Constrained Shape Analysis with Applications to RNA Structure

2025-02-22

AI Summary

This work addresses the limited conformational flexibility of biomacromolecules—particularly RNA—in low-resolution structural models, where rigid bond-length and bond-angle constraints artificially restrict degrees of freedom. To overcome this, we propose a geometric modeling framework based on the polyspheres manifold, parameterizing the constrained conformational space exclusively via intrinsic degrees of freedom—such as dihedral angles—while eliminating radial coordinates. We present the first polyspheres-manifold representation of RNA backbones, uncovering structural regularities of canonical motifs (e.g., five-key-point configurations) in polar coordinates. Integrating differential geometry, directional statistics, and an enhanced MINT-AGE algorithm, we establish a joint distribution inference framework for coupled size–shape variables under geometric constraints. Experimental results demonstrate substantial improvements in robust conformational clustering accuracy and biological interpretability for RNA at low resolution.

Technology Category

• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Constrained shape analysis
• RNA structure modelling
• Polypolar coordinates methodology

Innovation

• Constrained shape analysis
• Polypolar coordinates modeling
• Modified MINT-AGE algorithm