Faster Algorithms for RNA-folding using the Four-Russians method
Balaji Venkatachalam, Dan Gusfield, Yelena Frid
备注：
Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013). Editor's note: abstract was shortened to comply with arxiv requirements. Full abstract in PDF
The secondary structure that maximizes the number of non-crossing matchings between complimentary bases of an RNA sequence of length n can be computed in O(n^3) time using Nussinov's dynamic programming algorithm. The Four-Russians method is a technique that will reduce the running time for certain dynamic programming algorithms by a multiplicative factor after a preprocessing step where solutions to all smaller subproblems of a fixed size are exhaustively enumerated and solved. Frid and Gusfield designed an O(\frac{n^3}{\log n}) algorithm for RNA folding using the Four-Russians technique. In their algorithm the preprocessing is interleaved with the algorithm computation. (Algo. Mol. Biol., 2010).
We simplify the algorithm and the analysis by doing the preprocessing once prior to the algorithm computation. We call this the two-vector method. We also show variants where instead of exhaustive preprocessing, we only solve the subproblems encountered in the main algorithm once and memoize the results. We give a simple proof of correctness and explore the practical advantages over the earlier method. The Nussinov algorithm admits an O(n^2) time parallel algorithm. We show a parallel algorithm using the two-vector idea that improves the time bound to O(\frac{n^2}{log n}).
We discuss the organization of the data structures to exploit coalesced memory access for fast running times. The ideas to organize the data structures also help in improving the running time of the serial algorithms. For sequences of length up to 6000 bases the parallel algorithm takes only about 2.5 seconds and the two-vector serial method takes about 57 seconds on a desktop and 15 seconds on a server. Among the serial algorithms, the two-vector and memoized versions are faster than the Frid-Gusfield algorithm by a factor of 3, and are faster than Nussinov by up to a factor of 20.
Background: RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and \pairGU -base pairings (secondary structure) and additional cross-serial base pairs. These interactions are called pseudoknots and are observed across the whole spectrum of RNA functionalities. In the context of studying natural RNA structures, searching for new ribozymes and designing artificial RNA, it is of interest to find RNA sequences folding into a specific structure and to analyze their induced neutral networks. Since the established inverse…
Motivation: Predicting the secondary structure of an RNA sequence is useful in many applications. Existing algorithms (based on dynamic programming) suffer from a major limitation: their runtimes scale cubically with the RNA length, and this slowness limits their use in genome-wide applications. Results: We present a novel alternative $O(n^3)$-time dynamic programming algorithm for RNA folding that is amenable to heuristics that make it run in $O(n)$ time and $O(n)$ space, while producing a high-quality approximation to the optimal solution. Inspired by incremental parsing for context-free gra…
Differentiable Folding for Nearest Neighbor Model Optimization
School of Engineering and Applied Sciences（工程与应用科学学院）；Harvard University（哈佛大学）；Department of Biomedical Engineering and Genome Center（生物医学工程与基因组中心）；University of California, Davis（加州大学戴维斯分校）；Department of Biochemistry and Biophysics and Center for RNA Biology（生物化学与生物物理学系和RNA生物学中心）；University of the Rochester Medical Center（罗切斯特医学中心）；Department of Computer Science and Software Engineering（计算机科学与软件工程系）；The University of Western Australia（西澳大学）
Solving the RNA inverse folding problem is a critical prerequisite to RNA design, an emerging field in bioengineering with a broad range of applications from reaction catalysis to cancer therapy. Although significant progress has been made in developing machine-based inverse RNA folding algorithms, current approaches still have difficulty designing sequences for large or complex targets. On the other hand, human players of the online RNA design game EteRNA have consistently shown superior performance in this regard, being able to readily design sequences for targets that are challenging for ma…
Many ncRNAs function through RNA-RNA interactions. Fast and reliable RNA structure prediction with consideration of RNA-RNA interaction is useful. Some existing tools are less accurate due to omitting the competing of intermolecular and intramolecular base pairs, or focus more on predicting the binding region rather than predicting the complete secondary structure of two interacting strands. Vienna RNAcofold, which reduces the problem into the classical single sequence folding by concatenating two strands, scales in cubic time against the combined sequence length, and is slow for long sequence…
RNA structure prediction is a challenging problem, especially with pseudoknots. Recently, there has been a shift from the classical minimum free energy-based methods (MFE) to partition function-based ones that assemble structures using base-pairing probabilities. Two examples of the latter group are the popular maximum expected accuracy (MEA) method and the ProbKnot method. ProbKnot is a fast heuristic that pairs nucleotides that are reciprocally most probable pairing partners, and unlike MEA, can also predict structures with pseudoknots. However, ProbKnot's full potential has been largely ove…
Leveraging generative hallucination and biophysics-informed modeling for unified biomolecular sequence-structure co-design
University of Florida（佛罗里达大学）；University of Chicago（芝加哥大学）；Data Science Institute, University of Chicago（芝加哥大学数据科学研究所）；Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）；Mayo Clinic（梅奥诊所）；Argonne National Laboratory（阿贡国家实验室）
RNA function crucially depends on its structure. Thermodynamic models currently used for secondary structure prediction rely on computing the partition function of folding ensembles, and can thus estimate minimum free-energy structures and ensemble populations. These models sometimes fail in identifying native structures unless complemented by auxiliary experimental data. Here, we build a set of models that combine thermodynamic parameters, chemical probing data (DMS, SHAPE), and co-evolutionary data (Direct Coupling Analysis, DCA) through a network that outputs perturbations to the ensemble f…
