Continuum Electrostatics And MMPBSA

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Continuum Electrostatics AndMM-PBSA
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Topics

• Poisson Equation
• Poisson-Boltzmann Equation
• Finite Difference Method
• Born Model
• Generalized Born
• Hydrophobic effect
• Free Energy Component Analysis

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Electrostatics in Molecular Biophysics

• Electrostatic interactions are very long-ranged
• Most of the common biological macromolecules are
  highly charged so we cannot simply ignore
  electrostatic interactions!
• The cytoplasm of cells contains a relatively high
  concentration of dissolved ions such as Na, Ca2
  and Cl-

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Electrostatic Steering
AChE and Fasciculin 2 bind with
electrostatically-steered, diffusion-controlled
kinetics.
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Electrostatic Potential
Coulomb Equation
Electrostatic work required to bring a charge q
to the point rq in the potential
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Distance Dependent Dielectric Function
Local Dielectric Environment of B-DNA in
Solution Results from a 14 ns Molecular Dynamics
Trajectory M. A. Young, B. Jayaram, and D. L.
Beveridge J. Phys. Chem. B, 102 (39), 7666
-7669, 1998
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Dielectric Screening
Physical Basis of Dielectric Screening
Polarization
Dipoles Polarization Induced Electronic
2 Permanent Orientational 80
Reaction Field
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Molecule in Solution
Solute Low dielectric region with fixed partial
charges ep 2-4
Solvent High dielectric region with unlocalized
charges ep 80
Presence of dielectric boundaries presents the
effects of an induced surface charge
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Poisson Equation
where
- differential operator
If a dielectric medium screens the field
Relative permittivity
Electrostatic potential
Poisson Equation
Charge density
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Effect of Dissolved Electrolytes
Mobile ions are distributed according to the
Boltzmann statistics. Mean local concentration
(c(r))of ions relative to bulk concentration
(cbulk)
Ion Distribution
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Poisson-Boltzmann Equation
Poisson Equation
Charge Distribution
Poisson-Boltzmann Equation
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Linear Poisson-Boltzmann Equation
For
For a charge balanced system
where
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Finite Difference Approximation
N1 for linear equation
for nonlinear
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Features of Continuum Model

• Location and magnitude of charges
• Surface features of solute and solvent boundary
• Difference in dielectric across the boundary
• Ionic strength
• Weakness
• Ignores molecular nature of solvent
• Finite size of ions
• Ion-ion correlation effects

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Total Electrostatic Energy
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Molecular Surface Potential
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Applications of FDPB Methods

• Solvation energy
• pKa Shifts
• Binding energies
• Conformational analysis
• Effect of ionic strength on binding

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Solvation Energy
Solvation thermodynamics of amino acids S. B.
Dixit, B. Jayaram et al. J. Chem. Soc., Faraday
Trans., 1997, 93(6), 1105-1113
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Accessible Surface Area
Image source http//www.netsci.org/Science/Compch
em/feature14.html
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Born Model of Solvation
Generalized Born Equation
A modification of the generalized Born theory B.
Jayaram, Y. Liu and D. L. Beveridge J. Chem.
Phys., 109, 1465-1471.
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pKa Calculation
Study the effect of site-directed mutations on
change in pK value
Potential at site I due to the original group
Potential at site I due to the original group
-1 or 1 for an acidic or basic group
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Free Energy of Conformational Change
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Free Energy of Binding
Macroscopic Models of Aqueous Solutions Barry
Honig, Kim Sharp and An-Suei Yang J. Phys. Chem.
1993,97, 1101-1109
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Thermodynamics of Protein-DNA Binding
Jayaram et al. (1999) J. Comp. Phys. 151, 333.