1.  G Solvation Continuum Electrostatics

2.  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 Evaluate from a series of alkanes N H H H  r = 1-5  r = 78.54

3.  G Solvation  elec G = 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 =  elec G =  i q i  i = electrostatic potential for ion i and its ionic atmosphere of neighbors j

4. Electrostatic Potential  r = relative dielectric constant  r = 78.54 for water (attenuates interaction) r  (r) q1q1 q2q2

5. Poisson-Boltzmann Equation Continuum Electrostatics with Background Electrolyte )()(xuxε   )(sinh )( 2 xu x κ )( π4 2 i i i c xxδ z kT e     *N. A. Baker

6. )( π4 2 i i i c xxδ z kT e   Poisson-Boltzmann Equation   )()(xuxε   )(sinh )( 2 xu x κ *N. A. Baker

7. Poisson-Boltzmann Equation Linearized )()(xuxε   )( )( 2 xu x κ )( π4 2 i i i c xxδ z kT e    

8. sinh

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

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 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. )()(xuxε  )(sinh)( 2 xuxκ)( π4 2 i i i c xxδz kT e     Linearized Poisson - Boltzmann equation also useful:   i ii c xxδz kT πe xuxκxuxε)( 4 )()()()( 2 2 -   xx xgxu)()( Free energies and forces obtained from integrals ofu