Prediction of molecular alignment of nucleic acids in aligned media

Molecular Structure Refinement Based on Residual Dipolar Couplings: A Comparison of the Molecular Rotational-Sampling Method with the Alignment-Tensor Approach

In NMR experiments, residual dipolar couplings (RDCs) in a molecule can be measured by averaging the dipolar couplings (DCs) over the rotational motion of a molecule in an environment that induces a slight anisotropic orientation distribution of the molecule. Since the shape of the anisotropic distribution cannot be measured, it is standard practice to use a particular orientation distribution of the molecule with respect to the magnetic field, in the form of a so-called alignment tensor (AT), to calculate RDC-values for the molecule. Since the same alignment tensor is commonly used to calculate the different RDCs of a molecule, this approach rests on the assumption that the rotational motion of the molecule is decoupled from its internal motions and that the molecule is rigid. The validity of these two assumptions is investigated for a small, simple molecule, using a relatively rigid atomic interaction function or force field and a more flexible one. By simulating the molecule using an orientation-biasing force an anisotropic rotational distribution can be generated, for which RDCs can be obtained. Using these RDCs as target RDCs when applying one of the two approaches of structure refinement based on RDCs, it can be investigated how well the target RDCs are approximated in the RDC restraining and whether the corresponding nonuniform orientation distribution is reproduced. For the relatively rigid version of the molecule, the AT approach reproduces the target RDC-values, although the nonuniform orientation distribution of the angle θab,H between the vector r⃗ab connecting two atoms a and b in the molecule and the vector representing the direction of the magnetic field H⃗ as generated in the orientation-biasing simulation cannot be reproduced in the AT RDC-restraining simulation. For the relatively flexible version of the molecule, the AT approach fails to reproduce both the target RDC values and the nonuniform orientation distribution. For biomolecules with flexible parts, the application of the AT approach is thus not recommended. Instead, a method based on sampling of the rotational and internal degrees of freedom of the molecule should be applied in molecular structure determination or refinement based on measured RDCs.

A Method to Derive Structural Information on Molecules from Residual Dipolar Coupling NMR Data

A method for structure refinement of molecules based on residual dipolar coupling (RDC) data is proposed. It calculates RDC values using rotational and molecule-internal configurational sampling instead of the common refinement procedure that is based on the approximation of the nonuniform rotational distribution of the molecule by a single alignment tensor representing the average nonuniformity of this distribution. Using rotational sampling, as is occurring in the experiment leading to observable RDCs, the method stays close to the experiment. It avoids the use of an alignment tensor and thus the assumption that the overall rotation of the molecule is decoupled from its internal motions and that the molecule be rigid. Two simple molecules, two-united-atomic ethane and a cyclooctane molecule with eight side chains, containing 24 united atoms, serve as the so-called "toy model" test systems. The method demonstrates the influence of molecular flexibility and force-field deficiencies on the outcome of structure refinement based on RDCs. For a molecule of a given size (number of atoms N_at), there must be a sufficiently large number N_RDC of measured RDC values available to allow the restraining forces to bias the overall orientation distribution of the molecule. If the ratio N_RDC/N_at gets too small, the RDC-restraining forces will either not be strong enough to change the overall rotational direction of the molecule such that the target RDC values are approximated well or will be so strong that they induce a local deformation of the molecule. In the latter case, the size or inertia of the molecule hinders a restraining-induced overall rotation and the internal structure of the molecule is not strong enough to avoid local deformation due to the restraining forces.

Molecular Dynamics with Orientational Tensorial Constraints: A New Approach to Probe the Torsional Angle Distributions of Small Rotationally Flexible Molecules

The potential of residual dipolar couplings (RDCs) in conformational studies of small molecules is now widely recognized, but current theoretical approaches for their interpretation have several limitations and there is still the need for a general method to probe the torsional angle distributions applicable to any rotationally flexible molecule. Molecular dynamics simulations with RDC-based orientational tensorial constraints (MDOC), implemented in the software COSMOS, are presented here as a conceptually new strategy. For the cases of the fluorinated anti-inflammatory drug diflunisal and the disaccharide cellobiose, we demonstrate that MDOC simulations with one-bond RDCs as tensorial constraints unveil torsion distributions and allow the determination of relative configuration in the presence of rotational flexibility. The independence of the initial structure or any a priori assumption as well as the possibility to combine different experimental constraints represent features, which make the COSMOS software a promising tool for the investigation of torsional angle distributions of flexible molecules, regardless of their size and degree of freedom.

The structure of the SOLE element of oskar mRNA

mRNA localization by active transport is a regulated process that requires association of mRNPs with protein motors for transport along either the microtubule or the actin cytoskeleton. oskar mRNA localization at the posterior pole of the Drosophila oocyte requires a specific mRNA sequence, termed the SOLE, which comprises nucleotides of both exon 1 and exon 2 and is assembled upon splicing. The SOLE folds into a stem-loop structure. Both SOLE RNA and the exon junction complex (EJC) are required for oskar mRNA transport along the microtubules by kinesin. The SOLE RNA likely constitutes a recognition element for a yet unknown protein, which either belongs to the EJC or functions as a bridge between the EJC and the mRNA. Here, we determine the solution structure of the SOLE RNA by Nuclear Magnetic Resonance spectroscopy. We show that the SOLE forms a continuous helical structure, including a few noncanonical base pairs, capped by a pentanucleotide loop. The helix displays a widened major groove, which could accommodate a protein partner. In addition, the apical helical segment undergoes complex dynamics, with potential functional significance.

Direct prediction of residual dipolar couplings of small molecules in a stretched gel by stochastic molecular dynamics simulations

Residual dipolar couplings are highly useful NMR parameters for calculating and refining molecular structures, dynamics, and interactions. For some applications, however, it is inevitable that the preferred orientation of a molecule in an alignment medium is calculated a priori. Several methods have been developed to predict molecular orientations and residual dipolar couplings. Being beneficial for macromolecules and selected small-molecule applications, such approaches lack sufficient accuracy for a large number of organic compounds for which the fine structure and eventually the flexibility of all involved molecules have to be considered or are limited to specific, well-studied liquid crystals. We introduce a simplified model for detailed all-atom molecular dynamics calculations with a polymer strand lined up along the principal axis as a new approach to simulate the preferred orientation of small to medium-sized solutes in polymer-based, gel-type alignment media. As is shown by a first example of strychnine in a polystyrene/CDCl3 gel, the simulations potentially enable the accurate prediction of residual dipolar couplings taking into account structural details and dynamic averaging effects of both the polymer and the solute.

Equivalence between Euler angle conventions for the description of tensorial interactions in liquid NMR: application to different software programs

Long-range orientational restraints derived from alignment or rotational diffusion tensors have greatly contributed to the expansion of applications in biomolecular NMR. The orientation of the principal axis system of these tensors is usually described by the so-called Euler angles. However, no clear consensus has emerged concerning the convention of the associated orthogonal rotations. As a result, the different programs that derive or predict them have adopted different conventions, which make comparison between their results difficult. Moreover, the rotation schemes are seldom completely described. Here, we summarize the different conventions, determine which ones are adopted by commonly used software packages, and establish the formal equivalencies between the different calculated Euler angles.

A general method for constructing atomic-resolution RNA ensembles using NMR residual dipolar couplings: the basis for interhelical motions revealed

The ability to modulate alignment and measure multiple independent sets of NMR residual dipolar couplings (RDCs) has made it possible to characterize internal motions in proteins at atomic resolution and with time scale sensitivity ranging from picoseconds up to milliseconds. The application of such methods to the study of RNA dynamics, however, remains fundamentally limited by the inability to modulate alignment and by strong couplings between internal and overall motions that complicate the quantitative interpretation of RDCs. Here, we address this problem by showing that RNA alignment can be generally modulated, in a controlled manner, by variable elongation of A-form helices and that the information contained within the measured RDCs can be extracted even in the presence of strong couplings between motions and overall alignment via structure-based prediction of alignment. Using this approach, four RDC data sets, and a broad conformational pool obtained from a 8.2 μs molecular dynamics simulation, we successfully construct and validate an atomic resolution ensemble of human immunodeficiency virus type I transactivation response element RNA. This ensemble reveals local motions in and around the bulge involving changes in stacking and hydrogen-bonding interactions, which are undetectable by traditional spin relaxation and drive global changes in interhelical orientation. This new approach broadens the scope of using RDCs in characterizing the dynamics of nucleic acids.

Determination of Conformational Equilibria in Proteins Using Residual Dipolar Couplings

In order to carry out their functions, proteins often undergo significant conformational fluctuations that enable them to interact with their partners. The accurate characterization of these motions is key in order to understand the mechanisms by which macromolecular recognition events take place. Nuclear magnetic resonance spectroscopy offers a variety of powerful methods to achieve this result. We discuss a method of using residual dipolar couplings as replica-averaged restraints in molecular dynamics simulations to determine large amplitude motions of proteins, including those involved in the conformational equilibria that are established through interconversions between different states. By applying this method to ribonuclease A, we show that it enables one to characterize the ample fluctuations in interdomain orientations expected to play an important functional role.

Domain cooperativity in multidomain proteins: what can we learn from molecular alignment in anisotropic media?

Many proteins have modular design with multiple globular domains connected via flexible linkers. As a simple model of such system, we study a tandem construct consisting of two identical SH3 domains and a variable-length Gly/Ser linker. When the linker is short, this construct represents a dumbbell-shaped molecule with limited amount of domain-domain mobility. Due to its elongated shape, this molecule efficiently aligns in steric alignment media. As the length of the linker increases, the two domains become effectively uncoupled and begin to behave as independent entities. Consequently, their degree of alignment drops, approaching that found in the (near-spherical) isolated SH3 domains. To model the dependence of alignment parameters on the length of the interdomain linker, we have generated in silico a series of conformational ensembles representing SH3 tandems with different linker length. These ensembles were subsequently used as input for alignment prediction software PALES. The predicted alignment tensors were compared with the results of experimental measurements using a series of tandem-SH3 samples in PEG/hexanol alignment media. This comparison broadly confirmed the expected trends. At the same time, it has been found that the isolated SH3 domain aligns much stronger than expected. This finding can be attributed to complex morphology of the PEG/hexanol media and/or to weak site-specific interactions between the protein and the media. In the latter case, there are strong indications that electrostatic interactions may play a role. The fact that PEG/hexanol does not behave as a simple steric media should serve as a caution for studies that use PALES as a quantitative prediction tool (especially for disordered proteins). Further progress in this area depends on our ability to accurately model the anisotropic media and its site-specific interactions with protein molecules. Once this ability is improved, it should be possible to use the alignment parameters as a measure of domain-domain cooperativity, thus identifying the situations where two domains transiently interact with each other or become coupled through a partially structured linker.

Overview on the use of NMR to examine protein structure

Any protein structure determination process contains several steps, starting from obtaining a suitable sample, then moving on to acquiring data and spectral assignment, and lastly to the final steps of structure determination and validation. This unit describes all of these steps, starting with the basic physical principles behind NMR and some of the most commonly measured and observed phenomena such as chemical shift, scalar and residual coupling, and the nuclear Overhauser effect. Then, in somewhat more detail, the process of spectral assignment and structure elucidation is explained. Furthermore, the use of NMR to study protein-ligand interaction, protein dynamics, or protein folding is described.

Variable helix elongation as a tool to modulate RNA alignment and motional couplings

The application of residual dipolar couplings (RDCs) in studies of RNA structure and dynamics can be complicated by the presence of couplings between collective helix motions and overall alignment and by the inability to modulate overall alignment of the molecule by changing the ordering medium. Here, we show for a 27-nt TAR RNA construct that variable levels of helix elongation can be used to alter both overall alignment and couplings to collective helix motions in a semi-predictable manner. In the absence of elongation, a four base-pair helix II capped by a UUCG apical loop exhibits a higher degree of order compared to a six base-pair helix I (theta(I)/theta(II)=0.56+/-0.1). The principal S(zz) direction is nearly parallel to the axis of helix II but deviates by approximately 40 degrees relative to the axis of helix I. Elongating helix I by three base-pairs equalizes the alignment of the two helices and pushes the RNA into the motional coupling limit such that the two helices have comparable degrees of order (theta(I)/theta(II)=0.92+/-0.04) and orientations relative to S(zz) ( approximately 17 degrees ). Increasing the length of elongation further to 22 base-pairs pushes the RNA into the motional decoupling limit in which helix I dominates alignment (theta(II)/theta(I)=0.45+/-0.05), with S(zz) orientated nearly parallel to its helix axis. Many of these trends can be rationalized using PALES simulations that employ a previously proposed three-state dynamic ensemble of TAR. Our results provide new insights into motional couplings, offer guidelines for assessing their extent, and suggest that variable degrees of helix elongation can allow access to independent sets of RDCs for characterizing RNA structural dynamics.

The unstable part of the apical stem of duck hepatitis B virus epsilon shows enhanced base pair opening but not pico- to nanosecond dynamics and is essential for reverse transcriptase binding

Hepatitis B virus (HBV) replication starts with binding of reverse transcriptase (RT) to the apical stem-loop region of epsilon, a conserved element of the RNA pregenome. For duck HBV, an in vitro replication system has provided molecular details of this interaction. Further insights can be obtained from the structure and dynamics of the duck and human apical stem-loops. Previously, we reported these for the human apical stem-loop. Here, we present the same for the duck counterpart. Unlike its human counterpart, the duck apical stem is unstable in its middle/upper part and contains noncanonical base pairs. This dynamics study is the first of an unstable RNA-DNA stem. Similar to the human stem, the duck apical stem comprises two helical segments with a bend angle of ca. 10 degrees , separated by a nonpaired mobile U residue. It is capped by a well-structured conserved UGUU loop with two residues mobile on the pico- to nanosecond time scale, one of which is involved in RT binding. Remarkably, the unstable middle/upper part of the stem does not show enhanced pico- to nanosecond time scale dynamics. Instead, adenine dispersion relaxation studies indicate enhanced millisecond time scale dynamics involving base pair opening. It can then be concluded that base pair opening is essential for epsilon-RT binding, because stabilization of the stem abolishes binding. We hypothesize that binding occurs by conformational capture of bases in the base pair open state. The unstable secondary structure of the apical stem-loop makes duck epsilon-RT binding unusual in light of recent classifications of RNA target interactions that assume stable secondary structures.

Constructing atomic-resolution RNA structural ensembles using MD and motionally decoupled NMR RDCs

A broad structural landscape often needs to be characterized in order to fully understand how regulatory RNAs perform their biological functions at the atomic level. We present a protocol for visualizing thermally accessible RNA conformations at atomic-resolution and with timescales extending up to milliseconds. The protocol combines molecular dynamics (MD) simulations with experimental residual dipolar couplings (RDCs) measured in partially aligned (13)C/(15)N isotopically enriched elongated RNA samples. The structural ensembles generated in this manner provide insights into RNA dynamics and its role in functionally important transitions.

NMR: prediction of molecular alignment from structure using the PALES software

Orientational restraints such as residual dipolar couplings promise to overcome many of the problems that traditionally limited liquid-state nuclear magnetic resonance spectroscopy. Recently, we developed methods to predict a molecular alignment tensor and thus residual dipolar couplings for a given molecular structure. This provides many new opportunities for the study of the structure and dynamics of proteins, nucleic acids, oligosaccharides and small molecules. This protocol details the use of the software PALES (Prediction of AlignmEnt from Structure) for prediction of an alignment tensor from a known three-dimensional (3D) coordinate file of a solute. The method is applicable to alignment of molecules in many neutral and charged orienting media and takes into account the molecular shape and 3D charge distribution of the molecule.

Comparison of alignment tensors generated for native tRNA(Val) using magnetic fields and liquid crystalline media

Residual dipolar couplings (RDCs) complement standard NOE distance and J-coupling torsion angle data to improve the local and global structure of biomolecules in solution. One powerful application of RDCs is for domain orientation studies, which are especially valuable for structural studies of nucleic acids, where the local structure of a double helix is readily modeled and the orientations of the helical domains can then be determined from RDC data. However, RDCs obtained from only one alignment media generally result in degenerate solutions for the orientation of multiple domains. In protein systems, different alignment media are typically used to eliminate this orientational degeneracy, where the combination of RDCs from two (or more) independent alignment tensors can be used to overcome this degeneracy. It is demonstrated here for native E. coli tRNA(Val) that many of the commonly used liquid crystalline alignment media result in very similar alignment tensors, which do not eliminate the 4-fold degeneracy for orienting the two helical domains in tRNA. The intrinsic magnetic susceptibility anisotropy (MSA) of the nucleobases in tRNA(Val) was also used to obtain RDCs for magnetic alignment at 800 and 900 MHz. While these RDCs yield a different alignment tensor, the specific orientation of this tensor combined with the high rhombicity for the tensors in the liquid crystalline media only eliminates two of the four degenerate orientations for tRNA(Val). Simulations are used to show that, in optimal cases, the combination of RDCs obtained from liquid crystalline medium and MSA-induced alignment can be used to obtain a unique orientation for the two helical domains in tRNA(Val).

NMR studies of RNA dynamics and structural plasticity using NMR residual dipolar couplings

An increasing number of RNAs are being discovered that perform their functions by undergoing large changes in conformation in response to a variety of cellular signals, including recognition of proteins and small molecular targets, changes in temperature, and RNA synthesis itself. The measurement of NMR residual dipolar couplings (RDCs) in partially aligned systems is providing new insights into the structural plasticity of RNA through combined characterization of large-amplitude collective helix motions and local flexibility in noncanonical regions over a wide window of biologically relevant timescales (<milliseconds). Here, we review RDC methodology for studying RNA structural dynamics and survey what has been learnt thus far from application of these methods. Future methodological challenges are also identified.

Solution structure of the apical stem-loop of the human hepatitis B virus encapsidation signal

Hepatitis B virus (HBV) replication is initiated by HBV RT binding to the highly conserved encapsidation signal, epsilon, at the 5′ end of the RNA pregenome. Epsilon contains an apical stem–loop, whose residues are either totally conserved or show rare non-disruptive mutations. Here we present the structure of the apical stem–loop based on NOE, RDC and ¹H chemical shift NMR data. The ¹H chemical shifts proved to be crucial to define the loop conformation. The loop sequence 5′-CUGUGC-3′ folds into a UGU triloop with a CG closing base pair and a bulged out C and hence forms a pseudo-triloop, a proposed protein recognition motif. In the UGU loop conformations most consistent with experimental data, the guanine nucleobase is located on the minor groove face and the two uracil bases on the major groove face. The underlying helix is disrupted by a conserved non-paired U bulge. This U bulge adopts multiple conformations, with the nucleobase being located either in the major groove or partially intercalated in the helix from the minor groove side, and bends the helical stem. The pseudo-triloop motif, together with the U bulge, may represent important anchor points for the initial recognition of epsilon by the viral RT.