A model of interdomain mobility in a multidomain protein

Structural Insights into Linkage-Specific Ubiquitin Chains Using Ion Mobility Mass Spectrometry

The structural characterization and differentiation of four types of oligoubiquitin conjugates [linear (Met1)-, Lys11-, Lys48-, Lys63-linked di-, tri-, and tetraubiquitin chains] using ion mobility mass spectrometry are reported. A comparison of collision cross sections for the same linkage of di-, tri-, and tetraubiquitin chains shows differences in conformational elongation for higher charge states due to the interplay of linkage-derived structure and Coulombic repulsion. For di- and triubiquitin chains, this elongation results in a single narrow feature representing an elongated conformation type for multiple higher charge state species. In contrast, higher charge state tetraubiquitin species do not form a single conformer type as readily. A comparison of different linkages in tetraubiquitin chains reveals greater similarity in conformation type at lower charge states; with increasing charge state, the four linkage types diverge in the relative proportions of elongated conformer types with Met1- ≥ Lys11- > Lys63- > Lys48-linkage. These differences in conformational trends could be discussed with respect to biological functions of linkage-specific polyubiquitinated proteins.

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.

High-Resolution Conformational Analysis of RGDechi-Derived Peptides Based on a Combination of NMR Spectroscopy and MD Simulations

The crucial role of integrin in pathological processes such as tumor progression and metastasis formation has inspired intense efforts to design novel pharmaceutical agents modulating integrin functions in order to provide new tools for potential therapies. In the past decade, we have investigated the biological proprieties of the chimeric peptide RGDechi, containing a cyclic RGD motif linked to an echistatin C-terminal fragment, able to specifically recognize αvβ3 without cross reacting with αvβ5 and αIIbβ3 integrin. Additionally, we have demonstrated using two RGDechi-derived peptides, called RGDechi1-14 and ψRGDechi, that chemical modifications introduced in the C-terminal part of the peptide alter or abolish the binding to the αvβ3 integrin. Here, to shed light on the structural and dynamical determinants involved in the integrin recognition mechanism, we investigate the effects of the chemical modifications by exploring the conformational space sampled by RGDechi1-14 and ψRGDechi using an integrated natural-abundance NMR/MD approach. Our data demonstrate that the flexibility of the RGD-containing cycle is driven by the echistatin C-terminal region of the RGDechi peptide through a coupling mechanism between the N- and C-terminal regions.

On the use of residual dipolar couplings in multi-state structure calculation of two-domain proteins

Residual dipolar couplings (RDCs) are powerful nuclear magnetic resonance (NMR) probes for the structure calculation of biomacromolecules. Typically, an alignment tensor that defines the orientation of the entire molecule relative to the magnetic field is determined either before refinement of individual bond vectors or simultaneously with this refinement. For single-domain proteins this approach works well since all bond vectors can be described within the same coordinate frame, which is given by the alignment tensor. However, novel approaches are sought after for systems where no universal alignment tensor can be used. Here, we present an approach that can be applied to two-domain proteins that enables the calculation of multiple states within each domain as well as with respect to the relative positions of the two domains.

Conformational Dynamics of Intrinsically Disordered Proteins Regulate Biomolecular Condensate Chemistry

Motions in biomolecules are critical for biochemical reactions. In cells, many biochemical reactions are executed inside of biomolecular condensates formed by ultradynamic intrinsically disordered proteins. A deep understanding of the conformational dynamics of intrinsically disordered proteins in biomolecular condensates is therefore of utmost importance but is complicated by diverse obstacles. Here we review emerging data on the motions of intrinsically disordered proteins inside of liquidlike condensates. We discuss how liquid–liquid phase separation modulates internal motions across a wide range of time and length scales. We further highlight the importance of intermolecular interactions that not only drive liquid–liquid phase separation but appear as key determinants for changes in biomolecular motions and the aging of condensates in human diseases. The review provides a framework for future studies to reveal the conformational dynamics of intrinsically disordered proteins in the regulation of biomolecular condensate chemistry.

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.

An Integrative Approach to Determine 3D Protein Structures Using Sparse Paramagnetic NMR Data and Physical Modeling

Paramagnetic nuclear magnetic resonance (NMR) methods have emerged as powerful tools for structure determination of large, sparsely protonated proteins. However traditional applications face several challenges, including a need for large datasets to offset the sparsity of restraints, the difficulty in accounting for the conformational heterogeneity of the spin-label, and noisy experimental data. Here we propose an integrative approach to structure determination combining sparse paramagnetic NMR with physical modelling to infer approximate protein structural ensembles. We use calmodulin in complex with the smooth muscle myosin light chain kinase peptide as a model system. Despite acquiring data from samples labeled only at the backbone amide positions, we are able to produce an ensemble with an average RMSD of ∼2.8 Å from a reference X-ray crystal structure. Our approach requires only backbone chemical shifts and measurements of the paramagnetic relaxation enhancement and residual dipolar couplings that can be obtained from sparsely labeled samples.

In vivo modulation of ubiquitin chains by N-methylated non-proteinogenic cyclic peptides

Cancer and other disease states can change the landscape of proteins post-translationally tagged with ubiquitin (Ub) chains. Molecules capable of modulating Ub chains are potential therapeutic agents, but their discovery represents a significant challenge. Recently, it was shown that de novo cyclic peptides, selected from trillion-member random libraries, are capable of binding particular Ub chains. However, these peptides were overwhelmingly proteinogenic, so the prospect of in vivo activity was uncertain. Here, we report the discovery of small, non-proteinogenic cyclic peptides, rich in non-canonical features like N-methylation, which can tightly and specifically bind Lys48-linked Ub chains. These peptides engage three Lys48-linked Ub units simultaneously, block the action of deubiquitinases and the proteasome, induce apoptosis in vitro, and attenuate tumor growth in vivo. This highlights the potential of non-proteinogenic cyclic peptide screening to rapidly find in vivo-active leads, and the targeting of ubiquitin chains as a promising anti-cancer mechanism of action.

An Extended Conformation for K48 Ubiquitin Chains Revealed by the hRpn2:Rpn13:K48-Diubiquitin Structure

Rpn13/Adrm1 is recruited to the proteasome by PSMD1/Rpn2, where it serves as a substrate receptor that binds preferentially to K48-linked ubiquitin chains, an established signal for protein proteolysis. Here, we use NMR to solve the structure of hRpn13 Pru:hRpn2 (940-953):K48-diubiquitin. Surprisingly, hRpn2-bound hRpn13 selects a dynamic, extended conformation of K48-diubiquitin that is unique from previously determined structures. NMR experiments on free K48-diubiquitin demonstrate the presence of the reported "closed" conformation observed by crystallography, but also this more extended state, in which the hRpn13-binding surface is exposed. This extended K48-diubiquitin conformation is defined by interactions between L73 from G76-linked (distal) ubiquitin and a Y59-centered surface of K48-linked (proximal) ubiquitin. Furthermore, hRpn13 exchanges between the two ubiquitins within 100 ms, although prefers the proximal ubiquitin due to interactions with the K48 linker region. Altogether, these data lead to a revised model of how ubiquitinated substrates interact with the proteasome.

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.

Quantum Stochastic Trajectories: The Fokker-Planck-Bohm Equation Driven by the Reduced Density Matrix

The quantum molecular trajectory is the deterministic trajectory, arising from the Bohm theory, that describes the instantaneous positions of the nuclei of molecules by assuring the agreement with the predictions of quantum mechanics. Therefore, it provides the suitable framework for representing the geometry and the motions of molecules without neglecting their quantum nature. However, the quantum molecular trajectory is extremely demanding from the computational point of view, and this strongly limits its applications. To overcome such a drawback, we derive a stochastic representation of the quantum molecular trajectory, through projection operator techniques, for the degrees of freedom of an open quantum system. The resulting Fokker-Planck operator is parametrically dependent upon the reduced density matrix of the open system. Because of the pilot role played by the reduced density matrix, this stochastic approach is able to represent accurately the main features of the open system motions both at equilibrium and out of equilibrium with the environment. To verify this procedure, the predictions of the stochastic and deterministic representation are compared for a model system of six interacting harmonic oscillators, where one oscillator is taken as the open quantum system of interest. The undeniable advantage of the stochastic approach is that of providing a simplified and self-contained representation of the dynamics of the open system coordinates. Furthermore, it can be employed to study the out of equilibrium dynamics and the relaxation of quantum molecular motions during photoinduced processes, like photoinduced conformational changes and proton transfers.

Quantum stochastic trajectories: the Smoluchowski-Bohm equation

Molecular systems are quantum systems, but the complete characterization of molecular motions within a fully quantum framework might appear to be an unfeasible task because it would require that the actual nuclear positions are established at any time. One would like to use a quantum molecular trajectory that defines the instantaneous nuclear positions and satisfies the predictions of quantum mechanics in terms of its statistical properties. Even though it can be proven that the single Bohm trajectory provides a representation of the quantum molecular trajectory, this solves the issue only on a theoretical ground: exact solutions of the Schrödinger-Bohm dynamical system are extremely computationally demanding. Therefore, we derive a stochastic equation of Smoluchowski type from the Schrödinger-Bohm dynamics, through projection operator techniques, in order to characterize the molecular motions of open quantum systems. The main quantum features of the motions emerge from the equilibrium distribution, i.e., the wave function's squared modulus integrated on the environment degrees of freedom. Furthermore, we verify the accuracy of the stochastic equation by comparing its predictions with those of the deterministic dynamics for a model system of six interacting harmonic oscillators. The indisputable advantage of this full quantum mechanical approach is that of representing the molecular dynamics, which controls important phenomena like vibrational relaxation, conformational transitions and activated processes, in a self consistent way and at the low computational cost of solving simple stochastic equations.

Probing the Binding Modes of a Multidomain Protein to Lipid-based Nanoparticles by Relaxation-based NMR

The interactions of two model multidomain proteins-covalently linked diubiquitins, Ub₂-with lipid-based nanoparticles have been quantitatively probed by the measurements of NMR lifetime line broadening, ΔR₂. By combined analysis of ΔR₂ profiles arising from interactions with liposomes of varying sizes, an approach recently developed for the characterization of interactions of monoubiquitin with liposomes, we determine how the parameters of exchange (liposome binding) and dynamics of each individual domain of Ub₂ on the surface of liposomes change when the domains are covalently attached to one another by a flexible linker. Two different covalent linkages were used: K63-linked and K48-linked Ub₂. The possibility of three distinct modes of binding of Ub₂ to liposomes requires the introduction of simple but important modifications to the strategy of analysis originally developed for monoubiquitin.

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.

Investigating the Role of Large-Scale Domain Dynamics in Protein-Protein Interactions

Intrinsically disordered linkers provide multi-domain proteins with degrees of conformational freedom that are often essential for function. These highly dynamic assemblies represent a significant fraction of all proteomes, and deciphering the physical basis of their interactions represents a considerable challenge. Here we describe the difficulties associated with mapping the large-scale domain dynamics and describe two recent examples where solution state methods, in particular NMR spectroscopy, are used to investigate conformational exchange on very different timescales.

Characterizing Aciniform Silk Repetitive Domain Backbone Dynamics and Hydrodynamic Modularity

Spider aciniform (wrapping) silk is a remarkable fibrillar biomaterial with outstanding mechanical properties. It is a modular protein consisting, in Argiope trifasciata, of a core repetitive domain of 200 amino acid units (W units). In solution, the W units comprise a globular folded core, with five α-helices, and disordered tails that are linked to form a ~63-residue intrinsically disordered linker in concatemers. Herein, we present nuclear magnetic resonance (NMR) spectroscopy-based ¹⁵N spin relaxation analysis, allowing characterization of backbone dynamics as a function of residue on the ps–ns timescale in the context of the single W unit (W₁) and the two unit concatemer (W₂). Unambiguous mapping of backbone dynamics throughout W₂ was made possible by segmental NMR active isotope-enrichment through split intein-mediated trans-splicing. Spectral density mapping for W₁ and W₂ reveals a striking disparity in dynamics between the folded core and the disordered linker and tail regions. These data are also consistent with rotational diffusion behaviour where each globular domain tumbles almost independently of its neighbour. At a localized level, helix 5 exhibits elevated high frequency dynamics relative to the proximal helix 4, supporting a model of fibrillogenesis where this helix unfolds as part of the transition to a mixed α-helix/β-sheet fibre.

Distribution of Pico- and Nanosecond Motions in Disordered Proteins from Nuclear Spin Relaxation

Intrinsically disordered proteins and intrinsically disordered regions (IDRs) are ubiquitous in the eukaryotic proteome. The description and understanding of their conformational properties require the development of new experimental, computational, and theoretical approaches. Here, we use nuclear spin relaxation to investigate the distribution of timescales of motions in an IDR from picoseconds to nanoseconds. Nitrogen-15 relaxation rates have been measured at five magnetic fields, ranging from 9.4 to 23.5 T (400-1000 MHz for protons). This exceptional wealth of data allowed us to map the spectral density function for the motions of backbone NH pairs in the partially disordered transcription factor Engrailed at 11 different frequencies. We introduce an approach called interpretation of motions by a projection onto an array of correlation times (IMPACT), which focuses on an array of six correlation times with intervals that are equidistant on a logarithmic scale between 21 ps and 21 ns. The distribution of motions in Engrailed varies smoothly along the protein sequence and is multimodal for most residues, with a prevalence of motions around 1 ns in the IDR. We show that IMPACT often provides better quantitative agreement with experimental data than conventional model-free or extended model-free analyses with two or three correlation times. We introduce a graphical representation that offers a convenient platform for a qualitative discussion of dynamics. Even when relaxation data are only acquired at three magnetic fields that are readily accessible, the IMPACT analysis gives a satisfactory characterization of spectral density functions, thus opening the way to a broad use of this approach.

A New Method for Determining Structure Ensemble: Application to a RNA Binding Di-Domain Protein

Structure ensemble determination is the basis of understanding the structure-function relationship of a multidomain protein with weak domain-domain interactions. Paramagnetic relaxation enhancement has been proven a powerful tool in the study of structure ensembles, but there exist a number of challenges such as spin-label flexibility, domain dynamics, and overfitting. Here we propose a new (to our knowledge) method to describe structure ensembles using a minimal number of conformers. In this method, individual domains are considered rigid; the position of each spin-label conformer and the structure of each protein conformer are defined by three and six orthogonal parameters, respectively. First, the spin-label ensemble is determined by optimizing the positions and populations of spin-label conformers against intradomain paramagnetic relaxation enhancements with a genetic algorithm. Subsequently, the protein structure ensemble is optimized using a more efficient genetic algorithm-based approach and an overfitting indicator, both of which were established in this work. The method was validated using a reference ensemble with a set of conformers whose populations and structures are known. This method was also applied to study the structure ensemble of the tandem di-domain of a poly (U) binding protein. The determined ensemble was supported by small-angle x-ray scattering and nuclear magnetic resonance relaxation data. The ensemble obtained suggests an induced fit mechanism for recognition of target RNA by the protein.

Improved Accuracy from Joint X-ray and NMR Refinement of a Protein-RNA Complex Structure

Integrated experimental approaches play an increasingly important role in structural biology, taking advantage of the complementary information provided by different techniques. In particular, the combination of NMR data with X-ray diffraction patterns may provide accurate and precise information about local conformations not available from average-resolution X-ray structures alone. Here, we refined the structure of a ternary protein-protein-RNA complex comprising three domains, Sxl and Unr, bound to a single-stranded region derived in the msl2 mRNA. The joint X-ray and NMR refinement reveals that-despite the poor quality of the fit found for the original structural model-the NMR data can be largely accommodated within the uncertainty in the atom positioning (structural noise) from the primary X-ray data and that the overall domain arrangements and binding interfaces are preserved on passing from the crystalline state to the solution. The refinement highlights local conformational differences, which provide additional information on specific features of the structure. For example, conformational dynamics and heterogeneity observed at the interface between the CSD1 and the Sxl protein components in the ternary complex are revealed by the combination of NMR and crystallographic data. The joint refinement protocol offers unique opportunities to detect structural differences arising from various experimental conditions and reveals static or dynamic differences in the conformation of the biomolecule between the solution and the crystals.

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.

Polyhydroxylated [60]fullerene binds specifically to functional recognition sites on a monomeric and a dimeric ubiquitin

The use of nanoparticles (NPs) in biomedical applications requires an in-depth understanding of the mechanisms by which NPs interact with biomolecules. NPs associating with proteins may interfere with protein-protein interactions and affect cellular communication pathways, however the impact of NPs on biomolecular recognition remains poorly characterized. In this respect, particularly relevant is the study of NP-induced functional perturbations of proteins implicated in the regulation of key biochemical pathways. Ubiquitin (Ub) is a prototypical protein post-translational modifier playing a central role in numerous essential biological processes. To contribute to the understanding of the interactions between this universally distributed biomacromolecule and NPs, we investigated the adsorption of polyhydroxylated [60]fullerene on monomeric Ub and on a minimal polyubiquitin chain in vitro at atomic resolution. Site-resolved chemical shift and intensity perturbations of Ub's NMR signals, together with (15)N spin relaxation rate changes, exchange saturation transfer effects, and fluorescence quenching data were consistent with the reversible formation of soluble aggregates incorporating fullerenol clusters. The specific interaction epitopes were identified, coincident with functional recognition sites in a monomeric and lysine48-linked dimeric Ub. Fullerenol appeared to target the open state of the dynamic structure of a dimeric Ub according to a conformational selection mechanism. Importantly, the protein-NP association prevented the enzyme-catalyzed synthesis of polyubiquitin chains. Our findings provide an experiment-based insight into protein/fullerenol recognition, with implications in functional biomolecular communication, including regulatory protein turnover, and for the opportunity of therapeutic intervention in Ub-dependent cellular pathways.

Coupling between overall rotational diffusion and domain motions in proteins and its effect on dielectric spectra

In this work, we formulate a closed-form solution of the model of a semirigid molecule for the case of fluctuating and reorienting molecular electric dipole moment. We illustrate with numeric calculations the impact of protein domain motions on dielectric spectra using the example of the 128 kDa protein dimer of Enzyme I. We demonstrate that the most drastic effect occurs for situations when the characteristic time of protein domain dynamics is comparable to the time of overall molecular rotational diffusion. We suggest that protein domain motions could be a possible explanation for the high-frequency contribution that accompanies the major relaxation dispersion peak in the dielectric spectra of protein aqueous solutions. We propose that the presented computational methodology could be used for the simultaneous analysis of dielectric spectroscopy and nuclear magnetic resonance data. Proteins 2015; 83:1571-1581. © 2015 Wiley Periodicals, Inc.

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.

Towards understanding the molecular recognition process in prokaryotic zinc-finger domain

Eukaryotic Cys2His2 zinc finger domain is one of the most common and important structural motifs involved in protein-DNA interaction. The recognition motif is characterized by the tetrahedral coordination of a zinc ion by conserved cysteine and histidine residues. We have characterized the prokaryotic Cys2His2 zinc finger motif, included in the DNA binding region (Ros87) of Ros protein from Agrobacterium tumefaciens, demonstrating that, although possessing a similar zinc coordination sphere, this domain presents significant differences from its eukaryotic counterpart. Furthermore, basic residues flanking the zinc binding region on either side have been demonstrated, by Electrophoretic Mobility Shift Assay (EMSA) experiments, to be essential for Ros DNA binding. In spite of this wealth of knowledge, the structural details of the mechanism through which the prokaryotic zinc fingers recognize their target genes are still unclear. Here, to gain insights into the molecular DNA recognition process of prokaryotic zinc finger domains we applied a strategy in which we performed molecular docking studies using a combination of Nuclear Magnetic Resonance (NMR) and Molecular Dynamics (MD) simulations data. The results demonstrate that the MD ensemble provides a reasonable picture of Ros87 backbone dynamics in solution. The Ros87-DNA model indicates that the interaction involves the first two residue of the first α-helix, and several residues located in the basic regions flanking the zinc finger domain. Interestingly, the prokaryotic zinc finger domain, mainly with the C-terminal tail that is wrapped around the DNA, binds a more extended recognition site than the eukaryotic counterpart. Our analysis demonstrates that the introduction of the protein flexibility in docking studies can improve, in terms of accuracy, the quality of the obtained models and could be particularly useful for protein showing high conformational heterogeneity as well as for computational drug design applications.

Exploring regions of conformational space occupied by two-domain proteins

The presence of heterogeneity in the interdomain arrangement of several biomolecules is required for their function. Here we present a method to obtain crucial clues to distinguish between different kinds of protein conformational distributions based on experimental NMR data. The method explores subregions of the conformational space and provides both upper and lower bounds of probability for the system to be in each subregion.

Mechanisms of generating polyubiquitin chains of different topology

Ubiquitination is an important post-translational process involving attachment of the ubiquitin molecule to lysine residue/s on a substrate protein or on another ubiquitin molecule, leading to the formation of protein mono-, multi- or polyubiquitination. Protein ubiquitination requires a cascade of three enzymes, where the interplay between different ubiquitin-conjugating and ubiquitin-ligase enzymes generates diverse ubiquitinated proteins topologies. Structurally diverse ubiquitin conjugates are recognized by specific proteins with ubiquitin-binding domains (UBDs) to target the substrate proteins of different pathways. The mechanism/s for generating the different ubiquitinated proteins topologies is not well understood. Here, we will discuss our current understanding of the mechanisms underpinning the generation of mono- or polyubiquitinated substrates. In addition, we will discuss how linkage-specific polyubiquitin chains through lysines-11, -48 or -63 are formed to target proteins to different fates by binding specific UBD proteins.

PolyUbiquitin chain linkage topology selects the functions from the underlying binding landscape

Ubiquitin (Ub) can generate versatile molecular signals and lead to different celluar fates. The functional poly-valence of Ub is believed to be resulted from its ability to form distinct polymerized chains with eight linkage types. To provide a full picture of ubiquitin code, we explore the binding landscape of two free Ub monomers and also the functional landscapes of of all eight linkage types by theoretical modeling. Remarkably, we found that most of the compact structures of covalently connected dimeric Ub chains (diUbs) pre-exist on the binding landscape. These compact functional states were subsequently validated by corresponding linkage models. This leads to the proposal that the folding architecture of Ub monomer has encoded all functional states into its binding landscape, which is further selected by different topologies of polymeric Ub chains. Moreover, our results revealed that covalent linkage leads to symmetry breaking of interfacial interactions. We further propose that topological constraint not only limits the conformational space for effective switching between functional states, but also selects the local interactions for realizing the corresponding biological function. Therefore, the topological constraint provides a way for breaking the binding symmetry and reaching the functional specificity. The simulation results also provide several predictions that qualitatively and quantitatively consistent with experiments. Importantly, the K48 linkage model successfully predicted intermediate states. The resulting multi-state energy landscape was further employed to reconcile the seemingly contradictory experimental data on the conformational equilibrium of K48-diUb. Our results further suggest that hydrophobic interactions are dominant in the functional landscapes of K6-, K11-, K33- and K48 diUbs, while electrostatic interactions play a more important role in the functional landscapes of K27, K29, K63 and linear linkages.

Transient electrostatic interactions dominate the conformational equilibrium sampled by multidomain splicing factor U2AF65: a combined NMR and SAXS study

Multidomain proteins containing intrinsically disordered linkers exhibit large-scale dynamic modes that play key roles in a multitude of molecular recognition and signaling processes. Here, we determine the conformational space sampled by the multidomain splicing factor U2AF65 using complementary nuclear magnetic resonance spectroscopy and small-angle scattering data. Available degrees of conformational freedom are initially stochastically sampled and experimental data then used to delineate the potential energy landscape in terms of statistical probability. The spatial distribution of U2AF65 conformations is found to be highly anisotropic, comprising significantly populated interdomain contacts that appear to be electrostatic in origin. This hypothesis is supported by the reduction of signature PREs reporting on expected interfaces with increasing salt concentration. The described spatial distribution reveals the complete spectrum of the unbound forms of U2AF65 that coexist with the small percentage of a preformed RNA-bound domain arrangement required for polypyrimidine-tract recognition by conformational selection. More generally, the proposed approach to describing conformational equilibria of multidomain proteins can be further combined with other experimental data that are sensitive to domain dynamics.

Simultaneous use of solution NMR and X-ray data in REFMAC5 for joint refinement/detection of structural differences

The program REFMAC5 from CCP4 was modified to allow the simultaneous use of X-ray crystallographic data and paramagnetic NMR data (pseudocontact shifts and self-orientation residual dipolar couplings) and/or diamagnetic residual dipolar couplings. Incorporation of these long-range NMR restraints in REFMAC5 can reveal differences between solid-state and solution conformations of molecules or, in their absence, can be used together with X-ray crystallographic data for structural refinement. Since NMR and X-ray data are complementary, when a single structure is consistent with both sets of data and still maintains reasonably `ideal' geometries, the reliability of the derived atomic model is expected to increase. The program was tested on five different proteins: the catalytic domain of matrix metalloproteinase 1, GB3, ubiquitin, free calmodulin and calmodulin complexed with a peptide. In some cases the joint refinement produced a single model consistent with both sets of observations, while in other cases it indicated, outside the experimental uncertainty, the presence of different protein conformations in solution and in the solid state.

Decoding the components of dynamics in three-domain proteins

In this study, we examine the feasibility and limitations of describing the motional behavior of three-domain proteins in which the domains are linearly connected. In addition to attempting the determination of the internal and overall reorientational correlation times, we investigate the existence of correlations in the motions between the three domains. Since in linearly arranged three-domain proteins, there are typically no experimental data that can directly report on motional correlation between the first and the third domain, we address this question by dynamics simulations. Two limiting cases occur: (1) for weak repulsive potentials and (2) when strong repulsive potentials are applied between sequential domains. The motions of the terminal domains become correlated in the case of strong interdomain repulsive potentials when these potentials do not allow the angle between the sequential domains to be smaller than about 60°. Using the model-free (MF) and extended MF formalisms of Lipari and Szabo, we find that the motional behavior can be separated into two components; the first component represents the concerted overall motion of the three domains, and the second describes the independent component of the motion of each individual domain. We find that this division of the motional behavior of the protein is maintained only when their timescales are distinct and can be made when the angles between sequential domains remain between 60° and 160°. In this work, we identify and quantify interdomain motional correlations.

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.

Nanosecond time scale motions in proteins revealed by high-resolution NMR relaxometry

Understanding the molecular determinants underlying protein function requires the characterization of both structure and dynamics at atomic resolution. Nuclear relaxation rates allow a precise characterization of protein dynamics at the Larmor frequencies of spins. This usually limits the sampling of motions to a narrow range of frequencies corresponding to high magnetic fields. At lower fields one cannot achieve sufficient sensitivity and resolution in NMR. Here, we use a fast shuttle device where the polarization builds up and the signals are detected at high field, while longitudinal relaxation takes place at low fields 0.5 < B₀ < 14.1 T. The sample is propelled over a distance up to 50 cm by a blowgun-like system in about 50 ms. The analysis of nitrogen-15 relaxation in the protein ubiquitin over such a wide range of magnetic fields offers unprecedented insights into molecular dynamics. Some key regions of the protein feature structural fluctuations on nanosecond time scales, which have so far been overlooked in high-field relaxation studies. Nanosecond motions in proteins may have been underestimated by traditional high-field approaches, and slower supra-τ_c motions that have no effect on relaxation may have been overestimated. High-resolution relaxometry thus opens the way to a quantitative characterization of nanosecond motions in proteins.

Interdomain dynamics explored by paramagnetic NMR

An ensemble-based approach is presented to explore the conformational space sampled by a multidomain protein showing moderate interdomain dynamics in terms of translational and rotational motions. The strategy was applied on a complex of calmodulin (CaM) with the IQ-recognition motif from the voltage-gated calcium channel Ca(v)1.2 (IQ), which adopts three different interdomain orientations in the crystal. The N60D mutant of calmodulin was used to collect pseudocontact shifts and paramagnetically induced residual dipolar couplings for six different lanthanide ions. Then, starting from the crystal structure, pools of conformations were generated by free MD. We found the three crystal conformations in solution, but four additional MD-derived conformations had to be included into the ensemble to fulfill all the paramagnetic data and cross-validate optimally against unused paramagnetic data. Alternative approaches led to similar ensembles. Our "ensemble" approach is a simple and efficient tool to probe and describe the interdomain dynamics and represents a general method that can be used to provide a proper ensemble description of multidomain 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.

Determining interdomain structure and dynamics of a retroviral capsid protein in the presence of oligomerization: implication for structural transition in capsid assembly

Capsid (CA) proteins from all retroviruses, including HIV-1, are structurally homologous dual-domain helical proteins. They form a capsid lattice composed of unitary symmetric CA hexamers. X-ray crystallography has shown that within each hexamer a monomeric CA adopts a single conformation, where most helices are parallel to the symmetry axis. In solution, large differences in averaged NMR spin relaxation rates for the two domains were observed, suggesting they are dynamically independent. One relevant question for the capsid assembly remains: whether the interdomain conformer within a hexamer unit needs to be induced or pre-exists within the conformational space of a monomeric CA. The latter seems more consistent with the relaxation data. However, possible CA protein oligomerization and the structure of each domain will affect relaxation measurements and data interpretation. This study, using CA proteins from equine infectious anemia virus (EIAV) as an example, demonstrates a linear extrapolation approach to obtain backbone (15)N spin relaxation time ratios T1/T2 for a monomeric EIAV-CA in the presence of oligomerization equilibrium. The interdomain motion turns out to be limited. The large difference in the domain averaged <T1/T2> for a CA monomer is a consequence of the orthogonal distributions of helices in the two domains. The new monomeric interdomain conformation in solution is significantly different from that in CA hexamer. Therefore, if capsid assembly follows a nucleation-propagation process, the interdomain conformational change might be a key step during the nucleation, as the configuration in hexagonal assembly is never formed by diffusion of its two domains in solution.

Hypothesis: The unfolding power of protein dielectricity

A hypothesis is proposed on a potential role of protein dielectricity as an unfolding factor in protein-protein interactions. It is suggested that large protein complexes and aggregation seeds can unfold target proteins by virtue of their effect on the dielectric properties of water at the protein-solvent interface. Here, similar to the effect of membrane surfaces, protein surface can cause decrease in the local dielectric constant of solvent and thereby induce structural changes in a target protein approaching this surface. Some potential implementations of this hypothetical mechanism are also discussed.

NMR relaxation in proteins with fast internal motions and slow conformational exchange: model-free framework and Markov state simulations

Calculating NMR relaxation effects for proteins with dynamics on multiple time scales generally requires very long trajectories based on conventional molecular dynamics simulations. In this report, we have built Markov state models from multiple MD trajectories and used the resulting MSM to capture the very fast internal motions of the protein within a free energy basin on a time scale up to hundreds of picoseconds and the more than 3 orders of magnitude slower conformational exchange between macrostates. To interpret the relaxation data, we derive new equations using the model-free framework which includes two slowly exchanging macrostates, each of which also exhibits fast local motions. Using simulations of HIV-1 protease as an example, we show how the populations of slowly exchanging conformational states as well as order parameters for the different states can be determined from the NMR relaxation data.

Activation of UbcH5c~Ub is the result of a shift in interdomain motions of the conjugate bound to U-box E3 ligase E4B

Post-translational modification of proteins with ubiquitin is mediated by dynamic multienzyme machinery (E1, E2, and E3). E3 ubiquitin ligases play a key role acting as both scaffolds to bring reactants together and activators to catalyze ubiquitin (Ub) transfer from E2~Ub conjugates to substrates. Our recent studies provided insights into the mechanism of the activation event; binding of an E3 to an E2~Ub conjugate was found to affect the motions of E2~Ub and allosterically stimulate Ub transfer. This proposed mechanism implies that the dynamics of the conjugate, which has been shown to occupy a wide range of E2~Ub orientations, will be altered significantly upon binding of E3. To directly assess the effect of E3 binding on E2~Ub dynamics, we undertook an in-depth comparative analysis of (15)N nuclear magnetic resonance relaxation of UbcH5c~Ub in the absence and presence of the E3 ligase, E4B. Challenges encountered in deciphering interdomain motions for this ternary complex are discussed along with the limitations of the current approaches. Notably, although a reduction in interdomain dynamics of UbcH5c~Ub is observed upon binding to E4B, Ub retains an extensive degree of flexibility. These results provide strong support for our dynamic model of a significant orientational bias of Ub toward a more closed conformation in the E3/E2~Ub complex.

Mixed-linkage ubiquitin chains send mixed messages

Research on ubiquitin (Ub) signaling has focused primarily on homogeneously linked polyUb. Although polyUb containing different linkages within the same chain exist, their structures and signaling properties are unknown. These mixed-linkage chains could be unbranched (i.e., no more than one lysine or methionine linkage per Ub) or branched. Here, we examined the structure, dynamics, receptor selectivity, and disassembly of branched and unbranched tri-Ub containing both K48 and K63 linkages. Each linkage was virtually indistinguishable from its counterpart in homogeneously linked polyUb. Linkage-selective receptors from hHR23A and Rap80 preferentially bound to the K48 or K63 linkages in the branched trimer. Linkage-selective deubiquitinases specifically cleaved their cognate Ub-Ub linkages in mixed-linkage chains, and the 26S proteasome recognized and processed branched tri-Ub. We conclude that mixed-linkage chains retain the distinctive signaling properties of their K48 and K63 components and that these multiple signals can be recognized by multiple linkage-specific receptors. Finally, we propose a new, comprehensive notation for Ub and Ub-like polymers.

Dynamic control of electron transfers in diflavin reductases

Diflavin reductases are essential proteins capable of splitting the two-electron flux from reduced pyridine nucleotides to a variety of one electron acceptors. The primary sequence of diflavin reductases shows a conserved domain organization harboring two catalytic domains bound to the FAD and FMN flavins sandwiched by one or several non-catalytic domains. The catalytic domains are analogous to existing globular proteins: the FMN domain is analogous to flavodoxins while the FAD domain resembles ferredoxin reductases. The first structural determination of one member of the diflavin reductases family raised some questions about the architecture of the enzyme during catalysis: both FMN and FAD were in perfect position for interflavin transfers but the steric hindrance of the FAD domain rapidly prompted more complex hypotheses on the possible mechanisms for the electron transfer from FMN to external acceptors. Hypotheses of domain reorganization during catalysis in the context of the different members of this family were given by many groups during the past twenty years. This review will address the recent advances in various structural approaches that have highlighted specific dynamic features of diflavin reductases.

MaxOcc: a web portal for maximum occurrence analysis

The MaxOcc web portal is presented for the characterization of the conformational heterogeneity of two-domain proteins, through the calculation of the Maximum Occurrence that each protein conformation can have in agreement with experimental data. Whatever the real ensemble of conformations sampled by a protein, the weight of any conformation cannot exceed the calculated corresponding Maximum Occurrence value. The present portal allows users to compute these values using any combination of restraints like pseudocontact shifts, paramagnetism-based residual dipolar couplings, paramagnetic relaxation enhancements and small angle X-ray scattering profiles, given the 3D structure of the two domains as input. MaxOcc is embedded within the NMR grid services of the WeNMR project and is available via the WeNMR gateway at http://py-enmr.cerm.unifi.it/access/index/maxocc . It can be used freely upon registration to the grid with a digital certificate.

Paramagnetic relaxation enhancement for the characterization of the conformational heterogeneity in two-domain proteins

Multidomain proteins are often composed of rigid domains that can reorient in solution more or less freely. Calmodulin (CaM) is a two domain protein which can experience a large degree of conformational freedom thanks to a mobile linker connecting the N-terminal and C-terminal domains of the protein. The maximum occurrences (MOs) of the possible protein conformations have been analyzed using the paramagnetic relaxation enhancements (PREs) induced by a gadolinium(III) ion together with the paramagnetic pseudocontact shift and residual dipolar coupling restraints measured in the presence of terbium(III), thulium(III) or dysprosium(III) ions. The results suggest that the PREs provide complementary information useful for improving the description of the conformational heterogeneity of the protein. The data, acquired at 298 K and at 278 K, suggest that compact conformations are disfavoured by decreasing the temperature.

Coupling between internal dynamics and rotational diffusion in the presence of exchange between discrete molecular conformations

We present a general formalism for the computation of orientation correlation functions involving a molecular system undergoing rotational diffusion in the presence of transitions between discrete conformational states. In this formalism, there are no proscriptions on the time scales of conformational rearrangement relative to that for rotational diffusion, and the rotational diffusion tensors of the different states can be completely arbitrary. Although closed-form results are limited to the frequency domain, this is generally useful for many spectroscopic observables as the result allows the computation of the spectral density function. We specialize the results for the computation of the frequency-domain correlation function associated with the NMR relaxation.