Biophysical Chemistry G4170:

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Biophysical Chemistry G4170 Introduction
to Molecular Dynamics
Ruhong Zhou
IBM Thomas Watson Research Center Yorktown
Heights, NY 10598
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Polarizable Force Fields
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Solvent-Induced Dipole
It takes energy to change from gas-phase to
liquid-phase charges for H2O, DUpol 2-5
kcal/mol
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Conformational Effects
Wada, Adv. Biophys., 9, 1 (1976) Duijnen and
Thole, Biopolymers, 21, 1749 (1982)
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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
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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

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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
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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
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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
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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

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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

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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

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Relative Conformational Energy
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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

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II. Solvation Models
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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)

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Explicit Water modelsSPC, SPC/E, TIPnP, POL5
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Water Model Geometries
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Water Model Parameters

• SPC, SPC/E (Berendsen)
• TIP3P, TIP4P, TIP5P (Jorgensen)
• TIP4P/FQ, POL5 (Berne)

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Properties of Water Models
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Water density maximum
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Water structure comparison
M. Mahoney and W. L. Jorgensen, J. Chem. Phys.
112, 8910, 2000
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POL5 Model
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Gas-phase electrostatic properties
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Water dimer properties
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Trimer
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Tetramer
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Pentamer
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Hexamers
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Book hexamer
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Prism hexamer
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Liquid-state properties
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Water density revisited
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Implicit Solvent ModelsPBF, GB
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Continuum Solvent Model
continuum solvent e80
e1-4 protein
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Molecular Surfaces

• Dotted line Solvent Accessible Surface (SAS)
• Solid line molecular surface (MS)
• Shaded grey area van der Waals surface

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R. Levy, JCC 2002
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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.
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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
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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
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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
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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
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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

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Computational expenseSimulations using standard
Ewald summation and 256 molecules