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.

approximated

exact

Eibond

|R|0

KBT {

Covalent bonds Non-covalent interactions

==R

...,)( ,.

,.

,vdWrepCoul

kwinkelDihedral

dihek

iBindungen

jwinkelBindungs

anglej

bondiel EEEEEEE

Molecular Dynamics„Force-Field“

These are the forces that every MD program uses.

Possible ‘extras’:PlanarityHydrogen bondWeird metalInduced chargeMulti-body interactionPi-Pi stackingCoping with waterCoping with entropyand a few more

Molecular DynamicsNon-bonded interactions

Lennard-Jones potential Coulomb potential

Look at the scale difference at the two vertical axes.

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: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 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.

12

-15

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 describedpoor description of H-atoms (proton-transfer)poor description of low-T (quantum) effectssimplified electrostatic modelsimplified force fieldincomplete 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

Wt-U

Mut-U Mut-F

ΔGFwt

ΔGU

ΔGFmut

ΔGF

Wt-F So we want ΔGFwt-ΔGFmut;which is impossible.

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.