Molecular Dynamics: Review

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Molecular Dynamics Review
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Molecular Simulations

• NMR or X-ray structure refinements
• Protein structure prediction
• Protein folding kinetics and mechanics
• Conformational dynamics
• Global optimization
• DNA/RNA simulations
• Membrane proteins/lipid layers simulations

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Molecular Dynamics

• From Lecture 6 (Robert)
• MD is our approximation to how molecules explore
  their
• potential energy surface in the real world
• The atoms are heated by giving them a
  distribution of
• velocities corresponding to temperature we wish
  to simulate
• The wiggling and jiggling of the atoms is then
  obtained by
• integrating the Newtonian laws of motion
• This gives us the Ei's of all states i
  occupied at that
• temperature as long as we simulate long enough

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I. Force Fields
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Force Fields Typical Energy Functions

• Bond stretches
• Angle bending
• Torsional rotation
• Improper torsion (sp2)
• Electrostatic interaction
• Lennard-Jones interaction

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Bonding Terms bond stretch

• Most often Harmonic

r0
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Bonding Terms angle bending

• Most often Harmonic
• CHARMM force fields Urey-Bradley angle term

q0
This UB term is only found in CHARMM force
field to optimize the fit to vibrational
spectra. s the 1,3-distance.
Mackerell et al. J. Phys. Chem. B 102, 3586, 1998
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Bonding Terms Torsions

• Torsion energy rotation about a bond (dihedral
  angles)

i
k
f
l
j
i-j-k-l
Vn force constant n periodicity of the angle
( determines how many peaks and wells in
the potential, often from 1-6 ) d
phase of the angle (often 0º or 180º)
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Bonding Terms Improper Torsions

• Improper torsion is not a regular torsion angle.
  It is used to describe the energy of out-of-plane
  motions. It is often necessary for planar groups,
  such as sp2 hybridized carbons in carbonyl groups
  and in aromatic rings, because the normal torsion
  terms described above is not sufficient to
  maintain the planarity (w0).

j
w
k
l
i
or
i-j-k-l
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Non-bonded Terms

• Electrostatic interactions
• (Coulombs Law)
• Lennard-Jones interactions

1/r
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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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Implicit Solvent ModelsPBF, GB
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Continuum Solvent Model
continuum solvent e80
e1-4 protein
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III. Molecular Dynamics
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Molecular Dynamics

• Solve Newtons equation for a molecular system

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Integrator Verlet Algorithm
Start with r(t), v(t), integrate it to
r(tDt), v(tDt)
r(tDt), v(tDt)
The new position at tDt
r(t), v(t)
(1)
Similarly, the old position at t-Dt
(2)
Add (1) and (2)
(3)
Thus the velocity at t is
(4)
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Typical MD Flowchart
Program MYMD simple MD program call
init initialization t 0 do while (t .lt.
tmax) MD loop call force (x, f,
en) calculate the force call integrate (x,
f, en) integrate equation of motion t t
delt call sample sample averages enddo
stop end
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Periodic Boundary ConditionsMinimum Image



rc
Central simulation box
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One MD example Determining voltage threshold for
translocation of dsDNA through Si3N4 pores To
establish the threshold field required to drive
dsDNA through a 2.0 nanometer diameter pore. The
3.9 V path caused the partial unzipping of the
DNA strands prior to reaching the center of the
membrane. http//www.ks.uiuc.edu/Research/nano
pore/
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Historical Perspective on MD
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The Next Generation in MD

• Current longest MD simulations microsecond vs.
  time scale of many biologically interesting
  phenomena is millisecond
• Anton, Desmond
• Scientific advances Drug Discovery

Faculty in Computer Science Department at
Columbia University, till1986 D. E. Shaw  Co., In
c., founded in 1988 1994, pointed by President
Clinton, President's Council of Advisors on
Science and Technology
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Acknowledgement

• Powerpoint slices from Ruhong Zhou