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

Abstract

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 occur 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.

arXiv comment19 pages

References in corpus (12)

• Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
• A Doubly Nudged Elastic Band Method for Finding Transition States
• Finding pathways between distant local minima
• Dodging the crisis of folding proteins with knots
• Exploring the Free Energy Landscape: From Dynamics to Networks and Back
• Variational theory for site resolved protein folding free energy surfaces
• Energy Landscape of a Model Protein
• Diffusion mechanisms of localised knots along a polymer
• Graph Transformation Method for Calculating Waiting Times in Markov Chains
• Protein Structure Prediction Using Basin-Hopping
• Protein Structure Prediction: The Next Generation
• Intricate Knots in Proteins: Function and Evolution

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