background image
Université de Reims
CHAMPAGNE ARDENNE
INRA UMR FARE 614
Fractionnement des Agro Ressources
et Emballages,
CPCB Moulin de la Housse, BP 1039,
F 51687 REIMS cedex 2
Extensions
Extensions
MOLECULAR MODELING
at atomistic scale (II/II)
Molecular
Dynamics
Molecular
Dynamics
Simulation of a
small system
exchanging
energy with a
larger system
at a given fixed
temperature T
-3
-2
-1
0
1
2
3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Nose
10
14
10
13
10
13
10
6
10
5
10
5
10
5
1000
10
Time (fs)
3
Allosteric transition
7
Local denaturation
5
Buried side chain rotation
3
Hinge bending of chain
0.5
Buried side chain vibration
4
Water diffusive motion
5
Surface side chain rotation
0.5
Water hindered rotation
0.1
Bond vibration
Length (
Ĺ
)
Motion
Timescales
Values from McCammon & Harvey (1987) and Eisenberg
& Kauzmann
Periodic Boundary
Conditions
They make simulation system seem larger
than it is. On the 2D representation, the chain
in blue is the parent chain, all the other
chains are the images.
Thermodynamic Ensembles
Thermostat
Integrator
Molecular dynamics requires to integrate explicitly
positions of the particles in space and time to
produce a "true" dynamical trajectory (random
walk). We advance the system by some small time
step
t to recalculate subsequently forces and
velocities, and to fulfill stability requirement.
The most popular integrator is the Verlet algorithm.
Thermostats are needed in situations where
there might be a flux of energy in/out of the
system, e.g. to maintain a constant
temperature. A thermostat is time reversible,
deterministic and goes to the canonical
distribution.
Interactions with the thermostat are non
- local,
they propagate instantaneously.
Some statistical ensembles are listed below,
they are identified by their conserved
quantities:
· Microcanonical (N,V,E)
· Canonical (N,V,T)
· Grand canonical (
µ
,V,T)
· Isobaric isothermal (N,P,T)
...
Velocity
Time Step
Time step size is limited by the fasted motion you
want to integrate. Time step should be
1/10
th
the
period of the movement of high frequency for
flexible molecules (usually bond stretching: CH
around 10 fs so use 1 fs). When you simulate an
atomic fluid, the time step should be comparable to
the mean time between collisions.
Cut off Distance
For a system of 1500 atoms, 4500 bonded
terms and 1.1x10
6
non bonded terms must be
calculated.
Long range potentials (electrostatic) and also
vdW interactions are often truncated at a
finite cut off distance.
It is necessary to give each atom a velocity. If no
force, new position of atom (at t+
t) would be
determined only by velocity. Forces change the
velocity, complicating things immensely.
Configurational (q)
distribution using a
handful of
oscillators as a bath
(with a bit of help
from the large
timestep perturbed
Hamiltonian)
United atom approximation is used for simulating
large melts of long chain hydrocarbons, this
model replaces each CH
2
or CH
3
group with a
united atom that has modified vdW parameters
to take account of the missing hydrogens.
How to minimize the computational effort required?
Remove the highest frequency components from the
dynamics. Bond stretch potential use stiff spring with
rest length
replace with rigid rod constraint.
Voter's Hyperdynamics
Leimkuhler's Alternative
Non Equilibrium Molecular Dynamics
Simplified Force fields
Potential smoothing
Energy and Entropy
Many errors in modeling can be due
to the users. Be careful in choosing a force
field adapted to its problem and in taking
into account all the parameters of
simulation.
(non constant temperature dynamics, ...)
Due to the inertia of the atoms, Molecular
Dynamics enables the system to surmount
energy barriers.
Particles
moving in
a random
barrier
energy
landscape.
At each point (with coordinates ) on the
potential energy surface there is a well
defined "energy" . Entropy and free
energy are only defined for distinctly different
"states" ­ e.g. A ("unfolded") and B "(folded").
State B has a lower U
and its minimum is
more probable than
state A.
However, state A has
a broader minimum
that can be occupied
in more ways.
2
2
dU
d R
m
dR
dt
-
=
i
i
x
( )
i
U x
i
x
( )
U x