Ion-Dipole Correction and CWBSol of Integration Equation Theory of - - PowerPoint PPT Presentation

Ion-Dipole Correction and CWBSol

• f 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

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)

WaterFLAP 3D-RISM WaterMap Water placement Fragment based drug design SZMAP

Integration Equation Theory of Liquid

water around 1d5q

ρ(2)

ij (ri, rj) = ρiρjgij(ri, rj)

103 faster than MD; Perfect if accurate 3D-RISM RISM: reference interaction site model Two equations are enough

hij(rij) = cij(rij) + ∑

k

cik(rik) * (hkj(rkj) + skj(rkj)) ≈ cij(rij) + ∑

k

cik(rik) * (hkj(rkj) + skj(rkj)) ln gij = −vij+hij − cij+Bij

Multibody issues of IET

1 5 2 3 4 r (Å)

(a) (c) (d)

• f LYS
• n 5TXD

NH+

3

• f ARG
• n 5TJ1

NH+

2

1 2 5 r (Å)

PLHNC MD

(b)

5TXD 5TJ1

gPLHNC(r) = { e−vγ(r)+hγ(r)−c(r), ln g ≤ C 1 − vγ(r) + hγ(r) − c(r) − C + eC, ln g > C IET has issues for water around negative charge ions

Multibody issues of IET

r (Å) 5 1 2 3 5 5 5 4 1 2 3 5 5 5 5

around 5TXD

Cl−

• f GLU
• n 5TJ1

O−

5TXD 5TJ1

KH PSE2 PSE3 PLHNC MD

IET has issues for water around negative charge ions

Multibody issues of IET

Sketches from khanacademy.org

1 r (Å) 5 3 5 7 Water around a negative charge group 1 5 2 4 3 r (Å) Water around a positive charge group

Issue is related to multibody effect, but IET is single-body theory

In IET, both are treated in mean-field way: ∫ cH(r′ )ρb

HhHO(|r′ − r|)d3r′

= ℱ−1[cH(k)hHO(|k|)]

Hydrogen bond potential

H-bond was modeled with an explicit potential function, the General hydrogen bond function, in the last century:

[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)

General hydrogen bond used to be available in AMBER 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

An example: hydrogen bond interaction

Ion-Dipole Correction

ln gO(r) = − (vO(r) − ΔvIDC

O

(r)) + hO(r) − cO(r) + BO(r) ΔvIDC

αO (r) ≈ ⟨pOH ⋅ EO⟩ ≈

1 4πε0 ⟨ QαqH εr(rH)rαH − QαqH εr(rH)rαO⟩ rαH = rαO ± bOH bOH = 0.954Å

Implementation:

vLJ

αO(r) + ΔvIDC αO (r) → vnew αO (r)

εr(rH) = { εr(water) (rαH ≤ rαO) εr(surface) (rαH > rαO)

bOH rαH rαO

Ion-Dipole Correction (IDC): a potential function for multibody effect

Water distribution around ions

KH PSE2 PSE3 PLHNC MD

5TXD Original With IDC

r (Å) 1 2 3 5 5 5 5 1 2 3 5 5 5 5 4 4

Cl−

IDC works for ions

Water distribution around strongly polar group of protein

r (Å)

(b)

GLU . O−

1 2 3 5 5 5 5

(c)

1 2 3 KH PSE2 PSE3 5 5 5 5

Original With correction

PLHNC MD

(a)

5TJ1

IDC works for negatively charged groups of protein

Water distribution around strongly polar group of DNA

DT . O−

(b) (c)

Original With correction

r (Å) 1 2 3 5 5 5 5 1 2 3 5 5 5 5

6JCD

(a)

KH PSE2 PSE3 PLHNC MD

IDC works for negatively charged backbone of DNA

Water distribution around a large protein: chaperon

Ring 1 Ring 2 Ring 1 Ring 2 |------- Close -------| |------- Open -------|

5 5 5 5 5 5 5 5 5 5 5 5 1 2 3 1 2 3 5 5 5 5 5 5 5 5 5 5 5 5 1 2 3 1 2 3 Open Rings Close Rings Open Rings Close Rings |----- Ring 1 ------||--------------- Ring 2 ---------------| |----- Ring 1 ------||--------------- Ring 2 ---------------|

231ARG 230ILE 63GLU 65LYS 44PHE 2ALA 255GLU 226LYS 63GLU 65LYS 44PHE 2ALA 231ARG 230ILE 63GLU 65LYS 44PHE 2ALA 255GLU 226LYS 63GLU 65LYS 44PHE 2ALA

3DRISM-KH 3DRISM-PSE2-IDC MD

(a) (b) (c) (d)

r (nm)

Free energy calculation

Solvation free energy

ΔμKH = ∑

αγ ∫ [−cαγ(r) − 1

2 cαγ(r)hαγ(r) + 1 2 hαγ(r)2Θ(−hαγ(r))] ρb

γ d3r

ΔμS = ΔμKH + aV + b ΔμKH = ∫ dλ ⟨ ∂uIDC ∂λ ⟩ = ∫ dλ ⟨ ∂uuv ∂λ ⟩ + ∫ dλ ⟨ ∂ΔuIDC ∂λ ⟩

SFE in 1990s: the excessive chemical potential SFE in 2010s: the universal correction SFE with IDC correction: Approximation:

∫ dλ ⟨ ∂ΔuIDC ∂λ ⟩ ≈ LJorig − LJIDC 2

Universal correction scheme

• 30
• 20
• 10

10

• 20
• 10

10

• 30

FEP (kcal/mol) IET (kcal/mol)

〇 Straightforward UC with PSE2-IDC 〇 3DRISM-PSE2-UC with IDC

r MUE RMSE

kcal/mol

Straight 0.9705 1.8 2.5 LR 0.9859 1.2 1.7 r MUE RMSE

kcal/mol

GF-UC 0.9884 0.7 1.1 KH-UC 0.9955 0.6 1.0 PSE2-UC 0.9950 0.6 1.0

• 30
• 20
• 10

10

• 20
• 10

10

• 30

FEP (kcal/mol) IET (kcal/mol)

╳ 3DRISM-KH-GF-UC 〇 3DRISM-KH-UC

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

php -S 127.0.0.1:8080 -t path_of_CWBSol

CWBSol: a graphics interface 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 CWBSol: one-click install Configuration: all options are listed with explanations FFTW: one-click install

CWBSol: easy to run

Options are listed, with default values One-click to see help message Everything stored on server Support: PDB GRO XTC (need GROMACS enabled) TOP PRMTOP 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

5TXD 5TJ1 6JCD Chaperon MD AMBER RISMHI3D 1 100 10000

Efficiency 285 105 802 120715 Atom Number:

1000 10

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
• f 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