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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 pi of the N strands. For each pi, 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 performance bounds.
AuthorsLorenz R, Flamm C, Hofacker IL, Stadler PF
Published in (2020) page(s): 23-31


26. Evolving AVX512 parallel C code using GP
AuthorsLangdon WB, Lorenz R
Published inIn proceedings, European Conference on Genetic Programming (2019)


Chemical modifications of RNA nucleotides change their identity and characteristics and thus alter genetic and structural information encoded in the genomic DNA. tRNA and rRNA are probably the most heavily modified genes, and often depend on derivatization or isomerization of their nucleobases in order to correctly fold into their functional structures. Recent RNomics studies, however, report transcriptome wide RNA modification and suggest a more general regulation of structuredness of RNAs by this so called epitranscriptome. Modification seems to require specific substrate structures, which in turn are stabilized or destabilized and thus promote or inhibit refolding events of regulatory RNA structures. In this review, we revisit RNA modifications and the related structures from a computational point of view. We discuss known substrate structures, their properties such as sub-motifs as well as consequences of modifications on base pairing patterns and possible refolding events. Given that efficient RNA structure prediction methods for canonical base pairs have been established several decades ago, we review to what extend these methods allow the inclusion of modified nucleotides to model and study epitranscriptomic effects on RNA structures.
AuthorsTanzer A, Hofacker IL, Lorenz R
Published inMethods 156 (2018) page(s): 32-39
Grow and graft genetic programming (GGGP) evolves more than 50000 parameters in a state-of-the-art C program to make functional source code changes which give more accurate predictions of how RNA molecules fold up. Genetic improvement updates 29\% of the dynamic programming free energy model parameters. In most cases (50.3\%) GI gives better results on 4655 known secondary structures from RNA\_STRAND (29.0\% are worse and 20.7\% are unchanged). Indeed it also does better than parameters recommended by Andronescu, M., et al.: Bioinformatics 23(13) (2007) i19–i28.
AuthorsLangdon WB, Petke J, Lorenz R
Published inIn proceedings, Genetic Programming (2018)


23. Improving SSE Parallel Code with Grow and Graft Genetic Programming
AuthorsLangdon WB, Lorenz R
Published inIn proceedings, GECCO '17, Proceedings of the Genetic and Evolutionary Computation Conference Companion (2017)


BACKGROUND: A large class of RNA secondary structure prediction programs uses an elaborate energy model grounded in extensive thermodynamic measurements and exact dynamic programming algorithms. External experimental evidence can be in principle be incorporated by means of hard constraints that restrict the search space or by means of soft constraints that distort the energy model. In particular recent advances in coupling chemical and enzymatic probing with sequencing techniques but also comparative approaches provide an increasing amount of experimental data to be combined with secondary structure prediction. RESULTS: Responding to the increasing needs for a versatile and user-friendly inclusion of external evidence into diverse flavors of RNA secondary structure prediction tools we implemented a generic layer of constraint handling into the ViennaRNA Package. It makes explicit use of the conceptual separation of the “folding grammar” defining the search space and the actual energy evaluation, which allows constraints to be interleaved in a natural way between recursion steps and evaluation of the standard energy function. CONCLUSIONS: The extension of the ViennaRNA Package provides a generic way to include diverse types of constraints into RNA folding algorithms. The computational overhead incurred is negligible in practice. A wide variety of application scenarios can be accommodated by the new framework, including the incorporation of structure probing data, non-standard base pairs and chemical modifications, as well as structure-dependent ligand binding.
AuthorsLorenz R, Hofacker IL, Stadler PF
Published inAlgorithms for Molecular Biology 11:1 (2016) page(s): 1--13
RNA secondary structures have proven essential for understanding the regulatory functions performed by RNA such as microRNAs, bacterial small RNAs, or riboswitches. This success is in part due to the availability of efficient computational methods for predicting RNA secondary structures. Recent advances focus on dealing with the inherent uncertainty of prediction by considering the ensemble of possible structures rather than the single most stable one. Moreover, the advent of high-throughput structural probing has spurred the development of computational methods that incorporate such experimental data as auxiliary information.
AuthorsLorenz R, Wolfinger MT, Tanzer A, Hofacker IL
Published inMethods 103 (2016) page(s): 86--98
Summary: Chemical mapping experiments allow for nucleotide resolution assessment of RNA structure. We demonstrate that different strategies of integrating probing data with thermodynamics-based RNA secondary structure prediction algorithms can be implemented by means of soft constraints. This amounts to incorporating suitable pseudo-energies into the standard energy model for RNA secondary structures. As a showcase application for this new feature of the ViennaRNA Package we compare three distinct, previously published strategies to utilize SHAPE reactivities for structure prediction. The new tool is benchmarked on a set of RNAs with known reference structure.Availability and implementation: The capability for SHAPE directed RNA folding is part of the upcoming release of the ViennaRNA Package 2.2, for which a preliminary release is already freely available at information: Supplementary data are available at Bioinformatics online.
AuthorsLorenz R, Luntzer D, Hofacker IL, Stadler PF, Wolfinger MT
Published inBioinformatics 32:1 (2016) page(s): 145-147


Discovery and characterization of functional RNA structures remains challenging due to deficiencies in de novo secondary structure modeling. Here we describe a dynamic programming approach for model-free sequence comparison that incorporates high-throughput chemical probing data. Based on SHAPE probing data alone, ribosomal RNAs (rRNAs) from three diverse organisms – the eubacteria E. coli and C. difficile and the archeon H. volcanii – could be aligned with accuracies comparable to alignments based on actual sequence identity. When both base sequence identity and chemical probing reactivities were considered together, accuracies improved further. Derived sequence alignments and chemical probing data from protein-free RNAs were then used as pseudo-free energy constraints to model consensus secondary structures for the 16S and 23S rRNAs. There are critical differences between these experimentally-informed models and currently accepted models, including in the functionally important neck and decoding regions of the 16S rRNA. We infer that the 16S rRNA has evolved to undergo large-scale changes in base pairing as part of ribosome function. As high-quality RNA probing data become widely available, structurally-informed sequence alignment will become broadly useful for de novo motif and function discovery.
AuthorsLavender CA, Lorenz R, Zhang G, Tamayo R, Hofacker IL, Weeks KM
Published inPLoS Computational Biology 11:5 (2015)
Riboswitches are RNA-based regulators of gene expression composed of a ligand-sensing aptamer domain followed by an overlapping expression platform. The regulation occurs at either the level of transcription (by formation of terminator or antiterminator structures) or translation (by presentation or sequestering of the ribosomal binding site). Due to a modular composition, these elements can be manipulated by combining different aptamers and expression platforms and therefore represent useful tools to regulate gene expression in synthetic biology. Using computationally designed theophylline-dependent riboswitches we show that 2 parameters, terminator hairpin stability and folding traps, have a major impact on the functionality of the designed constructs. These have to be considered very carefully during design phase. Furthermore, a combination of several copies of individual riboswitches leads to a much improved activation ratio between induced and uninduced gene activity and to a linear dose-dependent increase in reporter gene expression. Such serial arrangements of synthetic riboswitches closely resemble their natural counterparts and may form the basis for simple quantitative read out systems for the detection of specific target molecules in the cell.
AuthorsWachsmuth M, Domin G, Lorenz R, Serfling R, Findeiß S, Stadler,Peter F , Mörl M
Published inRNA Biology 12:2 (2015) page(s): 221-231
Note(s)PMID: 25826571
The ViennaRNA package is a widely used collection of programs for thermodynamic RNA secondary structure prediction. Over the years, many additional tools have been developed building on the core programs of the package to also address issues related to noncoding RNA detection, RNA folding kinetics, or efficient sequence design considering RNA-RNA hybridizations. The ViennaRNA web services provide easy and user-friendly web access to these tools. This chapter describes how to use this online platform to perform tasks such as prediction of minimum free energy structures, prediction of RNA-RNA hybrids, or noncoding RNA detection. The ViennaRNA web services can be used free of charge and can be accessed via
AuthorsGruber AR, Bernhart SH, Lorenz R
Published inRNA Bioinformatics, Methods in Molecular Biology, 1269, (2015) page(s) 307-326, Publisher: Springer New York, Editor(s): Picardi, Ernesto


16. TSSAR: TSS annotation regime for dRNA-seq data
AuthorsAmman F, Wolfinger MT, Lorenz R, Hofacker IL, Stadler PF, Findeiß S
Published inBMC Bioinformatics 15:1 (2014) page(s): 89
RNA secondary structures can be predicted using efficient algorithms. A widely used software package implementing a large number of computational methods is the ViennaRNA Package. This chapter describes how to use programs from the ViennaRNA Package to perform common tasks such as prediction of minimum free-energy structures, suboptimal structures, or base pairing probabilities, and generating secondary structure plots with reliability annotation. Moreover, we present recent methods to assess the folding kinetics of an RNA via 2D projections of the energy landscape, identification of local minima and energy barriers, or simulation of RNA folding as a Markov process.
AuthorsHofacker IL, Lorenz R
Published in{RNA} Folding, Methods in Molecular Biology, 1086, (2014) page(s) 1-19, Publisher: Humana Press, Editor(s): Waldsich, Christina


G-quadruplexes are abundant locally stable structural elements in nucleic acids. The combinatorial theory of RNA structures and the dynamic programming algorithms for RNA secondary structure prediction are extended here to incorporate G-quadruplexes using a simple but plausible energy model. With preliminary energy parameters we find that the overwhelming majority of putative quadruplex-forming sequences in the human genome are likely to fold into canonical secondary structures instead. Stable G-quadruplexes are strongly enriched, however, in the 5' UTR of protein coding mRNAs.
AuthorsLorenz R, Bernhart S, Qin J, Höner zu Siederdissen C, Tanzer A, Amman F, Hofacker I, et al.
Published inComputational Biology and Bioinformatics, IEEE/ACM Transactions on PP:99 (2013) page(s): 1


Motivation: While there are numerous programs that can predict RNA or DNA secondary structures, a program that predicts RNA/DNA hetero-dimers is still missing. The lack of easy to use tools for predicting their structure may be in part responsible for the small number of reports of biologically relevant RNA/DNA hetero-dimers.Results: We present here an extension to the widely used ViennaRNA Package (Lorenz et al., 2011) for the prediction of the structure of RNA/DNA hetero-dimers.Availability: ronny/RNA/vrna2.htmlContact:
AuthorsLorenz R, Hofacker IL, Bernhart SH
Published inBioinformatics (2012)
G-quadruplexes are abundant locally stable structural elements in nucleic acids. The combinatorial theory of RNA structures and the dynamic programming algorithms for RNA secondary structure prediction are extended here to incorporate G-quadruplexes. Using a simple but plausible energy model for quadruplexes, we find that the overwhelming majority of putative quadruplex-forming sequences in the human genome are likely to fold into canonical secondary structures instead.
AuthorsLorenz R, Bernhart SH, Externbrink F, Qin J, Höner zu Siederdissen C, Amman F, Hofacker IL, et al.
Published inIn proceedings, Lecture Notes in Computer Science, Advances in Bioinformatics and Computational Biology (2012)
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BACKGROUND: Secondary structure forms an important intermediate level of description of nucleic acids that encapsulates the dominating part of the folding energy, is often well conserved in evolution, and is routinely used as a basis to explain experimental findings. Based on carefully measured thermodynamic parameters exact dynamic programming algorithms can be used to compute ground states, base pairing probabilities, as well as thermodynamic properties.
RESULTS: The ViennaRNA Package has been a widely used compilation of RNA secondary structure related computer programs for nearly two decades. Major changes in the structure of the standard energy model, the Turner 2004 parameters, the pervasive use of multi-core CPUs, and an increasing number of algorithmic variants prompted a major technical overhaul of both the underlying RNAlib and the interactive user programs. New features include an expanded repertoire of tools to assess RNA-RNA interactions and restricted ensembles of structures, additional output information such as centroid structures and maximum expected accuracy structures derived from base pairing probabilities, or z-scores for locally stable secondary structures, and support for input in fasta format. Updates were implemented without compromising the computational efficiency of the core algorithms and ensuring compatibility with earlier versions.
CONCLUSIONS: The ViennaRNA Package 2.0, supporting concurrent computations via OpenMP, can be downloaded from
AuthorsLorenz R, Bernhart SH, Höner zu Siederdissen C, Tafer H, Flamm C, Stadler PF, Hofacker IL
Published inAlgorithms for Molecular Biology 6:1 (2011) page(s): 26
The overwhelming majority of small nucleolar RNAs (snoRNAs) fall into two clearly de\ufb01ned classes characterized by distinctive secondary structures and sequence motifs. A small group of diverse ncRNAs, however, shares the hallmarks of one or both classes of snoRNAs but di\ufb00ers substantially from the norm in some respects. Here, we compile the available information on these exceptional cases, conduct a thorough homology search throughout the available metazoan genomes, provide improved and expanded alignments, and investigate the evolutionary histories of these ncRNA families as well as their mutual relationships.
AuthorsMarz M, Gruber A, Höner zu Siederdissen C, Amman F, Badelt S, Bartschat S, Bernhart S, et al.
Published inRNA Biology 8:6 (2011) page(s): 938--946


Stem-bulge RNAs (sbRNAs) are a group of small, functionally yet uncharacterized noncoding RNAs first described in C. elegans, with a few homologous sequences postulated in C. briggsae. In this study, we report on a comprehensive survey of this ncRNA family in the phylum Nematoda. Employing homology search strategies based on both sequence and secondary structure models and a computational promoter screen we identified a total of 240 new sbRNA homologs. For the majority of these loci we identified both promoter regions and transcription termination signals characteristic for pol-III transcripts. Sequence and structure comparison with known RNA families revealed that sbRNAs are homologs of vertebrate Y RNAs. Most of the sbRNAs show the characteristic Ro protein binding motif, and contain a region highly similar to a functionally required motif for DNA replication previously thought to be unique to vertebrate Y RNAs. The single Y RNA that was previously described in C. elegans, however, does not show this motif, and in general bears the hallmarks of a highly derived family member.
AuthorsBoria I, Gruber A, Tanzer A, Bernhart S, Lorenz R, Mueller M, Hofacker I, et al.
Published inJournal of Molecular Evolution 70:4 (2010) page(s): 346--358


The analysis of RNA folding landscapes yields insights into the kinetic folding behavior not available from classical structure prediction methods. This is especially important for multi-stable RNAs whose function is related to structural changes, as in the case of riboswitches. However, exact methods such as barrier tree analysis scale exponentially with sequence length. Here we present an algorithm that computes a projection of the energy landscape into two dimensions, namely the distances to two reference structures. This yields an abstraction of the high-dimensional energy landscape that can be conveniently visualized, and can serve as the basis for estimating energy barriers and refolding pathways. With an asymptotic time complexity of O(n^7) the algorithm is computationally demanding. However, by exploiting the sparsity of the dynamic programming matrices and parallelization for multi-core processors, our implementation is practical for sequences of up to 400 nt, which includes most RNAs of biological interest.
AuthorsLorenz R, Flamm C, Hofacker IL
Published inIn proceedings, Lecture Notes in Informatics, German Conference on Bioinformatics 2009 (2009)
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OBJECTIVES: The analysis of individual cell fates within a population of stem and progenitor cells is still a major experimental challenge in stem cell biology. However, new monitoring techniques, such as high-resolution time-lapse video microscopy, facilitate tracking and quantitative analysis of single cells and their progeny. Information on cellular development, divisional history and differentiation are naturally comprised into a pedigree-like structure, denoted as cellular genealogy. To extract reliable information concerning effecting variables and control mechanisms underlying cell fate decisions, it is necessary to analyse a large number of cellular genealogies.
MATERIALS AND METHODS: Here, we propose a set of statistical measures that are specifically tailored for the analysis of cellular genealogies. These measures address the degree and symmetry of cellular expansion, as well as occurrence and correlation of characteristic events such as cell death. Furthermore, we discuss two different methods for reconstruction of lineage fate decisions and show their impact on the interpretation of asymmetric developments. In order to illustrate these techniques, and to circumvent the present shortage of available experimental data, we obtain cellular genealogies from a single-cell-based mathematical model of haematopoietic stem cell organization.
RESULTS AND CONCLUSIONS: Based on statistical analysis of cellular genealogies, we conclude that effects of external variables, such as growth conditions, are imprinted in their topology. Moreover, we demonstrate that it is essential to analyse timing of cell fate-specific changes and of occurrence of cell death events in the divisional context in order to understand the mechanisms of lineage commitment.
AuthorsGlauche I, Lorenz R, Hasenclever D, Roeder I
Published inCell proliferation 42:2 (2009) page(s): 248--263


The Vienna RNA Websuite is a comprehensive collection of tools for folding, design and analysis of RNA sequences. It provides a web interface to the most commonly used programs of the Vienna RNA package. Among them, we find folding of single and aligned sequences, prediction of RNA-RNA interactions, and design of sequences with a given structure. Additionally, we provide analysis of folding landscapes using the barriers program and structural RNA alignments using LocARNA. The web server together with software packages for download is freely accessible at
AuthorsGruber AR, Lorenz R, Bernhart SH, Neuböck R, Hofacker IL
Published inNucleic Acids Research (2008)


Many experimental findings on heterogeneity, flexibility, and plasticity of tissue stem cells are currently challenging stem cell concepts that assume a cell intrinsically predefined, unidirectional differentiation program. In contrast to these classical concepts, nonhierarchical self-organizing systems provide an elegant and comprehensive alternative to explain the experimental data. Here we present the application of such a self-organizing concept to quantitatively describe the hematopoietic stem cell system. Focusing on the analysis of individual-stem-cell fates and clonal dynamics, we particularly discuss implications of the theoretical results on the interpretation of experimental findings. We demonstrate that it is possible to understand hematopoietic stem cell organization without assumptions on unidirectional developmental hierarchies, preprogrammed asymmetric division events or other assumptions implying the existence of a predetermined stem cell entity. The proposed perspective, therefore, changes the general paradigm of thinking about stem cells.
AuthorsRoeder I, Braesel K, Lorenz R, Loeffler M
Published inJournal of Biomedicine and Biotechnology 1 (2007) page(s): 84656
4. Analysis of cellular genealogies: Observations, simulations, and interpretations with respect to stem cell fate decisions
AuthorsGlauche I, Lorenz R, Kuska J, Franke K, Kurth I, Pompe T, Bornhaeuser M, et al.
Published inEXPERIMENTAL HEMATOLOGY 35:9, 2 (2007) page(s): 28
Note(s)36th Annual Meeting of the International-Society-for-Experimental-Hematology, Hamburg, GERMANY, SEP 28-30, 2007
RNAs play an important role in bioinformatic applications. Their ability to serve not only as information carrier, but also to develop catalytic properties highlights them in the set of organic macromolecules notably. As these catalytic properties are closely related to the three-dimensional configuration (tertiary structure) of the RNA molecule, the formation and prediction of this tertiary structure - a process called folding - is a crucial bioinformatic problem. RNA folding is considered as a hierarchical process, where a secondary structure precedes the tertiary structure, whereas tertiary interactions are energetically weaker than those yielded by the secondary structure. Generally, the secondary structure does not change when tertiary interactions are formed. Because there are efficient methods for predicting the secondary structure of an RNA molecule under certain conditions, but none for the tertiary structure, the secondary structure is used as a first step for the prediction of functional properties of the RNA molecule. However, most methods for the analysis of secondary structure(s) are designed for linear RNAs exclusively. As catalytic active circular RNA molecules occur in nature too, it is necessary to extend these methods. Based on the scheme for a memory efficient extension of previously existing methods for linear RNAs, suggested by the group of Ivo Hofacker, four basic algorithms are introduced, extended and therefore made accessible for circular RNA molecules within this work.
AuthorsLorenz R
Published inMaster's Thesis, University Leipzig (2007)
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Asymmetric cell division is a common concept to explain the capability of stem cells to simultaneously produce a continuous output of differentiated cells and to maintain their own population of undifferentiated cells. Whereas for some stem cell systems, an asymmetry in the division process has explicitly been demonstrated, no evidence for such a functional asymmetry has been shown for hematopoietic stem cells (HSC) so far. This raises the question regarding whether asymmetry of cell division is a prerequisite to explain obvious heterogeneity in the cellular fate of HSC. Through the application of a mathematical model based on self-organizing principles, we demonstrate that the assumption of asymmetric stem cell division is not necessary to provide a consistent account for experimentally observed asymmetries in the development of HSC. Our simulation results show that asymmetric cell fate can alternatively be explained by a reversible expression of functional stem cell potentials, controlled by changing cell-cell and cell-microenvironment interactions. The proposed view on stem cell organization is pointing to the potential role of stem cell niches as specific signaling environments, which induce developmental asymmetries and therefore, generate cell fate heterogeneity. The self-organizing concept is fully consistent with the functional definition of tissue stem cells. It naturally includes plasticity phenomena without contradicting a hierarchical appearance of the stem cell population. The concept implies that stem cell fate is only predictable in a probabilistic sense and that retrospective categorization of stem cell potential, based on individual cellular fates, provides an incomplete picture.
AuthorsRoeder I, Lorenz R
Published inStem Cell Reviews 2:3 (2006) page(s): 171--180


1. Non-Redundant Sampling and Statistical Estimators for RNA Structural Properties at the Thermodynamic Equilibrium
AuthorsRovetta C, Michalik J, Lorenz R, Tanzer A, Ponty Y
Published inComputational Biology and Bioinformatics, IEEE/ACM Transactions on (submitted)

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