Elastic Properties of a Single-Stranded Charged Homopolymeric Ribonucleotide

Understanding of the conformational ensemble of flexible polyelectrolytes, such as single-stranded nucleic acids (ssNAs), is complicated by the interplay of chain backbone entropy and saltdependent electrostatic repulsions. Molecular elasticity measurements are sensitive probes of the statistical conformation of polymers and have elucidated ssNA conformation at low force, where electrostatic repulsion leads to a strong excluded volume effect, and at high force, where details of the backbone structure become important. Here, we report measurements of ssDNA and ssRNA elasticity in the intermediate-force regime, corresponding to 5-to 100-pN forces and 50-85% extension. These data are explained by a modified wormlike chain model incorporating an internal electrostatic tension. Fits to the elastic data show that the internal tension decreases with salt, from >5 pN under 5 mM ionic strength to near zero at 1 M. This decrease is quantitatively described by an analytical model of electrostatic screening that ascribes to the polymer an effective charge density that is independent of force and salt. Our results thus connect microscopic chain physics to elasticity and structure at intermediate scales and provide a framework for understanding flexible polyelectrolyte elasticity across a broad range of relative extensions.single-stranded nucleic acids | flexible polyelectrolytes | force spectroscopy | electrostatics S ingle-stranded nucleic acids (ssNAs) occur in many biological processes, such as RNA folding (1, 2) and DNA replication (3-5), generally in disordered conformations that fluctuate between various structures. These fluctuations create a significant entropic elasticity; thus, direct measurements of molecular elasticity (extension, X , as a function of applied force, fapp) constitute a powerful tool for studying the ssNA structural ensemble (6). In particular, measurements at a particular fapp are sensitive to the conformation within the corresponding tensile length, kB T /fapp (to within a scaling factor), where kB T is the thermal energy (7).ssNA structure-and that of flexible polyelectrolytes more generally-is complicated by the strong negative charge of the molecule. Multiple electrostatic and structural length scales share a similar magnitude (roughly 1 nm), disallowing models that consider only electrostatics or only backbone structure. In an uncharged flexible chain, the key structural scale is the persistence length, lp, defining the distance beyond which thermal fluctuations strongly bend the polymer. Electrostatic interactions introduce several competing length scales: the distance, b, between charged phosphates along the ssNA backbone; the distance over which electrostatic fields are screened in salty solution (the Debye length, κ −1 ); and the distance at which interactions between elementary charges in water have energy kB T (the Bjerrum length, lB ).Prior studies have elucidated ssNA elastic behavior in the lowand high-force limits. At low forces, corresponding to tensile lengths larger than κ −1 (i....

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Single-stranded nucleic acid elasticity arises from internal electrostatic tension

Jacobson

McIntosh

Stevens

et al. 2017

“…Previous measurements of flexible single-stranded nucleic acids using fluorescence correlation spectroscopy (FCS) (17), single molecule Förster resonance energy transfer (smFRET) (18,19), and force spectroscopy (20)(21)(22)(23) have not provided a consensus picture of backbone conformations. These studies use a variety of nucleic acid constructs (of varying composition and length, with or without molecular handles or fluorescent tags) and interpret data with different models and starting assumptions.…”

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confidence: 99%

Ionic strength-dependent persistence lengths of single-stranded RNA and DNA

Chen

Meisburger

Pabit

et al. 2011

338

434

Dynamic RNA molecules carry out essential processes in the cell including translation and splicing. Base-pair interactions stabilize RNA into relatively rigid structures, while flexible non-base-paired regions allow RNA to undergo conformational changes required for function. To advance our understanding of RNA folding and dynamics it is critical to know the flexibility of these un-base-paired regions and how it depends on counterions. Yet, information about nucleic acid polymer properties is mainly derived from studies of ssDNA. Here we measure the persistence lengths (l p ) of ssRNA. We observe valence and ionic strength-dependent differences in l p in a direct comparison between 40-mers of deoxythymidylate (dT 40 ) and uridylate (rU 40 ) measured using the powerful combination of SAXS and smFRET. We also show that nucleic acid flexibility is influenced by local environment (an adjoining double helix). Our results illustrate the complex interplay between conformation and ion environment that modulates nucleic acid function in vivo.single molecule FRET | small angle X-ray scattering | worm-like chain | ion-nucleic acid interactions N ucleic acids in the cell are dynamic and undergo structural changes as they transmit and process genetic information. Dynamic processes related to biological function (e.g., transcription for DNA and recognition and folding for RNA) involve nonbase-paired regions that confer flexibility to the overall structure. For RNAs like riboswitches that exchange between multiple structures in equilibrium (1), conformational disorder is often an intrinsic property of the molecule and important for biological function. Even relatively stable molecules like catalytic introns and transfer RNA must pass through a disordered phase while folding. Thus, progress toward a mechanistic understanding of RNA folding and dynamics will require detailed knowledge of nucleic acid chain flexibility and its dependence on base content, solution conditions, and molecular context.In light of its importance to biology, it is surprising that RNA flexibility has not been studied in as much detail as DNA flexibility. Despite the chemical similarity of the RNA and DNA backbone, there is ample evidence from X-ray crystallography that the identity of the sugar (ribose vs. deoxy-ribose) affects backbone conformations (2). However, researchers have used the properties of DNA to understand RNA folding (3) because corresponding information for RNA was lacking. This difficulty motivates our present efforts to measure and directly compare the flexibilities of single-stranded nucleic acids (ssRNA and ssDNA).In the cell, RNA and DNA interact with cations that screen the negatively charged phosphate backbone. Both diffuse and specifically bound ions are important for RNA folding (4), and divalent ions are almost always required to stabilize RNA tertiary structures (5-8). A full mechanistic description of these ion effects is complicated by the fact that ions can interact with RNA differently during various stages of folding (9, ...

“…The U 7 linker (Fig. 1A) behaves as a random coil at the moderate ionic strengths and temperature ranges explored in this work (31), permitting isolation of the thermodynamic effects of [Mg 2þ ] on the TL-R tertiary interaction alone (16).…”

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confidence: 99%

Entropic origin of Mg ²⁺ -facilitated RNA folding

Fiore

Holmstrom

Nesbitt

2012

158

Mg 2þ is essential for the proper folding and function of RNA, though the effect of Mg 2þ concentration on the free energy, enthalpy, and entropy landscapes of RNA folding is unknown. This work exploits temperature-controlled single-molecule FRET methods to address the thermodynamics of RNA folding pathways by probing the intramolecular docking/undocking kinetics of the ubiquitous GAAA tetraloop−receptor tertiary interaction as a function of [Mg 2þ ]. These measurements yield the barrier and standard state enthalpies, entropies, and free energies for an RNA tertiary transition, in particular, revealing the thermodynamic origin of [Mg 2þ ]-facilitated folding. Surprisingly, these studies reveal that increasing [Mg 2þ ] promotes tetraloop-receptor interaction by reducing the entropic barrier (−T ΔS ‡ dock ) and the overall entropic penalty (−T ΔS°d ock ) for docking, with essentially negligible effects on both the activation enthalpy (ΔH ‡ dock ) and overall exothermicity (ΔH°d ock ). These observations contrast with the conventional notion that increasing [Mg 2þ ] facilitates folding by minimizing electrostatic repulsion of opposing RNA helices, which would incorrectly predict a decrease in ΔH ‡ dock and ΔH°d ock with [Mg 2þ ]. Instead we propose that higher [Mg 2þ ] can aid RNA folding by decreasing the entropic penalty of counterion uptake and by reducing disorder of the unfolded conformational ensemble.T he folding of RNA proceeds hierarchically, whereby secondary structure is formed rapidly and subsequent slow helical packing is mediated by tertiary interactions (1, 2). RNA secondary structure prediction from the known thermodynamics is quite reliable (3), though correspondingly accurate prediction of tertiary structure remains a major challenge (1). Static tertiary structure data alone are also not enough to predict RNA functionality, as time-dependent conformational dynamics occur during biochemical processes (4, 5). As a result, one needs the full free energy, enthalpy, and entropy landscapes for folding. A major road block in achieving a predictive understanding of RNA folding landscapes is that they are often "rugged,", i.e., with alternative conformations acting as kinetic traps (6, 7). Moreover, the electrostatic challenge of folding a charged biopolymer highlights the particularly critical role of Mg 2þ and other counterions in the folding process.Characterization of folding transition states-and the role of Mg 2þ in stabilizing transition states-remains a crucial bottleneck for reconciling the kinetics and thermodynamics of RNA folding (8-13). Some insight into the free energy landscapes for RNA folding can be obtained from temperature-dependent stopped-flow kinetic studies, which offer the ability to deconstruct free energy barriers (ΔG ‡ ) into enthalpic (ΔH ‡ ) and entropic (−TΔS ‡ ) components. However, with such methods, only the net rate constant (i.e., k total ¼ k fold þ k unfold ) for approach to equilibrium can be observed, which requires strong assumptions (e.g., that k fold ≫ k unfol...