  The thermodynamic behavior and structural properties of hydrophobic-polar
(HP) lattice proteins interacting with attractive surfaces are studied by means
of Wang-Landau sampling. Three benchmark HP sequences (48mer, 67mer, and
103mer) are considered with different types of surfaces, each of which attract
either all monomers, only hydrophobic (H) monomers, or only polar (P) monomers,
respectively. The diversity of folding behavior in dependence of surface
strength is discussed. Analyzing the combined patterns of various structural
observables, such as, e.g., the derivatives of the numbers of surface contacts,
together with the specific heat, we are able to identify generic categories of
folding and transition hierarchies. We also infer a connection between these
transition categories and the relative surface strengths, i.e., the ratio of
the surface attractive strength to the interchain attraction among H monomers.
The validity of our proposed classification scheme is reinforced by the
analysis of additional benchmark sequences. We thus believe that the folding
hierarchies and identification scheme are generic for HP proteins interacting
with attractive surfaces, regardless of chain length, sequence, or surface
attraction.
