Constrained Shape Analysis with Applications to RNA Structure

TL;DR

This paper introduces a new shape analysis method for biomolecules like RNA, modeling constrained structures using polar coordinates and applying it to clustering and RNA structure analysis.

Contribution

It presents a novel modeling strategy using polypolar coordinates for constrained shape analysis, specifically tailored for RNA structures with partial landmark identification.

Findings

New polypolar coordinate framework for constrained shape analysis

Application to RNA structure with partial landmark data

Modified clustering algorithm for biomolecular shape data

Abstract

In many applications of shape analysis, lengths between some landmarks are constrained. For instance, biomolecules often have some bond lengths and some bond angles constrained, and variation occurs only along unconstrained bonds and constrained bonds' torsions where the latter are conveniently modelled by dihedral angles. Our work has been motivated by low resolution biomolecular chain RNA where only some prominent atomic bonds can be well identified. Here, we propose a new modelling strategy for such constrained shape analysis starting with a product of polar coordinates (polypolars), where, due to constraints, for example, some radial coordinates should be omitted, leaving products of spheres (polyspheres). We give insight into these coordinates for particular cases such as five landmarks which are motivated by a practical RNA application. We also discuss distributions for polypolar coordinates and give a specific methodology with illustration when the constrained size-and-shape variables are concentrated. There are applications of this in clustering and we give some insight into a modified version of the MINT-AGE algorithm.