Cooperativity in Protein Folding: From Lattice Models with Side Chains to Real Proteins

We consider equilibrium folding transitions in lattice protein models with and without side chains. A dimensionless measure, $Omega_{c}$, is introduced to quantitatively assess the degree of cooperativity in lattice models and in real proteins. We show that larger values of $\Omega_{c}$ resembling those seen in proteins are obtained in lattice models with side chains (LMSC). The enhanced cooperativity in LMSC is due to the possibility of denser packing of side chains in the interior of the model protein. We also establish that $\Omega_{c}$ correlates extremely well with (\sigma = (T_{\theta} -T_{f} )/T_{\theta}), where (T_{\theta}) and (T_{f}) are collapse and folding transition temperatures, respectively. These theoretical ideas are used to analyze folding transitions in various real proteins. The values of $\Omega _{c}$ extracted from experiments show a correlation with $\sigma $. We conclude that the degree of cooperativity can be expressed in terms of the single parameter $\sigma $, which can be estimated from experimental data.