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**Published in:** LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

RNAs composed of Triplet Repeats (TR) have recently attracted much attention in the field of synthetic biology. We study the mimimum free energy (MFE) secondary structures of such RNAs and give improved algorithms to compute the MFE and the partition function. Furthermore, we study the interaction of multiple RNAs and design a new algorithm for computing MFE and partition function for RNA-RNA interactions, improving the previously known factorial running time to exponential. In the case of TR, we show computational hardness but still obtain a parameterized algorithm. Finally, we propose a polynomial-time algorithm for computing interactions from a base set of RNA strands and conduct experiments on the interaction of TR based on this algorithm. For instance, we study the probability that a base pair is formed between two strands with the same triplet pattern, allowing an assessment of a notion of orthogonality between TR.

Kimon Boehmer, Sarah J. Berkemer, Sebastian Will, and Yann Ponty. RNA Triplet Repeats: Improved Algorithms for Structure Prediction and Interactions. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 18:1-18:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{boehmer_et_al:LIPIcs.WABI.2024.18, author = {Boehmer, Kimon and Berkemer, Sarah J. and Will, Sebastian and Ponty, Yann}, title = {{RNA Triplet Repeats: Improved Algorithms for Structure Prediction and Interactions}}, booktitle = {24th International Workshop on Algorithms in Bioinformatics (WABI 2024)}, pages = {18:1--18:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-340-9}, ISSN = {1868-8969}, year = {2024}, volume = {312}, editor = {Pissis, Solon P. and Sung, Wing-Kin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.18}, URN = {urn:nbn:de:0030-drops-206625}, doi = {10.4230/LIPIcs.WABI.2024.18}, annote = {Keywords: RNA folding, RNA interactions, triplet repeats, dynamic programming, NP-hardness} }

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**Published in:** LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Inverse folding is a classic instance of negative RNA design which consists in finding a sequence that uniquely folds into a target secondary structure with respect to energy minimization. A breakthrough result of Bonnet et al. shows that, even in simple base pairs-based (BP) models, the decision version of a mildly constrained version of inverse folding is NP-hard.
In this work, we show that inverse folding can be solved in linear time for a large collection of targets, including every structure that contains no isolated BP and no isolated stack (or, equivalently, when all helices consist of 3^{+} base pairs). For structures featuring shorter helices, our linear algorithm is no longer guaranteed to produce a solution, but still does so for a large proportion of instances.
Our approach introduces a notion of modulo m-separability, generalizing a property pioneered by Hales et al. Separability is a sufficient condition for the existence of a solution to the inverse folding problem. We show that, for any input secondary structure of length n, a modulo m-separated sequence can be produced in time 𝒪(n 2^m) anytime such a sequence exists. Meanwhile, we show that any structure consisting of 3^{+} base pairs is either trivially non-designable, or always admits a modulo-2 separated solution (m = 2). Solution sequences can thus be produced in linear time, and even be uniformly generated within the set of modulo-2 separable sequences.

Théo Boury, Laurent Bulteau, and Yann Ponty. RNA Inverse Folding Can Be Solved in Linear Time for Structures Without Isolated Stacks or Base Pairs. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 19:1-19:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{boury_et_al:LIPIcs.WABI.2024.19, author = {Boury, Th\'{e}o and Bulteau, Laurent and Ponty, Yann}, title = {{RNA Inverse Folding Can Be Solved in Linear Time for Structures Without Isolated Stacks or Base Pairs}}, booktitle = {24th International Workshop on Algorithms in Bioinformatics (WABI 2024)}, pages = {19:1--19:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-340-9}, ISSN = {1868-8969}, year = {2024}, volume = {312}, editor = {Pissis, Solon P. and Sung, Wing-Kin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.19}, URN = {urn:nbn:de:0030-drops-206632}, doi = {10.4230/LIPIcs.WABI.2024.19}, annote = {Keywords: RNA structure, String Design, Parameterized Complexity, Uniform Sampling} }

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**Published in:** LIPIcs, Volume 273, 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)

Motivation. Recurrent substructures in RNA, known as 3D motifs, consist of networks of base pair interactions and are critical to understanding the relationship between structure and function. Their structure is naturally expressed as a graph which has led to many graph-based algorithms to automatically catalog identical motifs found in 3D structures. Yet, due to the complexity of the problem, state-of-the-art methods are often optimized to find exact matches, limiting the search to a subset of potential solutions, or do not allow explicit control over the desired variability.
Results. We developed FuzzTree, a method able to efficiently sample approximate instances of an RNA motif, abstracted as a subgraph within a target RNA structure. It is the first method that allows explicit control over (1) the admissible geometric variability in the interactions; (2) the number of missing edges; and (3) the introduction of discontinuities in the backbone given close distances in the 3D structure. Our tool relies on a multidimensional Boltzmann sampling, having complexity parameterized by the treewidth of the requested motif. We applied our method to the well-known internal loop Kink-Turn motif, which can be divided into 12 subgroups. Given only the graph representing the main Kink-Turn subgroup, FuzzTree retrieved over 3/4 of all kink-turns. We also highlighted two occurrences of new sampled patterns. Our tool is available as free software and can be customized for different parameters and types of graphs.

Théo Boury, Yann Ponty, and Vladimir Reinharz. Automatic Exploration of the Natural Variability of RNA Non-Canonical Geometric Patterns with a Parameterized Sampling Technique. In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{boury_et_al:LIPIcs.WABI.2023.20, author = {Boury, Th\'{e}o and Ponty, Yann and Reinharz, Vladimir}, title = {{Automatic Exploration of the Natural Variability of RNA Non-Canonical Geometric Patterns with a Parameterized Sampling Technique}}, booktitle = {23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)}, pages = {20:1--20:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-294-5}, ISSN = {1868-8969}, year = {2023}, volume = {273}, editor = {Belazzougui, Djamal and Ouangraoua, A\"{i}da}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2023.20}, URN = {urn:nbn:de:0030-drops-186460}, doi = {10.4230/LIPIcs.WABI.2023.20}, annote = {Keywords: Subgraph Isomorphism, 3D RNA, Parameterized Complexity, Tree Decomposition, Boltzmann sampling, Neighborhood metrics, Kink-Turn family} }

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**Published in:** Dagstuhl Reports, Volume 12, Issue 9 (2023)

This report documents the program and outcomes of Dagstuhl Seminar 22381 "Rational Design of RiboNucleic Acids" (RNAs). The seminar covered a wide array of models, algorithmic strategies, molecular scales and modalities, all targeting in silico design of RNAs performing predefined biological functions. It consisted in a series of talks, each being allocated a generous time budget enabling frequent (welcomed!) interruptions and fruitful discussions. Applications of rational RNA design include mRNA vaccines; RNAs acting as sensors; self-replicating RNAs, relevant to RNA world/origin of life studies; populations of RNAs performing computations, e.g. through strand-displacement systems; RNA origamis forming nano-architectures through self-assembly; weakly interacting RNAs inducing the formation of droplets within cells through liquid-liquid phase separation. Those diverse applications are typically tackled by Bioinformatics-inclined scientists, contributing to distinct areas of life science and, as a result, somewhat isolated and sometimes unaware of similar pursuits in neighboring fields. The overarching goals of this meeting were to gather computational scientists from multiple fields, increase awareness of relevant efforts in distant communities, and ultimately contribute to a transversal perspective where RNA design becomes an object of study in itself.

Sven Findeiß, Christoph Flamm, and Yann Ponty. Rational Design of RiboNucleic Acids (Dagstuhl Seminar 22381). In Dagstuhl Reports, Volume 12, Issue 9, pp. 121-149, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{findei_et_al:DagRep.12.9.121, author = {Findei{\ss}, Sven and Flamm, Christoph and Ponty, Yann}, title = {{Rational Design of RiboNucleic Acids (Dagstuhl Seminar 22381)}}, pages = {121--149}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2023}, volume = {12}, number = {9}, editor = {Findei{\ss}, Sven and Flamm, Christoph and Ponty, Yann}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.12.9.121}, URN = {urn:nbn:de:0030-drops-178110}, doi = {10.4230/DagRep.12.9.121}, annote = {Keywords: RNA, RNA design, Inverse folding, RNA structure, mRNA design, RNA sensors, Co-transcriptional folding, Molecular evolution, Distant homology, Drug design} }

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**Published in:** LIPIcs, Volume 242, 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)

Despite being a textbook application of dynamic programming (DP) and routine task in RNA structure analysis, RNA secondary structure prediction remains challenging whenever pseudoknots come into play. To circumvent the NP-hardness of energy minimization in realistic energy models, specialized algorithms have been proposed for restricted conformation classes that capture the most frequently observed configurations.
While these methods rely on hand-crafted DP schemes, we generalize and fully automatize the design of DP pseudoknot prediction algorithms. We formalize the problem of designing DP algorithms for an (infinite) class of conformations, modeled by (a finite number of) fatgraphs, and automatically build DP schemes minimizing their algorithmic complexity. We propose an algorithm for the problem, based on the tree-decomposition of a well-chosen representative structure, which we simplify and reinterpret as a DP scheme. The algorithm is fixed-parameter tractable for the tree-width tw of the fatgraph, and its output represents a 𝒪(n^{tw+1}) algorithm for predicting the MFE folding of an RNA of length n.
Our general framework supports general energy models, partition function computations, recursive substructures and partial folding, and could pave the way for algebraic dynamic programming beyond the context-free case.

Bertrand Marchand, Sebastian Will, Sarah J. Berkemer, Laurent Bulteau, and Yann Ponty. Automated Design of Dynamic Programming Schemes for RNA Folding with Pseudoknots. In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 7:1-7:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{marchand_et_al:LIPIcs.WABI.2022.7, author = {Marchand, Bertrand and Will, Sebastian and Berkemer, Sarah J. and Bulteau, Laurent and Ponty, Yann}, title = {{Automated Design of Dynamic Programming Schemes for RNA Folding with Pseudoknots}}, booktitle = {22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)}, pages = {7:1--7:24}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-243-3}, ISSN = {1868-8969}, year = {2022}, volume = {242}, editor = {Boucher, Christina and Rahmann, Sven}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2022.7}, URN = {urn:nbn:de:0030-drops-170414}, doi = {10.4230/LIPIcs.WABI.2022.7}, annote = {Keywords: RNA folding, treewidth, dynamic programming} }

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**Published in:** LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

In this paper, we study the Independent Set (IS) reconfiguration problem in graphs. An IS reconfiguration is a scenario transforming an IS L into another IS R, inserting/removing vertices one step at a time while keeping the cardinalities of intermediate sets greater than a specified threshold. We focus on the bipartite variant where only start and end vertices are allowed in intermediate ISs. Our motivation is an application to the RNA energy barrier problem from bioinformatics, for which a natural parameter would be the difference between the initial IS size and the threshold.
We first show the para-NP hardness of the problem with respect to this parameter. We then investigate a new parameter, the cardinality range, denoted by ρ which captures the maximum deviation of the reconfiguration scenario from optimal sets (formally, ρ is the maximum difference between the cardinalities of an intermediate IS and an optimal IS). We give two different routes to show that this problem is in XP for ρ: The first is a direct O(n²)-space, O(n^{2ρ+2.5})-time algorithm based on a separation lemma; The second builds on a parameterized equivalence with the directed pathwidth problem, leading to a O(n^{ρ+1})-space, O(n^{ρ+2})-time algorithm for the reconfiguration problem through an adaptation of a prior result by Tamaki [Tamaki, 2011]. This equivalence is an interesting result in its own right, connecting a reconfiguration problem (which is essentially a connectivity problem within a reconfiguration network) with a structural parameter for an auxiliary graph.
We demonstrate the practicality of these algorithms, and the relevance of our introduced parameter, by considering the application of our algorithms on random small-degree instances for our problem. Moreover, we reformulate the computation of the energy barrier between two RNA secondary structures, a classic hard problem in computational biology, as an instance of bipartite reconfiguration. Our results on IS reconfiguration thus yield an XP algorithm in O(n^{ρ+2}) for the energy barrier problem, improving upon a partial O(n^{2ρ+2.5}) algorithm for the problem.

Laurent Bulteau, Bertrand Marchand, and Yann Ponty. A New Parametrization for Independent Set Reconfiguration and Applications to RNA Kinetics. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bulteau_et_al:LIPIcs.IPEC.2021.11, author = {Bulteau, Laurent and Marchand, Bertrand and Ponty, Yann}, title = {{A New Parametrization for Independent Set Reconfiguration and Applications to RNA Kinetics}}, booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)}, pages = {11:1--11:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-216-7}, ISSN = {1868-8969}, year = {2021}, volume = {214}, editor = {Golovach, Petr A. and Zehavi, Meirav}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.11}, URN = {urn:nbn:de:0030-drops-153946}, doi = {10.4230/LIPIcs.IPEC.2021.11}, annote = {Keywords: reconfiguration problems - parameterized algorithms - RNA bioinformatics - directed pathwidth} }

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**Published in:** LIPIcs, Volume 201, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021)

Hard graph problems are ubiquitous in Bioinformatics, inspiring the design of specialized Fixed-Parameter Tractable algorithms, many of which rely on a combination of tree-decomposition and dynamic programming. The time/space complexities of such approaches hinge critically on low values for the treewidth tw of the input graph. In order to extend their scope of applicability, we introduce the Tree-Diet problem, i.e. the removal of a minimal set of edges such that a given tree-decomposition can be slimmed down to a prescribed treewidth tw'. Our rationale is that the time gained thanks to a smaller treewidth in a parameterized algorithm compensates the extra post-processing needed to take deleted edges into account.
Our core result is an FPT dynamic programming algorithm for Tree-Diet, using 2^{O(tw)}n time and space. We complement this result with parameterized complexity lower-bounds for stronger variants (e.g., NP-hardness when tw' or tw-tw' is constant). We propose a prototype implementation for our approach which we apply on difficult instances of selected RNA-based problems: RNA design, sequence-structure alignment, and search of pseudoknotted RNAs in genomes, revealing very encouraging results. This work paves the way for a wider adoption of tree-decomposition-based algorithms in Bioinformatics.

Bertrand Marchand, Yann Ponty, and Laurent Bulteau. Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 7:1-7:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{marchand_et_al:LIPIcs.WABI.2021.7, author = {Marchand, Bertrand and Ponty, Yann and Bulteau, Laurent}, title = {{Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics}}, booktitle = {21st International Workshop on Algorithms in Bioinformatics (WABI 2021)}, pages = {7:1--7:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-200-6}, ISSN = {1868-8969}, year = {2021}, volume = {201}, editor = {Carbone, Alessandra and El-Kebir, Mohammed}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2021.7}, URN = {urn:nbn:de:0030-drops-143604}, doi = {10.4230/LIPIcs.WABI.2021.7}, annote = {Keywords: RNA, treewidth, FPT algorithms, RNA design, structure-sequence alignment} }

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