RNA and protein folding: common themes and variations

A Deep Learning-Driven Sampling Technique to Explore the Phase Space of an RNA Stem-Loop

The folding and unfolding of RNA stem-loops are critical biological processes; however, their computational studies are often hampered by the ruggedness of their folding landscape, necessitating long simulation times at the atomistic scale. Here, we adapted DeepDriveMD (DDMD), an advanced deep learning-driven sampling technique originally developed for protein folding, to address the challenges of RNA stem-loop folding. Although tempering- and order parameter-based techniques are commonly used for similar rare-event problems, the computational costs or the need for a priori knowledge about the system often present a challenge in their effective use. DDMD overcomes these challenges by adaptively learning from an ensemble of running MD simulations using generic contact maps as the raw input. DeepDriveMD enables on-the-fly learning of a low-dimensional latent representation and guides the simulation toward the undersampled regions while optimizing the resources to explore the relevant parts of the phase space. We showed that DDMD estimates the free energy landscape of the RNA stem-loop reasonably well at room temperature. Our simulation framework runs at a constant temperature without external biasing potential, hence preserving the information on transition rates, with a computational cost much lower than that of the simulations performed with external biasing potentials. We also introduced a reweighting strategy for obtaining unbiased free energy surfaces and presented a qualitative analysis of the latent space. This analysis showed that the latent space captures the relevant slow degrees of freedom for the RNA folding problem of interest. Finally, throughout the manuscript, we outlined how different parameters are selected and optimized to adapt DDMD for this system. We believe this compendium of decision-making processes will help new users adapt this technique for the rare-event sampling problems of their interest.

Adjusting the Energy Profile for CH-O Interactions Leads to Improved Stability of RNA Stem-Loop Structures in MD Simulations

The role of ribonucleic acid (RNA) in biology continues to grow, but insight into important aspects of RNA behavior is lacking, such as dynamic structural ensembles in different environments, how flexibility is coupled to function, and how function might be modulated by small molecule binding. In the case of proteins, much progress in these areas has been made by complementing experiments with atomistic simulations, but RNA simulation methods and force fields are less mature. It remains challenging to generate stable RNA simulations, even for small systems where well-defined, thermostable structures have been established by experiments. Many different aspects of RNA energetics have been adjusted in force fields, seeking improvements that are transferable across a variety of RNA structural motifs. In this work, the role of weak CH···O interactions is explored, which are ubiquitous in RNA structure but have received less attention in RNA force field development. By comparing data extracted from high-resolution RNA crystal structures to energy profiles from quantum mechanics and force field calculations, it is shown that CH···O interactions are overly repulsive in the widely used Amber RNA force fields. A simple, targeted adjustment of CH···O repulsion that leaves the remainder of the force field unchanged was developed. Then, the standard and modified force fields were tested using molecular dynamics (MD) simulations with explicit water and salt, amassing over 300 μs of data for multiple RNA systems containing important features such as the presence of loops, base stacking interactions as well as canonical and noncanonical base pairing. In this work and others, standard force fields lead to reproducible unfolding of the NMR-based structures. Including a targeted CH···O adjustment in an otherwise identical protocol dramatically improves the outcome, leading to stable simulations for all RNA systems tested.

The energy landscape of the ribosome

The ribosome is a prototypical assembly that can be used to establish general principles and techniques for the study of biological molecular machines. Motivated by the fact that the dynamics of every biomolecule is governed by an underlying energy landscape, there has been great interest to understand and quantify ribosome energetics. In the present review, we will focus on theoretical and computational strategies for probing the interactions that shape the energy landscape of the ribosome, with an emphasis on more recent studies of the elongation cycle. These efforts include the application of quantum mechanical methods for describing chemical kinetics, as well as classical descriptions to characterize slower (microsecond to millisecond) large-scale (10-100 Å) rearrangements, where motion is described in terms of diffusion across an energy landscape. Together, these studies provide broad insights into the factors that control a diverse range of dynamical processes in this assembly.

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

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

R, de Oliveira R, Dunham C, Whitford P. Ratchet, swivel, tilt and roll: a complete description of subunit rotation in the ribosome

Protein synthesis by the ribosome requires large-scale rearrangements of the 'small' subunit (SSU; ∼1 MDa), including inter- and intra-subunit rotational motions. However, with nearly 2000 structures of ribosomes and ribosomal subunits now publicly available, it is exceedingly difficult to design experiments based on analysis of all known rotation states. To overcome this, we developed an approach where the orientation of each SSU head and body is described in terms of three angular coordinates (rotation, tilt and tilt direction) and a single translation. By considering the entire RCSB PDB database, we describe 1208 fully-assembled ribosome complexes and 334 isolated small subunits, which span >50 species. This reveals aspects of subunit rearrangements that are universal, and others that are organism/domain-specific. For example, we show that tilt-like rearrangements of the SSU body (i.e. 'rolling') are pervasive in both prokaryotic and eukaryotic (cytosolic and mitochondrial) ribosomes. As another example, domain orientations associated with frameshifting in bacteria are similar to those found in eukaryotic ribosomes. Together, this study establishes a common foundation with which structural, simulation, single-molecule and biochemical efforts can more precisely interrogate the dynamics of this prototypical molecular machine.

Catalytic RNA Oligomers Formed by Co-Oligomerization of a Pair of Bimolecular RNase P Ribozymes

Naturally occurring ribozymes with a modular architecture are promising platforms for construction of RNA nanostructures because modular redesign enables their oligomerization. The resulting RNA nanostructures can exhibit the catalytic function of the parent ribozyme in an assembly dependent manner. In this study, we designed and constructed open-form oligomers of a bimolecular form of an RNase P ribozyme. The ribozyme oligomers were analyzed biochemically and by atomic force microscopy (AFM).

A Biopharmaceutical Perspective on Higher-Order Structure and Thermal Stability of mRNA Vaccines

Preservation of the integrity of macromolecular higher-order structure is a tenet central to achieving biologic drug and vaccine product stability toward manufacturing, distribution, storage, handling, and administration. Given that mRNA lipid nanoparticles (mRNA-LNPs) are held together by an intricate ensemble of weak forces, there are some intriguing parallels to biologic drugs, at least at first glance. However, mRNA vaccines are not without unique formulation and stabilization challenges derived from the instability of unmodified mRNA and its limited history as a drug or vaccine. Since certain learning gained from biologic drug development may be applicable for the improvement of mRNA vaccines, we present a perspective on parallels and contrasts between the emerging role of higher-order structure pertaining to mRNA-LNPs compared to pharmaceutical proteins. In a recent publication, the location of mRNA encapsulated within lipid nanoparticles was identified, revealing new insights into the LNP structure, nanoheterogeneity, and microenvironment of the encapsulated mRNA molecules [Brader et al. Biophys. J. 2021, 120, 2766]. We extend those findings by considering the effect of encapsulation on mRNA thermal unfolding with the observation that encapsulation in LNPs increases mRNA unfolding temperatures.

Observing the base-by-base search for native structure along transition paths during the folding of single nucleic acid hairpins

Biomolecular folding involves searching among myriad possibilities for the native conformation, but the elementary steps expected from theory for this search have never been detected directly. We probed the dynamics of folding at high resolution using optical tweezers, measuring individual trajectories as nucleic acid hairpins passed through the high-energy transition states that dominate kinetics and define folding mechanisms. We observed brief but ubiquitous pauses in the transition states, with a dwell time distribution that matched microscopic theories of folding quantitatively. The sequence dependence suggested that pauses were dominated by microbarriers from nonnative conformations during the search by each nucleotide residue for the native base-pairing conformation. Furthermore, the pauses were position dependent, revealing subtle local variations in energy-landscape roughness and allowing the diffusion coefficient describing the microscopic dynamics within the barrier to be found without reconstructing the shape of the energy landscape. These results show how high-resolution measurements can elucidate key microscopic events during folding to test fundamental theories of folding.

Vfold2D-MC: A Physics-Based Hybrid Model for Predicting RNA Secondary Structure Folding

Accurate prediction of RNA structure and folding stability has a far-reaching impact on our understanding of RNA functions. Here we develop Vfold2D-MC, a new physics-based model, to predict RNA structure and folding thermodynamics from the sequence. The model employs virtual bond-based coarse-graining of RNA backbone conformation and generates RNA conformations through Monte Carlo sampling of the bond angles and torsional angles of the virtual bonds. Using a coarse-grained statistical potential derived from the known structures, we assign each conformation with a statistical weight. The weighted average over the conformational ensemble gives the entropy and free energy parameters for the hairpin, bulge, and internal loops, and multiway junctions. From the thermodynamic parameters, we predict RNA structures, melting curves, and structural changes from the sequence. Theory-experiment comparisons indicate that Vfold2D-MC not only gives improved structure predictions but also enables the interpretation of thermodynamic results for different RNA structures, including multibranched junctions. This new model sets a promising framework to treat more complicated RNA structures, such as pseudoknotted and intramolecular kissing loops, for which experimental thermodynamic parameters are often unavailable.

Action and function of helicases on RNA G-quadruplexes

•

Methodological progresses and piling evidence prove the rG4 biology in vivo.

•

rG4s step in virtually every aspect of RNA biology.

•

Helicases unwinding of rG4s is a fine regulatory layer to the downstream processes and general cell homeostasis.

•

The current knowledge is however limited to a few cell lines.

•

The regulation of helicases themselves is delineating as a important question.

•

Non-helicase rG4-processing proteins likely play a role.

The nucleic acid structure called G-quadruplex (G4) is currently discussed to function in nucleic acid-based mechanisms that influence several cellular processes. They can modulate the cellular machinery either positively or negatively, both at the DNA and RNA level. The majority of what we know about G4 biology comes from DNA G4 (dG4) research. RNA G4s (rG4), on the other hand, are gaining interest as researchers become more aware of their role in several aspects of cellular homeostasis. In either case, the correct regulation of G4 structures within cells is essential and demands specialized proteins able to resolve them. Small changes in the formation and unfolding of G4 structures can have severe consequences for the cells that could even stimulate genome instability, apoptosis or proliferation. Helicases are the most relevant negative G4 regulators, which prevent and unfold G4 formation within cells during different pathways. Yet, and despite their importance only a handful of rG4 unwinding helicases have been identified and characterized thus far. This review addresses the current knowledge on rG4s-processing helicases with a focus on methodological approaches. An example of a non-helicase rG4s-unwinding protein is also briefly described.

Shape changes and cooperativity in the folding of the central domain of the 16S ribosomal RNA

Both the small and large subunits of the ribosome, the molecular machine that synthesizes proteins, are complexes of ribosomal RNAs (rRNAs) and a number of proteins. In bacteria, the small subunit has a single 16S rRNA whose folding is the first step in its assembly. The central domain of the 16S rRNA folds independently, driven either by Mg²⁺ ions or by interaction with ribosomal proteins. To provide a quantitative description of ion-induced folding of the ∼350-nucleotide rRNA, we carried out extensive coarse-grained molecular simulations spanning Mg²⁺ concentration between 0 and 30 mM. The Mg²⁺ dependence of the radius of gyration shows that globally the rRNA folds cooperatively. Surprisingly, various structural elements order at different Mg²⁺ concentrations, indicative of the heterogeneous assembly even within a single domain of the rRNA. Binding of Mg²⁺ ions is highly specific, with successive ion condensation resulting in nucleation of tertiary structures. We also predict the Mg²⁺-dependent protection factors, measurable in hydroxyl radical footprinting experiments, which corroborate the specificity of Mg²⁺-induced folding. The simulations, which agree quantitatively with several experiments on the folding of a three-way junction, show that its folding is preceded by formation of other tertiary contacts in the central junction. Our work provides a starting point in simulating the early events in the assembly of the small subunit of the ribosome.

Learning the Fastest RNA Folding Path Based on Reinforcement Learning and Monte Carlo Tree Search

RNA molecules participate in many important biological processes, and they need to fold into well-defined secondary and tertiary structures to realize their functions. Like the well-known protein folding problem, there is also an RNA folding problem. The folding problem includes two aspects: structure prediction and folding mechanism. Although the former has been widely studied, the latter is still not well understood. Here we present a deep reinforcement learning algorithms 2dRNA-Fold to study the fastest folding paths of RNA secondary structure. 2dRNA-Fold uses a neural network combined with Monte Carlo tree search to select residue pairing step by step according to a given RNA sequence until the final secondary structure is formed. We apply 2dRNA-Fold to several short RNA molecules and one longer RNA 1Y26 and find that their fastest folding paths show some interesting features. 2dRNA-Fold is further trained using a set of RNA molecules from the dataset bpRNA and is used to predict RNA secondary structure. Since in 2dRNA-Fold the scoring to determine next step is based on possible base pairings, the learned or predicted fastest folding path may not agree with the actual folding paths determined by free energy according to physical laws.

Dynamically probing ATP-dependent RNA helicase A-assisted RNA structure conversion using single molecule fluorescence resonance energy transfer

RNA helicase A (RHA) as a member of DExH-box subgroup of helicase superfamily II, participates in diverse biological processes involved in RNA metabolism in organisms, and these RNA-mediated biological processes rely on RNA structure conversion. However, how RHA regulate the RNA structure conversion was still unknown. In order to unveil the mechanism of RNA structure conversion mediated by RHA, single molecule fluorescence resonance energy transfer was adopted to in our assay, and substrates RNA were from internal ribosome entry site of foot-and-mouth disease virus genome. We first found that the RNA structure conversion by RHA against thermodynamic equilibrium in vitro, and the process of dsRNA YZ converted to dsRNA XY through a tripartite intermediate state. In addition, the rate of the RNA structure conversion and the distribution of dsRNA YZ and XY were affected by ATP concentrations. Our study provides real-time insight into ATP-dependent RHA-assisted RNA structure conversion at the single molecule level, the mechanism displayed by RHA may help in understand how RHA contributes to many biological functions, and the basic mechanistic features illustrated in our work also underlay more complex protein-assisted RNA structure conversions.

Effect of RNA on Morphology and Dynamics of Membraneless Organelles

Membraneless organelles (MLOs) are spatiotemporally regulated structures that concentrate multivalent proteins or RNA, often in response to stress. The proteins enriched within MLOs are often classified as high-valency "scaffolds" or low-valency "clients", with the former being associated with a phase-separation promoting role. In this study, we employ a minimal model for P-body components, with a defined protein-protein interaction network, to study their phase separation at biologically realistic low protein concentrations. Without RNA, multivalent proteins can assemble into solid-like clusters only in the regime of high concentration and stable interactions. RNA molecules promote cluster formation in an RNA-length-dependent manner, even in the regime of weak interactions and low protein volume fraction. Our simulations reveal that long RNA chains act as superscaffolds that stabilize large RNA-protein clusters by recruiting low-valency proteins within them while also ensuring functional "liquid-like" turnover of components. Our results suggest that RNA-mediated phase separation could be a plausible mechanism for spatiotemporally regulated phase separation in the cell.

Thermodynamic uncertainty relation to assess biological processes

We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states and discuss how optimal these processes are in light of the universal bound set by the thermodynamic uncertainty relation (TUR). The values of the uncertainty product Q of TUR, which can be used as a measure of the precision of enzymatic processes realized for a given thermodynamic cost, are suboptimal when the substrate concentration is at the Michaelis constant, and some of the key biological processes are found to work around this condition. We illustrate the utility of Q in assessing how close the molecular motors and biomass producing machineries are to the TUR bound, and for the cases of biomass production (or biological copying processes), we discuss how their optimality quantified in terms of Q is balanced with the error rate in the information transfer process. We also touch upon the trade-offs in other error-minimizing processes in biology, such as gene regulation and chaperone-assisted protein folding. A spectrum of Q recapitulating the biological processes surveyed here provides glimpses into how biological systems are evolved to optimize and balance the conflicting functional requirements.

A steric gate controls P/E hybrid-state formation of tRNA on the ribosome

The ribosome is a biomolecular machine that undergoes multiple large-scale structural rearrangements during protein elongation. Here, we focus on a conformational rearrangement during translocation, known as P/E hybrid-state formation. Using a model that explicitly represents all non-hydrogen atoms, we simulated more than 120 spontaneous transitions, where the tRNA molecule is displaced between the P and E sites of the large subunit. In addition to predicting a free-energy landscape that is consistent with previous experimental observations, the simulations reveal how a six-residue gate-like region can limit P/E formation, where sub-angstrom structural perturbations lead to an order-of-magnitude change in kinetics. Thus, this precisely defined set of residues represents a novel target that may be used to control functional dynamics in bacterial ribosomes. This theoretical analysis establishes a direct relationship between ribosome structure and large-scale dynamics, and it suggests how next-generation experiments may precisely dissect the energetics of hybrid formation on the ribosome.

The ribosome undergoes multiple large-scale structural rearrangements during protein elongation. Here the authors present an all-atom model of the ribosome to study the energetics of P/E hybrid-state formation, an early conformational rearrangement occurring during translocation.

Modeling Loop Composition and Ion Concentration Effects in RNA Hairpin Folding Stability

The ability to accurately predict RNA hairpin structure and stability for different loop sequences and salt conditions is important for understanding, modeling, and designing larger RNA folds. However, traditional RNA secondary structure models cannot treat loop-sequence and ionic effects on RNA hairpin folding. Here, we describe a general, three-dimensional (3D) conformation-based computational method for modeling salt concentration-dependent conformational distributions and the detailed 3D structures for a set of three RNA hairpins that contain a variable, 15-nucleotide loop sequence. For a given RNA sequence, the new, to our knowledge, method integrates a Vfold2D two-dimensional structure folding model with IsRNA coarse-grained molecular dynamics 3D folding simulations and Monte Carlo tightly bound ion estimations of ion-mediated electrostatic interactions. The model predicts free-energy landscapes for the different RNA hairpin-forming sequences with variable salt conditions. The theoretically predicted results agree with the experimental fluorescence measurements, validating the strategy. Furthermore, the theoretical model goes beyond the experimental results by enabling in-depth 3D structural analysis, revealing energetic mechanisms for the sequence- and salt-dependent folding stability. Although the computational framework presented here is developed for RNA hairpin systems, the general method may be applied to investigate other RNA systems, such as multiway junctions or pseudoknots in mixed metal ion solutions.

Molecular dynamics study of ways of RNA base-pair formation

Base pairing is a fundamental phenomenon in RNA structure and function. However, although there have been considerable recent advances, some important aspects of base-pair formation are still unknown, including the ways of base-pair formation and detailed roles of metal ions. Here we show that base pairs can form through four different ways: stabilizing, bridging, rotating, and shifting. Among them the stabilizing and bridging ways involve direct binding of metal ions while the rotating and shifting ways do not in most cases. Furthermore, we find that the formations of base pairs in different positions of the hairpin stem may adopt different ways.

Charge Density of Cation Determines Inner versus Outer Shell Coordination to Phosphate in RNA

Divalent cations are often required to fold RNA, which is a highly charged polyanion. Condensation of ions, such as Mg²⁺ or Ca²⁺, in the vicinity of RNA renormalizes the effective charges on the phosphate groups, thus minimizing the intra RNA electrostatic repulsion. The prevailing view is that divalent ions bind diffusively in a nonspecific manner. In sharp contrast, we arrive at the exact opposite conclusion using a theory for the interaction of ions with the phosphate groups using RISM theory in conjunction with simulations based on an accurate three-interaction-site RNA model. The divalent ions bind in a nucleotide-specific manner using either the inner (partially dehydrated) or outer (fully hydrated) shell coordination. The high charge density Mg²⁺ ion has a preference to bind to the outer shell, whereas the opposite is the case for Ca²⁺. Surprisingly, we find that bridging interactions, involving ions that are coordinated to two or more phosphate groups, play a crucial role in maintaining the integrity of the folded state. Their importance could become increasingly prominent as the size of the RNA increases. Because the modes of interaction of divalent ions with DNA are likely to be similar, we propose that specific inner and outer shell coordination could play a role in DNA condensation, and perhaps genome organization as well.

Urea-aromatic interactions in biology

Noncovalent interactions are key determinants in both chemical and biological processes. Among such processes, the hydrophobic interactions play an eminent role in folding of proteins, nucleic acids, formation of membranes, protein-ligand recognition, etc.. Though this interaction is mediated through the aqueous solvent, the stability of the above biomolecules can be highly sensitive to any small external perturbations, such as temperature, pressure, pH, or even cosolvent additives, like, urea-a highly soluble small organic molecule utilized by various living organisms to regulate osmotic pressure. A plethora of detailed studies exist covering both experimental and theoretical regimes, to understand how urea modulates the stability of biological macromolecules. While experimentalists have been primarily focusing on the thermodynamic and kinetic aspects, theoretical modeling predominantly involves mechanistic information at the molecular level, calculating atomistic details applying the force field approach to the high level electronic details using the quantum mechanical methods. The review focuses mainly on examples with biological relevance, such as (1) urea-assisted protein unfolding, (2) urea-assisted RNA unfolding, (3) urea lesion interaction within damaged DNA, (4) urea conduction through membrane proteins, and (5) protein-ligand interactions those explicitly address the vitality of hydrophobic interactions involving exclusively the urea-aromatic moiety.

Nucleic Acid Catalysis under Potential Prebiotic Conditions

Catalysis by nucleic acids is indispensable for extant cellular life, and it is widely accepted that nucleic acid enzymes were crucial for the emergence of primitive life 3.5-4 billion years ago. However, geochemical conditions on early Earth must have differed greatly from the constant internal milieus of today's cells. In order to explore plausible scenarios for early molecular evolution, it is therefore essential to understand how different physicochemical parameters, such as temperature, pH, and ionic composition, influence nucleic acid catalysis and to explore to what extent nucleic acid enzymes can adapt to non-physiological conditions. In this article, we give an overview of the research on catalysis of nucleic acids, in particular catalytic RNAs (ribozymes) and DNAs (deoxyribozymes), under extreme and/or unusual conditions that may relate to prebiotic environments.

Confined crowded polymers near attractive surfaces

We present results from molecular dynamics simulations of a spherically confined neutral polymer in the presence of crowding particles, studying polymer shapes and conformations as a function of the strength of the attraction to the confining wall, solvent quality, and the density of crowders. The conformations of the polymer under good solvent conditions are weakly dependent on crowder particle density, even when the polymer is strongly confined. In contrast, under poor solvent conditions, when the polymer assumes a collapsed conformation when unconfined, it can exhibit transitions to two different adsorbed phases, when either the interaction with the wall or the density of crowder particles is changed. One such transition involves a desorbed collapsed phase change to an adsorbed extended phase as the attraction of the polymer towards the confining wall is increased. Such an adsorbed extended phase can exhibit a second transition to an ordered adsorbed collapsed phase as the crowder particle density is increased. The ordered adsorbed collapsed phase of the polymer differs significantly in its structure from the desorbed collapsed phase. We revisit the earlier understanding of the adsorption of confined polymers on attractive surfaces in light of our results.

Iterative annealing mechanism explains the functions of the GroEL and RNA chaperones

Molecular chaperones are ATP-consuming machines, which facilitate the folding of proteins and RNA molecules that are kinetically trapped in misfolded states. Unassisted folding occurs by the kinetic partitioning mechanism according to which folding to the native state, with low probability as well as misfolding to one of the many metastable states, with high probability, occur rapidly. GroEL is an all-purpose stochastic machine that assists misfolded substrate proteins to fold. The RNA chaperones such as CYT-19, which are ATP-consuming enzymes, help the folding of ribozymes that get trapped in metastable states for long times. GroEL does not interact with the folded proteins but CYT-19 disrupts both the folded and misfolded ribozymes. The structures of GroEL and RNA chaperones are strikingly different. Despite these differences, the iterative annealing mechanism (IAM) quantitatively explains all the available experimental data for assisted folding of proteins and ribozymes. Driven by ATP binding and hydrolysis and GroES binding, GroEL undergoes a catalytic cycle during which it samples three allosteric states, T (apo), R (ATP bound), and R^″ (ADP bound). Analyses of the experimental data show that the efficiency of the GroEL-GroES machinery and mutants is determined by the resetting rate k _{R ″  → T} , which is largest for the wild-type (WT) GroEL. Generalized IAM accurately predicts the folding kinetics of Tetrahymena ribozyme and its variants. Chaperones maximize the product of the folding rate and the steady-state native state fold by driving the substrates out of equilibrium. Neither the absolute yield nor the folding rate is optimized.

Heterogeneous Loop Model to Infer 3D Chromosome Structures from Hi-C

Adapting a well-established formalism in polymer physics, we develop a minimalist approach to infer three-dimensional folding of chromatin from Hi-C data. The three-dimensional chromosome structures generated from our heterogeneous loop model (HLM) are used to visualize chromosome organizations that can substantiate the measurements from fluorescence in situ hybridization, chromatin interaction analysis by paired-end tag sequencing, and RNA-seq signals. We demonstrate the utility of the HLM with several case studies. Specifically, the HLM-generated chromosome structures, which reproduce the spatial distribution of topologically associated domains from fluorescence in situ hybridization measurement, show the phase segregation between two types of topologically associated domains explicitly. We discuss the origin of cell-type-dependent gene-expression level by modeling the chromatin globules of α-globin and SOX2 gene loci for two different cell lines. We also use the HLM to discuss how the chromatin folding and gene-expression level of Pax6 loci, associated with mouse neural development, are modulated by interactions with two enhancers. Finally, HLM-generated structures of chromosome 19 of mouse embryonic stem cells, based on single-cell Hi-C data collected over each cell-cycle phase, visualize changes in chromosome conformation along the cell-cycle. Given a contact frequency map between chromatic loci supplied from Hi-C, HLM is a computationally efficient and versatile modeling tool to generate chromosome structures that can complement interpreting other experimental data.

Disordered RNA chaperones can enhance nucleic acid folding via local charge screening

RNA chaperones are proteins that aid in the folding of nucleic acids, but remarkably, many of these proteins are intrinsically disordered. How can these proteins function without a well-defined three-dimensional structure? Here, we address this question by studying the hepatitis C virus core protein, a chaperone that promotes viral genome dimerization. Using single-molecule fluorescence spectroscopy, we find that this positively charged disordered protein facilitates the formation of compact nucleic acid conformations by acting as a flexible macromolecular counterion that locally screens repulsive electrostatic interactions with an efficiency equivalent to molar salt concentrations. The resulting compaction can bias unfolded nucleic acids towards folding, resulting in faster folding kinetics. This potentially widespread mechanism is supported by molecular simulations that rationalize the experimental findings by describing the chaperone as an unstructured polyelectrolyte.

RNA chaperones, such as the hepatitic C virus (HCV) core protein, are proteins that aid in the folding of nucleic acids. Here authors use single‐molecule spectroscopy and simulation to show that the HCV core protein acts as a flexible macromolecular counterion which facilitates nucleic acid folding.

Proteins That Chaperone RNA Regulation

RNA-binding proteins chaperone the biological functions of noncoding RNA by reducing RNA misfolding, improving matchmaking between regulatory RNA and targets, and exerting quality control over RNP biogenesis. Recent studies of Escherichia coli CspA, HIV NCp, and E. coli Hfq are beginning to show how RNA-binding proteins remodel RNA structures. These different protein families use common strategies for disrupting or annealing RNA double helices, which can be used to understand the mechanisms by which proteins chaperone RNA-dependent regulation in bacteria.

Mechanobiology: protein refolding under force

The application of direct force to a protein enables to probe wide regions of its energy surface through conformational transitions as unfolding, extending, recoiling, collapsing, and refolding. While unfolding under force typically displayed a two-state behavior, refolding under force, from highly extended unfolded states, displayed a more complex behavior. The first recording of protein refolding at a force quench step displayed an initial rapid elastic recoil, followed by a plateau phase at some extension, concluding with a collapse to a final state, at which refolding occurred. These findings stirred a lively discussion, which led to further experimental and theoretical investigation of this behavior. It was demonstrated that the polymeric chain of the unfolded protein is required to fully collapse to a globular conformation for the maturation of native structure. This behavior was modeled using one-dimensional free energy landscape over the end-to-end length reaction coordinate, the collective measured variable. However, at low forces, conformational space is not well captured by such models, and using two-dimensional energy surfaces provides further insight into the dynamics of this process. This work reviews the main concepts of protein refolding under constant force, which is essential for understanding how mechanotransducing proteins operate in vivo.

Molecular Simulations of Ion Effects on the Thermodynamics of RNA Folding

How ions affect RNA folding thermodynamics and kinetics is an important but a vexing problem that remains unsolved. Experiments have shown that the free-energy change, Δ G( c), of RNA upon folding varies with the salt concentration ( c) as, Δ G( c) = k _c ln  c + const, where the coefficient k _c is proportional to the difference in the ion preferential coefficient, ΔΓ. We performed simulations of a coarse-grained model, by modeling electrostatic interactions implicitly and with explicit representation of ions, to elucidate the molecular underpinnings of the relationship between Δ G and ΔΓ. The simulations quantitatively reproduce the heat capacity for a pseudoknot, thus validating the model. We show that Δ G( c), calculated directly from ΔΓ, varies linearly with ln  c ( c < 0.2 M), for a hairpin and the pseudoknot, demonstrating a molecular link between the two quantities. Explicit ion simulations also show the linear dependence of Δ G( c) on ln  c at all c with k _c = 2 k_B T, except that Δ G( c) values are shifted by ∼2 kcal/mol higher than experiments. The discrepancy is due to an underestimation of Γ for both the folded and unfolded states while giving accurate values for ΔΓ. The predictions for the salt dependence of ΔΓ are amenable to test using single-molecule pulling experiments. The framework provided here can be used to obtain accurate thermodynamics for other RNA molecules as well.

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.

Compartmentalised RNA catalysis in membrane-free coacervate protocells

Phase separation of mixtures of oppositely charged polymers provides a simple and direct route to compartmentalisation via complex coacervation, which may have been important for driving primitive reactions as part of the RNA world hypothesis. However, to date, RNA catalysis has not been reconciled with coacervation. Here we demonstrate that RNA catalysis is viable within coacervate microdroplets and further show that these membrane-free droplets can selectively retain longer length RNAs while permitting transfer of lower molecular weight oligonucleotides.

Phase separation of mixtures of oppositely charged polymers provides a simple and direct route to compartmentalisation via coacervation. Here authors demonstrate that a coacervate microenvironment supports RNA catalysis whilst selectively sequestering RNA based on length.

RNA as a Complex Polymer with Coupled Dynamics of Ions and Water in the Outer Solvation Sphere

We unravel the internal and collective modes of a widely studied 58-nucleotide rRNA fragment in solvent using atomically detailed molecular dynamics simulations. The variation of lifetimes for water hydrogen bonds with nucleotide groups indicates heterogeneity of water dynamics on the RNA surface. The time scales of interactions of the discrete water molecules with RNA nucleotides extend from several hundred picoseconds to a few nanoseconds. We determine all of the association sites and the spatial distribution of residence times for Mg²⁺, K⁺, and water molecules in those sites. We provide insights into the population of Mg²⁺ and K⁺ ions and water molecules in the outer sphere and how their fluctuations are intricately linked with the kinetics of the 58-mer. We find that many of the long-lived Mg²⁺ sites identified from the simulations agree with the locations of ions in the X-ray structure. We determine the excess ion atmosphere around the rRNA and compare it with experimental data. We investigate the collective behavior of RNA, ions, and water, by performing a joint principle component analysis for the Cartesian coordinates of the RNA phosphorus atoms and for the occupation counts of the association sites. Our results indicate that the 58-mer system is a complex polymer, composed of RNA that is encased by a fluctuating network of associated counterions, co-ions, and water.

RNA melting and RNA chaperone activities of plant cold shock domain proteins are not correlated

Cold shock domain proteins (CSDPs) participate in plant development and resistance, but the underlying molecular mechanisms are poorly understood. In this study, we demonstrated that the CSDPs, including EsCSDP1, EsCSDP2, and EsCSDP3, from the extremophyte Eutrema salsugineum possess all basic properties of RNA chaperones. EsCSDP1-3 melt secondary structures in RNAs with various nucleotide sequences and exhibit RNA chaperone activity in vitro. EsCSDP1 and EsCSDP3 were shown to have higher RNA melting activity, whereasile EsCSDP2 had higher RNA chaperone activity. We demonstrated that higher RNA melting activity correlates with the longer C-terminal fragment in many zinc finger motifs, whereas increased RNA chaperone activity was most likely due to the higher glycine content and RGG repeat number in the C-terminal fragment.

Conformational profiling of a G-rich sequence within the c-KIT promoter

G-quadruplexes (G4) within oncogene promoters are considered to be promising anticancer targets. However, often they undergo complex structural rearrangements that preclude a precise description of the optimal target. Moreover, even when solved structures are available, they refer to the thermodynamically stable forms but little or no information is supplied about their complex multistep folding pathway. To shed light on this issue, we systematically followed the kinetic behavior of a G-rich sequence located within the c-KIT proximal promoter (kit2) in the presence of monovalent cations K⁺ and Na⁺. A very short-lived intermediate was observed to start the G4 folding process in both salt conditions. Subsequently, the two pathways diverge to produce distinct thermodynamically stable species (parallel and antiparallel G-quadruplex in K⁺ and Na⁺, respectively). Remarkably, in K⁺-containing solution a branched pathway is required to drive the wild type sequence to distribute between a monomeric and dimeric G-quadruplex. Our approach has allowed us to identify transient forms whose relative abundance is regulated by the environment; some of them were characterized by a half-life within the timescale of physiological DNA processing events and thus may represent possible unexpected targets for ligands recognition.

Single-molecule FRET studies on the cotranscriptional folding of a thiamine pyrophosphate riboswitch

Because RNAs fold as they are being synthesized, their transcription rate can affect their folding. Here, we report the results of single-molecule fluorescence studies that characterize the ligand-dependent cotranscriptional folding of the Escherichia coli thiM riboswitch that regulates translation. We found that the riboswitch aptamer folds into the "off" conformation independent of its ligand, but switches to the "on" conformation during transcriptional pausing near the translational start codon. Ligand binding maintains the riboswitch in the off conformation during transcriptional pauses. We expect our assay will permit the controlled study of the two main physical mechanisms that regulate cotranscriptional folding: transcriptional pausing and transcriptional speed.

Molecular chaperones maximize the native state yield on biological times by driving substrates out of equilibrium

Molecular chaperones facilitate the folding of proteins and RNA in vivo. Under physiological conditions, the in vitro folding of Tetrahymena ribozyme by the RNA chaperone CYT-19 behaves paradoxically; increasing the chaperone concentration reduces the yield of native ribozymes. In contrast, the protein chaperone GroEL works as expected; the yield of the native substrate increases with chaperone concentration. The discrepant chaperone-assisted ribozyme folding thus contradicts the expectation that it operates as an efficient annealing machine. To resolve this paradox, we propose a minimal stochastic model based on the Iterative Annealing Mechanism (IAM) that offers a unified description of chaperone-mediated folding of both proteins and RNA. Our theory provides a general relation that quantitatively predicts how the yield of native states depends on chaperone concentration. Although the absolute yield of native states decreases in the Tetrahymena ribozyme, the product of the folding rate and the steady-state native yield increases in both cases. By using energy from ATP hydrolysis, both CYT-19 and GroEL drive their substrate concentrations far out of equilibrium, thus maximizing the native yield in a short time. This also holds when the substrate concentration exceeds that of GroEL. Our findings satisfy the expectation that proteins and RNA be folded by chaperones on biologically relevant time scales, even if the final yield is lower than what equilibrium thermodynamics would dictate. The theory predicts that the quantity of chaperones in vivo has evolved to optimize native state production of the folded states of RNA and proteins in a given time.

Predicting Ion Effects in an RNA Conformational Equilibrium

We develop a partial charge-based tightly bound ion (PCTBI) model for the ion effects in RNA folding. On the basis of the Monte Carlo tightly bound ion (MCTBI) approach, the model can account for ion fluctuation and correlation effects, and can predict the ion distribution around the RNA. Furthermore, unlike the previous coarse-grained RNA charge models, where negative charges are placed on the phosphates only, the current new model considers the detailed all-atom partial charge distribution on the RNA. Thus, the model not only keeps the advantage of the MCTBI model, but also has the potential to provide important detailed information unattainable by the previous MCTBI models. For example, the model predicts the reduction in ion binding upon protein binding and ion-induced conformational switches. For hepatitis C virus genomic RNA, the model predicts a Mg²⁺-induced stabilization of a kissing motif for a cis-acting regulatory element in the genomic RNA. Extensive theory-experiment comparisons support the reliability of the theoretical predictions. Therefore, the model may serve as a robust starting point for further development of an accurate method for ion effects in an RNA conformational equilibrium and RNA-cofactor interactions.

Contact Statistics Highlight Distinct Organizing Principles of Proteins and RNA

Although both RNA and proteins have densely packed native structures, chain organizations of these two biopolymers are fundamentally different. Motivated by the recent discoveries in chromatin folding that interphase chromosomes have territorial organization with signatures pointing to metastability, we analyzed the biomolecular structures deposited in the Protein Data Bank and found that the intrachain contact probabilities, P(s) as a function of the arc length s, decay in power-law ∼s(-γ) over the intermediate range of s, 10 ≲ s ≲ 110. We found that the contact probability scaling exponent is γ ≈ 1.11 for large RNA (N > 110), γ ≈ 1.41 for small-sized RNA (N < 110), and γ ≈ 1.65 for proteins. Given that Gaussian statistics is expected for a fully equilibrated chain in polymer melts, the deviation of γ-value from γ = 1.5 for the subchains of large RNA in the native state suggests that the chain configuration of RNA is not fully equilibrated. It is visually clear that folded structures of large-sized RNA (N ≳ 110) adopt crumpled structures, partitioned into modular multidomains assembled by proximal sequences along the chain, whereas the polypeptide chain of folded proteins looks better mixed with the rest of the structure. Our finding of γ ≈ 1 for large RNA might be an ineluctable consequence of the hierarchical ordering of the secondary to tertiary elements in the folding process.

Comparative Visualization of the RNA Suboptimal Conformational Ensemble In Vivo

When a ribonucleic acid (RNA) molecule folds, it often does not adopt a single, well-defined conformation. The folding energy landscape of an RNA is highly dependent on its nucleotide sequence and molecular environment. Cellular molecules sometimes alter the energy landscape, thereby changing the ensemble of likely low-energy conformations. The effects of these energy landscape changes on the conformational ensemble are particularly challenging to visualize for large RNAs. We have created a robust approach for visualizing the conformational ensemble of RNAs that is well suited for in vitro versus in vivo comparisons. Our method creates a stable map of conformational space for a given RNA sequence. We first identify single point mutations in the RNA that maximally sample suboptimal conformational space based on the ensemble’s partition function. Then, we cluster these diverse ensembles to identify the most diverse partition functions for Boltzmann stochastic sampling. By using, to our knowledge, a novel nestedness distance metric, we iteratively add mutant suboptimal ensembles to converge on a stable 2D map of conformational space. We then compute the selective 2′ hydroxyl acylation by primer extension (SHAPE)-directed ensemble for the RNA folding under different conditions, and we project these ensembles on the map to visualize. To validate our approach, we established a conformational map of the Vibrio vulnificus add adenine riboswitch that reveals five classes of structures. In the presence of adenine, projection of the SHAPE-directed sampling correctly identified the on-conformation; without the ligand, only off-conformations were visualized. We also collected the whole-transcript in vitro and in vivo SHAPE-MaP for human β-actin messenger RNA that revealed similar global folds in both conditions. Nonetheless, a comparison of in vitro and in vivo data revealed that specific regions exhibited significantly different SHAPE-MaP profiles indicative of structural rearrangements, including rearrangement consistent with binding of the zipcode protein in a region distal to the stop codon.

Protein collapse is encoded in the folded state architecture

Folded states of single domain globular proteins are compact with high packing density. The radius of gyration, R_g, of both the folded and unfolded states increase as N^ν where N is the number of amino acids in the protein. The values of the Flory exponent ν are, respectively, ≈⅓ and ≈0.6 in the folded and unfolded states, coinciding with those for homopolymers. However, the extent of compaction of the unfolded state of a protein under low denaturant concentration (collapsibility), conditions favoring the formation of the folded state, is unknown. We develop a theory that uses the contact map of proteins as input to quantitatively assess collapsibility of proteins. Although collapsibility is universal, the propensity to be compact depends on the protein architecture. Application of the theory to over two thousand proteins shows that collapsibility depends not only on N but also on the contact map reflecting the native structure. A major prediction of the theory is that β-sheet proteins are far more collapsible than structures dominated by α-helices. The theory and the accompanying simulations, validating the theoretical predictions, provide insights into the differing conclusions reached using different experimental probes assessing the extent of compaction of proteins. By calculating the criterion for collapsibility as a function of protein length we provide quantitative insights into the reasons why single domain proteins are small and the physical reasons for the origin of multi-domain proteins. Collapsibility of non-coding RNA molecules is similar β-sheet proteins structures adding support to "Compactness Selection Hypothesis".

The folding competence of HIV-1 Tat mediated by interaction with TAR RNA

The trans-activator Tat protein of HIV-1 belongs to the large family of intrinsically disordered proteins (IDPs), and is known to recruit various host proteins for the transactivation of viral RNA synthesis. Tat protein interacts with the transactivator response RNA (TAR RNA), exhibiting RNA chaperone activities for structural rearrangement of interacting RNAs. Here, considering that Tat-TAR RNA interaction is mutually cooperative, we examined the potential role of TAR RNA as Chaperna - RNA that provides chaperone function to proteins - for the folding of HIV-1 Tat. Using EGFP fusion as an indirect indicator for folding status, we monitored Tat-EGFP folding in HeLa cells via time-lapse fluorescence microscopy. The live cell imaging showed that the rate and the extent of folding of Tat-EGFP were stimulated by TAR RNA. The purified Tat-EGFP was denatured and the fluorescence was monitored in vitro under renaturation condition. The fluorescence was significantly increased by TAR RNA, and the mutations in TAR RNA that affected the interaction with Tat protein failed to promote Tat refolding. The results suggest that TAR RNA stabilizes Tat as unfolded, but prevents it from misfolding, and maintaining its folding competence for interaction with multiple host factors toward its transactivation. The Chaperna function of virally encoded RNA in establishing proteome link at the viral-host interface provides new insights to as yet largely unexplored RNA mediated protein folding in normal and dysregulated cellular metabolism.

Decoding Single Molecule Time Traces with Dynamic Disorder

Single molecule time trajectories of biomolecules provide glimpses into complex folding landscapes that are difficult to visualize using conventional ensemble measurements. Recent experiments and theoretical analyses have highlighted dynamic disorder in certain classes of biomolecules, whose dynamic pattern of conformational transitions is affected by slower transition dynamics of internal state hidden in a low dimensional projection. A systematic means to analyze such data is, however, currently not well developed. Here we report a new algorithm—Variational Bayes-double chain Markov model (VB-DCMM)—to analyze single molecule time trajectories that display dynamic disorder. The proposed analysis employing VB-DCMM allows us to detect the presence of dynamic disorder, if any, in each trajectory, identify the number of internal states, and estimate transition rates between the internal states as well as the rates of conformational transition within each internal state. Applying VB-DCMM algorithm to single molecule FRET data of H-DNA in 100 mM-Na⁺ solution, followed by data clustering, we show that at least 6 kinetic paths linking 4 distinct internal states are required to correctly interpret the duplex-triplex transitions of H-DNA.

We have developed a new algorithm to better decode single molecule data with dynamic disorder. Our new algorithm, which represents a substantial improvement over other methodologies, can detect the presence of dynamic disorder in each trajectory and quantify the kinetic characteristics of underlying energy landscape. As a model system, we applied our algorithm to the single molecule FRET time traces of H-DNA. While duplex-triplex transitions of H-DNA are conventionally interpreted in terms of two-state kinetics, slowly varying dynamic patterns corresponding to hidden internal states can also be identified from the individual time traces. Our algorithm reveals that at least 4 distinct internal states are required to correctly interpret the data.