A new heuristic method for approximating the number of local minima in partial RNA energy landscapes

The analysis of energy landscapes plays an important role in mathematical modelling, simulation and optimisation. Among the main features of interest are the number and distribution of local minima within the energy landscape. Granier and Kallel proposed in 2002 a new sampling procedure for estimating the number of local minima. In the present paper, we focus on improved heuristic implementations of the general framework devised by Granier and Kallel with regard to run-time behaviour and accuracy of predictions. The new heuristic method is demonstrated for the case of partial energy landscapes induced by RNA secondary structures. While the computation of minimum free energy RNA secondary structures has been studied for a long time, the analysis of folding landscapes has gained momentum over the past years in the context of co-transcriptional folding and deeper insights into cell processes. The new approach has been applied to ten RNA instances of length between 99 nt and 504 nt and their respective partial energy landscapes defined by secondary structures within an energy offset ΔE above the minimum free energy conformation. The number of local minima within the partial energy landscapes ranges from 1440 to 3441. Our heuristic method produces for the best approximations on average a deviation below 3.0% from the true number of local minima.

[1]  B. Alberts,et al.  Some Molecular Details of the Secondary Structure of Ribonucleic Acid , 1960, Nature.

[2]  Peter Clote,et al.  Maximum expected accuracy structural neighbors of an RNA secondary structure , 2012, BMC Bioinformatics.

[3]  Thomas Dandekar,et al.  Riboswitch finder tool for identification of riboswitch RNAs , 2004, Nucleic Acids Res..

[4]  Andreas Alexander Albrecht,et al.  Approximating the set of local minima in partial RNA folding landscapes , 2012, Bioinform..

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

[6]  Michael T. Wolfinger,et al.  Barrier Trees of Degenerate Landscapes , 2002 .

[7]  D M Crothers,et al.  Prediction of RNA secondary structure. , 1971, Proceedings of the National Academy of Sciences of the United States of America.

[8]  P. Clote,et al.  Combinatorics of locally optimal RNA secondary structures , 2011, Journal of mathematical biology.

[9]  Gregg Lois,et al.  Protein folding on rugged energy landscapes: conformational diffusion on fractal networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Peter F. Stadler,et al.  Basin Hopping Graph: a computational framework to characterize RNA folding landscapes , 2014, Bioinform..

[11]  M. Waterman,et al.  RNA secondary structure: a complete mathematical analysis , 1978 .

[12]  M. Zuker.  On finding all suboptimal foldings of an RNA molecule. , 1989, Science.

[13]  P. Clote,et al.  Computing the Partition Function for Kinetically Trapped RNA Secondary Structures , 2011, PloS one.

[14]  Josselin Garnier,et al.  Efficiency of Local Search with Multiple Local Optima , 2001, SIAM J. Discret. Math..

[15]  Kathleen Steinhöfel,et al.  Accessibility of microRNA binding sites in metastable RNA secondary structures in the presence of SNPs , 2013, Bioinform..

[16]  Peter Clote,et al.  Combinatorics of Saturated Secondary Structures of RNA , 2006, J. Comput. Biol..

[17]  David Sankoff,et al.  RNA secondary structures and their prediction , 1984 .

[18]  Jerrold R. Griggs,et al.  Algorithms for Loop Matchings , 1978 .

[19]  R. Bellman.  The theory of dynamic programming , 1954 .

[20]  C. Burge,et al.  Prediction of Mammalian MicroRNA Targets , 2003, Cell.

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

[22]  P. Schuster,et al.  RNA folding at elementary step resolution. , 1999, RNA.

[23]  D. Turner,et al.  Thermodynamic parameters for an expanded nearest-neighbor model for formation of RNA duplexes with Watson-Crick base pairs. , 1998, Biochemistry.

[24]  Ivo L. Hofacker,et al.  Vienna RNA secondary structure server , 2003, Nucleic Acids Res..

[25]  Ronny Lorenz,et al.  The Vienna RNA Websuite , 2008, Nucleic Acids Res..

[26]  Stijn van Dongen,et al.  miRBase: tools for microRNA genomics , 2007, Nucleic Acids Res..

[27]  Hélène Touzet,et al.  RNA Locally Optimal Secondary Structures , 2012, J. Comput. Biol..

[28]  Christian N. S. Pedersen,et al.  RNA Pseudoknot Prediction in Energy-Based Models , 2000, J. Comput. Biol..

[29]  Mark A. Ragan,et al.  Quantitative Prediction of miRNA-mRNA Interaction Based on Equilibrium Concentrations , 2011, PLoS Comput. Biol..

[30]  I. Tinoco,et al.  Estimation of Secondary Structure in Ribonucleic Acids , 1971, Nature.

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