Cooperativity in protein folding: from lattice models with sidechains to real proteins

Over the past few years novel folding mechanisms of globular proteins have been proposed using minimal lattice and off-lattice models. The factors determining the cooperativity of folding in these models and especially their explicit relation to experiments have not been fully established, however.

We consider equilibrium folding transitions in lattice models with and without sidechains. 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 the values seen in proteins are obtained in lattice models with sidechains. The enhanced cooperativity of such models results from possible denser packing of sidechains in the interior of the model polypeptide chain. We also establish that omega c correlates extremely well with sigma T = (T o - T f) /T o, where T o and T f are collapse and folding transition temperatures, respectively. These theoretical ideas are used to analyze folding transitions in two-state folders (RNase A, chymotrypsin inhibitor 2, fibronectin type III modules and tendamistat) and three-state folders (apomyoglobin and lysozyme). The values of omega c extracted from experiments show a correlation with sigma T (suitably generalized when folding is induced by denaturants or acid).

A quantitative description of the cooperative transition of real proteins can be made by lattice models with sidechains. The degree of cooperativity in minimal models and real proteins can be expressed in terms of the single parameter sigma, which can be estimated from experimental data.