A Statistical model for helices with applications

Abstract

Motivated by a cutting edge problem related to the shape of α-helices in proteins, we formulate a parametricstatistical model, which incorporates the cylindrical nature of the helix. Our focus is to detect a “kink,” which is a drasticchange in the axial direction of the helix. We propose a statistical model for the straight α-helix and derive the maximumlikelihood 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 ahelix depends on a simultaneous shift of multiple data points rather than a single data point, and is less straightforward. Ourbiological building block is crowdsourced data on straight and kinked helices; which has set a gold standard. We use this datato identify salient features to construct Kink-detector, test its performance and gain some insights. We find the performanceof Kink-detector comparable to its computational competitor called “Kink-Finder.” We highlight that identification of kinksby visual assessment can have limitations and Kink-detector may hel p in such cases. Further, an analysis of crowdsourcedcurved α-helices finds that Kink-detector is also effective in detecting moderate changes in axial directions.