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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. Diffusion coefficient Number of random steps N corresponds to time t: From dimensional analysis: Diffusion coefficient and dissipation Einstein relation: Friction coefficient: Viscosity Particle size - velocity Force Osmotic pressure Free energy of ideal gas: N – number of particles V - volume concentration: Pressure: Osmotic forces: Protein solution Concentration difference induces osmotic pressure Semi-permeable membrane (only solvent can penetrate) Depletion force R Free energy gain: A – surface area of contact R – small particle radius - small particles concentration Depletion force Molecular size asymmetry leads to aggregation of large molecules Sometimes entropy can lead to order Disordered Liquid Ordered Solid Hydrophobic interactions • Amphiphiles (lipids): polar head-group and hydrophobic tail Lipid molecule Self assembly Hydrophobic interaction is due to disruption of entropy of hydrogen bonding of water chain (tail) (hate water) polar head (love water) Types of lipid molecules 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. Electrostatic interactions Two charges in medium with dielectric constant R Interaction energy: Two charges in salt solution with dielectric constant --- ----+- - + - + --- + R - ++ ++ + + + + ++ Screened interactions: Debye screening ---- ----+- - + - + --- + R - ++ ++ + + + + ++ Screened interactions: - Debye radius DNA condensation by multivalent ions Bacteriophage virus 100 nm Mg Cl (salt) ++ Cl- Cl Mg O. Lambert, L. Letellier , W. M. Gelbart, and J.-L. Rigaud* PNAS, 2000 DNA in solution V. Bloomfield I. Rouzina DNA is condensed after addition of multivalent salt 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 Phase separation Interactions can lead to phase separation: 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. Thank you!