The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N or C terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N terminus portion of the knot and a rate-determining step where the C terminus is incorporated. The low-lying minima with the N terminus knotted and the C terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N and C termini into the knot occurs late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.Author Summary: Proteins are chains, which must fold into a compact structure for the molecule to perform its biological function. There are a large number of ways the molecule can move into this final shape. Proteins have evolved sequences that perform this difficult task by having strong biases toward the final shape, while not getting stuck in different structures along the way. One way proteins can be trapped is by forming a knot in the chain. For the most part, proteins are remarkable in avoiding knotting. However, in order to function a few proteins form knots. We show how a model protein is able to knot itself, and estimate how fast this process occurs. Our goal is to treat a small and uncomplicated protein to estimate the fastest rate possible for the folding of a knotted protein. This rate is interesting when compared to the speed of folding of other proteins. We have visualized how the molecule changes shape to its functional position, and examined other paths the molecule may take.