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Motivated by a cutting edge problem related to the shape of α−helices in proteins, we formulate a parametric statistical model, which incorporates the cylindrical nature of the helix. Our focus is to detect a “kink”, which is a drastic change in the axial direction of the helix. We propose a statistical model for the straight α−helix and derive the maximum likelihood estimation procedure. The cylinder is an accepted geometric model for α−helices, but our statistical formulation, for the first time, quantifies the uncertainty in atom-positions around the cylinder. We propose a change point technique “Kink-Detector” to detect a kink location along the helix. Unlike classical change point problems, the change in direction of a helix depends on a simultaneous shift of multiple data points rather than a single data point, and is less straightforward. Our biological building block is crowdsourced data on straight and kinked helices; which has set a gold standard. We use this data to identify salient features to construct Kink-Detector, test its performance and gain some insights. We find the performance of Kink-Detector comparable to its computational competitor called “Kink-Finder”. We highlight that identification of kinks by visual assessment can have limitations and Kink-Detector may help in such cases. Further, an analysis of crowdsourced curved α−helices finds that Kink-Detector is also effective in detecting moderate changes in axial directions. |
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