Molecular Dynamics: Review
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Molecular Dynamics: Review. 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 Simulations. Molecular Dynamics.

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Molecular simulations l.jpg

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 Simulations


Molecular dynamics l.jpg
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



Force fields typical energy functions l.jpg
Force Fields: Typical Energy Functions

Bond stretches

Angle bending

Torsional rotation

Improper torsion (sp2)

Electrostatic interaction

Lennard-Jones interaction


Bonding terms bond stretch l.jpg
Bonding Terms: bond stretch

  • Most often Harmonic

r0


Bonding terms angle bending l.jpg
Bonding Terms: angle bending

  • Most often Harmonic

  • CHARMM force field’s Urey-Bradley angle term:

q0

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 l.jpg
Bonding Terms: Torsions

  • Torsion energy: rotation about a bond (dihedral angles)

i

k

f

j

l

i-j-k-l

Vn: force constant

n: periodicity of the angle ( determines

how many peaks and wells in the

potential, often from 1-6 )

d: phase of the angle (often 0º or 180º)


Bonding terms improper torsions l.jpg
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).

j

w

k

i

l

or

i-j-k-l


Non bonded terms l.jpg
Non-bonded Terms

  • Electrostatic interactions

    (Coulomb’s Law)

  • Lennard-Jones interactions

~1/r



Solvation models l.jpg
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 l.jpg

Explicit Water modelsSPC, SPC/E, TIPnP, POL5



Water model parameters l.jpg
Water Model Parameters

  • SPC, SPC/E (Berendsen)

  • TIP3P, TIP4P, TIP5P (Jorgensen)

  • TIP4P/FQ, POL5 (Berne)



Continuum solvent model l.jpg
Continuum Solvent Model

continuum solvent

e=80

e=1-4

protein



Molecular dynamics19 l.jpg
Molecular Dynamics

  • Solve Newton’s equation for a molecular system:


Integrator verlet algorithm l.jpg
Integrator: Verlet Algorithm

Start with {r(t), v(t)}, integrate it to {r(t+Dt), v(t+Dt)}:

{r(t+Dt), v(t+Dt)}

The new position at t+Dt:

{r(t), v(t)}

(1)

Similarly, the old position at t-Dt:

(2)

Add (1) and (2):

(3)

Thus the velocity at t is:

(4)


Typical md flowchart l.jpg
Typical MD Flowchart

Program MYMD simple MD program

call init initialization

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 sample sample averages

enddo

stop

end


Periodic boundary conditions minimum image l.jpg
Periodic Boundary ConditionsMinimum Image

rc

Central

simulation

box


Slide23 l.jpg

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.

http://www.ks.uiuc.edu/Research/nanopore/



The next generation in md l.jpg
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 1988

1994, pointed by President Clinton, President's Council of Advisors on Science and Technology


Acknowledgement l.jpg
Acknowledgement

  • Powerpoint slices from Ruhong Zhou