Helix modelling through the Mardia-Holmes model framework and an extension of the Mardia-Holmes model

TL;DR

This paper extends the Mardia-Holmes model to analyze three-dimensional helix data, providing methods for axis estimation and applications to protein alpha-helices, including a multivariate version for ellipsoids and cylinders.

Contribution

It adapts the Mardia-Holmes model for 3D helix data and introduces an iterative algorithm for unknown axis estimation, also presenting a multivariate extension.

Findings

Successfully fitted helix data using the extended model.

Developed an iterative algorithm for axis estimation.

Demonstrated application on simulated protein alpha-helices.

Abstract

For noisy two-dimensional data, which are approximately uniformly distributed near the circumference of an ellipse, Mardia and Holmes (1980) developed a model to fit the ellipse. In this paper we adapt their methodology to the analysis of helix data in three dimensions. If the helix axis is known, then the Mardia-Holmes model for the circular case can be fitted after projecting the helix data onto the plane normal to the helix axis. If the axis is unknown, an iterative algorithm has been developed to estimate the axis. The methodology is illustrated using simulated protein alpha-helices. We also give a multivariate version of the Mardia-Holmes model which will be applicable for fitting an ellipsoid and in particular a cylinder.