Non-specific binding of Na+ and Mg2+ to RNA determined by force spectroscopy methods

Competitive Influence of Alkali Metals in the Ion Atmosphere on Nucleic Acid Duplex Stability

The nonspecific atmosphere around nucleic acids, often termed the ion atmosphere, encompasses a collection of weak ion-nucleic acid interactions. Although nonspecific, the ion atmosphere has been shown to influence nucleic acid folding and structural stability. Studies investigating the composition of the ion atmosphere have shown competitive occupancy of the atmosphere between metal ions in the same solution. Many studies have investigated single ion effects on nucleic acid secondary structure stability; however, no comprehensive studies have investigated how the competitive occupancy of mixed ions in the ion atmosphere influences nucleic acid secondary structure stability. Here, six oligonucleotides were optically melted in buffers containing molar quantities, or mixtures, of either XCl (X = Li, K, Rb, or Cs) or NaCl. A correction factor was developed to better predict RNA duplex stability in solutions containing mixed XCl/NaCl. For solutions containing a 1:1 mixture of XCl/NaCl, one alkali metal chloride contributed more to duplex stability than the other. Overall, there was a 54% improvement in predictive capabilities with the correction factor compared with the standard 1.0 M NaCl nearest-neighbor models. This correction factor can be used in models to better predict RNA secondary structure in solutions containing mixed XCl/NaCl.

Exploring the conformational dynamics of the SARS-CoV-2 SL4 hairpin by combining optical tweezers and base analogues

The parasitic nature of the SARS-CoV-2 virus demands selective packaging of its RNA genome (gRNA) from the abundance of other nucleic acids present in infected cells. Despite increasing evidence that stem-loop 4 (SL4) of the gRNA 5' UTR is involved in the initiation of this process by binding the nucleocapsid (N) protein, little is known about its conformational dynamics. Here, we unravel the stability, dynamics and (un)folding pathways of SL4 using optical tweezers and a base analogue, tCO, that provides a local and subtle increase in base stacking without perturbing hydrogen bonding. We find that SL4 (un)folds mainly in a single step or through an intermediate, encompassing nucleotides from the central U bulge to the hairpin loop. Due to an upper-stem CU mismatch, SL4 is prone to misfold, the extent of which can be tuned by incorporating tCO at different positions. Our study contributes to a better understanding of SARS-CoV-2 packaging and the design of drugs targeting SL4. We also highlight the generalizability of using base analogues in optical tweezers experiments for probing intramolecular states and conformational transitions of various nucleic acids at the level of single molecules and with base-pair resolution.

Watching ion-driven kinetics of ribozyme folding and misfolding caused by energetic and topological frustration one molecule at a time

Folding of ribozymes into well-defined tertiary structures usually requires divalent cations. How Mg2+ ions direct the folding kinetics has been a long-standing unsolved problem because experiments cannot detect the positions and dynamics of ions. To address this problem, we used molecular simulations to dissect the folding kinetics of the Azoarcus ribozyme by monitoring the path each molecule takes to reach the folded state. We quantitatively establish that Mg2+ binding to specific sites, coupled with counter-ion release of monovalent cations, stimulate the formation of secondary and tertiary structures, leading to diverse pathways that include direct rapid folding and trapping in misfolded structures. In some molecules, key tertiary structural elements form when Mg2+ ions bind to specific RNA sites at the earliest stages of the folding, leading to specific collapse and rapid folding. In others, the formation of non-native base pairs, whose rearrangement is needed to reach the folded state, is the rate-limiting step. Escape from energetic traps, driven by thermal fluctuations, occurs readily. In contrast, the transition to the native state from long-lived topologically trapped native-like metastable states is extremely slow. Specific collapse and formation of energetically or topologically frustrated states occur early in the assembly process.

A microfluidic electrophoretic dual dynamic staining method for the identification and relative quantitation of dsRNA contaminants in mRNA vaccines

mRNA vaccines (i.e., COVID-19 vaccine) offer various advantages over traditional vaccines in preventing and reducing disease and shortening the time between pathogen discovery and vaccine creation. Production of mRNA vaccines results in several nucleic acid and enzymatic by-products, most of which can be detected and removed; however, double-stranded RNA (dsRNA) contaminants pose a particular challenge. Current purification and detection platforms for dsRNA vary in effectiveness, with problems in scalability for mass mRNA vaccine production. Effectively detecting dsRNA is crucial in ensuring the safety and efficacy of the vaccines, as these strands can cause autoimmune reactions with length-symptom dependency and enhance mRNA degradation. We present a new microfluidics method to rapidly identify and quantify dsRNA fragments in mRNA samples. Our innovation exploits the differences in the dynamic staining behavior between mRNA and dsRNA molecules to detect dsRNA contaminants in a high throughput approach. The limit of detection of the system for dsRNA was estimated to be between 17.7-76.6 pg μL-1 with a maximum loading capacity of mRNA of 12.99 ng μL-1. Based on these estimated values, our method allows for the detection of dsRNA contaminants present in percentages as low as 0.14-0.59% compared to the total mRNA concentration. Here, we discuss the molecular mechanism of the dynamic staining behavior of dsRNA and mRNA for two different stains. We believe our method will accelerate the mRNA vaccine development from initial development to quality control workflows.

Thermodynamic determination of RNA duplex stability in magnesium solutions

The prediction of RNA secondary structure and thermodynamics from sequence relies on free energy minimization and nearest neighbor parameters. Currently, algorithms used to make these predictions are based on parameters from optical melting studies performed in 1 M NaCl. However, many physiological and biochemical buffers containing RNA include much lower concentrations of monovalent cations and the presence of divalent cations. In order to improve these algorithms, thermodynamic data was previously collected for RNA duplexes in solutions containing 71, 121, 221, and 621 mM Na+. From this data, correction factors for free energy (ΔG°37) and melting temperature (Tm) were derived. Despite these newly derived correction factors for sodium, the stabilizing effects of magnesium have been ignored. Here, the same RNA duplexes were melted in solutions containing 0.5, 1.5, 3.0, and 10.0 mM Mg2+ in the absence of monovalent cations. Correction factors for Tm and ΔG°37 were derived to scale the current parameters to a range of magnesium concentrations. The Tm correction factor predicts the melting temperature within 1.2°C, and the ΔG°37 correction factor predicts the free energy within 0.30 kcalmol. These newly derived magnesium correction factors can be incorporated into algorithms that predict RNA secondary structure and stability from sequence.

Unravelling How Single-Stranded DNA Binding Protein Coordinates DNA Metabolism Using Single-Molecule Approaches

Single-stranded DNA-binding proteins (SSBs) play vital roles in DNA metabolism. Proteins of the SSB family exclusively and transiently bind to ssDNA, preventing the DNA double helix from re-annealing and maintaining genome integrity. In the meantime, they interact and coordinate with various proteins vital for DNA replication, recombination, and repair. Although SSB is essential for DNA metabolism, proteins of the SSB family have been long described as accessory players, primarily due to their unclear dynamics and mechanistic interaction with DNA and its partners. Recently-developed single-molecule tools, together with biochemical ensemble techniques and structural methods, have enhanced our understanding of the different coordination roles that SSB plays during DNA metabolism. In this review, we discuss how single-molecule assays, such as optical tweezers, magnetic tweezers, Förster resonance energy transfer, and their combinations, have advanced our understanding of the binding dynamics of SSBs to ssDNA and their interaction with other proteins partners. We highlight the central coordination role that the SSB protein plays by directly modulating other proteins' activities, rather than as an accessory player. Many possible modes of SSB interaction with protein partners are discussed, which together provide a bigger picture of the interaction network shaped by SSB.

Temperature-dependent elastic properties of DNA

Knowledge of the elastic properties, e.g., the persistence length or interphosphate distance, of single-stranded (ss) and double-stranded (ds) DNA under different experimental conditions is critical to characterizing molecular reactions studied with single-molecule techniques. While previous experiments have addressed the dependence of the elastic parameters upon varying ionic strength and contour length, temperature-dependent effects are less studied. Here, we examine the temperature-dependent elasticity of ssDNA and dsDNA in the range 5°C-50°C using a temperature-jump optical trap. We find a temperature softening for dsDNA and a temperature stiffening for ssDNA. Our results highlight the need for a general theory explaining the phenomenology observed.

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.

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.

Folding Free Energy Determination of an RNA Three-Way Junction Using Fluctuation Theorems

Nonequilibrium work relations and fluctuation theorems permit us to extract equilibrium information from nonequilibrium measurements. They find application in single-molecule pulling experiments where molecular free energies can be determined from irreversible work measurements by using unidirectional (e.g., Jarzynski’s equality) and bidirectional (e.g., Crooks fluctuation theorem and Bennet’s acceptance ratio (BAR)) methods. However, irreversibility and the finite number of pulls limit their applicability: the higher the dissipation, the larger the number of pulls necessary to estimate ΔG within a few kBT. Here, we revisit pulling experiments on an RNA three-way junction (3WJ) that exhibits significant dissipation and work-distribution long tails upon mechanical unfolding. While bidirectional methods are more predictive, unidirectional methods are strongly biased. We also consider a cyclic protocol that combines the forward and reverse work values to increase the statistics of the measurements. For a fixed total experimental time, faster pulling rates permit us to efficiently sample rare events and reduce the bias, compensating for the increased dissipation. This analysis provides a more stringent test of the fluctuation theorem in the large irreversibility regime.

Force-Dependent Folding Kinetics of Single Molecules with Multiple Intermediates and Pathways

Most single-molecule studies derive the kinetic rates of native, intermediate, and unfolded states from equilibrium hopping experiments. Here, we apply the Kramers kinetic diffusive model to derive the force-dependent kinetic rates of intermediate states from nonequilibrium pulling experiments. From the kinetic rates, we also extract the force-dependent kinetic barriers and the equilibrium folding energies. We apply our method to DNA hairpins with multiple folding pathways and intermediates. The experimental results agree with theoretical predictions. Furthermore, the proposed nonequilibrium single-molecule approach permits us to characterize kinetic and thermodynamic properties of native, unfolded, and intermediate states that cannot be derived from equilibrium hopping experiments.

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.

Complex Conformational Dynamics of the Heart Failure-Associated Pre-miRNA-377 Hairpin Revealed by Single-Molecule Optical Tweezers

Pre-miRNA-377 is a hairpin-shaped regulatory RNA associated with heart failure. Here, we use single-molecule optical tweezers to unzip pre-miRNA-377 and study its stability and dynamics. We show that magnesium ions have a strong stabilizing effect, and that sodium ions stabilize the hairpin more than potassium ions. The hairpin unfolds in a single step, regardless of buffer composition. Interestingly, hairpin folding occurs either in a single step (type 1) or through the formation of intermediates, in multiple steps (type 2) or gradually (type 3). Type 3 occurs only in the presence of both sodium and magnesium, while type 1 and 2 take place in all buffers, with type 1 being the most prevalent. By reducing the size of the native hairpin loop from fourteen to four nucleotides, we demonstrate that the folding heterogeneity originates from the large size of the hairpin loop. Further, while efficient pre-miRNA-377 binders are lacking, we demonstrate that the recently developed C2 ligand displays bimodal activity: it enhances the mechanical stability of the pre-miRNA-377 hairpin and perturbs its folding. The knowledge regarding pre-miRNA stability and dynamics that we provide is important in understanding its regulatory function and how it can be modulated to achieve a therapeutic effect, e.g., in heart failure treatment.

A Synthetic Riboswitch to Regulate Haloarchaeal Gene Expression

In recent years, synthetic riboswitches have become increasingly important to construct genetic circuits in all three domains of life. In bacteria, synthetic translational riboswitches are often employed that modulate gene expression by masking the Shine-Dalgarno (SD) sequence in the absence or presence of a cognate ligand. For (halo-)archaeal translation, a SD sequence is not strictly required. The application of synthetic riboswitches in haloarchaea is therefore limited so far, also because of the molar intracellular salt concentrations found in these microbes. In this study, we applied synthetic theophylline-dependent translational riboswitches in the archaeon Haloferax volcanii. The riboswitch variants A through E and E^∗ were chosen since they not only mask the SD sequence but also the AUG start codon by forming a secondary structure in the absence of the ligand theophylline. Upon addition of the ligand, the ribosomal binding site and start codon become accessible for translation initiation. Riboswitch E mediated a dose-dependent, up to threefold activation of the bgaH reporter gene expression. Raising the salt concentration of the culture media from 3 to 4 M NaCl resulted in a 12-fold increase in the switching capacity of riboswitch E, and switching activity increased up to 26-fold when the cultivating temperature was reduced from 45 to 30°C. To construct a genetic circuit, riboswitch E was applied to regulate the synthesis of the transcriptional activator GvpE allowing a dose-dependent activation of the mgfp6 reporter gene under P _pA promoter control.

Salt dependent mesoscopic model for RNA at multiple strand concentrations

Mesoscopic models can be used for the description of the thermodynamic properties of RNA duplexes. With the use of experimental melting temperatures, its parametrization can provide important insights into its hydrogen bonds and stacking interactions as has been done for high sodium concentrations. However, the RNA parametrization for lower salt concentrations is still missing due to the limited amount of published melting temperature data. While the Peyrard-Bishop (PB) parametrization was found to be largely independent of strand concentrations, it requires that all temperatures are provided at the same strand concentrations. Here we adapted the PB model to handle multiple strand concentrations and in this way we were able to make use of an experimental set of temperatures to model the hydrogen bond and stacking interactions at low and intermediate sodium concentrations. For the parametrizations we make a distinction between terminal and internal base pairs, and the resulting potentials were qualitatively similar as we obtained previously for DNA. The main difference from DNA parameters, was the Morse potentials at low sodium concentrations for terminal r(AU) which is stronger than d(AT), suggesting higher hydrogen bond strength.

Stabilization of DNA by sodium and magnesium ions during the synthesis of DNA-bridged gold nanoparticles

Nanostructures synthesized using DNA-conjugated gold nanoparticles have a wide range of applications in the field of biosensorics. The stability of the DNA duplex plays a critical role as it determines the final geometry of these nanostructures. The main way to control DNA stability is to maintain a high ionic strength of the buffer solution; at the same time, high salt concentrations lead to an aggregation of nanoparticles. In this study, by means of the instrumentality of DNA-bridged seeds using tris(hydroxymethyl)aminomethane as a soft reducing agent the dumbbell-like gold nanoparticles up to 35 nm were synthesized with a high concentration of sodium ions of up to 100 mM and magnesium ions up to 1 mM. We also examined at the atomic level the details of the effect of the gold nanoparticle surface, as well as Na⁺ and Mg²⁺ ions, on the stability of nucleotide pairs located in close proximity to the grafting site.

Retarded Translocation of Nucleic Acids through α-Hemolysin Nanopore in the Presence of a Calcium Flux

Electrophysiological measurement of molecular translocation through a nanopore is the fundamental basis of nanopore sensing. Free translocation of nucleic acids however is normally so fast that the identities of the compounds are not clearly resolvable. Inspired by recent progress in fluorescence imaging based nanopore sensing, we found that during electrophysiology measurements, translocation of nucleic acids is also retarded whenever a calcium flux around the pore vicinity is established. The residence time of nucleic acids has been extended to tens of milliseconds, a result of the strong coupling between nucleic acids and free calcium ions. The methodology presented here is applicable to both DNAs and RNAs and is able to clearly discriminate between different RNA homopolymers. This offers new insights for calcium imaging based nanopore sensing and suggests a new strategy of electrophysiology-based nanopore sensing aimed at a retarded motion of nucleic acids.

Stability prediction of canonical and non-canonical structures of nucleic acids in various molecular environments and cells

This review provides the biophysicochemical background and recent advances in stability prediction of canonical and non-canonical structures of nucleic acids in various molecular environments and cells.

Visualizing Disordered Single-Stranded RNA: Connecting Sequence, Structure, and Electrostatics

Disordered homopolymeric regions of single-stranded RNA, such as U or A tracts, are found within functional RNAs where they play distinct roles in defining molecular structure and facilitating recognition by partners. Despite this prominence, details of conformational and biophysical properties of these regions have not yet been resolved. We apply a number of experimental techniques to investigate the conformations of these biologically important motifs and provide quantitative measurements of their ion atmospheres. Single strands of RNA display pronounced sequence-dependent conformations that relate to the unique ion atmospheres each attracts. Chains of rU bases are relatively unstructured under all conditions, while chains of rA bases display distinct ordering through stacking or clustering motifs, depending on the composition of the surrounding solution. These dramatic structural differences are consistent with the measured disparity in ion composition and atmospheres around each homopolymer, revealing a complex interplay of base, ion, and single-strand ordering. The unique structural and ionic signatures of homopolymer ssRNAs explains their role(s) in folding structured RNAs and may explain their distinct recognition by protein partners.

Theory and simulations for RNA folding in mixtures of monovalent and divalent cations

RNA molecules cannot fold in the absence of counterions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the reference interaction site model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial for an accurate calculation of RNA folding thermodynamics. The RISM theory for ion-phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to predict accurately the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the rRNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.

Structural accommodations accompanying splicing of a group II intron RNP

Group II introns, the putative progenitors of spliceosomal introns and retrotransposons, are ribozymes that are capable of self-splicing and DNA invasion. In the cell, group II introns form ribonucleoprotein (RNP) complexes with an intron-encoded protein, which is essential to folding, splicing and retromobility of the intron. To understand the structural accommodations underlying splicing, in preparation for retromobility, we probed the endogenously expressed Lactococcus lactis Ll.LtrB group II intron RNP using SHAPE. The results, which are consistent in vivo and in vitro, provide insights into the dynamics of the intron RNP as well as RNA-RNA and RNA-protein interactions. By comparing the excised intron RNP with mutant RNPs in the precursor state, confined SHAPE profile differences were observed, indicative of rearrangements at the active site as well as disengagement at the functional RNA-protein interface in transition between the two states. The exon-binding sequences in the intron RNA, which interact with the 5' exon and the target DNA, show increased flexibility after splicing. In contrast, stability of major tertiary and protein interactions maintains the scaffold of the RNA through the splicing transition, while the active site is realigned in preparation for retromobility.

Single-Molecule Mechanical Folding and Unfolding of RNA Hairpins: Effects of Single A-U to A·C Pair Substitutions and Single Proton Binding and Implications for mRNA Structure-Induced -1 Ribosomal Frameshifting

A wobble A·C pair can be protonated at near physiological pH to form a more stable wobble A⁺·C pair. Here, we constructed an RNA hairpin (rHP) and three mutants with one A-U base pair substituted with an A·C mismatch on the top (near the loop, U22C), middle (U25C), and bottom (U29C) positions of the stem, respectively. Our results on single-molecule mechanical (un)folding using optical tweezers reveal the destabilization effect of A-U to A·C pair substitution and protonation-dependent enhancement of mechanical stability facilitated through an increased folding rate, or decreased unfolding rate, or both. Our data show that protonation may occur rapidly upon the formation of an apparent mechanical folding transition state. Furthermore, we measured the bulk -1 ribosomal frameshifting efficiencies of the hairpins by a cell-free translation assay. For the mRNA hairpins studied, -1 frameshifting efficiency correlates with mechanical unfolding force at equilibrium and folding rate at around 15 pN. U29C has a frameshifting efficiency similar to that of rHP (∼2%). Accordingly, the bottom 2-4 base pairs of U29C may not form under a stretching force at pH 7.3, which is consistent with the fact that the bottom base pairs of the hairpins may be disrupted by ribosome at the slippery site. U22C and U25C have a similar frameshifting efficiency (∼1%), indicating that both unfolding and folding rates of an mRNA hairpin in a crowded environment may affect frameshifting. Our data indicate that mechanical (un)folding of RNA hairpins may mimic how mRNAs unfold and fold in the presence of translating ribosomes.

Single-Stranded Condensation Stochastically Blocks G-Quadruplex Assembly in Human Telomeric RNA

TERRA is an RNA molecule transcribed from human subtelomeric regions toward chromosome ends potentially involved in regulation of heterochromatin stability, semiconservative replication, and telomerase inhibition, among others. TERRA contains tandem repeats of the sequence GGGUUA, with a strong tendency to fold into a four-stranded arrangement known as a parallel G-quadruplex. Here, we demonstrate by using single-molecule force spectroscopy that this potential is limited by the inherent capacity of RNA to self-associate randomly and further condense into entropically more favorable structures. We stretched RNA constructions with more than four and less than eight hexanucleotide repeats, thus unable to form several G-quadruplexes in tandem, flanked by non-G-rich overhangs of random sequence by optical tweezers on a one by one basis. We found that condensed RNA stochastically blocks G-quadruplex folding pathways with a near 20% probability, a behavior that is not found in DNA analogous molecules.

Derivation of nearest-neighbor DNA parameters in magnesium from single molecule experiments

DNA hybridization is an essential molecular reaction in biology with many applications. The nearest-neighbor (NN) model for nucleic acids predicts DNA thermodynamics using energy values for the different base pair motifs. These values have been derived from melting experiments in monovalent and divalent salt and applied to predict melting temperatures of oligos within a few degrees. However, an improved determination of the NN energy values and their salt dependencies in magnesium is still needed for current biotechnological applications seeking high selectivity in the hybridization of synthetic DNAs. We developed a methodology based on single molecule unzipping experiments to derive accurate NN energy values and initiation factors for DNA. A new set of values in magnesium is derived, which reproduces unzipping data and improves melting temperature predictions for all available oligo lengths, in a range of temperature and salt conditions where correlation effects between the magnesium bound ions are weak. The NN salt correction parameters are shown to correlate to the GC content of the NN motifs. Our study shows the power of single-molecule force spectroscopy assays to unravel novel features of nucleic acids such as sequence-dependent salt corrections.

MCTBI: a web server for predicting metal ion effects in RNA structures

Metal ions play critical roles in RNA structure and function. However, web servers and software packages for predicting ion effects in RNA structures are notably scarce. Furthermore, the existing web servers and software packages mainly neglect ion correlation and fluctuation effects, which are potentially important for RNAs. We here report a new web server, the MCTBI server (http://rna.physics.missouri.edu/MCTBI), for the prediction of ion effects for RNA structures. This server is based on the recently developed MCTBI, a model that can account for ion correlation and fluctuation effects for nucleic acid structures and can provide improved predictions for the effects of metal ions, especially for multivalent ions such as Mg²⁺ effects, as shown by extensive theory-experiment test results. The MCTBI web server predicts metal ion binding fractions, the most probable bound ion distribution, the electrostatic free energy of the system, and the free energy components. The results provide mechanistic insights into the role of metal ions in RNA structure formation and folding stability, which is important for understanding RNA functions and the rational design of RNA structures.

Theory and Modeling of RNA Structure and Interactions with Metal Ions and Small Molecules

In addition to continuous rapid progress in RNA structure determination, probing, and biophysical studies, the past decade has seen remarkable advances in the development of a new generation of RNA folding theories and models. In this article, we review RNA structure prediction models and models for ion-RNA and ligand-RNA interactions. These new models are becoming increasingly important for a mechanistic understanding of RNA function and quantitative design of RNA nanotechnology. We focus on new methods for physics-based, knowledge-based, and experimental data-directed modeling for RNA structures and explore the new theories for the predictions of metal ion and ligand binding sites and metal ion-dependent RNA stabilities. The integration of these new methods with theories about the cellular environment effects in RNA folding, such as molecular crowding and cotranscriptional kinetic effects, may ultimately lead to an all-encompassing RNA folding model.

Unraveling Mg2+-RNA binding with atomistic molecular dynamics

Interaction with divalent cations is of paramount importance for RNA structural stability and function. We report here a detailed molecular dynamics study of all the possible binding sites for Mg2+ on an RNA duplex, including both direct (inner sphere) and indirect (outer sphere) binding. In order to tackle sampling issues, we develop a modified version of bias-exchange metadynamics, which allows us to simultaneously compute affinities with previously unreported statistical accuracy. Results correctly reproduce trends observed in crystallographic databases. Based on this, we simulate a carefully chosen set of models that allows us to quantify the effects of competition with monovalent cations, RNA flexibility, and RNA hybridization. Our simulations reproduce the decrease and increase of Mg2+ affinity due to ion competition and hybridization, respectively, and predict that RNA flexibility has a site-dependent effect. This suggests a nontrivial interplay between RNA conformational entropy and divalent cation binding.

Force-Dependent Folding and Unfolding Kinetics in DNA Hairpins Reveals Transition-State Displacements along a Single Pathway

Biomolecules diffusively explore their energy landscape overcoming energy barriers via thermally activated processes to reach the biologically relevant conformation. Mechanically induced unfolding and folding reactions offer an excellent playground to feature these processes at the single-molecule level by monitoring changes in the molecular extension. Here we investigate two-state DNA hairpins designed to have the transition states at different locations. We use optical tweezers to characterize the force-dependent behavior of the kinetic barrier from nonequilibrium pulling experiments by using the continuous effective barrier approach (CEBA). We introduce the mechanical fragility and the molecular transition-state susceptibility, both useful quantities to characterize the response of the transition state to an applied force. Our results demonstrate the validity of the Leffler-Hammond postulate where the transition state approaches the folded state as force increases, implying monotonically decreasing fragility with force and a non-negative transition state susceptibility at all forces.

Elasticity of the transition state for oligonucleotide hybridization

Despite its fundamental importance in cellular processes and abundant use in biotechnology, we lack a detailed understanding of the kinetics of nucleic acid hybridization. In particular, the identity of the transition state, which determines the kinetics of the two-state reaction, remains poorly characterized. Here, we used optical tweezers with single-molecule fluorescence to observe directly the binding and unbinding of short oligonucleotides (7–12 nt) to a complementary strand held under constant force. Binding and unbinding rate constants measured across a wide range of forces (1.5–20 pN) deviate from the exponential force dependence expected from Bell's equation. Using a generalized force dependence model, we determined the elastic behavior of the transition state, which we find to be similar to that of the pure single-stranded state. Our results indicate that the transition state for hybridization is visited before the strands form any significant amount of native base pairs. Such a transition state supports a model in which the rate-limiting step of the hybridization reaction is the alignment of the two strands prior to base pairing.

Mechanical Folding and Unfolding of Protein Barnase at the Single-Molecule Level

The unfolding and folding of protein barnase has been extensively investigated in bulk conditions under the effect of denaturant and temperature. These experiments provided information about structural and kinetic features of both the native and the unfolded states of the protein, and debates about the possible existence of an intermediate state in the folding pathway have arisen. Here, we investigate the folding/unfolding reaction of protein barnase under the action of mechanical force at the single-molecule level using optical tweezers. We measure unfolding and folding force-dependent kinetic rates from pulling and passive experiments, respectively, and using Kramers-based theories (e.g., Bell-Evans and Dudko-Hummer-Szabo models), we extract the position of the transition state and the height of the kinetic barrier mediating unfolding and folding transitions, finding good agreement with previous bulk measurements. Measurements of the force-dependent kinetic barrier using the continuous effective barrier analysis show that protein barnase verifies the Leffler-Hammond postulate under applied force and allow us to extract its free energy of folding, ΔG0. The estimated value of ΔG0 is in agreement with our predictions obtained using fluctuation relations and previous bulk studies. To address the possible existence of an intermediate state on the folding pathway, we measure the power spectrum of force fluctuations at high temporal resolution (50 kHz) when the protein is either folded or unfolded and, additionally, we study the folding transition-path time at different forces. The finite bandwidth of our experimental setup sets the lifetime of potential intermediate states upon barnase folding/unfolding in the submillisecond timescale.

Computer Folding of RNA Tetraloops: Identification of Key Force Field Deficiencies

The computer-aided folding of biomolecules, particularly RNAs, is one of the most difficult challenges in computational structural biology. RNA tetraloops are fundamental RNA motifs playing key roles in RNA folding and RNA-RNA and RNA-protein interactions. Although state-of-the-art Molecular Dynamics (MD) force fields correctly describe the native state of these tetraloops as a stable free-energy basin on the microsecond time scale, enhanced sampling techniques reveal that the native state is not the global free energy minimum, suggesting yet unidentified significant imbalances in the force fields. Here, we tested our ability to fold the RNA tetraloops in various force fields and simulation settings. We employed three different enhanced sampling techniques, namely, temperature replica exchange MD (T-REMD), replica exchange with solute tempering (REST2), and well-tempered metadynamics (WT-MetaD). We aimed to separate problems caused by limited sampling from those due to force-field inaccuracies. We found that none of the contemporary force fields is able to correctly describe folding of the 5'-GAGA-3' tetraloop over a range of simulation conditions. We thus aimed to identify which terms of the force field are responsible for this poor description of TL folding. We showed that at least two different imbalances contribute to this behavior, namely, overstabilization of base-phosphate and/or sugar-phosphate interactions and underestimated stability of the hydrogen bonding interaction in base pairing. The first artifact stabilizes the unfolded ensemble, while the second one destabilizes the folded state. The former problem might be partially alleviated by reparametrization of the van der Waals parameters of the phosphate oxygens suggested by Case et al., while in order to overcome the latter effect we suggest local potentials to better capture hydrogen bonding interactions.

Specificity and Ligand Affinities of the Cocaine Aptamer: Impact of Structural Features and Physiological NaCl

The cocaine aptamer has been seen as a good candidate for development as a probe for cocaine in many contexts. Here, we demonstrate that the aptamer binds cocaine, norcocaine, and cocaethylene with similar affinities and aminoglycosides with similar or higher affinities in a mutually exclusive manner with cocaine. Analysis of its affinities for a series of cocaine derivatives shows that the aptamer specificity is the consequence of its interaction with all faces of the cocaine molecule. Circular dichroism spectroscopy and 2-aminopurine (2AP) fluorescence studies show no evidence of large structural rearrangement of the cocaine aptamer upon ligand binding, which is contrary to the general view of this aptamer. The aptamer's affinity for cocaine and neomycin-B decreases with the inclusion of physiological NaCl. The substitution of 2AP for A in position 6 (2AP6) of the aptamer sequence eliminated the effect of NaCl on its affinities for cocaine and analogues, but not for neomycin-B, showing a selective effect of 2AP substitution on cocaine binding. The affinity for cocaine also decreased with increasing concentrations of serum or urine, with the 2AP6 substitution blunting the effect of urine. Its low affinities for cocaine and metabolites and its ability to bind irrelevant compounds limit the opportunities for application of this aptamer in its current form as a selective and reliable sensor for cocaine. However, these studies also show that a small structural adjustment to the aptamer (2AP exchanged for adenine) can increase its specificity for cocaine in physiological NaCl relative to an off-target ligand.

Activation of PKR by short stem-loop RNAs containing single-stranded arms

Protein kinase R (PKR) is a central component of the innate immunity antiviral pathway and is activated by dsRNA. PKR contains a C-terminal kinase domain and two tandem dsRNA binding domains. In the canonical activation model, binding of multiple PKR monomers to dsRNA enhances dimerization of the kinase domain, leading to enzymatic activation. A minimal dsRNA of 30 bp is required for activation. However, short (∼15 bp) stem-loop RNAs containing flanking single-stranded tails (ss-dsRNAs) are capable of activating PKR. Activation was reported to require a 5'-triphosphate. Here, we characterize the structural features of ss-dsRNAs that contribute to activation. We have designed a model ss-dsRNA containing 15-nt single-stranded tails and a 15-bp stem and made systematic truncations of the tail and stem regions. Autophosphorylation assays and analytical ultracentrifugation experiments were used to correlate activation and binding affinity. PKR activation requires both 5'- and 3'-single-stranded tails but the triphosphate is dispensable. Activation potency and binding affinity decrease as the ssRNA tails are truncated and activation is abolished in cases where the binding affinity is strongly reduced. These results indicate that the single-stranded regions bind to PKR and support a model where ss-dsRNA induced dimerization is required but not sufficient to activate the kinase. The length of the duplex regions in several natural RNA activators of PKR is below the minimum of 30 bp required for activation and similar interactions with single-stranded regions may contribute to PKR activation in these cases.

Directly measuring single-molecule heterogeneity using force spectroscopy

One of the most intriguing results of single-molecule experiments on proteins and nucleic acids is the discovery of functional heterogeneity: the observation that complex cellular machines exhibit multiple, biologically active conformations. The structural differences between these conformations may be subtle, but each distinct state can be remarkably long-lived, with interconversions between states occurring only at macroscopic timescales, fractions of a second or longer. Although we now have proof of functional heterogeneity in a handful of systems-enzymes, motors, adhesion complexes-identifying and measuring it remains a formidable challenge. Here, we show that evidence of this phenomenon is more widespread than previously known, encoded in data collected from some of the most well-established single-molecule techniques: atomic force microscopy or optical tweezer pulling experiments. We present a theoretical procedure for analyzing distributions of rupture/unfolding forces recorded at different pulling speeds. This results in a single parameter, quantifying the degree of heterogeneity, and also leads to bounds on the equilibration and conformational interconversion timescales. Surveying 10 published datasets, we find heterogeneity in 5 of them, all with interconversion rates slower than 10 s(-1) Moreover, we identify two systems where additional data at realizable pulling velocities is likely to find a theoretically predicted, but so far unobserved crossover regime between heterogeneous and nonheterogeneous behavior. The significance of this regime is that it will allow far more precise estimates of the slow conformational switching times, one of the least understood aspects of functional heterogeneity.

Determination of the elastic properties of short ssDNA molecules by mechanically folding and unfolding DNA hairpins

The characterization of elastic properties of biopolymers is crucial to understand many molecular reactions determined by conformational bending fluctuations of the polymer. Direct measurement of such elastic properties using single-molecule methods is usually hindered by the intrinsic tendency of such biopolymers to form high-order molecular structures. For example, single-stranded deoxyribonucleic acids (ssDNA) tend to form secondary structures such as local double helices that prevent the direct measurement of the ideal elastic response of the ssDNA. In this work, we show how to extract the ideal elastic response in the entropic regime of short ssDNA molecules by mechanically pulling two-state DNA hairpins of different contour lengths. This is achieved by measuring the force dependence of the molecular extension and stiffness on mechanically folding and unfolding the DNA hairpin. Both quantities are fit to the worm-like chain elastic model giving values for the persistence length and the interphosphate distance. This method can be used to unravel the elastic properties of short ssDNA and RNA sequences and, more generally, any biopolymer that can exhibit a cooperative two-state transition between mechanically folded and unfolded states (such as proteins).

Exploring ion induced folding of a single-stranded DNA oligomer from molecular simulation studies

One crucial issue in DNA hydration is the effect of salts on its conformational features. This has relevance in biology as cations present in the cellular environment shield the negative charges on the DNA backbone, thereby reducing the repulsive force between them. By screening the negative charges along the backbone, cations stabilize the folded structure of DNA. To study the effect of the added salt on single-stranded DNA (ss-DNA) conformations, we have performed room temperature molecular dynamics simulations of an aqueous solution containing the ss-DNA dodecamer with the 5'-CGCGAATTCGCG-3' sequence in the presence of 0.2, 0.5, and 0.8 M NaCl. Our calculations reveal that in the presence of the salt, the DNA molecule forms more collapsed coil-like conformations due to the screening of negative charges along the backbone. Additionally, we demonstrated that the formation of an octahedral inner-sphere complex by the strongly bound ion plays an important role in the stabilization of such folded conformation of DNA. Importantly, it is found that ion-DNA interactions can also explain the formation of non-sequential base stackings with longer lifetimes. Such non-sequential base stackings further stabilize the collapsed coil-like folded form of the DNA oligomer.

Elastic Properties of Nucleic Acids by Single-Molecule Force Spectroscopy

We review the current knowledge on the use of single-molecule force spectroscopy techniques to extrapolate the elastic properties of nucleic acids. We emphasize the lesser-known elastic properties of single-stranded DNA. We discuss the importance of accurately determining the elastic response in pulling experiments, and we review the simplest models used to rationalize the experimental data as well as the experimental approaches used to pull single-stranded DNA. Applications used to investigate DNA conformational transitions and secondary structure formation are also highlighted. Finally, we provide an overview of the effects of salt and temperature and briefly discuss the effects of contour length and sequence dependence.

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.

A Temperature-Jump Optical Trap for Single-Molecule Manipulation

To our knowledge, we have developed a novel temperature-jump optical tweezers setup that changes the temperature locally and rapidly. It uses a heating laser with a wavelength that is highly absorbed by water so it can cover a broad range of temperatures. This instrument can record several force-distance curves for one individual molecule at various temperatures with good thermal and mechanical stability. Our design has features to reduce convection and baseline shifts, which have troubled previous heating-laser instruments. As proof of accuracy, we used the instrument to carry out DNA unzipping experiments in which we derived the average basepair free energy, entropy, and enthalpy of formation of the DNA duplex in a range of temperatures between 5°C and 50°C. We also used the instrument to characterize the temperature-dependent elasticity of single-stranded DNA (ssDNA), where we find a significant condensation plateau at low force and low temperature. Oddly, the persistence length of ssDNA measured at high force seems to increase with temperature, contrary to simple entropic models.

The DbpA catalytic core unwinds double-helix substrates by directly loading on them

DbpA is a DEAD-box RNA helicase implicated in the assembly of the large ribosomal subunit. Similar to all the members of the DEAD-box family, the DbpA protein has two N-terminal RecA-like domains, which perform the RNA unwinding. However, unlike other members of this family, the DbpA protein also possesses a structured C-terminal RNA-binding domain that mediates specific tethering of DbpA to hairpin 92 of the Escherichia coli 23S ribosomal RNA. Previous studies using model RNA molecules containing hairpin 92 show that the RNA molecules support the DbpA protein's double-helix unwinding activity, provided that the double helix has a 3' single-stranded region. The 3' single-stranded region was suggested to be the start site of the DbpA protein's catalytic unwinding activity. The data presented here demonstrate that the single-stranded region 3' of the double-helix substrate is not required for the DbpA protein's unwinding activity and the DbpA protein unwinds the double-helix substrates by directly loading on them.

A thin permeable-membrane device for single-molecule manipulation

Single-molecule manipulation instruments have unparalleled abilities to interrogate the structure and elasticity of single biomolecules. Key insights are derived by measuring the system response in varying solution conditions; yet, typical solution control strategies require imposing a direct fluid flow on the measured biomolecule that perturbs the high-sensitivity measurement and/or removes interacting molecules by advection. An alternate approach is to fabricate devices that permit solution changes by diffusion of the introduced species through permeable membranes, rather than by direct solution flow through the sensing region. Prior implementations of permeable-membrane devices are relatively thick, disallowing their use in apparatus that require the simultaneous close approach of external instrumentation from two sides, as occurs in single-molecule manipulation devices like the magnetic tweezer. Here, we describe the construction and use of a thin microfluidic device appropriate for single-molecule studies. We create a flow cell of only ∼500 μm total thickness by sandwiching glass coverslips around a thin plastic gasket and then create permeable walls between laterally separated channels in situ through photo-induced cross-linking of poly(ethylene glycol) diacrylate hydrogels. We show that these membranes permit passage of ions and small molecules (thus permitting solution equilibration in the absence of direct flow), but the membranes block the passage of larger biomolecules (thus retaining precious samples). Finally, we demonstrate the suitability of the device for high-resolution magnetic-tweezer experiments by measuring the salt-dependent folding of a single RNA hairpin under force.

Statistical investigation of surface bound ions and further development of BION server to include pH and salt dependence

Ions are engaged in multiple biological processes in cells. By binding to the macromolecules or being mobile in the solvent, they maintain the integrity of the structure of macromolecules; participate in their enzymatic activity; or screen electrostatic interactions. While experimental methods are not always able to assign the exact location of ions, computational methods are in demand. Although the majority of computational methods are successful in predicting the position of ions buried inside macromolecules, they are less effective in deciphering positions of surface bound ions. Here, we propose the new BION algorithm (http://compbio.clemson.edu/bion_server_ph/) that predicts the location of the surface bound ions. It is more efficient and accurate compared to the previous version since it uses more advanced clustering algorithm in combination with pairing rules. In addition, the BION webserver allows specifying the pH and the salt concentration in predicting ions positions.

Atomistic Free Energy Model for Nucleic Acids: Simulations of Single-Stranded DNA and the Entropy Landscape of RNA Stem-Loop Structures

While single-stranded (ss) segments of DNAs and RNAs are ubiquitous in biology, details about their structures have only recently begun to emerge. To study ssDNA and RNAs, we have developed a new Monte Carlo (MC) simulation using a free energy model for nucleic acids that has the atomisitic accuracy to capture fine molecular details of the sugar-phosphate backbone. Formulated on the basis of a first-principle calculation of the conformational entropy of the nucleic acid chain, this free energy model correctly reproduced both the long and short length-scale structural properties of ssDNA and RNAs in a rigorous comparison against recent data from fluorescence resonance energy transfer, small-angle X-ray scattering, force spectroscopy and fluorescence correlation transport measurements on sequences up to ∼100 nucleotides long. With this new MC algorithm, we conducted a comprehensive investigation of the entropy landscape of small RNA stem-loop structures. From a simulated ensemble of ∼10(6) equilibrium conformations, the entropy for the initiation of different size RNA hairpin loops was computed and compared against thermodynamic measurements. Starting from seeded hairpin loops, constrained MC simulations were then used to estimate the entropic costs associated with propagation of the stem. The numerical results provide new direct molecular insights into thermodynaimc measurement from macroscopic calorimetry and melting experiments.

Targeted binding of nucleocapsid protein transforms the folding landscape of HIV-1 TAR RNA

Retroviral nucleocapsid (NC) proteins are nucleic acid chaperones that play a key role in the viral life cycle. During reverse transcription, HIV-1 NC facilitates the rearrangement of nucleic acid secondary structure, allowing the transactivation response (TAR) RNA hairpin to be transiently destabilized and annealed to a cDNA hairpin. It is not clear how NC specifically destabilizes TAR RNA but does not strongly destabilize the resulting annealed RNA-DNA hybrid structure, which must be formed for reverse transcription to continue. By combining single-molecule optical tweezers measurements with a quantitative mfold-based model, we characterize the equilibrium TAR stability and unfolding barrier for TAR RNA. Experiments show that adding NC lowers the transition state barrier height while also dramatically shifting the barrier location. Incorporating TAR destabilization by NC into the mfold-based model reveals that a subset of preferential protein binding sites is responsible for the observed changes in the unfolding landscape, including the unusual shift in the transition state. We measure the destabilization induced at these NC binding sites and find that NC preferentially targets TAR RNA by binding to specific sequence contexts that are not present on the final annealed RNA-DNA hybrid structure. Thus, specific binding alters the entire RNA unfolding landscape, resulting in the dramatic destabilization of this specific structure that is required for reverse transcription.

Molecular knots in biology and chemistry

Knots and entanglements are ubiquitous. Beyond their aesthetic appeal, these fascinating topological entities can be either useful or cumbersome. In recent decades, the importance and prevalence of molecular knots have been increasingly recognised by scientists from different disciplines. In this review, we provide an overview on the various molecular knots found in naturally occurring biological systems (DNA, RNA and proteins), and those created by synthetic chemists. We discuss the current knowledge in these fields, including recent developments in experimental and, in some cases, computational studies which are beginning to shed light into the complex interplay between the structure, formation and properties of these topologically intricate molecules.