The pseudotorsional space of RNA

The characterization of the conformational landscape of the RNA backbone is rather complex due to the ability of RNA to assume a large variety of conformations. These backbone conformations can be depicted by pseudotorsional angles linking RNA backbone atoms, from which Ramachandran-like plots can be built. We explore here different definitions of these pseudotorsional angles, finding that the most accurate ones are the traditional η (eta) and θ (theta) angles, which represent the relative position of RNA backbone atoms P and C4'. We explore the distribution of η - θ in known experimental structures, comparing the pseudotorsional space generated with structures determined exclusively by one experimental technique. We found that the complete picture only appears when combining data from different sources. The maps provide a quite comprehensive representation of the RNA accessible space, which can be used in RNA-structural predictions. Finally, our results highlight that protein interactions lead to significant changes in the population of the η - θ space, pointing toward the role of induced-fit mechanisms in protein-RNA recognition.

Deflating the RNA Mg2+ bubble. Stereochemistry to the rescue!

Proper evaluation of the ionic structure of biomolecular systems through X ray and cryo-EM techniques remains challenging but is essential for advancing our understanding of the underlying structure/activity/solvent relationships. However, numerous studies overestimate the number of Mg2+ in deposited structures due to assignment errors finding their origin in improper consideration of stereochemical rules. Herein, to tackle such issues, we re-evaluate the PDBid 6QNR and 6SJ6 models of the ribosome ionic structure. We establish that stereochemical principles need to be carefully pondered when evaluating ion binding features, even when K+ anomalous signals are available as it is the case for the 6QNR PDB entry. For ribosomes, assignment errors can result in misleading conceptions of their solvent structure. For instance, present stereochemical analysis result in a significant decrease of the number of assigned Mg2+ in 6QNR, suggesting that K+ and not Mg2+ is the prevalent ion in the ribosome 1st solvation shell. We stress that the use of proper stereochemical guidelines in combination or not with other identification techniques, such as those pertaining to the detection of transition metals, of some anions and of K+ anomalous signals, is critical for deflating the current Mg2+ bubble witnessed in many ribosome and other RNA structures. We also stress that for the identification of lighter ions such as Mg2+, Na+, …, for which no anomalous signals can be detected, stereochemistry coupled with high resolution structures (<2.4 Å) remain the best currently available option.

The tilt-dependent potential of mean force of a pair of DNA oligomers from all-atom molecular dynamics simulations

Electrostatic interactions between DNA molecules have been extensively studied experimentally and theoretically, but several aspects (e.g. its role in determining the pitch of the cholesteric DNA phase) still remain unclear. Here, we performed large-scale all-atom molecular dynamics simulations in explicit water and 150 mM sodium chloride, to reconstruct the potential of mean force (PMF) of two DNA oligomers 24 base pairs long as a function of their interaxial angle and intermolecular distance. We find that the potential of mean force is dominated by total DNA charge, and not by the helical geometry of its charged groups. The theory of homogeneously charged cylinders fits well all our simulation data, and the fit yields the optimal value of the total compensated charge on DNA to  ≈65% of its total fixed charge (arising from the phosphorous atoms), close to the value expected from Manning's theory of ion condensation. The PMF calculated from our simulations does not show a significant dependence on the handedness of the angle between the two DNA molecules, or its size is on the order of [Formula: see text]. Thermal noise for molecules of the studied length seems to mask the effect of detailed helical charge patterns of DNA. The fact that in monovalent salt the effective interaction between two DNA molecules is independent on the handedness of the tilt may suggest that alternative mechanisms are required to understand the cholesteric phase of DNA.

Alkali Metal Cation versus Proton and Methyl Cation Affinities: Structure and Bonding Mechanism

We have analyzed the structure and bonding of gas‐phase Cl−X and [HCl−X]⁺ complexes for X⁺= H⁺, CH₃⁺, Li⁺, and Na⁺, using relativistic density functional theory (DFT). We wish to establish a quantitative trend in affinities of the anionic and neutral Lewis bases Cl⁻ and HCl for the various cations. The Cl−X bond becomes longer and weaker along X⁺ = H⁺, CH₃⁺, Li⁺, and Na⁺. Our main purpose is to understand the heterolytic bonding mechanism behind the intrinsic (i.e., in the absence of solvent) alkali metal cation affinities (AMCA) and how this compares with and differs from those of the proton affinity (PA) and methyl cation affinity (MCA). Our analyses are based on Kohn–Sham molecular orbital (KS‐MO) theory in combination with a quantitative energy decomposition analysis (EDA) that pinpoints the importance of the different features in the bonding mechanism. Orbital overlap appears to play an important role in determining the trend in cation affinities.

Sodium and Potassium Interactions with Nucleic Acids

Metal ions are essential cofactors for the structure and functions of nucleic acids. Yet, the early discovery in the 70s of the crucial role of Mg(2+) in stabilizing tRNA structures has occulted for a long time the importance of monovalent cations. Renewed interest in these ions was brought in the late 90s by the discovery of specific potassium metal ions in the core of a group I intron. Their importance in nucleic acid folding and catalytic activity is now well established. However, detection of K(+) and Na(+) ions is notoriously problematic and the question about their specificity is recurrent. Here we review the different methods that can be used to detect K(+) and Na(+) ions in nucleic acid structures such as X-ray crystallography, nuclear magnetic resonance or molecular dynamics simulations. We also discuss specific versus non-specific binding to different structures through various examples.

Symmetry-adapted perturbation theory study for some magnesium complexes

A systematic theoretical study on Mg–ligand interactions has been carried out employing both ab initio correlated wave function and density functional methods. The interactions of the Mg(CH3N2)2moiety with BF, CO, N2, NH3, and H2O ligands have been investigated by performing calculations at the B3LYP, MP2, MP4, and CCSD(T)/6–311++G(3df,3pd) levels of theory. Results indicate that the interaction energies of the Mg(CH3N2)2–L complexes increase in the order NH3 > H2O > BF > CO > N2. Symmetry-adapted perturbation theory (SAPT) analysis has been carried out to understand the nature of the forces involved in the bonding. The SAPT results indicate that the stabilities of the Mg–L interactions are attributed mainly to electrostatic effects, while induction and dispersion forces also play a significant role. The evaluated SAPT interaction energies for the Mg(CH3N2)2–L complexes are generally in good agreement with those obtained using the supermolecule CCSD(T) methods, suggesting that SAPT is a proper method to study the intermolecular interactions in these complexes. The results also suggest an explanation for the unique role of Mg2+as a carrier of water molecules that mediate enzymatic hydrolysis reactions.

The structural basis of RNA-catalyzed RNA polymerization

Early life presumably required polymerase ribozymes capable of replicating RNA. Known polymerase ribozymes best approximating such replicases use as their catalytic engine an RNA-ligase ribozyme originally selected from random RNA sequences. Here, we report 3.15 Å crystal structures of this ligase trapped in catalytically viable pre-ligation states, with the 3′-hydroxyl nucleophile positioned for in-line attack on the 5′-triphosphate. Guided by metal and solvent-mediated interactions, the 5′-triphosphate hooks into the major groove of the adjoining RNA duplex in an unanticipated conformation. Two phosphates and the nucleophile jointly coordinate an active-site metal ion. Atomic mutagenesis experiments demonstrate that active-site nucleobase and hydroxyl groups also participate directly in catalysis, collectively playing a role that in proteinaceous polymerases is performed by a second metal ion. Thus artificial ribozymes can employ complex catalytic strategies that differ dramatically from those of analogous biological enzymes.

Bidentate RNA-magnesium clamps: on the origin of the special role of magnesium in RNA folding

Magnesium plays a special role in RNA function and folding. Although water is magnesium's most common first-shell ligand, the oxyanions of RNA have significant affinity for magnesium. Here we provide a quantum mechanical description of first-shell RNA-magnesium and DNA-magnesium interactions, demonstrating the unique features that characterize the energetics and geometry of magnesium complexes within large folded RNAs. Our work focuses on bidentate chelation of magnesium by RNA or DNA, where multiple phosphate oxyanions enter the first coordination shell of magnesium. These bidentate RNA clamps of magnesium occur frequently in large RNAs. The results here suggest that magnesium, compared to calcium and sodium, has an enhanced ability to form bidentate clamps with RNA. Bidentate RNA-sodium clamps, in particular, are unstable and spontaneously open. Due to magnesium's size and charge density it binds more intimately than other cations to the oxyanions of RNA, so that magnesium clamps are stabilized not only by electrostatic interactions, but also by charge transfer, polarization, and exchange interactions. These nonelectrostatic components of the binding are quite substantial with the high charge and small interatomic distances within the magnesium complexes, but are less pronounced for calcium due to its larger size, and for sodium due to its smaller charge. Additionally, bidentate RNA clamps of magnesium are more stable than those with DNA. The source of the additional stability of RNA complexes is twofold: there is a slightly attenuated energetic penalty for ring closure in the formation of RNA bidentate chelation complexes and elevated electrostatic interactions between the RNA and cations. In sum, it can be seen why sodium and calcium cannot replicate the structures or energetics of RNA-magnesium complexes.

Homology recognition funnel

The recognition of homologous sequences of DNA before strand exchange is considered to be the most puzzling stage of homologous recombination. A mechanism for two homologous dsDNAs to recognize each other from a distance in electrolytic solution without unzipping had been proposed in an earlier paper [A. A. Kornyshev and S. Leikin, Phys. Rev. Lett. 86, 366 (2001)]. In that work, the difference in the electrostatic interaction energy between homologous duplexes and between nonhomologous duplexes, termed the recognition energy, has been calculated. That calculation was later extended in a series of papers to account for torsional elasticity of the molecules. A recent paper [A. A. Kornyshev and A. Wynveen, Proc. Natl. Acad. Sci. U.S.A. 106, 4683 (2009)] investigated the form of the potential well that homologous DNA molecules may feel when sliding along each other. A simple formula for the shape of the well was obtained. However, this latter study was performed under the approximation that the sliding molecules are torsionally rigid. Following on from this work, in the present article we investigate the effect of torsional flexibility of the molecules on the shape of the well. A variational approach to this problem results in a transcendental equation that is easily solved numerically. Its solutions show that at large interaxial separations the recognition well becomes wider and shallower, whereas at closer distances further unexpected features arise related to an abrupt change in the mean azimuthal alignment of the molecules. The energy surface as a function of interaxial separation and the axial shift defines what we call the recognition funnel. We show that it depends dramatically on the patterns of adsorption of counterions on DNA.

Undulations enhance the effect of helical structure on DNA interactions

During the past decade, theory and experiments have provided clear evidence that specific helical patterns of charged groups and adsorbed (condensed) counterions on the DNA surface are responsible for many important features of DNA-DNA interactions in hydrated aggregates. The effects of helical structure on DNA-DNA interactions result from a preferential juxtaposition of the negatively charged sugar phosphate backbone with counterions bound within the grooves of the opposing molecule. Analysis of X-ray diffraction experiments confirmed the mutual alignment of parallel molecules in hydrated aggregates required for such juxtaposition. However, it remained unclear how this alignment and molecular interactions might be affected by intrinsic and thermal fluctuations, which cause structural deviations away from an ideal double helical conformation. We previously argued that the torsional flexibility of DNA allows the molecules to adapt their structure to accommodate a more electrostatically favorable alignment between molecules, partially compensating disruptive fluctuation effects. In the present work, we develop a more comprehensive theory, incorporating also stretching and bending fluctuations of DNA. We found the effects of stretching to be qualitatively and quantitatively similar to those of twisting fluctuations. However, this theory predicts more dramatic and surprising effects of bending. Undulations of DNA in hydrated aggregates strongly amplify rather than weaken the helical structure effects. They enhance the structural adaptation, leading to better alignment of neighboring molecules and pushing the geometry of the DNA backbone closer to that of an ideal helix. These predictions are supported by a quantitative comparison of the calculated and measured osmotic pressures in DNA.

Fluctuations and interactions of semi-flexible polyelectrolytes in columnar assemblies

We have developed a statistical theory for columnar aggregates of semi-flexible polyelectrolytes. The applicability of previous, simplified theories was limited to polyelectrolytes with unrealistically high effective charge and, hence, with strongly suppressed thermal undulations. To avoid this problem, we utilized more consistent approximations for short-range image-charge forces and steric confinement, resulting in new predictions for polyelectrolytes with more practically important, lower effective linear charge densities. In the present paper, we focus on aggregates of wormlike chains with uniform surface charge density, although the same basic ideas may also be applied to structured polyelectrolytes. We find that undulations effectively extend the range of electrostatic interactions between polyelectrolytes upon decreasing aggregate density, in qualitative agreement with previous theories. However, in contrast to previous theories, we demonstrate that steric confinement provides the dominant rather than a negligible contribution at higher aggregate densities and significant quantitative corrections at lower densities, resulting in osmotic pressure isotherms that drastically differ from previous predictions.

A recurrent magnesium-binding motif provides a framework for the ribosomal peptidyl transferase center

The ribosome is an ancient macromolecular machine responsible for the synthesis of all proteins in all living organisms. Here we demonstrate that the ribosomal peptidyl transferase center (PTC) is supported by a framework of magnesium microclusters (Mg²⁺-μc's). Common features of Mg²⁺-μc's include two paired Mg²⁺ ions that are chelated by a common bridging phosphate group in the form Mg_(a)²⁺–(O1P-P-O2P)–Mg_(b)²⁺. This bridging phosphate is part of a 10-membered chelation ring in the form Mg_(a)²⁺–(OP-P-O5′-C5′-C4′-C3′-O3′-P-OP)–Mg_(a)²⁺. The two phosphate groups of this 10-membered ring are contributed by adjacent residues along the RNA backbone. Both Mg²⁺ ions are octahedrally coordinated, but are substantially dehydrated by interactions with additional RNA phosphate groups. The Mg²⁺-μc's in the LSU (large subunit) appear to be highly conserved over evolution, since they are unchanged in bacteria (Thermus thermophilus, PDB entry 2J01) and archaea (Haloarcula marismortui, PDB entry 1JJ2). The 2D elements of the 23S rRNA that are linked by Mg²⁺-μc's are conserved between the rRNAs of bacteria, archaea and eukarya and in mitochondrial rRNA, and in a proposed minimal 23S-rRNA. We observe Mg²⁺-μc's in other rRNAs including the bacterial 16S rRNA, and the P4–P6 domain of the tetrahymena Group I intron ribozyme. It appears that Mg²⁺-μc's are a primeval motif, with pivotal roles in RNA folding, function and evolution.