Implicit Solvation Method s for binding energy calculation PB, GB, - - PowerPoint PPT Presentation
Implicit Solvation Method s for binding energy calculation PB, GB, IET Siqin Cao April 1, 2019 Binding free energy calculation Binding free energy: Binding free energy and dissociation constant: G = RT ln K D RT ln c Samuel Genheden
April 1, 2019
Binding free energy calculation
Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015) Ratkova, Palmer, and Fedorov, Chem. Rev. 115, 6312−6356 (2005)
Binding free energy: Binding free energy and dissociation constant:
∆G = RT ln KD − RT ln c
Binding free energy calculation
Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015)
LRA: linear response approximation
GPL GPL′ GL GL′
Binding free energy:
Binding free energy calculation
Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015)
LRA: linear response approximation Linear response
G = Z 1 dλ Z dr∂E(r, λ) ∂λ g(r, λ) = Z 1 dλ Z drE(r, 1)g(r, λ) ⇡ Z 1 dλ Z drE(r, 1)g(r, 1)λ = 1 2hEiλ=1
Binding free energy:
Binding free energy calculation
Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015)
LIE: linear interaction energy
Gele+VdW
PL
GVdW
PL
Gele+VdW
L
GVdW
L
Binding free energy:
Binding free energy calculation
Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015)
LIE: linear interaction energy My understanding:
G = Z 1 dλ Z dr∂E(r, λ) ∂λ g(r, λ) = Z 1 dλ Z drE(r, 1)g(r, λ) ⇡ Z 1 dλ Z drE(r, 1)g(r, 1)λγ = 1 γ + 1hEiλ=1
Binding free energy:
MM/PBSA
Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015) Barry Honig and Anthony Nicholls, Science 268, 1144 (1995)
PB or GB non-polar solute energy Gnp = γAtotal + b
Solvation Free Energy MM energy Normal Mode Entropy
GPL G′
PL
GP + GL G′
P + G′ L
EMM − TS Gpol
P L + Gnp P L
⇣ Gpol
P
+ Gnp
P
⌘ + ⇣ Gpol
L
+ Gnp
L
⌘
MM/PBSA
Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015) Barry Honig and Anthony Nicholls, Science 268, 1144 (1995)
GPL G′
PL
GP + GL G′
P + G′ L
EMM − TS Gpol
P L + Gnp P L
⇣ Gpol
P
+ Gnp
P
⌘ + ⇣ Gpol
L
+ Gnp
L
⌘
Three-average MM/PBSA (3A-MM/PBSA):
MM/PBSA
Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015) Barry Honig and Anthony Nicholls, Science 268, 1144 (1995)
GPL G′
PL
GP + GL G′
P + G′ L
EMM − TS Gpol
P L + Gnp P L
⇣ Gpol
P
+ Gnp
P
⌘ + ⇣ Gpol
L
+ Gnp
L
⌘
One-average MM/PBSA (1A-MM/PBSA):
Poisson-Boltzmann theory
Barry Honig and Anthony Nicholls, Science 268, 1144 (1995)
PB or GB non-polar solute energy Gnp = γAtotal + b
Solvation Free Energy MM energy Normal Mode Entropy
Poisson-Boltzmann equation:
r · ε(r) · rqφ(r) ε(r)κ(r)2 sinh qφ(r) + 4πqρext(r)/kT = 0 qρe(r) = q2ρ+ − q2ρ− = ρ(r)q2 h e−qφ(r) − eqφ(r)i
Generalized Born Model
Donald Bashford & David A. Case, Annu. Rev. Phys. Chem. 51:129–52 (2000)
Based on Poisson-Boltzmann equation A different polar energy calculation:
⇒
Ri,j: Born radii
Integration equation theory of liquid
Ratkova, Palmer, and Fedorov, Chem. Rev. 115, 6312−6356 (2005)
Solvation Free Energy MM energy Normal Mode Entropy
∆Gsolv = Z 1 dλ ⌧∂U({r}, λ ∂λ
= Z 1 dλ Z d{r}g({r}, λ)∂U({r}, λ ∂λ )
Integration equation theory of liquid
Ratkova, Palmer, and Fedorov, Chem. Rev. 115, 6312−6356 (2005)
Solvation Free Energy MM energy Normal Mode Entropy
Z 1 dλ Z d{r}g({r}, λ)∂U Coul({r}, λ) ∂λ Z 1 dλ Z d{r}g({r}, λ)∂U LJ({r}, λ) ∂λ
?
Integration equation theory of liquid
Ratkova, Palmer, and Fedorov, Chem. Rev. 115, 6312−6356 (2005)
Solvation Free Energy MM energy Normal Mode Entropy
∆GKH
solv = −4πρkBT
X
sα
Z −hsα(r)2 2 Θ(−hsα(r)) + csα(r) + 1 2csα(r)hsα(r)
∆GGF
solv = −4πρkBT
X
sα
Z csα(r) + 1 2csα(r)hsα(r)
∆GUC
solv = ∆GGF solv + αGF 1
¯ V + αGF ∆GCC
solv = ∆GKH solv + kBT(1 − γ)
Z cnp
0 dV
∆GPC+
solv = ∆GRISM solv
− kBT 2 ✓ 1 ξT kBT − (Nsite − 2)ρtotal ◆ v
Methods to incorporate solvation effect
15
Jesse J. Howard, Gillian C. Lynch, B. M. Pettitt, JPCB 114, 7935–7941 (2010)
gij = e−vij+
R cik∗δhkj
∆Gsolv = Z h∂Vuv ∂λ idλ ρi(ri) = e−qiφ(ri)−qi
R φji(rj)ρj(rj)drj
∆Ges = 1 2 Z ρf(r)φ(r)dr
Poisson-Boltzmann based methods: Integral Equation Theory of Liquids:
A benchmark
Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015) Genheden S, Luchko T, Gusarov S, et al. JPCB 114: 8505-16 ( 2010)
Different implementations of RISM, MM/PBSA and MM/GBSA
Figure 2. Dependence of the MM/PBSA results on the continuum-solvation model for the binding of seven biotin analogues to avidin.
MM: Entropy-Enthalpy cancellation
Dor Ben-Amotz, Annu. Rev. Phys. Chem. 67, 617 (2016)
Solvation Free Energy MM energy Normal Mode Entropy