Geometric combinatorics and computational molecular biology: branching polytopes for RNA sequences

TL;DR

This paper introduces a new computational framework using geometric combinatorics to perform a complete parametric analysis of RNA secondary structure prediction models, enhancing understanding of parameter dependencies.

Contribution

It presents the first comprehensive parametric analysis of RNA secondary structure prediction using branching polytopes, advancing the application of geometric combinatorics in molecular biology.

Findings

First complete parametric analysis of RNA secondary structure models

Application of polytopes and normal fans to real RNA sequences

Demonstrates the framework's effectiveness for complex biological models

Abstract

Questions in computational molecular biology generate various discrete optimization problems, such as DNA sequence alignment and RNA secondary structure prediction. However, the optimal solutions are fundamentally dependent on the parameters used in the objective functions. The goal of a parametric analysis is to elucidate such dependencies, especially as they pertain to the accuracy and robustness of the optimal solutions. Techniques from geometric combinatorics, including polytopes and their normal fans, have been used previously to give parametric analyses of simple models for DNA sequence alignment and RNA branching configurations. Here, we present a new computational framework, and proof-of-principle results, which give the first complete parametric analysis of the branching portion of the nearest neighbor thermodynamic model for secondary structure prediction for real RNA sequences.