Molecular Dynamics
Inter-atomic interactions. Through-bond versus Through-space.
Or they are Covalent versus Non-covalent
Molecular Dynamics
The forces we use are also approximations in
themselves.
Non-covalent interactions
Covalent bonds
Eibond
approximated
exact
=
=
R
KBT {
0
E el 

Bindungen
i
|R|
E ibond 
E
Bindungs 
winkel j
angle
j

E
Dihedral 
winkel k
dihe
k
.
rep .
vdW
  ( ECoul
,   E ,   E ,  )  ...,
„ForceField“
Molecular Dynamics
These are the forces
that every MD
program uses.
Possible ‘extras’:
Planarity
Hydrogen bond
Weird metal
Induced charge
Multi-body interaction
Pi-Pi stacking
Coping with water
Coping with entropy
and a few more
Non-bonded interactions
Molecular Dynamics
Look at the scale difference at the two vertical axes.
Lennard-Jones potential
Coulomb potential
Molecular Dynamics
The average speed of nitrogen in air of 300K is about 520 m/s. The ensemble of
speeds is best described
by a Maxwell distribution. Back of the enveloppe calculation:
12
500 m/s = 5.10 Å/s
Let’s assume that we can have things fly 0.1 A in a straight line before we calculate
forces again, then-15
we need to recalculate forces every 20 femtosecond; one
femtosecond is 10 sec.
In practice 1 fsec integration steps are being used.
Many techniques have been developed to cope with the problem that forces
continuously change while we must calculate the motion in small steps. The most
expensive way to cope with the problem is taking shorter time steps. The most stupid
way is to take longer time steps.
Molecular Dynamics
periodic boundary conditions
Molecular Dynamics
H. Frauenfelder et al., Science 229 (1985) 337
Molecular Dynamics
Limits of MD-Simulations
classical description:
chemical reactions not described
poor description of H-atoms (proton-transfer)
poor description of low-T (quantum) effects
simplified electrostatic model
simplified force field
incomplete force field
only small systems accessible (104 ... 106 atoms)
only short time spans accessible (ps ... μs)
Molecular Dynamics
Stability of a protein is ΔG-folding, which is the
ΔG of the process Protein-U <-> Protein-F
ΔGFwt
Wt-U
Wt-F
So we want ΔGFwt-ΔGFmut;
which is impossible.
ΔGF
ΔGU
Mut-U
Mut-F
ΔGFmut
But we can calculate ΔGF-ΔGU;
which is the same!
Molecular Dynamics
Such cycles can be set up for ligand binding, for
membrane insertion, for catalysis, for mutant
stability prediction, etc.
In essence, when alchemy is needed, you can use
a thermodynamic cycle.