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

 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

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

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

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

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

sinh

Electrostatic potential of the 30S ribosomal subunit Top: face which contacts 50S subunit

Web links Nathan A. Baker; Jeffry D. Madura;

)()(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 )()()()(   xx xgxu)()( Free energies and forces obtained from integrals ofu