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Inter-atomic interactions. Through-bond versus Through-space.

Inter-atomic interactions. Through-bond versus Through-space. Or they are Covalent versus Non-covalent. =. =. R. The forces we use are also approximations in themselves. Non-covalent interactions. Covalent bonds. E i bond. approximated. exact. K B T {.  0. |R|. „Force-Field“.

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Inter-atomic interactions. Through-bond versus Through-space.

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

  2. = = R The forces we use are also approximations in themselves. Non-covalent interactions Covalent bonds Eibond approximated exact KBT { 0 |R|

  3. „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

  4. Look at the scale difference at the two vertical axes. Non-bonded interactions Coulomb potential Lennard-Jones potential

  5. 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

  6. periodic boundary conditions

  7. H. Frauenfelder et al., Science229 (1985) 337

  8. 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)

  9. 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 But we can calculate ΔGF-ΔGU; which is the same! Mut-U Mut-F ΔGFmut

  10. 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.

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