Molecular Dynamics Inter-atomic interactions. Through-bond versus Through-space. Or they are Covalent versus Non-covalent.

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Presentation transcript:

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 E i bond |R| 0 K B T { Covalent bonds Non-covalent interactions = = R

Molecular Dynamics „Force- Field“ 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

Molecular Dynamics Non-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

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 ( 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-UMut-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.