Related papers: RNA as a Permutation
Metrics for indirectly predicting the folding rates of RNA sequences are of interest. In this letter, we introduce a simple metric of RNA structural complexity, which accounts for differences in the energetic contributions of RNA base…
This work presents RNAdiffusion, a latent diffusion model for generating and optimizing discrete RNA sequences of variable lengths. RNA is a key intermediary between DNA and protein, exhibiting high sequence diversity and complex…
This contribution focuses on the fascinating RNA molecule, its sequence-dependent folding driven by base-pairing interactions, the interplay between these interactions and natural evolution, and its multiple regulatory roles. The four of us…
The RNA inverse folding problem, a key challenge in RNA design, involves identifying nucleotide sequences that can fold into desired secondary structures, which are critical for ensuring molecular stability and function. The inherent…
RNA protein interactions control the fate of cellular RNAs and play an important role in gene regulation. An interdependency between such interactions allows for the implementation of logic functions in gene regulation. We investigate the…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
Given a random RNA secondary structure, $S$, we study RNA sequences having fixed ratios of nuclotides that are compatible with $S$. We perform this analysis for RNA secondary structures subject to various base pairing rules and minimum arc-…
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…
In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial…
For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…
Classification of proteins based on their structure provides a valuable resource for studying protein structure, function and evolutionary relationships. With the rapidly increasing number of known protein structures, manual and…
RNA folding prediction remains challenging, but can be also studied using a topological mathematical approach. In the present paper, the mathematical method to compute the topological classification of RNA structures and based on matrix…
We tackle the problem of protein secondary structure prediction using a common task framework. This lead to the introduction of multiple ideas for neural architectures based on state of the art building blocks, used in this task for the…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
We describe a framework for encoding cluster combinatorics using categorical methods. We give a definition of an abstract cluster structure, which captures the essence of cluster mutation at a tropical level and show that cluster algebras,…
Identifying the secondary structure of an RNA is crucial for understanding its diverse regulatory functions. This paper focuses on how to enhance target identification in a Boltzmann ensemble of structures via chemical probing data. We…
Solving the RNA inverse folding problem is a critical prerequisite to RNA design, an emerging field in bioengineering with a broad range of applications from reaction catalysis to cancer therapy. Although significant progress has been made…
The Automated Protein Structure Analysis (APSA) method is used for the classification of supersecondary structures. Basis for the classification is the encoding of three-dimensional (3D) residue conformations into a 16-letter code (3D-1D…
RNA design aims to find a sequence that folds with highest probability into a designated target structure. However, certain structures are undesignable, meaning no sequence can fold into the target structure under the default (Turner) RNA…
Consider the network of all secondary structures of a given RNA sequence, where nodes are connected when the corresponding structures have base pair distance one. The expected degree of the network is the average number of neighbors, where…