Experimentally exploring the conformational space sampled by domain reorientation in calmodulin

Are Protein Conformational Ensembles in Agreement with Experimental Data? A Geometrical Interpretation of the Problem

The conformational variability of biological macromolecules can play an important role in their biological function. Therefore, understanding conformational variability is expected to be key for predicting the behavior of a particular molecule in the context of organism-wide studies. Several experimental methods have been developed and deployed for accessing this information, and computational methods are continuously updated for the profitable integration of different experimental sources. The outcome of this endeavor is conformational ensembles, which may vary significantly in properties and composition when different ensemble reconstruction methods are used, and this raises the issue of comparing the predicted ensembles against experimental data. In this article, we discuss a geometrical formulation to provide a framework for understanding the agreement of an ensemble prediction to the experimental observations.

Studying Peptide-Metal Ion Complex Structures by Solution-State NMR

Metal chelation can provide structural stability and form reactive centers in metalloproteins. Approximately one third of known protein structures are metalloproteins, and metal binding, or the lack thereof, is often implicated in disease, making it necessary to be able to study these systems in detail. Peptide-metal complexes are both present in nature and can provide a means to focus on the binding region of a protein and control experimental variables to a high degree. Structural studies of peptide complexes with metal ions by nuclear magnetic resonance (NMR) were surveyed for all the essential metal complexes and many non-essential metal complexes. The various methods used to study each metal ion are presented together with examples of recent research. Many of these metal systems have been individually reviewed and this current overview of NMR studies of metallopeptide complexes aims to provide a basis for inspiration from structural studies and methodology applied in the field.

Interdomain Dynamics via Paramagnetic NMR on the Highly Flexible Complex Calmodulin/Munc13-1

Paramagnetic NMR constraints are very useful to study protein interdomain motion, but their interpretation is not always straightforward. On the example of the particularly flexible complex Calmodulin/Munc13-1, we present a new approach to characterize this motion with pseudocontact shifts and residual dipolar couplings. Using molecular mechanics, we sampled the conformational space of the complex and used a genetic algorithm to find ensembles that are in agreement with the data. We used the Bayesian information criterion to determine the ideal ensemble size. This way, we were able to make an accurate, unambiguous, reproducible model of the interdomain motion of Calmodulin/Munc13-1 without prior knowledge about the domain orientation from crystallography.

Distinct stereospecific effect of chiral tether between a tag and protein on the rigidity of paramagnetic tag

Flexibility between the paramagnetic tag and its protein conjugates is a common yet unresolved issue in the applications of paramagnetic NMR spectroscopy in biological systems. The flexibility greatly attenuates the magnetic anisotropy and compromises paramagnetic effects especially for pseudocontact shift and residual dipolar couplings. Great efforts have been made to improve the rigidity of paramagnetic tag in the protein conjugates, however, the effect of local environment vicinal to the protein ligation site on the paramagnetic effects remains poorly understood. In the present work, the stereospecific effect of chiral tether between the protein and a tag on the paramagnetic effects produced by the tag attached via a D- and L-type linker between the protein and paramagnetic metal chelating moiety was assessed. The remarkable chiral effect of the D- and L-type tether between the tag and the protein on the rigidity of paramagnetic tag is disclosed in a number of protein-tag-Ln complexes. The chiral tether formed between the D-type tag and L-type protein surface minimizes the effect of the local environment surrounding the ligation site on the averaging of paramagnetic tag, which is helpful to preserve the rigidity of a paramagnetic tag in the protein conjugates.

Quantitative Agreement between Conformational Substates of Holo Calcium-Loaded Calmodulin Detected by Double Electron-Electron Resonance EPR and Predicted by Molecular Dynamics Simulations

Calcium-loaded calmodulin (CaM/4Ca²⁺) comprises two domains that undergo rigid body reorientation from a predominantly extended conformation to a compact one upon binding target peptides. A recent replica-exchange molecular dynamics (MD) simulation on holo CaM/4Ca²⁺ suggested the existence of distinct structural clusters (substates) along the path from extended to compact conformers in the absence of substrates. Here, we experimentally demonstrate the existence of CaM/4Ca²⁺ substates trapped in local minima by three freezing/annealing regimes (slow, 40 s; intermediate, 1.5 s; fast, 0.5 ms) using pulsed Q-band double electron-electron resonance (DEER) EPR spectroscopy to measure interdomain distances between nitroxide spin-labels positioned at A17C and A128C in the N- and C-terminal domains, respectively. The DEER echo curves were directly fit to population-optimized P(r) pairwise distance distributions calculated from the coordinates of the MD clusters and compact crystal structure. DEER data on fully deuterated CaM/4Ca²⁺ were acquired at multiple values of the second echo period (10-35 μs) and analyzed globally to eliminate instrumental and overfitting artifacts and ensure accurate populations, peak positions, and widths. The DEER data for all three freezing regimes are quantitatively accounted for within experimental error by 5-6 distinct conformers comprising a predominantly populated extended form (60-75%) and progressively more compact states whose populations decrease as the degree of compactness increases. The shortest interdomain separation is found in the compact crystal structure, which has an occupancy of 4-6%. Thus, CaM/4Ca²⁺ samples high energy local minima comprising a few discrete substates of increasing compactness in a rugged energy landscape.

Paramagnetic Chemical Probes for Studying Biological Macromolecules

Paramagnetic chemical probes have been used in electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) spectroscopy for more than four decades. Recent years witnessed a great increase in the variety of probes for the study of biological macromolecules (proteins, nucleic acids, and oligosaccharides). This Review aims to provide a comprehensive overview of the existing paramagnetic chemical probes, including chemical synthetic approaches, functional properties, and selected applications. Recent developments have seen, in particular, a rapid expansion of the range of lanthanoid probes with anisotropic magnetic susceptibilities for the generation of structural restraints based on residual dipolar couplings and pseudocontact shifts in solution and solid state NMR spectroscopy, mostly for protein studies. Also many new isotropic paramagnetic probes, suitable for NMR measurements of paramagnetic relaxation enhancements, as well as EPR spectroscopic studies (in particular double resonance techniques) have been developed and employed to investigate biological macromolecules. Notwithstanding the large number of reported probes, only few have found broad application and further development of probes for dedicated applications is foreseen.

DEER experiments reveal fundamental differences between calmodulin complexes with IQ and MARCKS peptides in solution

Calmodulin (CaM) is a calcium-binding protein that regulates the function of many proteins by indirectly conferring Ca²⁺ sensitivity, and it undergoes a large conformational change on partners' binding. We compared the solution binding mode of the target peptides MARCKS and IQ by double electron-electron resonance (DEER) distance measurements and paramagnetic NMR. We combined nitroxide and Gd(III) spin labels, including specific substitution of one of the Ca²⁺ ions in the CaM mutant N60D by a Gd(III) ion. The binding of MARCKS to holo-CaM resulted neither in a closed conformation nor in a unique relative orientation between the two CaM domains, in contrast with the crystal structure. Binding of IQ to holo-CaM did generate a closed conformation. Using elastic network modeling and 12 distance restraints obtained from multiple holo-CaM/IQ DEER data, we derived a model of the solution structure, which is in reasonable agreement with the crystal structure.

Structure determination of high-energy states in a dynamic protein ensemble

Macromolecular function frequently requires that proteins change conformation into high-energy states^1-4. However, methods for solving the structures of these functionally essential, lowly populated states are lacking. Here we develop a method for high-resolution structure determination of minorly populated states by coupling NMR spectroscopy-derived pseudocontact shifts⁵ (PCSs) with Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion⁶ (PCS-CPMG). Our approach additionally defines the corresponding kinetics and thermodynamics of high-energy excursions, thereby characterizing the entire free-energy landscape. Using a large set of simulated data for adenylate kinase (Adk), calmodulin and Src kinase, we find that high-energy PCSs accurately determine high-energy structures (with a root mean squared deviation of less than 3.5 angström). Applying our methodology to Adk during catalysis, we find that the high-energy excursion involves surprisingly small openings of the AMP and ATP lids. This previously unresolved high-energy structure solves a longstanding controversy about conformational interconversions that are rate-limiting for catalysis. Primed for either substrate binding or product release, the high-energy structure of Adk suggests a two-step mechanism combining conformational selection to this state, followed by an induced-fit step into a fully closed state for catalysis of the phosphoryl-transfer reaction. Unlike other methods for resolving high-energy states, such as cryo-electron microscopy and X-ray crystallography, our solution PCS-CPMG approach excels in cases involving domain rearrangements of smaller systems (less than 60 kDa) and populations as low as 0.5%, and enables the simultaneous determination of protein structure, kinetics and thermodynamics while proteins perform their function.

Time-resolved DEER EPR and solid-state NMR afford kinetic and structural elucidation of substrate binding to Ca2+-ligated calmodulin

Complex formation between calmodulin and target proteins underlies numerous calcium signaling processes in biology, yet structural and mechanistic details, which entail major conformational changes in both calmodulin and its substrates, have been unclear. We show that a combination of time-resolved electron paramagnetic and NMR measurements can elucidate the molecular mechanism, at the quantitative kinetic and structural levels, of the binding pathway of a peptide substrate from skeletal muscle myosin light-chain kinase to calcium-loaded calmodulin. The mechanism involves coupled folding and binding and comprises a bifurcated process, with rapid, direct complex formation when the peptide interacts first with the C-terminal domain of calmodulin or a slower, two-step complex formation when the peptide interacts initially with the N-terminal domain.

Recent advances in rapid mixing and freeze quenching have opened the path for time-resolved electron paramagnetic resonance (EPR)-based double electron-electron resonance (DEER) and solid-state NMR of protein–substrate interactions. DEER, in conjunction with phase memory time filtering to quantitatively extract species populations, permits monitoring time-dependent probability distance distributions between pairs of spin labels, while solid-state NMR provides quantitative residue-specific information on the appearance of structural order and the development of intermolecular contacts between substrate and protein. Here, we demonstrate the power of these combined approaches to unravel the kinetic and structural pathways in the binding of the intrinsically disordered peptide substrate (M13) derived from myosin light-chain kinase to the universal eukaryotic calcium regulator, calmodulin. Global kinetic analysis of the data reveals coupled folding and binding of the peptide associated with large spatial rearrangements of the two domains of calmodulin. The initial binding events involve a bifurcating pathway in which the M13 peptide associates via either its N- or C-terminal regions with the C- or N-terminal domains, respectively, of calmodulin/4Ca²⁺ to yield two extended “encounter” complexes, states A and A*, without conformational ordering of M13. State A is immediately converted to the final compact complex, state C, on a timescale τ ≤ 600 μs. State A*, however, only reaches the final complex via a collapsed intermediate B (τ ∼ 1.5 to 2.5 ms), in which the peptide is only partially ordered and not all intermolecular contacts are formed. State B then undergoes a relatively slow (τ ∼ 7 to 18 ms) conformational rearrangement to state C.

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.

Recent Developments in Data-Assisted Modeling of Flexible Proteins

Many proteins can fold into well-defined conformations. However, intrinsically-disordered proteins (IDPs) do not possess a defined structure. Moreover, folded multi-domain proteins often digress into alternative conformations. Collectively, the conformational dynamics enables these proteins to fulfill specific functions. Thus, most experimental observables are averaged over the conformations that constitute an ensemble. In this article, we review the recent developments in the concept and methods for the determination of the dynamic structures of flexible peptides and proteins. In particular, we describe ways to extract information from nuclear magnetic resonance small-angle X-ray scattering (SAXS), and chemical cross-linking coupled with mass spectroscopy (XL-MS) measurements. All these techniques can be used to obtain ensemble-averaged restraints or to re-weight the simulated conformational ensembles.

Pseudocontact Shifts in Biomolecular NMR Spectroscopy

Paramagnetic centers in biomolecules, such as specific metal ions that are bound to a protein, affect the nuclei in their surrounding in various ways. One of these effects is the pseudocontact shift (PCS), which leads to strong chemical shift perturbations of nuclear spins, with a remarkably long range of 50 Å and beyond. The PCS in solution NMR is an effect originating from the anisotropic part of the dipole-dipole interaction between the magnetic momentum of unpaired electrons and nuclear spins. The PCS contains spatial information that can be exploited in multiple ways to characterize structure, function, and dynamics of biomacromolecules. It can be used to refine structures, magnify effects of dynamics, help resonance assignments, allows for an intermolecular positioning system, and gives structural information in sensitivity-limited situations where all other methods fail. Here, we review applications of the PCS in biomolecular solution NMR spectroscopy, starting from early works on natural metalloproteins, following the development of non-natural tags to chelate and attach lanthanoid ions to any biomolecular target to advanced applications on large biomolecular complexes and inside living cells. We thus hope to not only highlight past applications but also shed light on the tremendous potential the PCS has in structural biology.

Advances in NMR Spectroscopy of Weakly Aligned Biomolecular Systems

The measurement and application of residual dipolar couplings (RDCs) in solution NMR studies of biological macromolecules has become well established over the past quarter of a century. Numerous methods for generating the requisite anisotropic orientational molecular distribution have been demonstrated, each with its specific strengths and weaknesses. In parallel, an enormous number of pulse schemes have been introduced to measure the many different types of RDCs, ranging from the most widely measured backbone amide ¹⁵N-¹H RDCs, to ¹H-¹H RDCs and couplings between low-γ nuclei. Applications of RDCs range from structure validation and refinement to the determination of relative domain orientations, the measurement of backbone and domain motions, and de novo structure determination. Nevertheless, it appears that the power of the RDC methodology remains underutilized. This review aims to highlight the practical aspects of sample preparation and RDC measurement while describing some of the most straightforward applications that take advantage of the exceptionally precise information contained in such data. Some emphasis will be placed on more recent developments that enable the accurate measurement of RDCs in larger systems, which is key to the ongoing shift in focus of biological NMR spectroscopy from structure determination toward gaining improved understanding of how molecular flexibility drives protein function.

Reconstruction of Coupled Intra- and Interdomain Protein Motion from Nuclear and Electron Magnetic Resonance

Proteins composed of multiple domains allow for structural heterogeneity and interdomain dynamics that may be vital for function. Intradomain structures and dynamics can influence interdomain conformations and vice versa. However, no established structure determination method is currently available that can probe the coupling of these motions. The protein Pin1 contains separate regulatory and catalytic domains that sample "extended" and "compact" states, and ligand binding changes this equilibrium. Ligand binding and interdomain distance have been shown to impact the activity of Pin1, suggesting interdomain allostery. In order to characterize the conformational equilibrium of Pin1, we describe a novel method to model the coupling between intra- and interdomain dynamics at atomic resolution using multistate ensembles. The method uses time-averaged nuclear magnetic resonance (NMR) restraints and double electron-electron resonance (DEER) data that resolve distance distributions. While the intradomain calculation is primarily driven by exact nuclear Overhauser enhancements (eNOEs), J couplings, and residual dipolar couplings (RDCs), the relative domain distribution is driven by paramagnetic relaxation enhancement (PREs), RDCs, interdomain NOEs, and DEER. Our data support a 70:30 population of the compact and extended states in apo Pin1. A multistate ensemble describes these conformations simultaneously, with distinct conformational differences located in the interdomain interface stabilizing the compact or extended states. We also describe correlated conformations between the catalytic site and interdomain interface that may explain allostery driven by interdomain contact.

Conformational Space Sampled by Domain Reorientation of Linear Diubiquitin Reflected in Its Binding Mode for Target Proteins

Linear polyubiquitin chains regulate diverse signaling proteins, in which the chains adopt various conformations to recognize different target proteins. Thus, the structural plasticity of the chains plays an important role in controlling the binding events. Herein, paramagnetic NMR spectroscopy is employed to explore the conformational space sampled by linear diubiquitin, a minimal unit of linear polyubiquitin, in its free state. Rigorous analysis of the data suggests that, regarding the relative positions of the ubiquitin units, particular regions of conformational space are preferentially sampled by the molecule. By combining these results with further data collected for charge-reversal derivatives of linear diubiquitin, structural insights into the factors underlying the binding events of linear diubiquitin are obtained.

Analyzing In Silico the Relationship Between the Activation of the Edema Factor and Its Interaction With Calmodulin

Molecular dynamics (MD) simulations have been recorded on the complex between the edema factor (EF) of Bacilllus anthracis and calmodulin (CaM), starting from a structure with the orthosteric inhibitor adefovir bound in the EF catalytic site. The starting structure has been destabilized by alternately suppressing different co-factors, such as adefovir ligand or ions, revealing several long-distance correlations between the conformation of CaM, the geometry of the CaM/EF interface, the enzymatic site and the overall organization of the complex. An allosteric communication between CaM/EF interface and the EF catalytic site, highlighted by these correlations, was confirmed by several bioinformatics approaches from the literature. A network of hydrogen bonds and stacking interactions extending from the helix V of of CaM, and the residues of the switches A, B and C, and connecting to catalytic site residues, is a plausible candidate for the mediation of allosteric communication. The greatest variability in volume between the different MD conditions was also found for cavities present at the EF/CaM interface and in the EF catalytic site. The similarity between the predictions from literature and the volume variability might introduce the volume variability as new descriptor of allostery.

Magnetically Induced Alignment of Natural Products for Stereochemical Structure Determination via NMR

Anisotropic NMR has gained increasing popularity to determine the structure and specifically the configuration of small, flexible, non-crystallizable molecules. However, it suffers from the necessity to dissolve the analyte in special media such as liquid crystals or polymer gels. Generally, small degrees of alignment are also caused by an anisotropic magnetic susceptibility of the molecule, for example, induced by aromatic moieties. For this mechanism, the alignment can be predicted via density functional theory. Here we show that both residual dipolar couplings and residual chemical shift anisotropies can be acquired from natural products without special sample preparation using magnetically induced alignment. On the two examples of the novel natural product gymnochrome G and the alkaloid strychnine, these data, together with the predicted alignment, yield the correct configuration with high certainty.

Lanthanide Tagging of Oligonucleotides to Nucleobase for Paramagnetic NMR

Although lanthanide tags, which have large anisotropic magnetic susceptibilities, have already been introduced to enrich NMR parameters by long‐range pseudoconact shifts (PCSs) and residual dipolar couplings (RDCs) of proteins, their application to nucleotides has so far been limited to one previous report, due to the high affinities of lanthanides for the phosphodiester backbone of nucleotides and difficult organic synthesis. Herein, we report successful attachment of a lanthanide tag to a chemically synthesized oligonucleotide via a disulfide bond. NMR experiments reveal PCSs of up to 1 ppm and H−H RDCs of up to 8 Hz at 950 MHz. Although weaker magnetic alignment was achieved than with proteins, the paramagnetic data could be fitted to the known structure of the DNA, taking the mobility of the tag into account. While further rigidification of the tag is desirable, this tag could also be used to measure heteronuclear RDCs of ¹³C,¹⁵N‐labeled chemically synthesized DNA and RNA.

Modulating the Stiffness of the Myosin VI Single α-Helical Domain

Highly charged, single α-helical (SAH) domains contain a high percentage of Arg, Lys, and Glu residues. Their dynamic salt bridge pairing creates the exceptional stiffness of these helical rods, with a persistence length of more than 200 Å for the myosin VI SAH domain. With the aim of modulating the stiffness of the helical structure, we investigated the effect, using NMR spectroscopy, of substituting key charged Arg, Lys, Glu, and Asp residues by Gly or His. Results indicate that such mutations result in the transient breaking of the helix at the site of mutation but with noticeable impact on amide hydrogen exchange rates extending as far as ±2 helical turns, pointing to a substantial degree of cooperativity in SAH stability. Whereas a single Gly substitution caused transient breaks ∼20% of the time, two consecutive Gly substitutions break the helix ∼65% of the time. NMR relaxation measurements indicate that the exchange rate between an intact and a broken helix is fast (>300,000 s^-1) and that for the wild-type sequence, the finite persistence length is dominated by thermal fluctuations of backbone torsion angles and H-bond lengths, not by transient helix breaking. The double mutation D27H/E28H causes a pH-dependent fraction of helix disruption, in which the helix breakage increases from 26% at pH 7.5 to 53% at pH 5.5. The ability to modulate helical integrity by pH may enable incorporation of externally tunable dynamic components in the design of molecular machines.

Protein NMR: Boundless opportunities

Over the past approximately three decades, isotope-directed NMR spectroscopy has become a powerful method for determining 3D structures of biological macromolecules and their complexes in solution. From a structural perspective NMR provides an invaluable tool for studying systems that are not amenable to crystallization, including intrinsically disordered proteins and weak complexes. In contrast to both X-ray crystallography and cryo-electron microscopy which afford a largely static view of the systems under consideration, the great power of NMR lies in its ability to quantitatively probe exchange dynamics between interconverting states, and to reveal and characterize at atomic resolution the existence of transient states that may be populated at levels as low as 1%. Such "excited" states play a key role in macromolecular recognition, allostery, signal transduction and macromolecular assembly, including the initial events involved in aggregation and amyloid formation. Optimal application of NMR to such systems of fundamental biological interest requires a sound footing of the physical underpinnings of today's and tomorrow's sophisticated NMR experiments.

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’.

Dynamic tuning of FRET in a green fluorescent protein biosensor

Förster resonance energy transfer (FRET) between mutants of green fluorescent protein is widely used to monitor protein-protein interactions and as a readout mode in fluorescent biosensors. Despite the fundamental importance of distance and molecular angles of fluorophores to each other, structural details on fluorescent protein FRET have been missing. Here, we report the high-resolution x-ray structure of the fluorescent proteins mCerulean3 and cpVenus within the biosensor Twitch-2B, as they undergo FRET and characterize the dynamics of this biosensor with B 0 2 -dependent paramagnetic nuclear magnetic resonance at 900 MHz and 1.1 GHz. These structural data provide the unprecedented opportunity to calculate FRET from the x-ray structure and to compare it to experimental data in solution. We find that interdomain dynamics limits the FRET effect and show that a rigidification of the sensor further enhances FRET.

Joint X-ray/NMR structure refinement of multidomain/multisubunit systems

Data integration in structural biology has become a paradigm for the characterization of biomolecular systems, and it is now accepted that combining different techniques can fill the gaps in each other's blind spots. In this frame, one of the combinations, which we have implemented in REFMAC-NMR, is residual dipolar couplings from NMR together with experimental data from X-ray diffraction. The first are exquisitely sensitive to the local details but does not give any information about overall shape, whereas the latter encodes more the information about the overall shape but at the same time tends to miss the local details even at the highest resolutions. Once crystals are obtained, it is often rather easy to obtain a complete X-ray dataset, however it is time-consuming to obtain an exhaustive NMR dataset. Here, we discuss the effect of including a-priori knowledge on the properties of the system to reduce the number of experimental data needed to obtain a more complete picture. We thus introduce a set of new features of REFMAC-NMR that allow for improved handling of RDC data for multidomain proteins and multisubunit biomolecular complexes, and encompasses the use of pseudo-contact shifts as an additional source of NMR-based information. The new feature may either help in improving the refinement, or assist in spotting differences between the crystal and the solution data. We show three different examples where NMR and X-ray data can be reconciled to a unique structural model without invoking mobility.

Remarkable Rigidity of the Single α-Helical Domain of Myosin-VI As Revealed by NMR Spectroscopy

Although the α-helix has long been recognized as an all-important element of secondary structure, it generally requires stabilization by tertiary interactions with other parts of a protein's structure. Highly charged single α-helical (SAH) domains, consisting of a high percentage (>75%) of Arg, Lys, and Glu residues, are exceptions to this rule but have been difficult to characterize structurally. Our study focuses on the 68-residue medial tail domain of myosin-VI, which is found to contain a highly ordered α-helical structure extending from Glu-6 to Lys-63. High hydrogen exchange protection factors (15-150), small (ca. 4 Hz) 3 JHNHα couplings, and a near-perfect fit to an ideal model α-helix for its residual dipolar couplings (RDCs), measured in a filamentous phage medium, support the high regularity of this helix. Remarkably, the hydrogen exchange rates are far more homogeneous than the protection factors derived from them, suggesting that for these transiently broken helices the intrinsic exchange rates derived from the amino acid sequence are not appropriate reference values. 15N relaxation data indicate a very high degree of rotational diffusion anisotropy ( D∥/ D⊥ ≈ 7.6), consistent with the hydrodynamic behavior predicted for such a long, nearly straight α-helix. Alignment of the helix by a paramagnetic lanthanide ion attached to its N-terminal region shows a decrease in alignment as the distance from the tagging site increases. This decrease yields a precise measure for the persistence length of 224 ± 10 Å at 20 °C, supporting the idea that the role of the SAH helix is to act as an extension of the myosin-VI lever arm.

The theory of frame ordering: observing motions in calmodulin complexes

Large scale functional motions of molecules are studied experimentally using numerous molecular and biophysics techniques, the data from which are subsequently interpreted using diverse models of Brownian molecular dynamics. To unify all rotational physics techniques and motional models, the frame order tensor - a universal statistical mechanics theory based on the rotational ordering of rigid body frames - is herein formulated. The frame ordering is the fundamental physics that governs how motions modulate rotational molecular physics and it defines the properties and maximum information content encoded in the observable physics. Using the tensor to link residual dipolar couplings and pseudo-contact shifts, two distinct information-rich and atomic-level biophysical measurements from the field of nuclear magnetic resonance spectroscopy, to a number of basic mechanical joint models, a highly dynamic state of calmodulin (CaM) bound to a target peptide in a tightly closed conformation was observed. Intra- and inter-domain motions reveal the CaM complex to be entropically primed for peptide release.

Paramagnetic NMR in solution and the solid state

The field of paramagnetic NMR has expanded considerably in recent years. This review addresses both the theoretical description of paramagnetic NMR, and the way in which it is currently practised. We provide a review of the theory of the NMR parameters of systems in both solution and the solid state. Here we unify the different languages used by the NMR, EPR, quantum chemistry/DFT, and magnetism communities to provide a comprehensive and coherent theoretical description. We cover the theory of the paramagnetic shift and shift anisotropy in solution both in the traditional formalism in terms of the magnetic susceptibility tensor, and using a more modern formalism employing the relevant EPR parameters, such as are used in first-principles calculations. In addition we examine the theory first in the simple non-relativistic picture, and then in the presence of spin-orbit coupling. These ideas are then extended to a description of the paramagnetic shift in periodic solids, where it is necessary to include the bulk magnetic properties, such as magnetic ordering at low temperatures. The description of the paramagnetic shift is completed by describing the current understanding of such shifts due to lanthanide and actinide ions. We then examine the paramagnetic relaxation enhancement, using a simple model employing a phenomenological picture of the electronic relaxation, and again using a more complex state-of-the-art theory which incorporates electronic relaxation explicitly. An additional important consideration in the solid state is the impact of bulk magnetic susceptibility effects on the form of the spectrum, where we include some ideas from the field of classical electrodynamics. We then continue by describing in detail the solution and solid-state NMR methods that have been deployed in the study of paramagnetic systems in chemistry, biology, and the materials sciences. Finally we describe a number of case studies in paramagnetic NMR that have been specifically chosen to highlight how the theory in part one, and the methods in part two, can be used in practice. The systems chosen include small organometallic complexes in solution, solid battery electrode materials, metalloproteins in both solution and the solid state, systems containing lanthanide ions, and multi-component materials used in pharmaceutical controlled-release formulations that have been doped with paramagnetic species to measure the component domain sizes.

Assessing protein conformational landscapes: integration of DEER data in Maximum Occurrence analysis

The properties of the conformational landscape of a biomolecule are of capital importance to understand its function. It is widely accepted that a statistical ensemble is far more representative than a single structure, especially for proteins with disordered regions. While experimental data provide the most important handle on the conformational variability that the system is experiencing, they usually report on either time or ensemble averages. Since the available conformations largely outnumber the (independent) available experimental data, the latter can be equally well reproduced by a variety of ensembles. We have proposed the Maximum Occurrence (MaxOcc) approach to provide an upper bound of the statistical weight of each conformation. This method is expected to converge towards the true statistical weights by increasing the number of independent experimental datasets. In this paper we explore the ability of DEER (Double Electron Electron Resonance) data, which report on the distance distribution between two spin labels attached to a biomolecule, to restrain the MaxOcc values and its complementarity to previously introduced experimental techniques such as NMR and Small-Angle X-ray Scattering. We here present the case of Ca2+ bound calmodulin (CaM) as a test case and show that DEER data impose a sizeable reduction of the conformational space described by high MaxOcc conformations.

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.

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.

Developing a molecular dynamics force field for both folded and disordered protein states

Many proteins that perform important biological functions are completely or partially disordered under physiological conditions. Molecular dynamics simulations could be a powerful tool for the structural characterization of such proteins, but it has been unclear whether the physical models (force fields) used in simulations are sufficiently accurate. Here, we systematically compare the accuracy of a number of different force fields in simulations of both ordered and disordered proteins, finding that each force field has strengths and limitations. We then describe a force field that substantially improves on the state-of-the-art accuracy for simulations of disordered proteins without sacrificing accuracy for folded proteins, thus broadening the range of biological systems amenable to molecular dynamics simulations.

Molecular dynamics (MD) simulation is a valuable tool for characterizing the structural dynamics of folded proteins and should be similarly applicable to disordered proteins and proteins with both folded and disordered regions. It has been unclear, however, whether any physical model (force field) used in MD simulations accurately describes both folded and disordered proteins. Here, we select a benchmark set of 21 systems, including folded and disordered proteins, simulate these systems with six state-of-the-art force fields, and compare the results to over 9,000 available experimental data points. We find that none of the tested force fields simultaneously provided accurate descriptions of folded proteins, of the dimensions of disordered proteins, and of the secondary structure propensities of disordered proteins. Guided by simulation results on a subset of our benchmark, however, we modified parameters of one force field, achieving excellent agreement with experiment for disordered proteins, while maintaining state-of-the-art accuracy for folded proteins. The resulting force field, a99SB-disp, should thus greatly expand the range of biological systems amenable to MD simulation. A similar approach could be taken to improve other force fields.

Gold nanocrystal labels provide a sequence-to-3D structure map in SAXS reconstructions

Small-angle x-ray scattering (SAXS) is a powerful technique to probe the structure of biological macromolecules and their complexes under virtually arbitrary solution conditions, without the need for crystallization. While it is possible to reconstruct molecular shapes from SAXS data ab initio, the resulting electron density maps have a resolution of ~1 nm and are often insufficient to reliably assign secondary structure elements or domains. We show that SAXS data of gold-labeled samples significantly enhance the information content of SAXS measurements, allowing the unambiguous assignment of macromolecular sequence motifs to specific locations within a SAXS structure. We first demonstrate our approach for site-specifically internally and end-labeled DNA and an RNA motif. In addition, we present a protocol for highly uniform and site-specific labeling of proteins with small (~1.4 nm diameter) gold particles and apply our method to the signaling protein calmodulin. In all cases, the position of the small gold probes can be reliably identified in low-resolution electron density maps. Enhancing low-resolution measurements by site-selective gold labeling provides an attractive approach to aid modeling of a large range of macromolecular systems.

Stable and rigid DTPA-like paramagnetic tags suitable for in vitro and in situ protein NMR analysis

Organic synthesis of a ligand with high binding affinities for paramagnetic lanthanide ions is an effective way of generating paramagnetic effects on proteins. These paramagnetic effects manifested in high-resolution NMR spectroscopy are valuable dynamic and structural restraints of proteins and protein-ligand complexes. A paramagnetic tag generally contains a metal chelating moiety and a reactive group for protein modification. Herein we report two new DTPA-like tags, 4PS-PyDTTA and 4PS-6M-PyDTTA that can be site-specifically attached to a protein with a stable thioether bond. Both protein-tag adducts form stable lanthanide complexes, of which the binding affinities and paramagnetic tensors are tunable with respect to the 6-methyl group in pyridine. Paramagnetic relaxation enhancement (PRE) effects of Gd(III) complex on protein-tag adducts were evaluated in comparison with pseudocontact shift (PCS), and the results indicated that both 4PS-PyDTTA and 4PS-6M-PyDTTA tags are rigid and present high-quality PREs that are crucially important in elucidation of the dynamics and interactions of proteins and protein-ligand complexes. We also show that these two tags are suitable for in-situ protein NMR analysis.

Statistical Measures to Quantify Similarity between Molecular Dynamics Simulation Trajectories

Molecular dynamics simulation is commonly employed to explore protein dynamics. Despite the disparate timescales between functional mechanisms and molecular dynamics (MD) trajectories, functional differences are often inferred from differences in conformational ensembles between two proteins in structure-function studies that investigate the effect of mutations. A common measure to quantify differences in dynamics is the root mean square fluctuation (RMSF) about the average position of residues defined by Cα-atoms. Using six MD trajectories describing three native/mutant pairs of beta-lactamase, we make comparisons with additional measures that include Jensen-Shannon, modifications of Kullback-Leibler divergence, and local p-values from 1-sample Kolmogorov-Smirnov tests. These additional measures require knowing a probability density function, which we estimate by using a nonparametric maximum entropy method that quantifies rare events well. The same measures are applied to distance fluctuations between Cα-atom pairs. Results from several implementations for quantitative comparison of a pair of MD trajectories are made based on fluctuations for on-residue and residue-residue local dynamics. We conclude that there is almost always a statistically significant difference between pairs of 100 ns all-atom simulations on moderate-sized proteins as evident from extraordinarily low p-values.

Utilizing tagged paramagnetic shift reagents to monitor protein dynamics by NMR

Calmodulin is a ubiquitous calcium sensor protein, known to serve as a critical interaction hub with a wide range of signaling partners. While the holo form of calmodulin (CaM-4Ca²⁺) has a well-defined ground state structure, it has been shown to undergo exchange, on a millisecond timescale, to a conformation resembling that of the peptide bound state. Tagged paramagnetic relaxation agents have been previously used to identify long-range dipolar interactions through relaxation effects on nuclear spins of interest. In the case of calmodulin, this lead to the determination of the relative orientation of the N- and C-terminal domains and the presence of a weakly populated peptide bound like state. Here, we make use of pseudocontact shifts from a tagged paramagnetic shift reagent which allows us to define minor states both in ¹³C and ¹⁵N NMR spectra and through ¹³C- and ¹⁵N-edited ¹H-CPMG relaxation dispersion measurements. This is validated by pulsed EPR (DEER) spectroscopy which reveals an ensemble consisting of a compact peptide-bound like conformer, an intermediate peptide-bound like conformer, and a (dumbbell-like) extended ground state conformer of CaM-4Ca²⁺, where addition of the MLCK peptide increases the population of the peptide-bound conformers. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

Conformational landscape mapping the difference between N-lobes and C-lobes of calmodulin

Calmodulin is a calcium binding protein that consists of four EF-hand domains. The two EF-lobes of calmodulin, called the N-lobe and the C-lobe, arose from duplication and fusion of a precursor EF-hand. The amino acid sequences and the structures of the N-lobe and of the C-lobe are quite similar to each other. The N-lobe and the C-lobe, however, have subtle differences in structure and function. We analyzed the helix positions of calmodulin lobes by the alignment with the pseudo-two fold axis of the EF-lobe. We made a map of conformational landscape of helix positions. The four states of the EF-lobe appeared on two lines in the landscape; these two lines show the trajectory of opening and closing of the EF-lobe. For the N-lobe of calmodulin, the calcium bound form and the apo-forms are on the lower line. The two apo-forms of the C-lobe of calmodulin, with target and without target, are on the upper line. The calcium bound form of the C-lobe is on the lower line. The rearrangement of helix interaction between two the EF-hands is necessary for calcium binding in the C-lobe. The hydrophobic packing in the apo-form of the N-lobe is similar to the packing of the N- and C-lobes of the calcium bound form. However, the packing of C-lobe side chains in the apo-form is different from these other three structures. Our detailed analysis should serve as an example that can be applied to other proteins that undergo changes in conformation upon binding effectors.

Perspectives on paramagnetic NMR from a life sciences infrastructure

The effects arising in NMR spectroscopy because of the presence of unpaired electrons, collectively referred to as "paramagnetic NMR" have attracted increasing attention over the last decades. From the standpoint of the structural and mechanistic biology, paramagnetic NMR provides long range restraints that can be used to assess the accuracy of crystal structures in solution and to improve them by simultaneous refinements through NMR and X-ray data. These restraints also provide information on structure rearrangements and conformational variability in biomolecular systems. Theoretical improvements in quantum chemistry calculations can nowadays allow for accurate calculations of the paramagnetic data from a molecular structural model, thus providing a tool to refine the metal coordination environment by matching the paramagnetic effects observed far away from the metal. Furthermore, the availability of an improved technology (higher fields and faster magic angle spinning) has promoted paramagnetic NMR applications in the fast-growing area of biomolecular solid-state NMR. Major improvements in dynamic nuclear polarization have been recently achieved, especially through the exploitation of the Overhauser effect occurring through the contact-driven relaxation mechanism: the very large enhancement of the ¹³C signal observed in a variety of liquid organic compounds at high fields is expected to open up new perspectives for applications of solution NMR.

Recent excitements in protein NMR: Large proteins and biologically relevant dynamics

The advent of Transverse Relaxation Optimized SpectroscopY (TROSY) and perdeuteration allowed biomolecular NMR spectroscopists to overcome the size limitation barrier (approx. 20 kDa) in de novo structure determination of proteins. The utility of these techniques was immediately demonstrated on large proteins and protein complexes (e.g. GroELGroES, ClpP protease, Hsp90-p53, 20S proteasome, etc.). Further, recent methodological developments such as Residual Dipolar Couplings and Paramagnetic Relaxation Enhancement allowed accurate measurement of long-range structural restraints. Additionally, Carr-Purcell-Meiboom-Gill (CPMG), rotating frame relaxation experiments (R1(rho)) and saturation transfer experiments (CEST and DEST) created never-before accessibility to the (mu)s-ms timescale dynamic parameters that led to the deeper understanding of biological processes. Meanwhile, the excitement in the field continued with a series of developments in the fast data acquisition methods allowing rapid structural studies on less stable proteins. This review aims to discuss important developments in the field of biomolecular NMR spectroscopy in the recent past, i.e., in the post TROSY era. These developments not only gave access to the structural studies of large protein assemblies, but also revolutionized tools in the arsenal of today's biomolecular NMR and point to a bright future of biomolecular NMR spectroscopy.

Block-restraining of residual dipolar couplings to allow fluctuating relative alignments of molecular subdomains

Residual dipolar couplings (RDCs), unlike most other types of NMR observables, provide orientational information, reporting on the alignment of inter-spin vectors (ISVs) relative to the magnetic field. A great challenge in using experimental RDCs to restrain molecular dynamics (MD) simulations is how to represent this alignment. An alignment tensor is often used to parameterise the contribution of molecular alignment to the angular dependence of RDCs. All ISVs that share the same tensor have fixed relative alignment, i.e. if just one tensor is used, the molecule is internally rigid. Here we propose and illustrate a method for subdividing molecules into individually aligned blocks during MD simulations restrained to fit RDCs. This allows the relative orientation of each block to vary during the simulation, which in turn ensures that the internal structure of each block is more realistically reproduced.

Modeling Protein Excited-state Structures from "Over-length" Chemical Cross-links

Chemical cross-linking coupled with mass spectroscopy (CXMS) provides proximity information for the cross-linked residues and is used increasingly for modeling protein structures. However, experimentally identified cross-links are sometimes incompatible with the known structure of a protein, as the distance calculated between the cross-linked residues far exceeds the maximum length of the cross-linker. The discrepancies may persist even after eliminating potentially false cross-links and excluding intermolecular ones. Thus the "over-length" cross-links may arise from alternative excited-state conformation of the protein. Here we present a method and associated software DynaXL for visualizing the ensemble structures of multidomain proteins based on intramolecular cross-links identified by mass spectrometry with high confidence. Representing the cross-linkers and cross-linking reactions explicitly, we show that the protein excited-state structure can be modeled with as few as two over-length cross-links. We demonstrate the generality of our method with three systems: calmodulin, enzyme I, and glutamine-binding protein, and we show that these proteins alternate between different conformations for interacting with other proteins and ligands. Taken together, the over-length chemical cross-links contain valuable information about protein dynamics, and our findings here illustrate the relationship between dynamic domain movement and protein function.