Thermal denaturation and folding rates of single domain proteins: size matters

We analyze the dependence of thermal denaturation transition and folding rates of globular proteins on the number of amino acid residues, N. Using lattice Go models we show that DeltaT/T-F similar to N-1, where T-F is the folding transition temperature and DeltaT is the transition width computed using the temperature dependence of the order parameter that distinguishes between the unfolded state and the native basin of attraction. This finding is consistent with finite size effects expected for the systems undergoing a phase transition from a disordered to an ordered phase. The dependence of the folding rates on N for lattice models and the dataset of 57 proteins and peptides shows that kF similar or equal to kF(0) exp(-CNbeta) with 0 < beta less than or equal to 2/3 provides a good fit, where C is a beta-dependent constant. We find that k(F) similar or equal to k(F)(0) exp(- 1.1N(1/2)) with an F average (over the dataset of proteins) k(F)(0) approximate to (0.4 mus)(-1), can estimate optimal protein folding rates, to within an order of magnitude in most F cases. By using this fit for a set of proteins with beta-sheet topology we find that k(F)(0) approximate to k(U)(0), the prefactor for unfolding. The maximum ratio of F U k(U)(0)/k(F)(0) approximate to 10 for this class of proteins. (C) 2003 Published by Elsevier Ltd.