Sampath Koppole

Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free energy  G sol --- its Components. What are we interested in ?? Popular Continuum Models: Simple Coulomb electrostatics. Poisson-Boltzmann Methods. Generalized Born Methods. Generalized Born Equation: Born – Onsager models  Born formula  Generalized Born methods. Limitations of GB Methods

What is Continuum Electrostatics ? A large molecule in a heterogeneous dielectric medium +  =80  =

Solvation Free Energy (  G sol ):  G sol has 3 major components: Vacuum Medium of High Dielectric + + Electrostatic component (modelled here as a continuum solvent)  G vdw =  G att +  G rep.  G cav = Cavity term Entropic penalty (+ ve)

Brief outline of the Talk: Summary: Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free energy  G sol --- its Components. What are we interested in ?? Popular Continuum Models: Simple Coulomb electrostatics. Poisson-Boltzmann Methods. Generalized Born Methods. Generalized Born and related approximations: Born – Onsager models  Born formula  Generalized Born methods. Limitations of GB Methods:

The Electrostatic contribution to the Solvation free energy  G sol can be evaluated by: Simple Coulomb equation: Electric field lines between two negative charges Electric field lines between a positive and negative charge Very inaccurate. Solvent polarization effects completely ignored. Solvation effects are completely ignored.

Poisson-Boltzmann Equation : Solution to the linearized Poisson-boltzmann equation  No Analytical solution to complex geometries  Solved by Finite Difference method (Numerical Method).  Approximate and for accuracy very tedious to solve.  CPU / Memory intensive.

Brief outline of the Talk: Summary: Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free energy  G sol --- its Components. What are we interested in ?? Popular Continuum Models: Simple Coulomb electrostatics. Poisson-Boltzmann Methods. Generalized Born Methods. Generalized Born and related approximations: Born – Onsager models  Born formula  Generalized Born methods. Limitations of GB Methods:

Born – Onsager Models: Work done to charge an ion in that particular dielectric (vacuum dielectric  = 1, water dielectric  = 80) q= charge on the ion b= radius of the ion  = Dielectric of medium Vacuum Medium of High Dielectric + + Difference in the solvation energy in Vacuum and in the solvent of high  Difference in the work to charge the ion in vacuum and in medium of high Dielectric   1 = Vacuum = 1  2 = Solvent dielectric = 

Generalized Born Equation: Consider a system of particles with radii b i and charge q i. The electrostatic solvation free energy (G (Elec) ) = Coulomb energy + Born free energy of Solvation Coulomb term Correction to the Coulomb term Charges are screened according the the Born eqn 1 What is Generalized in the Generalized Born Equation ? q i = charge on atom i q j = charge on atom j b i = born radii of atom i  = dielectric of solvent. r ij = distance betn atoms i and j

0 because for just one ion, q j = 0 and N =1 So we will have: Born equation N=1 So the Born equation for single ion is generalized to a system having N charges. So the name “Generalized Born Equation”

Still et al. in their JACS 1990 paper, combined the two terms into a single expression: Where ƒ(r ij, b) depends upon the inter-particle distances r ij and the Born radii b. A variety of terms for this function are proposed. Still et al. proposed the following: When r ij very large, When r ij is very small, approximately = 0

Brief outline of the Talk: Summary: Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free energy  G sol --- its Components. What are we interested in ?? Popular Continuum Models: Simple Coulomb electrostatics. Poisson-Boltzmann Methods. Generalized Born Methods. Generalized Born and related approximations: Born – Onsager models  Born formula  Generalized Born methods. Limitations of GB Methods:

Some limitations of GB methods:  Calculating the Self energy:  Calculating the Born Radii Self energy: It’s the interaction energy of a charge in the protein with the solvent when there are no other charges.  =80  =1 qiqi Coulomb field approximation The accuracy of the whole method is relies upon accurate calculation of the Born radii. Effective Born Radii in the Generalized Born Approximation: The Importance of Being Perfect. Alexey Onufriev in JCS(2002) showed that if one can compute the Born radii accurately then GB methods perform as good as PBEQ methods.

Brief outline of the Talk: Summary: Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free energy  G sol --- its Components. What are we interested in ?? Popular Continuum Models: Simple Coulomb electrostatics. Poisson-Boltzmann Methods. Generalized Born Methods. Generalized Born and related approximations: Born – Onsager models  Born formula  Generalized Born methods. Limitations of GB Methods:

Summary:  Solvation Free Energy  Born Equation  Generalized Born Equation  Bottle necks in the equation.  Improving the accuracy of this method.

Thanks… … for your attention!