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G Solvation

G Solvation. Continuum Electrostatics.  r = 1-5. G Solvation. H. H. N. H.  r = 78.54.  sol G =  sol G VdW +  sol G cav +  sol G elec  sol G VdW = solute-solvent Van der Waals  sol G cav = work to create cavity in solvent = surface tension x surface area

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G Solvation

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  1. G Solvation Continuum Electrostatics

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

  3. G Solvation • solGelec = difference in electrostatic work necessary to charge ion: • solGelec = NA wsoln – NA wgas • Work to transfer ion from vacuum to solution with the same electrostatic potential Work = solGelec = 0Zie i dqi • i=electrostatic potential for ion i and its ionic atmosphere of neighbors j

  4. uniform dielectric rij 0 qi qj i(r) Electrostatic Potential • r = relative dielectric constant • r = 78.54 for water (attenuates interaction)

  5. + + - + + uniform solvent dielectric + pj(r) - - - - - - - - - r qi qj rD Screening caused by ionic atmosphere • pj(r) dr = probability of finding an ion j at r to r+dr • rmp = rD= Debye length • thickness of ionic atmosphere

  6. + + - + + uniform solvent dielectric + pj(r) - - - - - - - - - r qi qj rD Boltzmann distribution • thermal jostling • collisions disrupt ionic halo Noj = number of ions j in volume V k = R/NA

  7. i(r) 2i higher r Poisson Equation • Non-electrolyte Solutions or Dilute Solution Limit for Electrolyte Solutions • i(r)= qi pi(r) = charge density • i(r)= charge per unit volume (r) • (r) =or(r)

  8. Poisson Equation– Spherical Ion • the higher the charge density the faster the potential drops i i r j j i j j i j

  9. Screened Coulomb Potential • Point charges, uniform solvent dielectric • (r) = ro • qj = zj e

  10. + + - + + uniform solvent dielectric + pj(r) - - - - - - - - - r qi qj rD Screened Coulomb Potential • Point charges, uniform solvent dielectric

  11. 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

  12. 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

  13. 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

  14. sinh

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

  16. 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

  17. 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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