Tertiary interactions determine the accuracy of RNA folding

RNAs must fold into unique three-dimensional structures to function in the cell, but how each polynucleotide finds its native structure is not understood. To investigate whether the stability of the tertiary structure determines the speed and accuracy of RNA folding, docking of a tetraloop with its receptor in a bacterial group I ribozyme was perturbed by site-directed mutagenesis. Disruption of the tetraloop or its receptor destabilizes tertiary interactions throughout the ribozyme by 2-3 kcal/mol, demonstrating that tertiary interactions form cooperatively in the transition from a native-like intermediate to the native state. Nondenaturing PAGE and RNase T1 digestion showed that base pairs form less homogeneously in the mutant RNAs during the transition from the unfolded state to the intermediate. Thus, tertiary interactions between helices bias the ensemble of secondary structures toward native-like conformations. Time-resolved hydroxyl radical footprinting showed that the wild-type ribozyme folds completely within 5-20 ms. By contrast, only 40-60% of a tetraloop mutant ribozyme folds in 30-40 ms, with the remainder folding in 30-200 s via nonnative intermediates. Therefore, destabilization of tetraloop-receptor docking introduces an alternate folding pathway in the otherwise smooth energy landscape of the wild-type ribozyme. Our results show that stable tertiary structure increases the flux through folding pathways that lead directly and rapidly to the native structure.     

Folding of human telomerase RNA pseudoknot using ion-jump and temperature-quench simulations

Globally RNA folding occurs in multiple stages involving chain compaction and subsequent rearrangement by a number of parallel routes to the folded state. However, the sequence-dependent details of the folding pathways and the link between collapse and folding are poorly understood. To obtain a comprehensive picture of the thermodynamics and folding kinetics we used molecular simulations of coarse-grained model of a pseudoknot found in the conserved core domain of the human telomerase (hTR) by varying both temperature (T) and ion concentration (C). The phase diagram in the [T,C] plane shows that the boundary separating the folded and unfolded state for the finite 47-nucleotide system is relatively sharp, implying that from a thermodynamic perspective hTR behaves as an apparent two-state system. However, the folding kinetics following single C-jump or T-quench is complicated, involving multiple channels to the native state. Although globally folding kinetics triggered by T-quench and C-jump are similar, the kinetics of chain compaction are vastly different, which reflects the role of initial conditions in directing folding and collapse. Remarkably, even after substantial reduction in the overall size of hTR, the ensemble of compact conformations are far from being nativelike, suggesting that the search for the folded state occurs among the ensemble of low-energy fluidlike globules. The rate of unfolding, which occurs in a single step, is faster upon C-decrease compared to a jump in temperature. To identify "hidden" states that are visited during the folding process we performed simulations by periodically interrupting the approach to the folded state by lowering C. These simulations show that hTR reaches the folded state through a small number of connected clusters that are repeatedly visited during the pulse sequence in which the folding or unfolding is interrupted. The results from interrupted folding simulations, which are in accord with non-equilibrium single-molecule folding of a large ribozyme, show that multiple probes are needed to reveal the invisible states that are sampled by RNA as it folds. Although we have illustrated the complexity of RNA folding using hTR as a case study, general arguments and qualitative comparisons to time-resolved scattering experiments on Azoarcus group I ribozyme and single-molecule non-equilibrium periodic ion-jump experiments establish the generality of our findings.     

Selective stabilization of natively folded RNA structure by DNA constraints

Learning how native RNA conformations can be stabilized relative to unfolded states is an important objective, for both understanding natural RNAs and improving the design of artificial functional RNAs. Here we show that covalently attached double-stranded DNA constraints (ca. 14 base pairs in length) can significantly stabilize the native conformation of an RNA molecule. Using the P4-P6 domain of the Tetrahymena group I intron as the test system, we identified pairs of RNA sites where attaching a DNA duplex is predicted to be structurally compatible with only the folded state of the RNA. The DNA-constrained RNAs were synthesized and shown by nondenaturing polyacrylamide gel electrophoresis (native PAGE) to have substantial decreases in their Mg2+ midpoints ([Mg2+]1/2 values). These changes are equivalent to free energy stabilizations as large as DeltaDeltaGdegrees = -2.5 kcal/mol, which is approximately 14% of the total tertiary folding energy. For comparison, the sole modification of P4-P6 previously reported to stabilize this RNA is a single-nucleotide deletion (DeltaC209) that provides only 1.1 kcal/mol of stabilization. Our findings indicate that nature has not completely optimized P4-P6 RNA folding. Furthermore, the DNA constraints are designed not to interact directly and extensively with the RNA, but rather more indirectly to modulate the relative stabilities of folded and unfolded RNA states. The successful implementation of this strategy to further stabilize a natively folded RNA conformation suggests an important element of modularity in stabilization of RNA structure, with implications for how nature might use other molecules such as proteins to stabilize specific RNA conformations.     

Understanding the role of the topology in protein folding by computational inverse folding experiments

Recent studies suggest that protein folding should be revisited as the emergent property of a complex system and that the nature allows only a very limited number of folds that seem to be strongly influenced by geometrical properties. In this work we explore the principles underlying this new view and show how helical protein conformations can be obtained starting from simple geometric considerations. We generated a large data set of C-alpha traces made of 65 points, by computationally solving a backbone model that takes into account only topological features of the all-alpha proteins; then, we built corresponding tertiary structures, by using the sequences associated to the crystallographic structures of four small globular all-alpha proteins from PDB, and analysed them in terms of structural and energetic properties. In this way we obtained four poorly populated sets of structures that are reasonably similar to the conformational states typical of the experimental PDB structures. These results show that our computational approach can capture the native topology of all-alpha proteins; furthermore, it generates backbone folds without the influence of the side chains and uses the protein sequence to select a specific fold among the generated folds. This agrees with the recent view that the backbone plays an important role in the protein folding process and that the amino acid sequence chooses its own fold within a limited total number of folds.     

Forced Folding of a Disordered Protein Accesses an Alternative Folding Landscape

Intrinsically disordered proteins (IDPs) are involved in diverse cellular functions. Many IDPs can interact with multiple binding partners, resulting in their folding into alternative ligand‐specific functional structures. For such multi‐structural IDPs, a key question is whether these multiple structures are fully encoded in the protein sequence, as is the case in many globular proteins. To answer this question, here we employed a combination of single‐molecule and ensemble techniques to compare ligand‐induced and osmolyte‐forced folding of α‐synuclein. Our results reveal context‐dependent modulation of the protein′s folding landscape, suggesting that the codes for the protein′s native folds are partially encoded in its primary sequence, and are completed only upon interaction with binding partners. Our findings suggest a critical role for cellular interactions in expanding the repertoire of folds and functions available to disordered proteins.     

Tertiary Motifs in RNA Structure and Folding

Specific tertiary structural motifs determine the complete architecture of RNA molecules (see picture for examples). Within the last few years a number of high-resolution crystal structures of complex RNAs have led to new insights into the mechanisms by which these complex folds are attained. In this review the structures of these tertiary motifs and how they influence the folding pathway of biological RNAs are discussed, as well as new developments in modeling RNA structure based upon these findings.     

Kinetics of cooperative protein folding involving two separate conformational families

The master equation that describes the kinetics of protein folding is solved numerically for a portion of Staphylococcal Protein A by a Laplace transformation. The calculations are carried out with 50 local-minimum conformations belonging to two conformational families. The master equation allows for transitions among all the 50 conformations in the evolution toward the final folded equilibrium distribution of conformations. It is concluded that the native protein folds in a fast cooperative process. The global energy minimum of a native protein can be reached after a sufficiently long folding time regardless of the initial state and the existence of a large number of local energy minima. Conformations representing non-native states of the protein can transform to the native state even if they do not belong to the native conformational family. Given a starting conformation, the protein molecule can fold to its final conformation through different paths. Finally, when the folding reaches the equilibrium distribution, the protein molecule adopts a set of conformations in which the global minimum has the largest average probability.     

Determining the Mg2+ stoichiometry for folding an RNA metal ion core

The folding and catalytic function of RNA molecules depend on their interactions with divalent metal ions, such as magnesium. As with every molecular process, the most basic knowledge required for understanding the close relationship of an RNA with its metal ions is the stoichiometry of the interaction. Unfortunately, inventories of the numbers of divalent ions associated with unfolded and folded RNA states have been unattainable. A common approach has been to interpret Hill coefficients fit to folding equilibria as the number of metal ions bound upon folding. However, this approach is vitiated by the presence of diffusely associated divalent ions in a dynamic ion atmosphere and by the likelihood of multiple transitions along a folding pathway. We demonstrate that the use of molar concentrations of background monovalent salt can alleviate these complications. These simplifying solution conditions allow a precise determination of the stoichiometry of the magnesium ions involved in folding the metal ion core of the P4-P6 domain of the Tetrahymena group I ribozyme. Hill analysis of hydroxyl radical footprinting data suggests that the P4-P6 RNA core folds cooperatively upon the association of two metal ions. This unexpectedly small stoichiometry is strongly supported by counting magnesium ions associated with the P4-P6 RNA via fluorescence titration and atomic emission spectroscopy. By pinpointing the metal ion stoichiometry, these measurements provide a critical but previously missing step in the thermodynamic dissection of the coupling between metal ion binding and RNA folding.     

Non-unity molecular heritability demonstrated by continuous evolution in vitro

INTRODUCTION: When catalytic RNA is evolved in vitro, the molecule's chemical reactivity is usually the desired selection target. Sometimes the phenotype of a particular RNA molecule cannot be unambiguously determined from its genotype, however. This can occur if a nucleotide sequence can adopt multiple folded states, an example of non-unity heritability (i.e. one genotype gives rise to more than one phenotype). In these cases, more rounds of selection are required to achieve a phenotypic shift. We tested the influence of non-unity heritability at the molecular level by selecting for variants of a ligase ribozyme via continuous evolution. RESULTS: During 20 bursts of continuous evolution of a 152-nucleotide ligase ribozyme in which the Mg2+ concentration was periodically lowered, a nine-error variant of the starting 'wild-type' molecule became dominant in the last eight bursts. This variant appears to be more active than the wild type. Kinetic analyses of the mutant suggest that it may not possess a higher first-order catalytic rate constant, however. Examination of the multiple RNA conformations present under the continuous evolution conditions suggests that the mutant is superior to the wild type because it is less likely to misfold into inactive conformers. CONCLUSIONS: The evolution of genotypes that are more likely to exhibit a particular phenotype is an epiphenomenon usually ascribed only to complex living systems. We show that this can occur at the molecular level, demonstrating that in vitro systems may have more life-like characteristics than previously thought, and providing additional support for an RNA world.     

Conformational dynamics of bistable RNAs studied by time-resolved NMR spectroscopy

The structural transition between two alternate conformations of bistable RNAs has been characterized by time-resolved NMR spectroscopy. The mechanism, kinetics, and thermodynamics underlying the global structural transition of bistable RNAs were delineated. Both bistable RNA conformations and a partial unstructured RNA of identical sequence could be trapped using photolabile protecting groups. This trapping allowed for an investigation of the initial folding from an unfolded RNA to one of the preferred conformations of the bistable RNA and of the structural transitions involved. Folding of the secondary structure elements occurs rapidly, while the global structural transition of the bistable RNA occurs on a time scale of minutes and shows marked temperature dependence. Comparison of these results with bistable systems previously investigated leads to the prediction of activation enthalpies (DeltaH++) associated with global structural transitions in RNA.     

Discrete structure of an RNA folding intermediate revealed by cryo-electron microscopy

RNA folding occurs via a series of transitions between metastable intermediate states. It is unknown whether folding intermediates are discrete structures folding along defined pathways or heterogeneous ensembles folding along broad landscapes. We use cryo-electron microscopy and single-particle image reconstruction to determine the structure of the major folding intermediate of the specificity domain of a ribonuclease P ribozyme. Our results support the existence of a discrete conformation for this folding intermediate.     

Strategies for the Design of Drugs Targeting RNA and RNA-Protein Complexes

In many steps of gene replication and expression, RNA molecules participate as key players, which renders them attractive targets for therapeutic intervention. While the function of nucleic acids as carriers of genetic material is based on their sequence, a number of important RNAs are involved in processes that depend on the defined three-dimensional structures of these molecules. As for proteins, numerous complex folds of RNA exist. The development of drugs that bind specifically to RNA folds opens exciting new ways to expand greatly the existing repertoire of protein-targeted therapeutics. Most functions of RNAs involve interactions with proteins that contain RNA-binding domains. Effector molecules targeted at RNA may either alter the functional three-dimensional structure of the nucleic acid, so the interaction with proteins is thereby inhibited or enhanced, or, as interface inhibitors, they may directly prevent the formation of competent RNA-protein complexes. While the same tools used for the design of protein-targeted drugs may be considered for studying effectors binding to nucleic acids, the differences between proteins and RNAs in the forces which dominate their three-dimensional folding call for novel drug design strategies. In the present review, I will outline how our rapidly expanding knowledge of RNA three-dimensional structure and function facilitates rational approaches to develop RNA-binding compounds. Putative RNA targets for therapeutic intervention will be discussed along with recent advances in understanding RNA-small molecule and RNA-protein interactions.     

Restoration of Ribozyme Tertiary Contact and Function by Using a Molecular Glue for RNA

Some RNA classes require folding into the proper higher‐order structures to exert their functions. Hammerhead ribozyme (HHR) requires a folding conformation stabilized by tertiary interaction for full activity. A rationally engineered HHR was developed that was inactive, but could be activated by a synthetic RNA‐binding ligand, naphthyridine carbamate tetramer with Z‐stilbene linker (Z‐NCTS). Binding of Z‐NCTS could induce the formation of an active folding structure and thereby restore ribozyme activity, where Z‐NCTS acts as a molecular glue to bring two isolated RNA loops into contact with each other. Next, we designed a Z‐NCTS‐responsive genetic switch using the HHR sequence inserted into the 3′ untranslated region as a cis‐acting element. We demonstrated that the rationally designed ribozyme switch enabled regulation of gene expression by Z‐NCTS and was functional in mammalian cells.     

Exploration of the relationship between topology and designability of conformations

Protein structures are evolutionarily more conserved than sequences, and sequences with very low sequence identity frequently share the same fold. This leads to the concept of protein designability. Some folds are more designable and lots of sequences can assume that fold. Elucidating the relationship between protein sequence and the three-dimensional (3D) structure that the sequence folds into is an important problem in computational structural biology. Lattice models have been utilized in numerous studies to model protein folds and predict the designability of certain folds. In this study, all possible compact conformations within a set of two-dimensional and 3D lattice spaces are explored. Complementary interaction graphs are then generated for each conformation and are described using a set of graph features. The full HP sequence space for each lattice model is generated and contact energies are calculated by threading each sequence onto all the possible conformations. Unique conformation giving minimum energy is identified for each sequence and the number of sequences folding to each conformation (designability) is obtained. Machine learning algorithms are used to predict the designability of each conformation. We find that the highly designable structures can be distinguished from other non-designable conformations based on certain graphical geometric features of the interactions. This finding confirms the fact that the topology of a conformation is an important determinant of the extent of its designability and suggests that the interactions themselves are important for determining the designability.     

De novo and inverse folding predictions of protein structure and dynamics

Summary In the last two years, the use of simplified models has facilitated major progress in the globular protein folding problem, viz., the prediction of the three-dimensional (3D) structure of a globular protein from its amino acid sequence. A number of groups have addressed the inverse folding problem where one examines the compatibility of a given sequence with a given (and already determined) structure. A comparison of extant inverse protein-folding algorithms is presented, and methodologies for identifying sequences likely to adopt identical folding topologies, even when they lack sequence homology, are described. Extension to produce structural templates or fingerprints from idealized structures is discussed, and for eight-membered β-barrel proteins, it is shown that idealized fingerprints constructed from simple topology diagrams can correctly identify sequences having the appropriate topology. Furthermore, this inverse folding algorithm is generalized to predict elements of supersecondary structure including β-hairpins, helical hairpins and α/β/α fragments. Then, we describe a very high coordination number lattice model that can predict the 3D structure of a number of globular proteins de novo; i.e. using just the amino acid sequence. Applications to sequences designed by DeGrado and co-workers [Biophys. J., 61 (1992) A265] predict folding intermediates, native states and relative stabilities in accord with experiment. The methodology has also been applied to the four-helix bundle designed by Richardson and co-workers [Science, 249 (1990) 884] and a redesigned monomeric version of a naturally occurring four-helix dimer, rop. Based on comparison to the rop dimer, the simulations predict conformations with rms values of 3–4 ? from native. Furthermore, the de novo algorithms can asses the stability of the folds predicted from the inverse algorithm, while the inverse folding algorithms can assess the quality of the de novo models. Thus, the synergism of the de novo and inverse folding algorthhm approaches provides a set of complementary tools that will facilitate further progress on the protein-folding problem.     

Hierarchy of folding and unfolding events of protein G, CI2, and ACBP from explicit-solvent simulations

The study of the mechanism which is at the basis of the phenomenon of protein folding requires the knowledge of multiple folding trajectories under biological conditions. Using a biasing molecular-dynamics algorithm based on the physics of the ratchet-and-pawl system, we carry out all-atom, explicit solvent simulations of the sequence of folding events which proteins G, CI2, and ACBP undergo in evolving from the denatured to the folded state. Starting from highly disordered conformations, the algorithm allows the proteins to reach, at the price of a modest computational effort, nativelike conformations, within a root mean square deviation (RMSD) of approximately 1 A?. A scheme is developed to extract, from the myriad of events, information concerning the sequence of native contact formation and of their eventual correlation. Such an analysis indicates that all the studied proteins fold hierarchically, through pathways which, although not deterministic, are well-defined with respect to the order of contact formation. The algorithm also allows one to study unfolding, a process which looks, to a large extent, like the reverse of the major folding pathway. This is also true in situations in which many pathways contribute to the folding process, like in the case of protein G.     

Inherent structure analysis of protein folding

An analysis in terms of the inherent structures (IS, local minima) of the multidimensional potential energy landscape is applied to proteins. Detailed calculations are performed for the 46 bead BLN model, which folds into a four-stranded beta-barrel. Enhanced sampling has allowed determination of 239 199 IS states, believed to encompass nearly all the compact, low-energy states, and of well-averaged thermodynamic quantities at low temperature. The density of states shows distinct lobes for compact and extended states, and entropic barriers for the collapse and local ordering transitions. A two-dimensional scatterplot or density of states clearly shows the multifunnel structure of the energy landscape. The anharmonic vibrational free energy is found to play a crucial role in protein folding. The problem of determining the folding transition in a multifunnel system is discussed, and novel indicators of folding are introduced. A particularly clear picture is obtained through the occupation probabilities, pi, of individual low-lying IS, which become finite below the collapse temperature; it is suggested that poor foldability corresponds to a large "misfolding interval" where the excited state pi>0 exceeds that of the native state p0.     

蛋白质结构的“限域下最低能量结构片段”假说与蛋白质进化的“石器时代”

蛋白质折叠问题被称为第二遗传密码,至今未破译;蛋白质序列的天书仍然是"句读之不知,惑之不解"。在最近工作的基础上,我们提出了蛋白质结构的"限域下最低能量结构片段"假说。这一假说指出,蛋白质中存在一些关键的长程强相互作用位点,这些位点相当于标点符号,将蛋白质序列的天书变成可读的句子(多肽片段)。这些片段的天然结构是在这些强长程相互作用位点限域下的能量最低状态。完整的蛋白质结构由这些"限域下最低能量结构片段"拼合而成,而蛋白质整体结构并不一定是全局性的能量最低状态。在蛋白质折叠过程中,局部片段的天然结构倾向性为强长程相互作用的形成提供主要基于焓效应的驱动力,而天然强长程相互作用的形成为局部片段的天然结构提供主要基于熵效应的稳定性。在蛋白质进化早期,可能存在一个"石器时代",即依附不同界面(比如岩石)的限域作用而稳定的多肽片段先进化出来,后由这些片段逐步进化(包括拼合)而成蛋白质。     

Informational complexity and functional activity of RNA structures

Very little is known about the distribution of functional DNA, RNA, and protein molecules in sequence space. The question of how the number and complexity of distinct solutions to a particular biochemical problem varies with activity is an important aspect of this general problem. Here we present a comparison of the structures and activities of eleven distinct GTP-binding RNAs (aptamers). By experimentally measuring the amount of information required to specify each optimal binding structure, we show that defining a structure capable of 10-fold tighter binding requires approximately 10 additional bits of information. This increase in information content is equivalent to specifying the identity of five additional nucleotide positions and corresponds to an approximately 1000-fold decrease in abundance in a sample of random sequences. We observe a similar relationship between structural complexity and activity in a comparison of two catalytic RNAs (ribozyme ligases), raising the possibility of a general relationship between the complexity of RNA structures and their functional activity. Describing how information varies with activity in other heteropolymers, both biological and synthetic, may lead to an objective means of comparing their functional properties. This approach could be useful in predicting the functional utility of novel heteropolymers.     

Folding a nonbiological polymer into a compact multihelical structure

The only molecules that are currently known to fold into unique three-dimensional conformations and perform sophisticated functions are biological polymers - proteins and some RNA molecules. Our aim is to create a nonbiological sequence-specific polymer that folds in aqueous solution. Toward that end, we synthesized sequence-specific 30mer, 45mer, and 60mer peptoid oligomers (N-substituted glycine polymers) consisting of 15mer units we chained together by disulfide and oxime linkages to mimic the helical bundle structures commonly found in proteins. Because these 15mer sequences were previously shown to form defined helical structures that aggregate together at submillimolar concentrations, we expected that by covalently linking multiple 15mers together, they might fold as helical bundles. To probe whether they folded, we used fluorescence resonance energy transfer (FRET) reporter groups. We found that certain constructs fold up with a hydrophobic core and have cooperative folding transitions. Such molecules may ultimately provide a platform for designing specific functions resembling those of proteins.