  Using Wang-Landau sampling with suitable Monte Carlo trial moves (pull moves
and bond-rebridging moves combined) we have determined the density of states
and thermodynamic properties for a short sequence of the HP protein model. For
free chains these proteins are known to first undergo a collapse "transition"
to a globule state followed by a second "transition" into a native state. When
placed in the proximity of an attractive surface, there is a competition
between surface adsorption and folding that leads to an intriguing sequence of
"transitions". These transitions depend upon the relative interaction strengths
and are largely inaccessible to "standard" Monte Carlo methods.
