Persistence length changes dramatically as RNA folds

Condensation Goes Viral: A Polymer Physics Perspective

The past decade has seen a revolution in our understanding of how the cellular environment is organized, where an incredible body of work has provided new insights into the role played by membraneless organelles. These rapid advancements have been made possible by an increasing awareness of the peculiar physical properties that give rise to such bodies and the complex biology that enables their function. Viral infections are not extraneous to this. Indeed, in host cells, viruses can harness existing membraneless compartments or, even, induce the formation of new ones. By hijacking the cellular machinery, these intracellular bodies can assist in the replication, assembly, and packaging of the viral genome as well as in the escape of the cellular immune response. Here, we provide a perspective on the fundamental polymer physics concepts that may help connect and interpret the different observed phenomena, ranging from the condensation of viral genomes to the phase separation of multicomponent solutions. We complement the discussion of the physical basis with a description of biophysical methods that can provide quantitative insights for testing and developing theoretical and computational models.

Differences in ion-RNA binding modes due to charge density variations explain the stability of RNA in monovalent salts

The stability of RNA increases as the charge density of the alkali metal cations increases. The molecular mechanism for this phenomenon remains elusive. To fill this gap, we performed all-atom molecular dynamics pulling simulations of HIV-1 trans-activation response RNA. We first established that the free energy landscape obtained in the simulations is in excellent agreement with the single-molecule optical tweezer experiments. The origin of the stronger stability in sodium compared to potassium is found to be due to the differences in the charge density-related binding modes. The smaller hydrated sodium ion preferentially binds to the highly charged phosphates that have high surface area. In contrast, the larger potassium ions interact with the major grooves. As a result, more cations condense around phosphate groups in the case of sodium ions, leading to the reduction of electrostatic repulsion. Because the proposed mechanism is generic, we predict that the same conclusions are valid for divalent alkaline earth metal cations.

RNA Secondary Structures Regulate Adsorption of Fragments onto Flat Substrates

RNA is a functionally rich molecule with multilevel, hierarchical structures whose role in the adsorption to molecular substrates is only beginning to be elucidated. Here, we introduce a multiscale simulation approach that combines a tractable coarse-grained RNA structural model with an interaction potential of a structureless flat adsorbing substrate. Within this approach, we study the specific role of stem-hairpin and multibranch RNA secondary structure motifs on its adsorption phenomenology. Our findings identify a dual regime of adsorption for short RNA fragments with and without the secondary structure and underline the adsorption efficiency in both cases as a function of the surface interaction strength. The observed behavior results from an interplay between the number of contacts formed at the surface and the conformational entropy of the RNA molecule. The adsorption phenomenology of RNA seems to persist also for much longer RNAs as qualitatively observed by comparing the trends of our simulations with a theoretical approach based on an ideal semiflexible polymer chain.

Systematic Quantification of Sequence and Structural Determinants Controlling mRNA stability in Bacterial Operons

mRNA degradation is a central process that affects all gene expression levels, and yet, the determinants that control mRNA decay rates remain poorly characterized. Here, we applied a synthetic biology, learn-by-design approach to elucidate the sequence and structural determinants that control mRNA stability in bacterial operons. We designed, constructed, and characterized 82 operons in Escherichia coli, systematically varying RNase binding site characteristics, translation initiation rates, and transcriptional terminator efficiencies in the 5' untranslated region (UTR), intergenic, and 3' UTR regions, followed by measuring their mRNA levels using reverse transcription quantitative polymerase chain reaction (RT-qPCR) assays during exponential growth. We show that introducing long single-stranded RNA into 5' UTRs reduced mRNA levels by up to 9.4-fold and that lowering translation rates reduced mRNA levels by up to 11.8-fold. We also found that RNase binding sites in intergenic regions had much lower effects on mRNA levels. Surprisingly, changing the transcriptional termination efficiency or introducing long single-stranded RNA into 3' UTRs had no effect on upstream mRNA levels. From these measurements, we developed and validated biophysical models of ribosome protection and RNase activity with excellent quantitative agreement. We also formulated design rules to rationally control a mRNA's stability, facilitating the automated design of engineered genetic systems with desired functionalities.

The mechanisms of a mammalian splicing enhancer

Exonic splicing enhancer (ESE) sequences are bound by serine & arginine-rich (SR) proteins, which in turn enhance the recruitment of splicing factors. It was inferred from measurements of splicing around twenty years ago that Drosophila doublesex ESEs are bound stably by SR proteins, and that the bound proteins interact directly but with low probability with their targets. However, it has not been possible with conventional methods to demonstrate whether mammalian ESEs behave likewise. Using single molecule multi-colour colocalization methods to study SRSF1-dependent ESEs, we have found that that the proportion of RNA molecules bound by SRSF1 increases with the number of ESE repeats, but only a single molecule of SRSF1 is bound. We conclude that initial interactions between SRSF1 and an ESE are weak and transient, and that these limit the activity of a mammalian ESE. We tested whether the activation step involves the propagation of proteins along the RNA or direct interactions with 3' splice site components by inserting hexaethylene glycol or abasic RNA between the ESE and the target 3' splice site. These insertions did not block activation, and we conclude that the activation step involves direct interactions. These results support a model in which regulatory proteins bind transiently and in dynamic competition, with the result that each ESE in an exon contributes independently to the probability that an activator protein is bound and in close proximity to a splice site.

Radial distribution function of semiflexible oligomers with stretching flexibility

The radial distribution of the end-to-end distance R_ee is crucial for quantifying the global size and flexibility of a linear polymer. For semiflexible polymers, several analytical formulas have been derived for the radial distribution of R_ee ignoring the stretching flexibility. However, for semiflexible oligomers, such as DNA or RNA, the stretching flexibility can be rather pronounced and can significantly affect the radial distribution of R_ee. In this study, we obtained an extended formula that includes the stretch modulus to describe the distribution of R_ee for semiflexible oligomers on the basis of previous formulas for semiflexible polymers without stretching flexibility. The extended formula was validated by extensive Monte Carlo simulations over wide ranges of the stretch modulus and persistence length, as well as all-atom molecular dynamics simulations of short DNAs and RNAs. Additionally, our analyses showed that the effect of stretching flexibility on the distribution of R_ee becomes negligible for DNAs longer than ∼130 base pairs and RNAs longer than ∼240 base pairs.

Investigating Structure and Dynamics of Proteins in Amorphous Phases Using Neutron Scattering

In order to increase shelf life and minimize aggregation during storage, many biotherapeutic drugs are formulated and stored as either frozen solutions or lyophilized powders. However, characterizing amorphous solids can be challenging with the commonly available set of biophysical measurements used for proteins in liquid solutions. Therefore, some questions remain regarding the structure of the active pharmaceutical ingredient during freezing and drying of the drug product and the molecular role of excipients. Neutron scattering is a powerful technique to study structure and dynamics of a variety of systems in both solid and liquid phases. Moreover, neutron scattering experiments can generally be correlated with theory and molecular simulations to analyze experimental data. In this article, we focus on the use of neutron techniques to address problems of biotechnological interest. We describe the use of small-angle neutron scattering to study the solution structure of biological molecules and the packing arrangement in amorphous phases, that is, frozen glasses and freeze-dried protein powders. In addition, we discuss the use of neutron spectroscopy to measure the dynamics of glassy systems at different time and length scales. Overall, we expect that the present article will guide and prompt the use of neutron scattering to provide unique insights on many of the outstanding questions in biotechnology.

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.

Flexibility of short DNA helices with finite-length effect: From base pairs to tens of base pairs

Flexibility of short DNA helices is important for the biological functions such as nucleosome formation and DNA-protein recognition. Recent experiments suggest that short DNAs of tens of base pairs (bps) may have apparently higher flexibility than those of kilo bps, while there is still the debate on such high flexibility. In the present work, we have studied the flexibility of short DNAs with finite-length of 5-50 bps by the all-atomistic molecular dynamics simulations and Monte Carlo simulations with the worm-like chain model. Our microscopic analyses reveal that short DNAs have apparently high flexibility which is attributed to the significantly strong bending and stretching flexibilities of ∼6 bps at each helix end. Correspondingly, the apparent persistence length lp of short DNAs increases gradually from ∼29 nm to ∼45 nm as DNA length increases from 10 to 50 bps, in accordance with the available experimental data. Our further analyses show that the short DNAs with excluding ∼6 bps at each helix end have the similar flexibility with those of kilo bps and can be described by the worm-like chain model with lp ∼ 50 nm.

Unexpected Swelling of Stiff DNA in a Polydisperse Crowded Environment

We investigate the conformations of DNA-like stiff chains, characterized by contour length (L) and persistence length (lp), in a variety of crowded environments containing monodisperse soft spherical (SS) and spherocylindrical (SC) particles, a mixture of SS and SC, and a milieu mimicking the composition of proteins in the Escherichia coli cytoplasm. The stiff chain, whose size modestly increases in SS crowders up to ϕ ≈ 0.1, is considerably more compact at low volume fractions (ϕ ≤ 0.2) in monodisperse SC particles than in a medium containing SS particles. A 1:1 mixture of SS and SC crowders induces greater chain compaction than the pure SS or SC crowders at the same ϕ, with the effect being highly nonadditive. We also discover a counterintuitive result that the polydisperse crowding environment, mimicking the composition of a cell lysate, swells the DNA-like polymer, which is in stark contrast to the size reduction of flexible polymers in the same milieu. Trapping of the stiff chain in a fluctuating tube-like environment created by large-sized crowders explains the dramatic increase in size and persistence length of the stiff chain. In the polydisperse medium, mimicking the cellular environment, the size of the DNA (or related RNA) is determined by L/lp. At low L/lp, the size of the polymer is unaffected, whereas there is a dramatic swelling at an intermediate value of L/lp. We use these results to provide insights into recent experiments on crowding effects on RNA and also make testable predictions.

Electrostatics, structure prediction, and the energy landscapes for protein folding and binding

While being long in range and therefore weakly specific, electrostatic interactions are able to modulate the stability and folding landscapes of some proteins. The relevance of electrostatic forces for steering the docking of proteins to each other is widely acknowledged, however, the role of electrostatics in establishing specifically funneled landscapes and their relevance for protein structure prediction are still not clear. By introducing Debye-Hückel potentials that mimic long-range electrostatic forces into the Associative memory, Water mediated, Structure, and Energy Model (AWSEM), a transferable protein model capable of predicting tertiary structures, we assess the effects of electrostatics on the landscapes of thirteen monomeric proteins and four dimers. For the monomers, we find that adding electrostatic interactions does not improve structure prediction. Simulations of ribosomal protein S6 show, however, that folding stability depends monotonically on electrostatic strength. The trend in predicted melting temperatures of the S6 variants agrees with experimental observations. Electrostatic effects can play a range of roles in binding. The binding of the protein complex KIX-pKID is largely assisted by electrostatic interactions, which provide direct charge-charge stabilization of the native state and contribute to the funneling of the binding landscape. In contrast, for several other proteins, including the DNA-binding protein FIS, electrostatics causes frustration in the DNA-binding region, which favors its binding with DNA but not with its protein partner. This study highlights the importance of long-range electrostatics in functional responses to problems where proteins interact with their charged partners, such as DNA, RNA, as well as membranes.

A molecular thermodynamic model for the stability of hepatitis B capsids

Self-assembly of capsid proteins and genome encapsidation are two critical steps in the life cycle of most plant and animal viruses. A theoretical description of such processes from a physiochemical perspective may help better understand viral replication and morphogenesis thus provide fresh insights into the experimental studies of antiviral strategies. In this work, we propose a molecular thermodynamic model for predicting the stability of Hepatitis B virus (HBV) capsids either with or without loading nucleic materials. With the key components represented by coarse-grained thermodynamic models, the theoretical predictions are in excellent agreement with experimental data for the formation free energies of empty T4 capsids over a broad range of temperature and ion concentrations. The theoretical model predicts T3/T4 dimorphism also in good agreement with the capsid formation at in vivo and in vitro conditions. In addition, we have studied the stability of the viral particles in response to physiological cellular conditions with the explicit consideration of the hydrophobic association of capsid subunits, electrostatic interactions, molecular excluded volume effects, entropy of mixing, and conformational changes of the biomolecular species. The course-grained model captures the essential features of the HBV nucleocapsid stability revealed by recent experiments.

The snakelike chain character of unstructured RNA

In the absence of base-pairing and tertiary structure, ribonucleic acid (RNA) assumes a random-walk conformation, modulated by the electrostatic self-repulsion of the charged, flexible backbone. This behavior is often modeled as a Kratky-Porod "wormlike chain" (WLC) with a Barrat-Joanny scale-dependent persistence length. In this study we report measurements of the end-to-end extension of poly(U) RNA under 0.1 to 10 pN applied force and observe two distinct elastic-response regimes: a low-force, power-law regime characteristic of a chain of swollen blobs on long length scales and a high-force, salt-valence-dependent regime consistent with ion-stabilized crumpling on short length scales. This short-scale structure is additionally supported by force- and salt-dependent quantification of the RNA ion atmosphere composition, which shows that ions are liberated under stretching; the number of ions liberated increases with increasing bulk salt concentration. Both this result and the observation of two elastic-response regimes directly contradict the WLC model, which predicts a single elastic regime across all forces and, when accounting for scale-dependent persistence length, the opposite trend in ion release with salt concentration. We conclude that RNA is better described as a "snakelike chain," characterized by smooth bending on long length scales and ion-stabilized crumpling on short length scales. In monovalent salt, these two regimes are separated by a characteristic length that scales with the Debye screening length, highlighting the determining importance of electrostatics in RNA conformation.

Elastic properties and secondary structure formation of single-stranded DNA at monovalent and divalent salt conditions

Single-stranded DNA (ssDNA) plays a major role in several biological processes. It is therefore of fundamental interest to understand how the elastic response and the formation of secondary structures are modulated by the interplay between base pairing and electrostatic interactions. Here we measure force-extension curves (FECs) of ssDNA molecules in optical tweezers set up over two orders of magnitude of monovalent and divalent salt conditions, and obtain its elastic parameters by fitting the FECs to semiflexible models of polymers. For both monovalent and divalent salts, we find that the electrostatic contribution to the persistence length is proportional to the Debye screening length, varying as the inverse of the square root of cation concentration. The intrinsic persistence length is equal to 0.7 nm for both types of salts, and the effectivity of divalent cations in screening electrostatic interactions appears to be 100-fold as compared with monovalent salt, in line with what has been recently reported for single-stranded RNA. Finally, we propose an analysis of the FECs using a model that accounts for the effective thickness of the filament at low salt condition and a simple phenomenological description that quantifies the formation of non-specific secondary structure at low forces.

Kinetics of loop formation in worm-like chain polymers

A common theoretical approach to calculating reaction kinetics is to approximate a high-dimensional conformational search with a one-dimensional diffusion along an effective reaction coordinate. We employed Brownian dynamics simulations to test the validity of this approximation for loop formation kinetics in the worm-like chain polymer model. This model is often used to describe polymers that exhibit backbone stiffness beyond the monomer length scale. We find that one-dimensional diffusion models overestimate the looping time and do not predict the quantitatively correct dependence of looping time on chain length or capture radius. Our findings highlight the difficulty of describing high-dimensional polymers with simple kinetic theories.

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

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

Crowders perturb the entropy of RNA energy landscapes to favor folding

Biological macromolecules have evolved to fold and operate in the crowded environment of the cell. We have shown previously that molecular crowding stabilizes folded RNA structures. Here we report SAXS measurements on a 64 kDa bacterial group I ribozyme in the presence of mono- and divalent ions and PEG crowders of different molecular weight. These experiments show that crowders always stabilize the folded RNA, but this stabilization is weaker in NaCl solutions than MgCl2 solutions. Additionally, we find that RNAs with the same global structure, parametrized by Rg, have different scattering functions depending upon the ratio of electrostatic and entropic stabilization by ions and crowders, respectively. We quantify this difference using the scattering length per scattering volume and find that this ratio is larger for RNAs that fold in lower ionic strength solutions due to the higher crowder content. We conclude that lower RNA flexibility, or reduced configurational entropy, widens the free energy gap between the unfolded and folded RNA in crowded MgCl2 solutions.

From flexible to stiff: systematic analysis of structural phases for single semiflexible polymers

Inspired by recent studies revealing unexpected pliability of semiflexible biomolecules like RNA and DNA, we systematically investigate the range of structural phases by means of a simple generic polymer model. Using a two-dimensional variant of Wang-Landau sampling to explore the conformational space in energy and stiffness within a single simulation, we identify the entire diversity of structures existing from the well-studied limit of flexible polymers to that of wormlike chains. We also discuss, in detail, the influence of finite-size effects in the formation of crystalline structures that are virtually inaccessible via conventional computational approaches.

On the origin of the unusual behavior in the stretching of single-stranded DNA

Force-extension curves (FECs), which quantify the response of a variety of biomolecules subject to mechanical force (f), are often quantitatively fit using worm-like chain (WLC) or freely jointed chain (FJC) models. These models predict that the chain extension, x, normalized by the contour length increases linearly at small f and at high forces scale as x ~ (1 - f(-α)), where α = 0.5 for WLC and unity for FJC. In contrast, experiments on single-stranded DNA (ssDNA) show that over a range of f and ionic concentration, x scales as x ~ ln f, which cannot be explained using WLC or FJC models. Using theory and simulations we show that this unusual behavior in FEC in ssDNA is due to sequence-independent polyelectrolyte effects. We show that the x ~ ln f arises because in the absence of force the tangent correlation function, quantifying chain persistence, decays algebraically on length scales on the order of the Debye length. Our theory, which is most appropriate for monovalent salts, quantitatively fits the experimental data and further predicts that such a regime is not discernible in double-stranded DNA.

Structural flexibility of RNA as molecular basis for Hfq chaperone function

In enteric bacteria, many small regulatory RNAs (sRNAs) associate with the RNA chaperone host factor Q (Hfq) and often require the protein for regulation of target mRNAs. Previous studies suggested that the hexameric Escherichia coli Hfq (Hfq(Ec)) binds sRNAs on the proximal site, whereas the distal site has been implicated in Hfq-mRNA interactions. Employing a combination of small angle X-ray scattering, nuclear magnetic resonance and biochemical approaches, we report the structural analysis of a 1:1 complex of Hfq(Ec) with a 34-nt-long subsequence of a natural substrate sRNA, DsrA (DsrA(34)). This sRNA is involved in post-transcriptional regulation of the E. coli rpoS mRNA encoding the stationary phase sigma factor RpoS. The molecular envelopes of Hfq(Ec) in complex with DsrA(34) revealed an overall asymmetric shape of the complex in solution with the protein maintaining its doughnut-like structure, whereas the extended DsrA(34) is flexible and displays an ensemble of different spatial arrangements. These results are discussed in terms of a model, wherein the structural flexibility of RNA ligands bound to Hfq stochastically facilitates base pairing and provides the foundation for the RNA chaperone function inherent to Hfq.

Visualizing large RNA molecules in solution

Single-stranded RNAs (ssRNAs) longer than a few hundred nucleotides do not have a unique structure in solution. Their equilibrium properties therefore reflect the average of an ensemble of structures. We use cryo-electron microscopy to image projections of individual long ssRNA molecules and characterize the anisotropy of their ensembles in solution. A flattened prolate volume is found to best represent the shapes of these ensembles. The measured sizes and anisotropies are in good agreement with complementary determinations using small-angle X-ray scattering and coarse-grained molecular dynamics simulations. A long viral ssRNA is compared with shorter noncoding transcripts to demonstrate that prolate geometry and flatness are generic properties independent of sequence length and origin. The anisotropy persists under physiological as well as low-ionic-strength conditions, revealing a direct correlation between secondary structure asymmetry and 3D shape and size. We discuss the physical origin of the generic anisotropy and its biological implications.

Understanding thermodynamic competitivity between biopolymer folding and misfolding under large-scale intermolecular interactions

Cooperativity is a hallmark of spontaneous biopolymer folding. The presence of intermolecular interactions could create off-pathway misfolding structures and suppress folding cooperativity. This raises the hypothesis that thermodynamic competitivity between off-pathway misfolding and on-pathway folding may intervene with cooperativity and govern biopolymer folding dynamics under conditions permitting large-scale intermolecular interactions. Here we report direct imaging and theoretical modeling of thermodynamic competitivity between biopolymer folding and misfolding under such conditions, using a two-dimensional array of proton-fueled DNA molecular motors packed at the maximal density as a model system. Time-resolved liquid-phase atomic force microscopy with enhanced phase contrast revealed that the misfolding and folding intermediates transiently self-organize into spatiotemporal patterns on the nanoscale in thermodynamic states far away from equilibrium as a result of thermodynamic competitivity. Computer simulations using a novel cellular-automaton network model provide quantitative insights into how large-scale intermolecular interactions correlate the structural dynamics of individual biomolecules together at the systems level.

SAXS studies of ion-nucleic acid interactions

Positively charged ions, atoms, or molecules compensate the high negative charge of the nucleic acid backbone. Their presence is critical to the biological function of DNA and RNA. This review focuses on experimental studies probing (a) interactions between small ions and nucleic acids and (b) ion-mediated interactions between nucleic acid duplexes. Experimental results on these simple model systems can be compared with specific theoretical models to validate their predictions. Small angle X-ray scattering (SAXS) provides unique insight into these interactions. Anomalous SAXS reports the spatial correlations of condensed (e.g., locally concentrated) counterions to individual DNA or RNA duplexes. SAXS very effectively reports interactions between nucleic acid helices, which range from strongly repulsive to strongly attractive depending on the ionic species present. The sign and strength of interparticle interactions are easily deduced from dramatic changes in the scattering profiles of interacting duplexes.

Prediction of folding nuclei in tRNA molecules

Prediction of folding nuclei in RNA molecules allows one to look in a new way at the problem of possible RNA base sequence folding and at problems associated with incorrect RNA folding, as well as at RNA structure stability. We have chosen a model and energy parameters for description of RNA structure. The algorithm for studying processes including protein folding/unfolding was successfully applied to calculations on tRNA. Four tRNA molecules were considered whose structures were obtained in the free state (tRNA(Phe), tRNA(Asp), tRNA(fMet), and tRNA(Lys)). The calculated Φ-values for tRNA molecules correlate with experimental data showing that nucleotide residues in the D and T hairpin regions are involved in tRNA structure last, or more exactly, they are not included in the tRNA folding nucleus. High Φ-values in the anticodon hairpin region show that the nucleus of tRNA folding is localized just in that place.

Multistage collapse of a bacterial ribozyme observed by time-resolved small-angle X-ray scattering

Ribozymes must fold into compact, native structures to function properly in the cell. The first step in forming the RNA tertiary structure is the neutralization of the phosphate charge by cations, followed by collapse of the unfolded molecules into more compact structures. The specificity of the collapse transition determines the structures of the folding intermediates and the folding time to the native state. However, the forces that enable specific collapse in RNA are not understood. Using time-resolved SAXS, we report that upon addition of 5 mM Mg(2+) to the Azoarcus group I ribozyme up to 80% of chains form compact structures in less than 1 ms. In 1 mM Mg(2+), the collapse transition produces extended structures that slowly approach the folded state, while > or = 1.5 mM Mg(2+) leads to an ensemble of random coils that fold with multistage kinetics. Increased flexibility of molecules in the intermediate ensemble correlates with a Mg(2+)-dependent increase in the fast folding population and a previously unobserved crossover in the collapse kinetics. Partial denaturation of the unfolded RNA with urea also increases the fraction of chains following the fast-folding pathway. These results demonstrate that the preferred collapse mechanism depends on the extent of Mg(2+)-dependent charge neutralization and that non-native interactions within the unfolded ensemble contribute to the heterogeneity of the ribozyme folding pathways at the very earliest stages of tertiary structure formation.

Theory of Biopolymer Stretching at High Forces

We provide a unified theory for the high force entropic elasticity of biopolymers solely in terms of the persistence length, ξ_p , and the monomer spacing, a. When the force f>ℱ _h ~ k_BTξ_p /a² the biopolymers behave as freely jointed chains (FJCs) while in the range ℱ _l ~ k_BT/ξ_p <f<ℱ _h the worm-like chain (WLC) is a better model. We show that ξ_p can be estimated from the force extension curve (FEC) at the extension x ≈ ¹/₂ (normalized by the contour length of the biopolymer). After validating the theory using simulations, we provide a quantitative analysis of the FECs for a diverse set of biopolymers (dsDNA, ssRNA, ssDNA, polysaccharides, and unstructured PEVK domain of titin) for x ≥ ¹/₂. The success of a specific polymer model (FJC or WLC) to describe the FEC of a given biopolymer is naturally explained by the theory. Only by probing the response of biopolymers over a wide range of forces can the f-dependent elasticity be fully described.

Metal ion dependence of cooperative collapse transitions in RNA

Positively charged counterions drive RNA molecules into compact configurations that lead to their biologically active structures. To understand how the valence and size of the cations influences the collapse transition in RNA, small-angle X-ray scattering was used to follow the decrease in the radius of gyration (R(g)) of the Azoarcus and Tetrahymena ribozymes in different cations. Small, multivalent cations induced the collapse of both ribozymes more efficiently than did monovalent ions. Thus, the cooperativity of the collapse transition depends on the counterion charge density. Singular value decomposition of the scattering curves showed that folding of the smaller and more thermostable Azoarcus ribozyme is well described by two components, whereas collapse of the larger Tetrahymena ribozyme involves at least one intermediate. The ion-dependent persistence length, extracted from the distance distribution of the scattering vectors, shows that the Azoarcus ribozyme is less flexible at the midpoint of transition in low-charge-density ions than in high-charge-density ions. We conclude that the formation of sequence-specific tertiary interactions in the Azoarcus ribozyme overlaps with neutralization of the phosphate charge, while tertiary folding of the Tetrahymena ribozyme requires additional counterions. Thus, the stability of the RNA structure determines its sensitivity to the valence and size of the counterions.

Detailed scaling analysis of low-force polyelectrolyte elasticity

Single-molecule force-extension data are typically compared to ideal models of polymer behavior that ignore the effects of self-avoidance. Here, we demonstrate a link between single-molecule data and the scaling pictures of a real polymer. We measure a low-force elasticity regime where the extension L of chemically denatured single-stranded DNA grows as a power law with force f : L approximately f;{gamma} , with gamma approximately 0.60-0.69 . This compares favorably with the "tensile-blob" model of a self-avoiding polymer, which predicts gamma=2/3 . We show that the transition out of the low-force regime is highly salt dependent, and use the tensile-blob model to relate this effect to the salt dependence of the polymer's Kuhn length and excluded-volume parameter. We find that, contrary to the well-known Odijk-Skolnick-Fixman theory, the Kuhn length of single-stranded DNA is linearly proportional to the Debye length of the solution. Finally, we show that the low-force elasticity becomes linear (gamma=1) at approximately 3 M salt, and interpret this as a Theta point of the polymer. At this point, the force-extension data is best described by the wormlike chain model, from which we estimate the bare (nonelectrostatic) persistence length of the polymer to be approximately 0.6 nm .

π-conjugation and conformation in a semiconducting polymer: small angle x-ray scattering study

Small angle x-ray scattering (SAXS) in a poly[2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV) solution has shown the important role of π-electron conjugation in controlling the chain conformation and assembly. By increasing the extent of conjugation from 30 to 100%, the persistence length (l(p)) increases from 20 to 66 Å. Moreover, a pronounced second peak in the pair distribution function has been observed in a fully conjugated chain, at larger length scales. This feature indicates that the chain segments tend to self-assemble as the conjugation along the chain increases. Xylene enhances the rigidity of the PPV backbone to yield extended structures, while tetrahydrofuran solvates the side groups to form compact coils in which the l(p) is much shorter.

Characterization of a fluorophore binding RNA aptamer by fluorescence correlation spectroscopy and small angle X-ray scattering

Using fluorescence correlation spectroscopy (FCS), we have established an in vitro assay to study RNA dynamics by analyzing fluorophore binding RNA aptamers at the single molecule level. The RNA aptamer SRB2m, a minimized variant of the initially selected aptamer SRB-2, has a high affinity to the disulfonated triphenylmethane dye sulforhodamine B. A mobility shift of sulforhodamine B after binding to SRB2m was measured. In contrast, patent blue V (PBV) is visible only if complexed with SRB2m due to increased molecular brightness and minimal background. With small angle X-ray scattering (SAXS), the three-dimensional structure of the RNA aptamer was characterized at low resolution to analyze the effect of fluorophore binding. The aptamer and sulforhodamine B-aptamer complex was found to be predominantly dimeric in solution. Interaction of PBV with SRB2m led to a dissociation of SRB2m dimers into monomers. Radii of gyration and hydrodynamic radii, gained from dynamic light scattering, FCS, and fluorescence cross-correlation experiments, led to comparable conclusions. Our study demonstrates how RNA-aptamer fluorophore complexes can be simultaneously structurally and photophysically characterized by FCS. Furthermore, fluorophore binding RNA aptamers provide a tool for visualizing single RNA molecules.

Probing the ionic atmosphere of single-stranded DNA using continuous flow capillary electrophoresis and fluorescence correlation spectroscopy

Two-beam fluorescence cross-correlation spectroscopy coupled with continuous flow capillary electrophoresis (2bFCCS-CFCE) was used to study the relationship between diffusion and effective charge of a fluorescently labeled 40-base polythymine single-stranded DNA (ssDNA) as a function of Mg2+ concentration. Cross-correlation analysis of the fluorescence monitored from two spatially offset microscopic detection volumes revealed the diffusion and electrophoretic migration of ssDNA at a range of Mg2+ concentrations and electric field strengths. The effective charge of the ssDNA could then be determined using simple calculations. It was found that as the Mg2+ concentration in the buffer solution increased, the diffusion of the ssDNA also increased, while the effective charge of the ssDNA decreased. This was believed to be caused by increased association of the Mg2+ counterions with the negatively charged backbone of the ssDNA, which partially neutralized the negatively charged functional groups and allowed the ssDNA to adopt a more compact structure. To our knowledge, this is the first demonstration of the measurement of effective charge of ssDNA in relation to Mg2+ concentration.

Toward resolution of ambiguity for the unfolded state

The unfolded states in proteins and nucleic acids remain weakly understood despite their importance in folding processes; misfolding diseases (Parkinson's and Alzheimer's); natively unfolded proteins (as many as 30% of eukaryotic proteins, according to Fink); and the study of ribozymes. Research has been hindered by the inability to quantify the residual (native) structure present in an unfolded protein or nucleic acid. Here, a scaling model is proposed to quantify the molar degree of folding and the unfolded state. The model takes a global view of protein structure and can be applied to a number of analytic methods and to simulations. Three examples are given of application to small-angle scattering from pressure-induced unfolding of SNase, from acid-unfolded cytochrome c, and from folding of Azoarcus ribozyme. These examples quantitatively show three characteristic unfolded states for proteins, the statistical nature of a protein folding pathway, and the relationship between extent of folding and chain size during folding for charge-driven folding in RNA.

Hinge stiffness is a barrier to RNA folding

Cation-mediated RNA folding from extended to compact, biologically active conformations relies on a temporal balance of forces. The Mg2 +-mediated folding of the Tetrahymena thermophila ribozyme is characterized by rapid nonspecific collapse followed by tertiary-contact-induced compaction. This article focuses on an autonomously folding portion of the Tetrahymena ribozyme, its P4-P6 domain, in order to probe one facet of the rapid collapse: chain flexibility. The time evolution of P4-P6 folding was followed by global and local measures as a function of Mg2 + concentration. While all concentrations of Mg2 + studied are sufficient to screen the charge on the helices, the rates of compaction and tertiary contact formation diverge as the concentration of Mg2 + increases; collapse is greatly accelerated by Mg2 +, while tertiary contact formation is not. These studies highlight the importance of chain stiffness to RNA folding; at 10 mM Mg2 +, a stiff hinge limits the rate of P4-P6 folding. At higher magnesium concentrations, the rate-limiting step shifts from hinge bending to tertiary contact formati

Electrostatic free energy landscapes for DNA helix bending

Nucleic acids are highly charged polyanionic molecules; thus, the ionic conditions are crucial for nucleic acid structural changes such as bending. We use the tightly bound ion theory, which explicitly accounts for the correlation and ensemble effects for counterions, to calculate the electrostatic free energy landscapes for DNA helix bending. The electrostatic free energy landscapes show that DNA bending energy is strongly dependent on ion concentration, valency, and size. In a Na(+) solution, DNA bending is electrostatically unfavorable because of the strong charge repulsion on backbone. With the increase of the Na(+) concentration, the electrostatic bending repulsion is reduced and thus the bending becomes less unfavorable. In contrast, in an Mg(2+) solution, ion correlation induces a possible attractive force between the different parts of the helical strands, resulting in bending. The electrostatically most favorable and unfavorable bending directions are toward the major and minor grooves, respectively. Decreasing the size of the divalent ions enhances the electrostatic bending attraction, causing an increased bending angle, and shifts the most favorable bending to the direction toward the minor groove. The microscopic analysis on ion-binding distribution reveals that the divalent ion-induced helix bending attraction may come from the correlated distribution of the ions across the grooves in the bending direction.

Spermidine modulated ribonuclease activity probed by RNA plasmon rulers

We extend the scope of nanometer distance measurements based on coupled pairs of gold nanoparticles, or plasmon rulers, to individual RNA molecules. These sensors were used to monitor the influence of spermidine on the cleavage kinetics of RNA by ribonuclease A. Time-resolved cleavage experiments of individual RNA plasmon rulers reveal transiently stabilized RNA sub-populations at increased spermidine concentrations that indicate spermidine-induced stabilization of weak secondary and tertiary structural elements.