We describe a minimalistic model of a protein undergoing folding into its native (ground) state. This HP protein model is composed of a lattice polymer with two types of monomers: hydrophobic (H) and polar (P). The specific sequence of the two types of monomers is often chosen to mimic real proteins. We explain how these kinds of minimalistic models are well suited to study fundamental phenomena of complex biological processes such as protein folding. We then show how Monte Carlo simulations and, in particular, Wang-Landau sampling, together with a properly chosen trial move set, provide a powerful computational means to investigate the rough energy landscape and native state(s) of this intriguingly simple system. We include the computer code which can be used to reproduce the results we discuss or as a template for further research.
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