[Note that this post is a word-for-word copy of my answer on Biology Stack Exchange. Moreover, I'm not sure if this question (or my answer to it) is on-topic in a Bioinformatics forum, since it asks about differences between the methods themselves and not the analyses.]
LIGR-seq
LIGR-seq (Figure 1A) employs in vivo crosslinking of RNA duplexes using the modified psoralen derivative 4′-aminomethyltrioxalen (AMT), which intercalates into RNA duplexes and, upon 365 nm UV irradiation, generates inter-strand adducts between juxtaposed pyrimidine bases (Calvet and Pederson, 1979). Following cell lysis and a limited single-strand S1 endonuclease digest, free RNA overhangs adjacent to duplexes are ligated using circRNA ligase. This ligase catalyzes the ATP-dependent ligation of proximal RNA ends and has optimal activity at elevated temperatures that reduce RNA hybridization. RNase R, a 3′→5′ exoribonuclease that digests linear and structured RNAs (Vincent and Deutscher, 2006), is then used to digest uncrosslinked RNA, thereby enriching AMT-crosslinked duplexes (Figures 1A and S1). Following reversal of crosslinks using 254 nm irradiation, the RNA samples are subjected to high-throughput sequencing to detect chimeras formed by ligation. To assess background ligation artifacts, uncrosslinked ("–AMT") samples are prepared in parallel, and unligated samples are used to determine the relative expression of transcripts forming chimeras for downstream normalization and analysis.
Summarized
AMT crosslinking ⟶ cell lysis ⟶ S1 endonuclease digestion ⟶ RNA-RNA ligation with circRNA ligase ⟶ RNase R digestion of uncrosslinked RNA ⟶ crosslink reversal ⟶ sequencing library preparation (adapter ligation, reverse transcription, etc.)
PARIS
HeLa, HEK293T, and mES cells were treated with or without AMT and crosslinked with 365 nm UV. Cell lysates were digested with S1 nuclease and RNA purified using TRIzol. Purified RNA was further digested with ShortCut RNase III to smaller fragments. RNA was separated by 12% native polyacrylamide gel and then the first dimension gel slices were further electrophoresed in a second dimension 20% urea-denatured gel. Crosslinked RNA above the main diagonal was eluted, proximity ligated with T4 RNA ligase I and photo-reversed with 254 nm UV. The proximity-ligated RNA molecules were then ligated to barcoded adapters and converted to libraries for Illumina sequencing.
Summarized
AMT crosslinking ⟶ cell lysis ⟶ S1 endonuclease digestion ⟶ TRIzol purificaiton ⟶ ShortCut RNase III digestion ⟶ 2D gel purification ⟶ RNA-RNA ligation with T4 RNA Ligase 1 ⟶ crosslink reversal ⟶ sequencing library preparation (adapter ligation, reverse transcription, etc.)
Concerning the capture of RNA-RNA interactions, these methods are essentially the same. Given that both papers were published in Cell Press journals in the same week, they were likely developed concurrently in competing labs. It may be the case that the editors coordinated publication so that neither group would feel they "got scooped".
From what I can tell, the major difference is in how the methods distinguish in vivo RNA interactors from transient RNA-RNA hybridization events that occur during the course of the protocols. In LIGR-seq, they include an uncrosslinked ("–AMT") control so that they can differentiate true interactions from background noise by looking for ligation chimeras that are enriched in the +AMT samples relative to –AMT. In PARIS, the second dimension of the 2D gel is 20% urea, which would serve to denature any non-crosslinked dsRNA molecules prior to ligation; see the full methods for more details:
Gel slices of each lane were embedded and polymerized into the top of the second dimension 20% urea-TBE denatured polyacrylamide gel ... The second dimension gel has higher temperature due to the high power, and the high temperature facilitates denaturation of the dsRNA fragments.
There may also be a difference in the length distributions of the chimeric RNA molecules obtained at the end each method, since LIGR-seq and PARIS use different RNase enzymes with different digestion parameters.
Thank you for the explanation. From my experience, I need to have at least some basic understanding of the methods used to obtain the data, thus this is not entirely off-topic IMHO.
My main interest is to reuse the LIGR dataset, for ncRNA structure prediction (this was done only in the PARIS paper). Based on your explanation, I don't see any step in the LIGRseq that would degrade intramolecular cross-links which I'm interested to see.