Thermodynamics of Heteropolymers in Confinement: A Wang-Landau Monte Carlo Study

We investigate the thermodynamic behavior of a generic, flexible, off-lattice A$_9$-(BA$_9$)$_{10}$ heteropolymer, for which BB interactions are strongly attractive, confined in spherical cavities. A modified Wang-Landau-type Monte-Carlo algorithm was used to compute densities-of-state, $\Omega(E)$, for various cavity sizes, $R$. Under no confinement, the heteropolymer considered displays a first order transition from an open coil to a partially collapsed structure with a core of 8 of the 10 B-type monomers, and a weaker second-order transition from the semi-collapsed state to the final structure with a core of all 10 B's and an A-type corona. Under moderate confinement, for which $R$ is somewhat larger than the polymer's unperturbed mean radius of gyration in bulk, the critical temperature of the first-order transition increases significantly. For strong confinement, we observe an even greater increase in the critical temperature. A detailed analysis of the accessible conformations at each energy level indicate that the mechanism responsible is an increase in stability of the {\em partially} collapsed structure relative to the open coil with increasing confinement. These results should contribute to the ongoing discussion of how crowding and confinement play roles in the thermodynamics and kinetics of heteropolymer intramolecular self-assembly.