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Survey of Molecular Dynamics Simulations By Will Welch For Jan Kubelka CHEM 4560/5560 Fall, 2014 University of Wyoming

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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

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Why Molecular Dynamics? 1. Scale: Large collections of interacting particles that cannot (and should not) be studied by quantum mechanics. 2. Dynamics: time dependent behavior and non-equilibrium processes. ~115 nm ~2,000,000 atoms ~25 nm ~500,000 atoms Quantum Classical limit? Still far from bulk material… Monte Carlo methods can predict many of the same things, but do not provide info on time dependent properties Lattice fluids Continuum models

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A Few Theoretical Concepts microcanonical grand canonical Isothermal-isobaric Statistical Ensembles In Equilibrium MD, we want to sample the ensemble as best as possible!

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A Few Theoretical Concepts Classical configuration Integral

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Lennard-Jones Potential Hard sphere Potential Potentials modeling pairwise interactions. The van Der Waals Equation

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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)

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Common types of force fields United Atom Beads include H atoms in CH 2 CH 3 etc. Most atoms uncharged, Exceptions for O-H groups etc. All Atom Includes explicit H atoms Partial charges on most atoms OPLS-AA, CHARMM, AMBER and many others OPLS-UA, TraPPE-UA, Coarse Grain Beads include large functional groups. 1 (nonpolar) Martini water bead represents 4 water molecules… Tip4p SPC σ/2 (http://espressomd.org) http://dx.doi.org/10.1063/1.4863329 ( graphic: sklog Wiki )

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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…

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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: How do the dynamics happen? The **basic** idea…

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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?

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What is a suitably short time step? How do the dynamics happen? Adequately Short Time step Time step Too long Must be significantly shorter than the fastest motion in your simulation: What is frequency of C-H stretch. O-H stretch? Constraint algorithms: Shake, Rattle, LINCS Minimum time step depends on what you are monitoring. At least, simulation must be stable. Normal restoring force Huge restoring force: simulation crashes

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Cuttoffs and Boundaries 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? Do we use the entire configuration integral? Cutoff (modified cutoff) radii For L-J, 2.5σ Long-range electrostatics Ewald Sums Graphic credit: http://server.ccl.net/cca/documents/molecular- modeling/node9.html Graphic credit: http://beam.acclab.helsinki.fi/~koehenri

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