Analysis and classification of disulphide connectivity in proteins. The entropic effect of cross-linkage

An analysis and a classification of protein disulphide connectivity in a set of distinct sequences are presented. We analyse the number of disulphides per sequence, the number of disulphides per residue and the length of disulphide cross-linked loops. Observed connectivities are classified according to the different possible types of arrangement. In addition, we classify disulphide connectivity by physical models describing the arrangement of multiple disulphides. Firstly, we consider whether the features of native connectivity arrangement are describable by the likelihood of diffusive contact in the unfolded state. This is referred to as the diffusion model, and was originated by Kauzmann. A second model, effectively the inverse of the diffusion model, describes native connectivity arrangement as dominated by the entropic stabilisation effect of cross-linkage. This is referred to as the entropic model. Additionally, we compare the distribution of disulphide cross-linked loops and of loops formed by disulphide-like contacts. For short sequences (less than about 75 residues) native connectivities tend to have entropically more-stabilising arrangement features, whilst for longer sequences (greater than about 200 residues) the diffusion model is appropriate. We introduce the concept of arrangement entropy as a measure of the complexity of a connectivity.