Dk. Klimov et D. Thirumalai, COOPERATIVITY IN PROTEIN-FOLDING - FROM LATTICE MODELS WITH SIDE-CHAINS TO REAL PROTEINS, Folding & design, 3(2), 1998, pp. 127-139
Background: Over the past few years novel folding mechanisms of globul
ar proteins have been proposed using minimal lattice and off-lattice m
odels. The factors determining the cooperativity of folding in these m
odels and especially their explicit relation to experiments have not b
een fully established, however. Results: We consider equilibrium foldi
ng transitions in lattice models with and without sidechains. A dimens
ionless measure, Omega(c), is introduced to quantitatively assess the
degree of cooperativity in lattice models and in real proteins. We sho
w that larger values of Omega(c) resembling the values seen in protein
s are obtained in lattice models with sidechains. The enhanced coopera
tivity of such models results from possible denser packing of sidechai
ns in the interior of the model polypeptide chain. We also establish t
hat Omega(c) correlates extremely well with sigma(T) = (T-theta - T-f)
/T-theta, where T-theta and T-f are collapse and folding transition te
mperatures, respectively. These theoretical ideas are used to analyze
folding transitions in two-state folders (RNase A, chymotrypsin inhibi
tor 2, fibronectin type III modules and tendamistat) and three-state f
olders (apomyoglobin and lysozyme). The values of Omega(c) extracted f
rom experiments show a correlation with sigma(T) (suitably generalized
when folding is induced by denaturants or acid). Conclusions: A quant
itative description of the cooperative transition of real proteins can
be made by lattice models with sidechains. The degree of cooperativit
y in minimal models and real proteins can be expressed in terms of the
single parameter sigma, which can be estimated from experimental data
.