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 ΔT/TF∼N−1, where TF is the folding transition temperature and ΔT 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≃kF0 exp(−CNβ) with 0<β≤2/3 provides a good fit, where C is a β-dependent constant. We find that kF≃kF0 exp(−1.1N1/2) with an average (over the dataset of proteins) kF0≈(0.4 μs)−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 β-sheet topology we find that kF0≈kU0, the prefactor for unfolding. The maximum ratio of kU0/kF0≈10 for this class of proteins.