Molecular Dynamics, Monte Carlo and Docking Lecture 21 Introduction to Bioinformatics MNW2

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Molecular Dynamics, Monte Carlo and
DockingLecture 21Introduction to
BioinformaticsMNW2
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Allowed phi-psi angles
Red areas are preferred, yellow areas are
allowed, and white is avoided
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2.3a Hamiltonian equations of motion

• Hamiltonian equations (one degree of freedom)
• H Hamiltonian function, Hamiltonian,
• q, p Canonical variables generalized coordinate
  (q) and momentum impulses (p).

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q coordinates p momentum
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v(t) (r(t ?t) - r(t - ?t))/2?t
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Molecular Dynamics

• Knowledge of the atomic forces and masses can be
  used to solve the position of each atom along a
  series of extremely small time steps (on the
  order of femtoseconds 10-15 seconds). The
  resulting series of snapshots of structural
  changes over time is called a trajectory. The use
  of this method to compute trajectories can be
  more easily seen when Newton's equation is
  expressed in the following form
• The "leapfrog" method is a common numerical
  approach to calculating trajectories based on
  Newton's equation. The steps can be summarized as
  follows

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Force field
The potential energy of a system can be expressed
as a sum of valence (or bond), crossterm, and
nonbond interactions The energy of valence
interactions comprises bond stretching (Ebond),
valence angle bending (Eangle), dihedral angle
torsion (Etorsion), and inversion (also called
out-of-plane interactions) (Einversion or Eoop)
terms, which are part of nearly all forcefields
for covalent systems. A Urey-Bradley term (EUB)
may be used to account for interactions between
atom pairs involved in 1-3 configurations (i.e.,
atoms bound to a common atom)
Evalence Ebond Eangle Etorsion
Eoop EUB Modern (second-generation)
forcefields include cross terms to account for
such factors as bond or angle distortions caused
by nearby atoms. Crossterms can include the
following terms stretch-stretch,
stretch-bend-stretch, bend-bend, torsion-stretch,
torsion-bend-bend, bend-torsion-bend,
stretch-torsion-stretch. The energy of
interactions between nonbonded atoms is accounted
for by van der Waals (EvdW), electrostatic
(ECoulomb), and (in some older forcefields)
hydrogen bond (Ehbond) terms
Enonbond EvdW ECoulomb
Ehbond
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Force field
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energy
distance
f a/r6 - b/r12 Van der Waals forces
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F kq1q1/r2
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Figure Snapshots of ubiquitin pulling with
constant velocity at three different time steps.
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antibody HyHEL-63 (cyan) complexed with Hen Egg
White Lysozyme
The X-ray structure of the antibody HyHEL-63
(cyan) uncomplexed and complexed with Hen Egg
White Lysozyme (yellow) has shown that there are
small but significant, local conformational
changes in the antibody paratope on binding. The
structure also reveals that most of the charged
epitope residues face the antibody. Details are
in Li YL, Li HM, Smith-Gill SJ and Mariuzza RA
(2000) The conformations of the X-ray structure
Three-dimensional structures of the free and
antigen-bound Fab from monoclonal antilysozyme
antibody HyHEL-63. Biochemistry 39 6296-6309.
Salt links and electrostatic interactions
provide much of the free energy of binding. Most
of the charged residues face in interface in the
X-ray structure. The importance of the salt link
between Lys97 of HEL and Asp27 of the antibody
heavy chain is revealed by molecular dynamics
simulations. After 1NSec of MD simulation at
100C the overall conformation of the complex has
changed, but the salt link persists. Details are
described in Sinha N and Smith-Gill SJ (2002)
Electrostatics in protein binding and function.
Current Protein Peptide Science 3 601-614.