Residual Dipolar Coupling Data Research Articles

Structural Characterization of a Heparan Sulfate Pentamer Interacting with LAR-Ig1-2.

Leukocyte common antigen-related (LAR) protein is one of the type IIa receptor protein tyrosine phosphatases (RPTPs) that are important for signal transduction in biological processes, including axon growth and regeneration. Glycosaminoglycan chains, including heparan sulfate (HS) and chondroitin sulfate (CS), act as ligands that regulate LAR signaling. Here, we report the structural characterization of the first two immunoglobulin domains (Ig1-2) of LAR interacting with an HS pentasaccharide (GlcNS6S-GlcA-GlcNS3,6S-IdoA2S-GlcNS6S-OME, fondaparinux) using multiple solution-based NMR methods. In the course of the study, we extended an assignment strategy useful for sparsely labeled proteins expressed in mammalian cell culture supplemented with a single type of isotopically enriched amino acid ([15N]-Lys in this case) by including paramagnetic perturbations to NMR resonances. The folded two-domain structure for LAR-Ig1-2 seen in previous crystal structures has been validated in solution using residual dipolar coupling data, and a combination of chemical shift perturbation on titration of LAR-Ig1-2 with fondaparinux, saturation transfer difference (STD) spectra, and transferred nuclear Overhauser effects (trNOEs) have been employed in the docking program HADDOCK to generate models for the LAR-fondaparinux complex. These models are further analyzed by postprocessing energetic analysis to identify key binding interactions. In addition to providing insight into the ligand interaction mechanisms of type IIa RPTPs and the origin of opposing effects of CS and HS ligands, these results may assist in future design of therapeutic compounds for nervous system repair.

AMOEBA Polarizable Atomic Multipole Force Field for Nucleic Acids.

The AMOEBA polarizable atomic multipole force field for nucleic acids is presented. Valence and electrostatic parameters were determined from high-level quantum mechanical data, including structures, conformational energy, and electrostatic potentials, of nucleotide model compounds. Previously derived parameters for the phosphate group and nucleobases were incorporated. A total of over 35 μs of condensed-phase molecular dynamics simulations of DNA and RNA molecules in aqueous solution and crystal lattice were performed to validate and refine the force field. The solution and/or crystal structures of DNA B-form duplexes, RNA duplexes, and hairpins were captured with an average root-mean-squared deviation from NMR structures below or around 2.0 Å. Structural details, such as base pairing and stacking, sugar puckering, backbone and χ-torsion angles, groove geometries, and crystal packing interfaces, agreed well with NMR and/or X-ray. The interconversion between A- and B-form DNAs was observed in ethanol-water mixtures at 328 K. Crystal lattices of B- and Z-form DNA and A-form RNA were examined with simulations. For the RNA tetraloop, single strand tetramers, and HIV TAR with 29 residues, the simulated conformational states, 3 J-coupling, nuclear Overhauser effect, and residual dipolar coupling data were compared with NMR results. Starting from a totally unstacked/unfolding state, the rCAAU tetranucleotide was folded into A-form-like structures during ∼1 μs molecular dynamics simulations.

Mollib: a molecular and NMR data analysis software.

Mollib is a software framework for the analysis of molecular structures, properties and data with an emphasis on data collected by NMR. It uses an open source model and a plugin framework to promote community-driven development of new and enhanced features. Mollib includes tools for the automatic retrieval and caching of protein databank (PDB) structures, the hydrogenation of biomolecules, the analysis of backbone dihedral angles and hydrogen bonds, and the fitting of residual dipolar coupling (RDC) and residual anisotropic chemical shift (RACS) data. In this article, we release version 1.0 of mollib and demonstrate its application to common molecular and NMR data analyses.

Xplor-NIH for molecular structure determination from NMR and other data sources.

Xplor-NIH is a popular software package for biomolecular structure determination from nuclear magnetic resonance (NMR) and other data sources. Here, some of Xplor-NIH's most useful data-associated energy terms are reviewed, including newer alternative options for using residual dipolar coupling data in structure calculations. Further, we discuss new developments in the implementation of strict symmetry for the calculation of symmetric homo-oligomers, and in the representation of the system as an ensemble of structures to account for motional effects. Finally, the different available force fields are presented, among other Xplor-NIH capabilities.

NMR characterization of HtpG, the E. coli Hsp90, using sparse labeling with 13C-methyl alanine.

A strategy for acquiring structural information from sparsely isotopically labeled large proteins is illustrated with an application to the E. coli heat-shock protein, HtpG (high temperature protein G), a 145kDa dimer. It uses 13C-alanine methyl labeling in a perdeuterated background to take advantage of the sensitivity and resolution of Methyl-TROSY spectra, as well as the backbone-centered structural information from 1H-13C residual dipolar couplings (RDCs) of alanine methyl groups. In all, 40 of the 47 expected crosspeaks were resolved and 36 gave RDC data. Assignments of crosspeaks were partially achieved by transferring assignments from those made on individual domains using triple resonance methods. However, these were incomplete and in many cases the transfer was ambiguous. A genetic algorithm search for consistency between predictions based on domain structures and measurements for chemical shifts and RDCs allowed 60% of the 40 resolved crosspeaks to be assigned with confidence. Chemical shift changes of these crosspeaks on adding an ATP analog to the apo-protein are shown to be consistent with structural changes expected on comparing previous crystal structures for apo- and complex- structures. RDCs collected on the assigned alanine methyl peaks are used to generate a new solution model for the apo-protein structure.

Synthesis of Poly-γ-S-2-methylbutyl-l-glutamate and Poly-γ-S-2-methylbutyl-d-glutamate and Their Use as Enantiodiscriminating Alignment Media in NMR Spectroscopy.

Lyotropic liquid crystalline (LLC) phases of polyglutamic acid derivatives, such as poly-γ-benzyl-l-glutamate, are suitable alignment media for organic structure elucidation by NMR spectroscopy. Their helical structure is responsible for enantiodiscrimination. As part of our ongoing investigations concerning the alignment mechanism(s) of these systems, we considered whether an additional chiral center in the side chain could improve enantiodiscrimination relative to the helical polymer with an achiral side chain. Therefore, the diastereoisomers poly-γ-S-2-methylbutyl-l-glutamate (PSMBLG) and poly-γ-S-2-methylbutyl-d-glutamate (PSMBDG) were synthesized. These two polymers were tested for their liquid crystallinity and suitability as alignment media. The spatial structure of the solutes (-)-curcumol and isopinocampheol (IPC) were validated by the residual dipolar coupling data obtained. Additionally, enantiodiscrimination of IPC was observed in the new alignment media and compared with the enantiodiscrimination of IPC in other homopolypeptides.

Flexibility in the Periplasmic Domain of BamA Is Important for Function

The β-barrel assembly machine (BAM) mediates the biogenesis of outer membrane proteins (OMPs) in Gram-negative bacteria. BamA, the central BAM subunit composed of a transmembrane β-barrel domain linked to five polypeptide transport-associated (POTRA) periplasmic domains, is thought to bind nascent OMPs and undergo conformational cycling to catalyze OMP folding and insertion. One model is that conformational flexibility between POTRA domains is part of this conformational cycling. Nuclear magnetic resonance (NMR) spectroscopy was used here to study the flexibility of the POTRA domains 1-5 in solution. NMR relaxation studies defined effective rotational correlational times and together with residual dipolar coupling data showed that POTRA1-2 is flexibly linked to POTRA3-5. Mutants of BamA that restrict flexibility between POTRA2 and POTRA3 by disulfide crosslinking displayed impaired function invivo. Together these data strongly support a model in which conformational cycling of hinge motions between POTRA2 and POTRA3 in BamA is required for biological function.

Glycosylation Alters Dimerization Properties of a Cell-surface Signaling Protein, Carcinoembryonic Antigen-related Cell Adhesion Molecule 1 (CEACAM1)

Human carcinoembryonic antigen-related cell adhesion molecule 1 (C?/Au: EACAM1) is a cell-surface signaling molecule involved in cell adhesion, proliferation, and immune response. It is also implicated in cancer angiogenesis, progression, and metastasis. This diverse set of effects likely arises as a result of the numerous homophilic and heterophilic interactions that CEACAM1 can have with itself and other molecules. Its N-terminal Ig variable (IgV) domain has been suggested to be a principal player in these interactions. Previous crystal structures of the β-sandwich-like IgV domain have been produced using Escherichia coli-expressed material, which lacks native glycosylation. These have led to distinctly different proposals for dimer interfaces, one involving interactions of ABED β-strands and the other involving GFCC'C″ β-strands, with the former burying one prominent glycosylation site. These structures raise questions as to which form may exist in solution and what the effect of glycosylation may have on this form. Here, we use NMR cross-correlation measurements to examine the effect of glycosylation on CEACAM1-IgV dimerization and use residual dipolar coupling (RDC) measurements to characterize the solution structure of the non-glycosylated form. Our findings demonstrate that even addition of a single N-linked GlcNAc at potential glycosylation sites inhibits dimer formation. Surprisingly, RDC data collected on E. coli expressed material in solution indicate that a dimer using the non-glycosylated GFCC'C″ interface is preferred even in the absence of glycosylation. The results open new questions about what other factors may facilitate dimerization of CEACAM1 in vivo, and what roles glycosylation may play in heterophylic interactions.

Structure of an Intrinsically Disordered Stress Protein Alone and Bound to a Membrane Surface

Dehydrins are a group of intrinsically disordered proteins that protect plants from damage caused by drought, cold, and high salinity. Like other intrinsically disordered proteins, dehydrins can gain structure when bound to a ligand. Previous studies have shown that dehydrins are able to protect liposomes from cold damage, but the interactions that drive membrane binding and the detailed structure of the bound and unbound forms are not known. We use an ensemble-structure approach to generate models of a dehydrin known as K2 in the presence and absence of sodium dodecyl sulfate micelles, and we docked the bound structure to the micelle. The collection of residual dipolar coupling data, amide protection factors, and paramagnetic relaxation enhancement distances, in combination with chemical shifts and relaxation measurements, allows for determining plausible structures that are not otherwise visible in time-averaged structural data. The results show that in the bound structure, the conserved lysines are important for membrane binding, whereas the flanking hydrophobic residues play a lesser role. The unbound structure shows a high level of disorder and an extended structure. We propose that the structural differences between bound and unbound forms allow dehydrins to act as molecular shields in their unbound state and as membrane protectants in their bound state. Unlike α-synuclein, the significant gain of α-helicity in K2 at low concentrations of sodium dodecyl sulfate is not due to a decrease in the critical micelle concentration. The study provides structural insight into how a disordered protein can interact with a membrane surface.

Direct Investigation of Slow Correlated Dynamics in Proteins via Dipolar Interactions.

The synchronization of native state motions as they transition between microstates influences catalysis kinetics, mediates allosteric interactions, and reduces the conformational entropy of proteins. However, it has proven difficult to describe native microstates because they are usually minimally frustrated and may interconvert on the micro- to millisecond time scale. Direct observation of concerted equilibrium fluctuations would therefore be an important tool for describing protein native states. Here we propose a strategy that relates NMR cross-correlated relaxation (CCR) rates between dipolar interactions to residual dipolar couplings (RDCs) of individual consecutive H(N)-N and H(α)-C(α) bonds, which act as a proxy for the peptide planes and the side chains, respectively. Using Xplor-NIH ensemble structure calculations restrained with the RDC and CCR data, we observe collective motions on time scales slower than nanoseconds in the backbone for GB3. To directly access the correlations from CCR, we develop a structure-free data analysis. The resulting dynamic correlation map is consistent with the ensemble-restrained simulations and reveals a complex network. In general, we find that the bond motions are on average slightly correlated and that the local environment dominates many observations. Despite this, some patterns are typical over entire secondary structure elements. In the β-sheet, nearly all bonds are weakly correlated, and there is an approximately binary alternation in correlation intensity corresponding to the solvent exposure/shielding alternation of the side chains. For α-helices, there is also a weak correlation in the H(N)-N bonds. The degree of correlation involving H(α)-C(α) bonds is directly affected by side-chain fluctuations, whereas loops show complex and nonuniform behavior.

Structure Calculation and Reconstruction of Discrete-State Dynamics from Residual Dipolar Couplings.

Residual dipolar couplings (RDCs) acquired by nuclear magnetic resonance (NMR) spectroscopy are an indispensable source of information in investigation of molecular structures and dynamics. Here, we present a comprehensive strategy for structure calculation and reconstruction of discrete-state dynamics from RDC data that is based on the singular value decomposition (SVD) method of order tensor estimation. In addition to structure determination, we provide a mechanism of producing an ensemble of conformations for the dynamical regions of a protein from RDC data. The developed methodology has been tested on simulated RDC data with ±1 Hz of error from an 83 residue α protein (PDB ID 1A1Z ) and a 213 residue α/β protein DGCR8 (PDB ID 2YT4 ). In nearly all instances, our method reproduced the structure of the protein including the conformational ensemble to within less than 2 Å. On the basis of our investigations, arc motions with more than 30° of rotation are identified as internal dynamics and are reconstructed with sufficient accuracy. Furthermore, states with relative occupancies above 20% are consistently recognized and reconstructed successfully. Arc motions with a magnitude of 15° or relative occupancy of less than 10% are consistently unrecognizable as dynamical regions within the context of ±1 Hz of error.

Structure of Guanylyl Cyclase Activator Protein 1 (GCAP1) Mutant V77E in a Ca2+-free/Mg2+-bound Activator State

GCAP1, a member of the neuronal calcium sensor subclass of the calmodulin superfamily, confers Ca(2+)-sensitive activation of retinal guanylyl cyclase 1 (RetGC1). We present NMR resonance assignments, residual dipolar coupling data, functional analysis, and a structural model of GCAP1 mutant (GCAP1(V77E)) in the Ca(2+)-free/Mg(2+)-bound state. NMR chemical shifts and residual dipolar coupling data reveal Ca(2+)-dependent differences for residues 170-174. An NMR-derived model of GCAP1(V77E) contains Mg(2+) bound at EF2 and looks similar to Ca(2+) saturated GCAP1 (root mean square deviations = 2.0 Å). Ca(2+)-dependent structural differences occur in the fourth EF-hand (EF4) and adjacent helical region (residues 164-174 called the Ca(2+) switch helix). Ca(2+)-induced shortening of the Ca(2+) switch helix changes solvent accessibility of Thr-171 and Leu-174 that affects the domain interface. Although the Ca(2+) switch helix is not part of the RetGC1 binding site, insertion of an extra Gly residue between Ser-173 and Leu-174 as well as deletion of Arg-172, Ser-173, or Leu-174 all caused a decrease in Ca(2+) binding affinity and abolished RetGC1 activation. We conclude that Ca(2+)-dependent conformational changes in the Ca(2+) switch helix are important for activating RetGC1 and provide further support for a Ca(2+)-myristoyl tug mechanism.

Allostery through Protein Motion at Different Length and Time Scales

The conformational dynamics of proteins are often critical for mediating their functions. They are particularly important for ubiquitin, which must adapt its structure to interact with a plethora of cellular interaction partners. Through an in-depth relaxation dispersion (RD) analysis, we determined how backbone and side chain motions mutually affect one another through a process we term “population shuffling”. Intriguingly, these motions form an allosteric network that operates using concerted motion throughout the protein. This network is a key part of enabling multispecificity and suggests that ubiquitin regulation may be more complex than previously thought. In addition to concerted motions, simulations and crystal structures have suggested that population shuffling also operates between distant parts of the backbone, and may serve as another mechanism behind allosteric communication. In an effort to further elucidate the details of these motions, we have collected a large dataset of time-dependent Nuclear Overhauser Effect (NOE) measurements on both the backbone and side chains. Through explicit modeling of the effect that fast and slow motions have on the NOE, we gain even more insight into energy landscape of ubiquitin. By computationally combining residual dipolar coupling (RDC), RD, and NOE data our structural ensembles incorporate protein dynamics from timescales covering nine orders of magnitude.

Structural characterization of eRF1 mutants indicate a complex mechanism of stop codon recognition.

Eukarya translation termination requires the stop codon recognizing protein eRF1. In contrast to the multiple proteins required for translation termination in Bacteria, eRF1 retains the ability to recognize all three of the stop codons. The details of the mechanism that eRF1 uses to recognize stop codons has remained elusive. This study describes the structural effects of mutations in the eRF1 N-domain that have previously been shown to alter stop codon recognition specificity. Here, we propose a model of eRF1 binding to the pre-translation termination ribosomal complex that is based in part on our solution NMR structures of the wild-type and mutant eRF1 N-domains. Since structural perturbations induced by these mutations were spread throughout the protein structure, residual dipolar coupling (RDC) data were recorded to establish the long-range effects of the specific mutations, E55Q, Y125F, Q122FM(Y)F126. RDCs were recorded on 15N-labeled eRF1 N-domain weakly aligned in either 5% w/v n-octyl-penta (ethylene glycol)/octanol (C8E5) or the filamentous phage Pf1. These data indicate that the mutations alter the conformation and dynamics of the GTS loop that is distant from the mutation sites. We propose that the GTS loop forms a switch that is key for the multiple codon recognition capability of eRF1.

Side Chain Conformational Distributions of a Small Protein Derived from Model-Free Analysis of a Large Set of Residual Dipolar Couplings.

Accurate quantitative measurement of structural dispersion in proteins remains a prime challenge to both X-ray crystallography and NMR spectroscopy. Here we use a model-free approach based on measurement of many residual dipolar couplings (RDCs) in differentially orienting aqueous liquid crystalline solutions to obtain the side chain χ1 distribution sampled by each residue in solution. Applied to the small well-ordered model protein GB3, our approach reveals that the RDC data are compatible with a single narrow distribution of side chain χ1 angles for only about 40% of the residues. For more than half of the residues, populations greater than 10% for a second rotamer are observed, and four residues require sampling of three rotameric states to fit the RDC data. In virtually all cases, sampled χ1 values are found to center closely around ideal g–, g+ and t rotameric angles, even though no rotamer restraint is used when deriving the sampled angles. The root-mean-square difference between experimental 3JHαHβ couplings and those predicted by the Haasnoot-parametrized, motion-adjusted Karplus equation reduces from 2.05 to 0.75 Hz when using the new rotamer analysis instead of the 1.1-Å X-ray structure as input for the dihedral angles. A comparison between observed and predicted 3JHαHβ values suggests that the root-mean-square amplitude of χ1 angle fluctuations within a given rotamer well is ca. 20°. The quantitatively defined side chain rotamer equilibria obtained from our study set new benchmarks for evaluating improved molecular dynamics force fields, and also will enable further development of quantitative relations between side chain chemical shift and structure.

Dynamic equilibrium between closed and partially closed states of the bacterial Enzyme I unveiled by solution NMR and X-ray scattering

Enzyme I (EI) is the first component in the bacterial phosphotransferase system, a signal transduction pathway in which phosphoryl transfer through a series of bimolecular protein-protein interactions is coupled to sugar transport across the membrane. EI is a multidomain, 128-kDa homodimer that has been shown to exist in two conformational states related to one another by two large (50-90°) rigid body domain reorientations. The open conformation of apo EI allows phosphoryl transfer from His189 located in the N-terminal domain α/β (EIN(α/β)) subdomain to the downstream protein partner bound to the EIN(α) subdomain. The closed conformation, observed in a trapped phosphoryl transfer intermediate, brings the EIN(α/β) subdomain into close proximity to the C-terminal dimerization domain (EIC), thereby permitting in-line phosphoryl transfer from phosphoenolpyruvate (PEP) bound to EIC to His189. Here, we investigate the solution conformation of a complex of an active site mutant of EI (H189A) with PEP. Simulated annealing refinement driven simultaneously by solution small angle X-ray scattering and NMR residual dipolar coupling data demonstrates unambiguously that the EI(H189A)-PEP complex exists in a dynamic equilibrium between two approximately equally populated conformational states, one corresponding to the closed structure and the other to a partially closed species. The latter likely represents an intermediate in the open-to-closed transition.

Guiding automated NMR structure determination using a global optimization metric, the NMR DP score.

ASDP is an automated NMR NOE assignment program. It uses a distinct bottom-up topology-constrained network anchoring approach for NOE interpretation, with 2D, 3D and/or 4D NOESY peak lists and resonance assignments as input, and generates unambiguous NOE constraints for iterative structure calculations. ASDP is designed to function interactively with various structure determination programs that use distance restraints to generate molecular models. In the CASD-NMR project, ASDP was tested and further developed using blinded NMR data, including resonance assignments, either raw or manually-curated (refined) NOESY peak list data, and in some cases (15)N-(1)H residual dipolar coupling data. In these blinded tests, in which the reference structure was not available until after structures were generated, the fully-automated ASDP program performed very well on all targets using both the raw and refined NOESY peak list data. Improvements of ASDP relative to its predecessor program for automated NOESY peak assignments, AutoStructure, were driven by challenges provided by these CASD-NMR data. These algorithmic improvements include (1) using a global metric of structural accuracy, the discriminating power score, for guiding model selection during the iterative NOE interpretation process, and (2) identifying incorrect NOESY cross peak assignments caused by errors in the NMR resonance assignment list. These improvements provide a more robust automated NOESY analysis program, ASDP, with the unique capability of being utilized with alternative structure generation and refinement programs including CYANA, CNS, and/or Rosetta.

Backbone hydration determines the folding signature of amino acid residues.

The relation between the sequence of a protein and its three-dimensional structure remains largely unknown. A lasting dream is to elucidate the side-chain-dependent driving forces that govern the folding process. Different structural data suggest that aromatic amino acids play a particular role in the stabilization of protein structures. To better understand the underlying mechanism, we studied peptides of the sequence EGAAXAASS (X = Gly, Ile, Tyr, Trp) through comparison of molecular dynamics (MD) trajectories and NMR residual dipolar coupling (RDC) measurements. The RDC data for aromatic substitutions provide evidence for a kink in the peptide backbone. Analysis of the MD simulations shows that the formation of internal hydrogen bonds underlying a helical turn is key to reproduce the experimental RDC values. The simulations further reveal that the driving force leading to such helical-turn conformations arises from the lack of hydration of the peptide chain on either side of the bulky aromatic side chain, which can potentially act as a nucleation point initiating the folding process.

The PRE-Derived NMR Model of the 38.8-kDa Tri-Domain IsdH Protein from Staphylococcus aureus Suggests That It Adaptively Recognizes Human Hemoglobin

Staphylococcus aureus is a medically important bacterial pathogen that, during infections, acquires iron from human hemoglobin (Hb). It uses two closely related iron-regulated surface determinant (Isd) proteins to capture and extract the oxidized form of heme (hemin) from Hb, IsdH and IsdB. Both receptors rapidly extract hemin using a conserved tri-domain unit consisting of two NEAT (near iron transporter) domains connected by a helical linker domain. To gain insight into the mechanism of extraction, we used NMR to investigate the structure and dynamics of the 38.8-kDa tri-domain IsdH protein (IsdHN2N3, A326–D660 with a Y642A mutation that prevents hemin binding). The structure was modeled using long-range paramagnetic relaxation enhancement (PRE) distance restraints, dihedral angle, small-angle X-ray scattering, residual dipolar coupling and inter-domain NOE nuclear Overhauser effect data. The receptor adopts an extended conformation wherein the linker and N3 domains pack against each other via a hydrophobic interface. In contrast, the N2 domain contacts the linker domain via a hydrophilic interface and, based on NMR relaxation data, undergoes inter-domain motions enabling it to reorient with respect to the body of the protein. Ensemble calculations were used to estimate the range of N2 domain positions compatible with the PRE data. A comparison of the Hb-free and Hb-bound forms reveals that Hb binding alters the positioning of the N2 domain. We propose that binding occurs through a combination of conformational selection and induced-fit mechanisms that may promote hemin release from Hb by altering the position of its F helix.

Visualizing the Inter-Domain Motions of a Pathogenic Protein using Sparse RDC Data

SpA-N is the N-terminal half of Staphylococcal protein A and it is composed of five protein binding domains. The five domains could bind to antibody, TNFR1 and von Willebrand factor and facilitate the evasion of Staphylococcus aureus into the human immune system. The functional plasticity is suggested to be the result of structural flexibility. Heteronuclear spin relaxation experiments demonstrated that the five domains of SpA-N are connected by four flexible linkers. In order to obtain additional dynamic information, we constructed a di-domain mimic of SpA-N with a lanthanide binding tag and measured residual dipolar couplings (RDCs). The di-domain construct can bind lanthanide ions and consequently be aligned in the presence of a strong magnetic field. By using different combinations of lanthanide ions and protein constructs, we obtained two orthogonal alignments, which have enough information content to determine a model with maximally 10 parameters. In addition, we designed a de novo method to extract dynamic information from RDCs. Instead of determining conventional structure ensembles, our method determines an inter-domain orientation distribution to describe the structure of a flexible protein using continuous probability distributions. By using continuous models, orientation distributions can be parameterized by a small number of variables and still remain general enough to describe a broad spectrum of inter-domain motions. As a result, the method can avoid the over-fitting problem even with sparse data. Because no force field is applied, the generated distribution is purely determined by RDC data and least biased. Using the method, we determined the inter-domain orientation distribution of the di-domain construct with only two orthogonal alignments. A strong correlation was observed in the distribution and conformations were well populated in a limited region.