pKa calculations

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pKa calculations

• Methods and Applications

A.H. Juffer The University of Oulu Finland-Suomi
A.H.Juffer The University of Oulu Finland-Suomi
A.H.Juffer The University of Oulu Finland-Suomi
A.H.Juffer The University of Oulu Finland-Suomi
A.H.Juffer The University of Oulu Finland-Suomi
A.H.Juffer The University of Oulu Finland-Suomi
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Definition of pKa (1)

• The pKa of a titrating site is defined as the pH
  for which the site is 50 occupied, that is
• The pH for which the occupancy q is 0.5.

Deprotonation reaction
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Definition of pKa (2)
q is degree of protonation or occupancy Number
of bound protons as a function of pH
Titration curve
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Definition of pKa (3)
One state transition
Computer simulation Calculation of ? as a
function of pH
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Method of calculation Shift in pKa

• Intrinsic pKa Transfer of site from model
  compound into protein location
• Self-term
• Background charges
• No site-site interaction
• Site-site interaction
• Sampling of accessible of protonation states as a
  function of pH gt Titration curve ?(pH)

J. Phys. Chem. B. 101, 7664-7673, 1997
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Method of calculation pKaintr
Model compound in solvent
Difference in solvation affects distribution
between AH and A-
Vacuum
In protein location
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Solvation free energy

• Continuum electrostatics
• Nonpolar contribution SAS
• Cancels for difference between A- and AH

J. Comput. Chem. 25, 393-411, 2004
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Continuum electrostatics
Total electrostatic energy

• Rigid protein molecule.
• No analytical solution.

Dielectric boundary
Solvent region
Inverse Debye Length
Protein
Partial charges
J. Comput. Phys. 97, 144, 1991
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Site-site interactions
Titrating curve AVERAGE occupancy
ss Number of bound protons for protonation
state s ps Probability of observing protonation
state s
Boltzmann factor
Changes in protonation state modifies molecular
charge distribution
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Monte Carlo
Protein Structure
Protein Thermodynamics Protein Function
Random displacement
Evaluate Energies
Analysis
Update ensemble
Accept or reject
Ensemble averages
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Monte Carlo simulation
Total occupancy
State 1

• 00001110101000110101001110
• ?
• 00011110111100110101001110
• ?
• 10011110111110110101001110

State 106
Site occupancy
Average site occupancy is ?0.66
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Outcome of computation
NMR experiment
Prediction
Biochem. Cell. Biol., 76,198-209 (1998).
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Predictions are useful

• Molecule level explanation of titration curves
• Details on electrostatic network protein
  structure
• Statements about enzyme activity protein
  function (J. Biol. Chem., 275, 25633-25640, 2000)

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Problems

• Correlation between protein dynamics and
  protonation state is commonly ignored.
• At low or high pH, proteins become unstable or
  denaturate.
• New models properly should sample both
  conformation and protonation states
  simultaneously
• Coarse grained model.

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Apo form of Calbindin
Calbindin Titration curves of ion ligating groups.
No structure relaxation upon ion release.
Xray holo structure with Ca2 removed
Proteins, 41, 554-567, 2000
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Apo form of Calbindin
Calbindin Titration curves of ion ligating groups.
With structure relaxation upon ion release.
NMR apo structure
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The Arg in the a-domain of PDI
J. Mol. Biol., 335, 283-295, 2004