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 & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015) Ratkova, Palmer, and Fedorov, Chem. Rev. 115 , 6312 − 6356 (2005)
Binding free energy calculation Binding free energy: LRA: linear response approximation G PL G L G PL ′ � G L ′ � Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015)
Binding free energy calculation Binding free energy: LRA: linear response approximation Linear response Z 1 Z 1 d r ∂ E ( r , λ ) Z Z G = g ( r , λ ) = d r E ( r , 1) g ( r , λ ) d λ d λ ∂λ 0 0 Z 1 d r E ( r , 1) g ( r , 1) λ = 1 Z ⇡ 2 h E i λ =1 d λ 0 Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015)
Binding free energy calculation Binding free energy: LIE: linear interaction energy G ele+VdW G ele+VdW PL L G VdW G VdW PL L Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015)
Binding free energy calculation Binding free energy: LIE: linear interaction energy My understanding: Z 1 Z 1 d r ∂ E ( r , λ ) Z Z G = g ( r , λ ) = d r E ( r , 1) g ( r , λ ) d λ d λ ∂λ 0 0 Z 1 1 Z d r E ( r , 1) g ( r , 1) λ γ = ⇡ γ + 1 h E i λ =1 d λ 0 Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015)
MM/PBSA MM energy Solvation Free Energy Normal Mode Entropy PB or GB non-polar solute energy G np = γ A total + b G PL G P + G L G pol P L + G np ⇣ ⌘ ⇣ ⌘ G pol + G np G pol + G np + P L P P L L E MM − TS G ′ � G ′ � P + G ′ � PL L Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015) Barry Honig and Anthony Nicholls, Science 268 , 1144 (1995)
MM/PBSA Three-average MM/PBSA (3A-MM/PBSA): G PL G P + G L G pol P L + G np ⇣ ⌘ ⇣ ⌘ G pol + G np G pol + G np + P L P P L L E MM − TS G ′ � G ′ � P + G ′ � PL L Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015) Barry Honig and Anthony Nicholls, Science 268 , 1144 (1995)
MM/PBSA One-average MM/PBSA (1A-MM/PBSA): G PL G P + G L G pol P L + G np ⇣ ⌘ ⇣ ⌘ G pol + G np G pol + G np + P L P P L L E MM − TS G ′ � G ′ � P + G ′ � PL L Samuel Genheden & Ulf Ryde, Expert Opin Drug Discov. 10(5): 449–461 (2015) Barry Honig and Anthony Nicholls, Science 268 , 1144 (1995)
Poisson-Boltzmann theory MM energy Solvation Free Energy Normal Mode Entropy PB or GB non-polar solute energy G np = γ A total + b Poisson-Boltzmann equation: r · ε ( r ) · r q φ ( r ) � ε ( r ) κ ( r ) 2 sinh q φ ( r ) + 4 π q ρ ext ( r ) /kT = 0 q ρ e ( r ) = q 2 ρ + − q 2 ρ − = ρ ( r ) q 2 h e − q φ ( r ) − e q φ ( r ) i Barry Honig and Anthony Nicholls, Science 268 , 1144 (1995)
Generalized Born Model Based on Poisson-Boltzmann equation A different polar energy calculation: R i,j : Born radii ⇒ Donald Bashford & David A. Case, Annu. Rev. Phys. Chem. 51 :129–52 (2000)
Integration equation theory of liquid MM energy Solvation Free Energy Normal Mode Entropy Z 1 ⌧ ∂ U ( { r } , λ � ∆ G solv = d λ ∂λ 0 λ Z 1 d { r } g ( { r } , λ ) ∂ U ( { r } , λ Z = ) d λ ∂λ 0 Ratkova, Palmer, and Fedorov, Chem. Rev. 115 , 6312 − 6356 (2005)
Integration equation theory of liquid MM energy Solvation Free Energy Normal Mode Entropy Z 1 d { r } g ( { r } , λ ) ∂ U Coul ( { r } , λ ) Z ? d λ ∂λ 0 Z 1 d { r } g ( { r } , λ ) ∂ U LJ ( { r } , λ ) Z d λ ∂λ 0 Ratkova, Palmer, and Fedorov, Chem. Rev. 115 , 6312 − 6356 (2005)
Integration equation theory of liquid MM energy Solvation Free Energy Normal Mode Entropy Z � c s α ( r ) + 1 X ∆ G GF d 3 r solv = − 4 πρ k B T 2 c s α ( r ) h s α ( r ) s α ∆ G UC solv = ∆ G GF solv + α GF V + α GF ¯ 1 0 Z − h s α ( r ) 2 Θ ( − h s α ( r )) + c s α ( r ) + 1 � X ∆ G KH d 3 r solv = − 4 πρ k B T 2 c s α ( r ) h s α ( r ) 2 s α Z c np ∆ G CC solv = ∆ G KH solv + k B T (1 − γ ) 0 dV ✓ 1 ◆ − k B T ∆ G PC+ solv = ∆ G RISM ξ T k B T − ( N site − 2) ρ total v solv 2 Ratkova, Palmer, and Fedorov, Chem. Rev. 115 , 6312 − 6356 (2005)
Methods to incorporate solvation effect Poisson-Boltzmann based methods: R ρ i ( r i ) = e − q i φ ( r i ) − q i φ ji ( r j ) ρ j ( r j ) d r j ∆ G es = 1 Z ρ f ( r ) φ ( r ) d r 2 Integral Equation Theory of Liquids: R c ik ∗ δ h kj g ij = e − v ij + h ∂ V uv Z ∂λ i d λ ∆ G solv = Jesse J. Howard, Gillian C. Lynch, B. M. Pettitt, JPCB 114 , 7935–7941 (2010) � 15 F. Fogolari, A. Brigo and H. Molinari, J. Mol. Recognit. 15 , 377–392 (2002)
A benchmark 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. 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)
MM: Entropy-Enthalpy cancellation MM energy Solvation Free Energy Normal Mode Entropy Dor Ben-Amotz, Annu. Rev. Phys. Chem. 67 , 617 (2016)
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