Modeling RNA folding paths with pseudoknots: application to hepatitis delta virus ribozyme

The effect of the loop on the thermodynamic and kinetic of single base pair in pseudoknot

RNA pseudoknots are RNA molecules with specialized three-dimensional structures that play important roles in various biological processes. To understand the functions and mechanisms of pseudoknots, it is essential to elucidate their structures and folding pathways. The most fundamental step in RNA folding is the opening and closing of a base pair. The effect of flexible loops on the base pair in pseudoknots remains unclear. In this work, we use molecular dynamics simulations and Markov state model to study the configurations, thermodynamic and kinetic of single base pair in pseudoknots. We find that the presence of the loop leads to a trap state. In addition, the rate-limiting step for the formation of base pair is the disruption of the trap state, rather than the open state to the closed state, which is quite different from the previous studies on non-pseudoknot RNA. For the thermodynamic parameters in pseudoknots, we find that the entropy difference upon opening the base pair between this simulation and the nearest-neighbor model results from the different entropy of different lengths of loop in solution. The thermodynamic parameters of the stack in pseudoknot are close to the nearest-neighbor parameters. The bases on the loop have different distribution patterns in different states, and the slow transition states of the loop are determined by the orientation of the bases.

Kinetic pathway of HIV-1 TAR cotranscriptional folding

The Trans-Activator Receptor (TAR) RNA, located at the 5'-end untranslated region (5' UTR) of the human immunodeficiency virus type 1 (HIV-1), is pivotal in the virus's life cycle. As the initial functional domain, it folds during the transcription of viral mRNA. Although TAR's role in recruiting the Tat protein for trans-activation is established, the detailed kinetic mechanisms at play during early transcription, especially at points of temporary transcriptional pausing, remain elusive. Moreover, the precise physical processes of transcriptional pause and subsequent escape are not fully elucidated. This study focuses on the folding kinetics of TAR and the biological implications by integrating computer simulations of RNA folding during transcription with nuclear magnetic resonance (NMR) spectroscopy data. The findings reveal insights into the folding mechanism of a non-native intermediate that triggers transcriptional pause, along with different folding pathways leading to transcriptional pause and readthrough. The profiling of the cotranscriptional folding pathway and identification of kinetic structural intermediates reveal a novel mechanism for viral transcriptional regulation, which could pave the way for new antiviral drug designs targeting kinetic cotranscriptional folding pathways in viral RNAs.

Knotify_V2.0: Deciphering RNA Secondary Structures with H-Type Pseudoknots and Hairpin Loops

Accurately predicting the pairing order of bases in RNA molecules is essential for anticipating RNA secondary structures. Consequently, this task holds significant importance in unveiling previously unknown biological processes. The urgent need to comprehend RNA structures has been accentuated by the unprecedented impact of the widespread COVID-19 pandemic. This paper presents a framework, Knotify_V2.0, which makes use of syntactic pattern recognition techniques in order to predict RNA structures, with a specific emphasis on tackling the demanding task of predicting H-type pseudoknots that encompass bulges and hairpins. By leveraging the expressive capabilities of a Context-Free Grammar (CFG), the suggested framework integrates the inherent benefits of CFG and makes use of minimum free energy and maximum base pairing criteria. This integration enables the effective management of this inherently ambiguous task. The main contribution of Knotify_V2.0 compared to earlier versions lies in its capacity to identify additional motifs like bulges and hairpins within the internal loops of the pseudoknot. Notably, the proposed methodology, Knotify_V2.0, demonstrates superior accuracy in predicting core stems compared to state-of-the-art frameworks. Knotify_V2.0 exhibited exceptional performance by accurately identifying both core base pairing that form the ground truth pseudoknot in 70% of the examined sequences. Furthermore, Knotify_V2.0 narrowed the performance gap with Knotty, which had demonstrated better performance than Knotify and even surpassed it in Recall and F1-score metrics. Knotify_V2.0 achieved a higher count of true positives (tp) and a significantly lower count of false negatives (fn) compared to Knotify, highlighting improvements in Prediction and Recall metrics, respectively. Consequently, Knotify_V2.0 achieved a higher F1-score than any other platform. The source code and comprehensive implementation details of Knotify_V2.0 are publicly available on GitHub.

Observation of coordinated RNA folding events by systematic cotranscriptional RNA structure probing

RNA begins to fold as it is transcribed by an RNA polymerase. Consequently, RNA folding is constrained by the direction and rate of transcription. Understanding how RNA folds into secondary and tertiary structures therefore requires methods for determining the structure of cotranscriptional folding intermediates. Cotranscriptional RNA chemical probing methods accomplish this by systematically probing the structure of nascent RNA that is displayed from an RNA polymerase. Here, we describe a concise, high-resolution cotranscriptional RNA chemical probing procedure called variable length Transcription Elongation Complex RNA structure probing (TECprobe-VL). We demonstrate the accuracy and resolution of TECprobe-VL by replicating and extending previous analyses of ZTP and fluoride riboswitch folding and mapping the folding pathway of a ppGpp-sensing riboswitch. In each system, we show that TECprobe-VL identifies coordinated cotranscriptional folding events that mediate transcription antitermination. Our findings establish TECprobe-VL as an accessible method for mapping cotranscriptional RNA folding pathways.

In silico methods for predicting functional synonymous variants

Single nucleotide variants (SNVs) contribute to human genomic diversity. Synonymous SNVs are previously considered to be "silent," but mounting evidence has revealed that these variants can cause RNA and protein changes and are implicated in over 85 human diseases and cancers. Recent improvements in computational platforms have led to the development of numerous machine-learning tools, which can be used to advance synonymous SNV research. In this review, we discuss tools that should be used to investigate synonymous variants. We provide supportive examples from seminal studies that demonstrate how these tools have driven new discoveries of functional synonymous SNVs.

Predicting DNA kinetics with a truncated continuous-time Markov chain method

Predicting the kinetics of reactions involving nucleic acid strands is a fundamental task in biology and biotechnology. Reaction kinetics can be modeled as an elementary step continuous-time Markov chain, where states correspond to secondary structures and transitions correspond to base pair formation and breakage. Since the number of states in the Markov chain could be large, rates are determined by estimating the mean first passage time from sampled trajectories. As a result, the cost of kinetic predictions becomes prohibitively expensive for rare events with extremely long trajectories. Also problematic are scenarios where multiple predictions are needed for the same reaction, e.g., under different environmental conditions, or when calibrating model parameters, because a new set of trajectories is needed multiple times. We propose a new method, called pathway elaboration, to handle these scenarios. Pathway elaboration builds a truncated continuous-time Markov chain through both biased and unbiased sampling. The resulting Markov chain has moderate state space size, so matrix methods can efficiently compute reaction rates, even for rare events. Also the transition rates of the truncated Markov chain can easily be adapted when model or environmental parameters are perturbed, making model calibration feasible. We illustrate the utility of pathway elaboration on toehold-mediated strand displacement reactions, show that it well-approximates trajectory-based predictions of unbiased elementary step models on a wide range of reaction types for which such predictions are feasible, and demonstrate that it performs better than alternative truncation-based approaches that are applicable for mean first passage time estimation. Finally, in a small study, we use pathway elaboration to optimize the Metropolis kinetic model of Multistrand, an elementary step simulator, showing that the optimized parameters greatly improve reaction rate predictions. Our framework and dataset are available at https://github.com/DNA-and-Natural-Algorithms-Group/PathwayElaboration.

Knotify+: Toward the Prediction of RNA H-Type Pseudoknots, Including Bulges and Internal Loops

The accurate "base pairing" in RNA molecules, which leads to the prediction of RNA secondary structures, is crucial in order to explain unknown biological operations. Recently, COVID-19, a widespread disease, has caused many deaths, affecting humanity in an unprecedented way. SARS-CoV-2, a single-stranded RNA virus, has shown the significance of analyzing these molecules and their structures. This paper aims to create a pioneering framework in the direction of predicting specific RNA structures, leveraging syntactic pattern recognition. The proposed framework, Knotify+, addresses the problem of predicting H-type pseudoknots, including bulges and internal loops, by featuring the power of context-free grammar (CFG). We combine the grammar's advantages with maximum base pairing and minimum free energy to tackle this ambiguous task in a performant way. Specifically, our proposed methodology, Knotify+, outperforms state-of-the-art frameworks with regards to its accuracy in core stems prediction. Additionally, it performs more accurately in small sequences and presents a comparable accuracy rate in larger ones, while it requires a smaller execution time compared to well-known platforms. The Knotify+ source code and implementation details are available as a public repository on GitHub.

Nucleic Acid Structure Prediction Including Pseudoknots Through Direct Enumeration of States: A User's Guide to the LandscapeFold Algorithm

Here we detail the LandscapeFold secondary structure prediction algorithm and how it is used. The algorithm was previously described and tested in (Kimchi O et al., Biophys J 117(3):520-532, 2019), though it was not named there. The algorithm directly enumerates all possible secondary structures into which up to two RNA or single-stranded DNA sequences can fold. It uses a polymer physics model to estimate the configurational entropy of structures including complex pseudoknots. We detail each of these steps and ways in which the user can adjust the algorithm as desired. The code is available on the GitHub repository https://github.com/ofer-kimchi/LandscapeFold .

Upstream Flanking Sequence Assists Folding of an RNA Thermometer

Many heat shock genes in bacteria are regulated through a class of temperature-sensitive stem-loop (SL) RNAs called RNA thermometers (RNATs). One of the most widely studied RNATs is the Repression Of heat Shock Expression (ROSE) element associated with expression of heat shock proteins. Located in the 5'UTR, the RNAT contains one to three auxiliary hairpins upstream of it. Herein, we address roles of these upstream SLs in the folding and function of an RNAT. Bradyrhizobium japonicum is a nitrogen-fixing bacterium that experiences a wide range of temperatures in the soil and contains ROSE elements, each having multiple upstream SLs. The 5'UTR of the messenger (mRNA) for heat shock protein A (hspA) in B. japonicum has an intricate secondary structure containing three SLs upstream of the RNAT SL. While structure-function studies of the hspA RNAT itself have been reported, it has been unclear if these auxiliary SLs contribute to the temperature-sensing function of the ROSE elements. Herein, we show that the full length (FL) sequence has several melting transitions indicating that the ROSE element unfolds in a non-two-state manner. The upstream SLs are more stable than the RNAT itself, and a variant with disrupted base pairing in the SL immediately upstream of the RNAT has little influence on the melting of the RNAT. On the basis of these results and modeling of the co-transcriptional folding of the ROSE element, we propose that the upstream SLs function to stabilize the transcript and aid proper folding and dynamics of the RNAT.

Effect of pausing on the cotranscriptional folding kinetics of RNAs

The pausing event in RNA molecule folding that occurs during the cotranscription process plays a critical role in cellular RNA function. Based on Conformational Resampling through Kinetic Relaxation (CRKR), this paper investigates a method to reveal the specifics of pausing for RNA cotranscriptional folding of 117-nucleotide E. coli SRP RNA and 73-nucleotide HIV-1 TAR RNA. It can be inferred from the results that pausing events generate valid cotranscriptional conformational rearrangement to protect the function structures and influence the folding pathway, which is remarkably consistent with the experimental results. Additionally, different transcription speeds result in different levels of protection capability. The folding pathway or conformational rearrangement can also be affected by a change in transcription speed after pausing site. These findings illuminate that RNAs with functional structures undergo complex rearrangement folding in pausing events, and different RNAs prefer different speeds for specific folding pathways. Moreover, pausing in particular circumstances can be employed to regulate the population of final functional structures. In conclusion, this paper offers fresh perspectives on the pausing event in the cotranscriptional folding of RNAs.

How does RNA fold dynamically?

Recent advances in interrogating RNA folding dynamics have shown the classical model of RNA folding to be incomplete. Here, we pose three prominent questions for the field that are at the forefront of our understanding of the importance of RNA folding dynamics for RNA function. The first centers on the most appropriate biophysical framework to describe changes to the RNA folding energy landscape that a growing RNA chain encounters during transcriptional elongation. The second focuses on the potential ubiquity of strand displacement - a process by which RNA can rapidly change conformations - and how this process may be generally present in broad classes of seemingly different RNAs. The third raises questions about the potential importance and roles of cellular protein factors in RNA conformational switching. Answers to these questions will greatly improve our fundamental knowledge of RNA folding and function, drive biotechnological advances that utilize engineered RNAs, and potentially point to new areas of biology yet to be discovered.

Landscape Zooming toward the Prediction of RNA Cotranscriptional Folding

RNA molecules fold as they are transcribed. Cotranscriptional folding of RNA plays a critical role in RNA functions in vivo. Present computational strategies focus on simulations where large structural changes may not be completely sampled. Here, we describe an alternative approach to predicting cotranscriptional RNA folding by zooming in and out of the RNA folding energy landscape. By classifying the RNA structural ensemble into "partitions" based on long, stable helices, we zoom out of the landscape and predict the overall slow folding kinetics from the interpartition kinetic network, and for each interpartition transition, we zoom in on the landscape to simulate the kinetics. Applications of the model to the 117-nucleotide E. coli SRP RNA and the 59-nucleotide HIV-1 TAR RNA show agreements with the experimental data and new structural and kinetic insights into biologically significant conformational switches and pathways for these important systems. This approach, by zooming in/out of an RNA folding landscape at different resolutions, might allow us to treat large RNAs in vivo with transcriptional pause, transcription speed, and other in vivo effects.

Knotify: An Efficient Parallel Platform for RNA Pseudoknot Prediction Using Syntactic Pattern Recognition

Obtaining valuable clues for noncoding RNA (ribonucleic acid) subsequences remains a significant challenge, acknowledging that most of the human genome transcribes into noncoding RNA parts related to unknown biological operations. Capturing these clues relies on accurate “base pairing” prediction, also known as “RNA secondary structure prediction”. As COVID-19 is considered a severe global threat, the single-stranded SARS-CoV-2 virus reveals the importance of establishing an efficient RNA analysis toolkit. This work aimed to contribute to that by introducing a novel system committed to predicting RNA secondary structure patterns (i.e., RNA’s pseudoknots) that leverage syntactic pattern-recognition strategies. Having focused on the pseudoknot predictions, we formalized the secondary structure prediction of the RNA to be primarily a parsing and, secondly, an optimization problem. The proposed methodology addresses the problem of predicting pseudoknots of the first order (H-type). We introduce a context-free grammar (CFG) that affords enough expression power to recognize potential pseudoknot pattern. In addition, an alternative methodology of detecting possible pseudoknots is also implemented as well, using a brute-force algorithm. Any input sequence may highlight multiple potential folding patterns requiring a strict methodology to determine the single biologically realistic one. We conscripted a novel heuristic over the widely accepted notion of free-energy minimization to tackle such ambiguity in a performant way by utilizing each pattern’s context to unveil the most prominent pseudoknot pattern. The overall process features polynomial-time complexity, while its parallel implementation enhances the end performance, as proportional to the deployed hardware. The proposed methodology does succeed in predicting the core stems of any RNA pseudoknot of the test dataset by performing a 76.4% recall ratio. The methodology achieved a F1-score equal to 0.774 and MCC equal 0.543 in discovering all the stems of an RNA sequence, outperforming the particular task. Measurements were taken using a dataset of 262 RNA sequences establishing a performance speed of 1.31, 3.45, and 7.76 compared to three well-known platforms. The implementation source code is publicly available under knotify github repo.

Cotranscriptional Kinetic Folding of RNA Secondary Structures Including Pseudoknots

Computational prediction of ribonucleic acid (RNA) structures is an important problem in computational structural biology. Studies of RNA structure formation often assume that the process starts from a fully synthesized sequence. Experimental evidence, however, has shown that RNA folds concurrently with its elongation. We investigate RNA secondary structure formation, including pseudoknots, that takes into account the cotranscriptional effects. We propose a single-nucleotide resolution kinetic model of the folding process of RNA molecules, where the polymerase-driven elongation of an RNA strand by a new nucleotide is included as a primitive operation, together with a stochastic simulation method that implements this folding concurrently with the transcriptional synthesis. Numerical case studies show that our cotranscriptional RNA folding model can predict the formation of conformations that are favored in actual biological systems. Our new computational tool can thus provide quantitative predictions and offer useful insights into the kinetics of RNA folding.

High bio-recognizing aptamer designing and optimization against human herpes virus-5

While the world is tackling one of the direst health emergencies, it has come to light that in the fight against viruses, preparedness is everything. A disease with the initial symptoms of the common flu has the capacity to disrupt the life of 7.8 billion people and thus no infection and especially no virus can be ignored. Hence, we have designed the high bio-recognizing DNA aptamer for diagnosis and therapeutics role against glycoprotein-B (gB) of Human Herpes Virus-5 (HHV-5). HHV-5 is linked with epidemiological and asymptomatic diseases leading to high mortality. Herein, we report potent aptamer (5'CTCGCTTACCCCTGGGTGTGCGGG3') which has high specificity to gB with energy score -523.28 kJ/mol, more than reference aptamer L19 (-363.50 kJ/mol). The stable binding of aptamer with gB was confirmed with atomic fluctuations 0.1 to 1.8 Å through anisotropic network analysis. Aptamer formed stem-loop conformation (-1.0 kcal/mol) by stochastic simulation and found stable with physicochemical properties. Importantly, aptamer was found biologically significant with consisting of putative transcription factors in its vicinity (SP1, GATA1, AP2, NF1) and also possesses homology with exonic sequence of SGSH gene which indicated regulatory role in blockade of viruses. Inaddition, we also proposed plausible mechanism of action of aptamer as antiviral therapeutics.

A lattice kinetic Monte-Carlo method for simulating chromosomal dynamics and other (non-)equilibrium bio-assemblies

Biological assemblies in living cells such as chromosomes constitute large many-body systems that operate in a fluctuating, out-of-equilibrium environment. Since a brute-force simulation of that many degrees of freedom is currently computationally unfeasible, it is necessary to perform coarse-grained stochastic simulations. Here, we develop all tools necessary to write a lattice kinetic Monte-Carlo (LKMC) algorithm capable of performing such simulations. We discuss the validity and limits of this approach by testing the results of the simulation method in simple settings. Importantly, we illustrate how at large external forces Metropolis-Hastings kinetics violate the fluctuation-dissipation and steady-state fluctuation theorems and discuss better alternatives. Although this simulation framework is rather general, we demonstrate our approach using a DNA polymer with interacting SMC condensin loop-extruding enzymes. Specifically, we show that the scaling behavior of the loop-size distributions that we obtain in our LKMC simulations of this SMC-DNA system is consistent with that reported in other studies using Brownian dynamics simulations and analytic approaches. Moreover, we find that the irreversible dynamics of these enzymes under certain conditions result in frozen, sterically jammed polymer configurations, highlighting a potential pitfall of this approach.

A Polymer Physics Framework for the Entropy of Arbitrary Pseudoknots

The accurate prediction of RNA secondary structure from primary sequence has had enormous impact on research from the past 40 years. Although many algorithms are available to make these predictions, the inclusion of non-nested loops, termed pseudoknots, still poses challenges arising from two main factors: 1) no physical model exists to estimate the loop entropies of complex intramolecular pseudoknots, and 2) their NP-complete enumeration has impeded their study. Here, we address both challenges. First, we develop a polymer physics model that can address arbitrarily complex pseudoknots using only two parameters corresponding to concrete physical quantities-over an order of magnitude fewer than the sparsest state-of-the-art phenomenological methods. Second, by coupling this model to exhaustive enumeration of the set of possible structures, we compute the entire free energy landscape of secondary structures resulting from a primary RNA sequence. We demonstrate that for RNA structures of ∼80 nucleotides, with minimal heuristics, the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. We further show that despite our loop entropy model's parametric sparsity, it performs better than or on par with previously published methods in predicting both pseudoknotted and non-pseudoknotted structures on a benchmark data set of RNA structures of ≤80 nucleotides. We suggest ways in which the accuracy of the model can be further improved.

Viroid research and its significance for RNA technology and basic biochemistry

Viroids were described 47 years ago as the smallest RNA molecules capable of infecting plants and autonomously self-replicating without an encoded protein. Work on viroids initiated the development of a number of innovative methods. Novel chromatographic and gelelectrophoretic methods were developed for the purification and characterization of viroids; these methods were later used in molecular biology, gene technology and in prion research. Theoretical and experimental studies of RNA folding demonstrated the general biological importance of metastable structures, and nuclear magnetic resonance spectroscopy of viroid RNA showed the partially covalent nature of hydrogen bonds in biological macromolecules. RNA biochemistry and molecular biology profited from viroid research, such as in the detection of RNA as template of DNA-dependent polymerases and in mechanisms of gene silencing. Viroids, the first circular RNA detected in nature, are important for studies on the much wider spectrum of circular RNAs and other non-coding RNAs.

An emergent understanding of strand displacement in RNA biology

DNA and RNA are generally regarded as central molecules in molecular biology. Recent advancements in the field of DNA/RNA nanotechnology successfully used DNA/RNA as programmable molecules to construct molecular machines and nanostructures with predefined shapes and functions. The key mechanism for dynamic control of the conformations of these DNA/RNA nanodevices is a reaction called strand displacement, in which one strand in a formed duplex is replaced by a third invading strand. While DNA/RNA strand displacement has mainly been used to de novo design molecular devices, we argue in this review that this reaction is also likely to play a key role in multiple cellular events such as gene recombination, CRISPR-based genome editing, and RNA cotranscriptional folding. We introduce the general mechanism of strand displacement reaction, give examples of its use in the construction of molecular machines, and finally review natural processes having characteristic which suggest that strand displacement is occurring.

Computational approaches for the discovery of splicing regulatory RNA structures

Global RNA structure and local functional motifs mediate interactions important in determining the rates and patterns of mRNA splicing. In this review, we overview approaches for the computational prediction of RNA secondary structure with a special emphasis on the discovery of motifs important to RNA splicing. The process of identifying and modeling potential splicing regulatory structures is illustrated using a recently-developed approach for RNA structural motif discovery, the ScanFold pipeline, which is applied to the identification of a known splicing regulatory structure in influenza virus.

Small-World Networks and RNA Secondary Structures

Let \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${{ \cal S}_n}$$ \end{document} denote the network of all RNA secondary structures of length n, in which undirected edges exist between structures s, t such that t is obtained from s by the addition, removal, or shift of a single base pair. Using context-free grammars, generating functions, and complex analysis, we show that the asymptotic average degree is \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$O ( n )$$ \end{document} , and that the asymptotic clustering coefficient is \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$O ( 1 / n )$$ \end{document} , from which it follows that the family \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${{ \cal S}_n}$$ \end{document} , \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$n = 1 , 2 , 3 , \ldots$$ \end{document} of secondary structure networks is not small world.

Effects of flanking regions on HDV cotranscriptional folding kinetics

Hepatitis delta virus (HDV) ribozyme performs the self-cleavage activity through folding to a double pseudoknot structure. The folding of functional RNA structures is often coupled with the transcription process. In this work, we developed a new approach for predicting the cotranscriptional folding kinetics of RNA secondary structures with pseudoknots. We theoretically studied the cotranscriptional folding behavior of the 99-nucleotide (nt) HDV sequence, two upstream flanking sequences, and one downstream flanking sequence. During transcription, the 99-nt HDV can effectively avoid the trap intermediates and quickly fold to the cleavage-active state. It is different from its refolding kinetics, which folds into an intermediate trap state. For all the sequences, the ribozyme regions (from 1 to 73) all fold to the same structure during transcription. However, the existence of the 30-nt upstream flanking sequence can inhibit the ribozyme region folding into the active native state through forming an alternative helix Alt1 with the segments 70-90. The longer upstream flanking sequence of 54 nt itself forms a stable hairpin structure, which sequesters the formation of the Alt1 helix and leads to rapid formation of the cleavage-active structure. Although the 55-nt downstream flanking sequence could invade the already folded active structure during transcription by forming a more stable helix with the ribozyme region, the slow transition rate could keep the structure in the cleavage-active structure to perform the activity.

Predicting Cotranscriptional Folding Kinetics For Riboswitch

On the basis of a helix-based transition rate model, we developed a new method for sampling cotranscriptional RNA conformational ensemble and the prediction of cotranscriptional folding kinetics. Applications to E. coli. SRP RNA and pbuE riboswitch indicate that the model may provide reliable predictions for the cotranscriptional folding pathways and population kinetics. For E. coli. SRP RNA, the predicted population kinetics and the folding pathway are consistent with the SHAPE profiles in the recent cotranscriptional SHAPE-seq experiments. For the pbuE riboswitch, the model predicts the transcriptional termination efficiency as a function of the force. The theoretical results show (a) a force-induced transition from the aptamer (antiterminator) to the terminator structure and (b) the different folding pathways for the riboswitch with and without the ligand (adenine). More specifically, without adenine, the aptamer structure emerges as a short-lived kinetic transient state instead of a thermodynamically stable intermediate state. Furthermore, from the predicted extension-time curves, the model identifies a series of conformational switches in the pulling process, where the predicted relative residence times for the different structures are in accordance with the experimental data. The model may provide a new tool for quantitative predictions of cotranscriptional folding kinetics, and results can offer useful insights into cotranscriptional folding-related RNA functions such as regulation of gene expression with riboswitches.

Computational approaches for alternative and transient secondary structures of ribonucleic acids

Transient and alternative structures of ribonucleic acids (RNAs) play essential roles in various regulatory processes, such as translation regulation in living cells. Because experimental analyses for RNA structures are difficult and time-consuming, computational approaches based on RNA secondary structures are promising. In this article, we review computational methods for detecting and analyzing transient/alternative secondary structures of RNAs, including static approaches based on probabilistic distributions of RNA secondary structures and dynamic approaches such as kinetic folding and folding pathway predictions.

Unfolding and Targeting Thermodynamics of a DNA Intramolecular Complex with Joined Triplex-Duplex Domains

Our laboratory is interested in developing methods that can be used for the control of gene expression. In this work, we are investigating the reaction of an intramolecular complex containing a triplex-duplex junction with partially complementary strands. We used a combination of isothermal titration calorimetry (ITC), differential scanning calorimetry (DSC), and spectroscopy techniques to determine standard thermodynamic profiles for these targeting reactions. Specifically, we have designed single strands to target one loop (CTTTC) or two loops (CTTTC and GCAA) of this complex. Both reactions yielded exothermic enthalpies of -66.3 and -82.8 kcal/mol by ITC, in excellent agreement with the reaction enthalpies of -72.7 and -88.7 kcal/mol, respectively, obtained from DSC Hess cycles. The favorable heat contributions result from the formation of base-pair stacks involving mainly the unpaired bases of the loops. This shows that each complementary strand is able to invade and disrupt the secondary structure. The simultaneous targeting of two loops yielded a more favorable reaction free energy, by approximately -8 kcal/mol, which corresponds to the formation of roughly four base-pair stacks involving the unpaired bases of the 5'-GCAA loop. The main conclusion is that the targeting of loops with a large number of unpaired bases results in a more favorable reaction free energy.

Ensemble simulations: folding, unfolding and misfolding of a high-efficiency frameshifting RNA pseudoknot

Massive all-atom molecular dynamics simulations were conducted across a distributed computing network to study the folding, unfolding, misfolding and conformational plasticity of the high-efficiency frameshifting double mutant of the 26 nt potato leaf roll virus RNA pseudoknot. Our robust sampling, which included over 40 starting structures spanning the spectrum from the extended unfolded state to the native fold, yielded nearly 120 μs of cumulative sampling time. Conformational microstate transitions on the 1.0 ns to 10.0 μs timescales were observed, with post-equilibration sampling providing detailed representations of the conformational free energy landscape and the complex folding mechanism inherent to the pseudoknot motif. Herein, we identify and characterize two alternative native structures, three intermediate states, and numerous misfolded states, the latter of which have not previously been characterized via atomistic simulation techniques. While in line with previous thermodynamics-based models of a general RNA folding mechanism, our observations indicate that stem-strand-sequence-separation may serve as an alternative predictor of the order of stem formation during pseudoknot folding. Our results contradict a model of frameshifting based on structural rigidity and resistance to mechanical unfolding, and instead strongly support more recent studies in which conformational plasticity is identified as a determining factor in frameshifting efficiency.

RNA folding kinetics using Monte Carlo and Gillespie algorithms

RNA secondary structure folding kinetics is known to be important for the biological function of certain processes, such as the hok/sok system in E. coli. Although linear algebra provides an exact computational solution of secondary structure folding kinetics with respect to the Turner energy model for tiny ([Formula: see text]20 nt) RNA sequences, the folding kinetics for larger sequences can only be approximated by binning structures into macrostates in a coarse-grained model, or by repeatedly simulating secondary structure folding with either the Monte Carlo algorithm or the Gillespie algorithm. Here we investigate the relation between the Monte Carlo algorithm and the Gillespie algorithm. We prove that asymptotically, the expected time for a K-step trajectory of the Monte Carlo algorithm is equal to [Formula: see text] times that of the Gillespie algorithm, where [Formula: see text] denotes the Boltzmann expected network degree. If the network is regular (i.e. every node has the same degree), then the mean first passage time (MFPT) computed by the Monte Carlo algorithm is equal to MFPT computed by the Gillespie algorithm multiplied by [Formula: see text]; however, this is not true for non-regular networks. In particular, RNA secondary structure folding kinetics, as computed by the Monte Carlo algorithm, is not equal to the folding kinetics, as computed by the Gillespie algorithm, although the mean first passage times are roughly correlated. Simulation software for RNA secondary structure folding according to the Monte Carlo and Gillespie algorithms is publicly available, as is our software to compute the expected degree of the network of secondary structures of a given RNA sequence-see http://bioinformatics.bc.edu/clote/RNAexpNumNbors .

In silico methods for co-transcriptional RNA secondary structure prediction and for investigating alternative RNA structure expression

RNA transcripts are the primary products of active genes in any living organism, including many viruses. Their cellular destiny not only depends on primary sequence signals, but can also be determined by RNA structure. Recent experimental evidence shows that many transcripts can be assigned more than a single functional RNA structure throughout their cellular life and that structure formation happens co-transcriptionally, i.e. as the transcript is synthesised in the cell. Moreover, functional RNA structures are not limited to non-coding transcripts, but can also feature in coding transcripts. The picture that now emerges is that RNA structures constitute an additional layer of information that can be encoded in any RNA transcript (and on top of other layers of information such as protein-context) in order to exert a wide range of functional roles. Moreover, different encoded RNA structures can be expressed at different stages of a transcript's life in order to alter the transcript's behaviour depending on its actual cellular context. Similar to the concept of alternative splicing for protein-coding genes, where a single transcript can yield different proteins depending on cellular context, it is thus appropriate to propose the notion of alternative RNA structure expression for any given transcript. This review introduces several computational strategies that my group developed to detect different aspects of RNA structure expression in vivo. Two aspects are of particular interest to us: (1) RNA secondary structure features that emerge during co-transcriptional folding and (2) functional RNA structure features that are expressed at different times of a transcript's life and potentially mutually exclusive.

Predicting RNA secondary structures from sequence and probing data

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.

The Complementarity of the Loop to the Stem in DNA Pseudoknots Gives Rise to Local TAT Base-Triplets

Pseudoknots belong to an RNA structural motif that has significant roles in the biological function of RNA. An example is ribosomal frameshifting; in this mechanism, the formation of a local triplex changes the reading frame that allows for differences in the translation of mRNAs. In this work, we have used a combination of temperature-dependent UV spectroscopy and differential scanning calorimetry (DSC) to determine the unfolding thermodynamics of a set of DNA pseudoknots with the following sequence: d(TCTCTTnAAAAAAAAGAGAT5TTTTTTT), where "Tn" is a thymine loop with n=5 (PsK-5), 7 (PsK-7), 9 (PsK-9), or 11 (PsK-11). All four oligonucleotides form intramolecular pseudoknots, and the increase in the length of this loop yielded more stable pseudoknots due to higher transition temperatures and higher unfolding enthalpies. This indicates formation of one and three TAT/TAT stacks in PsK-9 and PsK-11, respectively. We have flipped one AT for a TA base pair in the core stem of these pseudoknots, preventing in this way the formation of these base-triplet stacks. The DSC curves of these pseudoknots yielded lower unfolding enthalpies, confirming the formation of a local triplex in PsK-9 and PsK-11. Furthermore, we have investigated the reaction of PsK-5 and PsK-9 with their partially complementary strands: directly by isothermal titration calorimetry and indirectly by creating a Hess cycle with the DSC data. Relative to the PsK-5 reaction, PsK-9 reacts with its complementary strand with less favorable free energy and enthalpy contributions; this indicates PsK-9 is more stable and more compact due to the formation of a local triplex.

Pseudoknots in RNA folding landscapes

MOTIVATION

The function of an RNA molecule is not only linked to its native structure, which is usually taken to be the ground state of its folding landscape, but also in many cases crucially depends on the details of the folding pathways such as stable folding intermediates or the timing of the folding process itself. To model and understand these processes, it is necessary to go beyond ground state structures. The study of rugged RNA folding landscapes holds the key to answer these questions. Efficient coarse-graining methods are required to reduce the intractably vast energy landscapes into condensed representations such as barrier trees or basin hopping graphs : BHG) that convey an approximate but comprehensive picture of the folding kinetics. So far, exact and heuristic coarse-graining methods have been mostly restricted to the pseudoknot-free secondary structures. Pseudoknots, which are common motifs and have been repeatedly hypothesized to play an important role in guiding folding trajectories, were usually excluded.

RESULTS

We generalize the BHG framework to include pseudoknotted RNA structures and systematically study the differences in predicted folding behavior depending on whether pseudoknotted structures are allowed to occur as folding intermediates or not. We observe that RNAs with pseudoknotted ground state structures tend to have more pseudoknotted folding intermediates than RNAs with pseudoknot-free ground state structures. The occurrence and influence of pseudoknotted intermediates on the folding pathway, however, appear to depend very strongly on the individual RNAs so that no general rule can be inferred.

AVAILABILITY AND IMPLEMENTATION

The algorithms described here are implemented in C++ as standalone programs. Its source code and Supplemental material can be freely downloaded from http://www.tbi.univie.ac.at/bhg.html.

CONTACT

qin@bioinf.uni-leipzig.de

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Understanding the kinetic mechanism of RNA single base pair formation

RNA functions are intrinsically tied to folding kinetics. The most elementary step in RNA folding is the closing and opening of a base pair. Understanding this elementary rate process is the basis for RNA folding kinetics studies. Previous studies mostly focused on the unfolding of base pairs. Here, based on a hybrid approach, we investigate the folding process at level of single base pairing/stacking. The study, which integrates molecular dynamics simulation, kinetic Monte Carlo simulation, and master equation methods, uncovers two alternative dominant pathways: Starting from the unfolded state, the nucleotide backbone first folds to the native conformation, followed by subsequent adjustment of the base conformation. During the base conformational rearrangement, the backbone either retains the native conformation or switches to nonnative conformations in order to lower the kinetic barrier for base rearrangement. The method enables quantification of kinetic partitioning among the different pathways. Moreover, the simulation reveals several intriguing ion binding/dissociation signatures for the conformational changes. Our approach may be useful for developing a base pair opening/closing rate model.

Free energy landscape and multiple folding pathways of an H-type RNA pseudoknot

How RNA sequences fold to specific tertiary structures is one of the key problems for understanding their dynamics and functions. Here, we study the folding process of an H-type RNA pseudoknot by performing a large-scale all-atom MD simulation and bias-exchange metadynamics. The folding free energy landscapes are obtained and several folding intermediates are identified. It is suggested that the folding occurs via multiple mechanisms, including a step-wise mechanism starting either from the first helix or the second, and a cooperative mechanism with both helices forming simultaneously. Despite of the multiple mechanism nature, the ensemble folding kinetics estimated from a Markov state model is single-exponential. It is also found that the correlation between folding and binding of metal ions is significant, and the bound ions mediate long-range interactions in the intermediate structures. Non-native interactions are found to be dominant in the unfolded state and also present in some intermediates, possibly hinder the folding process of the RNA.

Thermodynamic and kinetic folding of riboswitches

Riboswitches are structured RNA regulatory elements located in the 5'-UTRs of mRNAs. Ligand-binding induces a structural rearrangement in these RNA elements, effecting events in downstream located coding sequences. Since they do not require proteins for their functions, they are ideally suited for computational analysis using the toolbox of RNA structure prediction methods. By their very definition riboswitch function depends on structural change. Methods that consider only the thermodynamic equilibrium of an RNA are therefore of limited use. Instead, one needs to employ computationally more expensive methods that consider the energy landscape and the folding dynamics on that landscape. Moreover, for the important class of kinetic riboswitches, the mechanism of riboswitch function can only be understood in the context of co-transcriptional folding. We present a computational approach to simulate the dynamic behavior of riboswitches during co-transcriptional folding in the presence and absence of a ligand. Our investigations show that the abstraction level of RNA secondary structure in combination with a dynamic folding landscape approach is expressive enough to understand how riboswitches perform their function. We apply our approach to a experimentally validated theophylline-binding riboswitch.

RNA folding: structure prediction, folding kinetics and ion electrostatics

Beyond the "traditional" functions such as gene storage, transport and protein synthesis, recent discoveries reveal that RNAs have important "new" biological functions including the RNA silence and gene regulation of riboswitch. Such functions of noncoding RNAs are strongly coupled to the RNA structures and proper structure change, which naturally leads to the RNA folding problem including structure prediction and folding kinetics. Due to the polyanionic nature of RNAs, RNA folding structure, stability and kinetics are strongly coupled to the ion condition of solution. The main focus of this chapter is to review the recent progress in the three major aspects in RNA folding problem: structure prediction, folding kinetics and ion electrostatics. This chapter will introduce both the recent experimental and theoretical progress, while emphasize the theoretical modelling on the three aspects in RNA folding.

Dual-selection for evolution of in vivo functional aptazymes as riboswitch parts

Both synthetic biology and metabolic engineering are aided by the development of genetic control parts. One class of riboswitch parts that has great potential for sensing and regulation of protein levels is aptamer-coupled ribozymes (aptazymes). These devices are comprised of an aptamer domain selected to bind a particular ligand, a ribozyme domain, and a communication module that regulates the ribozyme activity based on the state of the aptamer. We describe a broadly applicable method for coupling a novel, newly selected aptamer to a ribozyme to generate functional aptazymes via in vitro and in vivo selection. To illustrate this approach, we describe experimental procedures for selecting aptazymes assembled from aptamers that bind p-amino-phenylalanine and a hammerhead ribozyme. Because this method uses selection, it does not rely on sequence-specific design and thus should be generalizable for the generation of in vivo operational aptazymes that respond to any targeted molecules.

Basin Hopping Graph: a computational framework to characterize RNA folding landscapes

MOTIVATION

RNA folding is a complicated kinetic process. The minimum free energy structure provides only a static view of the most stable conformational state of the system. It is insufficient to give detailed insights into the dynamic behavior of RNAs. A sufficiently sophisticated analysis of the folding free energy landscape, however, can provide the relevant information.

RESULTS

We introduce the Basin Hopping Graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect basins when the direct transitions between them are 'energetically favorable'. Edge weights endcode the corresponding saddle heights and thus measure the difficulties of these favorable transitions. BHGs can be approximated accurately and efficiently for RNA molecules well beyond the length range accessible to enumerative algorithms.

AVAILABILITY AND IMPLEMENTATION

The algorithms described here are implemented in C++ as standalone programs. Its source code and supplemental material can be freely downloaded from http://www.tbi.univie.ac.at/bhg.html.

Molecular crowders and cosolutes promote folding cooperativity of RNA under physiological ionic conditions

Folding mechanisms of functional RNAs under idealized in vitro conditions of dilute solution and high ionic strength have been well studied. Comparatively little is known, however, about mechanisms for folding of RNA in vivo where Mg(2+) ion concentrations are low, K(+) concentrations are modest, and concentrations of macromolecular crowders and low-molecular-weight cosolutes are high. Herein, we apply a combination of biophysical and structure mapping techniques to tRNA to elucidate thermodynamic and functional principles that govern RNA folding under in vivo-like conditions. We show by thermal denaturation and SHAPE studies that tRNA folding cooperativity increases in physiologically low concentrations of Mg(2+) (0.5-2 mM) and K(+) (140 mM) if the solution is supplemented with physiological amounts (∼ 20%) of a water-soluble neutral macromolecular crowding agent such as PEG or dextran. Low-molecular-weight cosolutes show varying effects on tRNA folding cooperativity, increasing or decreasing it based on the identity of the cosolute. For those additives that increase folding cooperativity, the gain is manifested in sharpened two-state-like folding transitions for full-length tRNA over its secondary structural elements. Temperature-dependent SHAPE experiments in the absence and presence of crowders and cosolutes reveal extent of cooperative folding of tRNA on a nucleotide basis and are consistent with the melting studies. Mechanistically, crowding agents appear to promote cooperativity by stabilizing tertiary structure, while those low molecular cosolutes that promote cooperativity stabilize tertiary structure and/or destabilize secondary structure. Cooperative folding of functional RNA under physiological-like conditions parallels the behavior of many proteins and has implications for cellular RNA folding kinetics and evolution.

Energy-directed RNA structure prediction

In this chapter we present the classic dynamic programming algorithms for RNA structure prediction by energy minimization, as well as variations of this approach that allow to compute suboptimal foldings, or even the partition function over all possible secondary structures. The latter are essential in order to deal with the inaccuracy of minimum free energy (MFE) structure prediction, and can be used, for example, to derive reliability measures that assign a confidence value to all or part of a predicted structure. In addition, we discuss recently proposed alternatives to the MFE criterion such as the use of maximum expected accuracy (MEA) or centroid structures. The dynamic programming algorithms implicitly assume that the RNA molecule is in thermodynamic equilibrium. However, especially for long RNAs, this need not be the case. In the last section we therefore discuss approaches for predicting RNA folding kinetics and co-transcriptional folding.

Differences between cotranscriptional and free riboswitch folding

Riboswitches are part of noncoding regions of messenger RNA (mRNA) that act as RNA sensors regulating gene expression of the downstream gene. Typically, one out of two distinct conformations is formed depending on ligand binding when the transcript leaves RNA polymerase (RNAP). Elongation of the RNA chain by RNAP, folding and binding all occurs simultaneously and interdependently on the seconds' timescale. To investigate the effect of transcript elongation velocity on folding for the S-adenosylmethionine (SAM)-I and adenine riboswitches we employ two complementary coarse-grained in silico techniques. Native structure-based molecular dynamics simulations provide a 3D, atomically resolved model of folding with homogenous energetics. Energetically more detailed kinetic Monte Carlo simulations give access to longer timescale by describing folding on the secondary structure level and feature the incorporation of competing aptamer conformations and a ligand-binding model. Depending on the extrusion scenarios, we observe and quantify different pathways in structure formation with robust agreements between the two techniques. In these scenarios, free-folding riboswitches exhibit different folding characteristics compared with transcription-rate limited folding. The critical transcription rate distinguishing these cases is higher than physiologically relevant rates. This result suggests that in vivo folding of the analyzed SAM-I and adenine riboswitches is transcription-rate limited.

On the importance of cotranscriptional RNA structure formation

The expression of genes, both coding and noncoding, can be significantly influenced by RNA structural features of their corresponding transcripts. There is by now mounting experimental and some theoretical evidence that structure formation in vivo starts during transcription and that this cotranscriptional folding determines the functional RNA structural features that are being formed. Several decades of research in bioinformatics have resulted in a wide range of computational methods for predicting RNA secondary structures. Almost all state-of-the-art methods in terms of prediction accuracy, however, completely ignore the process of structure formation and focus exclusively on the final RNA structure. This review hopes to bridge this gap. We summarize the existing evidence for cotranscriptional folding and then review the different, currently used strategies for RNA secondary-structure prediction. Finally, we propose a range of ideas on how state-of-the-art methods could be potentially improved by explicitly capturing the process of cotranscriptional structure formation.

Kinetic Monte Carlo approach to RNA folding dynamics using structure-based models

RNA molecules form three-dimensional structures via base pairing that determine the function and biochemical activity of the molecule. Here we introduce a structure-based method for studying the folding dynamics of RNA secondary structures. The approach focuses on native contacts that are parametrized with standard empirical free energies. Kinetic Monte Carlo simulations for free folding of simple hairpins and complex structures such as a tRNA as well as for folding in the presence of an external force show good agreement with experimental data. A systematic comparison of simulated and experimental folding rates for various structures shows a strong correlation, indicating that the approach can predict folding rates within about an order of magnitude.

Transient RNA structure features are evolutionarily conserved and can be computationally predicted

Functional RNA structures tend to be conserved during evolution. This finding is, for example, exploited by comparative methods for RNA secondary structure prediction that currently provide the state-of-art in terms of prediction accuracy. We here provide strong evidence that homologous RNA genes not only fold into similar final RNA structures, but that their folding pathways also share common transient structural features that have been evolutionarily conserved. For this, we compile and investigate a non-redundant data set of 32 sequences with known transient and final RNA secondary structures and devise a dedicated computational analysis pipeline.

Visualizing RNA base-pairing probabilities with RNAbow diagrams

There are many effective ways to represent a minimum free energy RNA secondary structure that make it easy to locate its helices and loops. It is a greater challenge to visualize the thermal average probabilities of all folds in a partition function sum; dot plot representations are often puzzling. Therefore, we introduce the RNAbows visualization tool for RNA base pair probabilities. RNAbows represent base pair probabilities with line thickness and shading, yielding intuitive diagrams. RNAbows aid in disentangling incompatible structures, allow comparisons between clusters of folds, highlight differences between wild-type and mutant folds, and are also rather beautiful.

COFOLD: an RNA secondary structure prediction method that takes co-transcriptional folding into account

Existing state-of-the-art methods that take a single RNA sequence and predict the corresponding RNA secondary structure are thermodynamic methods. These aim to predict the most stable RNA structure. There exists by now ample experimental and theoretical evidence that the process of structure formation matters and that sequences in vivo fold while they are being transcribed. None of the thermodynamic methods, however, consider the process of structure formation. Here, we present a conceptually new method for predicting RNA secondary structure, called CoFold, that takes effects of co-transcriptional folding explicitly into account. Our method significantly improves the state-of-art in terms of prediction accuracy, especially for long sequences of >1000 nt in length.