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