RNA-Polynomial

Overview

This repository includes code and data for experiments in the following paper.

Pengyu Liu, Jacob Lusk, Nataša Jonoska, Mariel Vázquez, Analyzing the link between RNA secondary structures and R-loop formation with tree polynomials, Preprint (2023).

Setup

Running the code requires Matlab with the Bioinformatics Toolbox and the Statistics and Machine Learning Toolbox; see Matlab toolboxes.

After installing Matlab and required Matlab toolboxes,

1. clone (or download) this repository to a local directory;
2. go to the folder data and unzip the compressed files pfc8_snrpn.zip and pfc53_airn.zip;
3. keep the unzipped folders pfc8_snrpn and pfc53_airn in the folder data.

Then, the setup is complete.

Usage

To compute the tree polynomial representations of an RNA secondary structure

The function functions/dbn2pl.m converts a dot-bracket notation of an RNA secondary structure without pseudoknots into a parent list of its tree representation of a selected type. The function functions/pl2poly.m then computes the corresponding polynomial with the parent list of the tree representation. See the file Example.m for an example of using the functions to compute the tree polynomial representations of an RNA secondary structure.

To compute the tree polynomial representations of one's own data of RNA secondary structures,

1. convert an RNA secondary structure to the dot-bracket notation dbn;
2. use L = dbn2pl(dbn,type) convert the dot-bracket notation dbn to the parent list L of its tree representation of a selected type;
3. use P = pl2poly(dbn,type) to compute the corresponding polynomial P from the parent list L of the tree representation.

To reconduct the experiments and reproduce the results

For clustering non-coding RNA secondary structures, run the file Process_Clustering.m. This will compute the tree polynomial representations of the RNA secondary structures with dot-bracket notations stored in the folder data/bpRNA-Rfam and compute the pairwise polynomial distances between the RNA secondary structures. The results are stored in the file data/bpRNA_Rfam.mat.

For analyzing the link between RNA secondary structures and R-loop formation, run the file Process_Rloop.m. This will compute the polynomial representations of the RNA secondary structures produced by DrTransformer (repository, paper) with dot-bracket notations stored in the folder data/pfc8_snrpn and data/pfc53_airn and compute the coefficient sums. The results are stored in the files with names like data/pFC8_type2.mat.

If one would like to reproduce the RNA secondary structures with DrTransformer, then one should install DrTransformer (see the instructions in its repository) and use the drtransformer-runner script which segments the sequences of the plasmids stored in the files data/pfc8_snrpn_coding_strand.fa and pfc53_airn_coding_strand.fa and calls DrTransformer for predicting the secondary structrues of the sequence segments. This will generate the files of dot-bracket notations in the folder data/pfc8_snrpn and data/pfc53_airn.

To view the results in the paper and additional results

For clustering non-coding RNA secondary structures, run the file Results_Clustering.m. This will use the file data/bpRNA_Rfam.mat to perform tSNE visualization and k-medoids clustering with the pairwise polynomial distances between the non-coding RNA secondary structures and compute the misclassification rates.

For visualizing the correlations between the scaled sums and the probabilities of R-loop formation, run the file Results_Correlations.m. This will use the files with names like data/pFC8_type2.mat to compute the scaled sums and compare with probabilities of R-loop formation constructed from the files with names like data/pFC8_SUPERCOILED.bed.

For analyzing RNA secondary structures that contribute to large coefficient sums, run the file Results_Structures.m. This will use the files with names like data/pFC8_type2.mat to locate the RNA segments with the largest coefficient sums and visualize the RNA secondary structures predicted by DrTransformer with dot-bracket notations stored in the folder data/pfc8_snrpn and data/pfc53_airn.