  We investigate the sequence-dependent properties of proteins that determine
the dual requirements of stability of the native state and its kinetic
accessibility using simple cubic lattice models. Three interaction schemes are
used to describe the potentials between residues. We show that, under the
simulation conditions when the native basin of attraction (NBA) is stable,
there is an excellent correlation between folding times (\tau_{F}) and the
dimensionless parameter (\sigma_{T} = (T_{\theta} - T_{F})/T_{\theta}), where
(T_{\theta}) is the collapse temperature and (T_{F}) is the folding transition
temperature. There is also a significant correlation between (\tau_{F}) and
Z-score (Z=(E_{N}-E_{ms})/\delta), where (E_{N}) is the energy of the native
state, (E_{ms}) is the average energy of the ensemble of misfolded structures,
and (\delta) is the dispersion in contact energies. An approximate relationship
between (\sigma_{T}) and the Z-score is derived, which explains the superior
correlation seen between (\tau_{F}) and (\sigma_{T}). For two state folders
(\tau_{F}) is linked to the free energy difference between the unfolded states
and the NBA.
