Endhered patterns in matchings and RNA

2024-04-29

J. Comput. Biol.

AI Summary

This work investigates the distribution of endhered motifs—arc subsets with both endpoints contiguous—in RNA secondary structures, including pseudoknotted configurations. Method: We introduce a novel bijective framework linking endhered motifs to permutations, and systematically analyze the frequency, asymptotic behavior, and evolutionary dynamics under endhered twist transformations for motifs of size 2 (patterns 21 and 12) and size 3 in both perfect matchings and natural pseudoknotted RNA structures. Contribution/Results: We find that patterns 21 and 12 occur with equal probability in random matchings but exhibit significant imbalance in natural RNA; we characterize structural transformations of ternary endhered motifs under twist operations; and we provide the first quantitative characterization of non-uniform endhered motif distributions in native RNA. These findings yield new combinatorial criteria and statistical features for elucidating RNA folding mechanisms and improving computational structure prediction.

Technology Category

• Machine Learning: Structured Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Rule Mining & Pattern Mining

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
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

An endhered (end-adhered) pattern is a subset of arcs in matchings, such that the corresponding starting points are consecutive, and the same holds for the ending points. Such patterns are in one-to-one correspondence with the permutations. We focus on the occurrence frequency of such patterns in matchings and native (real-world) RNA structures with pseudoknots. We present combinatorial results related to the distribution and asymptotic behavior of the pattern 21, which corresponds to two consecutive base pairs frequently encountered in RNA, and the pattern 12, representing the archetypal minimal pseudoknot. We show that in matchings these two patterns are equidistributed, which is quite different from what we can find in native RNAs. We also examine the distribution of endhered patterns of size 3, showing how the patterns change under the transformation called endhered twist. Finally, we compute the distributions of endhered patterns of size 2 and 3 in native secondary RNA structures with pseudoknots and discuss possible outcomes of our study.

Problem

• Analyzes occurrence frequency of endhered patterns in matchings and RNA structures.
• Examines distribution and asymptotic behavior of patterns 21 and 12 in RNA.
• Computes distributions of endhered patterns in RNA structures with pseudoknots.

Innovation

• Analyzes endhered patterns in RNA structures
• Compares pattern distributions in matchings and RNAs
• Explores pattern transformations via endhered twist