De novo determination of internuclear vector orientations from residual dipolar couplings measured in three independent alignment media

Programming Peptide Liquid Crystal Media to Acquire Independent Sets of Residual Dipolar Couplings and Enantiodiscrimination in Multiple Solvent Systems

Multiple independent sets of residual dipolar couplings (RDCs) acquired by relying on different alignment media show the great potential for de novo structure determination of organic compounds. However, this methodology is severely compromised by the limited availability of multialignment media. In this work, an engineering strategy was developed to program the oligopeptide amphiphiles (OPAs) to create different peptide liquid crystal (LC) media for the acquisition of independent sets of RDCs. With no need for de novo design on peptide sequences, the molecular alignment can be simply modulated by varying the length of the hydrophobic tails within OPAs. Relying on these programmed peptide LC media, five independent sets of RDCs were extracted in a highly efficient and accurate manner. Because of the similar bulk composition of OPAs, this approach offers the significant advantage in circumventing the possible incompatibilities of analytes with one or several different alignment media, therefore avoiding the analysis complication. Notably, these peptide LC media show enantiodifferentiating properties, and the enantiodiscriminating capabilities could also be optimized through the programmed strategy. Furthermore, we show that these media are compatible with different polar solvents, allowing the possible de novo structure elucidation of organic compounds with varied polarities and solubilities.

Atropisomerism in a polyglutamate-based thermoresponsive alignment medium

Structure elucidation via residual dipolar couplings (RDCs) relies on alignment media. We report on lyotropic liquid crystals (LLCs) of poly-γ-p-biphenyl(2'-methoxy-2-methyl)methyl-L-glutamate (PBPM³LG). Temperature dependent atropisomerism within the biphenyl group enables the acquisition of multiple RDC-datasets within one sample.

Programmable alignment media from self-assembled oligopeptide amphiphiles for the measurement of independent sets of residual dipolar couplings in organic solvents

NMR spectroscopy in anisotropic media has emerged as a powerful technique for the structural elucidation of organic molecules. Its application requires weak alignment of analytes by means of suitable alignment media. Although a number of alignment media, that are compatible with organic solvents, have been introduced in the last 20 years, acquiring a number of independent, non-linearly related sets of anisotropic NMR data from the same organic solvent system remains a formidable challenge, which is however crucial for the alignment simulations and deriving dynamic and structural information of organic molecules unambiguously. Herein, we introduce a programmable strategy to construct several distinct peptide-based alignment media by adjusting the amino acid sequence, which allows us to measure independent sets of residual dipolar couplings (RDCs) in a highly efficient and accurate manner. This study opens a new avenue for de novo structure determination of organic compounds without requiring prior structural information.

We report a programmable strategy to construct multi-alignment media via peptide self-assembly for the measurement of independent sets of residual dipolar couplings (RDCs).

TITANIA: Model-Free Interpretation of Residual Dipolar Couplings in the Context of Organic Compounds

Residual dipolar couplings (RDCs) become increasingly important as additional NMR parameters in the structure elucidation of organic compounds but are usually used in fitting procedures to discriminate between (computed) structures that are in accordance with RDCs and others that can be ruled out. Thus, the determination of configurations requires prior structural information. The direct use of RDCs as restraints to construct structures based on RDCs has only recently begun also in organic compounds. No protocol has been published though that uses the vector and dynamics information available in multialignment data sets directly for the joint determination of conformation and configuration of organic compounds. This is proposed in the current study. We show that by employing these data, even a flat or random start structure converges into the correctly configured structure when employing multiple alignment data sets in our iterative procedure. The requirements in terms of the number of RDCs and alignment media necessary are discussed in detail.

REDCRAFT: A computational platform using residual dipolar coupling NMR data for determining structures of perdeuterated proteins in solution

Nuclear Magnetic Resonance (NMR) spectroscopy is one of the three primary experimental means of characterizing macromolecular structures, including protein structures. Structure determination by solution NMR spectroscopy has traditionally relied heavily on distance restraints derived from nuclear Overhauser effect (NOE) measurements. While structure determination of proteins from NOE-based restraints is well understood and broadly used, structure determination from Residual Dipolar Couplings (RDCs) is relatively less well developed. Here, we describe the new features of the protein structure modeling program REDCRAFT and focus on the new Adaptive Decimation (AD) feature. The AD plays a critical role in improving the robustness of REDCRAFT to missing or noisy data, while allowing structure determination of larger proteins from less data. In this report we demonstrate the successful application of REDCRAFT in structure determination of proteins ranging in size from 50 to 145 residues using experimentally collected data, and of larger proteins (145 to 573 residues) using simulated RDC data. In both cases, REDCRAFT uses only RDC data that can be collected from perdeuterated proteins. Finally, we compare the accuracy of structure determination from RDCs alone with traditional NOE-based methods for the structurally novel PF.2048.1 protein. The RDC-based structure of PF.2048.1 exhibited 1.0 Å BB-RMSD with respect to a high-quality NOE-based structure. Although optimal strategies would include using RDC data together with chemical shift, NOE, and other NMR data, these studies provide proof-of-principle for robust structure determination of largely-perdeuterated proteins from RDC data alone using REDCRAFT.

Residual Dipolar Couplings have the potential to improve the accuracy and reduce the time needed to characterize protein structures. In addition, RDC data have been demonstrated to concurrently elucidate structure of proteins, provide assignment of resonances, and characterize the internal dynamics of proteins. Given all the advantages associated with the study of proteins from RDC data, based on the statistics provided by the Protein Databank (PDB), surprisingly only 124 proteins (out of nearly 150,000 proteins) have utilized RDCs as part of their structure determination. Even a smaller subset of these proteins (approximately 7) have utilized RDCs as the primary source of data for structure determination. One key factor in the use of RDCs is the challenging computational and analytical aspects of this source of data. In this report, we demonstrate the success of the REDCRAFT software package in structure determination of proteins using RDC data that can be collected from small and large proteins in a routine fashion. REDCRAFT accomplishes the challenging task of structure determination from RDCs by introducing a unique search and optimization technique that is both robust and computationally tractable. Structure determination from routinely collectable RDC data using REDCRAFT can complement existing methods to provide faster and more accurate studies of larger and more complex protein structures by NMR spectroscopy in solution state.

The Advanced Floating Chirality Distance Geometry Approach-How Anisotropic NMR Parameters Can Support the Determination of the Relative Configuration of Natural Products

The configurational analysis of complex natural products by NMR spectroscopy is still a challenging task. The assignment of the relative configuration is usually carried out by analysis of interproton distances from NOESY or ROESY spectra (qualitative or quantitative) and scalar (J) couplings. About 15 years ago, residual dipolar couplings (RDCs) were introduced as a tool for the configurational determination of small organic molecules. In contrast to NOEs/ROEs which are local parameters (distances up to 400 pm can be detected for small organic molecules), RDCs are global parameters which allow to obtain structural information also from long-range relationships. RDCs have the disadvantage that the sample needs a setup in an alignment medium in order to obtain the required anisotropic environment. Here, we will discuss the configurational analysis of five complex natural products: axinellamine A (1), tetrabromostyloguanidine (2), 3,7-epi-massadine chloride (3), tubocurarine (4), and vincristine (5). Compounds 1-3 are marine natural products whereas 4 and 5 are from terrestrial sources. The chosen examples will carefully work out the limitations of NOEs/ROEs in the configurational analysis of natural products and will also provide an outlook on the information obtained from RDCs.

Concepts and Controversies: Lipid Management in Patients with Chronic Kidney Disease

Atherosclerotic cardiovascular disease (ASCVD) remains an important contributor of morbidity and mortality in patients with chronic kidney disease (CKD). CKD is recognized as an important risk enhancer that identifies patients as candidates for more intensive low-density lipoprotein (LDL) cholesterol lowering. However, there is controversy regarding the efficacy of lipid-lowering therapy, especially in patients on dialysis. Among patients with CKD, not yet on dialysis, there is clinical trial evidence for the use of statins with or without ezetimibe to reduce ASCVD events. Newer cholesterol lowering agents have been introduced for the management of hyperlipidemia to reduce ASCVD, but these therapies have not been tested in the CKD population except in secondary analyses of patients with primarily CKD stage 3. This review summarizes the role of hyperlipidemia in ASCVD and treatment strategies for hyperlipidemia in the CKD population.

Validation of protein backbone structures calculated from NMR angular restraints using Rosetta

Multidimensional solid-state NMR spectra of oriented membrane proteins can be used to infer the backbone torsion angles and hence the overall protein fold by measuring dipolar couplings and chemical shift anisotropies, which depend on the orientation of each peptide plane with respect to the external magnetic field. However, multiple peptide plane orientations can be consistent with a given set of angular restraints. This ambiguity is further exacerbated by experimental uncertainty in obtaining and interpreting such restraints. The previously developed algorithms for structure calculations using angular restraints typically involve a sequential walkthrough along the backbone to find the torsion angles between the consecutive peptide plane orientations that are consistent with the experimental data. This method is sensitive to experimental uncertainty in interpreting the peak positions of as low as ± 10 Hz, often yielding high structural RMSDs for the calculated structures. Here we present a significantly improved version of the algorithm which includes the fitting of several peptide planes at once in order to prevent propagation of error along the backbone. In addition, a protocol has been devised for filtering the structural solutions using Rosetta scoring functions in order to find the structures that both fit the spectrum and satisfy bioinformatics restraints. The robustness of the new algorithm has been tested using synthetic angular restraints generated from the known structures for two proteins: a soluble protein 2gb1 (56 residues), chosen for its diverse secondary structure elements, i.e. an alpha-helix and two beta-sheets, and a membrane protein 4a2n, from which the first two transmembrane helices (having a total of 64 residues) have been used. Extensive simulations have been performed by varying the number of fitted planes, experimental error, and the number of NMR dimensions. It has been found that simultaneously fitting two peptide planes always shifted the distribution of the calculated structures toward lower structural RMSD values as compared to fitting a single torsion-angle pair. For each protein, irrespective of the simulation parameters, Rosetta was able to distinguish the most plausible structures, often having structural RMSDs lower than 2 Å with respect to the original structure. This study establishes a framework for de-novo protein structure prediction using a combination of solid-state NMR angular restraints and bioinformatics.

Configurational Analysis by Residual Dipolar Coupling Driven Floating Chirality Distance Geometry Calculations

A new method implemented into a computer program (ConArch⁺ ) has been developed and applied to demonstrate the successful implementation of residual dipolar couplings (RDCs) in distance geometry (DG) calculations for the configurational assignment of chiral compounds. Unlike established protocols, the new approach combines floating chirality (fc) in 4D- and 3D-distance bounds driven dynamics (DDD) calculations with structural information from RDCs. Thus, relative configurations of chiral compounds were generated only by observables (e.g., NOEs, RDCs) rendering tedious evaluations of calculated structures against RDCs obsolete. We demonstrate the potential of this novel procedure by the simultaneous determination of the configuration and the conformation of three natural products, (-)-isopinocampheol (1), tubocurarine (2), and vincristine (3), as well as for diisopropylidene-β-d-fructopyranose (4).

Dynamic Nature of CTCF Tandem 11 Zinc Fingers in Multivalent Recognition of DNA As Revealed by NMR Spectroscopy

The 11 zinc fingers (ZFs) of the transcription factor CTCF play a versatile role in the regulation of gene expression. CTCF binds to numerous genomic sites to form chromatin loops and topologically associated domains and thus mediates the 3D architecture of chromatin. Although CTCF inter-ZF plasticity is essential for the recognition of multiple genomic sites, the dynamic nature of its 11 ZFs remains unknown. We assigned the chemical shifts of the CTCF ZFs 1-11 and solved the solution structures of each ZF. NMR backbone dynamics, residual dipolar couplings, and small-angle X-ray scattering experiments suggest a high inter-ZF plasticity of the free-form ZFs 1-11. As exemplified by two different protocadherin DNA sequences, the titration of DNAs to ¹⁵N-labeled CTCF ZFs 1-11 enabled systematic mapping of binding of CTCF ZFs to various chromatin sites. Our work paves the way for illustrating the molecular basis of the versatile DNA recognized by CTCF and has interesting implications for its conformational transition during DNA binding.

Ligand Proton Pseudocontact Shifts Determined from Paramagnetic Relaxation Dispersion in the Limit of NMR Intermediate Exchange

Delineation of protein-ligand interaction modes is key for rational drug discovery. The availability of complex crystal structures is often limited by the aqueous solubility of the compounds, while lead-like compounds with micromolar affinities normally fall into the NMR intermediate exchange regime, in which severe line broadening to beyond the detection of interfacial resonances limits NMR applications. Here, we developed a new method to retrieve low-populated bound-state ¹H pseudocontact shifts (PCSs) using paramagnetic relaxation dispersion (RD). We evaluated using a ¹H PCS-RD approach in a BRM bromodomain lead-like inhibitor to filter molecular docking poses using multiple intermolecular structural restraints. Considering the universal presence of proton atoms in druglike compounds, our work will have wide application in structure-guided drug discovery even under an extreme condition of NMR intermediate exchange and low aqueous solubility of ligands.

Conformational dynamics and alignment properties of loop lanthanide-binding-tags (LBTs) studied in interleukin-1β

Encodable lanthanide binding tags (LBTs) have become an attractive tool in modern structural biology as they can be expressed as fusion proteins of targets of choice. Previously, we have demonstrated the feasibility of inserting encodable LBTs into loop positions of interleukin-1β (Barthelmes et al. in J Am Chem Soc 133:808-819, 2011). Here, we investigate the differences in fast dynamics of selected loop-LBT interleukin-1β constructs by measuring ¹⁵N nuclear spin relaxation experiments. We show that the loop-LBT does not significantly alter the dynamic motions of the host protein in the sub-τ_c-timescale and that the loop-LBT adopts a rigid conformation with significantly reduced dynamics compared to the terminally attached encodable LBT leading to increased paramagnetic alignment strength. We further analyze residual dipolar couplings (RDCs) obtained by loop-LBTs and additional liquid crystalline media to assess the applicability of the loop-LBT approach for RDC-based methods to determine structure and dynamics of proteins, including supra-τc dynamics. Using orthogonalized linear combinations (OLCs) of RDCs and Saupe matrices, we show that the combined use of encodable LBTs and external alignment media yields up to five linear independent alignments.

Investigating protein conformational energy landscapes and atomic resolution dynamics from NMR dipolar couplings: a review

Nuclear magnetic resonance spectroscopy is exquisitely sensitive to protein dynamics. In particular inter-nuclear dipolar couplings, that become measurable in solution when the protein is dissolved in a dilute liquid crystalline solution, report on all conformations sampled up to millisecond timescales. As such they provide the opportunity to describe the Boltzmann distribution present in solution at atomic resolution, and thereby to map the conformational energy landscape in unprecedented detail. The development of analytical methods and approaches based on numerical simulation and their application to numerous biologically important systems is presented.

NMR studies of dynamic biomolecular conformational ensembles

Multidimensional heteronuclear NMR approaches can provide nearly complete sequential signal assignments of isotopically enriched biomolecules. The availability of assignments together with measurements of spin relaxation rates, residual spin interactions, J-couplings and chemical shifts provides information at atomic resolution about internal dynamics on timescales ranging from ps to ms, both in solution and in the solid state. However, due to the complexity of biomolecules, it is not possible to extract a unique atomic-resolution description of biomolecular motions even from extensive NMR data when many conformations are sampled on multiple timescales. For this reason, powerful computational approaches are increasingly applied to large NMR data sets to elucidate conformational ensembles sampled by biomolecules. In the past decade, considerable attention has been directed at an important class of biomolecules that function by binding to a wide variety of target molecules. Questions of current interest are: "Does the free biomolecule sample a conformational ensemble that encompasses the conformations found when it binds to various targets; and if so, on what time scale is the ensemble sampled?" This article reviews recent efforts to answer these questions, with a focus on comparing ensembles obtained for the same biomolecules by different investigators. A detailed comparison of results obtained is provided for three biomolecules: ubiquitin, calmodulin and the HIV-1 trans-activation response RNA.

Dynafold: a dynamic programming approach to protein backbone structure determination from minimal sets of Residual Dipolar Couplings

Residual Dipolar Couplings (RDCs) are a source of NMR data that can provide a powerful set of constraints on the orientation of inter-nuclear vectors, and are quickly becoming a larger part of the experimental toolset for molecular biologists. However, few reliable protocols exist for the determination of protein backbone structures from small sets of RDCs. DynaFold is a new dynamic programming algorithm designed specifically for this task, using minimal sets of RDCs collected in multiple alignment media. DynaFold was first tested utilizing synthetic data generated for the N--H , C(α)--H(α), and C--N vectors of 1BRF, 1F53, 110M, and 3LAY proteins, with up to ±1 Hz error in three alignment media, and was able to produce structures with less than 1.9 Å of the original structures. DynaFold was then tested using experimental data, obtained from the Biological Magnetic Resonance Bank, for proteins PDBID:1P7E and 1D3Z using RDC data from two alignment media. This exercise yielded structures within 1.0 Å of their respective published structures in segments with high data density, and less than 1.9 Å over the entire protein. The same sets of RDC data were also used in comparisons with traditional methods for analysis of RDCs, which failed to match the accuracy of DynaFold's approach to structure determination.

Unraveling long range residual dipolar coupling networks in strongly aligned proteins

Long-range residual dipolar couplings (lrRDCs) have the potential to serve as powerful structural restraints in protein NMR spectroscopy as they can provide both distance and orientation information about nuclei separate in sequence but close in space. Current nonselective methods for their measurement are limited to moderate alignment strengths due to the sheer abundance of active couplings at stronger alignment. This limits the overall magnitude and therefore distance across which couplings can be measured. We have developed a double resonance technique for the inversion of individual coupled spin pairs, called Selective Inversion by Single Transition Cross Polarization (SIST-CP). This technique enables the selective recoupling of lrRDCs, thus allowing the complex multiplets occurring in strongly aligned systems to be disentangled. This technique is demonstrated in the context of an application to the measurement of (13)C'-(1)H(N) lrRDCs in strongly aligned proteins.

Three-dimensional protein fold determination from backbone amide pseudocontact shifts generated by lanthanide tags at multiple sites

Site-specific attachment of paramagnetic lanthanide ions to a protein generates pseudocontact shifts (PCS) in the nuclear magnetic resonance (NMR) spectra of the protein that are easily measured as changes in chemical shifts. By labeling the protein with lanthanide tags at four different sites, PCSs are observed for most amide protons and accurate information is obtained about their coordinates in three-dimensional space. The approach is demonstrated with the chaperone ERp29, for which large differences have been reported between X-ray and NMR structures of the C-terminal domain, ERp29-C. The results unambiguously show that the structure of rat ERp29-C in solution is similar to the crystal structure of human ERp29-C. PCSs of backbone amides were the only structural restraints required. Because these can be measured for more dilute protein solutions than other NMR restraints, the approach greatly widens the range of proteins amenable to structural studies in solution.

Modulating alignment of membrane proteins in liquid-crystalline and oriented gel media by changing the size and charge of phospholipid bicelles

We demonstrate that alignment of a structured peptide or small protein solubilized in mixed phospholipid:detergent micelles or bicelles, when embedded in a compressed gel or liquid crystalline medium, can be altered by either changing the phospholipid aggregate shape, charge, or both together. For the hemagglutinin fusion peptide solubilized in bicelles, we show that bicelle shape and charge do not change its helical hairpin structure but impact its alignment relative to the alignment medium, both in charged compressed acrylamide gel and in liquid crystalline d(GpG). The method can be used to generate sets of residual dipolar couplings that correspond to orthogonal alignment tensors, and holds promise for high-resolution structural refinement and dynamic mapping of membrane proteins.

A Bayesian approach for determining protein side-chain rotamer conformations using unassigned NOE data

A major bottleneck in protein structure determination via nuclear magnetic resonance (NMR) is the lengthy and laborious process of assigning resonances and nuclear Overhauser effect (NOE) cross peaks. Recent studies have shown that accurate backbone folds can be determined using sparse NMR data, such as residual dipolar couplings (RDCs) or backbone chemical shifts. This opens a question of whether we can also determine the accurate protein side-chain conformations using sparse or unassigned NMR data. We attack this question by using unassigned nuclear Overhauser effect spectroscopy (NOESY) data, which records the through-space dipolar interactions between protons nearby in three-dimensional (3D) space. We propose a Bayesian approach with a Markov random field (MRF) model to integrate the likelihood function derived from observed experimental data, with prior information (i.e., empirical molecular mechanics energies) about the protein structures. We unify the side-chain structure prediction problem with the side-chain structure determination problem using unassigned NMR data, and apply the deterministic dead-end elimination (DEE) and A* search algorithms to provably find the global optimum solution that maximizes the posterior probability. We employ a Hausdorff-based measure to derive the likelihood of a rotamer or a pairwise rotamer interaction from unassigned NOESY data. In addition, we apply a systematic and rigorous approach to estimate the experimental noise in NMR data, which also determines the weighting factor of the data term in the scoring function derived from the Bayesian framework. We tested our approach on real NMR data of three proteins: the FF Domain 2 of human transcription elongation factor CA150 (FF2), the B1 domain of Protein G (GB1), and human ubiquitin. The promising results indicate that our algorithm can be applied in high-resolution protein structure determination. Since our approach does not require any NOE assignment, it can accelerate the NMR structure determination process.

Dynamics of biomolecules from picoseconds to seconds at atomic resolution

Although biomolecular dynamics has been investigated using NMR for at least 40 years, only in the past 20 years have internal motions been characterized at atomic resolution throughout proteins and nucleic acids. This development was made possible by multidimensional heteronuclear NMR approaches that provide near complete sequential signal assignments of uniformly labeled biomolecules. Recent methodological advances have enabled characterization of internal dynamics on timescales ranging from picoseconds to seconds, both in solution and in the solid state. The size, complexity and functional significance of biomolecules investigated by NMR continue to grow, as do the insights that have been obtained about function. In this article I review a number of recent advances that have made such studies possible, and provide a few examples of where NMR either by itself or in combination with other approaches has paved the way to a better understanding of the complex relationship between dynamics and biomolecular function. Finally, I discuss prospects for further advances in this field.

Protein side-chain resonance assignment and NOE assignment using RDC-defined backbones without TOCSY data

One bottleneck in NMR structure determination lies in the laborious and time-consuming process of side-chain resonance and NOE assignments. Compared to the well-studied backbone resonance assignment problem, automated side-chain resonance and NOE assignments are relatively less explored. Most NOE assignment algorithms require nearly complete side-chain resonance assignments from a series of through-bond experiments such as HCCH-TOCSY or HCCCONH. Unfortunately, these TOCSY experiments perform poorly on large proteins. To overcome this deficiency, we present a novel algorithm, called NASCA: (NOE Assignment and Side-Chain Assignment), to automate both side-chain resonance and NOE assignments and to perform high-resolution protein structure determination in the absence of any explicit through-bond experiment to facilitate side-chain resonance assignment, such as HCCH-TOCSY. After casting the assignment problem into a Markov Random Field (MRF), NASCA: extends and applies combinatorial protein design algorithms to compute optimal assignments that best interpret the NMR data. The MRF captures the contact map information of the protein derived from NOESY spectra, exploits the backbone structural information determined by RDCs, and considers all possible side-chain rotamers. The complexity of the combinatorial search is reduced by using a dead-end elimination (DEE) algorithm, which prunes side-chain resonance assignments that are provably not part of the optimal solution. Then an A* search algorithm is employed to find a set of optimal side-chain resonance assignments that best fit the NMR data. These side-chain resonance assignments are then used to resolve the NOE assignment ambiguity and compute high-resolution protein structures. Tests on five proteins show that NASCA: assigns resonances for more than 90% of side-chain protons, and achieves about 80% correct assignments. The final structures computed using the NOE distance restraints assigned by NASCA: have backbone RMSD 0.8-1.5 Å from the reference structures determined by traditional NMR approaches.

Residual dipolar couplings: are multiple independent alignments always possible?

RDCs for the 14 kDa protein hen egg-white lysozyme (HEWL) have been measured in eight different alignment media. The elongated shape and strongly positively charged surface of HEWL appear to limit the protein to four main alignment orientations. Furthermore, low levels of alignment and the protein's interaction with some alignment media increases the experimental error. Together with heterogeneity across the alignment media arising from constraints on temperature, pH and ionic strength for some alignment media, these data are suitable for structure refinement, but not the extraction of dynamic parameters. For an analysis of protein dynamics the data must be obtained with very low errors in at least three or five independent alignment media (depending on the method used) and so far, such data have only been reported for three small 6-8 kDa proteins with identical folds: ubiquitin, GB1 and GB3. Our results suggest that HEWL is likely to be representative of many other medium to large sized proteins commonly studied by solution NMR. Comparisons with over 60 high-resolution crystal structures of HEWL reveal that the highest resolution structures are not necessarily always the best models for the protein structure in solution.

The use of residual dipolar coupling in studying proteins by NMR

The development of residual dipolar coupling (RDC) in protein NMR spectroscopy, over a decade ago, has become a useful and almost routine tool for accurate protein solution structure determination. RDCs provide orientation information of magnetic dipole-dipole interaction vectors within a common reference frame. Its measurement requires a nonisotropic orientation, through a direct or indirect magnetic field alignment, of the protein in solution. There has been recent progress in the developments of alignment methods to allow the measurement of RDC and of methods to analyze the resulting data. In this chapter we briefly go through the mathematical expressions for the RDC and common descriptions of the alignment tensor, which may be represented using either Saupe order or the principal order matrix. Then we review the latest developments in alignment media. In particular we looked at the lipid-compatible media that allow the measurement of RDCs for membrane proteins. Other methods including conservative surface residue mutation have been invented to obtain up to five orthogonal alignment tensors that provide a potential for de novo structure and dynamics study using RDCs exclusively. We then discuss approximations assumed in RDC interpretations and different views on dynamics uncovered from the RDC method. In addition to routine usage of RDCs in refining a single structure, novel applications such as ensemble refinement against RDCs have been implemented to represent protein structure and dynamics in solution. The RDC application also extends to the study of protein-substrate interaction as well as to solving quaternary structure of oligomer in equilibrium with a monomer, opening an avenue for RDCs in high-order protein structure determination.

HNCO-based measurement of one-bond amide 15N-1H couplings with optimized precision

A pair of 3D HNCO-based experiments have been developed with the aim of optimizing the precision of measurement of (1)J(NH) couplings. Both pulse sequences record (1)J(NH) coupling evolution during the entire constant time interval that (15)N magnetization is dephasing or rephasing with respect to the directly bonded (13)C' nucleus, with (15)N(13)C' multiple quantum coherence maintained during the (13)C' evolution period. The first experiment, designed for smaller proteins, produces an apparent doubling of the (1)J(NH) coupling without any accompanying increases in line width. The second experiment is a J-scaled TROSY-HNCO experiment in which the (1)J(NH) coupling is measured by frequency difference between resonances offset symmetrically about the position of the downfield component of the (15)N doublet (i.e. the TROSY resonance). This experiment delivers significant gains in precision of (1)J(NH) coupling measurement compared to existing J-scaled TROSY-HNCO experiments. With the proper choice of acquisition parameters and sufficient sensitivity to acquire a 3D TROSY-HNCO experiment, it is shown that (1)J(NH) couplings can be measured with a precision which approaches or exceeds the precision of measurement with which the frequency of the TROSY resonance itself can be determined.

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.

High-resolution protein structure determination starting with a global fold calculated from exact solutions to the RDC equations

We present a novel structure determination approach that exploits the global orientational restraints from RDCs to resolve ambiguous NOE assignments. Unlike traditional approaches that bootstrap the initial fold from ambiguous NOE assignments, we start by using RDCs to compute accurate secondary structure element (SSE) backbones at the beginning of structure calculation. Our structure determination package, called RDC-PANDA: (RDC-based SSE PAcking with NOEs for Structure Determination and NOE Assignment), consists of three modules: (1) RDC-EXACT: ; (2) PACKER: ; and (3) HANA: (HAusdorff-based NOE Assignment). RDC-EXACT: computes the global optimal solution of backbone dihedral angles for each secondary structure element by exactly solving a system of quartic RDC equations derived by Wang and Donald (Proceedings of the IEEE computational systems bioinformatics conference (CSB), Stanford, CA, 2004a; J Biomol NMR 29(3):223-242, 2004b), and systematically searching over the roots, each of which is a backbone dihedral varphi- or psi-angle consistent with the RDC data. Using a small number of unambiguous inter-SSE NOEs extracted using only chemical shift information, PACKER: performs a systematic search for the core structure, including all SSE backbone conformations. HANA: uses a Hausdorff-based scoring function to measure the similarity between the experimental spectra and the back-computed NOE pattern for each side-chain from a statistically-diverse rotamer library, and drives the selection of optimal position-specific rotamers for filtering ambiguous NOE assignments. Finally, a local minimization approach is used to compute the loops and refine side-chain conformations by fixing the core structure as a rigid body while allowing movement of loops and side-chains. RDC-PANDA: was applied to NMR data for the FF Domain 2 of human transcription elongation factor CA150 (RNA polymerase II C-terminal domain interacting protein), human ubiquitin, the ubiquitin-binding zinc finger domain of the human Y-family DNA polymerase Eta (pol eta UBZ), and the human Set2-Rpb1 interacting domain (hSRI). These results demonstrated the efficiency and accuracy of our algorithm, and show that RDC-PANDA: can be successfully applied for high-resolution protein structure determination using only a limited set of NMR data by first computing RDC-defined backbones.

Evidence for conformational heterogeneity of fission protein Fis1 from Saccharomyces cerevisiae

Fission 1 (Fis1) is an evolutionarily conserved, type II integral membrane protein implicated in maintaining the proper morphology of mitochondria and peroxisomes. A concave surface on the cytosolic domain of Fis1 from Saccharomyces cerevisiae is implicated in binding other fission proteins, yet structural studies reveal that this surface is sterically occluded by its N-terminal arm. Here we address the question of whether the N-terminal arm of yeast Fis1 exists in a dynamic equilibrium that would allow access to this functionally important surface. NMR measurements sensitive to dynamics occurring on a wide range of time scales (picoseconds to minutes) were used to assess whether the Fis1 arm is dynamic. Hydrogen-deuterium exchange experiments revealed that the Fis1 arm, alpha-helix 6, and proximal loops were not protected from solvent exchange, consistent with motions on the second to minute time scale. An engineered cysteine, I85C, located on the concave surface that lies underneath the Fis1 arm, was readily modified by a fluorescent probe, revealing more solvent accessibility of this position than would be predicted from the structure. Chemical denaturation, NMR chemical shift perturbation, and residual dipolar coupling experiments support the idea that the dynamic equilibrium can be shifted on the basis of changing pH and temperature, with the changes primarily localizing to the Fis1 arm and proximal regions. The data as a whole are consistent with the Fis1 arm adopting a primarily "closed" conformational state able to undergo dynamic excursions that reveal the concave surface and therefore may be important for binding other fission factors and for Fis1 function.

Efficient and accurate estimation of relative order tensors from lambda-maps

The rapid increase in the availability of RDC data from multiple alignment media in recent years has necessitated the development of more sophisticated analyses that extract the RDC data's full information content. This article presents an analysis of the distribution of RDCs from two media (2D-RDC data), using the information obtained from a lambda-map. This article also introduces an efficient algorithm, which leverages these findings to extract the order tensors for each alignment medium using unassigned RDC data in the absence of any structural information. The results of applying this 2D-RDC analysis method to synthetic and experimental data are reported in this article. The relative order tensor estimates obtained from the 2D-RDC analysis are compared to order tensors obtained from the program REDCAT after using assignment and structural information. The final comparisons indicate that the relative order tensors estimated from the unassigned 2D-RDC method very closely match the results from methods that require assignment and structural information. The presented method is successful even in cases with small datasets. The results of analyzing experimental RDC data for the protein 1P7E are presented to demonstrate the potential of the presented work in accurately estimating the principal order parameters from RDC data that incompletely sample the RDC space. In addition to the new algorithm, a discussion of the uniqueness of the solutions is presented; no more than two clusters of distinct solutions have been shown to satisfy each lambda-map.

Ultrahigh resolution characterization of domain motions and correlations by multialignment and multireference residual dipolar coupling NMR

Nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) provide a unique opportunity for spatially characterizing complex motions in biomolecules with time scale sensitivity extending up to milliseconds. Up to five motionally averaged Wigner rotation elements, (D(0k)2(alphaalpha)), can be determined experimentally using RDCs measured in five linearly independent alignment conditions and applied to define motions of axially symmetric bond vectors. Here, we show that up to 25 motionally averaged Wigner rotation elements, (D(mk)2(alphabetagamma)), can be determined experimentally from multialignment RDCs and used to characterize rigid-body motions of chiral domains. The 25 (D(mk)2(alphabetagamma)) elements form a basis set that allows one to measure motions of a domain relative to an isotropic distribution of reference frames anchored on a second domain (and vice versa), thus expanding the 3D spatial resolution with which motions can be characterized. The 25 (D(mk)2(alphabetagamma)) elements can also be used to fit an ensemble consisting of up to eight equally or six unequally populated states. For more than two domains, changing the identity of the domain governing alignment allows access to new information regarding the correlated nature of the domain fluctuations. Example simulations are provided that validate the theoretical derivation and illustrate the high spatial resolution with which rigid-body domain motions can be characterized using multialignment and multireference RDCs. Our results further motivate the development of experimental approaches for both modulating alignment and anchoring it on specifically targeted domains.