Symmetric Connectivity of Secondary Structure Elements Enhances the Diversity of Folding Pathways

The influence of native connectivity of secondary structure elements (SSE) on folding is studied using coarse-grained models of proteins with mixed α and β structure and the analysis of the structural database of wild-type proteins. We found that the distribution of SSE along a sequence determines the diversity of folding pathways. If α and β SSE are localized in different parts of a sequence, the diversity of folding pathways is restricted. An even (symmetric) distribution of α and β SSE with respect to sequence midpoint favors multiple folding routes. Simulations are supplemented by the database analysis of the distribution of SSE in wild-type protein sequences. On an average, two-thirds of wild-type proteins with mixed α and β structure have symmetric distribution of α and β SSE. The propensity for symmetric distribution of SSE is especially evident for large proteins with the number of SSE ≥10. We suggest that symmetric SSE distribution in protein sequences may arise due to nearly random allocation of α and β structure along wild-type sequences. The tendency of long sequences to misfold is perhaps compensated by the enhanced pathway diversity. In addition, folding pathways are shown to progress via hierarchic assembly of SSE in accordance with their proximity along a sequence. We demonstrate that under mild denaturation conditions folding and unfolding pathways are similar. However, the reversibility of folding/unfolding pathways is shown to depend on the distribution of SSE. If α and β SSE are localized in different parts of a sequence, folding and unfolding pathways are likely to coincide.