RNA folding energy landscapes

Inferring phase transitions and critical exponents from limited observations with thermodynamic maps

Phase transitions are ubiquitous across life, yet hard to quantify and describe accurately. In this work, we develop an approach for characterizing generic attributes of phase transitions from very limited observations made deep within different phases' domains of stability. Our approach is called thermodynamic maps (TM), which combines statistical mechanics and molecular simulations with score-based generative models. TM enable learning the temperature dependence of arbitrary thermodynamic observables across a wide range of temperatures. We show its usefulness by calculating phase transition attributes such as melting temperature, temperature-dependent heat capacities, and critical exponents. For instance, we demonstrate the ability of TM to infer the ferromagnetic phase transition of the Ising model, including temperature-dependent heat capacity and critical exponents, despite never having seen samples from the transition region. In addition, we efficiently characterize the temperature-dependent conformational ensemble and compute melting curves of the two RNA systems: a GCAA tetraloop and the HIV-TAR RNA, which are notoriously hard to sample due to glassy-like energy landscapes.

Universal cold RNA phase transitions

RNA's diversity of structures and functions impacts all life forms since primordia. We use calorimetric force spectroscopy to investigate RNA folding landscapes in previously unexplored low-temperature conditions. We find that Watson-Crick RNA hairpins, the most basic secondary structure elements, undergo a glass-like transition below [Formula: see text]C where the heat capacity abruptly changes and the RNA folds into a diversity of misfolded structures. We hypothesize that an altered RNA biochemistry, determined by sequence-independent ribose-water interactions, outweighs sequence-dependent base pairing. The ubiquitous ribose-water interactions lead to universal RNA phase transitions below TG, such as maximum stability at [Formula: see text]C where water density is maximum, and cold denaturation at [Formula: see text]C. RNA cold biochemistry may have a profound impact on RNA function and evolution.

Origins of Life: The Protein Folding Problem all over again?

How did specific useful protein sequences arise from simpler molecules at the origin of life? This seemingly needle-in-a-haystack problem has remarkably close resemblance to the old Protein Folding Problem, for which the solution is now known from statistical physics. Based on the logic that Origins must have come only after there was an operative evolution mechanism-which selects on phenotype, not genotype-we give a perspective that proteins and their folding processes are likely to have been the primary driver of the early stages of the origin of life.

Charge transport in individual short base stacked single-stranded RNA molecules

Charge transport in biomolecules is crucial for many biological and technological applications, including biomolecular electronics devices and biosensors. RNA has become the focus of research because of its importance in biomedicine, but its charge transport properties are not well understood. Here, we use the Scanning Tunneling Microscopy-assisted molecular break junction method to measure the electrical conductance of particular 5-base and 10-base single-stranded (ss) RNA sequences capable of base stacking. These ssRNA sequences show single-molecule conductance values around [Formula: see text] ([Formula: see text]), while equivalent-length ssDNAs result in featureless conductance histograms. Circular dichroism (CD) spectra and MD simulations reveal the existence of extended ssRNA conformations versus folded ssDNA conformations, consistent with their different electrical behaviors. Computational molecular modeling and Machine Learning-assisted interpretation of CD data helped us to disentangle the structural and electronic factors underlying CT, thus explaining the observed electrical behavior differences. RNA with a measurable conductance corresponds to sequences with overall extended base-stacking stabilized conformations characterized by lower HOMO energy levels delocalized over a base-stacking mediating CT pathway. In contrast, DNA and a control RNA sequence without significant base-stacking tend to form closed structures and thus are incapable of efficient CT.

Nonequilibrium Theoretical Framework and Universal Design Principles of Oscillation-Driven Catalysis

At stationary environmental conditions, a catalyst's reaction kinetics may be restricted by its available designs and thermodynamic laws. Thus, its stationary performances may experience practical or theoretical restraints (e.g., catalysts cannot invert the spontaneous direction of a chemical reaction). However, many works have reported that if environments change rapidly, catalysts can be driven away from stationary states and exhibit anomalous performance. We present a general geometric nonequilibrium theory to explain anomalous catalytic behaviors driven by rapidly oscillating environments where stationary-environment restraints are broken. It leads to a universal design principle of novel catalysts with oscillation-pumped performances. Even though a single free energy landscape cannot describe catalytic kinetics at various environmental conditions, we propose a novel control-conjugate landscape to encode the reaction kinetics over a range of control parameters λ, inspired by the Arrhenius form. The control-conjugate landscape significantly simplifies the design principle applicable to large-amplitude environmental oscillations.

Origins of life: first came evolutionary dynamics

When life arose from prebiotic molecules 3.5 billion years ago, what came first? Informational molecules (RNA, DNA), functional ones (proteins), or something else? We argue here for a different logic: rather than seeking a molecule type, we seek a dynamical process. Biology required an ability to evolve before it could choose and optimise materials. We hypothesise that the evolution process was rooted in the peptide folding process. Modelling shows how short random peptides can collapse in water and catalyse the elongation of others, powering both increased folding stability and emergent autocatalysis through a disorder-to-order process.

Characterizing the Conformational Free-Energy Landscape of RNA Stem-Loops Using Single-Molecule Field-Effect Transistors

We have developed and used single-molecule field-effect transistors (smFETs) to characterize the conformational free-energy landscape of RNA stem-loops. Stem-loops are one of the most common RNA structural motifs and serve as building blocks for the formation of complex RNA structures. Given their prevalence and integral role in RNA folding, the kinetics of stem-loop (un)folding has been extensively characterized using both experimental and computational approaches. Interestingly, these studies have reported vastly disparate timescales of (un)folding, which has been interpreted as evidence that (un)folding of even simple stem-loops occurs on a highly rugged conformational energy landscape. Because smFETs do not rely on fluorophore reporters of conformation or mechanical (un)folding forces, they provide a unique approach that has allowed us to directly monitor tens of thousands of (un)folding events of individual stem-loops at a 200 μs time resolution. Our results show that under our experimental conditions, stem-loops (un)fold over a 1-200 ms timescale during which they transition between ensembles of unfolded and folded conformations, the latter of which is composed of at least two sub-populations. The 1-200 ms timescale of (un)folding we observe here indicates that smFETs report on complete (un)folding trajectories in which unfolded conformations of the RNA spend long periods of time wandering the free-energy landscape before sampling one of several misfolded conformations or the natively folded conformation. Our findings highlight the extremely rugged landscape on which even the simplest RNA structural elements fold and demonstrate that smFETs are a unique and powerful approach for characterizing the conformational free-energy of RNA.

Computationally-guided design and selection of high performing ribosomal active site mutants

Understanding how modifications to the ribosome affect function has implications for studying ribosome biogenesis, building minimal cells, and repurposing ribosomes for synthetic biology. However, efforts to design sequence-modified ribosomes have been limited because point mutations in the ribosomal RNA (rRNA), especially in the catalytic active site (peptidyl transferase center; PTC), are often functionally detrimental. Moreover, methods for directed evolution of rRNA are constrained by practical considerations (e.g. library size). Here, to address these limitations, we developed a computational rRNA design approach for screening guided libraries of mutant ribosomes. Our method includes in silico library design and selection using a Rosetta stepwise Monte Carlo method (SWM), library construction and in vitro testing of combined ribosomal assembly and translation activity, and functional characterization in vivo. As a model, we apply our method to making modified ribosomes with mutant PTCs. We engineer ribosomes with as many as 30 mutations in their PTCs, highlighting previously unidentified epistatic interactions, and show that SWM helps identify sequences with beneficial phenotypes as compared to random library sequences. We further demonstrate that some variants improve cell growth in vivo, relative to wild type ribosomes. We anticipate that SWM design and selection may serve as a powerful tool for rRNA engineering.

Computer Aided Development of Nucleic Acid Applications in Nanotechnologies

Utilization of nucleic acids (NAs) in nanotechnologies and nanotechnology-related applications is a growing field with broad application potential, ranging from biosensing up to targeted cell delivery. Computer simulations are useful techniques that can aid design and speed up development in this field. This review focuses on computer simulations of hybrid nanomaterials composed of NAs and other components. Current state-of-the-art molecular dynamics simulations, empirical force fields (FFs), and coarse-grained approaches for the description of deoxyribonucleic acid and ribonucleic acid are critically discussed. Challenges in combining biomacromolecular and nanomaterial FFs are emphasized. Recent applications of simulations for modeling NAs and their interactions with nano- and biomaterials are overviewed in the fields of sensing applications, targeted delivery, and NA templated materials. Future perspectives of development are also highlighted.

Nucleic Acid Thermodynamics Derived from Mechanical Unzipping Experiments

Force-spectroscopy techniques have led to significant progress in studying the physicochemical properties of biomolecules that are not accessible in bulk assays. The application of piconewton forces with laser optical tweezers to single nucleic acids has permitted the characterization of molecular thermodynamics and kinetics with unprecedented accuracy. Some examples are the hybridization reaction between complementary strands in DNA and the folding of secondary, tertiary, and other heterogeneous structures, such as intermediate and misfolded states in RNA. Here we review the results obtained in our lab on deriving the nearest-neighbor free energy parameters in DNA and RNA duplexes from mechanical unzipping experiments. Remarkable nonequilibrium effects are also observed, such as the large irreversibility of RNA unzipping and the formation of non-specific secondary structures in single-stranded DNA. These features originate from forming stem-loop structures along the single strands of the nucleic acid. The recently introduced barrier energy landscape model quantifies kinetic trapping effects due to stem-loops being applicable to both RNA and DNA. The barrier energy landscape model contains the essential features to explain the many behaviors observed in heterogeneous nucleic-acid folding.

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.

Designing strategies of small-molecule compounds for modulating non-coding RNAs in cancer therapy

Non-coding RNAs (ncRNAs) have been defined as a class of RNA molecules transcribed from the genome but not encoding proteins, such as microRNAs, long non-coding RNAs, Circular RNAs, and Piwi-interacting RNAs. Accumulating evidence has recently been revealing that ncRNAs become potential druggable targets for regulation of several small-molecule compounds, based on their complex spatial structures and biological functions in cancer therapy. Thus, in this review, we focus on summarizing some new emerging designing strategies, such as high-throughput screening approach, small-molecule microarray approach, structure-based designing approach, phenotypic screening approach, fragment-based designing approach, and pharmacological validation approach. Based on the above-mentioned approaches, a series of representative small-molecule compounds, including Bisphenol-A, Mitoxantrone and Enoxacin have been demonstrated to modulate or selectively target ncRNAs in different types of human cancers. Collectively, these inspiring findings would provide a clue on developing more novel avenues for pharmacological modulations of ncRNAs with small-molecule drugs for future cancer therapeutics.

The Energy Landscape Perspective: Encoding Structure and Function for Biomolecules

The energy landscape perspective is outlined with particular reference to biomolecules that perform multiple functions. We associate these multifunctional molecules with multifunnel energy landscapes, illustrated by some selected examples, where understanding the organisation of the landscape has provided new insight into function. Conformational selection and induced fit may provide alternative routes to realisation of multifunctionality, exploiting the possibility of environmental control and distinct binding modes.

Stem-loop formation drives RNA folding in mechanical unzipping experiments

Accurate knowledge of RNA hybridization is essential for understanding RNA structure and function. Here we mechanically unzip and rezip a 2-kbp RNA hairpin and derive the 10 nearest-neighbor base pair (NNBP) RNA free energies in sodium and magnesium with 0.1 kcal/mol precision using optical tweezers. Notably, force-distance curves (FDCs) exhibit strong irreversible effects with hysteresis and several intermediates, precluding the extraction of the NNBP energies with currently available methods. The combination of a suitable RNA synthesis with a tailored pulling protocol allowed us to obtain the fully reversible FDCs necessary to derive the NNBP energies. We demonstrate the equivalence of sodium and magnesium free-energy salt corrections at the level of individual NNBP. To characterize the irreversibility of the unzipping-rezipping process, we introduce a barrier energy landscape of the stem-loop structures forming along the complementary strands, which compete against the formation of the native hairpin. This landscape correlates with the hysteresis observed along the FDCs. RNA sequence analysis shows that base stacking and base pairing stabilize the stem-loops that kinetically trap the long-lived intermediates observed in the FDC. Stem-loops formation appears as a general mechanism to explain a wide range of behaviors observed in RNA folding.

Enhanced Ribozyme-Catalyzed Recombination and Oligonucleotide Assembly in Peptide-RNA Condensates

The ability of RNA to catalyze RNA ligation is critical to its central role in many prebiotic model scenarios, in particular the copying of information during self-replication. Prebiotically plausible ribozymes formed from short oligonucleotides can catalyze reversible RNA cleavage and ligation reactions, but harsh conditions or unusual scenarios are often required to promote folding and drive the reaction equilibrium towards ligation. Here, we demonstrate that ribozyme activity is greatly enhanced by charge-mediated phase separation with poly-L-lysine, which shifts the reaction equilibrium from cleavage in solution to ligation in peptide-RNA coaggregates and coacervates. This compartmentalization enables robust isothermal RNA assembly over a broad range of conditions, which can be leveraged to assemble long and complex RNAs from short fragments under mild conditions in the absence of exogenous activation chemistry, bridging the gap between pools of short oligomers and functional RNAs.

Kinetics of protein-assisted nucleic acid interconversion monitored by transient time resolved fluorescence in microfluidic droplets

Interconversions between nucleic acid structures play an important role in transcriptional and translational regulation and also in repair and recombination. These interconversions are frequently promoted by nucleic acid chaperone proteins. To monitor their kinetics, Förster resonance energy transfer (FRET) is widely exploited using ensemble fluorescence intensity measurements in pre-steady-state stopped-flow experiments. Such experiments only provide a weighted average of the emission of all species in solution and consume large quantities of materials. Herein, we lift these limitations by combining time-resolved fluorescence (TRF) with droplet microfluidics (DmF). We validate the innovative TRF-DmF approach by investigating the well characterized annealing of the HIV-1 (+)/(–) Primer Binding Sequences (PBS) promoted by a HIV-1 nucleocapsid peptide. Upon rapid mixing of the FRET-labelled (–)PBS with its complementary (+)PBS sequence inside microdroplets, the TRF-DmF set-up enables resolving the time evolution of sub-populations of reacting species and reveals an early intermediate with a ∼50 ps donor fluorescence lifetime never identified so far. TRF-DmF also favorably compares with single molecule experiments, as it offers an accurate control of concentrations with no upper limit, no need to graft one partner on a surface and no photobleaching issues.

Designing of RNA Molecule Translating for Activitable Melittin as Selective Targeting of Leishmania Infected Cells

Background

Leishmaniasis is characterized by strong inflammatory responses with high levels of inflammatory cytokines that induce microRNA 21 and matrix metalloproteinases. Melittin has inhibitory effects on proliferation of various cells via induction of apoptosis. Melittin can be integrated in cell membranes and induce apoptosis. Thus, designation of biomolecules for the selective destroy of the infected cells is a treatment option. One approach is the precise engineering of constructs for the selective expression of melittin in the infected cells.

Methods

For this aim we designed a construct composing melittin nucleotide sequence and nucleotide sequence coding for polyanionic peptide function inhibitory element to further guarantee the selective function of melittin in inflamed tissues and infected cells, were included in a construct as melittin inhibitor via matrix metalloproteinase degradable linker.

Results

Reverse complementary sequences were designed so melittin sequences for the selective targeting of Leishmania could be expressed in infected cells using cell microRNA machinery.

Conclusion

Translation machinery in infected cells with increased miR-21 could translate melittin, MMP linker and polyanionic inhibitor through a non-canonical pathway. Then, the MMP linker is degraded and selective killing of Leishmania infected cells would happen.

Lattice protein design using Bayesian learning

Protein design is the inverse approach of the three-dimensional (3D) structure prediction for elucidating the relationship between the 3D structures and amino acid sequences. In general, the computation of the protein design involves a double loop: A loop for amino acid sequence changes and a loop for an exhaustive conformational search for each amino acid sequence. Herein, we propose a novel statistical mechanical design method using Bayesian learning, which can design lattice proteins without the exhaustive conformational search. We consider a thermodynamic hypothesis of the evolution of proteins and apply it to the prior distribution of amino acid sequences. Furthermore, we take the water effect into account in view of the grand canonical picture. As a result, on applying the 2D lattice hydrophobic-polar (HP) model, our design method successfully finds an amino acid sequence for which the target conformation has a unique ground state. However, the performance was not as good for the 3D lattice HP models compared to the 2D models. The performance of the 3D model improves on using a 20-letter lattice proteins. Furthermore, we find a strong linearity between the chemical potential of water and the number of surface residues, thereby revealing the relationship between protein structure and the effect of water molecules. The advantage of our method is that it greatly reduces computation time, because it does not require long calculations for the partition function corresponding to an exhaustive conformational search. As our method uses a general form of Bayesian learning and statistical mechanics and is not limited to lattice proteins, the results presented here elucidate some heuristics used successfully in previous protein design methods.

RNA Modeling with the Computational Energy Landscape Framework

The recent advances in computational abilities, such as the enormous speed-ups provided by GPU computing, allow for large scale computational studies of RNA molecules at an atomic level of detail. As RNA molecules are known to adopt multiple conformations with comparable energies, but different two-dimensional structures, all-atom models are necessary to better describe the structural ensembles for RNA molecules. This point is important because different conformations can exhibit different functions, and their regulation or mis-regulation is linked to a number of diseases. Problematically, the energy barriers between different conformational ensembles are high, resulting in long time scales for interensemble transitions. The computational potential energy landscape framework was designed to overcome this problem of broken ergodicity by use of geometry optimization. Here, we describe the algorithms used in the energy landscape explorations with the OPTIM and PATHSAMPLE programs, and how they are used in biomolecular simulations. We present a recent case study of the 5'-hairpin of RNA 7SK to illustrate how the method can be applied to interpret experimental results, and to obtain a detailed description of molecular properties.

Engineering Crystal Packing in RNA Structures I: Past and Future Strategies for Engineering RNA Packing in Crystals

X-ray crystallography remains a powerful method to gain atomistic insights into the catalytic and regulatory functions of RNA molecules. However, the technique requires the preparation of diffraction-quality crystals. This is often a resource- and time-consuming venture because RNA crystallization is hindered by the conformational heterogeneity of RNA, as well as the limited opportunities for stereospecific intermolecular interactions between RNA molecules. The limited success at crystallization explains in part the smaller number of RNA-only structures in the Protein Data Bank. Several approaches have been developed to aid the formation of well-ordered RNA crystals. The majority of these are construct-engineering techniques that aim to introduce crystal contacts to favor the formation of well-diffracting crystals. A typical example is the insertion of tetraloop-tetraloop receptor pairs into non-essential RNA segments to promote intermolecular association. Other methods of promoting crystallization involve chaperones and crystallization-friendly molecules that increase RNA stability and improve crystal packing. In this review, we discuss the various techniques that have been successfully used to facilitate crystal packing of RNA molecules, recent advances in construct engineering, and directions for future research in this vital aspect of RNA crystallography.

Targeting RNA with small molecules: from fundamental principles towards the clinic

Recent advances in our understanding of RNA biology have uncovered crucial roles for RNA in multiple disease states, ranging from viral and bacterial infections to cancer and neurological disorders. As a result, multiple laboratories have become interested in developing drug-like small molecules to target RNA. However, this development comes with multiple unique challenges. For example, RNA is inherently dynamic and has limited chemical diversity. In addition, promiscuous RNA-binding ligands are often identified during screening campaigns. This Tutorial Review overviews important considerations and advancements for generating RNA-targeted small molecules, ranging from fundamental chemistry to promising small molecule examples with demonstrated clinical efficacy. Specifically, we begin by exploring RNA functional classes, structural hierarchy, and dynamics. We then discuss fundamental RNA recognition principles along with methods for small molecule screening and RNA structure determination. Finally, we review unique challenges and emerging solutions from both the RNA and small molecule perspectives for generating RNA-targeted ligands before highlighting a selection of the "Greatest Hits" to date. These molecules target RNA in a variety of diseases, including cancer, neurodegeneration, and viral infection, in cellular and animal model systems. Additionally, we explore the recently FDA-approved small molecule regulator of RNA splicing, risdiplam, for treatment of spinal muscular atrophy. Together, this Tutorial Review showcases the fundamental role of chemical and molecular recognition principles in enhancing our understanding of RNA biology and contributing to the rapidly growing number of RNA-targeted probes and therapeutics. In particular, we hope this widely accessible review will serve as inspiration for aspiring small molecule and/or RNA researchers.

Computationally reconstructing cotranscriptional RNA folding from experimental data reveals rearrangement of non-native folding intermediates

The series of RNA folding events that occur during transcription can critically influence cellular RNA function. Here, we present reconstructing RNA dynamics from data (R2D2), a method to uncover details of cotranscriptional RNA folding. We model the folding of the Escherichia coli signal recognition particle (SRP) RNA and show that it requires specific local structural fluctuations within a key hairpin to engender efficient cotranscriptional conformational rearrangement into the functional structure. All-atom molecular dynamics simulations suggest that this rearrangement proceeds through an internal toehold-mediated strand-displacement mechanism, which can be disrupted with a point mutation that limits local structural fluctuations and rescued with compensating mutations that restore these fluctuations. Moreover, a cotranscriptional folding intermediate could be cleaved in vitro by recombinant E. coli RNase P, suggesting potential cotranscriptional processing. These results from experiment-guided multi-scale modeling demonstrate that even an RNA with a simple functional structure can undergo complex folding and processing during synthesis.

Transcriptional Riboswitches Integrate Timescales for Bacterial Gene Expression Control

Transcriptional riboswitches involve RNA aptamers that are typically found in the 5' untranslated regions (UTRs) of bacterial mRNAs and form alternative secondary structures upon binding to cognate ligands. Alteration of the riboswitch's secondary structure results in perturbations of an adjacent expression platform that controls transcription elongation and termination, thus turning downstream gene expression "on" or "off." Riboswitch ligands are typically small metabolites, divalent cations, anions, signaling molecules, or other RNAs, and can be part of larger signaling cascades. The interconnectedness of ligand binding, RNA folding, RNA transcription, and gene expression empowers riboswitches to integrate cellular processes and environmental conditions across multiple timescales. For a successful response to an environmental cue that may determine a bacterium's chance of survival, a coordinated coupling of timescales from microseconds to minutes must be achieved. This review focuses on recent advances in our understanding of how riboswitches affect such critical gene expression control across time.

Requirements for efficient ligand-gated co-transcriptional switching in designed variants of the B. subtilis pbuE adenine-responsive riboswitch in E. coli

Riboswitches, generally located in the 5'-leader of bacterial mRNAs, direct expression via a small molecule-dependent structural switch that informs the transcriptional or translational machinery. While the structure and function of riboswitch effector-binding (aptamer) domains have been intensely studied, only recently have the requirements for efficient linkage between small molecule binding and the structural switch in the cellular and co-transcriptional context begun to be actively explored. To address this aspect of riboswitch function, we have performed a structure-guided mutagenic analysis of the B. subtilis pbuE adenine-responsive riboswitch, one of the simplest riboswitches that employs a strand displacement switching mechanism to regulate transcription. Using a cell-based fluorescent protein reporter assay to assess ligand-dependent regulatory activity in E. coli, these studies revealed previously unrecognized features of the riboswitch. Within the aptamer domain, local and long-range conformational dynamics influenced by sequences within helices have a significant effect upon efficient regulatory switching. Sequence features of the expression platform including the pre-aptamer leader sequence, a toehold helix and an RNA polymerase pause site all serve to promote strong ligand-dependent regulation. By optimizing these features, we were able to improve the performance of the B. subtilis pbuE riboswitch in E. coli from 5.6-fold induction of reporter gene expression by the wild type riboswitch to over 120-fold in the top performing designed variant. Together, these data point to sequence and structural features distributed throughout the riboswitch required to strike a balance between rates of ligand binding, transcription and secondary structural switching via a strand exchange mechanism and yield new insights into the design of artificial riboswitches.

Modeling Loop Composition and Ion Concentration Effects in RNA Hairpin Folding Stability

The ability to accurately predict RNA hairpin structure and stability for different loop sequences and salt conditions is important for understanding, modeling, and designing larger RNA folds. However, traditional RNA secondary structure models cannot treat loop-sequence and ionic effects on RNA hairpin folding. Here, we describe a general, three-dimensional (3D) conformation-based computational method for modeling salt concentration-dependent conformational distributions and the detailed 3D structures for a set of three RNA hairpins that contain a variable, 15-nucleotide loop sequence. For a given RNA sequence, the new, to our knowledge, method integrates a Vfold2D two-dimensional structure folding model with IsRNA coarse-grained molecular dynamics 3D folding simulations and Monte Carlo tightly bound ion estimations of ion-mediated electrostatic interactions. The model predicts free-energy landscapes for the different RNA hairpin-forming sequences with variable salt conditions. The theoretically predicted results agree with the experimental fluorescence measurements, validating the strategy. Furthermore, the theoretical model goes beyond the experimental results by enabling in-depth 3D structural analysis, revealing energetic mechanisms for the sequence- and salt-dependent folding stability. Although the computational framework presented here is developed for RNA hairpin systems, the general method may be applied to investigate other RNA systems, such as multiway junctions or pseudoknots in mixed metal ion solutions.

Finding the direct optimal RNA barrier energy and improving pathways with an arbitrary energy model

Motivation

RNA folding kinetics plays an important role in the biological functions of RNA molecules. An important goal in the investigation of the kinetic behavior of RNAs is to find the folding pathway with the lowest energy barrier. For this purpose, most of the existing methods use heuristics because the number of possible pathways is huge even if only the shortest (direct) folding pathways are considered.

Results

In this study, we propose a new method using a best-first search strategy to efficiently compute the exact solution of the minimum barrier energy of direct pathways. Using our method, we can find the exact direct pathways within a Hamming distance of 20, whereas the previous methods even miss the exact short pathways. Moreover, our method can be used to improve the pathways found by existing methods for exploring indirect pathways.

Availability and implementation

The source code and datasets created and used in this research are available at https://github.com/eukaryo/czno.

Supplementary information

Supplementary data are available at Bioinformatics online.

Energy Landscapes of Deoxyxylo- and Xylo-Nucleic Acid Octamers

Artificial analogues of the natural nucleic acids have attracted interest as a diverse class of information storage molecules capable of self-replication. In this study, we use the computational potential energy landscape framework to investigate the structural and dynamical properties of xylo- and deoxyxylo-nucleic acids (XyNA and dXyNA), which are derived from their respective RNA and DNA analogues by inversion of a single chiral center in the sugar moiety of the nucleotides. For an octameric XyNA sequence and the analogue dXyNA, we observe facile conformational transitions between a left-handed helix, which is the free energy global minimum, and a ladder-type structure with approximately zero helicity. The competing ensembles are better separated in the dXyNA, making it a more suitable candidate for a molecular switch, whereas the XyNA exhibits additional flexibility. Both energy landscapes exhibit greater frustration than we observe in RNA or DNA, in agreement with the higher degree of optimization expected from the principle of minimal frustration in evolved biomolecules.

Nucleic Acid Catalysis under Potential Prebiotic Conditions

Catalysis by nucleic acids is indispensable for extant cellular life, and it is widely accepted that nucleic acid enzymes were crucial for the emergence of primitive life 3.5-4 billion years ago. However, geochemical conditions on early Earth must have differed greatly from the constant internal milieus of today's cells. In order to explore plausible scenarios for early molecular evolution, it is therefore essential to understand how different physicochemical parameters, such as temperature, pH, and ionic composition, influence nucleic acid catalysis and to explore to what extent nucleic acid enzymes can adapt to non-physiological conditions. In this article, we give an overview of the research on catalysis of nucleic acids, in particular catalytic RNAs (ribozymes) and DNAs (deoxyribozymes), under extreme and/or unusual conditions that may relate to prebiotic environments.

Kinetic Mechanism of RNA Helix-Terminal Basepairing-A Kinetic Minima Network Analysis

RNA functions are often kinetically controlled. The folding kinetics of RNAs involves global structural changes and local nucleotide movement, such as base flipping. The most elementary step in RNA folding is the closing and opening of a basepair. By integrating molecular dynamics simulation, master equation, and kinetic Monte Carlo simulation, we investigate the kinetics mechanism of RNA helix-terminal basepairing. The study reveals a six-state folding scheme with three dominant folding pathways of tens, hundreds, and thousands of nanoseconds of folding timescales, respectively. The overall kinetics is rate limited by the detrapping of a misfolded state with the overall folding time of 10^-5 s. Moreover, the analysis examines the different roles of the various driving forces, such as the basepairing and stacking interactions and the ion binding/dissociation effects on structural changes. The results may provide useful insights for developing a basepair opening/closing rate model and further kinetics models of large RNAs.

Limits in accuracy and a strategy of RNA structure prediction using experimental information

RNA structural complexity and flexibility present a challenge for computational modeling efforts. Experimental information and bioinformatics data can be used as restraints to improve the accuracy of RNA tertiary structure prediction. Regarding utilization of restraints, the fundamental questions are: (i) What is the limit in prediction accuracy that one can achieve with arbitrary number of restraints? (ii) Is there a strategy for selection of the minimal number of restraints that would result in the best structural model? We address the first question by testing the limits in prediction accuracy using native contacts as restraints. To address the second question, we develop an algorithm based on the distance variation allowed by secondary structure (DVASS), which ranks restraints according to their importance to RNA tertiary structure prediction. We find that due to kinetic traps, the greatest improvement in the structure prediction accuracy is achieved when we utilize only 40-60% of the total number of native contacts as restraints. When the restraints are sorted by DVASS algorithm, using only the first 20% ranked restraints can greatly improve the prediction accuracy. Our findings suggest that only a limited number of strategically selected distance restraints can significantly assist in RNA structure modeling.

Disordered RNA chaperones can enhance nucleic acid folding via local charge screening

RNA chaperones are proteins that aid in the folding of nucleic acids, but remarkably, many of these proteins are intrinsically disordered. How can these proteins function without a well-defined three-dimensional structure? Here, we address this question by studying the hepatitis C virus core protein, a chaperone that promotes viral genome dimerization. Using single-molecule fluorescence spectroscopy, we find that this positively charged disordered protein facilitates the formation of compact nucleic acid conformations by acting as a flexible macromolecular counterion that locally screens repulsive electrostatic interactions with an efficiency equivalent to molar salt concentrations. The resulting compaction can bias unfolded nucleic acids towards folding, resulting in faster folding kinetics. This potentially widespread mechanism is supported by molecular simulations that rationalize the experimental findings by describing the chaperone as an unstructured polyelectrolyte.

RNA chaperones, such as the hepatitic C virus (HCV) core protein, are proteins that aid in the folding of nucleic acids. Here authors use single‐molecule spectroscopy and simulation to show that the HCV core protein acts as a flexible macromolecular counterion which facilitates nucleic acid folding.

A two-dimensional replica-exchange molecular dynamics method for simulating RNA folding using sparse experimental restraints

We present a 2D replica exchange protocol incorporating secondary structure information to dramatically improve 3D RNA folding using molecular dynamics simulations. We show that incorporating base-pairing restraints into all-atom, explicit solvent simulations enables the accurate recapitulation of the global tertiary fold for 4 representative RNAs ranging in length from 24 to 68 nt. This method can potentially utilize base-pairing information from a wide variety of experimental inputs to predict complex RNA tertiary folds including pseudoknots, multi-loop junctions, and non-canonical interactions.

Compartmentalised RNA catalysis in membrane-free coacervate protocells

Phase separation of mixtures of oppositely charged polymers provides a simple and direct route to compartmentalisation via complex coacervation, which may have been important for driving primitive reactions as part of the RNA world hypothesis. However, to date, RNA catalysis has not been reconciled with coacervation. Here we demonstrate that RNA catalysis is viable within coacervate microdroplets and further show that these membrane-free droplets can selectively retain longer length RNAs while permitting transfer of lower molecular weight oligonucleotides.

Phase separation of mixtures of oppositely charged polymers provides a simple and direct route to compartmentalisation via coacervation. Here authors demonstrate that a coacervate microenvironment supports RNA catalysis whilst selectively sequestering RNA based on length.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Time-Resolved Small-Angle X-ray Scattering Reveals Millisecond Transitions of a DNA Origami Switch

Self-assembled DNA structures enable creation of specific shapes at the nanometer-micrometer scale with molecular resolution. The construction of functional DNA assemblies will likely require dynamic structures that can undergo controllable conformational changes. DNA devices based on shape complementary stacking interactions have been demonstrated to undergo reversible conformational changes triggered by changes in ionic environment or temperature. An experimentally unexplored aspect is how quickly conformational transitions of large synthetic DNA origami structures can actually occur. Here, we use time-resolved small-angle X-ray scattering to monitor large-scale conformational transitions of a two-state DNA origami switch in free solution. We show that the DNA device switches from its open to its closed conformation upon addition of MgCl₂ in milliseconds, which is close to the theoretical diffusive speed limit. In contrast, measurements of the dimerization of DNA origami bricks reveal much slower and concentration-dependent assembly kinetics. DNA brick dimerization occurs on a time scale of minutes to hours suggesting that the kinetics depend on local concentration and molecular alignment.

Predicting Ion Effects in an RNA Conformational Equilibrium

We develop a partial charge-based tightly bound ion (PCTBI) model for the ion effects in RNA folding. On the basis of the Monte Carlo tightly bound ion (MCTBI) approach, the model can account for ion fluctuation and correlation effects, and can predict the ion distribution around the RNA. Furthermore, unlike the previous coarse-grained RNA charge models, where negative charges are placed on the phosphates only, the current new model considers the detailed all-atom partial charge distribution on the RNA. Thus, the model not only keeps the advantage of the MCTBI model, but also has the potential to provide important detailed information unattainable by the previous MCTBI models. For example, the model predicts the reduction in ion binding upon protein binding and ion-induced conformational switches. For hepatitis C virus genomic RNA, the model predicts a Mg²⁺-induced stabilization of a kissing motif for a cis-acting regulatory element in the genomic RNA. Extensive theory-experiment comparisons support the reliability of the theoretical predictions. Therefore, the model may serve as a robust starting point for further development of an accurate method for ion effects in an RNA conformational equilibrium and RNA-cofactor interactions.

Contact Statistics Highlight Distinct Organizing Principles of Proteins and RNA

Although both RNA and proteins have densely packed native structures, chain organizations of these two biopolymers are fundamentally different. Motivated by the recent discoveries in chromatin folding that interphase chromosomes have territorial organization with signatures pointing to metastability, we analyzed the biomolecular structures deposited in the Protein Data Bank and found that the intrachain contact probabilities, P(s) as a function of the arc length s, decay in power-law ∼s(-γ) over the intermediate range of s, 10 ≲ s ≲ 110. We found that the contact probability scaling exponent is γ ≈ 1.11 for large RNA (N > 110), γ ≈ 1.41 for small-sized RNA (N < 110), and γ ≈ 1.65 for proteins. Given that Gaussian statistics is expected for a fully equilibrated chain in polymer melts, the deviation of γ-value from γ = 1.5 for the subchains of large RNA in the native state suggests that the chain configuration of RNA is not fully equilibrated. It is visually clear that folded structures of large-sized RNA (N ≳ 110) adopt crumpled structures, partitioned into modular multidomains assembled by proximal sequences along the chain, whereas the polypeptide chain of folded proteins looks better mixed with the rest of the structure. Our finding of γ ≈ 1 for large RNA might be an ineluctable consequence of the hierarchical ordering of the secondary to tertiary elements in the folding process.

Molecular simulations and Markov state modeling reveal the structural diversity and dynamics of a theophylline-binding RNA aptamer in its unbound state

RNA aptamers are oligonucleotides that bind with high specificity and affinity to target ligands. In the absence of bound ligand, secondary structures of RNA aptamers are generally stable, but single-stranded and loop regions, including ligand binding sites, lack defined structures and exist as ensembles of conformations. For example, the well-characterized theophylline-binding aptamer forms a highly stable binding site when bound to theophylline, but the binding site is unstable and disordered when theophylline is absent. Experimental methods have not revealed at atomic resolution the conformations that the theophylline aptamer explores in its unbound state. Consequently, in the present study we applied 21 microseconds of molecular dynamics simulations to structurally characterize the ensemble of conformations that the aptamer adopts in the absence of theophylline. Moreover, we apply Markov state modeling to predict the kinetics of transitions between unbound conformational states. Our simulation results agree with experimental observations that the theophylline binding site is found in many distinct binding-incompetent states and show that these states lack a binding pocket that can accommodate theophylline. The binding-incompetent states interconvert with binding-competent states through structural rearrangement of the binding site on the nanosecond to microsecond timescale. Moreover, we have simulated the complete theophylline binding pathway. Our binding simulations supplement prior experimental observations of slow theophylline binding kinetics by showing that the binding site must undergo a large conformational rearrangement after the aptamer and theophylline form an initial complex, most notably, a major rearrangement of the C27 base from a buried to solvent-exposed orientation. Theophylline appears to bind by a combination of conformational selection and induced fit mechanisms. Finally, our modeling indicates that when Mg²⁺ ions are present the population of binding-competent aptamer states increases more than twofold. This population change, rather than direct interactions between Mg²⁺ and theophylline, accounts for altered theophylline binding kinetics.

Fusing Sensor Paradigms to Acquire Chemical Information: An Integrative Role for Smart Biopolymeric Hydrogels

The Information Age transformed our lives but it has had surprisingly little impact on the way chemical information (e.g., from our biological world) is acquired, analyzed and communicated. Sensor systems are poised to change this situation by providing rapid access to chemical information. This access will be enabled by technological advances from various fields: biology enables the synthesis, design and discovery of molecular recognition elements as well as the generation of cell-based signal processors; physics and chemistry are providing nano-components that facilitate the transmission and transduction of signals rich with chemical information; microfabrication is yielding sensors capable of receiving these signals through various modalities; and signal processing analysis enhances the extraction of chemical information. The authors contend that integral to the development of functional sensor systems will be materials that (i) enable the integrative and hierarchical assembly of various sensing components (for chemical recognition and signal transduction) and (ii) facilitate meaningful communication across modalities. It is suggested that stimuli-responsive self-assembling biopolymers can perform such integrative functions, and redox provides modality-spanning communication capabilities. Recent progress toward the development of electrochemical sensors to manage schizophrenia is used to illustrate the opportunities and challenges for enlisting sensors for chemical information processing.

Sequence-Dependent Mechanism of DNA Oligonucleotide Dehybridization Resolved through Infrared Spectroscopy

Despite its important role in biology and nanotechnology, many questions remain regarding the molecular mechanism and dynamics by which oligonucleotides recognize and hybridize to their complementary sequence. The thermodynamics and kinetics of DNA oligonucleotide hybridization and dehybridization are often assumed to involve an all-or-nothing two-state dissociation pathway, but deviations from this behavior can be considerable even for short sequences. We introduce a new strategy to characterize the base-pair-specific thermal dissociation mechanism of DNA oligonucleotides through steady-state and time-resolved infrared spectroscopy. Experiments are interpreted with a lattice model to provide a structure-specific interpretation. This method is applied to a model set of self-complementary 10-base-pair sequences in which the placement of GC base pairs is varied in an otherwise AT strand. Through a combination of Fourier transform infrared and two-dimensional infrared spectroscopy, experiments reveal varying degrees of deviation from simple two-state behavior. As the temperature is increased, duplexes dissociate through a path in which the terminal bases fray, without any significant contribution from loop configurations. Transient temperature jump experiments reveal time scales of 70-100 ns for fraying and 10-30 μs for complete dissociation near the melting temperature. Whether or not frayed states are metastable intermediates or short-lived configurations during the full dissociation of the duplex is dictated by the nucleobase sequence.

Monte Carlo Tightly Bound Ion Model: Predicting Ion-Binding Properties of RNA with Ion Correlations and Fluctuations

Experiments have suggested that ion correlation and fluctuation effects can be potentially important for multivalent ions in RNA folding. However, most existing computational methods for the ion electrostatics in RNA folding tend to ignore these effects. The previously reported tightly bound ion (TBI) model can treat ion correlation and fluctuation but its applicability to biologically important RNAs is severely limited by the low computational efficiency. Here, on the basis of Monte Carlo sampling for the many-body ion distribution, we develop a new computational model, the Monte Carlo tightly bound ion (MCTBI) model, for ion-binding properties around an RNA. Because of an enhanced sampling algorithm for ion distribution, the model leads to a significant improvement in computational efficiency. For example, for a 160-nt RNA, the model causes a more than 10-fold increase in the computational efficiency, and the improvement in computational efficiency is more pronounced for larger systems. Furthermore, unlike the earlier model that describes ion distribution using the number of bound ions around each nucleotide, the current MCTBI model is based on the three-dimensional coordinates of the ions. The higher efficiency of the model allows us to treat the ion effects for medium to large RNA molecules, RNA-ligand complexes, and RNA-protein complexes. This new model together with proper RNA conformational sampling and the energetics model may serve as a starting point for further development for the ion effects in RNA folding and conformational changes and for large nucleic acid systems.

Salt contribution to the flexibility of single-stranded nucleic acid offinite length

Nucleic acids are negatively charged macromolecules and their structure properties are strongly coupled to metal ions in solutions. In this article, the salt effects on the flexibility of single-stranded (ss) nucleic acid chain ranging from 12 to 120 nucleotides are investigated systematically by the coarse-grained Monte Carlo simulations where the salt ions are considered explicitly and the ss chain is modeled with the virtual-bond structural model. Our calculations show that, the increase of ion concentration causes the structural collapse of ss chain and multivalent ions are much more efficient in causing such collapse, and both trivalent/small divalent ions can induce more compact state than a random relaxation state. We found that monovalent, divalent, and trivalent ions can all overcharge ss chain, and the dominating source for such overcharging changes from ion-exclusion-volume effect to ion Coulomb correlations. In addition, the predicted Na(+) and Mg(2+)-dependent persistence length l(p)'s of ss nucleic acid are in accordance with the available experimental data, and through systematic calculations, we obtained the empirical formulas for l(p) as a function of [Na(+)], [Mg(2+)] and chain length.

PSRna: Prediction of small RNA secondary structures based on reverse complementary folding method

Prediction of RNA secondary structures is an important problem in computational biology and bioinformatics, since RNA secondary structures are fundamental for functional analysis of RNA molecules. However, small RNA secondary structures are scarce and few algorithms have been specifically designed for predicting the secondary structures of small RNAs. Here we propose an algorithm named "PSRna" for predicting small-RNA secondary structures using reverse complementary folding and characteristic hairpin loops of small RNAs. Unlike traditional algorithms that usually generate multi-branch loops and 5[Formula: see text] end self-folding, PSRna first estimated the maximum number of base pairs of RNA secondary structures based on the dynamic programming algorithm and a path matrix is constructed at the same time. Second, the backtracking paths are extracted from the path matrix based on backtracking algorithm, and each backtracking path represents a secondary structure. To improve accuracy, the predicted RNA secondary structures are filtered based on their free energy, where only the secondary structure with the minimum free energy was identified as the candidate secondary structure. Our experiments on real data show that the proposed algorithm is superior to two popular methods, RNAfold and RNAstructure, in terms of sensitivity, specificity and Matthews correlation coefficient (MCC).

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.

An active site rearrangement within the Tetrahymena group I ribozyme releases nonproductive interactions and allows formation of catalytic interactions

Biological catalysis hinges on the precise structural integrity of an active site that binds and transforms its substrates and meeting this requirement presents a unique challenge for RNA enzymes. Functional RNAs, including ribozymes, fold into their active conformations within rugged energy landscapes that often contain misfolded conformers. Here we uncover and characterize one such "off-pathway" species within an active site after overall folding of the ribozyme is complete. The Tetrahymena group I ribozyme (E) catalyzes cleavage of an oligonucleotide substrate (S) by an exogenous guanosine (G) cofactor. We tested whether specific catalytic interactions with G are present in the preceding E•S•G and E•G ground-state complexes. We monitored interactions with G via the effects of 2'- and 3'-deoxy (-H) and -amino (-NH(2)) substitutions on G binding. These and prior results reveal that G is bound in an inactive configuration within E•G, with the nucleophilic 3'-OH making a nonproductive interaction with an active site metal ion termed MA and with the adjacent 2'-OH making no interaction. Upon S binding, a rearrangement occurs that allows both -OH groups to contact a different active site metal ion, termed M(C), to make what are likely to be their catalytic interactions. The reactive phosphoryl group on S promotes this change, presumably by repositioning the metal ions with respect to G. This conformational transition demonstrates local rearrangements within an otherwise folded RNA, underscoring RNA's difficulty in specifying a unique conformation and highlighting Nature's potential to use local transitions of RNA in complex function.

pH-Responsive Self-Assembly of Polysaccharide through a Rugged Energy Landscape

Self-assembling polysaccharides can form complex networks with structures and properties highly dependent on the sequence of triggering cues. Controlling the emergence of such networks provides an opportunity to create soft matter with unique features; however, it requires a detailed understanding of the subtle balance between the attractive and repulsive forces that drives the stimuli-induced self-assembly. Here we employ all-atom molecular dynamics simulations on the order of 100 ns to study the mechanisms of the pH-responsive gelation of the weakly basic aminopolysaccharide chitosan. We find that low pH induces a sharp transition from gel to soluble state, analogous to pH-dependent folding of proteins, while at neutral and high pH self-assembly occurs via a rugged energy landscape, reminiscent of RNA folding. A surprising role of salt is to lubricate the conformational search for the thermodynamically stable states. Although our simulations represent the early events in the self-assembly process of chitosan, which may take seconds or minutes to complete, the atomically detailed insights are consistent with recent experimental observations and provide a basis for understanding how environmental conditions modulate the structure and mechanical properties of the self-assembled polysaccharide systems. The ability to control structure and properties via modification of process conditions will aid in the technological efforts to create complex soft matter with applications ranging from bioelectronics to regenerative medicine.