Improvement and analysis of computational methods for prediction of residual dipolar couplings

Reweighting methods for elucidation of conformation ensembles of proteins

Proteins are inherently dynamic macromolecules that exist in equilibrium among multiple conformational states, and motions of protein backbone and side chains are fundamental to biological function. The ability to characterize the conformational landscape is particularly important for intrinsically disordered proteins, multidomain proteins, and weakly bound complexes, where single-structure representations are inadequate. As the focus of structural biology shifts from relatively rigid macromolecules toward larger and more complex systems and molecular assemblies, there is a need for structural approaches that can paint a more realistic picture of such conformationally heterogeneous systems. Here, we review reweighting methods for elucidation of structural ensembles based on experimental data, with the focus on applications to multidomain proteins.

Characterizing conformational ensembles of multi-domain proteins using anisotropic paramagnetic NMR restraints

It has been over two decades since paramagnetic NMR started to form part of the essential techniques for structural analysis of proteins under physiological conditions. Paramagnetic NMR has significantly expanded our understanding of the inherent flexibility of proteins, in particular, those that are formed by combinations of two or more domains. Here, we present a brief overview of techniques to characterize conformational ensembles of such multi-domain proteins using paramagnetic NMR restraints produced through anisotropic metals, with a focus on the basics of anisotropic paramagnetic effects, the general procedures of conformational ensemble reconstruction, and some representative reweighting approaches.

Assessing Structural Preferences of Unstructured Protein Regions by NMR

Biomacromolecules, such as proteins, often exhibit significant motions intimately associated with their function. Intrinsically disordered proteins and proteins with intrinsically disordered regions, although extremely important for a plethora of cellular functions, are difficult to structurally characterize at the atomic level because the experimental parameters report on ensemble and time averages. Here, we demonstrate for the C-terminal domain of the human immunodeficiency virus type 1 capsid protein that NMR and, in particular, residual dipolar couplings (RDCs) measured for the folded portion of the protein can inform on the structural preferences of the unstructured portion using RDC-prediction tools and the maximum occurrence approach.

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.

Integrative Approaches in Structural Biology: A More Complete Picture from the Combination of Individual Techniques

With the recent technological and computational advancements, structural biology has begun to tackle more and more difficult questions, including complex biochemical pathways and transient interactions among macromolecules. This has demonstrated that, to approach the complexity of biology, one single technique is largely insufficient and unable to yield thorough answers, whereas integrated approaches have been more and more adopted with successful results. Traditional structural techniques (X-ray crystallography and Nuclear Magnetic Resonance (NMR)) and the emerging ones (cryo-electron microscopy (cryo-EM), Small Angle X-ray Scattering (SAXS)), together with molecular modeling, have pros and cons which very nicely complement one another. In this review, three examples of synergistic approaches chosen from our previous research will be revisited. The first shows how the joint use of both solution and solid-state NMR (SSNMR), X-ray crystallography, and cryo-EM is crucial to elucidate the structure of polyethylene glycol (PEG)ylated asparaginase, which would not be obtainable through any of the techniques taken alone. The second deals with the integrated use of NMR, X-ray crystallography, and SAXS in order to elucidate the catalytic mechanism of an enzyme that is based on the flexibility of the enzyme itself. The third one shows how it is possible to put together experimental data from X-ray crystallography and NMR restraints in order to refine a protein model in order to obtain a structure which simultaneously satisfies both experimental datasets and is therefore closer to the ‘real structure’.

Treating Biomacromolecular Conformational Variability

The function of a biomacromolecule is related not only to its structure but also to the different conformations that its structural elements can sample. It is therefore important to determine the extent of the structural fluctuations and to identify the states that are actually populated as a result of the rearrangement. However, this accomplishment is undermined by an intrinsic limitation: the amount of experimental data is by and large inferior to the number of the states that a biomacromolecule can actually sample. This means that additional, a priori information must be applied in order to derive the most from the available experimental data but not to run into overinterpretation. In this chapter we will give a summary of the experimental observables that can be used towards the reconstruction of structural ensembles, how the data can be profitably combined and to what extent the data are affected by error; finally we will give an overview of the computational methods that have been developed to model structural ensembles, highlighting their difference and similarities, advantages and disadvantages.

Inter-helical conformational preferences of HIV-1 TAR-RNA from maximum occurrence analysis of NMR data and molecular dynamics simulations

Detecting conformational heterogeneity in biological macromolecules is a key for the understanding of their biological function. We here provide a comparison between two independent approaches to assess conformational heterogeneity: molecular dynamics simulations, performed without inclusion of any experimental data, and maximum occurrence (MaxOcc) distribution over the topologically available conformational space. The latter only reflects the extent of the averaging and identifies regions which are most compliant with the experimentally measured NMR Residual Dipolar Couplings (RDCs). The analysis was performed for the HIV-1 TAR RNA, consisting of two helical domains connected by a flexible bulge junction, for which four sets of RDCs were available as well as an 8.2 μs all-atom molecular dynamics simulation. A sample and select approach was previously applied to extract from the molecular dynamics trajectory conformational ensembles in agreement with the four sets of RDCs. The MaxOcc analysis performed here identifies the most likely sampled region in the conformational space of the system which, strikingly, overlaps well with the structures independently sampled in the molecular dynamics calculations and even better with the RDC selected ensemble.

A critical assessment of methods to recover information from averaged data

Conformational heterogeneity is key to the function of many biomacromolecules, but only a few groups have tried to characterize it until recently. Now, thanks to the increased throughput of experimental data and the increased computational power, the problem of the characterization of protein structural variability has become more and more popular. Several groups have devoted their efforts in trying to create quantitative, reliable and accurate protocols for extracting such information from averaged data. We analyze here different approaches, discussing strengths and weaknesses of each. All approaches can roughly be clustered into two groups: those satisfying the maximum entropy principle and those recovering ensembles composed of a restricted number of molecular conformations. In the first case, the solution focuses on the features that are common to all the infinite solutions satisfying the experimental data; in the second case, the reconstructed ensemble shows the conformational regions where a large probability can be placed. The upper limits for conformational probabilities (MaxOcc) can also be calculated. We also give an overview of the mainstream experimental observables, with considerations on the assumptions underlying their usage.

Linkage-specific conformational ensembles of non-canonical polyubiquitin chains

Polyubiquitination is a critical protein post-translational modification involved in a variety of processes in eukaryotic cells. The molecular basis for selective recognition of the polyubiquitin signals by cellular receptors is determined by the conformations polyubiquitin chains adopt; this has been demonstrated for K48- and K63-linked chains. Recent studies of the so-called non-canonical chains (linked via K6, K11, K27, K29, or K33) suggest they play important regulatory roles in growth, development, and immune system pathways, but biophysical studies are needed to elucidate the physical/structural basis of their interactions with receptors. A first step towards this goal is characterization of the conformations these chains adopt in solution. We assembled diubiquitins (Ub2) comprised of every lysine linkage. Using solution NMR measurements, small-angle neutron scattering (SANS), and in silico ensemble generation, we determined population-weighted conformational ensembles that shed light on the structure and dynamics of the non-canonical polyubiquitin chains. We found that polyubiquitin is conformationally heterogeneous, and each chain type exhibits unique conformational ensembles. For example, K6-Ub2 and K11-Ub2 (at physiological salt concentration) are in dynamic equilibrium between at least two conformers, where one exhibits a unique Ub/Ub interface, distinct from that observed in K48-Ub2 but similar to crystal structures of these chains. Conformers for K29-Ub2 and K33-Ub2 resemble recent crystal structures in the ligand-bound state. Remarkably, a number of diubiquitins adopt conformers similar to K48-Ub2 or K63-Ub2, suggesting potential overlap of biological function among different lysine linkages. These studies highlight the potential power of determining function from elucidation of conformational states.

Linkage via K27 Bestows Ubiquitin Chains with Unique Properties among Polyubiquitins

Polyubiquitination, a critical protein post-translational modification, signals for a diverse set of cellular events via the different isopeptide linkages formed between the C terminus of one ubiquitin (Ub) and the ɛ-amine of K6, K11, K27, K29, K33, K48, or K63 of a second Ub. We assembled di-ubiquitins (Ub2) comprising every lysine linkage and examined them biochemically and structurally. Of these, K27-Ub2 is unique as it is not cleaved by most deubiquitinases. As this remains the only structurally uncharacterized lysine linkage, we comprehensively examined the structures and dynamics of K27-Ub2 using nuclear magnetic resonance, small-angle neutron scattering, and in silico ensemble modeling. Our structural data provide insights into the functional properties of K27-Ub2, in particular that K27-Ub2 may be specifically recognized by K48-selective receptor UBA2 domain from proteasomal shuttle protein hHR23a. Binding studies and mutagenesis confirmed this prediction, further highlighting structural/recognition versatility of polyubiquitins and the potential power of determining function from elucidation of conformational ensembles.

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.

Information content of long-range NMR data for the characterization of conformational heterogeneity

Long-range NMR data, namely residual dipolar couplings (RDCs) from external alignment and paramagnetic data, are becoming increasingly popular for the characterization of conformational heterogeneity of multidomain biomacromolecules and protein complexes. The question addressed here is how much information is contained in these averaged data. We have analyzed and compared the information content of conformationally averaged RDCs caused by steric alignment and of both RDCs and pseudocontact shifts caused by paramagnetic alignment, and found that, despite the substantial differences, they contain a similar amount of information. Furthermore, using several synthetic tests we find that both sets of data are equally good towards recovering the major state(s) in conformational distributions.

FANTEN: a new web-based interface for the analysis of magnetic anisotropy-induced NMR data

Pseudocontact shifts (PCSs) and residual dipolar couplings (RDCs) arising from the presence of paramagnetic metal ions in proteins as well as RDCs due to partial orientation induced by external orienting media are nowadays routinely measured as a part of the NMR characterization of biologically relevant systems. PCSs and RDCs are becoming more and more popular as restraints (1) to determine and/or refine protein structures in solution, (2) to monitor the extent of conformational heterogeneity in systems composed of rigid domains which can reorient with respect to one another, and (3) to obtain structural information in protein-protein complexes. The use of both PCSs and RDCs proceeds through the determination of the anisotropy tensors which are at the origin of these NMR observables. A new user-friendly web tool, called FANTEN (Finding ANisotropy TENsors), has been developed for the determination of the anisotropy tensors related to PCSs and RDCs and has been made freely available through the WeNMR ( http://fanten-enmr.cerm.unifi.it:8080 ) gateway. The program has many new features not available in other existing programs, among which the possibility of a joint analysis of several sets of PCS and RDC data and the possibility to perform rigid body minimizations.

Recovering a representative conformational ensemble from underdetermined macromolecular structural data

Structural analysis of proteins and nucleic acids is complicated by their inherent flexibility, conferred, for example, by linkers between their contiguous domains. Therefore, the macromolecule needs to be represented by an ensemble of conformations instead of a single conformation. Determining this ensemble is challenging because the experimental data are a convoluted average of contributions from multiple conformations. As the number of the ensemble degrees of freedom generally greatly exceeds the number of independent observables, directly deconvolving experimental data into a representative ensemble is an ill-posed problem. Recent developments in sparse approximations and compressive sensing have demonstrated that useful information can be recovered from underdetermined (ill-posed) systems of linear equations by using sparsity regularization. Inspired by these advances, we designed the Sparse Ensemble Selection (SES) method for recovering multiple conformations from a limited number of observations. SES is more general and accurate than previously published minimum-ensemble methods, and we use it to obtain representative conformational ensembles of Lys48-linked diubiquitin, characterized by the residual dipolar coupling data measured at several pH conditions. These representative ensembles are validated against NMR chemical shift perturbation data and compared to maximum-entropy results. The SES method reproduced and quantified the previously observed pH dependence of the major conformation of Lys48-linked diubiquitin, and revealed lesser-populated conformations that are preorganized for binding known diubiquitin receptors, thus providing insights into possible mechanisms of receptor recognition by polyubiquitin. SES is applicable to any experimental observables that can be expressed as a weighted linear combination of data for individual states.

A tensor-free method for the structural and dynamical refinement of proteins using residual dipolar couplings

Residual dipolar couplings (RDCs) are parameters measured in nuclear magnetic resonance spectroscopy that can provide exquisitely detailed information about the structure and dynamics of biological macromolecules. We describe here a method of using RDCs for the structural and dynamical refinement of proteins that is based on the observation that the RDC between two atomic nuclei depends directly on the angle ϑ between the internuclear vector and the external magnetic field. For every pair of nuclei for which an RDC is available experimentally, we introduce a structural restraint to minimize the deviation from the value of the angle ϑ derived from the measured RDC and that calculated in the refinement protocol. As each restraint involves only the calculation of the angle ϑ of the corresponding internuclear vector, the method does not require the definition of an overall alignment tensor to describe the preferred orientation of the protein with respect to the alignment medium. Application to the case of ubiquitin demonstrates that this method enables an accurate refinement of the structure and dynamics of this protein to be obtained.

Capping motifs stabilize the leucine-rich repeat protein PP32 and rigidify adjacent repeats

Capping motifs are found to flank most β-strand-containing repeat proteins. To better understand the roles of these capping motifs in organizing structure and stability, we carried out folding and solution NMR studies on the leucine-rich repeat (LRR) domain of PP32, which is composed of five tandem LRR, capped by α-helical and β-hairpin motifs on the N- and C-termini. We were able to purify PP32 constructs lacking either cap and containing destabilizing substitutions. Removing the C-cap results in complete unfolding of PP32. Removing the N-cap has a much less severe effect, decreasing stability but retaining much of its secondary structure. In contrast, the dynamics and tertiary structure of the first two repeats are significantly perturbed, based on (1)H-(15)N relaxation studies, chemical shift perturbations, and residual dipolar couplings. However, more distal repeats (3 to C-cap) retain their native tertiary structure. In this regard, the N-cap drives the folding of adjacent repeats from what appears to be a molten-globule-like state. This interpretation is supported by extensive analysis using core packing substitutions in the full-length and N-cap-truncated PP32. This work highlights the importance of caps to the stability and structural integrity of β-strand-containing LRR proteins, and emphasizes the different contributions of the N- and C-terminal caps.

New opportunities for tensor-free calculations of residual dipolar couplings for the study of protein dynamics

Residual dipolar couplings (RDCs) can provide exquisitely detailed information about the structure and dynamics of proteins. It is challenging, however, to extract such information from RDC measurements in conformationally heterogeneous states of proteins because of the complex relationship between RDCs and protein structures. To obtain new insights into this problem, we discuss methods of calculating the RDCs that do not require the definition of an alignment tensor. These methods can help in particular in the search of effective ways to use RDCs to characterise disordered or partially disordered states of proteins.

A method of determining RNA conformational ensembles using structure-based calculations of residual dipolar couplings

We describe a method of determining the conformational fluctuations of RNA based on the incorporation of nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) as replica-averaged structural restraints in molecular dynamics simulations. In this approach, the alignment tensor required to calculate the RDCs corresponding to a given conformation is estimated from its shape, and multiple replicas of the RNA molecule are simulated simultaneously to reproduce in silico the ensemble-averaging procedure performed in the NMR measurements. We provide initial evidence that with this approach it is possible to determine accurately structural ensembles representing the conformational fluctuations of RNA by applying the reference ensemble test to the trans-activation response element of the human immunodeficiency virus type 1.

Deriving quantitative dynamics information for proteins and RNAs using ROTDIF with a graphical user interface

To facilitate rigorous analysis of molecular motions in proteins, DNA, and RNA, we present a new version of ROTDIF, a program for determining the overall rotational diffusion tensor from single- or multiple-field nuclear magnetic resonance relaxation data. We introduce four major features that expand the program's versatility and usability. The first feature is the ability to analyze, separately or together, (13)C and/or (15)N relaxation data collected at a single or multiple fields. A significant improvement in the accuracy compared to direct analysis of R2/R1 ratios, especially critical for analysis of (13)C relaxation data, is achieved by subtracting high-frequency contributions to relaxation rates. The second new feature is an improved method for computing the rotational diffusion tensor in the presence of biased errors, such as large conformational exchange contributions, that significantly enhances the accuracy of the computation. The third new feature is the integration of the domain alignment and docking module for relaxation-based structure determination of multi-domain systems. Finally, to improve accessibility to all the program features, we introduced a graphical user interface that simplifies and speeds up the analysis of the data. Written in Java, the new ROTDIF can run on virtually any computer platform. In addition, the new ROTDIF achieves an order of magnitude speedup over the previous version by implementing a more efficient deterministic minimization algorithm. We not only demonstrate the improvement in accuracy and speed of the new algorithm for synthetic and experimental (13)C and (15)N relaxation data for several proteins and nucleic acids, but also show that careful analysis required especially for characterizing RNA dynamics allowed us to uncover subtle conformational changes in RNA as a function of temperature that were opaque to previous analysis.

Comparative studies of disordered proteins with similar sequences: application to Aβ40 and Aβ42

Quantitative comparisons of intrinsically disordered proteins (IDPs) with similar sequences, such as mutant forms of the same protein, may provide insights into IDP aggregation-a process that plays a role in several neurodegenerative disorders. Here we describe an approach for modeling IDPs with similar sequences that simplifies the comparison of the ensembles by utilizing a single library of structures. The relative population weights of the structures are estimated using a Bayesian formalism, which provides measures of uncertainty in the resulting ensembles. We applied this approach to the comparison of ensembles for Aβ40 and Aβ42. Bayesian hypothesis testing finds that although both Aβ species sample β-rich conformations in solution that may represent prefibrillar intermediates, the probability that Aβ42 samples these prefibrillar states is roughly an order of magnitude larger than the frequency in which Aβ40 samples such structures. Moreover, the structure of the soluble prefibrillar state in our ensembles is similar to the experimentally determined structure of Aβ that has been implicated as an intermediate in the aggregation pathway. Overall, our approach for comparative studies of IDPs with similar sequences provides a platform for future studies on the effect of mutations on the structure and function of disordered proteins.

Examination of matrix metalloproteinase-1 in solution: a preference for the pre-collagenolysis state

Catalysis of collagen degradation by matrix metalloproteinase 1 (MMP-1) has been proposed to critically rely on flexibility between the catalytic (CAT) and hemopexin-like (HPX) domains. A rigorous assessment of the most readily accessed conformations in solution is required to explain the onset of substrate recognition and collagenolysis. The present study utilized paramagnetic NMR spectroscopy and small angle x-ray scattering (SAXS) to calculate the maximum occurrence (MO) of MMP-1 conformations. The MMP-1 conformations with large MO values (up to 47%) are restricted into a relatively small conformational region. All conformations with high MO values differ largely from the closed MMP-1 structures obtained by x-ray crystallography. The MO of the latter is ~20%, which represents the upper limit for the presence of this conformation in the ensemble sampled by the protein in solution. In all the high MO conformations, the CAT and HPX domains are not in tight contact, and the residues of the HPX domain reported to be responsible for the binding to the collagen triple-helix are solvent exposed. Thus, overall analysis of the highest MO conformations indicated that MMP-1 in solution was poised to interact with collagen and then could readily proceed along the steps of collagenolysis.

Characterization of the interdomain motions in hen lysozyme using residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations

Hen lysozyme is an enzyme characterized by the presence of two domains whose relative motions are involved in the mechanism of binding and release of the substrates. By using residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations, we characterize the breathing motions describing the interdomain fluctuations of this protein. We found that the ensemble of conformations that we determined spans the entire range of structures of hen lysozyme deposited in the Protein Data Bank, including both the free and bound states, suggesting that the thermal motions in the free state provide access to the structures populated upon binding. The approach that we present illustrates how the use of residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations makes it possible to explore conformational fluctuations of a relatively large amplitude in proteins.

Flexible-meccano: a tool for the generation of explicit ensemble descriptions of intrinsically disordered proteins and their associated experimental observables

MOTIVATION

Intrinsically disordered proteins (IDPs) represent a significant fraction of the human proteome. The classical structure function paradigm that has successfully underpinned our understanding of molecular biology breaks down when considering proteins that have no stable tertiary structure in their functional form. One convenient approach is to describe the protein in terms of an equilibrium of rapidly inter-converting conformers. Currently, tools to generate such ensemble descriptions are extremely rare, and poorly adapted to the prediction of experimental data.

RESULTS

We present flexible-meccano-a highly efficient algorithm that generates ensembles of molecules, on the basis of amino acid-specific conformational potentials and volume exclusion. Conformational sampling depends uniquely on the primary sequence, with the possibility of introducing additional local or long-range conformational propensities at an amino acid-specific resolution. The algorithm can also be used to calculate expected values of experimental parameters measured at atomic or molecular resolution, such as nuclear magnetic resonance (NMR) and small angle scattering, respectively. We envisage that flexible-meccano will be useful for researchers who wish to compare experimental data with those expected from a fully disordered protein, researchers who see experimental evidence of deviation from 'random coil' behaviour in their protein, or researchers who are interested in working with a broad ensemble of conformers representing the flexibility of the IDP of interest.

AVAILABILITY

A fully documented multi-platform executable is provided, with examples, at http://www.ibs.fr/science-213/scientific-output/software/flexible-meccano/

CONTACT

martin.blackledge@ibs.fr.

Determination of structural fluctuations of proteins from structure-based calculations of residual dipolar couplings

Residual dipolar couplings (RDCs) have the potential of providing detailed information about the conformational fluctuations of proteins. It is very challenging, however, to extract such information because of the complex relationship between RDCs and protein structures. A promising approach to decode this relationship involves structure-based calculations of the alignment tensors of protein conformations. By implementing this strategy to generate structural restraints in molecular dynamics simulations we show that it is possible to extract effectively the information provided by RDCs about the conformational fluctuations in the native states of proteins. The approach that we present can be used in a wide range of alignment media, including Pf1, charged bicelles and gels. The accuracy of the method is demonstrated by the analysis of the Q factors for RDCs not used as restraints in the calculations, which are significantly lower than those corresponding to existing high-resolution structures and structural ensembles, hence showing that we capture effectively the contributions to RDCs from conformational fluctuations.

Searching and optimizing structure ensembles for complex flexible sugars

NMR restrictions are suitable to specify the geometry of a molecule when a single well-defined global free energy minimum exists that is significantly lower than other local minima. Carbohydrates are quite flexible, and therefore, NMR observables do not always correlate with a single conformer but instead with an ensemble of low free energy conformers that can be accessed by thermal fluctuations. In this communication, we describe a novel procedure to identify and weight the contribution to the ensemble of local minima conformers based on comparison to residual dipolar couplings (RDCs) or other NMR observables, such as scalar couplings. A genetic algorithm is implemented to globally minimize the R factor comparing calculated RDCs to experiment. This is done by optimizing the weights of different conformers derived from the exhaustive local minima conformational search program, fast sugar structure prediction software (FSPS). We apply this framework to six human milk sugars, LND-1, LNF-1, LNF-2, LNF-3, LNnT, and LNT, and are able to determine corresponding population weights for the ensemble of conformers. Interestingly, our results indicate that in all cases the RDCs can be well represented by only a few most important conformers. This confirms that several, but not all of the glycosidic linkages in histo-blood group "epitopes" are quite rigid.

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.

Fast approximations of the rotational diffusion tensor and their application to structural assembly of molecular complexes

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols.

Constructing ensembles for intrinsically disordered proteins

The relatively flat energy landscapes associated with intrinsically disordered proteins makes modeling these systems especially problematic. A comprehensive model for these proteins requires one to build an ensemble consisting of a finite collection of structures, and their corresponding relative stabilities, which adequately capture the range of accessible states of the protein. In this regard, methods that use computational techniques to interpret experimental data in terms of such ensembles are an essential part of the modeling process. In this review, we critically assess the advantages and limitations of current techniques and discuss new methods for the validation of these ensembles.

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.

Structural assembly of molecular complexes based on residual dipolar couplings

We present and evaluate a rigid-body molecular docking method, called PATIDOCK, that relies solely on the three-dimensional structure of the individual components and the experimentally derived residual dipolar couplings (RDCs) for the complex. We show that, given an accurate ab initio predictor of the alignment tensor from a protein structure, it is possible to accurately assemble a protein-protein complex by utilizing the RDCs' sensitivity to molecular shape to guide the docking. The proposed docking method is robust against experimental errors in the RDCs and computationally efficient. We analyze the accuracy and efficiency of this method using experimental or synthetic RDC data for several proteins, as well as synthetic data for a large variety of protein-protein complexes. We also test our method on two protein systems for which the structure of the complex and steric-alignment data are available (Lys48-linked diubiquitin and a complex of ubiquitin and a ubiquitin-associated domain) and analyze the effect of flexible unstructured tails on the outcome of docking. The results demonstrate that it is fundamentally possible to assemble a protein-protein complex solely on the basis of experimental RDC data and the prediction of the alignment tensor from 3D structures. Thus, despite the purely angular nature of RDCs, they can be converted into intermolecular distance/translational constraints. Additionally, we show a method for combining RDCs with other experimental data, such as ambiguous constraints from interface mapping, to further improve structure characterization of protein complexes.