The rate-limiting step in the folding of a large ribozyme without kinetic traps

Folding and Misfolding Dynamics of Irisin Protein Revealed by Single-Molecule Magnetic Tweezers

Irisin, a fibronectin III protein secreted by muscles during physical exercise, plays a significant role in the browning of white fat and cell adhesion, highlighting the importance of its conformational transitions. In this study, we investigated the folding and unfolding dynamics of a single irisin domain using a single-molecule manipulation technique known as magnetic tweezers. In addition to the native state, irisin can also fold transiently into a misfolded state. We determined the folding free energies of the native and misfolded states as well as their force-dependent folding and unfolding rates. The free energy of the misfolded state is higher than that of the unfolded state, and the misfolded state has a homogeneous force-dependent unfolding rate. The stable native state demonstrates heterogeneous unfolding rates that are within ∼1 order of magnitude. Via comparison with the well-studied 10th fibronectin III domain that has a partially folded intermediate state, our study demonstrates that proteins with similar structure can have distinct folding pathways.

Late consolidation of rRNA structure during co-transcriptional assembly in E. coli by time-resolved DMS footprinting

The production of new ribosomes requires proper folding of the rRNA and the addition of more than 50 ribosomal proteins. The structures of some assembly intermediates have been determined by cryo-electron microscopy, yet these structures do not provide information on the folding dynamics of the rRNA. To visualize the changes in rRNA structure during ribosome assembly in E. coli cells, transcripts were pulse-labeled with 4-thiouridine and the structure of newly made rRNA probed at various times by dimethyl sulfate modification and mutational profiling sequencing (4U-DMS-MaPseq). The in-cell DMS modification patterns revealed that many long-range rRNA tertiary interactions and protein binding sites through the 16S and 23S rRNA remain partially unfolded 1.5 min after transcription. By contrast, the active sites were continually shielded from DMS modification, suggesting that these critical regions are guarded by cellular factors throughout assembly. Later, bases near the peptidyl tRNA site exhibited specific rearrangements consistent with the binding and release of assembly factors. Time-dependent structure-probing in cells suggests that many tertiary interactions throughout the new ribosomal subunits remain mobile or unfolded until the late stages of subunit maturation.

Viscoelasticity and advective flow of RNA underlies nucleolar form and function

The nucleolus is the largest biomolecular condensate and facilitates transcription, processing, and assembly of ribosomal RNA (rRNA). Although nucleolar function is thought to require multiphase liquid-like properties, nucleolar fluidity and its connection to the highly coordinated transport and biogenesis of ribosomal subunits are poorly understood. Here, we use quantitative imaging, mathematical modeling, and pulse-chase nucleotide labeling to examine nucleolar material properties and rRNA dynamics. The mobility of rRNA is several orders of magnitude slower than that of nucleolar proteins, with rRNA steadily moving away from the transcriptional sites in a slow (∼1 Å/s), radially directed fashion. This constrained but directional mobility, together with polymer physics-based calculations, suggests that nascent rRNA forms an entangled gel, whose constant production drives outward flow. We propose a model in which progressive maturation of nascent rRNA reduces its initial entanglement, fluidizing the nucleolar periphery to facilitate the release of assembled pre-ribosomal particles.

Factors That Control the Force Needed to Unfold a Membrane Protein in Silico Depend on the Mode of Denaturation

Single-molecule force spectroscopy methods, such as AFM and magnetic tweezers, have proved extremely beneficial in elucidating folding pathways for soluble and membrane proteins. To identify factors that determine the force rupture levels in force-induced membrane protein unfolding, we applied our near-atomic-level Upside molecular dynamics package to study the vertical and lateral pulling of bacteriorhodopsin (bR) and GlpG, respectively. With our algorithm, we were able to selectively alter the magnitudes of individual interaction terms and identify that, for vertical pulling, hydrogen bond strength had the strongest effect, whereas other non-bonded protein and membrane-protein interactions had only moderate influences, except for the extraction of the last helix where the membrane-protein interactions had a stronger influence. The up-down topology of the transmembrane helices caused helices to be pulled out as pairs. The rate-limiting rupture event often was the loss of H-bonds and the ejection of the first helix, which then propagated tension to the second helix, which rapidly exited the bilayer. The pulling of the charged linkers across the membrane had minimal influence, as did changing the bilayer thickness. For the lateral pulling of GlpG, the rate-limiting rupture corresponded to the separation of the helices within the membrane, with the H-bonds generally being broken only afterward. Beyond providing a detailed picture of the rupture events, our study emphasizes that the pulling mode greatly affects the factors that determine the forces needed to unfold a membrane protein.

RNA Captures More Cations than DNA: Insights from Molecular Dynamics Simulations

The distribution of cations around nucleic acids is essential for a broad variety of processes ranging from DNA condensation and RNA folding to the detection of biomolecules in biosensors. Predicting the exact distribution of ions remains challenging since the distribution and, hence, a broad variety of nucleic acid properties depend on the salt concentration, the valency of the ions, and the ion type. Despite the importance, a general theory to quantify ion-specific effects for highly charged biomolecules is still lacking. Moreover, recent experiments reveal that despite their similar building blocks, DNA and RNA duplexes can react differently to the same ionic conditions. The aim of our current work is to provide a comprehensive set of molecular dynamics simulations using more than 180 μs of simulation time. For the mono- and divalent cations Li⁺, Na⁺, K⁺, Cs⁺, Ca²⁺, Sr²⁺, and Ba²⁺, the simulations allow us to reveal the ion-specific distributions and binding patterns for DNA and RNA duplexes. The microscopic insights from the simulations display the origin of ion-specificity and shed light on the question of why DNA and RNA show opposing behavior in the same ionic conditions. Finally, the detailed binding patterns from the simulations reveal why RNA can capture more cations than DNA.

Comparative study on tertiary contacts and folding of RNase P RNAs from a psychrophilic, a mesophilic/radiation-resistant, and a thermophilic bacterium

In most bacterial type A RNase P RNAs (P RNAs), two major loop-helix tertiary contacts (L8-P4 and L18-P8) help to orient the two independently folding S- and C-domains for concerted recognition of precursor tRNA substrates. Here, we analyze the effects of mutations in these tertiary contacts in P RNAs from three different species: (i) the psychrophilic bacterium Pseudoalteromonas translucida (Ptr), (ii) the mesophilic radiation-resistant bacterium Deinococcus radiodurans (Dra), and (iii) the thermophilic bacterium Thermus thermophilus (Tth). We show by UV melting experiments that simultaneous disruption of these two interdomain contacts has a stabilizing effect on all three P RNAs. This can be inferred from reduced RNA unfolding at lower temperatures and a more concerted unfolding at higher temperatures. Thus, when the two domains tightly interact via the tertiary contacts, one domain facilitates structural transitions in the other. P RNA mutants with disrupted interdomain contacts showed severe kinetic defects that were most pronounced upon simultaneous disruption of the L8-P4 and L18-P8 contacts. At 37°C, the mildest effects were observed for the thermostable Tth RNA. A third interdomain contact, L9-P1, makes only a minor contribution to P RNA tertiary folding. Furthermore, D. radiodurans RNase P RNA forms an additional pseudoknot structure between the P9 and P12 of its S-domain. This interaction was found to be particularly crucial for RNase P holoenzyme activity at near-physiological Mg²⁺ concentrations (2 mM). We further analyzed an exceptionally stable folding trap of the G,C-rich Tth P RNA.

Hofmeister Series for Metal-Cation-RNA Interactions: The Interplay of Binding Affinity and Exchange Kinetics

A large variety of physicochemical properties involving RNA depends on the type of metal cation present in solution. In order to gain microscopic insight into the origin of these ion specific effects, we apply molecular dynamics simulations to describe the interactions of metal cations and RNA. For the three most common ion binding sites on RNA, we calculate the binding affinities and exchange rates of eight different mono- and divalent metal cations. Our results reveal that binding sites involving phosphate groups preferentially bind metal cations with high charge density (such as Mg²⁺) in inner-sphere conformations while binding sites involving N7 or O6 atoms preferentially bind cations with low charge density (such as K⁺). The binding affinity therefore follows a direct Hofmeister series at the backbone but is reversed at the nucleobases leading to a high selectivity of ion binding sites on RNA. In addition, the exchange rates for cation binding cover almost 5 orders of magnitude, leading to a vastly different time scale for the lifetimes of contact pairs. Taken together, the site-specific binding affinities and the specific lifetime of contact pairs provide the microscopic explanation of ion specific effects observed in a wide variety of macroscopic RNA properties. Finally, combining the results from atomistic simulations with extended Poisson-Boltzmann theory allows us to predict the distribution of metal cations around double-stranded RNA at finite concentrations and to reproduce the results of ion counting experiments with good accuracy.

Refolding through a Linear Transition State Enables Fast Temperature Adaptation of a Translational Riboswitch

The adenine-sensing riboswitch from the Gram-negative bacterium Vibrio vulnificus is an RNA-based gene regulatory element that acts in response to both its cognate low-molecular weight ligand and temperature. The combined sensitivity to environmental temperature and ligand concentration is maintained by an equilibrium of three distinct conformations involving two ligand-free states and one ligand-bound state. The key structural element that undergoes refolding in the ligand-free states comprises a 35-nucleotide temperature response module. Here, we present the structural characterization of this temperature response module. We employ high-resolution NMR spectroscopy and photocaged RNAs as molecular probes to decipher the kinetic and thermodynamic framework of the secondary structure transition in the apo state of the riboswitch. We propose a model for the transition state adopted during the thermal refolding of the temperature response module that connects two mutually exclusive long-lived and stable conformational states. This transition state is characterized by a comparatively low free activation enthalpy. A pseudoknot conformation in the transition state, as commonly seen in RNA refolding, is therefore unlikely. More likely, the transition state of the adenine-sensing riboswitch temperature response module features a linear conformation.

Divalent ions tune the kinetics of a bacterial GTPase center rRNA folding transition from secondary to tertiary structure

Folding of an RNA from secondary to tertiary structure often depends on divalent ions for efficient electrostatic charge screening (nonspecific association) or binding (specific association). To measure how different divalent cations modify folding kinetics of the 60 nucleotide Ecoli rRNA GTPase center, we combined stopped-flow fluorescence in the presence of Mg²⁺, Ca²⁺, or Sr²⁺ together with time-resolved small angle X-ray scattering (SAXS) in the presence of Mg²⁺ to observe the folding process. Immediately upon addition of each divalent ion, the RNA undergoes a transition from an extended state with secondary structure to a more compact structure. Subsequently, specific divalent ions modulate populations of intermediates in conformational ensembles along the folding pathway with transition times longer than 10 msec. Rate constants for the five folding transitions act on timescales from submillisecond to tens of seconds. The sensitivity of RNA tertiary structure to divalent cation identity affects all but the fastest events in RNA folding, and allowed us to identify those states that prefer Mg²⁺ The GTPase center RNA appears to have optimized its folding trajectory to specifically utilize this most abundant intracellular divalent ion.

Effects of Preferential Counterion Interactions on the Specificity of RNA Folding

The real-time search for native RNA structure is essential for the operation of regulatory RNAs. We previously reported that a fraction of the Azoarcus ribozyme achieves a compact structure in less than a millisecond. To scrutinize the forces that drive initial folding steps, we used time-resolved SAXS to compare the folding dynamics of this ribozyme in thermodynamically isostable concentrations of different counterions. The results show that the size of the fast-folding population increases with the number of available counterions and correlates with the flexibility of initial RNA structures. Within 1 ms of folding, Mg²⁺ exhibits a smaller preferential interaction coefficient per charge, ΔΓ₊/ Z, than Na⁺ or [Co(NH₃)₆]³⁺. The lower ΔΓ₊/ Z corresponds to a smaller yield of folded RNA, although Mg²⁺ stabilizes native RNA more efficiently than other ions at equilibrium. These results suggest that strong Mg²⁺-RNA interactions impede the search for globally native structure during early folding stages.

Formation of Tertiary Interactions during rRNA GTPase Center Folding

The 60-nt GTPase center (GAC) of 23S rRNA has a phylogenetically conserved secondary structure with two hairpin loops and a 3-way junction. It folds into an intricate tertiary structure upon addition of Mg(2+) ions, which is stabilized by the L11 protein in cocrystal structures. Here, we monitor the kinetics of its tertiary folding and Mg(2+)-dependent intermediate states by observing selected nucleobases that contribute specific interactions to the GAC tertiary structure in the cocrystals. The fluorescent nucleobase 2-aminopurine replaced three individual adenines, two of which make long-range stacking interactions and one that also forms hydrogen bonds. Each site reveals a unique response to Mg(2+) addition and temperature, reflecting its environmental change from secondary to tertiary structure. Stopped-flow fluorescence experiments revealed that kinetics of tertiary structure formation upon addition of MgCl2 are also site specific, with local conformational changes occurring from 5 ms to 4s and with global folding from 1 to 5s. Site-specific substitution with (15)N-nucleobases allowed observation of stable hydrogen bond formation by NMR experiments. Equilibrium titration experiments indicate that a stable folding intermediate is present at stoichiometric concentrations of Mg(2+) and suggest that there are two initial sites of Mg(2+) ion association.

Mss116p: a DEAD-box protein facilitates RNA folding

RNA folding is an essential aspect underlying RNA-mediated cellular processes. Many RNAs, including large, multi-domain ribozymes, are capable of folding to the native, functional state without assistance of a protein cofactor in vitro. In the cell, trans-acting factors, such as proteins, are however known to modulate the structure and thus the fate of an RNA. DEAD-box proteins, including Mss116p, were recently found to assist folding of group I and group II introns in vitro and in vivo. The underlying mechanism(s) have been studied extensively to explore the contribution of ATP hydrolysis and duplex unwinding in helicase-stimulated intron splicing. Here we summarize the ongoing efforts to understand the novel role of DEAD-box proteins in RNA folding.

Milestoning with transition memory

Milestoning is a method used to calculate the kinetics and thermodynamics of molecular processes occurring on time scales that are not accessible to brute force molecular dynamics (MD). In milestoning, the conformation space of the system is sectioned by hypersurfaces (milestones), an ensemble of trajectories is initialized on each milestone, and MD simulations are performed to calculate transitions between milestones. The transition probabilities and transition time distributions are then used to model the dynamics of the system with a Markov renewal process, wherein a long trajectory of the system is approximated as a succession of independent transitions between milestones. This approximation is justified if the transition probabilities and transition times are statistically independent. In practice, this amounts to a requirement that milestones are spaced such that trajectories lose position and velocity memory between subsequent transitions. Unfortunately, limiting the number of milestones limits both the resolution at which a system's properties can be analyzed, and the computational speedup achieved by the method. We propose a generalized milestoning procedure, milestoning with transition memory (MTM), which accounts for memory of previous transitions made by the system. When a reaction coordinate is used to define the milestones, the MTM procedure can be carried out at no significant additional expense as compared to conventional milestoning. To test MTM, we have applied its version that allows for the memory of the previous step to the toy model of a polymer chain undergoing Langevin dynamics in solution. We have computed the mean first passage time for the chain to attain a cyclic conformation and found that the number of milestones that can be used, without incurring significant errors in the first passage time is at least 8 times that permitted by conventional milestoning. We further demonstrate that, unlike conventional milestoning, MTM permits milestones to be spaced such that trajectories do not have enough time to lose their velocity memory between successively crossed milestones.

Magnesium Ion-Water Coordination and Exchange in Biomolecular Simulations

Magnesium ions have an important role in the structure and folding mechanism of ribonucleic acid systems. To properly simulate these biophysical processes, the applied molecular models should reproduce, among other things, the kinetic properties of the ions in water solution. Here, we have studied the kinetics of the binding of magnesium ions with water molecules and nucleic acid systems using molecular dynamics simulation in detail. We have validated the parameters used in biomolecular force fields, such as AMBER and CHARMM, for Mg(2+) ions and also for the biologically relevant ions Na(+), K(+), and Ca(2+) together with three different water models (TIP3P, SPC/E, and TIP5P). The results show that Mg(2+) ions have a slower exchange rate than Na(+), K(+), and Ca(2+) in agreement with the experimental trend, but the simulated value underestimates the experimentally observed Mg(2+)-water exchange rate by several orders of magnitude, irrespective of the force field and water model. A new set of parameters for Mg(2+) was developed to reproduce the experimental kinetic data. This set also leads to better reproduction of structural data than existing models. We have applied the new parameter set to Mg(2+) binding with a monophosphate model system and with the purine riboswitch, add A-riboswitch. In line with the Mg(2+)-water results, the newly developed parameters show a better description of the structure and kinetics of the Mg(2+)-phosphate binding than all other models. The characterization of the ion binding to the riboswitch system shows that the new parameter set does not affect the global structure of the ribonucleic acid system or the number of ions involved in direct or indirect binding. A slight decrease in the number of water-bridged contacts between A-riboswitch and the Mg(2+) ion is observed. The results support the ability of the newly developed parameters to improve the kinetic description of the Mg(2+) and phosphate ions and their applicability in nucleic acid simulation.

Entropic origin of Mg2+-facilitated RNA folding

Mg(2+) is essential for the proper folding and function of RNA, though the effect of Mg(2+) 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(2+)]. 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(2+)]-facilitated folding. Surprisingly, these studies reveal that increasing [Mg(2+)] promotes tetraloop-receptor interaction by reducing the entropic barrier (-TΔS(++)(dock)) and the overall entropic penalty (-TΔS(+) (dock)) for docking, with essentially negligible effects on both the activation enthalpy (ΔH(++)(dock)) and overall exothermicity (ΔH(+)(dock)). These observations contrast with the conventional notion that increasing [Mg(2+)] facilitates folding by minimizing electrostatic repulsion of opposing RNA helices, which would incorrectly predict a decrease in ΔH(++)(dock)) and ΔH(+)(dock)) with [Mg(2+)]. Instead we propose that higher [Mg(2+)] can aid RNA folding by decreasing the entropic penalty of counterion uptake and by reducing disorder of the unfolded conformational ensemble.

Fast folding of RNA pseudoknots initiated by laser temperature-jump

RNA pseudoknots are examples of minimal structural motifs in RNA with tertiary interactions that stabilize the structures of many ribozymes. They also play an essential role in a variety of biological functions that are modulated by their structure, stability, and dynamics. Therefore, understanding the global principles that determine the thermodynamics and folding pathways of RNA pseudoknots is an important problem in biology, both for elucidating the folding mechanisms of larger ribozymes as well as addressing issues of possible kinetic control of the biological functions of pseudoknots. We report on the folding/unfolding kinetics of a hairpin-type pseudoknot obtained with microsecond time-resolution in response to a laser temperature-jump perturbation. The kinetics are monitored using UV absorbance as well as fluorescence of extrinsically attached labels as spectroscopic probes of the transiently populated RNA conformations. We measure folding times of 1-6 ms at 37 °C, which are at least 100-fold faster than previous observations of very slow folding pseudoknots that were trapped in misfolded conformations. The measured relaxation times are remarkably similar to predictions of a computational study by Thirumalai and co-workers (Cho, S. S.; Pincus, D.L.; Thirumalai, D. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 17349-17354). Thus, these studies provide the first observation of a fast-folding pseudoknot and present a benchmark against which computational models can be refined.

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.

Time resolved SAXS and RNA folding

Small angle X-ray scattering provides low resolution structural information about macromolecules in solution. When coupled with rapid mixing methods, SAXS reports time-dependent conformational changes of RNA induced by the addition of Mg(2+) to trigger folding. Thus time-resolved SAXS provides unique information about the global or overall structures of transient intermediates populated during folding. Notably, SAXS provides information about the earliest folding events, which can evade detection by other methods.

Taming free energy landscapes with RNA chaperones

Many non-coding RNAs fold into complex three-dimensional structures, yet the self-assembly of RNA structure is hampered by mispairing, weak tertiary interactions, electrostatic barriers, and the frequent requirement that the 5' and 3' ends of the transcript interact. This rugged free energy landscape for RNA folding means that some RNA molecules in a population rapidly form their native structure, while many others become kinetically trapped in misfolded conformations. Transient binding of RNA chaperone proteins destabilize misfolded intermediates and lower the transition states between conformations, producing a smoother landscape that increases the rate of folding and the probability that a molecule will find the native structure. DEAD-box proteins couple the chemical potential of ATP hydrolysis with repetitive cycles of RNA binding and release, expanding the range of conditions under which they can refold RNA structures.

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.

Compact intermediates in RNA folding

Large noncoding RNAs fold into their biologically functional structures via compact yet disordered intermediates, which couple the stable secondary structure of the RNA with the emerging tertiary fold. The specificity of the collapse transition, which coincides with the assembly of helical domains, depends on RNA sequence and counterions. It determines the specificity of the folding pathways and the magnitude of the free energy barriers to the ensuing search for the native conformation. By coupling helix assembly with nascent tertiary interactions, compact folding intermediates in RNA also play a crucial role in ligand binding and RNA-protein recognition.

A divalent cation stabilizes the active conformation of the B. subtilis RNase P x pre-tRNA complex: a role for an inner-sphere metal ion in RNase P

Metal ions interact with RNA to enhance folding, stabilize structure, and, in some cases, facilitate catalysis. Assigning functional roles to specifically bound metal ions presents a major challenge in analyzing the catalytic mechanisms of ribozymes. Bacillus subtilis ribonuclease P (RNase P), composed of a catalytically active RNA subunit (PRNA) and a small protein subunit (P protein), catalyzes the 5'-end maturation of precursor tRNAs (pre-tRNAs). Inner-sphere coordination of divalent metal ions to PRNA is essential for catalytic activity but not for the formation of the RNase P x pre-tRNA (enzyme-substrate, ES) complex. Previous studies have demonstrated that this ES complex undergoes an essential conformational change (to the ES* conformer) before the cleavage step. Here, we show that the ES* conformer is stabilized by a high-affinity divalent cation capable of inner-sphere coordination, such as Ca(II) or Mg(II). Additionally, a second, lower-affinity Mg(II) activates cleavage catalyzed by RNase P. Structural changes that occur upon binding Ca(II) to the ES complex were determined by time-resolved Förster resonance energy transfer measurements of the distances between donor-acceptor fluorophores introduced at specific locations on the P protein and pre-tRNA 5' leader. These data demonstrate that the 5' leader of pre-tRNA moves 4 to 6 A closer to the PRNA x P protein interface during the ES-to-ES* transition and suggest that the metal-dependent conformational change reorganizes the bound substrate in the active site to form a catalytically competent ES* complex.

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.

Probing metal binding in the 8-17 DNAzyme by TbIII luminescence spectroscopy

Metal-dependent cleavage activities of the 8-17 DNAzyme were found to be inhibited by Tb(III) ions, and the apparent inhibition constant in the presence of 100 microM of Zn(II) was measured to be 3.3+/-0.3 microM. The apparent inhibition constants increased linearly with increasing Zn(II) concentration, and the inhibition effect could be fully rescued with addition of active metal ions, indicating that Tb(III) is a competitive inhibitor and that the effect is completely reversible. The sensitized Tb(III) luminescence at 543 nm was dramatically enhanced when Tb(III) was added to the DNAzyme-substrate complex. With an inactive DNAzyme in which the GT wobble pair was replaced with a GC Watson-Crick base pair, the luminescence enhancement was slightly decreased. In addition, when the DNAzyme strand was replaced with a complete complementary strand to the substrate, no significant luminescence enhancement was observed. These observations suggest that Tb(III) may bind to an unpaired region of the DNAzyme, with the GT wobble pair playing a role. Luminescence lifetime measurements in D(2)O and H(2)O suggested that Tb(III) bound to DNAzyme is coordinated by 6.7+/-0.2 water molecules and two or three functional groups from the DNAzyme. Divalent metal ions competed for the Tb(III) binding site(s) in the order Co(II)>Zn(II)>Mn(II)>Pb(II)>Ca(II) approximately Mg(II). This order closely follows the order of DNAzyme activity, with the exception of Pb(II). These results indicate that Pb(II), the most active metal ion, competes for Tb(III) binding differently from other metal ions such as Zn(II), suggesting that Pb(II) may bind to a different site from that for the other metal ions including Zn(II) and Tb(III).

Energy barriers, pathways, and dynamics during folding of large, multidomain RNAs

Large, multidomain RNA molecules are generally thought to fold following multiple pathways down rugged landscapes populated with intermediates and traps. A challenge to understanding RNA folding reactions is the complex relationships that exist between the structure of the RNA and its folding landscape. The identification of intermediate species that populate folding landscapes and characterization of elements of their structures are the key components to solving the RNA folding problem. This review explores recent studies that characterize the dominant pathways by which RNA folds, structural and dynamic features of intermediates that populate the folding landscape, and the energy barriers that separate the distinct steps of the folding process.

Single-molecule studies of group II intron ribozymes

Group II intron ribozymes fold into their native structure by a unique stepwise process that involves an initial slow compaction followed by fast formation of the native state in a Mg(2+)-dependent manner. Single-molecule fluorescence reveals three distinct on-pathway conformations in dynamic equilibrium connected by relatively small activation barriers. From a most stable near-native state, the unobserved catalytically active conformer is reached. This most compact conformer occurs only transiently above 20 mM Mg(2+) and is stabilized by substrate binding, which together explain the slow cleavage of the ribozyme. Structural dynamics increase with increasing Mg(2+) concentrations, enabling the enzyme to reach its active state.

Kinetic barriers and the role of topology in protein and RNA folding

This review compares the folding behavior of proteins and RNAs. Topics covered include the role of topology in the determination of folding rates, major folding events including collapse, properties of denatured states, pathway heterogeneity, and the influence of the mode of initiation on the folding pathway.

Ultrafast active mixer using polyelectrolytic ion extractor

We report on a low voltage, straight/smooth surface, and efficient active micromixer. The mixing principle is based on alternative ion depletion-enrichment using a pair of positively charged polyelectrolytic gel electrodes (pPGEs), which face each other joined by a microchannel. This system has an external AC signal source electrically connected to the pPGEs via the respective 1 M KCl solutions and Ag/AgCl electrodes. When an electric bias is applied between the two pPGEs, anions are extracted through one of the pPGEs to create a local ion-deficient region. Simultaneously, an ion-rich area appears near the other pPGE due to an inward anionic flux. As the direction of the charge flow is periodically reversed by the AC signal source, the ion depletion-enrichment regions are alternately swapped with each other on the 'push-pull' basis. The turmoil between the pPGEs quickly mixes the solutions in the microchannel without any mechanical moving part or specially machined structures. In the proposed system, both AC frequency and current density can be easily and finely controlled so that one can quickly find the optimal conditions for a given sample. The micromixer as made showed a mixing efficiency higher than 90% for sample solutions of 1 mM Rhodamine 6G and PBS at pH 7.4 when the flow rate was under 6 mm s(-1). In addition to the solution-solution mixing, the micromixer can effectively mix suspended microparticles with solution. As a representative example, rapid and efficient lysis of human red blood cells was demonstrated allowing minimal damage of the white blood cells.

Single-molecule nonequilibrium periodic Mg2+-concentration jump experiments reveal details of the early folding pathways of a large RNA

The evolution of RNA conformation with Mg(2+) concentration ([Mg(2+)]) is typically determined from equilibrium titration measurements or nonequilibrium single [Mg(2+)]-jump measurements. We study the folding of single RNA molecules in response to a series of periodic [Mg(2+)] jumps. The 260-residue catalytic domain of RNase P RNA from Bacillus stearothermophilus is immobilized in a microfluidic flow chamber, and the RNA conformational changes are probed by fluorescence resonance energy transfer (FRET). The kinetics of population redistribution after a [Mg(2+)] jump and the observed connectivity of FRET states reveal details of the folding pathway that complement and transcend information from equilibrium or single-jump measurements. FRET trajectories for jumps from [Mg(2+)] = 0.01 to 0.1 mM exhibit two-state behavior whereas jumps from 0.01 mM to 0.4 mM exhibit two-state unfolding but multistate folding behavior. RNA molecules in the low and high FRET states before the [Mg(2+)] increase are observed to undergo dynamics in two distinct regions of the free energy landscape separated by a high barrier. We describe the RNA structural changes involved in crossing this barrier as a "hidden" degree of freedom because the changes do not alter the detected FRET value but do alter the observed dynamics. The associated memory prevents the populations from achieving their equilibrium values at the end of the 5- to 10-sec [Mg(2+)] interval, thereby creating a nonequilibrium steady-state condition. The capability of interrogating nonequilibrium steady-state RNA conformations and the adjustable period of [Mg(2+)]-jump cycles makes it possible to probe regions of the free energy landscape that are infrequently sampled in equilibrium or single-jump measurements.

A large collapsed-state RNA can exhibit simple exponential single-molecule dynamics

The process of large RNA folding is believed to proceed from many collapsed structures to a unique functional structure requiring precise organization of nucleotides. The diversity of possible structures and stabilities of large RNAs could result in non-exponential folding kinetics (e.g. stretched exponential) under conditions where the molecules have not achieved their native state. We describe a single-molecule fluorescence resonance energy transfer (FRET) study of the collapsed-state region of the free energy landscape of the catalytic domain of RNase P RNA from Bacillus stearothermophilus (C(thermo)). Ensemble measurements have shown that this 260 residue RNA folds cooperatively to its native state at >or=1 mM Mg(2+), but little is known about the conformational dynamics at lower ionic strength. Our measurements of equilibrium conformational fluctuations reveal simple exponential kinetics that reflect a small number of discrete states instead of the expected inhomogeneous dynamics. The distribution of discrete dwell times, collected from an "ensemble" of 300 single molecules at each of a series of Mg(2+) concentrations, fit well to a double exponential, which indicates that the RNA conformational changes can be described as a four-state system. This finding is somewhat unexpected under [Mg(2+)] conditions in which this RNA does not achieve its native state. Observation of discrete well-defined conformations in this large RNA that are stable on the seconds timescale at low [Mg(2+)] (<0.1 mM) suggests that even at low ionic strength, with a tremendous number of possible (weak) interactions, a few critical interactions may produce deep energy wells that allow for rapid averaging of motions within each well, and yield kinetics that are relatively simple.

RNA misfolding and the action of chaperones

RNA folds to a myriad of three-dimensional structures and performs an equally diverse set of functions. The ability of RNA to fold and function in vivo is all the more remarkable because, in vitro, RNA has been shown to have a strong propensity to adopt misfolded, non-functional conformations. A principal factor underlying the dominance of RNA misfolding is that local RNA structure can be quite stable even in the absence of enforcing global tertiary structure. This property allows non-native structure to persist, and it also allows native structure to form and stabilize non-native contacts or non-native topology. In recent years it has become clear that one of the central reasons for the apparent disconnect between the capabilities of RNA in vivo and its in vitro folding properties is the presence of RNA chaperones, which facilitate conformational transitions of RNA and therefore mitigate the deleterious effects of RNA misfolding. Over the past two decades, it has been demonstrated that several classes of non-specific RNA binding proteins possess profound RNA chaperone activity in vitro and when overexpressed in vivo, and at least some of these proteins appear to function as chaperones in vivo. More recently, it has been shown that certain DExD/H-box proteins function as general chaperones to facilitate folding of group I and group II introns. These proteins are RNA-dependent ATPases and have RNA helicase activity, and are proposed to function by using energy from ATP binding and hydrolysis to disrupt RNA structure and/or to displace proteins from RNA-protein complexes. This review outlines experimental studies that have led to our current understanding of the range of misfolded RNA structures, the physical origins of RNA misfolding, and the functions and mechanisms of putative RNA chaperone proteins.

Single-molecule mechanical unfolding and folding of a pseudoknot in human telomerase RNA

RNA unfolding and folding reactions in physiological conditions can be facilitated by mechanical force one molecule at a time. By using force-measuring optical tweezers, we studied the mechanical unfolding and folding of a hairpin-type pseudoknot in human telomerase RNA in a near-physiological solution, and at room temperature. Discrete two-state folding transitions of the pseudoknot are seen at approximately 10 and approximately 5 piconewtons (pN), with ensemble rate constants of approximately 0.1 sec(-1), by stepwise force-drop experiments. Folding studies of the isolated 5'-hairpin construct suggested that the 5'-hairpin within the pseudoknot forms first, followed by formation of the 3'-stem. Stepwise formation of the pseudoknot structure at low forces are in contrast with the one-step unfolding at high forces of approximately 46 pN, at an average rate of approximately 0.05 sec(-1). In the constant-force folding trajectories at approximately 10 pN and approximately 5 pN, transient formation of nonnative structures were observed, which is direct experimental evidence that folding of both the hairpin and pseudoknot takes complex pathways. Possible nonnative structures and folding pathways are discussed.

Selective quenching of fluorescence from unbound oligonucleotides by gold nanoparticles as a probe of RNA structure

Binding of small oligonucleotides to the periphery of folded RNA can provide insight into the secondary structure of complex RNA in solution. To discriminate between bound and unbound fluorescein-labeled 2'-O-methyl RNA probes, we use ionically coated gold nanoparticles to selectively adsorb unbound probes and quench their fluorescence. The target is the 3' untranslated region of Bombyx mori R2 RNA. Fluorescence indicates that R2 sequences complementary to some of the probes are accessible for binding in the three-dimensional structure. Hybridization occurs under homogeneous conditions in the absence of the gold nanoparticles so that steric issues associated with chip-based assays are avoided. The assay is compatible with well plate formats, takes less than 5 min, and requires only 2 pmol or less of unlabeled target RNA per probe sequence tested.

Folding of a universal ribozyme: the ribonuclease P RNA

Ribonuclease P is among the first ribozymes discovered, and is the only ubiquitously occurring ribozyme besides the ribosome. The bacterial RNase P RNA is catalytically active without its protein subunit and has been studied for over two decades as a model system for RNA catalysis, structure and folding. This review focuses on the thermodynamic, kinetic and structural frameworks derived from the folding studies of bacterial RNase P RNA.

Distinct contribution of electrostatics, initial conformational ensemble, and macromolecular stability in RNA folding

We distinguish the contribution of the electrostatic environment, initial conformational ensemble, and macromolecular stability on the folding mechanism of a large RNA using a combination of time-resolved "Fast Fenton" hydroxyl radical footprinting and exhaustive kinetic modeling. This integrated approach allows us to define the folding landscape of the L-21 Tetrahymena thermophila group I intron structurally and kinetically from its earliest steps with unprecedented accuracy. Distinct parallel pathways leading the RNA to its native form upon its Mg(2+)-induced folding are observed. The structures of the intermediates populating the pathways are not affected by variation of the concentration and type of background monovalent ions (electrostatic environment) but are altered by a mutation that destabilizes one domain of the ribozyme. Experiments starting from different conformational ensembles but folding under identical conditions show that whereas the electrostatic environment modulates molecular flux through different pathways, the initial conformational ensemble determines the partitioning of the flux. This study showcases a robust approach for the development of kinetic models from collections of local structural probes.

Charge density of divalent metal cations determines RNA stability

RNA molecules are exquisitely sensitive to the properties of counterions. The folding equilibrium of the Tetrahymena ribozyme is measured by nondenaturing gel electrophoresis in the presence of divalent group IIA metal cations. The stability of the folded ribozyme increases with the charge density (zeta) of the cation. Similar scaling is found when the free energy of the RNA folded in small and large metal cations is measured by urea denaturation. Brownian dynamics simulations of a polyelectrolyte show that the experimental observations can be explained by nonspecific ion-RNA interactions in the absence of site-specific metal chelation. The experimental and simulation results establish that RNA stability is largely determined by a combination of counterion charge and the packing efficiency of condensed cations that depends on the excluded volume of the cations.

Folding of group II introns: a model system for large, multidomain RNAs?

Group II introns are among the largest ribozymes in nature. They have a highly complex tertiary architecture that enables them to catalyze numerous processes, including self-splicing and transposition reactions that have probably contributed to the evolution of eukaryotic genomes. Biophysical analyses show that, despite their large size, these RNAs can fold to their native state through direct pathways that are populated by structurally defined intermediates. In addition, proteins have specific and important roles in this folding process. As a consequence, the study of the group II introns provides a valuable system for both exploring the driving forces behind the folding of multidomain RNA molecules and investigating ribonucleoprotein assembly.

Group II introns: structure, folding and splicing mechanism

Group II introns are large autocatalytic RNAs found in organellar genomes of plants and lower eukaryotes, as well as in some bacterial genomes. Interestingly, these ribozymes share characteristic traits with both spliceosomal introns and non-LTR retrotransposons and may have a common evolutionary ancestor. Furthermore, group II intron features such as structure, folding and catalytic mechanism differ considerably from those of other large ribozymes, making group II introns an attractive model system to gain novel insights into RNA biology and biochemistry. This review explores recent advances in the structural and mechanistic characterization of group II intron architecture and self-splicing.

A folding control element for tertiary collapse of a group II intron ribozyme

Ribozymes derived from the group II intron ai5gamma collapse to a compact intermediate, folding to the native state through a slow, direct pathway that is unperturbed by kinetic traps. Molecular collapse of ribozyme D135 requires high magnesium concentrations and is thought to involve a structural element in domain 1 (D1). We used nucleotide analog interference mapping, in combination with nondenaturing gel electrophoresis, to identify RNA substructures and functional groups that are essential for D135 tertiary collapse. This revealed that the most crucial atoms for compaction are located within a small section of D1 that includes the kappa and zeta elements. This small substructure controls specific collapse of the molecule and, in later steps of the folding pathway, it forms the docking site for catalytic D5. In this way, the stage is set for proper active site formation during the earliest steps of ribozyme folding.

The paradoxical behavior of a highly structured misfolded intermediate in RNA folding

Like many structured RNAs, the Tetrahymena group I ribozyme is prone to misfolding. Here we probe a long-lived misfolded species, referred to as M, and uncover paradoxical aspects of its structure and folding. Previous work indicated that a non-native local secondary structure, termed alt P3, led to formation of M during folding in vitro. Surprisingly, hydroxyl radical footprinting, fluorescence measurements with site-specifically incorporated 2-aminopurine, and functional assays indicate that the native P3, not alt P3, is present in the M state. The paradoxical behavior of alt P3 presumably arises because alt P3 biases folding toward M, but, after commitment to this folding pathway and before formation of M, alt P3 is replaced by P3. Further, structural and functional probes demonstrate that the misfolded ribozyme contains extensive native structure, with only local differences between the two states, and the misfolded structure even possesses partial catalytic activity. Despite the similarity of these structures, re-folding of M to the native state is very slow and is strongly accelerated by urea, Na+, and increased temperature and strongly impeded by Mg2+ and the presence of native peripheral contacts. The paradoxical observations of extensive native structure within the misfolded species but slow conversion of this species to the native state are readily reconciled by a model in which the misfolded state is a topological isomer of the native state, and computational results support the feasibility of this model. We speculate that the complex topology of RNA secondary structures and the inherent rigidity of RNA helices render kinetic traps due to topological isomers considerably more common for RNA than for proteins.

Counterion charge density determines the position and plasticity of RNA folding transition states

The self-assembly of RNA structure depends on the interactions of counterions with the RNA and with each other. Comparison of various polyamines showed that the tertiary structure of the Tetrahymena ribozyme is more stable when the counterions are small and highly charged. By monitoring the folding kinetics of the ribozyme as a function of polyamine concentration, we now find that the charge density of the counterions determines the positions of the folding transition states. The transition state ensemble (TSE) between U and N moves away from the native state as the counterion valence and charge density increase, as predicted by the Hammond postulate. The TSE is broader and less structured when the RNA is refolded in polyamines rather than Mg2+. That the charge density of the counterions determines the plasticity of the TSE demonstrates the importance of interactions among condensed counterions for the self-assembly of RNA structures. We propose that the major barrier to RNA folding is dominated by entropy changes when counterion charge density is low and enthalpy differences when it is high.

An obligate intermediate along the slow folding pathway of a group II intron ribozyme

Most RNA molecules collapse rapidly and reach the native state through a pathway that contains numerous traps and unproductive intermediates. The D135 group II intron ribozyme is unusual in that it can fold slowly and directly to the native state, despite its large size and structural complexity. Here we use hydroxyl radical footprinting and native gel analysis to monitor the timescale of tertiary structure collapse and to detect the presence of obligate intermediates along the folding pathway of D135. We find that structural collapse and native folding of Domain 1 precede assembly of the entire ribozyme, indicating that D1 contains an on-pathway intermediate to folding of the D135 ribozyme. Subsequent docking of Domains 3 and 5, for which D1 provides a preorganized scaffold, appears to be very fast and independent of one another. In contrast to other RNAs, the D135 ribozyme undergoes slow tertiary collapse to a compacted state, with a rate constant that is also limited by the formation D1. These findings provide a new paradigm for RNA folding and they underscore the diversity of RNA biophysical behaviors.

Perturbation of the hierarchical folding of a large RNA by the destabilization of its Scaffold's tertiary structure

The P4-P6 domain serves as a scaffold against which the periphery and catalytic core organize and fold during Mg2+-mediated folding of the Tetrahymena thermophila ribozyme. The most prominent structural motif of the P4-P6 domain is the tetraloop-tetraloop receptor interaction which "clamps" the distal parts of its hairpin-like structure. Destabilization of the tertiary structure of the P4-P6 domain by perturbation of the tetraloop-tetraloop receptor interaction alters the Mg2+-mediated folding pathway. The folding hierarchy of P5c approximately P4-P6 > periphery > catalytic core that is a striking attribute of the folding of the wild-type RNA is abolished. The initial steps in folding of the mutant RNA are > or =50-fold faster than those of the wild-type ribozyme with the earliest observed tertiary contacts forming around regions known to specifically bind Mg2+. The interaction between the mutant tetraloop and the tetraloop receptor appears coincidently with slowly forming catalytic core tertiary contacts. Thus, the stability conferred upon the P4-P6 domain by the tetraloop-tetraloop receptor interaction dictates the preferred folding pathway by stabilizing an early intermediate. A sub-denaturing concentration of urea diminishes the early barrier to folding the wild-type ribozyme along with complex effects on the subsequent steps of folding the wild-type and mutant RNA.

RNA tertiary interactions mediate native collapse of a bacterial group I ribozyme

Large RNAs collapse into compact intermediates in the presence of counterions before folding to the native state. We previously found that collapse of a bacterial group I ribozyme correlates with the formation of helices within the ribozyme core, but occurs at Mg2+ concentrations too low to support stable tertiary structure and catalytic activity. Here, using small-angle X-ray scattering, we show that Mg2+-induced collapse is a cooperative folding transition that can be fit by a two-state model. The Mg2+ dependence of collapse is similar to the Mg2+ dependence of helix assembly measured by partial ribonuclease T1 digestion and of an unfolding transition measured by UV hypochromicity. The correspondence between multiple probes of RNA structure further supports a two-state model. A mutation that disrupts tertiary contacts between the L9 tetraloop and its helical receptor destabilized the compact state by 0.8 kcal/mol, while mutations in the central triplex were less destabilizing. These results show that native tertiary interactions stabilize the compact folding intermediates under conditions in which the RNA backbone remains accessible to solvent.

Metal ions and RNA folding: a highly charged topic with a dynamic future

Metal ions are required to stabilize RNA tertiary structure and to begin the folding process. How different metal ions enable RNAs to fold depends on the electrostatic potential of the RNA and correlated fluctuations in the positions of the ions themselves. Theoretical models, fluorescence spectroscopy, small angle scattering and structural biology reveal that metal ions alter the RNA dynamics and folding transition states. Specifically coordinated divalent metal ions mediate conformational rearrangements within ribozyme active sites.

Thermodynamic and kinetic aspects of RNA pulling experiments

Recent single-molecule pulling experiments have shown how it is possible to manipulate RNA molecules using laser tweezers. In this article we investigate a minimal model for the experimental setup which includes an RNA molecule connected to two polymers (handles) and a bead trapped in the optical potential and attached to one of the handles. We start by considering the case of small single-domain RNA molecules, which unfold in a cooperative way. The model qualitatively reproduces the experimental results and allows us to investigate the influence of the bead and handles on the unfolding reaction. A main ingredient of the model is to consider the appropriate statistical ensemble and the corresponding thermodynamic potential describing thermal fluctuations in the system. We then investigate several questions relevant to extract thermodynamic information from experimental data. The kinetics of unfolding is also studied by introducing a dynamical model. Finally, we apply the model to the more general problem of a multidomain RNA molecule with Mg(2+) tertiary contacts that unfolds in a sequential way.