Examples of Electrostatics Calculations

1
Examples of Electrostatics Calculations

• Nathan A. Baker
• Department of Biochemistry and Molecular
  Biophysics
• Center for Computational Biology
• Washington University in St. Louis
• BME 590 N
• October 7, 2003

2
Examples

• What well cover
• Ion solvation
• Ion-ion PMFs
• Ionic screening
• Ion condensation
• Ligand binding
• What we wont cover
• Protein-protein interactions
• pKa calculations
• Force evaluation/dynamics

3
What the user tells APBS

• Molecule input and calculation data
• Solver method
• Grid specifications
• Resolution
• Length
• Center
• Charge discretization
• Version of PBE to solve
• Boundary conditions
• Mobile ion species
• Charge
• Concentration
• Radius
• Dielectric values
• Solute value
• Solvent value
• Surface definition
• Apolar coefficient
• Temperature

• read
• mol pqr mol.pqr
• end
• elec
• mg-auto
• mol 1
• dime 97 97 97
• cglen 100 100 100 fglen 50 50 50
• cgcent mol 1 fgcent mol 1
• chgm spl0
• lpbe
• bcfl mdh
• ion 1.0 0.150 2.0 ion -1.0 0.150 2.0
• pdie 2.0
• sdie 78.54
• srfm smol srad 1.4 swin 0.3
• temp 298.15
• gamma 0.00072
• calcenergy yes

4
The Born ion

• Simple ion model
• Non-polarizable sphere (e1), embedded point
  charge, high dielectric medium outside
• Analytical expressions known for potential and
  energy
• This example
• Calculate electrostatic potential
• Calculate solvation energy
• Software
• APBS (http//agave.wustl.edu/apbs/)
• Gnuplot (http//www.gnuplot.info/)

5
Ion-ion potential of mean force

• Two-ion PMF
• Illustrates reaction field effects
• Continuum description of desolvation
• This example
• Calculate desolvation energies from PBE
• Calculate direct interactions from Coulombs law
• Software
• APBS (http//agave.wustl.edu/apbs/)
• Gnuplot (http//www.gnuplot.info/)

6
Ligand binding energies

• Balanol and protein kinase A
• Part of a investigation of selectivity of kinase
  inhibtors
• See
• Wong CF, et al. J. Med. Chem. 44 1530-1539,
  2001.
• Hünenberger PH, et al. Biochemistry 38
  2358-2366, 1999.
• Used PB and SASA methods
• Ranked inhibitor binding (??G)
• This example
• Calculate electrostatic potential for complex,
  PKA, and balanol using PBE
• Calculate binding energy
• Visualize interaction of balanol potential with
  PKA binding site
• Software
• APBS (http//agave.wustl.edu/apbs/)
• VMD (http//www.ks.uiuc.edu/Research/vmd/)

7
Non-specific ion interactions screening

• Mouse acetylcholinesterase electrostatics
• Hydrolyzes acetylcholine
• Diffusion-limited reaction rate
• Highly-sensitive to ionic strength
• This example
• Calculate electrostatic potential for AChE using
  PBE
• Look at 1 kT/e isocontours at 0 mM and 150 mM
  NaCl
• Implied effect on binding rate
• Simulations of binding rate
• Software
• APBS (http//agave.wustl.edu/apbs/)
• VMD (http//www.ks.uiuc.edu/Research/vmd/)

8
Non-specific ion interactions condensation

• Examine DNA 36-mer (B form)
• Look at NaCl condensation (typical of other
  cations as well)
• 67 of ions at 17 Å
• This example
• Calculate electrostatic potential for DNA in 100
  mM NaCl
• Convert to charge density
• Visualize charge density contours
• Software
• APBS (http//agave.wustl.edu/apbs/)
• VMD (http//www.ks.uiuc.edu/Research/vmd/)

9
Computational Electrostatics State of the Art

• Computational methods have varying strengths and
  weaknesses
• Usually trade efficiency for accuracy
• Implicit solvent methods
• Much faster than explicit approaches
• In the ??G regime (at best) for prediction
• Very sensitive to model and parameters
• Poor treatment of ion effects
• Explicit solvent methods
• More accurate ?G-quality predictions
• Only as good as the force field
• Very slow limited by rate of sampling