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1. Optimal gap-affine alignment in O ( s ) space

   https://doi.org/10.1093/bioinformatics/btad074  

   Marco-Sola, Santiago; Eizenga, Jordan M; Guarracino, Andrea; Paten, Benedict; Garrison, Erik; Moreto, Miquel (February 2023, Bioinformatics)

   Martelli, Pier Luigi (Ed.)

   Abstract MotivationPairwise sequence alignment remains a fundamental problem in computational biology and bioinformatics. Recent advances in genomics and sequencing technologies demand faster and scalable algorithms that can cope with the ever-increasing sequence lengths. Classical pairwise alignment algorithms based on dynamic programming are strongly limited by quadratic requirements in time and memory. The recently proposed wavefront alignment algorithm (WFA) introduced an efficient algorithm to perform exact gap-affine alignment in O(ns) time, where s is the optimal score and n is the sequence length. Notwithstanding these bounds, WFA’s O(s2) memory requirements become computationally impractical for genome-scale alignments, leading to a need for further improvement. ResultsIn this article, we present the bidirectional WFA algorithm, the first gap-affine algorithm capable of computing optimal alignments in O(s) memory while retaining WFA’s time complexity of O(ns). As a result, this work improves the lowest known memory bound O(n) to compute gap-affine alignments. In practice, our implementation never requires more than a few hundred MBs aligning noisy Oxford Nanopore Technologies reads up to 1 Mbp long while maintaining competitive execution times. Availability and implementationAll code is publicly available at https://github.com/smarco/BiWFA-paper. Supplementary informationSupplementary data are available at Bioinformatics online. 

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2. LinearPartition: linear-time approximation of RNA folding partition function and base-pairing probabilities

   https://doi.org/10.1093/bioinformatics/btaa460  

   Zhang, He; Zhang, Liang; Mathews, David H; Huang, Liang (July 2020, Bioinformatics)

   Abstract Motivation RNA secondary structure prediction is widely used to understand RNA function. Recently, there has been a shift away from the classical minimum free energy methods to partition function-based methods that account for folding ensembles and can therefore estimate structure and base pair probabilities. However, the classical partition function algorithm scales cubically with sequence length, and is therefore prohibitively slow for long sequences. This slowness is even more severe than cubic-time free energy minimization due to a substantially larger constant factor in runtime. Results Inspired by the success of our recent LinearFold algorithm that predicts the approximate minimum free energy structure in linear time, we design a similar linear-time heuristic algorithm, LinearPartition, to approximate the partition function and base-pairing probabilities, which is shown to be orders of magnitude faster than Vienna RNAfold and CONTRAfold (e.g. 2.5 days versus 1.3 min on a sequence with length 32 753 nt). More interestingly, the resulting base-pairing probabilities are even better correlated with the ground-truth structures. LinearPartition also leads to a small accuracy improvement when used for downstream structure prediction on families with the longest length sequences (16S and 23S rRNAs), as well as a substantial improvement on long-distance base pairs (500+ nt apart). Availability and implementation Code: http://github.com/LinearFold/LinearPartition; Server: http://linearfold.org/partition. Supplementary information Supplementary data are available at Bioinformatics online. 

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3. RNA design via structure-aware multifrontier ensemble optimization

   https://doi.org/10.1093/bioinformatics/btad252  

   Zhou, Tianshuo; Dai, Ning; Li, Sizhen; Ward, Max; Mathews, David H; Huang, Liang (June 2023, Bioinformatics)

   Abstract MotivationRNA design is the search for a sequence or set of sequences that will fold to desired structure, also known as the inverse problem of RNA folding. However, the sequences designed by existing algorithms often suffer from low ensemble stability, which worsens for long sequence design. Additionally, for many methods only a small number of sequences satisfying the MFE criterion can be found by each run of design. These drawbacks limit their use cases. ResultsWe propose an innovative optimization paradigm, SAMFEO, which optimizes ensemble objectives (equilibrium probability or ensemble defect) by iterative search and yields a very large number of successfully designed RNA sequences as byproducts. We develop a search method which leverages structure level and ensemble level information at different stages of the optimization: initialization, sampling, mutation, and updating. Our work, while being less complicated than others, is the first algorithm that is able to design thousands of RNA sequences for the puzzles from the Eterna100 benchmark. In addition, our algorithm solves the most Eterna100 puzzles among all the general optimization based methods in our study. The only baseline solving more puzzles than our work is dependent on handcrafted heuristics designed for a specific folding model. Surprisingly, our approach shows superiority on designing long sequences for structures adapted from the database of 16S Ribosomal RNAs. Availability and implementationOur source code and data used in this article is available at https://github.com/shanry/SAMFEO. 

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4. An alignment-free heuristic for fast sequence comparisons with applications to phylogeny reconstruction

   https://doi.org/10.1186/s12859-020-03738-5  

   Chockalingam, Sriram P.; Pannu, Jodh; Hooshmand, Sahar; Thankachan, Sharma V.; Aluru, Srinivas (November 2020, BMC Bioinformatics)

   null (Ed.)

   Abstract Background Alignment-free methods for sequence comparisons have become popular in many bioinformatics applications, specifically in the estimation of sequence similarity measures to construct phylogenetic trees. Recently, the average common substring measure, ACS , and its k -mismatch counterpart, ACS k , have been shown to produce results as effective as multiple-sequence alignment based methods for reconstruction of phylogeny trees. Since computing ACS k takes O ( n log k n ) time and hence impractical for large datasets, multiple heuristics that can approximate ACS k have been introduced. Results In this paper, we present a novel linear-time heuristic to approximate ACS k , which is faster than computing the exact ACS k while being closer to the exact ACS k values compared to previously published linear-time greedy heuristics. Using four real datasets, containing both DNA and protein sequences, we evaluate our algorithm in terms of accuracy, runtime and demonstrate its applicability for phylogeny reconstruction. Our algorithm provides better accuracy than previously published heuristic methods, while being comparable in its applications to phylogeny reconstruction. Conclusions Our method produces a better approximation for ACS k and is applicable for the alignment-free comparison of biological sequences at highly competitive speed. The algorithm is implemented in Rust programming language and the source code is available at https://github.com/srirampc/adyar-rs . 

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5. End-to-end learning of multiple sequence alignments with differentiable Smith–Waterman

   https://doi.org/10.1093/bioinformatics/btac724  

   Petti, Samantha; Bhattacharya, Nicholas; Rao, Roshan; Dauparas, Justas; Thomas, Neil; Zhou, Juannan; Rush, Alexander M; Koo, Peter; Ovchinnikov, Sergey (November 2022, Bioinformatics)

   Borgwardt, Karsten (Ed.)

   Abstract Motivation Multiple sequence alignments (MSAs) of homologous sequences contain information on structural and functional constraints and their evolutionary histories. Despite their importance for many downstream tasks, such as structure prediction, MSA generation is often treated as a separate pre-processing step, without any guidance from the application it will be used for. Results Here, we implement a smooth and differentiable version of the Smith–Waterman pairwise alignment algorithm that enables jointly learning an MSA and a downstream machine learning system in an end-to-end fashion. To demonstrate its utility, we introduce SMURF (Smooth Markov Unaligned Random Field), a new method that jointly learns an alignment and the parameters of a Markov Random Field for unsupervised contact prediction. We find that SMURF learns MSAs that mildly improve contact prediction on a diverse set of protein and RNA families. As a proof of concept, we demonstrate that by connecting our differentiable alignment module to AlphaFold2 and maximizing predicted confidence, we can learn MSAs that improve structure predictions over the initial MSAs. Interestingly, the alignments that improve AlphaFold predictions are self-inconsistent and can be viewed as adversarial. This work highlights the potential of differentiable dynamic programming to improve neural network pipelines that rely on an alignment and the potential dangers of optimizing predictions of protein sequences with methods that are not fully understood. Availability and implementation Our code and examples are available at: https://github.com/spetti/SMURF. Supplementary information Supplementary data are available at Bioinformatics online. 

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