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Register a new userCombinatorial analysis of interacting RNA molecules
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Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backbones drawn horizontally on top of each other such that (1) intramolecular and intermolecular bonds are noncrossing and (2) there is no zig-zag configuration. This paper studies joint structures with arc-length at least four in which both, interior and exterior stack-lengths are at least two (no isolated arcs). The key idea in this paper is to consider a new type of shape, based on which joint structures can be derived via symbolic enumeration. Our results imply simple asymptotic formulas for the number of joint structures with surprisingly small exponential growth rates. They are of interest in the context of designing prediction algorithms for RNA-RNA interactions.
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In this paper we study properties of topological RNA structures, i.e.~RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures within this framework are topological structures having genus zero. We derive a new bivariate generating function whose singular expansion allows us to analyze the distributions of arcs, stacks, hairpin- , interior- and multi-loops. We then extend this analysis to H-type pseudoknots, kissing hairpins as well as $3$-knots and compute their respective expectation values. Finally we discuss our results and put them into context with data obtained by uniform sampling structures of fixed genus.
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- and stack-length restrictions. Our main result reads as follows: in the simplex of the nucleotide ratios there exists a convex region in which, in the limit of long sequences, a random structure a.a.s.~has compatible sequence with these ratios and outside of which a.a.s.~a random structure has no such compatible sequence. We localize this region for RNA secondary structures subject to various base pairing rules and minimum arc- and stack-length restrictions. In particular, for {bf GC}-sequences having a ratio of {bf G} nucleotides smaller than $1/3$, a random RNA secondary structure without any minimum arc- and stack-length restrictions has a.a.s.~no such compatible sequence. For sequences having a ratio of {bf G} nucleotides larger than $1/3$, a random RNA secondary structure has a.a.s. such compatible sequences. We discuss our results in the context of various families of RNA structures.
A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed topological genus there exist only finitely many such shapes. We shall express topological RNA structures as unicellular maps, i.e. graphs together with a cyclic ordering of their half-edges. In this paper we prove a bijection of shapes of topological RNA structures. We furthermore derive a linear time algorithm generating shapes of fixed topological genus. We derive explicit expressions for the coefficients of the generating polynomial of these shapes and the generating function of RNA structures of genus $g$. Furthermore we outline how shapes can be used in order to extract essential information of RNA structure databases.
There exists many complicated $k$-noncrossing pseudoknot RNA structures in nature based on some special conditions. The special characteristic of RNA structures gives us great challenges in researching the enumeration, prediction and the analysis of prediction algorithm. We will study two kinds of typical $k$-noncrossing pseudoknot RNAs with complex structures separately.
How to produce expressive molecular representations is a fundamental challenge in AI-driven drug discovery. Graph neural network (GNN) has emerged as a powerful technique for modeling molecular data. However, previous supervised approaches usually suffer from the scarcity of labeled data and have poor generalization capability. Here, we proposed a novel Molecular Pre-training Graph-based deep learning framework, named MPG, that leans molecular representations from large-scale unlabeled molecules. In MPG, we proposed a powerful MolGNet model and an effective self-supervised strategy for pre-training the model at both the node and graph-level. After pre-training on 11 million unlabeled molecules, we revealed that MolGNet can capture valuable chemistry insights to produce interpretable representation. The pre-trained MolGNet can be fine-tuned with just one additional output layer to create state-of-the-art models for a wide range of drug discovery tasks, including molecular properties prediction, drug-drug interaction, and drug-target interaction, involving 13 benchmark datasets. Our work demonstrates that MPG is promising to become a novel approach in the drug discovery pipeline.
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