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My supervisor says that GROMACS can do both (all-atom) MD and MC simulations of proteins.

I never found anything while searching the Internet about MC-only simulations. As far as I found, GROMACS can do MD+MC hybrid smulation, not pure MC.

Does GROMACS have the capability to do Monte Carlo simulations of proteins?

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GROMACS does not support "pure MC" calculations, but it uses MC algorithms for many things. According to the GROMACS mailing list, there is a very old version (pre-2016) which has a plug-in to perform GCMC, but you'd have to validate it (i.e. make sure it still works, and produces sensible output).

I have extremely limited experience with MC software and methods, but I did notice some people on the comp. chem. mailing lists recommending CAMPARI. Maybe it will be useful for you as well.

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