sampath koppole. brief outline of the talk: summary introduction to continuum electrostatics:...

Sampath Koppole

Brief outline of the Talk:

• Summary

• 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

What is Continuum Electrostatics ?

A large molecule in a heterogeneous dielectric medium

+

=80

=1

+

+

+

+

)()()()( CavityVDWElecSol GGGG

Solvation Free Energy (Gsol):

Gsol has 3 major components:

Vacuum

Medium ofHigh Dielectric

+

+

Electrostatic component (modelled here as a continuum solvent)

Gvdw= Gatt + Grep.

Gcav= Cavity termEntropic penalty (+ ve)


• Summary:



• 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 Gsol can be evaluated by:

• Simple Coulomb equation:

11

4

1

02

21

r

qqGelec

Electric field lines betweentwo negative charges

Electric field lines betweena 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

rrrIrr 48

Solved by Finite Difference method (Numerical Method).

Approximate and for accuracy very tedious to solve.

CPU / Memory intensive.


• Summary:





Born – Onsager Models:

Work done to charge an ion in that particular dielectric (vacuum dielectric = 1, water dielectric = 80)

bq 2/2 q= charge on the ionb= radius of the ion= Dielectric of medium

Vacuum

Medium ofHigh Dielectric

+

+

)(ElecG Difference in the solvation energy inVacuum and in the solvent of high

Difference in the work to charge the ion in vacuum and in medium of high Dielectric

21

2

2

2

1

2

)(

11

222 b

q

b

q

b

qG Elec

b

q

b

q

b

qG Elec

222

)(

11

2

1

22

1= Vacuum = 12= Solvent dielectric =

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

N

i i

iN

i

N

ij ij

jiElec b

q

r

qqG

1

2

1 1)(

11

2

1

.

Coulomb term Correction to the Coulomb termCharges are screened according the the Born eqn

1

What is Generalized in the Generalized Born Equation ?

qi = charge on atom iqj = charge on atom jbi = born radii of atom i= dielectric of solvent.rij = distance betn atoms i and j

N

i i

iN

i

N

ij ij

jielec b

q

r

qqG

1

2

1 1

11

2

111

0 because for just one ion, qj = 0 and N =1

So we will have:

i

iN

i i

i

b

q

b

q 2

1

2 11

2

111

2

1

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”

N

i i

iN

i

N

ij ij

jiElec b

q

r

qqG

1

2

1 1)(

11

2

111

Still et al. in their JACS 1990 paper, combined the two terms into a single expression:

N

i i

iN

i

N

ij ij

jiElec b

q

r

qqG

1

2

1 1)(

11

2

111

N

i

N

ij ij

jiElec brf

qqG

1 1)( ,

11

2

1

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:

ji

ijjiijij bb

rbbrbrf

4exp),(

22 When rij very large, 0

4exp

2

ji

ij

bb

r

When rij is very small, approximately = 0

14

exp2

ji

ij

bb

r


• Summary:





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 thereare no other charges.

=80

=1

qi

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.


• Summary:





Summary:

Solvation Free Energy

Born Equation

Generalized Born Equation

Bottle necks in the equation.

Improving the accuracy of this method.

Thanks…

… for your attention!

sampath koppole. brief outline of the talk: summary introduction to continuum electrostatics:...

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