Kinetic and thermodynamic framework for P4-P6 RNA reveals tertiary motif modularity and modulation of the folding preferred pathway

Influence of Magnesium Ions and Crowding Agents on Structure and Stability of RNA Aptamers

Aptamers bind to their targets with exceptional affinity and specificity. However, their intracellular application is hampered by the lack of knowledge about the effect of the cellular milieu on the RNA structure/stability. In this study, cellular crowding was mimicked using polyethylene glycol (PEG), and the crucial role of Mg2+ ions in stabilizing the structure of an RNA aptamer was investigated. Increasing the concentration of Mg2+ or PEG increased the thermal stability of the aptamer. The crowding effect lowered the requirement of the Mg2+ ion to form the binding-competent conformer of the aptamer. This suggests that crowding and other factors may compensate for a lower concentration of Mg2+ for proper folding of aptamers inside cells. Selective 2'-hydroxyl acylation and primer extension (SHAPE) probing permitted residue-level analysis of the aptamer. Mg2+ and/or PEG were shown to be involved in increasing the rigidity or flexibility of different regions of the aptamer. Fluorescence correlation spectroscopy showed a significantly low hydrodynamic radius (RH) in the presence of molecular crowders and Mg2+ ions. We believe that the decreased water activity due to crowding may be responsible for reduced RH. Our results show that in a crowded environment, the RNA aptamer was exposed to conformers that were not available to it in simple buffer solutions or solely in the presence of lower concentrations of Mg2+.

Impact of Ion-Mixing Entropy on Orientational Preferences of DNA Helices: FRET Measurements and Computer Simulations

Biological processes require DNA and RNA helices to pack together in specific interhelical orientations. While electrostatic repulsion between backbone charges is expected to be maximized when helices are in parallel alignment, such orientations are commonplace in nature. To better understand how the repulsion is overcome, we used experimental and computational approaches to investigate how the orientational preferences of DNA helices depend on the concentration and valence of mobile cations. We used Förster resonance energy transfer (FRET) to probe the relative orientations of two 24-bp helices held together via a freely rotating PEG linker. At low cation concentrations, the helices preferred more "cross"-like orientations over those closer to parallel, and this preference was reduced with increasing salt concentrations. The results were in good quantitative agreement with Poisson-Boltzmann (PB) calculations for monovalent salt (Na+). However, PB underestimated the ability of mixtures of monovalent and divalent ions (Mg2+) to reduce the conformational preference. As a complementary approach, we performed all-atom molecular dynamics (MD) simulations and found better agreement with the experimental results. While MD and PB predict similar electrostatic forces, MD predicts a greater accumulation of Mg2+ in the ion atmosphere surrounding the DNA. Mg2+ occupancy is predicted to be greater in conformations close to the parallel orientation than in conformations close to the crossed orientation, enabling a greater release of Na+ ions and providing an entropic gain (one bound ion for two released). MD predicts an entropy gain larger than that of PB because of the increased Mg2+ occupancy. The entropy changes have a negligible effect at low Mg2+ concentrations because the free energies are dominated by electrostatic repulsion. However, as the Mg2+ concentration increases, charge screening is more effective and the mixing entropy produces readily detectable changes in packing preferences. Our results underline the importance of mixing entropy of counterions in nucleic acid interactions and provide a new understanding on the impact of a mixed ion atmosphere on the packing of DNA helices.

RNA 3D Modeling with FARFAR2, Online

Understanding the three-dimensional structure of an RNA molecule is often essential to understanding its function. Sampling algorithms and energy functions for RNA structure prediction are improving, due to the increasing diversity of structural data available for training statistical potentials and testing structural data, along with a steady supply of blind challenges through the RNA-Puzzles initiative. The recent FARFAR2 algorithm enables near-native structure predictions on fairly complex RNA structures, including automated selection of final candidate models and estimation of model accuracy. Here, we describe the use of a publicly available webserver for RNA modeling for realistic scenarios using FARFAR2, available at https://rosie.rosettacommons.org/farfar2 . We walk through two cases in some detail: a simple model pseudoknot from the frameshifting element of beet western yellows virus modeled using the "basic interface" to the webserver and a replication of RNA-Puzzle 20, a metagenomic twister sister ribozyme, using the "advanced interface." We also describe example runs of FARFAR2 modeling including two kinds of experimental data: a c-di-GMP riboswitch modeled with low-resolution restraints from MOHCA-seq experiments and a tandem GA motif modeled with 1H NMR chemical shifts.

Measurement of the specific and non-specific binding energies of Mg2+ to RNA

Determining the non-specific and specific electrostatic contributions of magnesium binding to RNA is a challenging problem. We introduce a single-molecule method based on measuring the folding energy of a native RNA in magnesium and at its equivalent sodium concentration. The latter is defined so that the folding energy in sodium equals the non-specific electrostatic contribution in magnesium. The sodium equivalent can be estimated according to the empirical 100/1 rule (1 M NaCl is equivalent to 10 mM MgCl2), which is a good approximation for most RNAs. The method is applied to an RNA three-way junction (3WJ) that contains specific Mg2+ binding sites and misfolds into a double hairpin structure without binding sites. We mechanically pull the RNA with optical tweezers and use fluctuation theorems to determine the folding energies of the native and misfolded structures in magnesium (10 mM MgCl2) and at the equivalent sodium condition (1 M NaCl). While the free energies of the misfolded structure are equal in magnesium and sodium, they are not for the native structure, the difference being due to the specific binding energy of magnesium to the 3WJ, which equals ΔG≃ 10 kcal/mol. Besides stabilizing the 3WJ, Mg2+ also kinetically rescues it from the misfolded structure over timescales of tens of seconds in a force-dependent manner. The method should generally be applicable to determine the specific binding energies of divalent cations to other tertiary RNAs.

Combining Coarse-Grained Simulations and Single Molecule Analysis Reveals a Three-State Folding Model of the Guanidine-II Riboswitch

Riboswitch RNAs regulate gene expression by conformational changes induced by environmental conditions and specific ligand binding. The guanidine-II riboswitch is proposed to bind the small molecule guanidinium and to subsequently form a kissing loop interaction between the P1 and P2 hairpins. While an interaction was shown for isolated hairpins in crystallization and electron paramagnetic resonance experiments, an intrastrand kissing loop formation has not been demonstrated. Here, we report the first evidence of this interaction in cis in a ligand and Mg²⁺ dependent manner. Using single-molecule FRET spectroscopy and detailed structural information from coarse-grained simulations, we observe and characterize three interconvertible states representing an open and kissing loop conformation as well as a novel Mg²⁺ dependent state for the guanidine-II riboswitch from E. coli. The results further substantiate the proposed switching mechanism and provide detailed insight into the regulation mechanism for the guanidine-II riboswitch class. Combining single molecule experiments and coarse-grained simulations therefore provides a promising perspective in resolving the conformational changes induced by environmental conditions and to yield molecular insights into RNA regulation.

FRETraj: Integrating single-molecule spectroscopy with molecular dynamics

SUMMARY

Quantitative interpretation of single-molecule FRET experiments requires a model of the dye dynamics to link experimental energy transfer efficiencies to distances between atom positions. We have developed FRETraj, a Python module to predict FRET distributions based on accessible-contact volumes (ACV) and simulated photon statistics. FRETraj helps to identify optimal fluorophore positions on a biomolecule of interest by rapidly evaluating donor-acceptor distances. FRETraj is scalable and fully integrated into PyMOL and the Jupyter ecosystem. Here we describe the conformational dynamics of a DNA hairpin by computing multiple ACVs along a molecular dynamics trajectory and compare the predicted FRET distribution with single-molecule experiments. FRET-assisted modeling will accelerate the analysis of structural ensembles in particular dynamic, non-coding RNAs and transient protein-nucleic acid complexes.

AVAILABILITY

FRETraj is implemented as a cross-platform Python package available under the GPL-3.0 on Github (https://github.com/RNA-FRETools/fretraj) and is documented at https://RNA-FRETools.github.io/fretraj.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

High-throughput dissection of the thermodynamic and conformational properties of a ubiquitous class of RNA tertiary contact motifs

Despite RNA's diverse secondary and tertiary structures and its complex conformational changes, nature utilizes a limited set of structural "motifs"-helices, junctions, and tertiary contact modules-to build diverse functional RNAs. Thus, in-depth descriptions of a relatively small universe of RNA motifs may lead to predictive models of RNA tertiary conformational landscapes. Motifs may have different properties depending on sequence and secondary structure, giving rise to subclasses that expand the universe of RNA building blocks. Yet we know very little about motif subclasses, given the challenges in mapping conformational properties in high throughput. Previously, we used "RNA on a massively parallel array" (RNA-MaP), a quantitative, high-throughput technique, to study thousands of helices and two-way junctions. Here, we adapt RNA-MaP to study the thermodynamic and conformational properties of tetraloop/tetraloop receptor (TL/TLR) tertiary contact motifs, analyzing 1,493 TLR sequences from different classes. Clustering analyses revealed variability in TL specificity, stability, and conformational behavior. Nevertheless, natural GAAA/11ntR TL/TLRs, while varying in tertiary stability by ∼2.5 kcal/mol, exhibited conserved TL specificity and conformational properties. Thus, RNAs may tune stability without altering the overall structure of these TL/TLRs. Furthermore, their stability correlated with natural frequency, suggesting thermodynamics as the dominant selection pressure. In contrast, other TL/TLRs displayed heterogenous conformational behavior and appear to not be under strong thermodynamic selection. Our results build toward a generalizable model of RNA-folding thermodynamics based on the properties of isolated motifs, and our characterized TL/TLR library can be used to engineer RNAs with predictable thermodynamic and conformational behavior.

Cooperativity and Allostery in RNA Systems

Allostery is among the most basic biological principles employed by biological macromolecules to achieve a biologically active state in response to chemical cues. Although initially used to describe the impact of small molecules on the conformation and activity of protein enzymes, the definition of this term has been significantly broadened to describe long-range conformational change of macromolecules in response to small or large effectors. Such a broad definition could be applied to RNA molecules, which do not typically serve as protein-free cellular enzymes but fold and form macromolecular assemblies with the help of various ligand molecules, including ions and proteins. Ligand-induced allosteric changes in RNA molecules are often accompanied by cooperative interactions between RNA and its ligand, thus streamlining the folding and assembly pathways. This chapter provides an overview of the interplay between cooperativity and allostery in RNA systems and outlines methods to study these two biological principles.

The roles of structural dynamics in the cellular functions of RNAs

RNAs fold into 3D structures that range from simple helical elements to complex tertiary structures and quaternary ribonucleoprotein assemblies. The functions of many regulatory RNAs depend on how their 3D structure changes in response to a diverse array of cellular conditions. In this Review, we examine how the structural characterization of RNA as dynamic ensembles of conformations, which form with different probabilities and at different timescales, is improving our understanding of RNA function in cells. We discuss the mechanisms of gene regulation by microRNAs, riboswitches, ribozymes, post-transcriptional RNA modifications and RNA-binding proteins, and how the cellular environment and processes such as liquid-liquid phase separation may affect RNA folding and activity. The emerging RNA-ensemble-function paradigm is changing our perspective and understanding of RNA regulation, from in vitro to in vivo and from descriptive to predictive.

Magnesium controls aptamer-expression platform switching in the SAM-I riboswitch

Investigations of most riboswitches remain confined to the ligand-binding aptamer domain. However, during the riboswitch mediated transcription regulation process, the aptamer domain and the expression platform compete for a shared strand. If the expression platform dominates, an anti-terminator helix is formed, and the transcription process is active (ON state). When the aptamer dominates, transcription is terminated (OFF state). Here, we use an expression platform switching experimental assay and structure-based electrostatic simulations to investigate this ON-OFF transition of the full length SAM-I riboswitch and its magnesium concentration dependence. Interestingly, we find the ratio of the OFF population to the ON population to vary non-monotonically as magnesium concentration increases. Upon addition of magnesium, the aptamer domain pre-organizes, populating the OFF state, but only up to an intermediate magnesium concentration level. Higher magnesium concentration preferentially stabilizes the anti-terminator helix, populating the ON state, relatively destabilizing the OFF state. Magnesium mediated aptamer-expression platform domain closure explains this relative destabilization of the OFF state at higher magnesium concentration. Our study reveals the functional potential of magnesium in controlling transcription of its downstream genes and underscores the importance of a narrow concentration regime near the physiological magnesium concentration ranges, striking a balance between the OFF and ON states in bacterial gene regulation.

Hidden Structural Modules in a Cooperative RNA Folding Transition

Large-scale, cooperative rearrangements underlie the functions of RNA in RNA-protein machines and gene regulation. To understand how such rearrangements are orchestrated, we used high-throughput chemical footprinting to dissect a seemingly concerted rearrangement in P5abc RNA, a paradigm of RNA folding studies. With mutations that systematically disrupt or restore putative structural elements, we found that this transition reflects local folding of structural modules, with modest and incremental cooperativity that results in concerted behavior. First, two distant secondary structure changes are coupled through a bridging three-way junction and Mg²⁺-dependent tertiary structure. Second, long-range contacts are formed between modules, resulting in additional cooperativity. Given the sparseness of RNA tertiary contacts after secondary structure formation, we expect that modular folding and incremental cooperativity are generally important for specifying functional structures while also providing productive kinetic paths to these structures. Additionally, we expect our approach to be useful for uncovering modularity in other complex RNAs.

How the Conformations of an Internal Junction Contribute to Fold an RNA Domain

Like proteins, some RNAs fold to compact structures. We can model functional RNAs as a series of short, rigid, base-paired elements, connected by non-base-paired nucleotides that serve as junctions. These connecting regions bend and twist, facilitating the formation of tertiary contacts that stabilize compact states. Here, we explore the roles of salt and junction sequence in determining the structures of a ubiquitous connector: an asymmetric internal loop. We focus on the J5/5a junction from the widely studied P4-P6 domain of the Tetrahymena ribozyme. Following the addition of magnesium ions to fold P4-P6, this junction bends dramatically, bringing the two halves of the RNA domain together for tertiary contact engagement. Using single-molecule fluorescence resonance energy transfer (smFRET), we examine the role of sequence and salt on model RNA constructs that contain these junction regions. We explore the wild-type J5/5a junction as well as two sequence variants. These junctions display distinct, salt-dependent conformations. Small-angle X-ray scattering (SAXS) measurements verify that these effects persist in the full-length P4-P6 domain. These measurements underscore the importance of junction sequence and interactions with ions in facilitating RNA folding.

The Story of RNA Folding, as Told in Epochs

The past decades have witnessed tremendous developments in our understanding of RNA biology. At the core of these advances have been studies aimed at discerning RNA structure and at understanding the forces that influence the RNA folding process. It is easy to take the present state of understanding for granted, but there is much to be learned by considering the path to our current understanding, which has been tortuous, with the birth and death of models, the adaptation of experimental tools originally developed for characterization of protein structure and catalysis, and the development of novel tools for probing RNA. In this review we tour the stages of RNA folding studies, considering them as "epochs" that can be generalized across scientific disciplines. These epochs span from the discovery of catalytic RNA, through biophysical insights into the putative primordial RNA World, to characterization of structured RNAs, the building and testing of models, and, finally, to the development of models with the potential to yield generalizable predictive and quantitative models for RNA conformational, thermodynamic, and kinetic behavior. We hope that this accounting will aid others as they navigate the many fascinating questions about RNA and its roles in biology, in the past, present, and future.

Revealing the distinct folding phases of an RNA three-helix junction

Remarkable new insight has emerged into the biological role of RNA in cells. RNA folding and dynamics enable many of these newly discovered functions, calling for an understanding of RNA self-assembly and conformational dynamics. Because RNAs pass through multiple structures as they fold, an ensemble perspective is required to visualize the flow through fleetingly populated sets of states. Here, we combine microfluidic mixing technology and small angle X-ray scattering (SAXS) to measure the Mg-induced folding of a small RNA domain, the tP5abc three helix junction. Our measurements are interpreted using ensemble optimization to select atomically detailed structures that recapitulate each experimental curve. Structural ensembles, derived at key stages in both time-resolved studies and equilibrium titrations, reproduce the features of known intermediates, and more importantly, offer a powerful new structural perspective on the time-progression of folding. Distinct collapse phases along the pathway appear to be orchestrated by specific interactions with Mg ions. These key interactions subsequently direct motions of the backbone that position the partners of tertiary contacts for later bonding, and demonstrate a remarkable synergy between Mg and RNA across numerous time-scales.

Single-Molecule Fluorescence Reveals Commonalities and Distinctions among Natural and in Vitro-Selected RNA Tertiary Motifs in a Multistep Folding Pathway

Decades of study of the RNA folding problem have revealed that diverse and complex structured RNAs are built from a common set of recurring structural motifs, leading to the perspective that a generalizable model of RNA folding may be developed from understanding of the folding properties of individual structural motifs. We used single-molecule fluorescence to dissect the kinetic and thermodynamic properties of a set of variants of a common tertiary structural motif, the tetraloop/tetraloop-receptor (TL/TLR). Our results revealed a multistep TL/TLR folding pathway in which preorganization of the ubiquitous AA-platform submotif precedes the formation of the docking transition state and tertiary A-minor hydrogen bond interactions form after the docking transition state. Differences in ion dependences between TL/TLR variants indicated the occurrence of sequence-dependent conformational rearrangements prior to and after the formation of the docking transition state. Nevertheless, varying the junction connecting the TL/TLR produced a common kinetic and ionic effect for all variants, suggesting that the global conformational search and compaction electrostatics are energetically independent from the formation of the tertiary motif contacts. We also found that in vitro-selected variants, despite their similar stability at high Mg²⁺ concentrations, are considerably less stable than natural variants under near-physiological ionic conditions, and the occurrence of the TL/TLR sequence variants in Nature correlates with their thermodynamic stability in isolation. Overall, our findings are consistent with modular but complex energetic properties of RNA structural motifs and will aid in the eventual quantitative description of RNA folding from its secondary and tertiary structural elements.

Quantitative tests of a reconstitution model for RNA folding thermodynamics and kinetics

Decades of study of the architecture and function of structured RNAs have led to the perspective that RNA tertiary structure is modular, made of locally stable domains that retain their structure across RNAs. We formalize a hypothesis inspired by this modularity-that RNA folding thermodynamics and kinetics can be quantitatively predicted from separable energetic contributions of the individual components of a complex RNA. This reconstitution hypothesis considers RNA tertiary folding in terms of ΔG_align, the probability of aligning tertiary contact partners, and ΔG_tert, the favorable energetic contribution from the formation of tertiary contacts in an aligned state. This hypothesis predicts that changes in the alignment of tertiary contacts from different connecting helices and junctions (ΔG_HJH) or from changes in the electrostatic environment (ΔG_+/-) will not affect the energetic perturbation from a mutation in a tertiary contact (ΔΔG_tert). Consistent with these predictions, single-molecule FRET measurements of folding of model RNAs revealed constant ΔΔG_tert values for mutations in a tertiary contact embedded in different structural contexts and under different electrostatic conditions. The kinetic effects of these mutations provide further support for modular behavior of RNA elements and suggest that tertiary mutations may be used to identify rate-limiting steps and dissect folding and assembly pathways for complex RNAs. Overall, our model and results are foundational for a predictive understanding of RNA folding that will allow manipulation of RNA folding thermodynamics and kinetics. Conversely, the approaches herein can identify cases where an independent, additive model cannot be applied and so require additional investigation.

A magnesium-induced triplex pre-organizes the SAM-II riboswitch

Our 13C- and 1H-chemical exchange saturation transfer (CEST) experiments previously revealed a dynamic exchange between partially closed and open conformations of the SAM-II riboswitch in the absence of ligand. Here, all-atom structure-based molecular simulations, with the electrostatic effects of Manning counter-ion condensation and explicit magnesium ions are employed to calculate the folding free energy landscape of the SAM-II riboswitch. We use this analysis to predict that magnesium ions remodel the landscape, shifting the equilibrium away from the extended, partially unfolded state towards a compact, pre-organized conformation that resembles the ligand-bound state. Our CEST and SAXS experiments, at different magnesium ion concentrations, quantitatively confirm our simulation results, demonstrating that magnesium ions induce collapse and pre-organization. Agreement between theory and experiment bolsters microscopic interpretation of our simulations, which shows that triplex formation between helix P2b and loop L1 is highly sensitive to magnesium and plays a key role in pre-organization. Pre-organization of the SAM-II riboswitch allows rapid detection of ligand with high selectivity, which is important for biological function.