Using motion planning to study protein folding pathways.
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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. Our focus in this work is to study the protein folding mechanism assuming we know the native fold. That is, 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 of the folding pathway on the initial denatured conformation. Our work uses probabilistic roadmap (PRM) motion planning techniques which have proven successful for problems involving high-dimensional configuration spaces. A strength of these methods is their efficiency in rapidly covering the planning space without becoming trapped in local minima. We have applied our PRM technique to several small proteins (~60 residues) and validated the pathways computed by comparing the secondary structure formation order on our paths to known hydrogen exchange experimental results. An advantage of the PRM framework over other simulation methods is that it enables one to easily and efficiently compute folding pathways from any denatured starting state to the (known) native fold. This aspect makes our approach ideal for studying global properties of the protein's potential landscape, most of which are difficult to simulate and study with other methods. For example, in the proteins we study, the folding pathways starting from different denatured states sometimes share common portions when they are close to the native fold, and moreover, the formation order of the secondary structure appears largely independent of the starting denatured conformation. Another feature of our technique is that the distribution of the sampled conformations is correlated with the formation of secondary structure and, in particular, appears to differentiate situations in which secondary structure clearly forms first and those in which the tertiary structure is obtained more directly. Overall, our results applying PRM techniques are very encouraging and indicate the promise of our approach for studying proteins for which experimental results are not available.