Stability constraints and protein evolution: the role of chain length, composition and disulfide bonds.

Stability of the native state is an essential requirement in protein evolution and design. Here we investigated the interplay between chain length and stability constraints using a simple model of protein folding and a statistical study of the Protein Data Bank. We distinguish two types of stability of the native state: with respect to the unfolded state (unfolding stability) and with respect to misfolded configurations (misfolding stability). Several contributions to stability are evaluated and their correlations are disentangled through principal components analysis, with the following main results. (1) We show that longer proteins can fulfil more easily the requirements of unfolding and misfolding stability, because they have a higher number of native interactions per residue. Consistently, in longer proteins native interactions are weaker and they are less optimized with respect to non-native interactions. (2) Stability against misfolding is negatively correlated with the strength of native interactions, which is related to hydrophobicity. Hence there is a trade-off between unfolding and misfolding stability. This trade-off is influenced by protein length: less hydrophobic sequences are observed in very long proteins. (3) The number of disulfide bonds is positively correlated with the deficit of free energy stabilizing the native state. Chain length and the number of disulfide bonds per residue are negatively correlated in proteins with short chains and uncorrelated in proteins with long chains. (4) The number of salt bridges per residue and per native contact increases with chain length. We interpret these observations as an indication that the constraints imposed by unfolding stability are less demanding in long proteins and they are further reduced by the competing requirement for stability against misfolding. In particular, disulfide bonds appear to be positively selected in short proteins, whereas they evolve in an effectively neutral way in long proteins.