Collapse transition in the HP model

We studied the collapse transition on small homopolymeric and heteropolymeric sequences in the HP model on a two-dimensional square lattice both with exact enumerations and Monte Carlo simulations. For heteropolymers, our analysis is restricted to native sequences (sequences which present one single minimal energy configuration) with a fixed fraction of hydrophobic residues (ρ = NH/N = 0.5). In the homopolymer limit (ρ = 1) we were able to reproduce several known results such as the exponent v and the critical temperature for the collapse transition. For the heteropolymer case, we devised a combinatorial extrapolation scheme based on the method used for homopolymers which enabled us to study the dependence of the collapse critical temperature on the monomer sequence in the thermodynamic limit. For the small chain lengths studied we find that the θ-point is strongly dependent on the monomer sequence, our extrapolation scheme suggests that even in the thermodynamic limit, the critical temperature of the collapse transition in the HP model in the square lattice depends on the specific location of the hydrophobic residues in the chain. We have also studied the folding transition, our preliminary results for the chain lengths studied do not indicate the existence of an equilibrium folding transition occurring at a temperature different from that of the collapse transition.