In structure-based models of proteins, one often assumes that folding is
accomplished when all contacts are established. This assumption may frequently
lead to a conceptual problem that folding takes place in a temperature region
of very low thermodynamic stability, especially when the contact map used is
too sparse. We consider six different structure-based models and show that
allowing for a small, but model-dependent, percentage of the native contacts
not being established boosts the folding temperature substantially while
affecting the time scales of folding only in a minor way. We also compare other
properties of the six models. We show that the choice of the description of the
backbone stiffness has a substantial effect on the values of characteristic
temperatures that relate both to equilibrium and kinetic properties. Models
without any backbone stiffness (like the self-organized polymer) are found to
perform similar to those with the stiffness, including in the studies of
stretching.Comment: 8 pages, 4 figure