1 Molecular Simulation 黃鎮剛交通大學生物科技系及生物資訊所. 2 Empirical Force Field jkhwang/molsim

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Molecular SimulationMolecular Simulation

黃鎮剛交通大學

生物科技系及生物資訊所

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Empirical Force FieldEmpirical Force Field

• http://life.nctu.edu.tw/~jkhwang/molsim

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Free softwareFree software

• VMD & NAMD Molecular Dynamics, Graphics (OpenGL)

• SwissPDB Viewer Minimization, Modeling, Graphics (OpenGL)

• Cn3D Strutcure alignment, Graphics (OpenGL)

• Rasmol Graphics (2D)

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Warming upWarming up

• Let's take a look at VMD

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Molecular Simulation Jump Start

Molecular Simulation Jump Start

• Quick Start

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A simple empirical force fieldA simple empirical force field

€

V r( ) = Kb b − b0( )bonds

∑

+ Kθ θ i −θ0( )angles

∑

+ Vn 1+ cos nφ − φ0( )( )torsions

∑

+AiA j

rij12

−BiB j

rij6

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

j

∑i

∑ +332QiQ j

rij

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Analysis of molecular topology

Analysis of molecular topology

• Bonded interactions The number of bonds

• 1-2 interactions

The number of angles• 1-3 interactions

The number of torsions• 1-4 interactions

• Non-bonded interactions Van der Waals and electrostatic interactions

• The nunmber of nonbonded interactions

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?? bonds?? angle terms?? torsional terms?? non-bonded interactions

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How many types of bonds?

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C-C C-H

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C-C 2C-H 8

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10 bonds?? angle terms?? torsional terms?? non-bonded interactions


C-C 2C-H 8

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How many types of angles?

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C-C-CC-C-HH-C-H


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C-C-C 1C-C-H 10H-C-H 7


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10 bonds18 angle terms?? torsional terms?? non-bonded interactions

C-C-C 1C-C-H 10H-C-H 7


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How many types of torsions?

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H-C-C-HH-C-C-C

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10 bonds18 angle terms18 torsional terms?? non-bonded interactions


H-C-C-H 12H-C-C-C 6

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How many types of nonbonded ineractions?

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H-HC-C

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10 bonds18 angle terms18 torsional terms27 non-bonded interactions


H-H 21C-C 6

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Force field parametersForce field parameters

• Transferability A C-H is a C-H, no matter where it occurs. Force fields are empirical, there is no so-

called "correct" form for a force field. The form of force field is a compromise

between "accuracy" and "computational efficiency".

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• Atom types Contains information about hybridization and

sometimes the local environment. sp3, sp2, sp The reference angles is 109.5 for sp3 carbon

and 110 for sp2 carbon

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Bond stretchingBond stretching

• Morse potential

• Harmonic potential€

V = D 1− exp −a b − b0( )[ ]{ }2

a = ω μ /2D

€

V =K

2b − b0( )

2

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€

V = K b − b0( )2

C_04 H_01 250.0 1.090C_04 C_04 250.0 1.523C_04 C_03 250.0 1.534C_04 N_03 250.0 1.470C_04 N_04 200.0 1.430C_04 O_01 200.0 1.430C_03 C_03 500.0 1.393C_03 H_01 50.00 1.024C_03 N_03 500.0 1.324C_03 N_04 500.0 1.339C_03 O_00 500.0 1.235C_03 O_01 500.0 1.460C_04 S_02 250.0 1.789N_03 H_01 250.0 1.040N_04 H_01 250.0 1.039O_01 H_01 252.0 0.970S_02 H_01 250.0 1.000

K in kcal/mol/A2

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€

V = K b − b0( )2

C_04 H_01 250.0 1.090C_04 C_04 250.0 1.523C_04 C_03 250.0 1.534C_04 N_03 250.0 1.470C_04 N_04 200.0 1.430C_04 O_01 200.0 1.430C_03 C_03 500.0 1.393C_03 H_01 50.00 1.024C_03 N_03 500.0 1.324C_03 N_04 500.0 1.339C_03 O_00 500.0 1.235C_03 O_01 500.0 1.460C_04 S_02 250.0 1.789N_03 H_01 250.0 1.040N_04 H_01 250.0 1.039O_01 H_01 252.0 0.970S_02 H_01 250.0 1.000

K in kcal/mol/A2

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€

V = Kθ θ −θ0( )2

H_01 C_04 H_01 60.0 109.2 H_01 C_04 O_01 60.0 109.2 C_04 C_04 C_04 60.0 111.1 C_04 C_04 H_01 60.0 109.2 C_04 C_04 N_03 60.0 108.2 C_04 C_04 O_01 60.0 109.8 C_03 C_04 C_04 60.0 109.8 C_03 C_04 H_01 60.0 109.2 C_03 C_04 N_03 60.0 112.3 C_03 C_04 O_01 60.0 110.0 N_04 C_04 C_04 60.0 110.9 N_04 C_04 H_01 60.0 109.2 N_03 C_04 H_01 60.0 108.2 N_03 C_04 N_03 120.0 120.0 H_01 C_03 H_01 40.0 120.0 N_03 C_03 O_00 120.0 123.1 N_04 C_03 N_04 120.0 119.9 O_00 C_03 H_01 120.0 119.9 O_01 C_03 O_00 120.0 122.3 C_04 C_03 H_01 60.0 119.2 C_04 C_03 N_03 60.0 117.5 C_04 C_03 O_00 60.0 119.2 C_04 C_03 O_01 60.0 119.2

K in kcal/mol

C_03 C_03 C_04 120.0 120.0 C_03 C_03 C_03 120.0 119.9 C_03 C_03 H_01 60.0 120.0 C_03 N_04 C_04 60.0 124.0 C_03 N_04 H_01 60.0 120.0 C_04 N_04 H_01 60.0 109.9 H_01 N_04 H_01 60.0 120.0 H_01 N_03 H_01 60.0 113.9 C_04 N_03 C_04 60.0 110.6 C_04 N_03 H_01 60.0 113.0 C_03 N_03 C_04 60.0 120.9 C_03 N_03 H_01 60.0 120.4 Lp__ N_03 Lp__ 50.0 130.0 Lp__ N_03 H_01 50.0 109.0 Lp__ N_03 C_04 50.0 109.0 C_03 O_01 H_01 60.0 120.0 C_03 O_01 H_01 40.0 120.0 C_04 O_01 H_01 60.0 120.9 C_04 O_01 C_04 50.0 119.0 H_01 O_01 H_01 50.0 110.0 Lp__ O_01 Lp__ 50.0 130.0 Lp__ O_01 H_01 50.0 109.0 Lp__ O_01 C_04 50.0 109.0 Lp__ O_01 C_03 50.0 120.0

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€

V = Kφ 1+ cos nφ + φ0( )[ ]

C_04 C_04 1.40 3 0.0 C_04 C_03 0.00 2 180.0 C_04 O_01 0.60 3 0.0 C_03 C_03 10.00 2 180.0 C_03 C_00 10.00 2 180.0 C_03 H_01 10.00 2 180.0 C_03 N_03 7.50 2 180.0 C_03 O_00 0.00 1 0.0 C_03 O_01 0.00 1 0.0 H_01 N_03 7.50 2 180.0 N_03 C_04 0.00 3 0.0 N_04 C_04 1.40 3 0.0 N_04 C_03 10.00 2 180.0 N_04 H_01 7.50 2 180.0 S_02 C_04 1.00 3 0.0 S_02 C_03 0.00 3 0.0 S_02 S_02 6.00 2 0.0

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€

V = Kφ 1+ cos nφ + φ0( )[ ]

C_04 C_04 1.40 3 0.0 C_04 C_03 0.00 2 180.0 C_04 O_01 0.60 3 0.0 C_03 C_03 10.00 2 180.0 C_03 C_00 10.00 2 180.0 C_03 H_01 10.00 2 180.0 C_03 N_03 7.50 2 180.0 C_03 O_00 0.00 1 0.0 C_03 O_01 0.00 1 0.0 H_01 N_03 7.50 2 180.0 N_03 C_04 0.00 3 0.0 N_04 C_04 1.40 3 0.0 N_04 C_03 10.00 2 180.0 N_04 H_01 7.50 2 180.0 S_02 C_04 1.00 3 0.0 S_02 C_03 0.00 3 0.0 S_02 S_02 6.00 2 0.0

The parameters depend only on 2,3 atoms

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€

V =1.4 1+ cos 3φ + 0( )[ ]

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€

V =1.4 1+ cos 3φ + 0( )[ ]

50 100 150 200 250 300 350

0.5

1

1.5

2

2.5

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€

V =10 1+ cos 2φ + π( )[ ]

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€

V =10 1+ cos 2φ + π( )[ ]

50 100 150 200 250 300 350

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35

40

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Improper torsional angles

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Improper torsional anglesImproper torsional angles1

2

3 4

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Improper torsional angles

1

2

3 4

€

V = Vφ 1+ cos 2φ + π( )[ ]

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Atom ro

C_03 1.75 3.9202 0.0376 C_04 1.85 3.9150 0.0738 H_01 1.10 2.6525 0.0010 N_03 1.65 3.2171 0.4132 O_00 1.60 3.2005 0.1848 O_01 1.60 3.2005 0.1848 S_02 1.85 3.9150 0.0738 Lp__ 1.10 2.6525 0.0010

€

V r( ) =AiA j

rij12

−BiB j

rij6

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

j

∑i

∑ +332QiQ j

rij

Ai = εr06

Bi = 2εr03

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Cross-term interactions

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Cross termsCross terms

• Stretch-stretch• Stretch-torsion• Stretch-bend• Bend-torsion• Bend-bend• These terms are important for vibrational fr

equency prediction.

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Staggering effectStaggering effect

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Staggering effect

Carbon: +1Lone electron -1/2

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PolarizationPolarization

€

μind = αE

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Polarization

€

μind = αE

€

μind ,i = αEi

Ei =q jrij

rij3

j≠ i

∑ +

r μ ijrij

3j≠ i

∑ 3rij

rij

rij

−1 ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

Approximation

Electrostatic field does not include contributions from atom i

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Polarization

New model

H

H

O

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• Polarization is computational intensive

• Its effects is important in the simulation of ionic solution. The system usually contains atom or ions and small molecules.

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Solvent dielectric modelsSolvent dielectric models

€

V =QiQ j

εrij

Effetive dielectric constant

€

eff r( ) = εr −εr −1

2rS( )

2+ 2rS + 2[ ]e

−rS

S = 0.15Å−1 ~ 0.3Å−1

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Hydrogen bondsHydrogen bonds

• Hydrogen bond is of electrostatic nature. No special term for hydrogen bonds

• Or

• 10-12 potential

€

VHB =C

d6−

D

d4

⎛

⎝ ⎜

⎞

⎠ ⎟cos4 θ

is the angle formed by A…H-D

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Water modelsWater models

• SPC, SPC/E, TIP3P

• TIP4P, BF

• ST2

Documents

1 Molecular Simulation 黃鎮剛 交通大學 生物科技系及生物資訊所. 2 Empirical Force Field jkhwang/molsim

1 Molecular Simulation 黃鎮剛交通大學生物科技系及生物資訊所. 2 Empirical Force Field jkhwang/molsim