sampath koppole. brief outline of the talk: summary introduction to continuum electrostatics:...
TRANSCRIPT
![Page 1: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/1.jpg)
Sampath Koppole
![Page 2: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/2.jpg)
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
![Page 3: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/3.jpg)
What is Continuum Electrostatics ?
A large molecule in a heterogeneous dielectric medium
+
=80
=1
+
+
+
+
![Page 4: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/4.jpg)
)()()()( 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)
![Page 5: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/5.jpg)
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:
![Page 6: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/6.jpg)
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.
![Page 7: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/7.jpg)
• 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.
![Page 8: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/8.jpg)
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:
![Page 9: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/9.jpg)
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 =
![Page 10: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/10.jpg)
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
![Page 11: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/11.jpg)
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
![Page 12: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/12.jpg)
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
![Page 13: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/13.jpg)
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:
![Page 14: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/14.jpg)
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.
![Page 15: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/15.jpg)
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:
![Page 16: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/16.jpg)
Summary:
Solvation Free Energy
Born Equation
Generalized Born Equation
Bottle necks in the equation.
Improving the accuracy of this method.
![Page 17: Sampath Koppole. Brief outline of the Talk: Summary Introduction to Continuum Electrostatics: Continuum Electrostatics --- What is it ?? Solvation free](https://reader033.vdocuments.site/reader033/viewer/2022052414/56649d0c5503460f949dfebb/html5/thumbnails/17.jpg)
Thanks…
… for your attention!