Transcript Computational Modeling of Macromolecular Systems Dr. GuanHua CHEN Department of Chemistry University of Hong Kong.

Computational Modeling of
Macromolecular Systems
Dr. GuanHua CHEN
Department of Chemistry
University of Hong Kong
Computational Chemistry
• Quantum Chemistry
SchrÖdinger Equation
H = E
• Molecular Mechanics
F = Ma
F : Force Field
Computational Chemistry Industry
Company
Gaussian Inc.
Schrödinger Inc.
Wavefunction
Q-Chem
Accelrys
HyperCube
Informatix
Celera Genomics
Software
Gaussian 94, Gaussian 98
Jaguar
Spartan
Q-Chem
InsightII, Cerius2
HyperChem
Applications: material discovery, drug design & research
R&D in Chemical & Pharmaceutical industries in 2000: US$ 80 billion
Bioinformatics: Total Sales in 2001
Project Sales in 2006
US$ 225 million
US$ 1.7 billion
Cytochrome c (involved in the ATP synthesis)
heme
1997 Nobel Prize
in Biology:
ATP Synthase in
Mitochondria
Cytochrome c is a peripheral membrane protein
involved in the long distance electron transfers
Simulation of a pair of polypeptides
Duration: 100 ps. Time step: 1 ps (Ng, Yokojima & Chen, 2000)
Protein Dynamics
1. Atomic Fluctuations
10-15 to 10-11 s; 0.01 to 1 Ao
2. Collective Motions
10-12 to 10-3 s; 0.01 to >5 Ao
3. Conformational Changes
o
-9
3
10 to 10 s; 0.5 to >10 A
Theoretician leaded the way ! (Karplus at Harvard U.)
Quantum Chemistry Methods
• Ab initio Molecular Orbital Methods
Hartree-Fock, Configurationa Interaction (CI)
MP Perturbation, Coupled-Cluster, CASSCF
• Density Functional Theory
• Semiempirical Molecular Orbital
Methods
Huckel, PPP, CNDO, INDO, MNDO, AM1
PM3, CNDO/S, INDO/S
SchrÖdinger Equation
H=E
Wavefunction
Hamiltonian
H = (-h2/2m)2 - (h2/2me)ii2
- i  Ze2/ri (+  ZZe2/r )
+ i j e2/rij
Energy
One-electron terms:
(-h2/2m)2 - (h2/2me)ii2 - i  Ze2/ri
Two-electron term:
i j e2/rij
Hartree-Fock Method
Orbitals
1. Hartree-Fock Equation
F fi = ei fi
F Fock operator
fi the i-th Hartree-Fock orbital
ei the energy of the i-th Hartree-Fock orbital
2. Roothaan Method (introduction of Basis functions)
fi = k cki k LCAO-MO
{ k } is a set of atomic orbitals (or basis functions)
3. Hartree-Fock-Roothaan equation
j ( Fij - ei Sij ) cji = 0
Fij  < i|F | j >
Sij  < i| j >
4. Solve the Hartree-Fock-Roothaan equation
self-consistently (HFSCF)
Graphic Representation of Hartree-Fock Solution
0 eV
Ionization
Energy
Electron
Affinity
A Gaussian Input File for H2O
# HF/6-31G(d)
Route section
water energy
Title
0
O
H
H
Molecule Specification
(in Cartesian coordinates
1
-0.464 0.177 0.0
-0.464 1.137 0.0
0.441 -0.143 0.0
Basis Set fi = p cip p
{ k } is a set of atomic orbitals (or basis functions)
STO-3G, 3-21G, 4-31G, 6-31G, 6-31G*, 6-31G**
-------------------------------------------------------------------------------------
complexity & accuracy
Gaussian type functions
gijk = N xi yj zk exp(-r2)
(primitive Gaussian function)
p = u dup gu
(contracted Gaussian-type function, CGTF)
u = {ijk}
p = {nlm}
STO-3G Basis Set
Atom
H
Shell
1S
C
1S
2S
2P
N
1S
2S
2P
O
1S
2S
2P
3.
6.
1.
7.
1.
3.
2.
6.
2.
2.
6.
2.
9.
1.
4.
3.
8.
2.
3.
8.
2.
1.
2.
6.
5.
1.
3.
5.
1.
3.
Exponents
425250914E+00
239137298E- 01
688554040E- 01
161683735E+01
304509632E+01
530512160E+00
941249355E+00
834830964E- 01
222899159E- 01
941249355E+00
834830964E- 01
222899159E- 01
910616896E+01
805231239E+01
885660238E+00
780455879E+00
784966449E- 01
857143744E- 01
780455879E+00
784966449E- 01
857143744E- 01
307093214E+02
380886605E+01
443608313E+00
033151319E+00
169596125E+00
803889600E- 01
033151319E+00
169596125E+00
803889600E- 01
Coefficients
1. 543289673E- 01
5. 353281423E- 01
4. 446345422E- 01
1. 543289673E- 01
5. 353281423E- 01
4. 446345422E- 01
- 9. 996722919E- 02
3. 995128261E- 01
7. 001154689E- 01
1. 559162750E- 01
6. 076837186E- 01
3. 919573931E- 01
1. 543289673E- 01
5. 353281423E- 01
4. 446345422E- 01
- 9. 996722919E- 02
3. 995128261E- 01
7. 001154689E- 01
1. 559162750E- 01
6. 076837186E- 01
3. 919573931E- 01
1. 543289673E- 01
5. 353281423E- 01
4. 446345422E- 01
- 9. 996722919E- 02
3. 995128261E- 01
7. 001154689E- 01
1. 559162750E- 01
6. 076837186E- 01
3. 919573931E- 01
3-21G Basis Set
Atom
H
Shell
1S
C
1S'
1S
2S
2P
N
2S'
2P'
1S
2S
2P
O
2S'
2P'
1S
2S
2P
2S'
2P'
5.
8.
1.
1.
2.
5.
3.
7.
3.
7.
1.
1.
2.
3.
7.
5.
1.
5.
1.
2.
2.
3.
4.
1.
7.
1.
7.
1.
3.
3.
Exponents
447178000E+00
245472400E- 01
831915800E- 01
722560000E+02
591090000E+01
533350000E+00
664980000E+00
705450000E- 01
664980000E+00
705450000E- 01
958570000E- 01
958570000E- 01
427660000E+02
648510000E+01
814490000E+00
425220000E+00
149150000E+00
425220000E+00
149150000E+00
832050000E- 01
832050000E- 01
220370000E+02
843080000E+01
042060000E+01
402940000E+00
576200000E+00
402940000E+00
576200000E+00
736840000E- 01
736840000E- 01
Coefficients
1. 562850000E- 01
9. 046910000E- 01
1. 000000000E+00
6. 176690000E- 02
3. 587940000E- 01
7. 007130000E- 01
- 3. 958970000E- 01
1. 215840000E+00
2. 364600000E- 01
8. 606190000E- 01
1. 000000000E+00
1. 000000000E+00
5. 986570000E- 02
3. 529550000E- 01
7. 065130000E- 01
- 4. 133010000E- 01
1. 224420000E+00
- 4. 133010000E- 01
1. 224420000E+00
1. 000000000E+00
1. 000000000E+00
5. 923940000E- 02
3. 515000000E- 01
7. 076580000E- 01
- 4. 044530000E- 01
1. 221560000E+00
2. 445860000E- 01
8. 539550000E- 01
1. 000000000E+00
1. 000000000E+00
6-31G Basis Set
Atom
H
C
Shell
1S
1S'
1S
2S
2P
N
2S'
2P'
1S
2S
2P
O
2S'
2P'
1S
2S
2P
2S'
2P'
1.
2.
6.
1.
3.
4.
1.
2.
9.
3.
7.
1.
5.
7.
1.
5.
1.
1.
4.
6.
1.
4.
1.
4.
1.
2.
7.
1.
2.
7.
2.
2.
5.
8.
1.
5.
1.
5.
1.
3.
1.
1.
3.
1.
2.
2.
Exponents
8 7 3 1 1 3 6 9 6 E+0 1
8 2 5 3 9 4 3 6 5 E+0 0
4 0 1 2 1 6 9 2 3 E- 0 1
6 1 2 7 7 7 5 8 8 E- 0 1
0 4 7 5 2 4 8 8 0 E+0 3
5 7 3 6 9 5 1 8 0 E+0 2
0 3 9 4 8 6 8 5 0 E+0 2
9 2 1 0 1 5 5 3 0 E+0 1
2 8 6 6 6 2 9 6 0 E+0 0
1 6 3 9 2 6 9 6 0 E+0 0
8 6 8 2 7 2 3 5 0 E+0 0
8 8 1 2 8 8 5 4 0 E+0 0
4 4 2 4 9 2 5 8 0 E- 0 1
8 6 8 2 7 2 3 5 0 E+0 0
8 8 1 2 8 8 5 4 0 E+0 0
4 4 2 4 9 2 5 8 0 E- 0 1
6 8 7 1 4 4 7 8 2 E- 0 1
6 8 7 1 4 4 7 8 2 E- 0 1
1 7 3 5 1 1 4 6 0 E+0 3
2 7 4 5 7 9 1 1 0 E+0 2
4 2 9 0 2 0 9 3 0 E+0 2
0 2 3 4 3 2 9 3 0 E+0 1
2 8 2 0 2 1 2 9 0 E+0 1
3 9 0 4 3 7 0 1 0 E+0 0
1 6 2 6 3 6 1 8 6 E+0 1
7 1 6 2 7 9 8 0 7 E+0 0
7 2 2 1 8 3 9 6 6 E- 0 1
1 6 2 6 3 6 1 8 6 E+0 1
7 1 6 2 7 9 8 0 7 E+0 0
7 2 2 1 8 3 9 6 6 E- 0 1
1 2 0 3 1 4 9 7 5 E- 0 1
1 2 0 3 1 4 9 7 5 E- 0 1
4 8 4 6 1 6 6 0 0 E+0 3
2 5 2 3 4 9 4 6 0 E+0 2
8 8 0 4 6 9 5 8 0 E+0 2
2 9 6 4 5 0 0 0 0 E+0 1
6 8 9 7 5 7 0 4 0 E+0 1
7 9 9 6 3 5 3 4 0 E+0 0
5 5 3 9 6 1 6 2 5 E+0 1
5 9 9 9 3 3 5 8 6 E+0 0
0 1 3 7 6 1 7 5 0 E+0 0
5 5 3 9 6 1 6 2 5 E+0 1
5 9 9 9 3 3 5 8 6 E+0 0
0 1 3 7 6 1 7 5 0 E+0 0
7 0 0 0 5 8 2 2 6 E- 0 1
7 0 0 0 5 8 2 2 6 E- 0 1
Coefficients
3 . 3 4 9 4 6 0 4 3 4 E- 0 2
2 . 3 4 7 2 6 9 5 3 5 E- 0 1
8 . 1 3 7 5 7 3 2 6 2 E- 0 1
1 . 0 0 0 0 0 0 0 0 0 E+0 0
1 . 8 3 4 7 3 7 1 3 0 E- 0 3
1 . 4 0 3 7 3 2 2 8 0 E- 0 2
6 . 8 8 4 2 6 2 2 2 0 E- 0 2
2 . 3 2 1 8 4 4 4 3 0 E- 0 1
4 . 6 7 9 4 1 3 4 8 0 E- 0 1
3 . 6 2 3 1 1 9 8 5 0 E- 0 1
- 1 . 1 9 3 3 2 4 2 0 0 E- 0 1
- 1 . 6 0 8 5 4 1 5 2 0 E- 0 1
1 . 1 4 3 4 5 6 4 4 0 E- 0 1
6 . 8 9 9 9 0 6 6 6 0 E- 0 2
3 . 1 6 4 2 3 9 6 1 0 E- 0 1
7 . 4 4 3 0 8 2 9 1 0 E- 0 1
1 . 0 0 0 0 0 0 0 0 0 E+0 0
1 . 0 0 0 0 0 0 0 0 0 E+0 0
1 . 8 3 4 7 7 2 1 6 0 E- 0 3
1 . 3 9 9 4 6 2 7 0 0 E- 0 2
6 . 8 5 8 6 5 5 1 8 0 E- 0 2
2 . 3 2 2 4 0 8 7 3 0 E- 0 1
4 . 6 9 0 6 9 9 4 8 0 E- 0 1
3 . 6 0 4 5 5 1 9 9 0 E- 0 1
- 1 . 1 4 9 6 1 1 8 2 0 E- 0 1
- 1 . 6 9 1 1 7 4 7 9 0 E- 0 1
1 . 1 4 5 8 5 1 9 5 0 E+0 0
6 . 7 5 7 9 7 4 3 9 0 E- 0 2
3 . 2 3 9 0 7 2 9 6 0 E- 0 1
7 . 4 0 8 9 5 1 4 0 0 E- 0 1
1 . 0 0 0 0 0 0 0 0 0 E+0 0
1 . 0 0 0 0 0 0 0 0 0 E+0 0
1 . 8 3 1 0 7 4 4 3 0 E- 0 3
1 . 3 9 5 0 1 7 2 2 0 E- 0 2
6 . 8 4 4 5 0 7 8 1 0 E- 0 2
2 . 3 2 7 1 4 3 3 6 0 E- 0 1
4 . 7 0 1 9 2 8 9 8 0 E- 0 1
3 . 5 8 5 2 0 8 5 3 0 E- 0 1
- 1 . 1 0 7 7 7 5 4 9 0 E- 0 1
- 1 . 4 8 0 2 6 2 6 2 0 E- 0 1
1 . 1 3 0 7 6 7 0 1 0 E+0 0
7 . 0 8 7 4 2 6 8 2 0 E- 0 2
3 . 3 9 7 5 2 8 3 9 0 E- 0 1
7 . 2 7 1 5 8 5 7 7 0 E- 0 1
1 . 0 0 0 0 0 0 0 0 0 E+0 0
1 . 0 0 0 0 0 0 0 0 0 E+0 0
Electron Correlation:
avoiding each other
The reason of the instantaneous correlation:
Coulomb repulsion (not included in the HF)
Beyond the Hartree-Fock
Configuration Interaction (CI)
Perturbation theory
Coupled Cluster Method
Density functional theory
Configuration Interaction (CI)
+
+ …
Single Electron Excitation or Singly Excited
Double Electrons Excitation or Doubly Excited
Singly Excited Configuration Interaction (CIS):
Changes only the excited states
+
Doubly Excited CI (CID):
Changes ground & excited states
+
Singly & Doubly Excited CI (CISD):
Most Used CI Method
Full CI (FCI):
Changes ground & excited states
+
+ ...
+
Perturbation Theory
H = H0 + H’
H0n(0) = En(0) n(0)
n(0) is an eigenstate for unperturbed system
H’ is small compared with H0
Moller-Plesset (MP) Perturbation Theory
The MP unperturbed Hamiltonian H0
H0 = m F(m)
where F(m) is the Fock operator for electron m.
And thus, the perturbation H’
H’ = H - H0
Therefore, the unperturbed wave function is
simply the Hartree-Fock wave function .
Ab initio methods: MP2, MP4
Coupled-Cluster Method
 = eT (0)
(0): Hartree-Fock ground state wave function
: Ground state wave function
T = T1 + T2 + T3 + T4 + T5 + …
Tn : n electron excitation operator
T1
=
Coupled-Cluster Doubles (CCD) Method
CCD = eT (0)
2
(0): Hartree-Fock ground state wave function
CCD: Ground state wave function
T2 : two electron excitation operator
T2
=
Complete Active Space SCF (CASSCF)
Active space
All possible configurations
Density-Functional Theory (DFT)
Hohenberg-Kohn Theorem: Phys. Rev. 136, B864 (1964)
The ground state electronic density (r) determines
uniquely all possible properties of an electronic system
(r)  Properties P (e.g. conductance), i.e. P  P[(r)]
Density-Functional Theory (DFT)
E0 = - (h2/2me)i <i |i2 |i >-   dr Ze2(r) / r1
+ (1/2)   dr1 dr2 e2/r12 + Exc[(r)]
Kohn-Sham Equation Ground State: Phys. Rev. 140, A1133 (1965)
FKS i = ei i
FKS  - (h2/2me)ii2 -  Ze2 / r1 + j Jj + Vxc
Vxc  dExc[(r)] / d(r)
A popular exchange-correlation functional Exc[(r)]: B3LYP
Ground State Excited State CPU Time Correlation Geometry Size Consistent
(CHNH,6-31G*)
HFSCF


1
0
OK

DFT


~1


CIS


<10
OK

CISD


17


CISDTQ




MP2


1.5
MP4


CCD

CCSDT

80-90%
(20 electrons)
very large 98-99%


5.8
85-95%
(DZ+P)
>90%



large
>90%



very large
~100%


Four Sources of error in ab initio Calculation
(1) Neglect or incomplete treatment of electron correlation
(2) Incompleteness of the Basis set
How to simulate large molecules?
Quantum Chemistry for
Complex Systems
Semiempirical Molecular Orbital Calculation
Extended Huckel MO Method
(Wolfsberg, Helmholz, Hoffman)
Independent electron approximation
Hval = i Heff(i)
Heff(i) = -(h2/2m) i2 + Veff(i)
Schrodinger equation for electron i
Heff(i) fi = ei fi
LCAO-MO:
fi = r cri r
s ( Heffrs - ei Srs ) csi = 0
Heffrs  < r| Heff | s >
Srs  < r| s >
Parametrization:
Heffrr  < r| Heff | r >
= minus the valence-state ionization
potential (VISP)
-----------------------------------------------------------------------
Atomic Orbital Energy
e5
e4
e3
e2
e1
Heffrs = ½ K (Heffrr + Heffss) Srs
VISP
-e5
-e4
-e3
-e2
-e1
K:
13
CNDO, INDO, NDDO
(Pople and co-workers)
Hamiltonian with effective potentials
Hval = i [ -(h2/2m) i2 + Veff(i) ] + ij>i e2 / rij
two-electron integral:
(rs|tu) = <r(1) t(2)| 1/r12 | s(1) u(2)>
CNDO: complete neglect of differential overlap
(rs|tu) = drs dtu (rr|tt)  drs dtu rt
INDO: intermediate neglect of differential overlap
(rs|tu) = 0 when r, s, t and u are not on the same atom.
NDDO: neglect of diatomic differential overlap
(rs|tu) = 0 if r and s (or t and u) are not on the
same atom.
CNDO, INDO are parametrized so that the overall
results fit well with the results of minimal basis ab
initio Hartree-Fock calculation.
CNDO/S, INDO/S are parametrized to predict
optical spectra.
MINDO, MNDO, AM1, PM3
(Dewar and co-workers, University of Texas,
Austin)
MINDO: modified INDO
MNDO: modified neglect of diatomic overlap
AM1: Austin Model 1
PM3: MNDO parametric method 3
*based on INDO & NDDO
*reproduce the binding energy
Linear Scaling Quantum
Mechanical Methods
Ground State: ab initio Hartree-Fock calculation
Computational Time: protein w/ 10,000 atoms
ab initio Hartree-Fock ground state calculation:
~20,000 years on CRAY YMP
In 2010:
~24 months on 100 processor machine
One Problem:
Transitor with a few atoms
Current Computer Technology will fail !
Quantum Chemist’s Solution
Linear-Scaling Method: O(N)
Computational time scales linearly with system size
Time
Size
Linear Scaling Calculation for Ground State
Divide-and-Conqure (DAC)
W. Yang, Phys. Rev. Lett. 1991
Linear Scaling Calculation for Ground State
Yang, Phys. Rev. Lett. 1991
Li, Nunes & Vanderbilt, Phy. Rev. B. 1993
Baroni & Giannozzi, Europhys. Lett. 1992.
Gibson, Haydock & LaFemina, Phys. Rev. B 1993.
Aoki, Phys. Rev. Lett. 1993.
Cortona, Phys. Rev. B 1991.
Galli & Parrinello, Phys. Rev. Lett. 1992.
Mauri, Galli & Car, Phys. Rev. B 1993.
Ordejón et. al., Phys. Rev. B 1993.
Drabold & Sankey, Phys. Rev. Lett. 1993.
York, Lee & Yang, JACS, 1996
Superoxide Dismutase (4380 atoms) AM1
Strain, Scuseria & Frisch, Science (1996):
LSDA / 3-21G DFT calculation on 1026 atom
RNA Fragment
Carbon Nanotube
Chirality: (m, n)
Smalley et. al., Nature (1998)
Quantum mechanical investigation of the field
emission from the tips of carbon nanotubes
Experimental Results
Elocal
 =
E applied
J-M. Bonard et al., Phys. Rev. Lett. 89 19 (2002)
F-N theory breaks down
For strong CNT emission
Field Emission Basics
Classical Model :
Laplace’s Equation:

 V (r ) = 0
2
Boundary Conditions:
V(anode)
= Va
V(cathode-tube) = 0
Single nanotube model outline
Quantum Model
Boundary conditions:
V(anode) = Va V(cathode) = 0
Problems:
1. 100,000 atoms
2. Boundary Condition: OPEN SYSTEM!
3. Number of electrons transferred to CNT
Boundary Condition
Mirror image of charges
(5,5)
Charge distributions before & after external field
Potential energy contour plot for SWNT (5,5)
under a 14 V/μm applied field
Potential energy contour plot in the vicinity of cap under a 14 V/µm applied field
Equipotential line corresponding to the Fermi energy (-4.5 eV) is presented
Potential energy distributions along the central axis of entire tube
A layer of atoms is sufficient to shield most of external field!
Penetration does occur at the tip !
Eappl
Barrier height
0
10 V/mm
14 V/mm
4.5 eV
3.0 eV
2.0 eV
Effective enhancement factor :
500 for Eappl = 10 V/mm
1200 for Eappl = 14 V/mm
Calculated emission currents:
0.34 pA for Eapply = 10 V/mm
0.20 µA for Eapply = 14 V/mm
Experiment [Zettl et. al., PRL 88, 56804 (2002)]:
A Multi-Walled CNT:
0.40 pA for Eapply = 11.7 V/mm
0.54 µA for Eapply = 20.0 V/mm
The multi-walled CNT is of same potential !!!
Experiment
Simulation
Linear Scaling Calculation for
EXCITED STATE ?
A Much More Difficult Problem !
Linear-Scaling Calculation for excited states
Localized-Density-Matrix (LDM) Method
(0)

=
+ d
E(t)
(0)
ij = 0
rij > r0
dij = 0
rij > r1
Yokojima & Chen, Phys. Rev. B, 1999
Principle of the nearsightedness of
equilibrium systems (Kohn, 1996)
Heisenberg Equation of Motion

i  = H ,  
Time-Dependent Hartree-Fock
Random Phase Approximation
CH
Polyacetylene
4
2
8
6
10
CH
N
2
N
N-2
12
...
1
3
5
7
9
11
N-3
PPP Semiempirical Hamitonian
Hˆ = Hˆ Huckel + Hˆ c + Hˆ ext
N-1
Linear Scaling Calculation for Excited State
Liang, Yokojima & Chen, JPC, 2000
Flat Panel Display
Cambridge Display Technology
Weight: 15 gram
Resolution: 800x236
Size:
45x37 mm
Voltage:
DC, 10V
Intensity
electron
hole
Energy
Application of O(N) method for excited states
Low-Lying Excited States of Light
Harvesting System II in Purple Bacteria
1.
Ng, Zhao and Chen, J. Phys. Chem. B 107, 9589 (2003)
“
Photo-excitations in Light Harvesting System II
strong absorption: ~800 nm
generated by VMD
generated by VMD
Frenkel Exciton Model:
H= nJnBn+Bn+ nnJnmBm+Bn
Wi , j
 
   
 d i  d j 3(rij  d i )( rij  d j ) 

= C
3
5
 r

rij
 ij

generated by VMD
B800 ring: strong absorption
@ 800nm
B850 ring: strong absorption @ 850nm
W
2α
~8.9Å
1β
~9.2Å
J1
1α
J
Two issues:
1. Is the Frenkel exciton model a good description of
the low-lying excitations in LH2?
does the electron-hole pair span one B-chlorophyll at a time?
values of J1 & J2
2. What is the energy transfer mechanism on B850?
Energy transfer mechanisms:
1. Förster Incoherent hopping (Markovian) process; (small polaron)
2. Coherent exciton migration. (large polaron)
The size of electron-hole pair is determined by the ratio of
the n.n. coupling constant vs. the disorder in energy
Static energy disorder:
Dynamic disorder:
n.n. coupling << disorder:
n.n. coupling >> disorder:
200 ~ 500 cm-1
~200 cm-1
localized (Förster Incoherent hopping)
delocalized (Coherent exciton transfer)
Calculated Parameters by others (Zerner, Fleming, Mukamel & etc.)
INDO/S-CEO (a)
2
4 J nm
= e 2 -  2
PDA with (b)
INDO/S-CIS
(c)
J1 / cm-1
408
339
790
J2 / cm-1
366
336
369
(a)
(b)
(c)
Tretiak, S.; Chernyak, V.; Mukamel, S. J. Phys. Chem., 104 9540, 2000
Pullerits, T.; Sundstrom, V.; van Grondelle, R. J. Phys. Chem. 1999, 103, 2327
Cory, M. G.; Zerner, M.C.; Hu, X.; Schulten, X. K.; J. Phys. Chem. B 1998, 102, 7640
Our task: what are J1 & J2 ?
Cory, M. G.; Zerner, M.C.; Hu, X.; Schulten, X. K.;
J. Phys. Chem. B 1998, 102, 7640
Photo-excitations in Light Harvesting System II
736 atoms
P3 / 700 MHz
500 MB RAM
Distorted field
+ +
+
+
+
+
+ +
K= +/-/8
+
- -
+
+ +
K=0,+/-/4,+/-/2, +/-3/4
+
-+- +
-
+
-
+
-
+ - + -
+
K = +/-7/8
COS(/2·n) & COS(7/8·n): K = +/-3/8, +/-5/8 & K = , respectively
k=8
k=7
k=6
k=5
k=4
k=3
k=2
k=1
k=0
CIS (Zerner et. al.)
LDM
The B850 energies (eV) calculated by LDM
B850
0.926
0.980
1.056
1.114
1.132
1.178
1.198
1.220
1.230
1.237
 Doubly degenerate
Calculated parameters in Frenkel excition model (least square fitting)
/ cm-1
J1
J2
e1
e2
Dimer#
528
455
9421
9292
B850
593
490
9117
9117
640725
118
Zerner
790
369
13242
13242
506000
260
C*
150
*transition dipole of monomer = 2.326 e·A: C = 639765 cm-1
Wi , j
rms
 
   
 d i  d j 3(rij  d i )( rij  d j ) 

= C
3
5
 r

rij
 ij

Solvation Correction
J1 ~ 445 cm-1
J2 ~ 367 cm-1
Static disorder:
200 ~ 500 cm-1
Dynamic disorder: ~200 cm-1
Fast Multiple Method
LDM-TDDFT: CnH2n+2
LODESTAR: Software Package for Complex Systems
Characteristics：
O(N) Divide-and-Conquer
O(N) TDHF (ab initio & semiemptical)
O(N) TDDFT
Nonlinear Optical Light Harvesting System
CNDO/S-, PM3-, AM1-, INDO/S-, & TDDFT-LDM
Quantum Mechanics / Molecular
Mechanics (QM/MM) Method
Combining quantum mechanics and
molecular mechanics methods:
QM
MM
Hamiltonian of entire system:
H = HQM +HMM +HQM/MM
Energy of entire system:
E = EQM(QM) + EMM(MM) + EQM/MM(QM/MM)
EQM/MM(QM/MM) = Eelec(QM/MM) + Evdw(MM) + EMM-bond(MM)
EQM(QM) + Eelec(QM/MM) = <| Heff |>
Heff = -1/2 ii2 + ij 1/rij - i Z/ri - i q/ri
+ i Vv-b(ri) + d Z Zd/rd +  Zq/r
QM
MM
Molecular Mechanics Force Field
•
•
•
•
Bond Stretching Term
Bond Angle Term
Torsional Term
Electrostatic Term
• van der Waals interaction
Molecular Mechanics
F = Ma
F : Force Field
Bond Stretching Potential
Eb = 1/2 kb (l)2
where, kb : stretch force constant
l : difference between equilibrium
& actual bond length
Two-body interaction
Bond Angle Deformation Potential
Ea = 1/2 ka ()2
where, ka : angle force constant
 : difference between equilibrium
& actual bond angle

Three-body interaction
Periodic Torsional Barrier Potential
Et = (V/2) (1+ cosn )
where, V : rotational barrier
 : torsion angle
n : rotational degeneracy
Four-body interaction
Non-bonding interaction
van der Waals interaction
for pairs of non-bonded atoms
Coulomb potential
for all pairs of charged atoms
Force Field Types
•
•
•
•
•
MM2
AMBER
CHAMM
BIO
OPLS
Molecules
Polymers
Polymers
Polymers
Solvent Effects
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
#############################
##
##
## Atom Type Definitions ##
##
##
#############################
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
C
C
C
C
H
O
O
N
N
N
F
Cl
Br
I
S
S+
S
S
Si
Lp
MM2 Force Field
"CSP3 ALKANE"
"CSP2 ALKENE"
"CSP2 CARBONYL"
"CSP ALKYNE, C=C=O"
"NONPOLAR HYDROGEN"
"-O- ALCOHOL, ETHER"
"=O CARBONYL"
"NSP3"
"NSP2 AMIDE"
"NSP"
"FLUORIDE"
"CHLORIDE"
"BROMIDE"
"IODIDE"
"-S- SULFIDE"
">S+ SULFONIUM"
">S=O SULFOXIDE"
">SO2 SULFONE"
"SILANE"
"LONE PAIR"
6
6
6
6
1
8
8
7
7
7
9
17
35
53
16
16
16
16
14
0
12.000
12.000
12.000
12.000
1.008
15.995
15.995
14.003
14.003
14.003
18.998
34.969
78.918
126.900
31.972
31.972
31.972
31.972
27.977
0.000
4
3
3
2
1
4
1
4
3
1
1
1
1
1
2
2
3
4
4
1
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
H
C
H
H
P
B
B
H
C*
C+
Ge
Sn
Pb
Se
Te
D
N
C
N+
N
O
S
N
H
N
N
O
H
"-OH ALCOHOL"
"CYCLOPROPANE"
"NH AMINE"
"COOH CARBOXYL"
">P- PHOSPHINE"
">B- TRIGONAL"
">B< TETRAHEDRAL"
"-H AMIDE, ENOL"
"CARBON RADICAL"
"CARBONIUM ION"
"GERMANIUM"
"TIN"
"LEAD (IV)"
"SELENIUM"
"TELLURIUM"
"DEUTERIUM"
"-N= AZO,PYRIDINE"
"CSP2 CYCLOPROPENE"
"NSP3 AMMONIUM"
"NSP2 PYRROLE"
"OSP2 FURAN"
"SSP2 THIOPHENE"
"-N=N-O AZOXY"
"-SH THIOL"
"AZIDE (CENTER-N)"
"NO2 NITRO"
"CARBOXYLATE"
"AMMONIUM"
1
6
1
1
15
5
5
1
6
6
32
50
82
34
52
1
7
6
7
7
8
16
7
1
7
7
8
1
1.008
12.000
1.008
1.008
30.994
11.009
11.009
1.008
12.000
12.000
73.922
117.902
207.977
79.917
129.907
2.014
14.003
12.000
14.003
14.003
15.995
31.972
14.003
1.008
14.003
14.003
15.995
1.008
1
4
1
1
3
3
4
1
3
3
2
2
4
2
2
1
3
3
4
3
3
2
2
1
2
3
1
1
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
49
50
51
52
53
54
55
59
60
61
62
63
64
65
66
69
70
71
72
73
74
75
O
C
He
Ne
Ar
Kr
Xe
Mg
P
Fe
Fe
Ni
Ni
Co
Co
O
O
C
N
N+
N+
N
"EPOXY"
"BENZENE"
"HELIUM"
"NEON"
"ARGON"
"KRYPTON"
"XENON"
"MAGNESIUM"
"PHOSPHORUS (V)"
"IRON (II)"
"IRON (III)"
"NICKEL (II)"
"NICKEL (III)"
"COBALT (II)"
"COBALT (III)"
"AMINE OXIDE"
"KETONIUM OXYGEN"
"KETONIUM CARBON"
"=N- IMINE, OXIME"
"=N(+)- PYRIDINIUM"
"=N(+)- IMMINIUM"
"N-OH OXIME"
8
6
2
10
18
36
54
12
15
26
26
27
27
28
28
8
8
6
7
7
7
7
15.995
12.000
4.003
20.179
39.948
83.800
131.300
24.301
30.994
55.847
55.847
58.710
58.710
58.933
58.933
15.995
15.995
12.000
14.003
14.003
14.003
14.003
4
3
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
2
3
3
3
3
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
################################
##
##
## Van der Waals Parameters ##
##
##
################################
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1.900
1.940
1.940
1.940
1.500
1.740
1.740
1.820
1.820
1.820
1.650
2.030
2.180
2.320
2.110
2.110
2.110
2.110
2.250
1.200
0.044
0.044
0.044
0.044
0.047
0.050
0.066
0.055
0.055
0.055
0.078
0.240
0.320
0.424
0.202
0.202
0.202
0.202
0.140
0.016
bond
bond
bond
bond
bond
bond
bond
bond
bond
bond
bond
bond
bond
bond
bond
bond
bond
##################################
##
##
## Bond Stretching Parameters ##
##
##
##################################
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
3
1
2
3
4
14
15
16
17
18
19
2
3
4
42
46
72
3
4.400
4.400
4.400
5.200
2.200
3.213
3.213
3.213
3.213
2.970
9.600
9.600
9.900
6.471
5.050
11.090
9.600
1.523
1.497
1.509
1.470
2.149
1.815
1.816
1.805
1.784
1.880
1.337
1.351
1.313
1.459
1.463
1.260
1.415
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
################################
##
##
## Angle Bending Parameters ##
##
##
################################
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
8
9
11
12
13
14
15
16
0.450
0.450
0.450
0.450
0.360
0.700
0.570
0.500
0.650
0.560
0.630
0.490
0.550
0.420
109.470
109.470
107.800
109.470
109.390
107.500
109.470
109.280
109.500
108.200
108.200
108.900
109.000
107.800
109.510
109.510
109.900
112.400
109.410
107.700
108.800
110.780
107.500
0.000
0.000
0.000
107.000
0.000
109.500
109.500
110.000
109.000
110.000
107.400
109.500
109.280
109.500
0.000
0.000
0.000
106.500
0.000
############################
##
##
## Torsional Parameters ##
##
##
############################
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
torsion
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
8
9
11
12
13
14
15
16
17
0.200
0.170
0.050
0.200
0.000
0.100
0.100
0.000
0.000
0.000
0.000
0.000
0.140
0.000
0.000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.270
0.270
0.370
-0.260
0.000
0.100
0.400
0.000
-0.086
-0.250
-0.410
-0.500
0.000
0.000
0.000
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0.093
0.093
0.000
0.093
0.267
0.180
0.500
0.400
0.930
0.550
1.060
0.267
0.000
0.483
0.000
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
CHAMM FORCE FIELD FILE
########################################################
##
##
## TINKER Atom Class Numbers to CHARMM22 Atom Names ##
##
##
##
1 HA
11 CA
21 CY
31 NR3
##
##
2 HP
12 CC
22 CPT
32 NY
##
##
3 H
13 CT1
23 CT
33 NC2
##
##
4 HB
14 CT2
24 NH1
34 O
##
##
5 HC
15 CT3
25 NH2
35 OH1
##
##
6 HR1
16 CP1
26 NH3
36 OC
##
##
7 HR2
17 CP2
27 N
37 S
##
##
8 HR3
18 CP3
28 NP
38 SM
##
##
9 HS
19 CH1
29 NR1
##
##
10 C
20 CH2
30 NR2
##
##
##
########################################################
atom
1
atom
1
atom
1
atom
1
atom
1
atom
1
atom
1
atom
1
atom
1
atom
1
atom
1
atom
1
1
1
HA
"Nonpolar Hydrogen"
1
1.008
2
2
HP
"Aromatic Hydrogen"
1
1.008
3
3
H
"Peptide Amide HN"
1
1.008
4
4
HB
"Peptide HCA"
1
1.008
5
4
HB
"N-Terminal HCA"
1
1.008
6
5
HC
"N-Terminal Hydrogen"
1
1.008
7
5
HC
"N-Terminal PRO HN"
1
1.008
8
3
H
"Hydroxyl Hydrogen"
1
1.008
9
3
H
"TRP Indole HE1"
1
1.008
10
3
H
"HIS+ Ring NH"
1
1.008
11
3
H
"HISDE Ring NH"
1
1.008
12
6
HR1
"HIS+ HD2/HISDE HE1"
1
1.008
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
vdw
################################
##
##
## Van der Waals Parameters ##
##
##
################################
/Ao
1
2
3
4
5
6
7
8
9
10
1.3200
1.3582
0.2245
1.3200
0.2245
0.9000
0.7000
1.4680
0.4500
2.0000
/(kcal/mol)
-0.0220
-0.0300
-0.0460
-0.0220
-0.0460
-0.0460
-0.0460
-0.0078
-0.1000
-0.1100
bond
bond
bond
bond
bond
bond
bond
bond
bond
##################################
##
##
## Bond Stretching Parameters ##
##
##
##################################
/(kcal/mol/Ao2)
1
1
1
1
1
1
1
1
1
10
11
12
13
14
15
17
18
21
330.00
340.00
317.13
309.00
309.00
322.00
309.00
309.00
330.00
/Ao
1.1000
1.0830
1.1000
1.1110
1.1110
1.1110
1.1110
1.1110
1.0800
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
################################
##
##
## Angle Bending Parameters ##
##
##
################################
/(kcal/mol/rad2)
3
13
13
13
14
14
14
15
15
15
16
16
10
10
10
10
10
10
10
10
10
10
10
10
34
24
27
34
24
27
34
24
27
34
24
27
50.00
80.00
20.00
80.00
80.00
20.00
80.00
80.00
20.00
80.00
80.00
20.00
/deg
121.70
116.50
112.50
121.00
116.50
112.50
121.00
116.50
112.50
121.00
116.50
112.50
############################
##
##
## Torsional Parameters ##
##
##
############################
torsion
1
11
11
1
torsion
1
11
11
11
torsion
1
11
11
22
torsion
2
11
11
2
torsion
2
11
11
11
torsion
2
11
11
14
torsion
2
11
11
15
torsion
2
11
11
22
torsion
2
11
11
35
torsion
2
11
11
36
torsion
11
11
11
11
torsion
11
11
11
14
torsion
11
11
11
15
torsion
11
11
11
22
torsion
11
11
11
35
torsion
11
11
11
36
/(kcal/mol)
2.500
3.500
3.500
2.400
4.200
4.200
4.200
3.000
4.200
4.200
3.100
3.100
3.100
3.100
3.100
3.100
/deg
n
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
180.0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
AMBER FORCE FIELD
########################################################
##
##
## TINKER Atom Class Numbers to Amber-95 Atom Names ##
##
##
##
1 CT
11 CN
21 OW
31 HO
##
##
2 C
12 CK
22 OH
32 HS
##
##
3 CA
13 CQ
23 OS
33 HA
##
##
4 CM
14 N
24 O
34 HC
##
##
5 CC
15 NA
25 O2
35 H1
##
##
6 CV
16 NB
26 S
36 H2
##
##
7 CW
17 NC
27 SH
37 H3
##
##
8 CR
18 N*
28 P
38 HP
##
##
9 CB
19 N2
29 H
39 H4
##
##
10 C*
20 N3
30 HW
40 H5
##
##
##
########################################################
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
OPLS Force Field
#############################
##
##
## Atom Type Definitions ##
##
##
#############################
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
C
O
N
H
CH2
CH
CH3
CH
CH2
CH3
C
N
H
CH
CH2
CH2
C
O
CH2
N
"C Peptide Amide"
"O Peptide Amide"
"NH Peptide Amide"
"H(N) Peptide Amide"
"CH2 (alpha) Gly"
"CH (alpha) Ala"
"CH3 (beta) Ala"
"CH (beta) V/L/I"
"CH2 (generic)"
"CH3 (delta) Ile"
"CH Phe/Tyr/Trp"
"NH2 Primary Amide"
"H2N Primary Amide"
"CH (alpha) Pro"
"CH2 (delta) Pro"
"CH2COO- Asp/Glu"
"COO- Carboxylate"
"O- Carboxylate"
"CH2 (epsilon) Lys"
"NH3+ Ammonium"
6
8
7
1
6
6
6
6
6
6
6
7
1
6
6
6
6
8
6
7
12.011
15.999
14.007
1.008
14.027
13.019
15.035
13.019
14.027
15.035
12.011
14.007
1.008
13.019
14.027
14.027
12.011
15.999
14.027
14.007
3
1
3
1
2
3
1
3
2
1
3
3
1
3
2
2
3
1
2
4
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
H
CH2
O
H
CH
C
CH2
CH2
CH
CH
CH2
S
H
CH2
S
CH3
CH2
S
CH3
N
H
N
C
C
C
N
H
C
C
C
"H(N) Ammonium"
"CH2 (beta) Ser"
"OH Ser/Thr"
"H(O) Ser/Thr/Tyr"
"CHOH (beta) Thr"
"COH (zeta) Tyr"
"CH2 N-terminal Gly"
"CH2 C-terminal Gly"
"CH (alpha) N-term"
"CH (alpha) C-term"
"CH2 (beta) Cys"
"SH Cysteine"
"H(S) Cysteine"
"CH2 (gamma) Met"
"-S- Met"
"CH3 (epsilon) Met"
"CH2 (beta) Cystine"
"-SS- Cystine"
"CH3 N-Methyl Amide"
"NH HisD/HisE/Trp"
"H(N) HisD/HisE/Trp"
"C=N-C HisD/E"
"CH (epsilon) HisD/E"
"C (gamma) HisE"
"CH (delta) HisE/Trp"
"NH HisP"
"H(N) HisP"
"CH (epsilon) HisP"
"CH (delta) HisP"
"C (gamma) Trp"
1
6
8
1
6
6
6
6
6
6
6
16
1
6
16
6
6
16
6
7
1
7
6
6
6
7
1
6
6
6
1.008
14.027
15.999
1.008
13.019
12.011
14.027
14.027
13.019
13.019
14.027
32.066
1.008
14.027
32.066
15.035
14.027
32.066
15.035
14.007
1.008
14.007
12.011
12.011
12.011
14.007
1.008
12.011
12.011
12.011
1
2
2
1
3
3
2
2
3
3
2
2
1
2
2
1
2
2
1
3
1
2
3
3
3
3
1
3
3
3
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
atom
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
N
H
C
N
H
CH2
CH2
C
O
CH
CH2
O
CH3
C
CH3
CH2
C
C
C
CH
CH
CH
C
C
H
O
"N (eta) Arg"
"H(N) Arg"
"C (zeta) Arg"
"N (epsilon) Arg"
"H(N) Arg"
"CH2 (delta) Arg"
"CH2 (gamma) Arg"
"COOR Ester"
"=O Ester"
"CH (alpha Me Ester)"
"CH2 (Gly Me Ester)"
"-O- Ether/Ester"
"CH3 Methyl Ester"
"C (alpha) Aib"
"CH3 (beta) Aib"
"CH2 (beta) F/Y/W/H"
"C (epsilon) Trp"
"C (delta) Trp"
"C (gamma) HisP"
"CH N-terminal Pro"
"CH C-terminal Pro"
"HCO N-Formyl"
"C (gamma) HisD"
"CH (delta) HisD"
"H(C) Aromatic"
"OH Tyr"
7
1
6
7
1
6
6
6
8
6
6
8
6
6
6
6
6
6
6
6
6
6
6
6
1
8
14.007
1.008
12.011
14.007
1.008
14.027
14.027
12.011
15.999
13.019
14.027
15.999
15.035
12.011
15.035
14.027
12.011
12.011
12.011
13.019
13.019
13.019
12.011
12.011
1.008
15.999
3
1
3
3
1
2
2
3
1
3
2
2
1
4
1
2
3
3
3
3
3
2
3
3
1
2
Algorithms for Molecular Dynamics
Runge-Kutta methods:
x(t+t) = x(t) + (dx/dt) t
Fourth-order Runge-Kutta
x(t+t) = x(t) + (1/6) (s1+2s2+2s3+s4) t +O(t5)
s1 = dx/dt
s2 = dx/dt
[w/ t=t+t/2, x = x(t)+s1t/2]
s3 = dx/dt
[w/ t=t+t/2, x = x(t)+s2t/2]
s4 = dx/dt
[w/ t=t+t, x = x(t)+s3 t]
Very accurate but slow!
Algorithms for Molecular Dynamics
Verlet Algorithm:
x(t+t) = x(t) + (dx/dt) t + (1/2) d2x/dt2 t2 + ...
x(t -t) = x(t) - (dx/dt) t + (1/2) d2x/dt2 t2 - ...
x(t+t) = 2x(t) - x(t -t) + d2x/dt2 t2 + O(t4)
Efficient & Commonly Used!
Multiple Scale Simulation
Goddard, Caltech
Large Gear Drives Small Gear
G. Hong et. al., 1999
Nano-oscillators
Nanoscopic Electromechanical Device
(NEMS)
Zhao, Ma, Chen & Jiang, Phys. Rev. Lett. 2003
Computer-Aided Drug Design
Human Genome Project
GENOMICS
Computer-aided drug design
Chemical Synthesis
Screening using in vitro assay
Animal Tests
Clinical Trials
ALDOSE REDUCTASE
HO
HO
OH HO
OH HO
Aldose Reductase
Diabetes
HO
O
HO
glucose
OH
Glucose
NADPH
NADP
HO
sorbitol
OH
Sorbitol
Diabetic
Complications
Inhibitor
Aldose Reductase
Design of Aldose Reductase Inhibitors
Aldose Reductase Active Site Structure
CYS298
LEU300
TYP219
TRP111
Cerius2 LigandFit
PHE122
NADPH
HIS110
TRP20
TRP79
TYR48
VAL47
LYS77
To further confirm the AR-ARI binding,
We perform QM/MM calculations on
drug leads.
CHARMM
O
NH
5'-OH, 6'-F, 7'-OH
5' HN
O
6'
NMe
X
7'
8'
N
H
O
Binding energy is found to be –45 kcal / mol
Docking of aldose reductase inhibitor
Aldose reducatse
Inhibitor
(4R)-6’-fluoro-7’-hydroxyl-8’-bromo-3’-methylspiro[imidazoli-dine-4,4’(1’H)-quinazoline]-2,2’,5(3’H)-trione
Cerius2 LigandFit
Hu & Chen, 2003
Interaction energy between ligand and protein
Quantum Mechanics/Molecular Mechanics
(QM / MM)
Hu & Chen, 2003
O
NH
5' HN
O
6'
NMe
X
7'
8'
N
H
O
a:Inhibitor concentration of inhibit Aldose Reductase;
b: the percents of lower sciatic nerve sorbitol levels
c: interaction with AR in Fig. 4
SARS 3CL Protease
B
A
Inhibitor site
Complex with
hexapeptidyl
CMK inhibitor
“Identification of novel small molecule inhibitors of severe acute respiratory syndrome associated coronavirus
by chemical genetics”, Richard Y. Kao, Wayne H.W. Tsui, Terri S. W. Lee, Julian A. Tanner, Rory M. Watt,
Jian-Dong Huang, Lihong Hu, Guanhua Chen, Zhiwei Chen, linqi Zhang, Tien He, Kwok-Hung Chan, Herman
Tse, Amanda P. C. To, Louisa W. Y. Ng, Bonnie C. W. Wong, Hoi-Wah Tsoi, Dan Yang, David D. Ho,
Kwok-Yung Yuen, Chemistry & Biology 11, 1293 (2004).
New ligand candidates for SARS 3Cl-Protease
generated by a known compound AG7088
H
O
O
N
AG7088
O
N
O
N
N
H
O
H
O
O
F
Anand, et al, Science, 300, 1763 (2003)
Our prediction
H
O
O
O
O
O
N
O N
H
N
H
O
N
O
O
N
H
O N
O
N
H
N
O
H
O
O
O
H
O
O
N
O
O
O
O
N
N
O N
H
N
H
O N
N
O
H
O
OH
O
H
N
O
H
O
O