  The folding ability of a heteropolymer model for proteins subject to Monte
Carlo dynamics on a simple cubic lattice is shown to be strongly correlated
with the energy gap between the native state and the structurally dissimilar
part of the spectrum. We consider a number of estimates of the energy gap that
can be determined without simulation, including the gap in energy between the
native and first excited fully compact states for sequences with fully compact
native states. These estimates are found to be more robust predictors of
folding ability than a parameter $\sigma$ that requires simulation for its
evaluation: $\sigma = 1 - T_f/T_\theta$, where $T_f$ is the temperature at
which the fluctuation of the order parameter is at its maximum and $T_\theta$
is the temperature at which the specific heat is at its maximum. We show that
the interpretation of $T_\theta$ as the collapse transition temperature is not
correct in general and that the correlation between $\sigma$ and the folding
ability arises from the fact that $\sigma$ is essentially a measure of the
energy gap.
