Protein folding trajectory analysis using patterned clusters

Understanding how protein folds into a functional and structural configuration is arguably one of the most important and challenging problems in computational biology. Currently, the protein folding mechanism is often characterized by calculating the free energy landscape versus the reaction coordinates such as the fraction of native contacts, the radius of gyration, the principal components and so on. In this paper, we present a combinatorial algorithmic approach towards understanding the global state changes of the configurations. The approach is based on cluster computation, each cluster being defined by a pattern of a combination of various reaction coordinates. We present an algorithm of time complexity O((N + nm) log n) where N is the size of the output and n×m is the size of the input. To date, this is the best time complexity for the problem. We next demonstrate that this approach extracts crucial information about protein folding intermediate states and mechanism. (1) The method recovers states previously obtained by visually analyzing free energy contour maps. (2) It also succeeds in extracting meaningful patterns and structures that had been overlooked in previous works, which provide a better understanding of the folding mechanism (of a β-hairpin protein). These new patterns also interconnect various states in existing free energy contour maps versus different reaction coordinates. (3) The approach does not require the free energy values, yet it offers analysis comparable and sometimes better than the methods that use free energy landscapes, thus validating the choice of reaction coordinates.