Characterizing Intermediate Conformations in Protein Conformational Space

In this paper we present a novel parallel coordinate based clustering method using Gaussian mixture distribution models to characterize the conformational space of proteins. An algorithm is proposed to detect highly populated regions which may correspond to interesting intermediate states that are difficult to detect experimentally. The data is represented as feature vectors of N dimensions, which are lower-dimension projections of the protein conformations. First, we cluster each dimension separately, using model-based clustering with Gaussian mixture models for density estimation. The resulting partitions are used to model relations between pairs of dimensions. Finally, disjoint multi-dimensional clusters of conformations as well as groups of conformations that are unlikely to exist as significant intermediates are identified, based on the progressive analysis of how data flows between those pairs. The idea has its roots in parallel coordinates, which is a visualization technique that lays out coordinate axes in parallel rather than orthogonal to each other, thereby allowing patterns between pairs of axis as well as outliers to be visually identified in multi-dimensional data. We believe that the size of the resulting clusters may provide information about the likelihood of the corresponding conformations to exist as important intermediates. We tested our method on the conformational space for the enzyme AdK which undergoes large scale conformational changes and used our method to detect clusters which may correspond to experimentally known intermediates. Finally, we compare our clusters with the ones generated by the K-Means clustering algorithm and discuss the advantages of our method for the problem of characterizing proteins conformational space.