  We study a random heteropolymer model with Langevin dynamics, in the
supersymmetric formulation. Employing a procedure similar to one that has been
used in static calculations, we construct an ensemble in which the affinity of
the system for a native state is controlled by a "selection temperature" T0. In
the limit of high T0, the model reduces to a random heteropolymer, while for
T0-->0 the system is forced into the native state. Within the Gaussian
variational approach that we employed previously for the random heteropolymer,
we explore the phases of the system for large and small T0. For large T0, the
system exhibits a (dynamical) spin glass phase, like that found for the random
heteropolymer, below a temperature Tg. For small T0, we find an ordered phase,
characterized by a nonzero overlap with the native state, below a temperature
Tn \propto 1/T0 > Tg. However, the random-globule phase remains locally stable
below Tn, down to the dynamical glass transition at Tg. Thus, in this model,
folding is rapid for temperatures between Tg and Tn, but below Tg the system
can get trapped in conformations uncorrelated with the native state. At a lower
temperature, the ordered phase can also undergo a dynamical glass transition,
splitting into substates separated by large barriers.
