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

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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/TF N-1, where TF is the folding transition temperature and DeltaT is the folding transition width. 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 kF on N for lattice models and the dataset of 57 proteins and peptides shows that kF = kF⁰ exp(-CNᵇeta) provides a good fit, if 0 < beta <= 2/3 and C is a constant. We find that kF = kF⁰ exp(-1.1N⁰.5) with kF⁰ =(0.4x10-6 s)-1 can estimate optimal protein folding rates to within an order of magnitude in most cases. By using this fit for a set of proteins with beta-sheet topology we find that kF⁰ is approximately equal to kᵤ⁰, the prefactor for unfolding rates. The maximum ratio of kᵤ⁰/kF⁰ is 10 for this class of proteins.