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 nonbonded 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 ${\tau }_F$ and the dimensionless parameter ${\sigma }_T{\mathrm{=(T}}_{\theta }{\mathrm{-T}}_F{\mathrm{)/T}}_{\theta },$ 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 another dimensionless quantity ${\mathrm{Z=(E}}_N{\mathrm{-E}}_{\mathrm{ms}}\mathrm{)/\delta ,}$ where $E_N$ is the energy of the native state, $E_{\mathrm{ms}}$ is the average energy of the ensemble of misfolded structures, and δ is the dispersion in the contact energies. In contrast, there is no significant correlation between ${\tau }_F$ and the $Z$ -score gap ${\Delta }_Z{\mathrm{=E}}_N{\mathrm{-E}}_{\mathrm{ms}}.$ 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 (not simply energy gap, however it is defined) between the unfolded states and the NBA.