Apappendix A: Entropy of a Partially Collapsed Protein as a Function of the Number of Native and Non-native Contacts

In terms of the packing fraction the total number of non-native contacts is MA = Mη(1 − Q) , (A.1) where η is the packing fraction of non-native polymer surrounding the dense (η = 1) native core. The mean-field configurational entropy of a self-avoiding polymer of n links with packing fraction η is given by [62, 63] S SA c (η) n = ln ν e − 1 − η η ln (1 − η) (A.2) The conformational entropy of the self-avoiding walk in terms of the fraction of non-native contacts A is given by S SA c (A) = S SA c (η)| η=A/(1−Q). (A.3) Expressions (A.2) and (A.3) imply that the polymer chain in question will tend to have η = 0 and A = 0 since this maximizes the entropy. However a finite-length chain of n links tends to have a non-zero packing fraction given by η(n) ≈ na 3 R g (n) 3 ≈ na 3 ∆R 3 (A.4) where a 3 is the volume per monomer and R g is the radius of gyration of the chain. Up to factors of order unity the Electronic Supplementary Material for Clementi and Plotkin (2004). The effects of non-native interactions on protein folding rates: Theory and Simulation. Protein Science 13(7).