A statistical model for helices with applications.
Motivated by a cutting edge problem related to the shape of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> -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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> -helix and derive the maximum likelihood estimation procedure. The cylinder is an accepted geometric model for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> -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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> -helices finds that Kink-detector is also effective in detecting moderate changes in axial directions.
['Mardia|Kanti V|KV|', 'Sriram|Karthik|K|0000-0002-2839-0384', 'Deane|Charlotte M|CM|']
D016013:Likelihood Functions D015233:Models, Statistical D000072756:Protein Conformation, alpha-Helical D011506:Proteins D035501:Uncertainty
Change point Crowdsourced data Helix fitting Kink detection Membrane protein Protein structure