Molecular Modelling - Lecture 2 Techniques for Conformational Sampling Uses CHARMM force field Written in C++
Dec 13, 2015
Molecular Modelling - Lecture 2
Techniques for Conformational Sampling
Uses CHARMM force field
Written in C++
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
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
Monte Carlo Integration : finding value of πMonte 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 (x2+y2<1; π=4*ratio) .
Area= π2
2
Area of square=4
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
Monte Carlo Simulations
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Z= Configurational integral
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(xand counts them equally (simple Monte Carlo would generate them with equal
probability and then weight them by exp(x
Monte Carlo Advantages/DisadvantagesAdvantages:
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
Molecular Dynamics
Newton’s equations of motions are integrated to propagate the structure through time
€
dx idt
= v i
dv idt
=Fim
Fi =∇ iE
Molecular Dynamics
fast: large systems can be modelledhistory of molecular motion and
interactions conformational distribution for simulation
t
360
0
P
3600
Molecular Dynamics - Integration methodsFinite 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
Molecular Dynamics - Integration methodsMany algorithms:
Verlet Leap frog method Predictor-corrector Velocity-Verlet
Molecular Dynamics - Verlet Integration Method
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Most widely used method
MD Production Run Protocol
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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
Truncating Long-Range forces and the minimum image conventionNon-bonded interactions most time-
consuming part of a simulation N2
Minimum image convention: Interaction for a molecule i are only counted
between it and it’s closest image
Truncation of potential creates problems with consistent potential and force
Truncating Long-Range forces and the minimum image conventionUse 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.