Efficient Computation of Base-pairing Probabilities in Multi-strand RNA Folding

RNA folding algorithms, including McCaskill’s partition function algorithm for computing base pairing probabilities, can be extended to N ≥ 2 interacting strands by considering all permutations π of the N strands. For each π, the inside dynamic programming recursion for connected structures needs to be extended by only a single extra case corresponding to a base pair connecting exactly two connected substructures. This leaves the cubic running time unchanged. A straightforward implementation of the corresponding outside recursion, however results in a quartic algorithm. We show here how cubic running time asymptotically equal to McCaskill’s partition function algorithm can be achieved by introducing linear-size auxiliary arrays. The algorithm is implemented within the framework of the ViennaRNA package and conforms to the theoretical

[1]  Fariza Tahi,et al.  RCPred: RNA complex prediction as a constrained maximum weight clique problem , 2019, BMC Bioinformatics.

[2]  Qiangfeng Cliff Zhang,et al.  Advances and challenges towards the study of RNA-RNA interactions in a transcriptome-wide scale , 2018, Quantitative Biology.

[3]  T. Dutta,et al.  Small RNA-mediated regulation in bacteria: A growing palette of diverse mechanisms. , 2018, Gene.

[4]  Peter F. Stadler,et al.  RNA folding with hard and soft constraints , 2016, Algorithms for Molecular Biology.

[5]  Sonja J. Prohaska,et al.  Algebraic Dynamic Programming over general data structures , 2015, BMC Bioinformatics.

[6]  Kyle E. Watters,et al.  A renaissance in RNA synthetic biology: new mechanisms, applications and tools for the future. , 2015, Current opinion in chemical biology.

[7]  Manel Esteller,et al.  RNA-RNA interactions in gene regulation: the coding and noncoding players. , 2015, Trends in biochemical sciences.

[8]  S. A. Ahmed,et al.  Multiple RNA Interaction: Beyond Two , 2015, IEEE Transactions on NanoBioscience.

[9]  Erik Winfree,et al.  Stochastic Simulation of the Kinetics of Multiple Interacting Nucleic Acid Strands , 2015, DNA.

[10]  Peter F. Stadler,et al.  2D Meets 4G: G-Quadruplexes in RNA Secondary Structure Prediction , 2013, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[11]  Christian M. Reidys,et al.  Symmetric circular matchings and RNA folding , 2012, Discret. Math..

[12]  L. Jaeger,et al.  Multistrand RNA secondary structure prediction and nanostructure design including pseudoknots. , 2011, ACS nano.

[13]  Peter F. Stadler,et al.  ViennaRNA Package 2.0 , 2011, Algorithms for Molecular Biology.

[14]  Conrad Steenberg,et al.  NUPACK: Analysis and design of nucleic acid systems , 2011, J. Comput. Chem..

[15]  Stephan H. Bernhart,et al.  RNA Accessibility in cubic time , 2011, Algorithms for Molecular Biology.

[16]  David H. Mathews,et al.  NNDB: the nearest neighbor parameter database for predicting stability of nucleic acid secondary structure , 2009, Nucleic Acids Res..

[17]  Ralf Bundschuh,et al.  Modeling the interplay of single-stranded binding proteins and nucleic acid secondary structure , 2010, Bioinform..

[18]  Christian M. Reidys,et al.  Partition function and base pairing probabilities for RNA-RNA interaction prediction , 2009, Bioinform..

[19]  Hamidreza Chitsaz,et al.  A partition function algorithm for interacting nucleic acid strands , 2009, Bioinform..

[20]  Rolf Backofen,et al.  IntaRNA: efficient prediction of bacterial sRNA targets incorporating target site accessibility and seed regions , 2008, Bioinform..

[21]  Peter F. Stadler,et al.  Translational Control by RNA-RNA Interaction: Improved Computation of RNA-RNA Binding Thermodynamics , 2008, BIRD.

[22]  Erik Winfree,et al.  Thermodynamic Analysis of Interacting Nucleic Acid Strands , 2007, SIAM Rev..

[23]  Farren J. Isaacs,et al.  RNA synthetic biology , 2006, Nature Biotechnology.

[24]  Peter F. Stadler,et al.  Partition function and base pairing probabilities of RNA heterodimers , 2006, Algorithms for Molecular Biology.

[25]  Kaizhong Zhang,et al.  RNA-RNA Interaction Prediction and Antisense RNA Target Search , 2006, J. Comput. Biol..

[26]  A. Condon,et al.  Secondary structure prediction of interacting RNA molecules. , 2005, Journal of molecular biology.

[27]  M. Zuker,et al.  Prediction of hybridization and melting for double-stranded nucleic acids. , 2004, Biophysical journal.

[28]  Ye Ding,et al.  Sfold web server for statistical folding and rational design of nucleic acids , 2004, Nucleic Acids Res..

[29]  P. Schuster,et al.  Complete suboptimal folding of RNA and the stability of secondary structures. , 1999, Biopolymers.

[30]  Walter Fontana,et al.  Fast folding and comparison of RNA secondary structures , 1994 .

[31]  J. McCaskill.  The equilibrium partition function and base pair binding probabilities for RNA secondary structure , 1990, Biopolymers.

[32]  Michael Zuker,et al.  Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information , 1981, Nucleic Acids Res..