotic forces:
Concentration difference induces
osmotic pressure
Semi-permeable membrane
(only solvent can penetrate)
Protein solution

5. Depletion force R Free energy gain: A – surface area of contact
concentration=density
Free energy gain:
A – surface area of contact
R – small particle radius
- small particles concentration

6. Depletion force
Molecular size asymmetry leads to aggregation of large molecules

7. Sometimes entropy can lead to order
Disordered Liquid
Ordered Solid

8. Hydrophobic interactions
Amphiphiles (lipids): polar head-group and hydrophobic tail
Lipid
molecule
Self assembly
chain (tail) (hate water)
polar head (love water)
Hydrophobic interaction
is due to disruption of entropy of hydrogen bonding of water

9. Types of lipid molecules

10. Hydration repulsion
At small separations (<1 nm), there is a repulsion between
surfaces in water due to disruption of water molecular ordering
(layering) at the surfaces.
Hydration repulsion constitutes energetic barrier for
membrane fusion.

11. Electrostatic interactions
Two charges in medium with dielectric constant R
Interaction energy:
Two charges in salt solution with dielectric constant
Screened interactions: R + -
DNA molecules: 1 elementary charge per 1.7 A of the contour length.

12. Debye screening R + -
Screened interactions:
- Debye radius

13. DNA condensation by multivalent ions
Bacteriophage virus 100 nm
Mg Cl (salt) ++ Mg Cl - Cl -
O. Lambert, L. Letellier , W. M. Gelbart, and J.-L. Rigaud* PNAS, 2000
DNA in solution
DNA is condensed after addition of
multivalent salt
V. Bloomfield
I. Rouzina

14. van der Waals attraction
Always present between molecules:
- Usually attractive between same species
- Long range (power law)
van der Waals attraction between two atoms:
Hamaker constant
vdW attraction is due to fluctuations of electron clouds in atoms

15. Phase separation
Interactions can lead to phase separation:

16. Main Questions and Ideas
Conclusions
Main Questions and Ideas
How can living organisms be so highly ordered ?
Equilibrium versus non-equilibrium systems. Living systems
are not at equilibrium, and they are open. Quasi equilibrium.
Interactions can lead to a spontaneous ordering even
at equilibrium.
Entropy can lead to a spontaneous ordering at equilibrium !
Flow of information characterizes living organisms.
Evolution is the biological “pressure”.
Living organisms are robust.

17. Thank you!