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G Solvation

G Solvation. Continuum Electrostatics. G Solvation.  sol G =  VdW G +  cav G +  elec G  VdW G = solute-solvent Van der Waals  cav G = work to create cavity in solvent = surface tension x surface area Entropy penalty for rearrangement of water molecules

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G Solvation

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  1. G Solvation Continuum Electrostatics

  2. G Solvation • solG = VdWG + cavG + elecG • VdWG = solute-solvent Van der Waals • cavG = work to create cavity in solvent • = surface tension x surface area • Entropy penalty for rearrangement of water molecules • Evaluate from a series of alkanes r= 1-5 H H N H r= 78.54

  3. G Solvation • elecG = difference in electrostatic work necessary to charge ion: soln – gas • Work necessary to transfer ion from vacuum to solution with the same electrostatic potential • Work = elecG = i qi • i=electrostatic potential for ion i and its ionic atmosphere of neighbors j

  4. (r) q1 q2 Electrostatic Potential • r = relative dielectric constant • r = 78.54 for water (attenuates interaction) r

  5. 2 4 π e å c = - 2 ( x ) z - sinh u ( x ) δ ( x x ) + ε ( x ) u ( x ) Ñ × Ñ κ kT i i i Poisson-Boltzmann Equation • Continuum Electrostatics with Background Electrolyte *N. A. Baker

  6. 2 4 π e å c - 2 ( x ) z - sinh u ( x ) δ ( x x ) ε ( x ) u ( x ) Ñ × Ñ κ kT i i i Poisson-Boltzmann Equation = + *N. A. Baker

  7. 2 = ( x ) u ( x ) + κ 2 4 π e å c - z - δ ( x x ) ε ( x ) u ( x ) Ñ × Ñ kT i i i Poisson-Boltzmann Equation • Linearized

  8. sinh

  9. Electrostatic potential of the 30S ribosomal subunit Top: face which contacts 50S subunit http://agave.wustl.edu/apbs/images/images/30S-canonical.html

  10. Web links • http://ashtoret.tau.ac.il/Homepage/courses/Poisson-Boltzmann.pdf • http://www.biophysics.org/btol/img/Gilson.M.pdf • Nathan A. Baker; http://www.npaci.edu/ahm2002/ahm_ppt/Parallel_methods_cellular.ppt • Jeffry D. Madura; http://www.ccbb.pitt.edu/BBSI/6-11_class_jm.pdf

  11. 2 4 π e å = - 2 - Ñ × Ñ c κ ( x ) sinh u ( x ) z δ ( x x ) + ε ( x ) u ( x ) i i kT i = u ( x ) g ( x ) Î ¶ W Î ¶ W x x 2 4 πe å - Ñ × Ñ + = - 2 c ε ( x ) u ( x ) κ ( x ) u ( x ) z δ ( x x ) i i kT i - Linearized Poisson Boltzmann equation also useful: - Free energies and forces obtained from integrals of u

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