G Solvation

Continuum Electrostatics

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

NH

H H

r = 1-5

r = 78.54

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

Electrostatic Potential

r = relative dielectric constant

r = 78.54 for water (attenuates interaction)

r

V(r) = q1 q2

4o

r r = (r) q2

(r) = q1

4o

r r (r)

q1 q2

Poisson-Boltzmann Equation Continuum Electrostatics with

Background Electrolyte

)()( xuxε )(sinh)(2 xuxκ )(π4 2

ii i

cxxδz

kT

e

*N. A. Baker

)(π4 2

ii i

cxxδz

kT

e

Poisson-Boltzmann Equation

)()( xuxε )(sinh)(2 xuxκ

*N. A. Baker

Poisson-Boltzmann Equation Linearized

)()( xuxε )()(2 xuxκ )(π4 2

ii i

cxxδz

kT

e

sinh

Electrostatic potential of the 30S ribosomal subunit

http://agave.wustl.edu/apbs/images/images/30S-canonical.html

Top: face which contacts 50S subunit

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

)()( xuxε )(sinh)(2 xuxκ )(π4 2

iii

c xxδzkTe

Linearized Poisson

-

Boltzmann equation also useful:

iii

c xxδzkT

πexuxκxuxε )(

4)()()()(

22

-

xxxgxu )()(

Free energies and forces obtained from integrals of u