Chain length determines the folding rates of RNA

Costs of ribosomal RNA stabilization affect ribosome composition at maximum growth rate

Ribosomes are key to cellular self-fabrication and limit growth rate. While most enzymes are proteins, ribosomes consist of 1/3 protein and 2/3 ribonucleic acid (RNA) (in E. coli).Here, we develop a mechanistic model of a self-fabricating cell, validated across diverse growth conditions. Through resource balance analysis (RBA), we explore the variation in maximum growth rate with ribosome composition, assuming constant kinetic parameters.Our model highlights the importance of RNA instability. If we neglect it, RNA synthesis is always cheaper than protein synthesis, leading to an RNA-only ribosome at maximum growth rate. Upon accounting for RNA turnover, we find that a mixed ribosome composed of RNA and proteins maximizes growth rate. To account for RNA turnover, we explore two scenarios regarding the activity of RNases. In (a) degradation is proportional to RNA content. In (b) ribosomal proteins cooperatively mitigate RNA instability by protecting it from misfolding and subsequent degradation. In both cases, higher protein content elevates protein synthesis costs and simultaneously lowers RNA turnover expenses, resulting in mixed RNA-protein ribosomes. Only scenario (b) aligns qualitatively with experimental data across varied growth conditions.Our research provides fresh insights into ribosome biogenesis and evolution, paving the way for understanding protein-rich ribosomes in archaea and mitochondria.

A Proposal of the Ur-RNAome

It is widely accepted that the earliest RNA molecules were folded into hairpins or mini-helixes. Herein, we depict the 2D and 3D conformations of those earliest RNA molecules with only RNY triplets, which Eigen proposed as the primeval genetic code. We selected 26 species (13 bacteria and 13 archaea). We found that the free energy of RNY hairpins was consistently lower than that of their corresponding shuffled controls. We found traces of the three ribosomal RNAs (16S, 23S, and 5S), tRNAs, 6S RNA, and the RNA moieties of RNase P and the signal recognition particle. Nevertheless, at this stage of evolution there was no genetic code (as seen in the absence of the peptidyl transferase centre and any vestiges of the anti-Shine-Dalgarno sequence). Interestingly, we detected the anticodons of both glycine (GCC) and threonine (GGU) in the hairpins of proto-tRNA.

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.

Cooperativity and Folding Kinetics in a Multidomain Protein with Interwoven Chain Topology

Although a large percentage of eukaryotic proteomes consist of proteins with multiple domains, not much is known about their assembly mechanism, especially those with intricate native state architectures. Some have a complex topology in which the structural elements along the sequence are interwoven in such a manner that the domains cannot be separated by cutting at any location along the sequence. Such proteins are multiply connected multidomain proteins (MMPs) with the three-domain (NMP, LID, and CORE) phosphotransferase enzyme adenylate kinase (ADK) being an example. We devised a coarse-grained model to simulate ADK folding initiated by changing either the temperature or guanidinium chloride (GdmCl) concentration. The simulations reproduce the experimentally measured melting temperatures (associated with two equilibrium transitions), FRET efficiency as a function of GdmCl concentration, and the folding times quantitatively. Although the NMP domain orders independently, cooperative interactions between the LID and the CORE domains are required for complete assembly of the enzyme. Kinetic simulations show that, on the collapse time scale, multiple interconnected metastable states are populated, attesting to the folding heterogeneity. The network of kinetically connected states reveals that the CORE domain folds only after the NMP and LID domains, reflecting the interwoven nature of the chain topology.

Mg2+ Impacts the Twister Ribozyme through Push-Pull Stabilization of Nonsequential Phosphate Pairs

RNA molecules perform a variety of biological functions for which the correct three-dimensional structure is essential, including as ribozymes where they catalyze chemical reactions. Metal ions, especially Mg2+, neutralize these negatively charged nucleic acids and specifically stabilize RNA tertiary structures as well as impact the folding landscape of RNAs as they assume their tertiary structures. Specific binding sites of Mg2+ in folded conformations of RNA have been studied extensively; however, the full range of interactions of the ion with compact intermediates and unfolded states of RNA is challenging to investigate, and the atomic details of the mechanism by which the ion facilitates tertiary structure formation is not fully known. Here, umbrella sampling combined with oscillating chemical potential Grand Canonical Monte Carlo/molecular dynamics simulations are used to capture the energetics and atomic-level details of Mg2+-RNA interactions that occur along an unfolding pathway of the Twister ribozyme. The free energy profiles reveal stabilization of partially unfolded states by Mg2+, as observed in unfolding experiments, with this stabilization being due to increased sampling of simultaneous interactions of Mg2+ with two or more nonsequential phosphate groups. Notably, these results indicate a push-pull mechanism in which the Mg2+-RNA interactions actually lead to destabilization of specific nonsequential phosphate-phosphate interactions (i.e., pushed apart), whereas other interactions are stabilized (i.e., pulled together), a balance that stabilizes unfolded states and facilitates the folding of Twister, including the formation of hydrogen bonds associated with the tertiary structure. This study establishes a better understanding of how Mg2+-ion interactions contribute to RNA structural properties and stability.

A highly ordered, nonprotective MALAT1 ENE structure is adopted prior to triplex formation

The 3' end of the ∼7 kb lncRNA MALAT1 contains an evolutionarily and structurally conserved element for nuclear expression (ENE) which confers protection from cellular degradation pathways. Formation of an ENE triple helix is required to support transcript accumulation, leading to persistent oncogenic activity of MALAT1 in multiple cancer types. Though the specific mechanism of triplex-mediated protection remains unknown, the MALAT1 ENE triplex has been identified as a promising target for therapeutic intervention. Interestingly, a maturation step of the nascent lncRNA 3' end is required prior to triplex formation. We hypothesize that disruption of the maturation or folding process may be a viable mechanism of inhibition. To assess putative cotranscriptional ENE conformations prior to triplex formation, we perform microsecond MD simulations of a partially folded ENE conformation and the ENE triplex. We identify a highly ordered ENE structure prior to triplex formation. Extensive formation of U•U base pairs within the large U-rich internal loops produces a global rod-like architecture. We present a three-dimensional structure of the isolated ENE motif, the global features of which are consistent with small angle X-ray scattering (SAXS) experiments. Our structural model represents a nonprotective conformation of the MALAT1 ENE, providing a molecular description useful for future mechanistic and inhibition studies. We anticipate that targeting stretches of U•U pairs within the ENE motif will prove advantageous for the design of therapeutics targeting this oncogenic lncRNA.

Systems NMR: single-sample quantification of RNA, proteins and metabolites for biomolecular network analysis

Cellular behavior is controlled by the interplay of diverse biomolecules. Most experimental methods, however, can only monitor a single molecule class or reaction type at a time. We developed an in vitro nuclear magnetic resonance spectroscopy (NMR) approach, which permitted dynamic quantification of an entire 'heterotypic' network-simultaneously monitoring three distinct molecule classes (metabolites, proteins and RNA) and all elementary reaction types (bimolecular interactions, catalysis, unimolecular changes). Focusing on an eight-reaction co-transcriptional RNA folding network, in a single sample we recorded over 35 time points with over 170 observables each, and accurately determined five core reaction constants in multiplex. This reconstruction revealed unexpected cross-talk between the different reactions. We further observed dynamic phase-separation in a system of five distinct RNA-binding domains in the course of the RNA transcription reaction. Our Systems NMR approach provides a deeper understanding of biological network dynamics by combining the dynamic resolution of biochemical assays and the multiplexing ability of 'omics'.

Evolution of macromolecular structure: a 'double tale' of biological accretion and diversification

The evolution of structure in biology is driven by accretion and diversification. Accretion brings together disparate parts to form bigger wholes. Diversification provides opportunities for growth and innovation. Here, we review patterns and processes that are responsible for a 'double tale' of accretion and diversification at various levels of complexity, from proteins and nucleic acids to high-rise building structures in cities. Parts are at first weakly linked and associate variously. As they diversify, they compete with each other and are selected for performance. The emerging interactions constrain their structure and associations. This causes parts to self-organise into modules with tight linkage. In a second phase, variants of the modules evolve and become new parts for a new generative cycle of higher-level organisation. Evolutionary genomics and network biology support the 'double tale' of structural module creation and validate an evolutionary principle of maximum abundance that drives the gain and loss of modules.

Frictional Effects on RNA Folding: Speed Limit and Kramers Turnover

We investigated frictional effects on the folding rates of a human telomerase hairpin (hTR HP) and H-type pseudoknot from the Beet Western Yellow Virus (BWYV PK) using simulations of the Three Interaction Site (TIS) model for RNA. The heat capacity from TIS model simulations, calculated using temperature replica exchange simulations, reproduces nearly quantitatively the available experimental data for the hTR HP. The corresponding results for BWYV PK serve as predictions. We calculated the folding rates ( k_F) from more than 100 folding trajectories for each value of the solvent viscosity (η) at a fixed salt concentration of 200 mM. By using the theoretical estimate (∝ √N where N is the number of nucleotides) for folding free energy barrier, k_F data for both the RNAs are quantitatively fit using one-dimensional Kramers's theory with two parameters specifying the curvatures in the unfolded basin and the barrier top. In the high-friction regime (η ≳ 10^-5 Pa·s), for both HP and PK, k_F values decrease as 1/η, whereas in the low friction regime, k_F values increase as η increases, leading to a maximum folding rate at a moderate viscosity (∼10^-6 Pa·s), which is the Kramers turnover. From the fits, we find that the speed limit to RNA folding at water viscosity is between 1 and 4 μs, which is in accord with our previous theoretical prediction as well as results from several single molecule experiments. Both the RNA constructs fold by parallel pathways. Surprisingly, we find that the flux through the pathways could be altered by changing solvent viscosity, a prediction that is more easily testable in RNA than in proteins.

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.

Ultrasensitivity of Water Exchange Kinetics to the Size of Metal Ion

Metal ions play a vital role in many biological processes. An important factor in these processes is the dynamics of exchange between ion bound-water molecules and the bulk. Although structural and dynamical properties of labile waters bound to metal ions, such as Na⁺ and Ca²⁺, can be elucidated using molecular dynamics simulations, direct evaluation of rates of exchange of waters rigidly bound to high charge density Mg²⁺, has been elusive. Here, we report a universal relationship, allowing us to determine the water exchange time on metal ions as a function of valence and hydration radius. The proposed relationship, which covers times spanning 14 orders of magnitude, highlights the ultrasensitivity of water lifetime to the ion size, as exemplified by divalent ions, Ca²⁺ (∼100 ps) and Mg²⁺ (∼1.5 μs). We show that even when structures, characterized by radial distributions are similar, a small difference in hydration radius leads to a qualitatively different (associative or dissociative) mechanism of water exchange. Our work provides a theoretical basis for determination of hydration radius, which is critical for accurately modeling the water dynamics around multivalent ions, and hence in describing all electrostatically driven events such as ribozyme folding and catalysis.

Role of Proteome Physical Chemistry in Cell Behavior

We review how major cell behaviors, such as bacterial growth laws, are derived from the physical chemistry of the cell’s proteins. On one hand, cell actions depend on the individual biological functionalities of their many genes and proteins. On the other hand, the common physics among proteins can be as important as the unique biology that distinguishes them. For example, bacterial growth rates depend strongly on temperature. This dependence can be explained by the folding stabilities across a cell’s proteome. Such modeling explains how thermophilic and mesophilic organisms differ, and how oxidative damage of highly charged proteins can lead to unfolding and aggregation in aging cells. Cells have characteristic time scales. For example, E. coli can duplicate as fast as 2–3 times per hour. These time scales can be explained by protein dynamics (the rates of synthesis and degradation, folding, and diffusional transport). It rationalizes how bacterial growth is slowed down by added salt. In the same way that the behaviors of inanimate materials can be expressed in terms of the statistical distributions of atoms and molecules, some cell behaviors can be expressed in terms of distributions of protein properties, giving insights into the microscopic basis of growth laws in simple cells.

Computing the origin and evolution of the ribosome from its structure - Uncovering processes of macromolecular accretion benefiting synthetic biology

Accretion occurs pervasively in nature at widely different timeframes. The process also manifests in the evolution of macromolecules. Here we review recent computational and structural biology studies of evolutionary accretion that make use of the ideographic (historical, retrodictive) and nomothetic (universal, predictive) scientific frameworks. Computational studies uncover explicit timelines of accretion of structural parts in molecular repertoires and molecules. Phylogenetic trees of protein structural domains and proteomes and their molecular functions were built from a genomic census of millions of encoded proteins and associated terminal Gene Ontology terms. Trees reveal a ‘metabolic-first’ origin of proteins, the late development of translation, and a patchwork distribution of proteins in biological networks mediated by molecular recruitment. Similarly, the natural history of ancient RNA molecules inferred from trees of molecular substructures built from a census of molecular features shows patchwork-like accretion patterns. Ideographic analyses of ribosomal history uncover the early appearance of structures supporting mRNA decoding and tRNA translocation, the coevolution of ribosomal proteins and RNA, and a first evolutionary transition that brings ribosomal subunits together into a processive protein biosynthetic complex. Nomothetic structural biology studies of tertiary interactions and ancient insertions in rRNA complement these findings, once concentric layering assumptions are removed. Patterns of coaxial helical stacking reveal a frustrated dynamics of outward and inward ribosomal growth possibly mediated by structural grafting. The early rise of the ribosomal ‘turnstile’ suggests an evolutionary transition in natural biological computation. Results make explicit the need to understand processes of molecular growth and information transfer of macromolecules.

The Role of Packaging Sites in Efficient and Specific Virus Assembly

During the life cycle of many single-stranded RNA viruses, including many human pathogens, a protein shell called the capsid spontaneously assembles around the viral genome. Understanding the mechanisms by which capsid proteins selectively assemble around the viral RNA amidst diverse host RNAs is a key question in virology. In one proposed mechanism, short sequences (packaging sites) within the genomic RNA promote rapid and efficient assembly through specific interactions with the capsid proteins. In this work, we develop a coarse-grained particle-based computational model for capsid proteins and RNA that represents protein-RNA interactions arising both from nonspecific electrostatics and from specific packaging site interactions. Using Brownian dynamics simulations, we explore how the efficiency and specificity of assembly depend on solution conditions (which control protein-protein and nonspecific protein-RNA interactions) and the strength and number of packaging sites. We identify distinct regions in parameter space in which packaging sites lead to highly specific assembly via different mechanisms and others in which packaging sites lead to kinetic traps. We relate these computational predictions to in vitro assays for specificity in which cognate viral RNAs compete against non-cognate RNAs for assembly by capsid proteins.

Splicing of designer exons informs a biophysical model for exon definition

Pre-mRNA molecules in humans contain mostly short internal exons flanked by longer introns. To explain the removal of such introns, exon recognition instead of intron recognition has been proposed. We studied this exon definition using designer exons (DEs) made up of three prototype modules of our own design: an exonic splicing enhancer (ESE), an exonic splicing silencer (ESS), and a Reference Sequence (R) predicted to be neither. Each DE was examined as the central exon in a three-exon minigene. DEs made of R modules showed a sharp size dependence, with exons shorter than 14 nt and longer than 174 nt splicing poorly. Changing the strengths of the splice sites improved longer exon splicing but worsened shorter exon splicing, effectively displacing the curve to the right. For the ESE we found, unexpectedly, that its enhancement efficiency was independent of its position within the exon. For the ESS we found a step-wise positional increase in its effects; it was most effective at the 3' end of the exon. To apply these results quantitatively, we developed a biophysical model for exon definition of internal exons undergoing cotranscriptional splicing. This model features commitment to inclusion before the downstream exon is synthesized and competition between skipping and inclusion fates afterward. Collision of both exon ends to form an exon definition complex was incorporated to account for the effect of size; ESE/ESS effects were modeled on the basis of stabilization/destabilization. This model accurately predicted the outcome of independent experiments on more complex DEs that combined ESEs and ESSs.

Unzippers, resolvers and sensors: a structural and functional biochemistry tale of RNA helicases

The centrality of RNA within the biological world is an irrefutable fact that currently attracts increasing attention from the scientific community. The panoply of functional RNAs requires the existence of specific biological caretakers, RNA helicases, devoted to maintain the proper folding of those molecules, resolving unstable structures. However, evolution has taken advantage of the specific position and characteristics of RNA helicases to develop new functions for these proteins, which are at the interface of the basic processes for transference of information from DNA to proteins. RNA helicases are involved in many biologically relevant processes, not only as RNA chaperones, but also as signal transducers, scaffolds of molecular complexes, and regulatory elements. Structural biology studies during the last decade, founded in X-ray crystallography, have characterized in detail several RNA-helicases. This comprehensive review summarizes the structural knowledge accumulated in the last two decades within this family of proteins, with special emphasis on the structure-function relationships of the most widely-studied families of RNA helicases: the DEAD-box, RIG-I-like and viral NS3 classes.

Proteome folding kinetics is limited by protein halflife

How heterogeneous are proteome folding timescales and what physical principles, if any, dictate its limits? We answer this by predicting copy number weighted folding speed distribution – using the native topology – for E.coli and Yeast proteome. E.coli and Yeast proteomes yield very similar distributions with average folding times of 100 milliseconds and 170 milliseconds, respectively. The topology-based folding time distribution is well described by a diffusion-drift mutation model on a flat-fitness landscape in free energy barrier between two boundaries: i) the lowest barrier height determined by the upper limit of folding speed and ii) the highest barrier height governed by the lower speed limit of folding. While the fastest time scale of the distribution is near the experimentally measured speed limit of 1 microsecond (typical of barrier-less folders), we find the slowest folding time to be around seconds (8 seconds for Yeast distribution), approximately an order of magnitude less than the fastest halflife (approximately 2 minutes) in the Yeast proteome. This separation of timescale implies even the fastest degrading protein will have moderately high (96%) probability of folding before degradation. The overall agreement with the flat-fitness landscape model further hints that proteome folding times did not undergo additional major selection pressures – to make proteins fold faster – other than the primary requirement to “sufficiently beat the clock” against its lifetime. Direct comparison between the predicted folding time and experimentally measured halflife further shows 99% of the proteome have a folding time less than their corresponding lifetime. These two findings together suggest that proteome folding kinetics may be bounded by protein halflife.

Universal relations in the self-assembly of proteins and RNA

Concepts rooted in physics are becoming increasingly important in biology as we transition to an era in which quantitative descriptions of all processes from molecular to cellular level are needed. In this perspective I discuss two unexpected findings of universal behavior, uncommon in biology, in the self-assembly of proteins and RNA. These findings, which are surprising, reveal that physics ideas applied to biological problems, ranging from folding to gene expression to cellular movement and communication between cells, might lead to discovery of universal principles operating in adoptable living systems.

Viral RNAs are unusually compact

A majority of viruses are composed of long single-stranded genomic RNA molecules encapsulated by protein shells with diameters of just a few tens of nanometers. We examine the extent to which these viral RNAs have evolved to be physically compact molecules to facilitate encapsulation. Measurements of equal-length viral, non-viral, coding and non-coding RNAs show viral RNAs to have among the smallest sizes in solution, i.e., the highest gel-electrophoretic mobilities and the smallest hydrodynamic radii. Using graph-theoretical analyses we demonstrate that their sizes correlate with the compactness of branching patterns in predicted secondary structure ensembles. The density of branching is determined by the number and relative positions of 3-helix junctions, and is highly sensitive to the presence of rare higher-order junctions with 4 or more helices. Compact branching arises from a preponderance of base pairing between nucleotides close to each other in the primary sequence. The density of branching represents a degree of freedom optimized by viral RNA genomes in response to the evolutionary pressure to be packaged reliably. Several families of viruses are analyzed to delineate the effects of capsid geometry, size and charge stabilization on the selective pressure for RNA compactness. Compact branching has important implications for RNA folding and viral assembly.

Generalized iterative annealing model for the action of RNA chaperones

As a consequence of the rugged landscape of RNA molecules their folding is described by the kinetic partitioning mechanism according to which only a small fraction (φF) reaches the folded state while the remaining fraction of molecules is kinetically trapped in misfolded intermediates. The transition from the misfolded states to the native state can far exceed biologically relevant time. Thus, RNA folding in vivo is often aided by protein cofactors, called RNA chaperones, that can rescue RNAs from a multitude of misfolded structures. We consider two models, based on chemical kinetics and chemical master equation, for describing assisted folding. In the passive model, applicable for class I substrates, transient interactions of misfolded structures with RNA chaperones alone are sufficient to destabilize the misfolded structures, thus entropically lowering the barrier to folding. For this mechanism to be efficient the intermediate ribonucleoprotein complex between collapsed RNA and protein cofactor should have optimal stability. We also introduce an active model (suitable for stringent substrates with small φF), which accounts for the recent experimental findings on the action of CYT-19 on the group I intron ribozyme, showing that RNA chaperones do not discriminate between the misfolded and the native states. In the active model, the RNA chaperone system utilizes chemical energy of adenosine triphosphate hydrolysis to repeatedly bind and release misfolded and folded RNAs, resulting in substantial increase of yield of the native state. The theory outlined here shows, in accord with experiments, that in the steady state the native state does not form with unit probability.

Analysing RNA-kinetics based on folding space abstraction

BACKGROUND

RNA molecules, especially non-coding RNAs, play vital roles in the cell and their biological functions are mostly determined by structural properties. Often, these properties are related to dynamic changes in the structure, as in the case of riboswitches, and thus the analysis of RNA folding kinetics is crucial for their study. Exact approaches to kinetic folding are computationally expensive and, thus, limited to short sequences. In a previous study, we introduced a position-specific abstraction based on helices which we termed helix index shapes (hishapes) and a hishape-based algorithm for near-optimal folding pathway computation, called HiPath. The combination of these approaches provides an abstract view of the folding space that offers information about the global features.

RESULTS

In this paper we present HiKinetics, an algorithm that can predict RNA folding kinetics for sequences up to several hundred nucleotides long. This algorithm is based on RNAHeliCes, which decomposes the folding space into abstract classes, namely hishapes, and an improved version of HiPath, namely HiPath2, which estimates plausible folding pathways that connect these classes. Furthermore, we analyse the relationship of hishapes to locally optimal structures, the results of which strengthen the use of the hishape abstraction for studying folding kinetics. Finally, we show the application of HiKinetics to the folding kinetics of two well-studied RNAs.

CONCLUSIONS

HiKinetics can calculate kinetic folding based on a novel hishape decomposition. HiKinetics, together with HiPath2 and RNAHeliCes, is available for download at http://www.cyanolab.de/software/RNAHeliCes.htm.

Sequence-dependent folding landscapes of adenine riboswitch aptamers

Expression of a large fraction of genes in bacteria is controlled by riboswitches, which are found in the untranslated region of mRNA. Structurally riboswitches have a conserved aptamer domain to which a metabolite binds, resulting in a conformational change in the downstream expression platform. Prediction of the functions of riboswitches requires a quantitative description of the folding landscape so that the barriers and time scales for the conformational change in the switching region in the aptamer can be estimated. Using a combination of all atom molecular dynamics (MD) and coarse-grained model simulations we studied the response of adenine (A) binding add and pbuE A-riboswitches to mechanical force. The two riboswitches contain a structurally similar three-way junction formed by three paired helices, P1, P2, and P3, but carry out different functions. Using pulling simulations, with structures generated in MD simulations, we show that after P1 rips the dominant unfolding pathway in the add A-riboswitch is the rupture of P2 followed by unraveling of P3. In the pbuE A-riboswitch, after P1 unfolds P3 ruptures ahead of P2. The order of unfolding of the helices, which is in accord with single molecule pulling experiments, is determined by the relative stabilities of the individual helices. Our results show that the stability of isolated helices determines the order of assembly and response to force in these non-coding regions. We use the simulated free energy profile for the pbuE A-riboswitch to estimate the time scale for allosteric switching, which shows that this riboswitch is under kinetic control lending additional support to the conclusion based on single molecule pulling experiments. A consequence of the stability hypothesis is that a single point mutation (U28C) in the P2 helix of the add A-riboswitch, which increases the stability of P2, would make the folding landscapes of the two riboswitches similar. This prediction can be tested in single molecule pulling experiments.

Differences between cotranscriptional and free riboswitch folding

Riboswitches are part of noncoding regions of messenger RNA (mRNA) that act as RNA sensors regulating gene expression of the downstream gene. Typically, one out of two distinct conformations is formed depending on ligand binding when the transcript leaves RNA polymerase (RNAP). Elongation of the RNA chain by RNAP, folding and binding all occurs simultaneously and interdependently on the seconds' timescale. To investigate the effect of transcript elongation velocity on folding for the S-adenosylmethionine (SAM)-I and adenine riboswitches we employ two complementary coarse-grained in silico techniques. Native structure-based molecular dynamics simulations provide a 3D, atomically resolved model of folding with homogenous energetics. Energetically more detailed kinetic Monte Carlo simulations give access to longer timescale by describing folding on the secondary structure level and feature the incorporation of competing aptamer conformations and a ligand-binding model. Depending on the extrusion scenarios, we observe and quantify different pathways in structure formation with robust agreements between the two techniques. In these scenarios, free-folding riboswitches exhibit different folding characteristics compared with transcription-rate limited folding. The critical transcription rate distinguishing these cases is higher than physiologically relevant rates. This result suggests that in vivo folding of the analyzed SAM-I and adenine riboswitches is transcription-rate limited.

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

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

Kinetics of allosteric transitions in S-adenosylmethionine riboswitch are accurately predicted from the folding landscape

Riboswitches are RNA elements that allosterically regulate gene expression by binding cellular metabolites. The SAM-III riboswitch, one of several classes that binds S-adenosylmethionine (SAM), represses translation upon binding SAM (OFF state) by encrypting the ribosome binding sequence. We have carried out simulations of the RNA by applying mechanical force (f) to the ends of SAM-III, with and without SAM, to get quantitative insights into the f-dependent structural changes. Force-extension (z) curves (FECs) for the apo (ON) state, obtained in simulations in which f is increased at a constant loading rate, show three intermediates, with the first one being the rupture of SAM binding region, which is greatly stabilized in the OFF state. Force-dependent free energy profiles, G(z,f), as a function of z, obtained in equilibrium constant force simulations, reveal the intermediates observed in FECs. The predicted stability difference between the ON and OFF states using G(z,f) is in excellent agreement with experiments. Remarkably, using G(z,f)s and estimate of an effective diffusion constant at a single value of f allows us to predict the f-dependent transition rates using theory of first passage times for both the apo and holo states. To resolve the kinetics of assembly of SAM-III riboswitch in structural terms, we use force stretch-quench pulse sequences in which the force on RNA is maintained at a low (fq) value starting from a high value for a time period tq. Variation of tq over a wide range results in resolution of elusive states involved in the SAM binding pocket and leads to accurate determination of folding times down to fq = 0. Quantitative measure of the folding kinetics, obtained from the folding landscape, allows us to propose that, in contrast to riboswitches regulating transcription, SAM-III functions under thermodynamic control provided the basal concentration of SAM exceeds a small critical value. All of the predictions are amenable to tests in single molecule pulling experiments.

Gene regulation by riboswitches with and without negative feedback loop

Riboswitches, structured elements in the untranslated regions of messenger RNAs, regulate gene expression by binding specific metabolites. We introduce a kinetic network model that describes the functions of riboswitches at the systems level. Using experimental data for flavin mononucleotide riboswitch as a guide, we show that efficient function, implying a large dynamic range without compromising the requirement to suppress transcription, is determined by a balance between the transcription speed, the folding and unfolding rates of the aptamer, and the binding rates of the metabolite. We also investigated the effect of negative feedback accounting for binding to metabolites, which are themselves the products of genes that are being regulated. For a range of transcription rates negative feedback suppresses gene expression by nearly 10-fold. Negative feedback speeds the gene expression response time, and suppresses the change of steady-state protein concentration by half relative to that without feedback, when there is a modest spike in DNA concentration. A dynamic phase diagram expressed in terms of transcription speed, folding rates, and metabolite binding rates predicts different scenarios in riboswitch-mediated transcription regulation.

RNA under tension: Folding Landscapes, Kinetic partitioning Mechanism, and Molecular Tensegrity

Non-coding RNA sequences play a great role in controlling a number of cellular functions, thus raising the need to understand their complex conformational dynamics in quantitative detail. In this perspective, we first show that single molecule pulling when combined with with theory and simulations can be used to quantitatively explore the folding landscape of nucleic acid hairpins, and riboswitches with tertiary interactions. Applications to riboswitches, which are non-coding RNA elements that control gene expression by undergoing dynamical conformational changes in response to binding of metabolites, lead to an organization principle that assembly of RNA is determined by the stability of isolated helices. We also point out the limitations of single molecule pulling experiments, with molecular extension as the only accessible parameter, in extracting key parameters of the folding landscapes of RNA molecules.

Insights into the regulatory landscape of the lysine riboswitch

A prevalent means of regulating gene expression in bacteria is by riboswitches found within mRNA leader sequences. Like protein repressors, these RNA elements must bind an effector molecule with high specificity against a background of other cellular metabolites of similar chemical structure to elicit the appropriate regulatory response. Current crystal structures of the lysine riboswitch do not provide a complete understanding of selectivity as recognition is substantially mediated through main-chain atoms of the amino acid. Using a directed set of lysine analogs and other amino acids, we have determined the relative contributions of the polar functional groups to binding affinity and the regulatory response. Our results reveal that the lysine riboswitch has >1000-fold specificity for lysine over other amino acids. The aptamer is highly sensitive to the precise placement of the ε-amino group and relatively tolerant of alterations to the main-chain functional groups in order to achieve this specificity. At low nucleotide triphosphate (NTP) concentrations, we observe good agreement between the half-maximal regulatory activity (T(50)) and the affinity of the receptor for lysine (K(d)), as well as many of its analogs. However, above 400 μM [NTP], the concentration of lysine required to elicit transcription termination rises, moving into the riboswitch into a kinetic control regime. These data demonstrate that, under physiologically relevant conditions, riboswitches can integrate both effector and NTP concentrations to generate a regulatory response appropriate for global metabolic state of the cell.