Effects of crowding and confinement on the structures of the transition state ensemble in proteins.

Characterization of the structures of the transition state ensemble is a key step in describing the folding reaction. Using two variants of a coarse-grained model of the three-stranded beta-sheet WW domain and a fully automated progress variable clustering (PVC) algorithm, we have dissected the effect of macromolecular crowding and confinement on the changes in the transition state structures in comparison to bulk. Each amino acid is represented using a Calpha atom and a side chain. The distance between the Calpha atom and center of mass of the side chain is taken to be its effective van der Waals radius. For the bulk case, we predict using the PVC algorithm, which does not assume knowledge of the underlying folding reaction coordinate, that there are two classes of structures in the transition state ensemble (TSE). The structures in both of the classes are compact. The dominant cluster is more structured than the structures in the less populated class. In accord with bulk experiments, the residues in strands beta2 and beta3 and the interactions at the beta2-beta3 interface are structured. When only excluded volume interactions between the crowding particles and the WW domain are taken into account or when the protein is confined to an inert spherical pore, the overall structure of the TSE does not change dramatically. However, in this entropy dominated regime, the width of the TSE decreases and the structures become more oblate and less spherical as the volume fraction of crowding particle increases or when the pore radius decreases. It suggests that the shape changes, which are computed using the moment of inertia tensor, may represent the slow degrees of freedom during the folding process. When non-native interactions between side chains and interactions with the cavity of the pores are taken into account, the TSE becomes considerably broader. Although the topology in the transition has a fold similar to the native state, the structures are far more plastic than in the bulk. The TSE is sensitive to the size of the pore as well as interactions between the pore and the protein. The differences between the two cases (confinement in an inert pore and when pore-protein interactions are considered) arise due to the increased importance of enthalpic interactions in the transition state as the strength of the protein-pore interaction increases.