  Using Monte Carlo dynamics and the Monte Carlo Histogram Method, the simple
three-dimensional 27 monomer lattice copolymer is examined in depth. The
thermodynamic properties of various sequences are examined contrasting the
behavior of good and poor folding sequences. The good (fast folding) sequences
have sharp well-defined thermodynamic transitions while the slow folding
sequences have broad ones. We find two independent transitions: a collapse
transition to compact states and a folding transition from compact states to
the native state. The collapse transition is second order-like, while folding
is first order. The system is also studied as a function of the energy
parameters. In particular, as the average energetic drive toward compactness is
reduced, the two transitions approach each other. At zero average drive,
collapse and folding occur almost simultaneously; i.e., the chain collapses
directly into the native state. At a specific value of this energy drive the
folding temperature falls below the glass point, indicating that the chain is
now trapped in local minimum. By varying one parameter in this simple model, we
obtain a diverse array of behaviors which may be useful in understanding the
different folding properties of various proteins.
