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PRISM: Partition-Function Decomposition into Structural Classes for Hierarchically Constrained RNA Pseudoknot Ensembles

Authors Mateo Gray , Sebastian Will , Hosna Jabbari

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LIPIcs.WABI.2026.30.pdf
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Subject Classification

ACM Subject Classification
  • Applied computing → Computational biology
Keywords
  • RNA
  • MFE
  • Secondary Structure Prediction
  • Pseudoknot
  • Partition Function
  • Centroid
  • MEA
  • RNA shape
  • Stochastic traceback

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Abstract

While structure ensemble analysis became a valuable routinely applied tool for pseudoknot-free RNA, the extension to pseudoknots remains challenging due to the computational hardness of the general problem. The existing efficient algorithms for the computation of partition function with pseudoknots were still computationally expensive and were restricted to simple pseudoknots. This changed only with CParty, which computes pseudoknotted partition functions with the efficiency of pseudoknot-free folding. At its core, CParty follows the hierarchical folding hypothesis, such that ensemble structures can form pseudoknots only with a given input constraint structure. For an RNA sequence S and pseudoknot-free structure G, CParty limits the ensemble to "density-2" structures G∪ G' for a second, disjoint pseudoknot-free structure G'.
We present PRISM that extends CParty from pure partition function calculation to full-fledged posterior probability analysis. By stochastic traceback through CParty’s dynamic programming matrices, it samples structures from the conditional Boltzmann ensemble. From estimated base pair probabilities, it generates ensemble representations, predicts centroid and maximum expected accuracy structures and calculates properties. In addition to position-specific summaries, PRISM maps sampled structures to RNA shapes, producing a posterior distribution over topological abstractions. This shape-level summary captures ensemble diversity even when a conserved pseudoknotted motif appears with shifted base-pair positions across samples.
We validate PRISM in the pseudoknot-free limit, where it reproduces RNAFold quantities for minimum free energy, ensemble free energy, centroid expected distance, and maximum expected accuracy. We further show that stochastic traceback recovers Boltzmann structure probabilities and that sampling error decreases at the expected Monte Carlo rate while runtime grows linearly with the number of samples. Our case study demonstrate that RNA-shape summaries can reveal dominant pseudoknotted topologies that centroid decoding may miss. PRISM thus converts the CParty partition function into a practical framework for posterior decoding and topology-aware analysis of hierarchically constrained pseudoknotted RNA ensembles.

Cite As Get BibTex

Mateo Gray, Sebastian Will, and Hosna Jabbari. PRISM: Partition-Function Decomposition into Structural Classes for Hierarchically Constrained RNA Pseudoknot Ensembles. In 26th International Conference on Algorithms for Bioinformatics (WABI 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 390, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.WABI.2026.30

Author Details

Mateo Gray
  • Department of Biomedical Engineering, University of Alberta, Edmonton, Canada
Sebastian Will
  • Department of Computer Science, Institut Polytechnique de Paris, Palaiseau, France
Hosna Jabbari
  • Department of Biomedical Engineering, University of Alberta, Edmonton, Canada

Supplementary Materials

References

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