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I have recently been reading about coarse-graining in the molecular dynamics. Generally, the potential of a coarse grain site is computed using two methods: Force matching (FM) and Iterative Boltzman Inversion. Both these methods use all-atom simulation as reference. My question is, if we need to do all-atom simulation to find the potentials in the coarse grained model anyways, what is the benefit of having a coarse grained model?

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This is a very broad question that, most likely, would be answered differently from different people working in different fields. However, I think everyone will agree on the fact that the characteristic time- and length-scales of atomic and coarse-grained potentials are different, with the latter's being always larger. This means that, once the coarse-grained potential has been derived, it will be possible to run simulations of larger systems for longer times using the same computational effort.

More in practice, imagine you want to derive an implicit-solvent coarse-grained potential for a macromolecule such as a simple polymer. You decide (for instance) to use a repeating unit, containing, say, 20 atoms, as the coarse-graining unit. You will need to simulate a short-ish polymer to obtain your coarse-grained interaction (say, 20 repeating units), which will be simulated in an explicit solvent. The whole simulation might contain thousands of atoms, and you use it to parametrise the coarse-grained interaction. Once this is ready, you will be able to simulate the same system at a fraction of the computational cost, since your thousands atoms have become $\approx 20$ beads.

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