Molecular Dynamics: Review

Molecular Simulations NMR or X-ray structure refinements Protein structure prediction Protein folding kinetics and mechanics Conformational dynamics Global optimization DNA/RNA simulations Membrane proteins/lipid layers simulations

Molecular Dynamics From Lecture 6 (Robert): MD is our approximation to how molecules explore their potential energy surface in the real world – The atoms are “heated” by giving them a distribution of velocities corresponding to temperature we wish to simulate – The wiggling and jiggling of the atoms is then obtained by integrating the Newtonian laws of motion – This gives us the Ei's of all states “i” occupied at that temperature as long as we simulate long enough

I. Force Fields

Force Fields: Typical Energy Functions Bond stretches Angle bending Torsional rotation Improper torsion (sp2) Electrostatic interaction Lennard-Jones interaction

Bonding Terms: bond stretch Most often Harmonic r0r0

Bonding Terms: angle bending Most often Harmonic CHARMM force field ’ s Urey-Bradley angle term: 00 This UB term is only found in CHARMM force field to optimize the fit to vibrational spectra. s: the 1,3-distance. Mackerell et al. J. Phys. Chem. B 102, 3586, 1998

Bonding Terms: Torsions Torsion energy: rotation about a bond (dihedral angles) Vn: force constant n: periodicity of the angle ( determines how many peaks and wells in the potential, often from 1-6 )  : phase of the angle (often 0º or 180º) i lj k i-j-k-l 

Bonding Terms: Improper Torsions Improper torsion is not a regular torsion angle. It is used to describe the energy of out-of-plane motions. It is often necessary for planar groups, such as sp2 hybridized carbons in carbonyl groups and in aromatic rings, because the normal torsion terms described above is not sufficient to maintain the planarity (w~0). or j li k i-j-k-l 

Non-bonded Terms Electrostatic interactions (Coulomb ’ s Law) Lennard-Jones interactions ~1/r

II. Solvation Models

Solvation Models Explicit solvent models –Fixed charge models: SPC, SPC/E, TIP3P, TIP4P, TIP5P, ST2,… –Polarizable water models: TIP4P/FQ, POL5, MCDHO,… Implicit Solvent models –Poisson-Boltzman solver (Delphi, Honig) –Generalized Born Model (Still) –Karplus’ EEF1 model –Benoit Roux’s Spherical Solvent Boundary Potential (SSBP)

Explicit Water models SPC, SPC/E, TIPnP, POL5

Water Model Geometries

Water Model Parameters SPC, SPC/E (Berendsen) TIP3P, TIP4P, TIP5P (Jorgensen) TIP4P/FQ, POL5 (Berne)

Implicit Solvent Models PBF, GB

Continuum Solvent Model continuum solvent  =80  =1-4 protein

III. Molecular Dynamics

Molecular Dynamics Solve Newton ’ s equation for a molecular system:

Integrator: Verlet Algorithm Start with {r(t), v(t)}, integrate it to {r(t+  t), v(t+  t)}: {r(t), v(t)} {r(t+  t), v(t+  t)} The new position at t+  t: Similarly, the old position at t-  t: (1) (2) Add (1) and (2): Thus the velocity at t is: (3) (4)

Typical MD Flowchart Program MYMDsimple MD program call initinitialization t = 0 do while (t.lt. tmax)MD loop call force (x, f, en)calculate the force call integrate (x, f, en)integrate equation of motion t = t + delt call samplesample averages enddo stop end

Periodic Boundary Conditions Minimum Image Central simulation box rcrc

One MD example Determining voltage threshold for translocation of dsDNA through Si3N4 pores To establish the threshold field required to drive dsDNA through a 2.0 nanometer diameter pore. The 3.9 V path caused the partial unzipping of the DNA strands prior to reaching the center of the membrane. anopore/

Historical Perspective on MD

The Next Generation in MD Current longest MD simulations: microsecond vs. time scale of many biologically interesting phenomena is millisecond Anton, Desmond Scientific advances & Drug Discovery Faculty in Computer Science Department at Columbia University, till1986 D. E. Shaw & Co., Inc., founded in , pointed by President Clinton, President's Council of Advisors on Science and Technology

Acknowledgement Powerpoint slices from Ruhong Zhou