Ion-Dipole Correction and CWBSol of Integration Equation Theory of Liquid Siqin CAO Department of Chemistry The Hong Kong University of Science and Technology May 25, 2020
Integration Equation Theory of Liquid with Ion-Dipole Correction
Solvation Water placement Fragment based drug design SZMAP WaterFLAP 3D-RISM WaterMap Denis Bucher, Pieter Stouten, Nicolas Triballeau, J. Chem. Inf. Model 58 , 692 − 699 (2018) Takashi Imai, Koji Oda, Andriy Kovalenko, Fumio Hirata, Akinori Kidera, JACS 131 , 12430–12440 (2009)
Integration Equation Theory of Liquid 3D-RISM RISM: reference interaction site model ρ (2) ij ( r i , r j ) = ρ i ρ j g ij ( r i , r j ) Two equations are enough c ik ( r ik ) * ( h kj ( r kj ) + s kj ( r kj ) ) h ij ( r ij ) = c ij ( r ij ) + ∑ k c ik ( r ik ) * ( h kj ( r kj ) + s kj ( r kj ) ) ≈ c ij ( r ij ) + ∑ k ln g ij = − v ij + h ij − c ij + B ij 10 3 faster than MD; Perfect if accurate water around 1d5q
Multibody issues of IET IET has issues for water around negative charge ions PLHNC MD (a) (b) (c) (d) 4 2 3 of ARG of LYS on 5TJ1 2 1 on 5TXD 1 NH + NH + 2 3 0 0 0 5 0 5 5TXD 5TJ1 r (Å) r (Å) g PLHNC ( r ) = { e − v γ ( r )+ h γ ( r ) − c ( r ) , ln g ≤ C 1 − v γ ( r ) + h γ ( r ) − c ( r ) − C + e C , ln g > C
Multibody issues of IET IET has issues for water around negative charge ions KH PSE2 PSE3 PLHNC MD 4 around 3 5TXD 2 Cl − 1 0 5TJ1 0 5 0 5 0 5 0 5 3 of GLU on 5TJ1 2 1 O − 0 5TXD 0 5 0 5 0 5 0 5 r (Å)
Multibody issues of IET Issue is related to multibody effect, but IET is single-body theory Water around a Water around a In IET, both are treated in positive charge group negative charge group mean-field way: ∫ c H ( r ′ H h HO ( | r ′ − r | ) d 3 r ′ ) ρ b = ℱ − 1 [ c H ( k ) h HO ( | k | )] 4 7 3 5 2 3 1 1 0 0 5 r (Å) 0 5 r (Å) Sketches from khanacademy.org
Hydrogen bond potential An example: hydrogen bond interaction H-bond was modeled with an explicit potential function, the General hydrogen bond function, in the last century: General hydrogen bond used to be available in AMBER [1] A. T. Hagler, S. Lifson, and P . Dauber, JACS 101 , 5122 (1979) [2] F . A. Momany, R. F . McGuire, A. W. Burgess, and . A. Scheraga, J. Phys. Chem. 79 , 2361 (1975) [3] Wendy D. Cornell, ..., Peter A. Kollman, JACS 117 , 5179 (1995) [4] Garret Vanderkool, J. Phys. Chem. 87 , 5121-5129 (1983) [5] Felcy Fabiola, Richard Bertram, Andrei Korostelev, and Michael S. Chapman, Protein Sci. 11 : 1415–1423 (2002) (DOI 10.1110/ps.4890102) Now, people believe H-Bond is resulted from electric interactions. Therefore: (1) H-bond interaction is short range; (2) The nature of H-bond interaction is electric interaction
Ion-Dipole Correction Ion-Dipole Correction (IDC): a potential function for multibody effect ln g O ( r ) = − ( v O ( r ) − Δ v IDC ( r ) ) + h O ( r ) − c O ( r ) + B O ( r ) O 4 πε 0 ⟨ ε r ( r H ) r α O ⟩ 1 α O ( r ) ≈ ⟨ p OH ⋅ E O ⟩ ≈ Q α q H Q α q H Δ v IDC − ε r ( r H ) r α H ε r ( r H ) = { ε r (water) ( r α H ≤ r α O ) ε r (surface) ( r α H > r α O ) b OH r α H = r α O ± b OH r α H r α O b OH = 0.954Å Implementation: v LJ α O ( r ) + Δ v IDC α O ( r ) → v new α O ( r )
Water distribution around ions IDC works for ions KH PSE2 PSE3 PLHNC MD Original 4 Cl − 3 2 1 0 0 5 0 5 0 5 0 5 With IDC 4 3 2 1 5TXD 0 0 5 0 5 0 5 0 5 r (Å)
Water distribution around strongly polar group of protein IDC works for negatively charged groups of protein KH PSE2 PSE3 (a) (b) PLHNC MD Original 3 2 1 GLU . O − 0 0 5 0 5 0 5 0 5 (c) With correction 3 2 1 0 0 5 0 5 0 5 0 5 5TJ1 r (Å)
Water distribution around strongly polar group of DNA IDC works for negatively charged backbone of DNA KH PSE2 PSE3 (a) (b) PLHNC MD Original 3 2 1 0 0 5 0 5 0 5 0 5 (c) With correction 3 DT . O − 2 1 0 0 5 0 5 0 5 0 5 6JCD r (Å)
Water distribution around a large protein: chaperon |------- Close -------| |------- Open -------| MD 3DRISM-KH 3DRISM-PSE2-IDC Ring 1 Ring 2 Ring 2 Ring 1 (a) (b) |----- Ring 1 ------||--------------- Ring 2 ---------------| 231ARG 230ILE 63GLU 65LYS 44PHE 2ALA 3 Open 2 Rings 1 0 0 5 0 5 0 5 0 5 0 5 0 5 63GLU 65LYS 44PHE 2ALA 255GLU 226LYS 3 Close 2 Rings 1 0 0 5 0 5 0 5 0 5 0 5 0 5 (c) (d) |----- Ring 1 ------||--------------- Ring 2 ---------------| 231ARG 230ILE 63GLU 65LYS 44PHE 2ALA 3 Open 2 Rings 1 0 0 5 0 5 0 5 0 5 0 5 0 5 255GLU 226LYS 63GLU 65LYS 44PHE 2ALA 3 Close 2 Rings 1 0 0 5 0 5 0 5 0 5 0 5 0 5 r (nm)
Free energy calculation Solvation free energy SFE in 1990s: the excessive chemical potential αγ ∫ [ − c αγ ( r ) − 1 2 c αγ ( r ) h αγ ( r ) + 1 Δ μ KH = ∑ 2 h αγ ( r ) 2 Θ ( − h αγ ( r )) ] ρ b γ d 3 r SFE in 2010s: the universal correction Δ μ S = Δ μ KH + aV + b SFE with IDC correction: Δ μ KH = ∫ d λ ⟨ ∂ λ ⟩ + ∫ d λ ⟨ ⟩ = ∫ d λ ⟨ ⟩ ∂ u IDC ∂ u uv ∂Δ u IDC ∂ λ ∂ λ Approximation: ∫ d λ ⟨ ⟩ ≈ LJ orig − LJ IDC ∂Δ u IDC 2 ∂ λ
Universal correction scheme 〇 Straightforward UC with PSE2-IDC ╳ 3DRISM-KH-GF-UC 〇 3DRISM-PSE2-UC with IDC 〇 3DRISM-KH-UC 10 10 0 0 IET (kcal/mol) IET (kcal/mol) -10 -10 -20 -20 -30 -30 -30 -20 -10 0 10 -30 -20 -10 0 10 FEP (kcal/mol) FEP (kcal/mol) MUE RMSE MUE RMSE r r kcal/mol kcal/mol GF-UC 0.9884 0.7 1.1 Straight 0.9705 1.8 2.5 KH-UC 0.9955 0.6 1.0 LR 0.9859 1.2 1.7 PSE2-UC 0.9950 0.6 1.0
Summary • 3DRISM-HNC is good for positively charged ionic solutes, but has deviations of solvation peaks around negatively charged solutes. • Ion-Dipole Correction will generate first solvation peaks at correct locations. • PSE2 is the recommended closure. • Solvation free energy functional needs to be investigated.
CWBSol: The Clear Water Bay Solvation Package
CWBSol CWBSol: a graphics interface php -S 127.0.0.1:8080 -t path_of_CWBSol to IET calculations Platforms: Server: Linux with PHP 5+ and GCC 4+ MacOS 10.9+ with PHP 5+ Windows with WSL or Cygwin Client: Chrome, FireFox, Safari, Edge (Internet Explorer not supported)
CWBSol: easy to install Only required: FFTW FFTW: one-click install CWBSol: one-click install Configuration: all options are listed with explanations
CWBSol: easy to run Options are listed, with default values One-click to see help message Everything stored on server Support: TOP PRMTOP PDB GRO XTC (need GROMACS enabled) And more...
CWBSol: easy to visualize RDF 3D distributions One-click to view (need ImageMagick and GNUPLOT)
CWBSol: an one-click tutorial Do calculation: Watch the calculation: See the results: If troubles encountered:
CWBSol: the efficiency MD AMBER RISMHI3D 10000 1000 E ffi ciency 100 10 1 5TXD 5TJ1 6JCD Chaperon Atom Number: 105 285 802 120715
Summary • CWBSol can efficiently perform IET. • Can run on laptop or a remote server. • Easy to install. No need to suffer from installing a lot of libraries. • Support the most common file formats: TOP and PRMTOP; PDB / GRO and XTC • Support all the closures that I can find on paper • Not yet 100% finished
Thank you
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