?G Solvation

1
?G Solvation

• Continuum Electrostatics

2
?G Solvation

• ?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 wideal
• 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
Electrostatic Potential

• ?r relative dielectric constant
• ?r 78.54 for water (attenuates interaction)

5
Electrostatic Potential

• Difficult to solve in general.
• Examples two extreme cases
• Spherical ions
• Point charge in an electrolyte solution
• Ionic atmosphere or ionic halo
• Charged solute radius ri in very dilute solution
  or non-electrolyte solution

6
Screening caused by ionic atmosphere

• pj(r) dr probability of finding an ion j at r
  to rdr
• rmp rD Debye length
• thickness of ionic atmosphere

7
Boltzmann distribution

• thermal jostling
• collisions disrupt ionic halo

Noj number of ions j k R/NA
8
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)

9
Poisson Equation Spherical Ion

• the higher the charge density the faster the
  potential drops

i
i
r
j
j
i
j
j
i
j
10
Screened Coulomb Potential

• Point charges, uniform solvent dielectric
• ?(r) ?r?o
• qj zj e

11
Screened Coulomb Potential

• Point charges, uniform solvent dielectric

12
Born Approximation

• Spherical solute with radius ri and charge zi
• Very dilute solution or non-electrolyte
• Electrostatic potential is caused by polarization
  of the solvent by the partial charges of the
  solute.
• ?i(ri)

??r 1
zi

ri
??r 78.54
13
Born Approximation Self Potential
welec


welec
14
Born Approximation Solvation Free Energy

• ?elecG NA welec(real) NA welec(ideal)
• ?elecG NA wsolution NA wvacuum

?elecG
-
15
Poisson-Boltzmann Equation

• Continuum Electrostatics with Background
  Electrolyte

N. A. Baker
16
Poisson-Boltzmann Equation


N. A. Baker
17
Poisson-Boltzmann Equation

• Linearized

18
sinh
19
Electrostatic potential of the 30S ribosomal
subunit
Top face which contacts 50S subunit
http//agave.wustl.edu/apbs/images/images/30S-cano
nical.html
20
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

21
-
Linearized Poisson
Boltzmann equation also useful
-
Free energies and forces obtained from integrals
of
u