Rational Design of RiboNucleic Acids

In this talk, we will present the databases developed to support benchmarking of bioinformatics algorithms targeting RNA, including the ones for RNA design. RNAsolo⁴⁴4https://rnasolo.cs.put.poznan.pl/ collects experimentally determined 3D RNA structures from RNAs alone, protein-RNA complexes, and DNA-RNA hybrids and organizes them into classes of equivalent structures. Their sequences and tertiary structures are grouped in 192 benchmark sets ready for download and automated processing. RNAloops⁵⁵5https://rnaloops.cs.put.poznan.pl/ aims to facilitate the study of multiloops in RNA molecules. It collects n-way junctions found in experimental RNA structures and allows to search them by sequence, secondary structure topology, or structure parameters. Both data sources address RNA-related studies by providing reliable sequence and structure data and efficient search facilities.

Compilation from high level languages to low level languages is a fundamental concept in computer science, and it enables researchers to program silicon-based machines even though they have no understanding of assembler code or transistors. In previous work, we have shown that a description of nucleic acid circuits at the domain level (equipped with an approximate biophysical model for DNA), can be formally derived from a high level language, e.g. compilation from a boolean circuit to formal chemical reaction network to a domain-level strand displacement system.

The next challenge is to ensure a correct compilation from the domain-level system specification to the nucleotide level, which must involve both nucleic acid sequence design and a verification based on folding kinetics at the secondary structure level. Currently, we are exploring new sequence design techniques for large and complex nucleic acid reaction networks, that also systematically incorporate feedback from experimental work.

Cotranscriptional folding has the exciting potential to encode multiple functional important structures into a single molecule and visit them in a controlled manner. Unfortunately, the interpretation of experimental data on cotranscriptional folding is still heavily dependent on computational structure prediction, and it is easy to misinterpret data when using thermodynamic models. We use the stochastic simulator Kinfold, as well as a newly developed deterministic heuristic DrTransformer to show how cotranscriptional simulations can help with understanding experimental results and point out common mistakes in existing interpretations of data.

The inverse RNA folding problem for designing sequences that fold into a given RNA secondary structure was introduced in the early 1990’s in Vienna. By an extension of this problem we use a coarse-grained approach to possibly detect novel eukaryotic riboswitches. The approach can tentatively be used for other domains and applications.

Various genetic disorders are caused by expansion of short tandem repeats as they aggregate in cells and form so-called RNA droplets or foci. However, themolecular mechanisms of RNA foci formation remains unclear. The aim of being able to design RNA tandem repeats and model RNA foci formation is twofold: it will help understand the mechanisms and therapies related to genetic disorders such as Huntigton’s disease but at the same time serve as a method to spatial engineering inside cells as RNA droplets cause a liquid-liquid phase separation which can serve as process isolation and help to organize proteins and multienzyme pathways without fine-tuning RNA expression levels.

Phase-separating RNA molecule complexes are contructed from small repeating sequences, e.g. triplet repeats. Visualization of RNA foci is conducted by tagging droplets with e.g. GFP and corresponding adapters such as the MS2 aptamer.

Previous studies successfully showed the formation of RNA foci using various types of RNA triplet repeats and even longer repeat sequences where the formation of G-quadruplexes seems to be an important part for the interaction between two tandem repeat RNAs [1, 2, 3, 4].

Existing studies could experimentally show which RNA triplets are the most successful in forming RNA foci, however, the structure of RNA foci and their dynamics are not yet understood. Additionally, the liquid-liquid phase separation opens numerous possibilities for spatial engineering inside the cells, but we still lack the knowledge of structural and chemical properties of the RNA droplets and the space inside the foci. By designing RNA molecules that form droplets, we need to take into account interactions of more than two RNA sequences as well as possible interactions with binding proteins. Hence, we aim to develop design strategies for interacting short tandem RNA repeats and explore properties of RNA droplets and their formation.

Since it has been shown that DNA strand displacement (DSD) reactions can implement arbitrary chemical reaction networks, they have become a popular substrate for molecular computing applications. One question worth asking if whether and where there exists upper limits on the size and complexity of realistically achievable DSD circuits. To address this question, I am presenting as example application the design for a molecular QR code generator that displays a dedicated QR code for any configuration of n molecular input DNA strands. By increasing the number of inputs, the complexity of the circuit increases in a superexponential manner, as well as our current attempts to tame the number of required DSD gates that implement the requred function. The second part of the talk presents experimental results on the scalability of DSD circuits and limits that arise from toehold occlusion or partially complementary toeholds. Motivation for this study is the realization that reversible toehold binding imposes an upper limit on toehold length of typically six to eight nucleotides. This in turn puts a hard limit on the number of distinct toeholds a circuit can employ. While the number of distinct nucleotide sequences is still quite large, crosstalk appears in system with significantly fewer toehold sequences once the sequence of supposedly distinct toeholds becomes similar enough to cause undesired interactions. We have systematically analyzed noise in DSD systems caused by crosstalk between signals with single and double mismatches. Our main result is that toehold occlusion might occur already in systems one order of magnitude below the theoretical upper limit to toehold domains.

Restricted Boltzmann machines (RBM) are energy-based latent variable generative models, consisting of two layers, that can offer interpretable representations of complex data. Recently they have been applied to modelling protein sequence data. In this talk, I will present evidence suggesting RBM are effective generative models of structured RNA. In particular, I consider the SAM riboswitch family, which regulates expression of downstream bacterial mRNAs by adopting competing structural conformations in response to the presence of a cellular metabolite. The RBM automatically infers relevant statistical features from the sequence data, such as conservation patterns, complementarity constraints consistent with the secondary structure, and the presence of a pseudoknot. The functionality of designed sequences has been validated experimentally by SHAPE mapping.

I will talk about the collaborative projects with the group of Mario Mörl (Biochemistry department at Leipzig University) on transcription termination regulating riboswitches and how we put tRNA processing under ligand control. The presentation will summarize how the corresponding design models have been developed, implemented, and analyzed in silico, as well as the biochemical investigations in vitro and in vivo. I will not only show the success story but the main emphasis will be on the problems we faced, how we solved them, and especially the issues that remain.

RNA is the punk-brother of DNA. While DNA plays by rules, RNA is more rebellious. The diverse structural features of RNA that make it a powerfully-functional molecule in biology also make it difficult to tame and rationally-design.

In contrast to engineered DNA nanostructures such as DNA origamis, natural RNA molecules in cells must fold under non-equilibrium conditions; the RNAs fold continuously while the strand is still emerging from the polymerase. While design of staple strands to produce DNA origami nanostructures can be easily automated by simple algorithms, producing a single-stranded RNA origami requires the entire sequence of the RNA to be designed by inverse folding, which is computationally much more challenging.

Our RNA design software ROAD begins with a random starting sequence, and over many iterations mutates that sequence to improve its folding into a target fold. ROAD uses both positive and negative design cycles to perform a gradient descent based on an adapting scoring function. The strategy is based on in vitro selection methods where the selection conditions gradually become more difficult over successive rounds.

I will present two design cases. The first case concern non-enzymatic isothermal strand displacement and amplification for rapid detection of SARS-CoV-2, which we accomplished through design of DNA probes that opens and binds to targeted locations of the SARS-CoV-2 genome. Through RNA folding considerations, we show why one of two probes are more successful and makes the detection possible. In the second case, design of CRISPR/Cas9 guide RNA (gRNA) are made from first generating cleavage efficiency data and subsequently train a deep learning-based neural network which has cutting-edge performance tested on independent data sets.

Branching is a critical characteristic of RNA design, yet can be challenging to validate with thermodynamic optimization approaches. Using mathematical methods (convex polytopes and their normal fans), we can improve prediction accuracy on well-defined families while also illuminating why the general problem is so difficult.

Machine learning (ML) and in particular deep learning techniques have the potential to overcome shortcomings of current RNA secondary structure prediction methods, such as the inability to predict pseudoknots and poor treatment of non-canonical pairs. Several recent publications have proposed deep neural networks for RNA secondary structure prediction and reported excellent accuracies. However, these works build upon training sets that are derived from a relatively small number of RNA families and therefore do not properly represent the RNA structure space.

By folding random sequences using the RNAfold program of the ViennaRNA package, we can generate synthetic data sets that allow to test in detail which properties of the RNA folding map are easy or hard to learn for these networks. We find that structure features that are local in the base pairing matrix, such as stacks and interior loops, are easy to learn, while less local multi-loops are much harder. Most strikingly, the number of base pairs predicted by convolutional networks grows quadratically, rather than linearly, with sequence length.

Using inverse folding, we designed a further synthetic training set that contains the same structures as the widely used bpRNA data set, and therefore exhibits the same lack of structure diversity in spite of near perfect randomness of the sequences. Networks trained on this data set achieve excellent performance on sequence that have no similarity to training sequences but fold into structures well represented in the training set. Nevertheless, the networks perform poorly on sequence folding into novel structures. This suggests, that the excellent performance reported in the literature is largely due biases in the data sets, i.e. that training and test sets that exhibit the same overrepresentation of a few well studied RNA families and their structures.

The structure of an RNA molecule is often a crucial characteristic to be able to explain its biological function. While studying the thermodynmaically optimal (MFE) structure often yields important information, there are relevant cases where a computation of the MFE structure alone is not sufficient to understand a molecule’s behaviour, for example in transcriptional riboswitches. Cotranscriptional folding simulations can thus be a helpful tool to gain a deeper understanding a given RNA.

In this talk, I present the software pipeline BarMap-QA, which relies on the BarMap framework by Hofacker et al., to simulate cotranscriptional folding of RNAs. The pipeline is not only very streamlined and easy to set up and run, but it also provides several quality measures to assess the quality of the conducted analysis and thus allow the user to optimally ballance computational efficiency against simulation accuracy for a specific use case.

The RNA world hypothesis proposes that RNAs carry catalytic activity necessary for primordial evolution. A first necessary condition for evolution is reproduction. Whether self-reproduction is rare or common in the space of RNA sequences is central to assess the plausibility of this scenario. To date, two ribozymes have been shown to autocatalytically sustain their self-reproduction in the laboratory, starting from RNA oligomers: the Azoarcus ribozyme derived from the group I intron family (Hayden and Lehman 2006) and a fragmented ligase (Lincoln and Joyce 2009). In this project, we assess the probability of self-reproducing RNAs in sequence space by using as a starting point the Azoarcus ribozyme that can autocatalytically self-reproduce. We show that combining in silico and in vitro screening allows for the discovery of a large number of artificial self-reproducing ribozymes. For this, the strategy consists of: i) Identifying natural self-reproducing GIIs; ii) Applying physics-based and machine learning methods to generate artificial candidates for self-reproduction; iii) Testing designed sequences for self-reproduction using high-throughput sequencing; v) characterizing the representative self-reproducers. We find that generative models that combine statistical signatures from pair correlations and secondary structure prediction are efficient at producing functional ribozymes more than 60 nucleotides away from the original sequence, whereas random mutations destroy activity after only a few. These methods interpolate the natural diversity found in group I introns, from which self-reproducers can be successfully re-engineered. This overall shows that self-reproduction is not an exceptional property of a few laboratory-made RNAs, but is relatively widespread in the sequence space.

RNA molecules are characterized by the existence of a multitude of stable states that that result in a frustrated energy landscape, where the observed structures depend sensibly on experimental conditions and can depend on the initial, unfolded, structure. Using both atomistic and coarse-grained physical models for RNAs, combined with enhanced sampling methods, we investigate the energy landscape of these systems to understand what are the most relevant structures in the different conditions. Using a few significant examples we show how the combination of these methods allowed us to rationalize the experimental evidence showing the concurrent existence of multiple states [1, 2]. The coarse-grained model we develop [3] is also a useful starting point to couple simulations with experimental data, moving toward intergrative modeling. We have recently developed a simulation technique allowing to bias MD coarse-grained simulations with SAXS data on-the-fly [4], and a theoretical framework to perform fast constant pH simulations where we can model the system considering the exchange of charges with the solvent [5]. These developments allow us to account for the environment to obtain reasonable structures to then be studied more thoroughly with high-resolution modeling.

Many functions of RNA depend on rearrangements in secondary structure that are triggered by external factors, such as protein or small molecule binding. These transitions can feature on one hand localized structural changes in base-pairs or can be presented by a change in chemical identity of e.g. a nucleo-base tautomer [1]. We use and develop R1$\rho$ relaxation-dispersion NMR methods [2] for characterizing transient structures of RNA that exist in low abundance (populations <10%) and that are sampled on timescales spanning three orders of magnitude (µs to s).

The characterization of transient structures in microRNA miR-34a targeting the mRNA of Sirt1 [3] will be discussed and a first glimpse into ribosomal dynamics will be provided. We have trapped these short-lived states and characterized their structure and impact on function.

We consider two minimalistic instances of RNA Design, restricting our attention to a minimal instance of RNA inverse folding based on a simplified energy model, where any canonical base pair contributes equally to the free-energy. This greatly simplifies the study of algorithmic questions, hopefully enabling new (exact? efficient?) solutions to design problems that are usually approached in a heuristic fashion.

First, we consider the problem of counting/sampling sequences that are simultaneously compatible with a collection of secondary (2D) structures. Valid sequence assignments turn out to be in bijection, up to trivial symmetry, to independent sets of a compatibility graph, built as the union of base pairs from all structures. As all graphs can be obtained as unions of 2D structures, this implies #P-hardness of the counting problem. Yet, the problem can be solved using an DP algorithm that is fixed parameter tractable for the tree-width of the graph. The associated algorithm can be further generalized to compute the partition function for generic constraints, and represents the engine of our declarative framework InfraRed for sequence sampling.

Next, we consider the inverse folding problem which starts from a single target 2D structure, and consists in finding a sequence that folds uniquely into the target with respect to base pair maximization. We first provide a complete characterization for designable structures without unpaired bases. More generally, we characterize extensive classes of (non-)designable structures, and prove the closure of the set of designable structures under the stutter operation. Finally, we consider a structure-approximating relaxation of the design, given a structure S (avoiding 2 basic undesignable motifs) transforms S into a designable structure by adding at most one base-pair to each helix. For all designable structures, a sequence can be generated in linear time, suggesting this relaxed version of design may be easier that the rigid version of the problem.

RNA structures depends largely on the geometry of interactions between its nucleotides. While the classical canonical/wobble interactions drive the folding of the major helices, there is a wide variety of different shapes that can connect through hydrogen bonds any nucleotide to any other. They have been classified by Leontis-Westhof into 12 non-canonical families. Graph algorithms have allowed to automatically retrieve all conserved network of non-canonical interactions in all known RNA structures. This work has exhibited the modularity and composability of theses structures. Nonetheless, most of them don’t have any associated thermodynamic parameter and it is still unknown if their folding is opportunistic or actually pushed for by these interactions. We ask as questions: What would be a rational scheme to design novel sequences folding in these shapes? How much of the context must be taken into account to ensure the correct folding? And how can chemical modifications enable unique modules?

Machine learning (ML) and especially deep learning (DL) approaches recently achieved remarkable results in different domains of life sciences. While such methods have entered many areas of molecular research, the field of RNA design still largely lacks deep learning-based approaches. To close this gap, we present two machine learning based approaches to tackle two different problems related to the field of RNA design. We present an automated deep reinforcement learning (AutoRL) approach that is capable of generating RNA sequences that fold into a desired secondary structure (inverse RNA folding) while often requiring only very few shots to yield a solution. Due to the sensitivity of deep RL algorithms to their hyperparameter settings and the lack of similar work in the field, we use a meta-optimization approach to automatically find the best RL setting for solving the problem. Since inverse RNA Folding is fundamentally linked to RNA folding, we present a probabilistic Transformer for the secondary structure prediction problem. We show that our method outperforms previous work on a commonly used benchmark dataset from the literature and that it improves the quality of non-canonical base pair and pseudoknot predictions compared to previous work. Besides the advantages of a global reception due to self-attention compared to convolution neural networks, the probabilistic nature of our method allows to reconstruct structure ensembles learned from data.

The development of reliable RNA design processes requires experimental validation. RNA structure modelling from chemical probing experiments has made tremendous progress, however accurately predicting large RNA structures is still challenging for several reasons. In particular interactions such as pseudoknots and non-canonical base pairs which are not captured by the available incomplete thermodynamic model are hardly predicted efficiently. To identify nucleotides involved in pseudoknots and non-canonical interactions, we scrutinized the SHAPE reactivity of each nucleotide of a benchmark RNA under multiple conditions. We show that probing at increasing temperature was remarkably efficient at pointing to non-canonical interactions and pseudoknot pairings. The SHAPE probing technology was then use to screen for RNA computationally designed to interact with a small molecule

Since the 1990s, increasingly complex nanostructures have been reliably obtained out of self-assembled DNA strands: from “simple” 2D shapes to 3D gears and articulated nano-objects, and even computing structures. The success of the assembly of these structures relies on a fine tuning of their structure to match the peculiar geometry of DNA helices. Various softwares have been developed to help the designer. These softwares provides essentially four kind of tools: an abstract representation of DNA helices (e.g. cadnano, scadnano, DNApen, 3DNA, Hex-tiles); a 3D view of the design (e.g., vHelix, Adenita, oxDNAviewer); fully automated design (e.g., BScOR, Daedalus, Perdix, Talos, Athena), generally dedicated to a specific kind of design, such as wireframe origamis; and coarse grain or thermodynamical physics simulations (e.g., oxDNA, MrDNA, SNUPI, Nupack, ViennaRNA,…). MagicDNA combines some of these approaches to ease the design of configurable DNA origamis.

We present our first step in the direction of conciliating all these different approaches and purposes into one single reliable GUI solution: the first fully usable version (design from scratch to export) of our general purpose 3D DNA nanostructure design software ENSnano. We believe that its intuitive, swift and yet powerful graphical interface, combining 2D and 3D editable views, allows fast and precise editing of DNA nanostructures. It also handles editing of large 2D/3D structures smoothly, and imports from the most common solutions. Our software extends the concept of grids introduced in cadnano; grids allows to abstract and articulated the different parts of a design. ENSnano also provides new design tools which speeds up considerably the design of complex large 3D structures, most notably: a 2D split view, which allows to edit intricate 3D structures which cannot easily be mapped in a 2D view, and a copy & repeat functionality, which takes advantage of the grids to design swiftly large repetitive chunks of a structure. ENSnano has been validated experimentally, as proven by the AFM images of a DNA origami entirely designed in ENSnano.

ENSnano is a light-weight ready-to-run independent single-file app, running seamlessly in most of the operating systems (Windows 10, MacOS 10.13+ and Linux), it thus does not require the installation of any other softwares such as Matlab, Maya or Samson. Precompiled versions for Windows and MacOS are ready to download on ENSnano website. In the coming months, we will add new features to our software to extend its capacities in the various directions discussed in this article. We decided to release now this first version of our software as its 3D and 2D editing interface is meeting our usability goals. Because of its stability and ease of use, we believe that ENSnano should find already its place in anyone’s design chain, when precise editing of a larger nanostructure is needed.

Furthermore, we propose a new method for designing curved origamis that deviates radically from the pattern-based previous approaches. We have developed a new model for DNA double helices curved in 3D that allows us to directly position the DNA double helices constituting the desired shape in the 3D interface of our software ENSnano. The crossovers positions are then simply deduced from the 3D positions of the nucleotides, as predicted by our model. This geometry-based interactive approach shortcuts the tedious process of manually coming up with a pattern suited for the desired curvature, and furthermore allows to deal transparently with structure whose curvature varies continuously. We also propose an innovative 2D representation synchronizing curved parallel double helices without relying on insertions or deletions, by automatically adapting the cell width for each nucleotide in the array representation.

We provide experimental data validating our curvy DNA model by successfully annealing two DNA origamis conceived thanks to two new DNA design methods. The first origami consists in a 6-helices bundle following an interactively created bezier curve whose curvature gets as low as 4.7nm. The second is an asymetrical Möbius torus whose DNA strands are routed along 2 spiraling helices covering its whole surface. This new spiraling technique, allowed by our DNA curvy model, enables to grasp xovers within a continuous range which results in an easier-to-design and smoother surface. Both of our designs folded as is, without any need to redesign their xover schemes.

Oritatami (folding in Japanese) is a mathematical model of computation by co-transcriptional folding we proposed in 2016 and have been studying, primarily on its computational power. In this model, RNA co-transcriptional folding is generalized so that the bases (called “beads” herein) can be of arbitrarily defined, finitely-many types that may have arbitrary affinities with each other (rather than just the four bases in RNA with their fixed set of affinities), but restricted on the 2D plane. In this talk, we present the latest universal oritatami architecture that enables us to compute all computable functions (Turing universality) co-transcriptionally, with particular emphasis on simplicity of mechanisms it employs to read/write a bit, to store information, and to merge computational paths (erasure).

Nucleic acid nanotechnology uses designed DNA or RNA strands that self-assemble into larger complexes and nanodevices. Computer modeling and simulations can provide crucial insights into function and design of such nanostructures. However, the sizes (up to thousands of base pairs) and timescales of their assembly (minutes to hours) of such nanodevices presents major challenge for modeling approaches. Here, we will present a coarse-grained model, oxDNA/oxRNA, specifically designed to simulate DNA and RNA nanotechnology, and we will demonstrate its application to RNA strand displacement reaction, a key mechanism in active nanotechnology devices which has recently been also identified to occur during RNA folding in vivo. We will then discuss applications of our modeling platform for inverse design of multicomponent nanostructure assemblies: how to design individual nucleic acid building blocks that self-assemble reliable into target mutlicomponent structure while avoiding kinetic traps and alternative free-energy minima? We show that through combination of multiscale modeling and mapping of the inverse design problem to Boolean Satisfiability Problem (SAT), it is possible to design nanostructures that assemble large-scale 3D assemblies, opening ways to use nucleic acids to biotemplated manufacturing.

Can one persuade a half-artificial tRNA to bind to a stop codon, pretend to be a tRNA-Ala and incorporate an alanine residue in a growing protein ? If so, you might be on the way to alleviating a disease caused by an unwanted stop codon.

If you want to design an RNA sequence, you want a series of real nucleotides at the end of the day, but you may well go through some non-physical mixed states along the way. You can represent a base as some fraction of A plus C plus.. If you have an energy model, you can take the derivative of energy with respect to the composition at each site. This lets you use gradient-based methods to optimise your sequence.

We used the program DSS-Opt to find our artificial tRNA sequences, although this was no longer a de novo problem. The tRNA does not just have to fold correctly. It has to be able to convince an amino-acyl synthetase to charge it and then sneak past a host of recognition factors before a ribosome would consider taking it seriously. This means our calculations were far from de novo design. Only about 45% of the bases were actually optimised.

About half a dozen candidates were tested for charging by an alanine amino acyl-tRNA synthetase and then for stop-codon read-through with a luciferase assay. The winner of this was fed to an antibiotic-stalled ribosome and the structure solved by cryo-EM (acquisition code 7B5K). A bouncing baby half-designed tRNA smiled at the authors from the coordinates.

You could either view this as a triumph of design or you could say, less than half the sites in the molecule were actually chosen.

Interactions between RNAs are an essential mechanism in gene regulation. State-of-the-art computational genome-wide screens predict targets of regulatory RNAs based on thermodynamic stability but largely neglect kinetic effects. To overcome this limitation, we propose novel models of RNA-RNA interaction dynamics. On this basis we can improve our understanding of general principles that govern RNA-RNA interaction formation and improve target prediction tools.

While the dynamics of secondary structure formation of single RNAs have been successfully modeled using transition systems between conformations, analogous approaches for RNA-RNA interaction quickly lead to infeasibly large systems. Therefore, we propose reducing the interaction system to the direct trajectories (shortest paths) from possible first contacts to full hybridization. This key idea enables studying general principles and relevant features of the interaction formation as well as model details; e.g. the relative speed of intra- and intermolecular folding. Specifically, we isolate kinetic effects by comparing experimentally confirmed interactions from Salmonella and E. coli to a randomized background with similar thermodynamic properties.

These experiments indicate that native interactions are kinetically favored. Moreover, folding trajectories often look remarkably different depending on the site of the initial contact. Based on a machine learning classifier, we were able to identify a combination of interaction features that provide most information on the behavior of native RNA-RNA interactions. These features can be exploited to filter target predictions.

Due to the design of our RNA kinetics model, features like energy barriers can be computed efficiently. This enables refining genome-wide target predictions through kinetic criteria. Beyond these immediate practical improvements, we shed light on general principles like the long-debated influence of the accessibility of the initial contact site.

In the context of this seminar I would like to present this direct path models for interaction formation as well as the kinetic features that we identified and discuss how such features could extend current RNA design strategies.

Infrared is a modeling framework for efficient targeted sampling and optimization. It was originally developed for implementing complex sequence design approaches with multiple objectives and side constraints, e.g. design of sequences with multiple RNA target structures while controlling the GC-content (RNARedPrint). Due to its declarative, compositional application programming/modeling interface, Infrared allows extending existing design tools to solve very specific design tasks, e.g. optimizing codon-usage while targeting RNA structures and (possibly) additional constraints. In the same way, it enables rapid development of completely new design tools like RNAPOND (and, due to its generality, even methods beyond design, e.g. alignment of RNAs with pseudoknots). A main feature of the system is its automatic adaptation to the complexity of the declaratively modeled task. For this purpose, the system implicitly derives fixed- parameter-tractable sampling and optimization algorithms using tree-decomposition. The talk outlines main properties and background of the system, its elementary usage, and presents concrete examples of design applications.

The problem of RNA design attempts to construct RNA sequences that perform a predefined biological function, identified by several additional constraints. One of the foremost objectives of RNA negative design is that the designed RNA sequence should adopt a predefined target secondary structure preferentially to any alternative structure, according to a given metrics and folding model. It was observed in several works that some secondary structures are undesignable, i.e. no RNA sequence can fold into the target structure while satisfying some criterion measuring how preferential this folding is compared to alternative conformations.

We show that the proportion of designable secondary structures decreases exponentially with the size of the target secondary structure, for various popular combinations of energy models and design objectives. This exponential decay is, at least in part, due to the existence of forbidden motifs, which can be generically constructed, and jointly analyzed to yield asymptotic upper bounds on the number of designable structures. Moreover, we define a lower bound of the structural ensemble defect. We show that, across uniformly distributed secondary structures, such a lower bound has a Normal limiting distribution with the expected value and the variance both linear to the size of the secondary structure.