Molecular Modelling - Lecture 2

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Molecular Modelling - Lecture 2

• Techniques for Conformational Sampling
• Uses CHARMM force field
• Written in C

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Protein example
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Monte Carlo Simulations

• Technique used to perform first computer
  simulation of a molecular system
• Monte Carlo some kind of random sampling

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Monte Carlo Methods

• Basis of Monte Carlo methods is the use of random
  selections in calculations that lead to the
  solution of numerical and physical problems e.g.
• brownian motion
• molecular modelling
• designing nuclear reactors
• predicting the evolution of stars
• forecasting the stock market
• Each calculation is independent of the others and
  hence amenable to embarrassingly parallel methods

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Monte Carlo Integration finding value of p

• Monte Carlo integration
• Compute r by generating random points in a square
  of side 2 and counting how many of them are in
  the circle with radius 1 (x2y2lt1 p4ratio) .

Area of square4
Area p
2
2
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Monte Carlo Simulations

• Configurations are generated by making random
  changes to the positions of the atoms
• Importance sampling
• Samples from 3N dimensional space of positions of
  molecules

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Monte Carlo Simulations
Z Configurational integral
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Metropolis Monte Carlo

• Biases generation of configurations towards those
  that make the most significant contributions to
  the integral
• Low energy states for most thermodynamic
  properties
• Generates states with probability exp(?????x??and
  counts them equally
• (simple Monte Carlo would generate them with
  equal probability and then weight them by
  exp(?????x? ?

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Markov chain of states
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Monte Carlo Advantages/Disadvantages

• Advantages
• Does not require a continuous energy function (as
  in MD)
• Number of particles can easily vary (very hard in
  MD)
• Disadvantages
• Highly correlated motions hard to simulate
• Poor sampling of large-scale changes

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Molecular Dynamics

• Newtons equations of motions are integrated to
  propagate the structure through time

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Molecular Dynamics

• fast large systems can be modelled
• history of molecular motion and interactions
• conformational distribution for simulation

?
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Molecular Dynamics - Integration methods

• Finite difference methods
• Used to generate molecular dynamics trajectories
  with continuous potentials
• Integration broken into stages separated by time
  ?t
• Total force on each particle at time t is
  calculated as a vector sum of all the
  interactions with other particles
• From force can determine accelerations
• Combined with positions and velocities at time t
  to calculate positions and velocities at time t
  ?t
• Force assumed to be constant during time step

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Molecular Dynamics - Integration methods

• Many algorithms
• Verlet
• Leap frog method
• Predictor-corrector
• Velocity-Verlet

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Molecular Dynamics - Verlet Integration Method

• Most widely used method

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Timescale Limitations
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MD Production Run Protocol
Initial coords obtained from experimental data or
theoretical model
Can be done by randomly selecting from a
Maxwell-Boltzmann distribution at the temperature
of interest
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Truncating Long-Range forces and the minimum
image convention

• Non-bonded interactions most time-consuming part
  of a simulation
• N2
• Minimum image convention
• Interaction for a molecule i are only counted
  between it and its closest image
• Truncation of potential creates problems with
  consistent potential and force

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Truncating Long-Range forces and the minimum
image convention

• Use smoothing functions to smoothly switch off
  the interaction between a cut-on and a
  cut-off distance.

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Simulated Annealing

• special case of either MD (quenched' MD) or MC
  simulation, in which the temperature is gradually
  reduced during the simulation.
• Often, the system is first heated and then cooled
• the system is given the opportunity to surmount
  energetic barriers in a search for conformations
  with energies lower than the local-minimum energy
  found by energy minimization.
• can lead to more realistic simulations of
  dynamics at low temperature
• more expensive than energy minimization.