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Biophysical Chemistry G4170:

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9, 1 (1976); Duijnen and Thole, Biopolymers, 21, 1749 (1982) Polarizable Force Fields ... Thole 1981; Rullmann & van Duijnen 1988; Cieplak & Kollman 1990; ... – PowerPoint PPT presentation

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Title: Biophysical Chemistry G4170:


1
Biophysical Chemistry G4170 Introduction
to Molecular Dynamics
Ruhong Zhou
IBM Thomas Watson Research Center Yorktown
Heights, NY 10598
2
Polarizable Force Fields
3
Solvent-Induced Dipole
It takes energy to change from gas-phase to
liquid-phase charges for H2O, DUpol 2-5
kcal/mol
4
Conformational Effects
Wada, Adv. Biophys., 9, 1 (1976) Duijnen and
Thole, Biopolymers, 21, 1749 (1982)
5
Polarizable Force Fields
  • Atomic charges adjust to different chemical
    environments
  • Electrostatic interactions are long-ranged
    interactions, accurate models needed
  • Needed to calculate many-body interactions
  • Hopefully a better transferability

A
C
B
EAB (C) Energy between A B depends on Cs
position
6
Polarizable Force Fields
  • Friesner Berne Polarizable OPLSAA
  • Fluctuating charges and fluctuating dipoles
  • Kollman Case AMBER2002
  • Dipole polarizability
  • Ponder TINKER Force Field
  • Dipole polarizability, and higher multipoles
    such as quadruples

7
Fluctuating Charge Model
  • Dqi change in partial charge on atom i
  • Vi applied electrostatic potential at atom i
  • Jij coefficient representing interaction between
    partial charges at sites i,j depends on nuclear
    configuration
  • Minimize Upolarization to find Dqi, yielding a
    set of linear equations.
  • Alternatively, treat Dqi as dynamical variables
    and propagate them along with the coordinates
    xi,yi,zi,qi

S. Rick, S. Stuart, and B. Berne, J. Chem. Phys.
1994
8
Dipolar Polarizability Models
  • ai polarizability of atom i
  • mi induced dipole on atom i
  • Ei applied electric field at atom i
  • Jij dipole interaction tensor representing
    interaction between dipoles at sites i,j

After defining ai 1/Jii, we can rewrite it into
Thole 1981 Rullmann van Duijnen 1988 Cieplak
Kollman 1990 Bernardo, Ding, Krogh-Jerpersen,
Levy 1994
9
Combined Fluctuating Charge Dipole Model
Each atom can have both a partial charge and a
dipole, so it might have up to four variables
one charge and three dipole moments
Charges on atoms A and dipoles on atoms B.
All models may be written succinctly in matrix
form
where vectors fV, Ex, Ey, Ez and qq, mx,
my, mz
Minimize to determine charges and/or dipole
Moments on each atom
J. Bank, G. Kaminski, R. Zhou, D. Mainz, B.
Berne, R. Friesner, J. Chem. Phys. 110, 741,
1999 H. Stern, G. Kaminski, J. Banks, R. Zhou, B.
Berne, R. Friesner, J. Phys. Chem. B103, 4730,
1999 G Kaminski, H. Stern, B. Berne, R. Friesner,
Y. Cao, R. Murphy, R. Zhou, J. Comput. Chem. 23,
1515, 2002 G. Kaminski, R. Friesner, R. Zhou, J.
Comput. Chem. 24, 267, 2003
10
Polarizable FF Fitting Philosophy
  • Polarization
  • Treat long-range interactions by Coulombs law.
    Scale short-range interactions by adjustable
    parameters
  • Apply a series of electrostatic perturbations to
    a molecule
  • For each perturbation, compute the change in the
    electrostatic potential at a series of grid
    points from ab initio calculations on the
    unperturbed and perturbed molecules
  • Fit the parameters of the model so as to best
    reproduce these changes when the same
    perturbation are applied
  • Gas-phase electrostatics choose fixed charges so
    that the total electrostatic potential of the
    model best reproduces high-level ab initio
    gas-phase calculations
  • Intramolecular, Lennard-Jones, and torsional
    terms take from OPLSAA. Refit key torsions to ab
    initio relative conformational energies

11
Three-body Energies for molecules with two probes
  • E(3) E123 E12 E23 E13 E1 E2 E3
  • 3-body energies are all zero in standard force
    fields
  • RMS errors are from comparisons to high
    level QM calculations

12
Cases where fluctuating charge model fails
  • Two cases that point-charge-only model fails for
    three-body energies
  • Bifurcated hydrogen bond
  • Probes above or below aromatic rings,
    out-of-plane polarization

13
Relative Conformational Energy
14
Summary on Polarizable OPLSAA
  • Force fields incorporating explicit polarization
    have been developed that accurately predict
    many-body effects
  • Polarizable FF dramatically improves the
    prediction of relative conformational energies
    for small peptides
  • Dipolar model can correct errors in fluctuating
    charge model alone for cases with out-of-plane
    polarization (aromatic rings) or bifurcated
    hydrogen bonds (O, S atoms)
  • Parameterization was systematic and transferable

15
II. Solvation Models
16
Solvation Models
  • Explicit solvent models
  • Fixed charge models SPC, SPC/E, TIP3P, TIP4P,
    TIP5P, ST2,
  • Polarizable water models TIP4P/FQ, POL5, MCDHO,
  • Implicit Solvent models
  • Poisson-Boltzman solver (Delphi, Honig)
  • Generalized Born Model (Still)
  • Karplus EEF1 model
  • Benoit Rouxs Spherical Solvent Boundary
    Potential (SSBP)

17
Explicit Water modelsSPC, SPC/E, TIPnP, POL5
18
Water Model Geometries
19
Water Model Parameters
  • SPC, SPC/E (Berendsen)
  • TIP3P, TIP4P, TIP5P (Jorgensen)
  • TIP4P/FQ, POL5 (Berne)

20
Properties of Water Models
21
Water density maximum
22
Water structure comparison
M. Mahoney and W. L. Jorgensen, J. Chem. Phys.
112, 8910, 2000
23
POL5 Model
24
Gas-phase electrostatic properties
25
Water dimer properties
26
Trimer
27
Tetramer
28
Pentamer
29
Hexamers
30
Book hexamer
31
Prism hexamer
32
Liquid-state properties
33
Water density revisited
34
Implicit Solvent ModelsPBF, GB
35
Continuum Solvent Model
continuum solvent e80
e1-4 protein
36
Molecular Surfaces
  • Dotted line Solvent Accessible Surface (SAS)
  • Solid line molecular surface (MS)
  • Shaded grey area van der Waals surface

37
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42
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43
R. Levy, JCC 2002
44
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45
Molecular Surface Colored by Potential
The molecular surface of acetyl choline esterase
molecule color coded by electrostatic potential.
the view is directly into the active site and
acetyl choline is present in a bond
representation. note the depth of the pocket, its
negative nature corresponding to the positive
charge on the acetyl choline.
46
Trp-cage Folding Kinetics
  • OPLS united atom Force Field
  • Continuum Solvent GBSA
  • Langevin dynamics
  • Water viscosity g91/ps

B MD simulation C NMR structure 2.1 A Ca
RMSD Folding time 1.5ms (3.0 A cutoff) to 8.7 ms
(2.5 A cutoff)
M. Snow, B. Zagrovic, V. Pande, JACS 124, 14548,
2002
47
Trp-cage Folding Structure
Blue MD simulation Grey NMR structure 0.97 A Ca
RMSD 1.4 A RMSD heavy atoms
  • AMBER99 Force Field
  • Continuum Solvent GBSA
  • NVT ensemble

C. Simmerling, B. Strockbine, A. Roitberg, JACS
124, 11258, 2002
48
Protein (un)Folding Example a b-hairpin
Protein G (2gb1)
  • Res. 41-56

GEWTYDDATKTFTVTE
V. Munoz, P. Thompson, J. Hofrichter, W. Eaton,
Nature, 390, 196, 1997 R. Zhou, B. Berne and R.
Germain, PNAS, 98, 14931, 2001
49
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50
b-hairpin Folding in Various Models
  • OPLSAA/SPC (explicit)
  • OPLSAA/SGB
  • OPLSAA/PB

R. Zhou, B. J. Berne, PNAS 99, 2002 R. Zhou, G.
Krilov, B. J. Berne, JPC, 2004
R. Zhou, et al, PNAS 98, 2001 R. Zhou, and B.
Berne, PNAS 99, 2002
51
Lowest free energy structures
Explicit
SGB
PB
  • Erroneous salt-bridges exist in all continuum
    solvent models
  • Overly strongly salt-bridge effects expelled F50
    out of the hydrophobic core in SGB
  • PB models behaves significantly better than the
    GB model
  • Both PB and GB models need improvements

52
Computational expenseSimulations using standard
Ewald summation and 256 molecules
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