Generalized Born Approach to Continuum Electrostatics

1. Generalized Born Approach to Continuum Electrostatics Sampath Koppole

2. Brief outline of the Talk: • Introduction to Continuum Electrostatics: • Continuum Electrostatics --- What is it ?? • Solvation free energy Gsol --- 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 • Summary

3.  =80 +  =1 + + + + What is Continuum Electrostatics ? A large molecule in a heterogeneous dielectric medium

4. + + Vacuum Medium of High Dielectric DGcav= Cavity term Entropic penalty (+ ve) Electrostatic component (modelled here as a continuum solvent) DGvdw= DGatt + DGrep. Solvation Free Energy (Gsol): Gsolhas 3 major components:

5. Brief outline of the Talk: • Introduction to Continuum Electrostatics: • Continuum Electrostatics --- What is it ?? • Solvation free energy Gsol --- 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:

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

7. 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.

8. Brief outline of the Talk: • Introduction to Continuum Electrostatics: • Continuum Electrostatics --- What is it ?? • Solvation free energy Gsol --- 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:

9. 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  + 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 1= Vacuum = 1 2= Solvent dielectric =  Born – Onsager Models:

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

11. 0 N=1 Born equation because for just one ion, qj = 0 and N =1 So we will have: So the Born equation for single ionis generalized to a system having N charges. So the name “Generalized Born Equation”

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

13. Brief outline of the Talk: • Introduction to Continuum Electrostatics: • Continuum Electrostatics --- What is it ?? • Solvation free energy Gsol --- 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:

14.  =80  =1 qi Some limitations of GB methods: • Calculating the Self energy: Self energy: It’s the interaction energy of a charge in the protein with the solvent when there are no other charges. Coulomb field approximation • Calculating the Born Radii The accuracy of the whole method is relies upon accurate calculation of the Born radii. Effective Born Radii in the Generalized BornApproximation: 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.

15. Brief outline of the Talk: • Introduction to Continuum Electrostatics: • Continuum Electrostatics --- What is it ?? • Solvation free energy Gsol --- 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:

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

17. Thanks… … for your attention!