Using motion planning to study protein folding pathways

We present a framework for studying protein folding pathways and potential landscapes which is based on techniques recently developed in the robotics motion planning community. In particular, our work uses Probabilistic Roadmap (PRM) motion planning techniques which have proven to be very successful for problems involving high-dimensional configuration spaces. Our results applying PRM techniques to several small proteins (60 residues) are very encouraging. The framework enables one to easily and efficiently compute folding pathways from any denatured starting state to the native fold. This aspect makes our approach ideal for studying global properties of the protein's potential landscape. For example, our results show that folding pathways from different starting denatured states sometimes share some common `gullies', mainly when they are close to the native fold. Such global issues are difficult to simulate and study with other methods. Our focus in this work is to study the protein folding mechanism assuming we know the native fold. Therefore, instead of performing fold prediction, we aim to study issues related to the folding process, such as the formation of secondary and tertiary structure, and the dependence on the initial conformation. Our results indicate that for some proteins, secondary structure clearly forms first while for others the tertiary structure is obtained more directly, and moreover, these situations seem to be differentiated in the distributions of the conformations sampled by our technique. We also find that the formation order is independent of the starting denatured conformation. We validate our results by comparing the secondary structure formation order on our paths to known pulse-labeling experimental results. This indicates the promise of our approach for studying proteins for which experimental results are not available.