Linking Rates of Folding in Lattice Models of Proteins with Underlying Thermodynamic Characteristics

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 nearest neighbor non-bonded beads. We show that, under the simulation conditions when the native basin of attraction (NBA) is the most stable, there is an excellent correlation between folding times τF and the dimensionless parameter σT = (Tθ−TF )/Tθ, where Tθ is the collapse temperature and TF is the folding transition temperature. There is also a significant correlation between τF and another dimensionless quantity Z = (EN − Ems)/δ, where EN is the energy of the native state, Ems is the average energy of the ensemble of misfolded structures, and δ is the dispersion in the contact energies. An approximate relationship between σT and the Zscore is derived, which explains the superior correlation seen between τF and σT . For two state folders τF is linked to the free energy difference (not simply energy gap, however it is defined) between the unfolded states and the NBA.