Transcript Molecular Dynamics Lecture 1 (.pptx)

Survey of Molecular Dynamics
Simulations
By Will Welch
For Jan Kubelka
CHEM 4560/5560
Fall, 2014
University of Wyoming
Overview
• Week 1—Keep it simple
– Basic concepts in MD
– GROMACS tutorial, solvated, ionized protein
– Building and Visualization
• Week 2—Deeper concepts
– Sampling, Equilibrium vs. Non-equilibrium.
– Umbrella Sampling??
– Applications: Research examples
Why Molecular Dynamics?
1. Scale: Large collections of interacting particles that cannot
(and should not) be studied by quantum mechanics .
Classical limit?
Quantum
~500,000
atoms
~115 nm
~25 nm
~2,000,000
atoms
Still far from
bulk
material…
Lattice
fluids
2. Dynamics: time dependent behavior
and non-equilibrium processes.
Monte Carlo methods can predict many of the same
things, but do not provide info on time dependent
properties
Continuum
models
A Few Theoretical Concepts
Statistical Ensembles
𝑒 −𝛽𝐸𝑖
𝑄 𝑁, 𝑉, 𝛽 =
𝑖
Q is called the
Canonical Partition Function.
A 𝑁, 𝑉, 𝑇 = −𝑘𝑇𝑙𝑛𝑄
𝑆 𝑁, 𝑉, 𝐸 = −𝑘𝑙𝑛𝛺
𝑝𝑉 𝑉, 𝑇, 𝜇 = −𝑘𝑇𝑙𝑛𝛯
𝐺 𝑁, 𝑃, 𝑇 = −𝑘𝑇𝑙𝑛𝛥
microcanonical
grand canonical
Isothermal-isobaric
In Equilibrium MD, we want to sample the ensemble as best as possible!
A Few Theoretical Concepts
Classical configuration Integral
𝑈 𝑥1 = 𝑈 ′ 𝑥1 , 𝑦1 𝑧1 + 𝑓(𝑥2 … 𝑧𝑛 )
𝑓 𝑥2 … 𝑧𝑛 = ? ? ?
The van Der Waals Equation
Potentials modeling pairwise interactions.
Hard sphere Potential
Lennard-Jones Potential
Molecular Dynamics: Nuts and Bolts
 Particles (atoms and molecules): non-reactive, stable species (generally).
 trajectories determined by solving Newtonian equations of motion
 Forces on particles due to molecular mechanics force fields.
Basic Force Field components
+ other possibilites (implicit solvent, external potentials)
Common types of force fields
United Atom
OPLS-UA,
TraPPE-UA,
Includes explicit H atoms
Beads include
H atoms in CH2
CH3 etc.
All Atom
Partial charges on most atoms
Most atoms
uncharged,
Exceptions for
O-H groups
etc.
Tip4p
(graphic: sklog Wiki)
OPLS-AA, CHARMM, AMBER
and many others
Coarse Grain
Beads include large
functional groups.
SPC
σ/2
http://dx.doi.org/10.1063/1.4863329
1 (nonpolar) Martini
water bead
represents 4 water
molecules…
(http://espressomd.org)
Force Field Parametrization
• Force Fields are largely empirical
– You get so many parameters: Make them fit experiment!
• Ab initio calculations can be used
– How does one get charges?
– OPLS obtained dihedrals from QM simulations
• Practical stipulations:
– AMBER—all residues have integer charge
– TraPPE—Carbon hybridization dictates parameters
– CHARMM22—parameterized for tip3P water
• Transferability
– Want to model systems containing mixtures of particles which
were parameterized (want parameters to “transfer” to new
systems). Possible if all parameters derived in same way…
How do the dynamics happen?
 Forces on each particle are calculated at time t. The forces provide
trajectories, which are propagated for a small duration of time, Δt,
producing new particle positions at time t+ Δt. Forces due to new
positions are then calculated and the process continues:
The **basic** idea…
How do the dynamics happen?
• Verlet algorithm (http://www.fisica.uniud.it/~ercolessi/md/md/node21.html)
• Velocity Verlet algorithm
• Leap-Frog algorithm (From Wikipedia)
How do the dynamics happen?
What is a suitably short time step?
Must be significantly shorter than
the fastest motion in your
simulation:
What is frequency of C-H stretch. O-H stretch?
Adequately
Short Time
step
Normal
restoring
force
Huge restoring
force:
simulation
crashes
Time step
Too long
Minimum time step depends on what you are
monitoring. At least, simulation must be stable.
Constraint algorithms: Shake, Rattle, LINCS
Cuttoffs and Boundaries
Do we use the entire configuration integral?
Cutoff (modified cutoff) radii
For L-J, 2.5σ
Long-range electrostatics
Ewald Sums
Graphic credit: http://beam.acclab.helsinki.fi/~koehenri
How do you keep your particles from
drifting
out of the cell?
1.Create some type of a wall
2. PERIODIC BOUNDARY CONDITIONS
What’s the maximum cutoff?
Graphic credit: http://server.ccl.net/cca/documents/molecularmodeling/node9.html