Computational Modeling of Macromolecular Systems

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 Software

Gaussian Inc. Gaussian 94, Gaussian 98Schrödinger Inc. Jaguar Wavefunction SpartanQ-Chem Q-ChemAccelrys InsightII, Cerius2

HyperCube HyperChemInformatixCelera Genomics

Applications: material discovery, drug design & research

R&D in Chemical & Pharmaceutical industries in 2000: US$ 80 billionBioinformatics: Total Sales in 2001 US$ 225 million

Project Sales in 2006 US$ 1.7 billion

Cytochrome c (involved in the ATP synthesis)

heme

Cytochrome c is a peripheral membrane protein involved in the long distance electron transfers

1997 Nobel Prizein Biology:

ATP Synthase inMitochondria

Simulation of a pair of polypeptides

Duration: 100 ps. Time step: 1 ps (Ng, Yokojima & Chen, 2000)

Protein Dynamics

Theoretician leaded the way ! (Karplus at Harvard U.)

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 Changes10-9 to 103 s; 0.5 to >10 Ao

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

H E

SchrÖdinger Equation

HamiltonianH = (h2/2m

h2/2me)ii2

i e2/ri+ ZZer

ije2/rij

Wavefunction

Energy

One-electron terms: (h2/2m

h2/2me)ii2i e2/ri

Two-electron term:

ije2/rij

1. Hartree-Fock EquationF i = i i

  F Fock operator

i the i-th Hartree-Fock orbital

i the energy of the i-th Hartree-Fock orbital

Hartree-Fock MethodOrbitals

2. Roothaan Method (introduction of Basis functions)i = k cki k LCAO-MO

  {k } is a set of atomic orbitals (or basis functions)

3. Hartree-Fock-Roothaan equation j ( Fij - i Sij ) cji = 0

  Fij iF j Sij ij

4. Solve the Hartree-Fock-Roothaan equation self-consistently (HFSCF)

Graphic Representation of Hartree-Fock Solution

0 eV

IonizationEnergy

ElectronAffinity

Basis Set i = 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

# HF/6-31G(d) Route section water energy Title

0 1 Molecule Specification O -0.464 0.177 0.0 (in Cartesian coordinatesH -0.464 1.137 0.0H 0.441 -0.143 0.0

A Gaussian Input File for H2O

Gaussian type functionsgijk = 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 SetAtom Shell Exponents Coefficients

H 1S 3. 425250914E+00 1. 543289673E-016. 239137298E-01 5. 353281423E-011. 688554040E-01 4. 446345422E-01

C 1S 7. 161683735E+01 1. 543289673E-011. 304509632E+01 5. 353281423E-013. 530512160E+00 4. 446345422E-01

2S 2. 941249355E+00 -9. 996722919E-026. 834830964E-01 3. 995128261E-012. 222899159E-01 7. 001154689E-01

2P 2. 941249355E+00 1. 559162750E-016. 834830964E-01 6. 076837186E-012. 222899159E-01 3. 919573931E-01

N 1S 9. 910616896E+01 1. 543289673E-011. 805231239E+01 5. 353281423E-014. 885660238E+00 4. 446345422E-01

2S 3. 780455879E+00 -9. 996722919E-028. 784966449E-01 3. 995128261E-012. 857143744E-01 7. 001154689E-01

2P 3. 780455879E+00 1. 559162750E-018. 784966449E-01 6. 076837186E-012. 857143744E-01 3. 919573931E-01

O 1S 1. 307093214E+02 1. 543289673E-012. 380886605E+01 5. 353281423E-016. 443608313E+00 4. 446345422E-01

2S 5. 033151319E+00 -9. 996722919E-021. 169596125E+00 3. 995128261E-013. 803889600E-01 7. 001154689E-01

2P 5. 033151319E+00 1. 559162750E-011. 169596125E+00 6. 076837186E-013. 803889600E-01 3. 919573931E-01

3-21G Basis SetAtom Shell Exponents Coefficients

H 1S 5. 447178000E+00 1. 562850000E-018. 245472400E-01 9. 046910000E-01

1S' 1. 831915800E-01 1. 000000000E+00C 1S 1. 722560000E+02 6. 176690000E-02

2. 591090000E+01 3. 587940000E-015. 533350000E+00 7. 007130000E-01

2S 3. 664980000E+00 -3. 958970000E-017. 705450000E-01 1. 215840000E+00

2P 3. 664980000E+00 2. 364600000E-017. 705450000E-01 8. 606190000E-01

2S' 1. 958570000E-01 1. 000000000E+002P' 1. 958570000E-01 1. 000000000E+00

N 1S 2. 427660000E+02 5. 986570000E-023. 648510000E+01 3. 529550000E-017. 814490000E+00 7. 065130000E-01

2S 5. 425220000E+00 -4. 133010000E-011. 149150000E+00 1. 224420000E+00

2P 5. 425220000E+00 -4. 133010000E-011. 149150000E+00 1. 224420000E+00

2S' 2. 832050000E-01 1. 000000000E+002P' 2. 832050000E-01 1. 000000000E+00

O 1S 3. 220370000E+02 5. 923940000E-024. 843080000E+01 3. 515000000E-011. 042060000E+01 7. 076580000E-01

2S 7. 402940000E+00 -4. 044530000E-011. 576200000E+00 1. 221560000E+00

2P 7. 402940000E+00 2. 445860000E-011. 576200000E+00 8. 539550000E-01

2S' 3. 736840000E-01 1. 000000000E+002P' 3. 736840000E-01 1. 000000000E+00

6-31G Basis SetAtom Shell Exponents Coefficients

H 1S 1. 873113696E+01 3. 349460434E-022. 825394365E+00 2. 347269535E-016. 401216923E-01 8. 137573262E-01

1S' 1. 612777588E-01 1. 000000000E+00C 1S 3. 047524880E+03 1. 834737130E-03

4. 573695180E+02 1. 403732280E-021. 039486850E+02 6. 884262220E-022. 921015530E+01 2. 321844430E-019. 286662960E+00 4. 679413480E-013. 163926960E+00 3. 623119850E-01

2S 7. 868272350E+00 -1. 193324200E-011. 881288540E+00 -1. 608541520E-015. 442492580E-01 1. 143456440E-01

2P 7. 868272350E+00 6. 899906660E-021. 881288540E+00 3. 164239610E-015. 442492580E-01 7. 443082910E-01

2S' 1. 687144782E-01 1. 000000000E+002P' 1. 687144782E-01 1. 000000000E+00

N 1S 4. 173511460E+03 1. 834772160E-036. 274579110E+02 1. 399462700E-021. 429020930E+02 6. 858655180E-024. 023432930E+01 2. 322408730E-011. 282021290E+01 4. 690699480E-014. 390437010E+00 3. 604551990E-01

2S 1. 162636186E+01 -1. 149611820E-012. 716279807E+00 -1. 691174790E-017. 722183966E-01 1. 145851950E+00

2P 1. 162636186E+01 6. 757974390E-022. 716279807E+00 3. 239072960E-017. 722183966E-01 7. 408951400E-01

2S' 2. 120314975E-01 1. 000000000E+002P' 2. 120314975E-01 1. 000000000E+00

O 1S 5. 484616600E+03 1. 831074430E-038. 252349460E+02 1. 395017220E-021. 880469580E+02 6. 844507810E-025. 296450000E+01 2. 327143360E-011. 689757040E+01 4. 701928980E-015. 799635340E+00 3. 585208530E-01

2S 1. 553961625E+01 -1. 107775490E-013. 599933586E+00 -1. 480262620E-011. 013761750E+00 1. 130767010E+00

2P 1. 553961625E+01 7. 087426820E-023. 599933586E+00 3. 397528390E-011. 013761750E+00 7. 271585770E-01

2S' 2. 700058226E-01 1. 000000000E+002P' 2. 700058226E-01 1. 000000000E+00

Electron Correlation: avoiding each other

The reason of the instantaneous correlation:Coulomb repulsion (not included in the HF)

Beyond the Hartree-FockConfiguration Interaction (CI)Perturbation theoryCoupled Cluster MethodDensity 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

++

+ ...

H = H0 + H’H0n

(0) = En(0)n

(0)

n(0) is an eigenstate for unperturbed system

H’ is small compared with H0

Perturbation Theory

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

= eT(0)

(0): Hartree-Fock ground state wave function: Ground state wave functionT = T1 + T2 + T3 + T4 + T5 + …Tn : n electron excitation operator

Coupled-Cluster Method

=T1

CCD = eT2(0)

(0): Hartree-Fock ground state wave functionCCD: Ground state wave functionT2 : two electron excitation operator

Coupled-Cluster Doubles (CCD) Method

=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 |i

2 |i > dr e2(r) /

r1 dr1 dr2 e2/r12 + Exc[(r)]

Kohn-Sham Equation Ground State: Phys. Rev. 140, A1133 (1965)

FKS i = i i

FKS h2/2me)ii2 e2 / r1jJj + Vxc

Vxc Exc[(r)] / (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 80-90% (20 electrons)CISDTQ very large 98-99%

MP2 1.5 85-95% (DZ+P)MP4 5.8 >90% CCD large >90%

CCSDT very large ~100%

(1) Neglect or incomplete treatment of electron correlation

(2) Incompleteness of the Basis set

Four Sources of error in ab initio Calculation

How to simulate large molecules?

Quantum Chemistry for Complex Systems

Semiempirical Molecular Orbital Calculation

Extended Huckel MO Method (Wolfsberg, Helmholz, Hoffman)

Independent electron approximation

Schrodinger equation for electron i 

Hval = i Heff(i)

Heff(i) = -(h2/2m) i2 + Veff(i)

Heff(i) i = i i

LCAO-MO: i = r cri r

  s ( Heff

rs - i Srs ) csi = 0

  Heffrs rHeff s Srs

rs Parametrization: Heff

rr rHeff r minus the valence-state ionization potential (VISP)

Atomic Orbital Energy VISP--------------- e5 -e5

--------------- e4 -e4

--------------- e3 -e3

--------------- e2 -e2

--------------- e1 -e1

 Heff

rs = ½ K (Heffrr + Heff

ss) Srs K:

13

CNDO, INDO, NDDO(Pople and co-workers)

Hamiltonian with effective potentialsHval = i [ -(h

2/2m) i2 + Veff(i) ] + ij>i e

2 / rij

two-electron integral:(rs|tu) = <r(1) t(2)| 1/r12 | s(1) u(2)>

 CNDO: complete neglect of differential overlap (rs|tu) = rs tu (rr|tt) rs tu 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 overallresults fit well with the results of minimal basis abinitio 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 INDOMNDO: modified neglect of diatomic overlap AM1: Austin Model 1PM3: 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

W. Yang, Phys. Rev. Lett. 1991

Divide-and-Conqure (DAC)

Linear Scaling Calculation for Ground State

Yang, Phys. Rev. Lett. 1991Li, Nunes & Vanderbilt, Phy. Rev. B. 1993Baroni & 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.

Superoxide Dismutase (4380 atoms)

York, Lee & Yang, JACS, 1996

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 Quantum mechanical investigation of the field emission from the tips of carbon nanotubesemission from the tips of carbon nanotubes

Experimental ResultsExperimental Results

applied

local

E

E

J-M. Bonard et al., Phys. Rev. Lett. 89 19 (2002)

F-N theory breaks down For strong CNT emission

Field Emission BasicsField Emission BasicsClassical Model :Classical Model :

Laplace’s Equation:Laplace’s Equation:

02 rV

Boundary ConditionsBoundary Conditions::

V(anode) = VV(anode) = Vaa

V(cathode-tube) = 0V(cathode-tube) = 0Single nanotube model outlineSingle nanotube model outline

Boundary conditions:Boundary conditions:V(anode) = VV(anode) = Vaa V(cathode) = 0 V(cathode) = 0

Quantum ModelQuantum Model

Problems:1. 100,000 atoms2. Boundary Condition: OPEN SYSTEM!3. Number of electrons transferred to CNT

Boundary Condition

Mirror image of charges

Charge distributions before & after external field

(5,5)

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!

Eappl 0 10 V/m 14 V/m

Barrier height 4.5 eV 3.0 eV 2.0 eV

Penetration does occur at the tip !

Effective enhancement factor :500 for Eappl = 10 V/m

1200 for Eappl = 14 V/m

Calculated emission currents:0.34 pA for Eapply = 10 V/m

0.20 µA for Eapply = 14 V/m

Experiment [Zettl et. al., PRL 88, 56804 (2002)]:A Multi-Walled CNT:

0.40 pA for Eapply = 11.7 V/m

0.54 µA for Eapply = 20.0 V/m

Experiment Simulation

The multi-walled CNT is of same potential !!!

Linear Scaling Calculation for EXCITED STATE ?

A Much More Difficult Problem !

Localized-Density-Matrix (LDM) Method

ij(0) = 0 rij > r0

ij = 0 rij > r1Yokojima & Chen, Phys. Rev. B, 1999

Principle of the nearsightedness of equilibrium systems (Kohn, 1996)

Linear-Scaling Calculation for excited states

t

,Hi

Heisenberg Equation of Motion

Time-Dependent Hartree-Fock Random Phase Approximation

PPP Semiempirical Hamitonian

Polyacetylene

1

2

3

4

5

6

7

8

9

10

11

12

N-3

N-2

N-1

N

...

CH CH2N

extcckeluH HHHH ˆˆˆˆ

Liang, Yokojima & Chen, JPC, 2000

Linear Scaling Calculation for Excited State

Flat Panel Display

Cambridge Display Technology

Weight: 15 gramResolution: 800x236Size: 45x37 mmVoltage: DC, 10V

Energy

Inte

nsi

ty

electron

hole

Low-Lying Excited States of Light Harvesting System II in Purple Bacteria

1.      “Ng, Zhao and Chen, J. Phys. Chem. B 107, 9589 (2003)

Application of O(N) method for excited states

Photo-excitations in Light Harvesting System II

generated by VMD

strong absorption: ~800 nm

generated by VMD

B800 ring: strong absorption @ 800nmB850 ring: strong absorption @ 850nm

1α1β

2α~8.9Å

~9.2Å

generated by VMD

J1

J2

W

53,

))((3

ij

jijiij

ij

jiji

r

drdr

r

ddCW

Frenkel Exciton Model:

nJnn+nnnJnmm

+n

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: 200 ~ 500 cm-1

Dynamic disorder: ~200 cm-1

n.n. coupling << disorder: localized (Förster Incoherent hopping) n.n. coupling >> disorder: delocalized (Coherent exciton transfer)

Calculated Parameters by others (Zerner, Fleming, Mukamel & etc.)

2224 nmJINDO/S-CEO (a) PDA with (b) INDO/S-CIS

(c)

J1 / cm-1 408 339 790

J2 / cm-1 366 336 369

(a) Tretiak, S.; Chernyak, V.; Mukamel, S. J. Phys. Chem., 104 9540, 2000 (b) Pullerits, T.; Sundstrom, V.; van Grondelle, R. J. Phys. Chem. 1999, 103, 2327(c) Cory, M. G.; Zerner, M.C.; Hu, X.; Schulten, X. K.; J. Phys. Chem. B 1998, 102, 7640

Cory, M. G.; Zerner, M.C.; Hu, X.; Schulten, X. K.;

J. Phys. Chem. B 1998, 102, 7640

Our task: what are J1 & J2 ?

Photo-excitations in Light Harvesting System II

736 atomsP3 / 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 = 0k = 1

k = 2k = 3

k = 4k = 5

k = 6k = 7 k = 8

CIS (Zerner et. al.)

LDM

/ cm-1 J1 J2 1 2 C* rms

Dimer# 528 455 9421 9292 150

B850 593 490 9117 9117 640725 118

Zerner 790 369 13242 13242 506000 260

Calculated parameters in Frenkel excition model (least square fitting)

*transition dipole of monomer = 2.326 e·A: C = 639765 cm-1

B850 0.926 0.980 1.056 1.114 1.132

1.178 1.198 1.220 1.230 1.237

Doubly degenerate

The B850 energies (eV) calculated by LDM

53,

))((3

ij

jijiij

ij

jiji

r

drdr

r

ddCW

Solvation Correction

J1 ~ 445 cm-1

J2 ~ 367 cm-1

Static disorder: 200 ~ 500 cm-1

Dynamic disorder: ~200 cm-1

LDM-TDDFT: CnH2n+2

Fast Multiple Method

LODESTAR: Software Package for Complex Systems

Characteristics ：O(N) Divide-and-ConquerO(N) TDHF (ab initio & semiemptical)

O(N) TDDFT

CNDO/S-, PM3-, AM1-, INDO/S-, & TDDFT-LDM

Light Harvesting SystemNonlinear Optical

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 ii2 + ij 1/rij - i Z/ri - i q/ri

+ i Vv-b(ri) + ZZ/r + Zq/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 PotentialEb = 1/2 kb (l)2

where, kb : stretch force constantl : difference between equilibrium & actual bond length

Two-body interaction

Bond Angle Deformation PotentialEa = 1/2 ka ()2

where, ka : angle force constant

: difference between equilibrium & actual bond angle

Three-body interaction

Periodic Torsional Barrier PotentialEt = (V/2) (1+ cosn )where, V : rotational barrier

: torsion angle n : rotational degeneracy

Four-body interaction

Non-bonding interaction

van der Waals interactionfor pairs of non-bonded atoms

Coulomb potential

for all pairs of charged atoms

Force Field Types

• MM2 Molecules

• AMBER Polymers

• CHAMM Polymers

• BIO Polymers

• OPLS Solvent Effects

############################# ## ## ## Atom Type Definitions ## ## ## #############################

atom 1 C "CSP3 ALKANE" 6 12.000 4atom 2 C "CSP2 ALKENE" 6 12.000 3atom 3 C "CSP2 CARBONYL" 6 12.000 3atom 4 C "CSP ALKYNE, C=C=O" 6 12.000 2atom 5 H "NONPOLAR HYDROGEN" 1 1.008 1atom 6 O "-O- ALCOHOL, ETHER" 8 15.995 4atom 7 O "=O CARBONYL" 8 15.995 1atom 8 N "NSP3" 7 14.003 4atom 9 N "NSP2 AMIDE" 7 14.003 3atom 10 N "NSP" 7 14.003 1atom 11 F "FLUORIDE" 9 18.998 1atom 12 Cl "CHLORIDE" 17 34.969 1atom 13 Br "BROMIDE" 35 78.918 1atom 14 I "IODIDE" 53 126.900 1atom 15 S "-S- SULFIDE" 16 31.972 2atom 16 S+ ">S+ SULFONIUM" 16 31.972 2atom 17 S ">S=O SULFOXIDE" 16 31.972 3atom 18 S ">SO2 SULFONE" 16 31.972 4atom 19 Si "SILANE" 14 27.977 4atom 20 Lp "LONE PAIR" 0 0.000 1

MM2 Force Field

atom 21 H "-OH ALCOHOL" 1 1.008 1atom 22 C "CYCLOPROPANE" 6 12.000 4atom 23 H "NH AMINE" 1 1.008 1atom 24 H "COOH CARBOXYL" 1 1.008 1atom 25 P ">P- PHOSPHINE" 15 30.994 3atom 26 B ">B- TRIGONAL" 5 11.009 3atom 27 B ">B< TETRAHEDRAL" 5 11.009 4atom 28 H "-H AMIDE, ENOL" 1 1.008 1atom 29 C* "CARBON RADICAL" 6 12.000 3atom 30 C+ "CARBONIUM ION" 6 12.000 3atom 31 Ge "GERMANIUM" 32 73.922 2atom 32 Sn "TIN" 50 117.902 2atom 33 Pb "LEAD (IV)" 82 207.977 4atom 34 Se "SELENIUM" 34 79.917 2atom 35 Te "TELLURIUM" 52 129.907 2atom 36 D "DEUTERIUM" 1 2.014 1atom 37 N "-N= AZO,PYRIDINE" 7 14.003 3atom 38 C "CSP2 CYCLOPROPENE" 6 12.000 3atom 39 N+ "NSP3 AMMONIUM" 7 14.003 4atom 40 N "NSP2 PYRROLE" 7 14.003 3atom 41 O "OSP2 FURAN" 8 15.995 3atom 42 S "SSP2 THIOPHENE" 16 31.972 2atom 43 N "-N=N-O AZOXY" 7 14.003 2atom 44 H "-SH THIOL" 1 1.008 1atom 45 N "AZIDE (CENTER-N)" 7 14.003 2atom 46 N "NO2 NITRO" 7 14.003 3atom 47 O "CARBOXYLATE" 8 15.995 1atom 48 H "AMMONIUM" 1 1.008 1

atom 49 O "EPOXY" 8 15.995 4atom 50 C "BENZENE" 6 12.000 3atom 51 He "HELIUM" 2 4.003 0atom 52 Ne "NEON" 10 20.179 0atom 53 Ar "ARGON" 18 39.948 0atom 54 Kr "KRYPTON" 36 83.800 0atom 55 Xe "XENON" 54 131.300 0atom 59 Mg "MAGNESIUM" 12 24.301 0atom 60 P "PHOSPHORUS (V)" 15 30.994 4atom 61 Fe "IRON (II)" 26 55.847 0atom 62 Fe "IRON (III)" 26 55.847 0atom 63 Ni "NICKEL (II)" 27 58.710 0atom 64 Ni "NICKEL (III)" 27 58.710 0atom 65 Co "COBALT (II)" 28 58.933 0atom 66 Co "COBALT (III)" 28 58.933 0atom 69 O "AMINE OXIDE" 8 15.995 1atom 70 O "KETONIUM OXYGEN" 8 15.995 1atom 71 C "KETONIUM CARBON" 6 12.000 2atom 72 N "=N- IMINE, OXIME" 7 14.003 3atom 73 N+ "=N(+)- PYRIDINIUM" 7 14.003 3atom 74 N+ "=N(+)- IMMINIUM" 7 14.003 3atom 75 N "N-OH OXIME" 7 14.003 3

################################ ## ## ## Van der Waals Parameters ## ## ## ################################

vdw 1 1.900 0.044vdw 2 1.940 0.044vdw 3 1.940 0.044vdw 4 1.940 0.044vdw 5 1.500 0.047vdw 6 1.740 0.050vdw 7 1.740 0.066vdw 8 1.820 0.055vdw 9 1.820 0.055vdw 10 1.820 0.055vdw 11 1.650 0.078vdw 12 2.030 0.240vdw 13 2.180 0.320vdw 14 2.320 0.424vdw 15 2.110 0.202vdw 16 2.110 0.202vdw 17 2.110 0.202vdw 18 2.110 0.202vdw 19 2.250 0.140vdw 20 1.200 0.016

################################## ## ## ## Bond Stretching Parameters ## ## ## ##################################

bond 1 1 4.400 1.523bond 1 2 4.400 1.497bond 1 3 4.400 1.509bond 1 4 5.200 1.470bond 1 14 2.200 2.149bond 1 15 3.213 1.815bond 1 16 3.213 1.816bond 1 17 3.213 1.805bond 1 18 3.213 1.784bond 1 19 2.970 1.880bond 2 2 9.600 1.337bond 2 3 9.600 1.351bond 2 4 9.900 1.313bond 2 42 6.471 1.459bond 2 46 5.050 1.463bond 2 72 11.090 1.260bond 3 3 9.600 1.415bond 3 5 4.600 1.113bond 3 6 5.050 1.338bond 3 7 10.800 1.208bond 3 9 6.400 1.385bond 3 22 4.400 1.447bond 3 36 4.600 1.130bond 3 72 11.090 1.280bond 4 4 15.600 1.212bond 4 5 5.900 1.090bond 4 10 17.730 1.158bond 5 15 3.800 1.345bond 5 31 2.570 1.530bond 5 32 2.229 1.696bond 5 33 1.894 1.775bond 5 34 3.170 1.472bond 5 35 2.850 1.670bond 5 38 4.600 1.072

################################ ## ## ## Angle Bending Parameters ## ## ## ################################

angle 1 1 1 0.450 109.470 109.510 109.500angle 1 1 2 0.450 109.470 109.510 109.500angle 1 1 3 0.450 107.800 109.900 110.000angle 1 1 4 0.450 109.470 112.400 109.000angle 1 1 5 0.360 109.390 109.410 110.000angle 1 1 6 0.700 107.500 107.700 107.400angle 1 1 8 0.570 109.470 108.800 109.500angle 1 1 9 0.500 109.280 110.780 109.280angle 1 1 11 0.650 109.500 107.500 109.500angle 1 1 12 0.560 108.200 0.000 0.000angle 1 1 13 0.630 108.200 0.000 0.000angle 1 1 14 0.490 108.900 0.000 0.000angle 1 1 15 0.550 109.000 107.000 106.500angle 1 1 16 0.420 107.800 0.000 0.000

############################ ## ## ## Torsional Parameters ## ## ## ############################

torsion 1 1 1 1 0.200 0.0 1 0.270 180.0 2 0.093 0.0 3torsion 1 1 1 2 0.170 0.0 1 0.270 180.0 2 0.093 0.0 3torsion 1 1 1 3 0.050 0.0 1 0.370 180.0 2 0.000 0.0 3torsion 1 1 1 4 0.200 0.0 1 -0.260 180.0 2 0.093 0.0 3torsion 1 1 1 5 0.000 0.0 1 0.000 180.0 2 0.267 0.0 3torsion 1 1 1 6 0.100 0.0 1 0.100 180.0 2 0.180 0.0 3torsion 1 1 1 8 0.100 0.0 1 0.400 180.0 2 0.500 0.0 3torsion 1 1 1 9 0.000 0.0 1 0.000 180.0 2 0.400 0.0 3torsion 1 1 1 11 0.000 0.0 1 -0.086 180.0 2 0.930 0.0 3torsion 1 1 1 12 0.000 0.0 1 -0.250 180.0 2 0.550 0.0 3torsion 1 1 1 13 0.000 0.0 1 -0.410 180.0 2 1.060 0.0 3torsion 1 1 1 14 0.000 0.0 1 -0.500 180.0 2 0.267 0.0 3torsion 1 1 1 15 0.140 0.0 1 0.000 180.0 2 0.000 0.0 3torsion 1 1 1 16 0.000 0.0 1 0.000 180.0 2 0.483 0.0 3torsion 1 1 1 17 0.000 0.0 1 0.000 180.0 2 0.000 0.0 3

######################################################## ## ## ## 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 ## ## ## ########################################################

CHAMM FORCE FIELD FILE

atom 1 1 HA "Nonpolar Hydrogen" 1 1.0081atom 2 2 HP "Aromatic Hydrogen" 1 1.0081atom 3 3 H "Peptide Amide HN" 1 1.0081atom 4 4 HB "Peptide HCA" 1 1.0081atom 5 4 HB "N-Terminal HCA" 1 1.0081atom 6 5 HC "N-Terminal Hydrogen" 1 1.0081atom 7 5 HC "N-Terminal PRO HN" 1 1.0081atom 8 3 H "Hydroxyl Hydrogen" 1 1.0081atom 9 3 H "TRP Indole HE1" 1 1.0081atom 10 3 H "HIS+ Ring NH" 1 1.0081atom 11 3 H "HISDE Ring NH" 1 1.0081atom 12 6 HR1 "HIS+ HD2/HISDE HE1" 1 1.0081

################################ ## ## ## Van der Waals Parameters ## ## ## ################################

vdw 1 1.3200 -0.0220vdw 2 1.3582 -0.0300vdw 3 0.2245 -0.0460vdw 4 1.3200 -0.0220vdw 5 0.2245 -0.0460vdw 6 0.9000 -0.0460vdw 7 0.7000 -0.0460vdw 8 1.4680 -0.0078vdw 9 0.4500 -0.1000vdw 10 2.0000 -0.1100

/Ao /(kcal/mol)

################################## ## ## ## Bond Stretching Parameters ## ## ## ##################################

bond 1 10 330.00 1.1000bond 1 11 340.00 1.0830bond 1 12 317.13 1.1000bond 1 13 309.00 1.1110bond 1 14 309.00 1.1110bond 1 15 322.00 1.1110bond 1 17 309.00 1.1110bond 1 18 309.00 1.1110bond 1 21 330.00 1.0800

/(kcal/mol/Ao2) /Ao

################################ ## ## ## Angle Bending Parameters ## ## ## ################################

angle 3 10 34 50.00 121.70angle 13 10 24 80.00 116.50angle 13 10 27 20.00 112.50angle 13 10 34 80.00 121.00angle 14 10 24 80.00 116.50angle 14 10 27 20.00 112.50angle 14 10 34 80.00 121.00angle 15 10 24 80.00 116.50angle 15 10 27 20.00 112.50angle 15 10 34 80.00 121.00angle 16 10 24 80.00 116.50angle 16 10 27 20.00 112.50

/(kcal/mol/rad2) /deg

############################ ## ## ## Torsional Parameters ## ## ## ############################torsion 1 11 11 1 2.500 180.0 2torsion 1 11 11 11 3.500 180.0 2torsion 1 11 11 22 3.500 180.0 2torsion 2 11 11 2 2.400 180.0 2torsion 2 11 11 11 4.200 180.0 2torsion 2 11 11 14 4.200 180.0 2torsion 2 11 11 15 4.200 180.0 2torsion 2 11 11 22 3.000 180.0 2torsion 2 11 11 35 4.200 180.0 2torsion 2 11 11 36 4.200 180.0 2torsion 11 11 11 11 3.100 180.0 2torsion 11 11 11 14 3.100 180.0 2torsion 11 11 11 15 3.100 180.0 2torsion 11 11 11 22 3.100 180.0 2torsion 11 11 11 35 3.100 180.0 2torsion 11 11 11 36 3.100 180.0 2

/(kcal/mol) /deg n

######################################################## ## ## ## 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 ## ## ## ########################################################

AMBER FORCE FIELD

############################# ## ## ## Atom Type Definitions ## ## ## #############################

atom 1 C "C Peptide Amide" 6 12.011 3atom 2 O "O Peptide Amide" 8 15.999 1atom 3 N "NH Peptide Amide" 7 14.007 3atom 4 H "H(N) Peptide Amide" 1 1.008 1atom 5 CH2 "CH2 (alpha) Gly" 6 14.027 2atom 6 CH "CH (alpha) Ala" 6 13.019 3atom 7 CH3 "CH3 (beta) Ala" 6 15.035 1atom 8 CH "CH (beta) V/L/I" 6 13.019 3atom 9 CH2 "CH2 (generic)" 6 14.027 2atom 10 CH3 "CH3 (delta) Ile" 6 15.035 1atom 11 C "CH Phe/Tyr/Trp" 6 12.011 3atom 12 N "NH2 Primary Amide" 7 14.007 3atom 13 H "H2N Primary Amide" 1 1.008 1atom 14 CH "CH (alpha) Pro" 6 13.019 3atom 15 CH2 "CH2 (delta) Pro" 6 14.027 2atom 16 CH2 "CH2COO- Asp/Glu" 6 14.027 2atom 17 C "COO- Carboxylate" 6 12.011 3atom 18 O "O- Carboxylate" 8 15.999 1atom 19 CH2 "CH2 (epsilon) Lys" 6 14.027 2atom 20 N "NH3+ Ammonium" 7 14.007 4

OPLS Force Field

atom 21 H "H(N) Ammonium" 1 1.008 1atom 22 CH2 "CH2 (beta) Ser" 6 14.027 2atom 23 O "OH Ser/Thr" 8 15.999 2atom 24 H "H(O) Ser/Thr/Tyr" 1 1.008 1atom 25 CH "CHOH (beta) Thr" 6 13.019 3atom 26 C "COH (zeta) Tyr" 6 12.011 3atom 27 CH2 "CH2 N-terminal Gly" 6 14.027 2atom 28 CH2 "CH2 C-terminal Gly" 6 14.027 2atom 29 CH "CH (alpha) N-term" 6 13.019 3atom 30 CH "CH (alpha) C-term" 6 13.019 3atom 31 CH2 "CH2 (beta) Cys" 6 14.027 2atom 32 S "SH Cysteine" 16 32.066 2atom 33 H "H(S) Cysteine" 1 1.008 1atom 34 CH2 "CH2 (gamma) Met" 6 14.027 2atom 35 S "-S- Met" 16 32.066 2atom 36 CH3 "CH3 (epsilon) Met" 6 15.035 1atom 37 CH2 "CH2 (beta) Cystine" 6 14.027 2atom 38 S "-SS- Cystine" 16 32.066 2atom 39 CH3 "CH3 N-Methyl Amide" 6 15.035 1atom 40 N "NH HisD/HisE/Trp" 7 14.007 3atom 41 H "H(N) HisD/HisE/Trp" 1 1.008 1atom 42 N "C=N-C HisD/E" 7 14.007 2atom 43 C "CH (epsilon) HisD/E" 6 12.011 3atom 44 C "C (gamma) HisE" 6 12.011 3atom 45 C "CH (delta) HisE/Trp" 6 12.011 3atom 46 N "NH HisP" 7 14.007 3atom 47 H "H(N) HisP" 1 1.008 1atom 48 C "CH (epsilon) HisP" 6 12.011 3atom 49 C "CH (delta) HisP" 6 12.011 3atom 50 C "C (gamma) Trp" 6 12.011 3

atom 51 N "N (eta) Arg" 7 14.007 3atom 52 H "H(N) Arg" 1 1.008 1atom 53 C "C (zeta) Arg" 6 12.011 3atom 54 N "N (epsilon) Arg" 7 14.007 3atom 55 H "H(N) Arg" 1 1.008 1atom 56 CH2 "CH2 (delta) Arg" 6 14.027 2atom 57 CH2 "CH2 (gamma) Arg" 6 14.027 2atom 58 C "COOR Ester" 6 12.011 3atom 59 O "=O Ester" 8 15.999 1atom 60 CH "CH (alpha Me Ester)" 6 13.019 3atom 61 CH2 "CH2 (Gly Me Ester)" 6 14.027 2atom 62 O "-O- Ether/Ester" 8 15.999 2atom 63 CH3 "CH3 Methyl Ester" 6 15.035 1atom 64 C "C (alpha) Aib" 6 12.011 4atom 65 CH3 "CH3 (beta) Aib" 6 15.035 1atom 66 CH2 "CH2 (beta) F/Y/W/H" 6 14.027 2atom 67 C "C (epsilon) Trp" 6 12.011 3atom 68 C "C (delta) Trp" 6 12.011 3atom 69 C "C (gamma) HisP" 6 12.011 3atom 70 CH "CH N-terminal Pro" 6 13.019 3atom 71 CH "CH C-terminal Pro" 6 13.019 3atom 72 CH "HCO N-Formyl" 6 13.019 2atom 73 C "C (gamma) HisD" 6 12.011 3atom 74 C "CH (delta) HisD" 6 12.011 3atom 75 H "H(C) Aromatic" 1 1.008 1atom 76 O "OH Tyr" 8 15.999 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)+s1t/2] s3 = dx/dt [w/ t=t+t/2, x = x(t)+s2t/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!

Goddard, CaltechGoddard, Caltech

Multiple Scale Simulation

Large Gear Drives Small Gear

G. Hong et. al., 1999

Nano-oscillators

Zhao, Ma, Chen & Jiang, Phys. Rev. Lett. 2003

Nanoscopic Electromechanical Device (NEMS)

Computer-Aided Drug Design

GENOMICS

Human Genome Project

Computer-aided drug design

Chemical Synthesis

Screening using in vitro assay

Animal Tests

Clinical Trials

ALDOSE REDUCTASE

O

HO OH

HO OH

HO

glucose

HO

HO OH

HO OH

HO

sorbitol

Aldose Reductase

NADPH NADP

Diabetes DiabeticComplications

Glucose Sorbitol

Design of Aldose Reductase Inhibitors

Aldose Reductase

Inhibitor

TYR48 LYS77

HIS110

TRP111

PHE122

TYP219

TRP20

CYS298LEU300

NADPH

TRP79

VAL47

Aldose Reductase Active Site Structure

Cerius2 LigandFit

To further confirm the AR-ARI binding,We perform QM/MM calculations on drug leads.

CHARMM

5'-OH, 6'-F, 7'-OH

NH

NMe

NH

HN

O

O

O

5'

6'

7'8'

X

Binding energy is found to be –45 kcal / mol

Docking of aldose reductase inhibitor

Cerius2 LigandFit

Aldose reducatse

(4R)-6’-fluoro-7’-hydroxyl-8’-bromo-3’-methylspiro-[imidazoli-dine-4,4’(1’H)-quinazoline]-2,2’,5(3’H)-trione

Inhibitor

Hu & Chen, 2003

Interaction energy between ligand and protein

Quantum Mechanics/Molecular Mechanics (QM / MM)

Hu & Chen, 2003

a:Inhibitor concentration of inhibit Aldose Reductase;b: the percents of lower sciatic nerve sorbitol levelsc: interaction with AR in Fig. 4

NH

NMe

NH

HN

O

O

O

5'

6'

7'8'

X

SARS 3CL Protease

“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).

ABInhibitor siteComplex withhexapeptidylCMK inhibitor

New ligand candidates for SARS 3Cl-Protease generated by a known compound AG7088

NON

O

O

O

N

N

O

O

O

H H

HO

NON

O

O

O

N

N

O

O

O

H H

H

OH

NON

O

O

O

N

N

O

O

O

H H

H

OH

NO

N

O

O

O

N

N

O

O

O

F

H H

H

AG7088

Anand, et al, Science, 300, 1763 (2003)

Our prediction

NON

O

O

O

N

N

O

O

O

H H

H