RNA-Puzzles Round IV: 3D structure predictions of four ribozymes and two aptamers.

RNA-Puzzles is a collective endeavor dedicated to the advancement and improvement of RNA 3D structure prediction. With agreement from crystallographers, the RNA structures are predicted by various groups before the publication of the crystal structures. We now report the prediction of 3D structures for six RNA sequences: four nucleolytic ribozymes and two riboswitches. Systematic protocols for comparing models and crystal structures are described and analyzed. In these six puzzles, we discuss (i) the comparison between the automated web servers and human experts; (ii) the prediction of coaxial stacking; (iii) the prediction of structural details and ligand binding; (iv) the development of novel prediction methods; and (v) the potential improvements to be made. We show that correct prediction of coaxial stacking and tertiary contacts is essential for the prediction of RNA architecture, while ligand binding modes can only be predicted with low resolution and simultaneous prediction of RNA structure with accurate ligand binding still remains out of reach. All the predicted models are available for the future development of force field parameters and the improvement of comparison and assessment tools.

Mutual effects between single-stranded DNA conformation and Na+-Mg2+ ion competition in mixed salt solutions.

The ion-dependence of single-stranded DNA (ssDNA) conformational changes has attracted growing attention because of its biological and technological importance. Although single-species ion effects have been extensively explored, it is challenging to study the ssDNA conformational properties under mixed monovalent/divalent ion conditions due to the complications of ssDNA flexibility and ion-ion competition. In this study, we apply Langevin dynamics simulations to investigate mixed Na+/Mg2+ ion-dependent ssDNA conformations. The ssDNA structure is described using a coarse-grained model, in which the phosphate, base, and sugar of each nucleotide are represented by three different beads. A novel improvement in our simulation model is that mixed-salt-related electrostatic interactions are computed via combining Manning counterion condensation (MCC) theory with the Monte Carlo tightly bound ion (MCTBI) model. Based on this MCC-MCTBI combination, we report new empirical functions to describe the ion-concentration-dependent and ssDNA conformation/structure-dependent electrostatic effects. The calculation results relating to the ion binding properties and the simulation results relating to the ssDNA conformational properties are validated against experimental results. In addition, our simulation results suggest a quantitative relationship between the ssDNA conformation and Na+-Mg2+ competition; this in turn reveals their mutual impact in the ion atmosphere.

Translocation of a looped polymer threading through a nanopore.

Recent experiments reported that the complicated translocation dynamics of a looped DNA chain through a nanopore can be detected by ionic current blockade profiles. Inspired by the experimental results, we systematically study the translocation dynamics of a looped polymer, formed by three building blocks of a loop in the middle and two tails of the same length connected with the loop, by using Langevin dynamics simulations. Based on two entering modes (tail-leading and loop-leading) and three translocation orders (loop-tail-tail, tail-loop-tail, and tail-tail-loop), the translocation of the looped polymer is classified into six translocation pathways, corresponding to different current blockade profiles. The probabilities of the six translocation pathways are dependent on the loop length, polymer length, and pore radius. Moreover, the translocation times of the entire polymer and the loop are investigated. We find that the two translocation times show different dependencies on the translocation pathways and on the lengths of the loop and the entire polymer.

Effects of electrostatic interactions on global folding and local conformational dynamics of a multidomain Y-family DNA polymerase.

The Y-family DNA polymerases specialize in translesion DNA synthesis, which is essential for replicating damaged DNA. The Y-family polymerases, which are made up of four stable domains, exhibit extensive distributions of charged residues, and are responsible for the tight formation of the protein-DNA complex. However, it is still unclear how the electrostatic interactions influence the conformational dynamics of the polymerases. Here, we focus on the case of a prototype Y-family DNA polymerase, Dpo4. Using coarse-grained models including a salt-dependent electrostatic potential, we investigate the effects of the electrostatic interactions on the folding process of Dpo4. Our simulations show that strong electrostatic interactions result in a three-state folding of Dpo4, consistent with the experimental observations. This folding process exhibits low cooperativity led by low salt concentration, where the individual domains fold one by one through one single pathway. Since the refined folding order of domains in multidomain proteins can shrink the configurational space, we suggest that the electrostatic interactions facilitate the Dpo4 folding. In addition, we study the local conformational dynamics of Dpo4 in terms of fluctuation and frustration analyses. We show that the electrostatic interactions can exaggerate the local conformational properties, which are in favor of the large-scale conformational transition of Dpo4 during the functional DNA binding. Our results underline the importance of electrostatic interactions in the conformational dynamics of Dpo4 at both the global and local scale, providing useful guidance in protein engineering at the multidomain level.

The translocation dynamics of the polymer through a conical pore: Non-stuck, weak-stuck, and strong-stuck modes.

The external voltage-driven polymer translocation through a conical pore (with a large opening at the entry and a small tip at the exit) is studied by using the Langevin dynamics simulation in this paper. The entire translocation process is divided into an approaching stage and a threading stage. First, the approaching stage starts from the polymer entering the large opening and ends up at a terminal monomer reaching the pore tip. In this stage, the polymer will undergo the conformation adjustment to fit the narrowed cross-sectional area of the pore, leading to three approaching modes: the non-stuck mode with a terminal monomer arriving at the pore tip smoothly, the weak-stuck mode for the polymer stuck inside the pore for a short duration with minor conformational adjustments, and the strong-stuck mode with major conformational changes and a long duration. The approaching times (the duration of the approaching stage) of the three approaching modes show different behavior as a function of the pore apex angle. Second, the threading stage describes that the polymer threads through the pore tip with a linear fashion. In this stage, an increase in the apex angle causes the reduction of the threading time (the duration of the threading stage) due to the increase in the driving force with the apex angle at the tip. Moreover, we also find that with the increase in the apex angle or the polymer length, the polymer threading dynamics will change from the quasi-equilibrium state to the non-equilibrium state.

Predicting RNA-Metal Ion Binding with Ion Dehydration Effects.

Metal ions play essential roles in nucleic acids folding and stability. The interaction between metal ions and nucleic acids can be highly complicated because of the interplay between various effects such as ion correlation, fluctuation, and dehydration. These effects may be particularly important for multivalent ions such as Mg2+ ions. Previous efforts to model ion correlation and fluctuation effects led to the development of the Monte Carlo tightly bound ion model. Here, by incorporating ion hydration/dehydration effects into the Monte Carlo tightly bound ion model, we develop a, to our knowledge, new approach to predict ion binding. The new model enables predictions for not only the number of bound ions but also the three-dimensional spatial distribution of the bound ions. Furthermore, the new model reveals several intriguing features for the bound ions such as the mutual enhancement/inhibition in ion binding between the fully hydrated (diffuse) ions, the outer-shell dehydrated ions, and the inner-shell dehydrated ions and novel features for the monovalent-divalent ion interplay due to the hydration effect.

Kinetic Mechanism of RNA Helix-Terminal Basepairing-A Kinetic Minima Network Analysis.

RNA functions are often kinetically controlled. The folding kinetics of RNAs involves global structural changes and local nucleotide movement, such as base flipping. The most elementary step in RNA folding is the closing and opening of a basepair. By integrating molecular dynamics simulation, master equation, and kinetic Monte Carlo simulation, we investigate the kinetics mechanism of RNA helix-terminal basepairing. The study reveals a six-state folding scheme with three dominant folding pathways of tens, hundreds, and thousands of nanoseconds of folding timescales, respectively. The overall kinetics is rate limited by the detrapping of a misfolded state with the overall folding time of 10-5 s. Moreover, the analysis examines the different roles of the various driving forces, such as the basepairing and stacking interactions and the ion binding/dissociation effects on structural changes. The results may provide useful insights for developing a basepair opening/closing rate model and further kinetics models of large RNAs.

MCTBI: a web server for predicting metal ion effects in RNA structures.

Metal ions play critical roles in RNA structure and function. However, web servers and software packages for predicting ion effects in RNA structures are notably scarce. Furthermore, the existing web servers and software packages mainly neglect ion correlation and fluctuation effects, which are potentially important for RNAs. We here report a new web server, the MCTBI server (http://rna.physics.missouri.edu/MCTBI), for the prediction of ion effects for RNA structures. This server is based on the recently developed MCTBI, a model that can account for ion correlation and fluctuation effects for nucleic acid structures and can provide improved predictions for the effects of metal ions, especially for multivalent ions such as Mg2+ effects, as shown by extensive theory-experiment test results. The MCTBI web server predicts metal ion binding fractions, the most probable bound ion distribution, the electrostatic free energy of the system, and the free energy components. The results provide mechanistic insights into the role of metal ions in RNA structure formation and folding stability, which is important for understanding RNA functions and the rational design of RNA structures.

Trapped and non-trapped polymer translocations through a spherical pore.

The polymer translocation through a spherical pore is studied using the Langevin dynamics simulation. The translocation events are classified into two types: one is the trapped translocation in which the entire polymer is trapped in the pore and the other is the non-trapped translocation where the pore cannot hold the whole polymer. We find that the trapped translocation is favored at large spheres and small external voltages. However, the monomer-pore attraction would lead to the non-monotonic behavior of the trapped translocation possibility out of all translocation events. Moreover, both the trapped and non-trapped translocation times are dependent on the polymer length, pore size, external voltage, and the monomer-pore attraction. There exist two pathways for the polymer in the trapped translocation: an actively trapped pathway for the polymer trapped in the pore before the head monomer arrives at the pore exit, and a passively trapped pathway for the polymer trapped in the pore while the head monomer is struggling to move out of the pore. The studies of trapped pathways can provide a deep understanding of the polymer translocation behavior.

Simulation study on the migration of diblock copolymers in periodically patterned slits.

The forced migration of diblock copolymers (ANABNB) in periodically patterned slits was investigated by using Langevin dynamics simulation. The lower surface of the slit consists of stripe α and stripe ß distributed in alternating sequence, while the upper one is formed only by stripe ß. The interaction between block A and stripe α is strongly attractive, while all other interactions are purely repulsive. Simulation results show that the migration of the diblock copolymer is remarkably dependent on the driving force and there is a transition region at moderate driving force. The transition driving force ft, where the transition region occurs, decreases monotonously with increasing length of block B (NB) but is independent of the polymer length and the periodic length of the slit, which is interpreted from the free energy landscape of diblock copolymer migration. The results also show that periodic slits could be used to separate diblock polymers with different NB by tuning the external driving force.

Randomness of Eigenstates of Many-Body Quantum Systems.

The emergence of random eigenstates of quantum many-body systems in integrable-chaos transitions is the underlying mechanism of thermalization for these quantum systems. We use fidelity and modulus fidelity to measure the randomness of eigenstates in quantum many-body systems. Analytic results of modulus fidelity between random vectors are obtained to be a judge for the degree of randomness. Unlike fidelity, which just refers to a kind of criterion of necessity, modulus fidelity can measure the degree of randomness in eigenstates of a one-dimension (1D) hard-core boson system and identifies the integrable-chaos transition in this system.

Theoretical study on the polymer translocation into an attractive sphere.

We report a non-sampling model, combining the blob method with the standard lattice-based approximation, to calculate the free energy for the polymer translocation into an attractive sphere (i.e., spherical confined trans side) through a small pore. The translocation time is then calculated by the Fokker-Planck equation based on the free energy profile. There is a competition between the confinement effect of the sphere and the polymer-sphere attraction. The translocation time is increased due to the confinement effect of the sphere, whereas it is reduced by the polymer-sphere attraction. The two effects offset each other at a special polymer-sphere attraction which is dependent on the sphere size, the polymer length, and the driving force. Moreover, the entire translocation process can be divided into an uncrowded stage where the polymer does not experience the confinement effect of the sphere and a crowded stage where the polymer is confined by the sphere. At the critical sphere radius, the durations of the two (uncrowded and crowded) stages are the same. The critical sphere radius R* has a scaling relation with the polymer length N as R* ∼ Nß. The calculation results show that the current model can effectively treat the translocation of a three-dimensional self-avoiding polymer into the spherical confined trans side.

Nuclear Magnetic Resonance Study of RNA Structures at the 3'-End of the Hepatitis C Virus Genome.

The 3'-end of the genomic RNA of the hepatitis C virus (HCV) embeds conserved elements that regulate viral RNA synthesis and protein translation by mechanisms that have yet to be elucidated. Previous studies with oligo-RNA fragments have led to multiple, mutually exclusive secondary structure predictions, indicating that HCV RNA structure may be context-dependent. Here we employed a nuclear magnetic resonance (NMR) approach that involves long-range adenosine interaction detection, coupled with site-specific 2H labeling, to probe the structure of the intact 3'-end of the HCV genome (385 nucleotides). Our data reveal that the 3'-end exists as an equilibrium mixture of two conformations: an open conformation in which the 98 nucleotides of the 3'-tail (3'X) form a two-stem-loop structure with the kissing-loop residues sequestered and a closed conformation in which the 3'X rearranges its structure and forms a long-range kissing-loop interaction with an upstream cis-acting element 5BSL3.2. The long-range kissing species is favored under high-Mg2+ conditions, and the intervening sequences do not affect the equilibrium as their secondary structures remain unchanged. The open and closed conformations are consistent with the reported function regulation of viral RNA synthesis and protein translation, respectively. Our NMR detection of these RNA conformations and the structural equilibrium in the 3'-end of the HCV genome support its roles in coordinating various steps of HCV replication.

Temperature dependence of the translocation time of polymer through repulsive nanopores.

The forced translocation of a polymer chain through repulsive nanopores was studied by using Langevin dynamics simulations. The polymer is in the compact globule state at low temperature and in the random coil state at high temperature. Simulation results show that the mean translocation time 〈τ〉 is highly dependent on the temperature T and the minimal 〈τ〉 is located near the coil-globule transition temperature. Moreover, the scaling behaviors 〈τ〉 ∼ Nα and 〈τ〉 ∼ F-δ are studied, with N the polymer length and F the driving force inside the nanopore. Universal values α = 1.4 and δ = 0.85 are observed for the polymer in the random coil state. While for the polymer in the compact globule state, α decreases from α = 2 at weak driving to 1.2 at strong driving for short N and δ increases with decreasing T in the low F region, but we find universal exponents α = 1.6 for long N and δ = 0.85 in the large F region. Results show that polymer's conformation plays a much more important role than the diffusion coefficient in controlling the translocation time of the polymer chain.

Na+-Mg2+ ion effects on conformation and translocation dynamics of single-stranded RNA: Cooperation and competition.

The nanopore-based translocation of a single-stranded RNA (ssRNA) in mixed salt solution has garnered increasing interest for its biological and technological significance. However, it is challenging to comprehensively understand the effects of the mixed ion species on the translocation dynamics due to their cooperation and competition, which can be directly reflected by the ion screening and neutralizing effects, respectively. In this study, Langevin dynamics simulation is employed to investigate the properties of ssRNA conformation and translocation in mixed Na+-Mg2+ ion environments. Simulation results reveal that the ion screening effect dominates the change in the ssRNA conformational size, the ion neutralizing effect controls the capture rate of the ssRNA by the nanopore, and both of them take charge of the different changes in translocation time of the ssRNA under various mixed ion environments. Under high Na+ ion concentration, as Mg2+ concentration increases, the ion neutralizing effect strengthens, weakening the driving force inside the nanopore, leading to longer translocation time. Conversely, at low Na+ concentration, an increase in Mg2+ concentration enhances the ion screening effect, aiding in faster translocation. Furthermore, these simulation results will be explained by quantitative analysis, advancing a deeper understanding of the complicated effects of the mixed Na+-Mg2+ ions.

Simulation on the translocation of polymer through compound channels.

The translocation of a polymer through compound channels under external electrical field was investigated by Monte Carlo simulation on a three-dimensional simple cubic lattice. The compound channel is composed of two parts: part α with length L(pα) and part ß with length L(pß). The two parts have different polymer-channel interactions: a strong attractive interaction with strength ε(α) for part α and a variable interaction with strength ε(ß) for part ß. Results show that the translocation process is remarkably affected by both ε(ß) and L(pα), and the fastest translocation can be achieved with a proper choice of ε(ß) and L(pα). When ε(ß) is large, the translocation is dominated by the last escaping process as it is difficult for the polymer chain to leave the channel. Whereas when L(pα) is small and ε(ß) ≪ ε(α), the translocation is determined by the initial filling process. For this case, there is a free-energy well at the interface between the part α and the part ß, which not only influences the filling dynamics but also affects the translocation probability.

Polymer translocation through a gradient channel.

The translocation of polymer through a channel with a gradient interaction between the polymer and the channel is studied. The interaction is expressed by E = E0 + kx, where E0 is the initial potential energy at the entrance, x is the position of the monomer inside the channel, and k is the energy gradient. The mean first passage time τ is calculated by using Fokker-Planck equation for two cases (1) N > L and (2) N < L under the assumption that the diffusion rate D is a constant, here N is the polymer length and L is the length of channel. Results show that there is a minimum of τ at k = k(c) for both cases, and the value kc is dependent on E0 and driving force f. At large f, the scaling relation τ ∼ N is observed for long polymer chains. But the scaling relation is dependent on the energy gradient k for an unforced driving translocation.

Moving dynamics of a nanorobot with three DNA legs on nanopore-based tracks.

DNA nanorobots have garnered increasing attention in recent years due to their unique advantages of modularity and algorithm simplicity. To accomplish specific tasks in complex environments, various walking strategies are required for the DNA legs of the nanorobot. In this paper, we employ computational simulations to investigate a well-designed DNA-legged nanorobot moving along a nanopore-based track on a planar membrane. The nanorobot consists of a large nanoparticle as the robot core and three single-stranded DNAs (ssDNAs) as the robot legs. The nanopores linearly embedded in the membrane serve as the toeholds for the robot legs. A charge gradient along the pore distribution mainly powers the activation of the nanorobot. The nanorobot can move in two modes: a walking mode, where the robot legs sequentially enter the nanopores, and a jumping mode, where the robot legs may skip a nanopore to reach the next one. Moreover, we observe that the moving dynamics of the nanorobot on the nanopore-based tracks depends on pore-pore distance, pore charge gradient, external voltage, and leg length.

Simulation study on the translocation of a partially charged polymer through a nanopore.

The translocation of a partially charged polymer through a neutral nanopore under external electrical field is studied by using dynamic Monte Carlo method on a simple cubic lattice. One monomer in the polymer is charged and it suffers a driving force when it locates inside the pore. Two time scales, mean first passage time τ(FP) with the first monomer restricted to never draw back into cis side and translocation time τ for polymer continuously threading through nanopore, are calculated. The first passage time τ(FP) decreases with the increase in the driving force f, and the dependence of τ(FP) on the position of charged monomer M is in agreement with the theoretical results using Fokker-Planck equation [A. Mohan, A. B. Kolomeisky, and M. Pasquali, J. Chem. Phys. 128, 125104 (2008)]. But the dependence of τ on M shows a different behavior: It increases with f for M < N/2 with N the polymer length. The novel behavior of τ is explained qualitatively from dynamics of polymer during the translocation process and from the free energy landscape.

Dataset of normalized probability distributions of virtual bond lengths, bond angles, and dihedral angles for the coarse-grained single-stranded DNA structures.

The utility of the coarse-grained (CG) single-stranded DNA (ssDNA) model can drastically reduce the compute time for simulating the ssDNA dynamics. The model-matched CG potentials and the inherent potential constants can be derived by coarse-graining the experimentally measured ssDNA structures. A useful and widespread treatment of the CG model is to use three different pseudo-atoms P, S, and B to represent the atomic groups of phosphate, sugar, and base, respectively, in each nucleotide of the ssDNA structures. The three pseudo-atoms generate nine types of the structural parameters to characterize the unstructured ssDNA conformations, including three (virtual) bond lengths (P-S, S-B, and S-P) between two neighbouring beads, four bond angles (P-S-P, S-P-S, P-S-B, and B-S-P) between three adjacent bonds, and two dihedral angles (P-S-P-S and S-P-S-P) between three successive bonds. This paper mainly presents the data of normalized probability distributions of the bond lengths, bond angles, and dihedral angles for the CG ssDNAs.