An efficient computational method for predicting rotational diffusion tensors of globular proteins using an ellipsoid representation

Specifying conformational heterogeneity of multi-domain proteins at atomic resolution

The conformational landscape of multi-domain proteins is inherently linked to their specific functions. This also holds for polyubiquitin chains that are assembled by two or more ubiquitin domains connected by a flexible linker thus showing a large interdomain mobility. However, molecular recognition and signal transduction are associated with particular conformational substates that are populated in solution. Here, we apply high-resolution NMR spectroscopy in combination with dual-scale MD simulations to explore the conformational space of K6-, K29-, and K33-linked diubiquitin molecules. The conformational ensembles are evaluated utilizing a paramagnetic cosolute reporting on solvent exposure plus a set of complementary NMR parameters. This approach unravels a conformational heterogeneity of diubiquitins and explains the diversity of structural models that have been determined for K6-, K29-, and K33-linked diubiquitins in free and ligand-bound states so far. We propose a general application of the approach developed here to demystify multi-domain proteins occurring in nature.

Energetics and dynamics of the proton shuttle of carbonic anhydrase II

Human carbonic anhydrase II catalyzes the reversible reaction of carbon dioxide and water to form bicarbonate and a proton. His64-mediated proton shuttling between the active site and the bulk solvent is rate limiting. Here we investigate the protonation behavior of His64 as well as its structural and dynamic features in a pH dependent way. We derive two pKa values for His64, 6.25 and 7.60, that we were able to assign to its inward and outward conformation. Furthermore, we show that His64 exists in both conformations equally, independent of pH. Both conformations display an equal distribution of their two neutral tautomeric states. The life time of each conformation is short and both states display high flexibility within their orientation. Therefore, His64 is never static, but rather poised to change conformation. These findings support an energetic, dynamic and solution ensemble-based framework for the high enzymatic activity of human carbonic anhydrase II.

Disorder in the Human Skp1 Structure is the Key to its Adaptability to Bind Many Different Proteins in the SCF Complex Assembly

Skp1(S-phase kinase-associated protein 1 - Homo sapiens) is an adapter protein of the SCF(Skp1-Cullin1-Fbox) complex, which links the constant components (Cul1-RBX) and the variable receptor (F-box proteins) in Ubiquitin E3 ligase. It is intriguing how Skp1 can recognise and bind to a variety of structurally different F-box proteins. For practical reasons, previous efforts have used truncated Skp1, and thus it has not been possible to track the crucial aspects of the substrate recognition process. In this background, we report the solution structure of the full-length Skp1 protein determined by NMR spectroscopy for the first time and investigate the sequence-dependent dynamics in the protein. The solution structure reveals that Skp1 has an architecture: β1-β2-H1-H2-L1-H3-L2-H4-H5-H6-H7(partially formed) and a long tail-like disordered C-terminus. Structural analysis using DALI (Distance Matrix Alignment) reveals conserved domain structure across species for Skp1. Backbone dynamics investigated using NMR relaxation suggest substantial variation in the motional timescales along the length of the protein. The loops and the C-terminal residues are highly flexible, and the (R2/R1) data suggests μs-ms timescale motions in the helices as well. Further, the dependence of amide proton chemical shift on temperature and curved profiles of their residuals indicate that the residues undergo transitions between native state and excited state. The curved profiles for several residues across the length of the protein suggest that there are native-like low-lying excited states, particularly for several C-terminal residues. Our results provide a rationale for how the protein can adapt itself, bind, and get functionally associated with other proteins in the SCF complex by utilising its flexibility and conformational sub-states.

Structure and dynamics of the quaternary hunchback mRNA translation repression complex

A key regulatory process during Drosophila development is the localized suppression of the hunchback mRNA translation at the posterior, which gives rise to a hunchback gradient governing the formation of the anterior-posterior body axis. This suppression is achieved by a concerted action of Brain Tumour (Brat), Pumilio (Pum) and Nanos. Each protein is necessary for proper Drosophila development. The RNA contacts have been elucidated for the proteins individually in several atomic-resolution structures. However, the interplay of all three proteins during RNA suppression remains a long-standing open question. Here, we characterize the quaternary complex of the RNA-binding domains of Brat, Pum and Nanos with hunchback mRNA by combining NMR spectroscopy, SANS/SAXS, XL/MS with MD simulations and ITC assays. The quaternary hunchback mRNA suppression complex comprising the RNA binding domains is flexible with unoccupied nucleotides functioning as a flexible linker between the Brat and Pum-Nanos moieties of the complex. Moreover, the presence of the Pum-HD/Nanos-ZnF complex has no effect on the equilibrium RNA binding affinity of the Brat RNA binding domain. This is in accordance with previous studies, which showed that Brat can suppress mRNA independently and is distributed uniformly throughout the embryo.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Applications of KBFF20

Here, we perform structural, thermodynamic, and kinetics tests of the Kirkwood-Buff-derived force field, KBFF20, for peptides and proteins developed in the previous article. The physical/structural tests measure the ability of KBFF20 to capture the experimental J-couplings for small peptides, to keep globular monomeric and oligomeric proteins folded, and to produce the experimentally relevant expanded conformational ensembles of intrinsically disordered proteins. The thermodynamic-based tests probe KBFF20's ability to quantify the preferential interactions of sodium chloride around native β-lactoglobulin and urea around native lysozyme, to reproduce the melting curves for small helix- and sheet-based peptides, and to fold the small proteins Trp-cage and Villin. The kinetics-based tests quantify how well KBFF20 can match the experimental contact formation rates of small, repeat-sequence peptides of variable lengths and the rotational diffusion coefficients of globular proteins. The results suggest that KBFF20 is naturally able to reproduce properties of both folded and disordered proteins, which we attribute to the use of the Kirkwood-Buff theory as the foundation of the force field's development. However, we show that KBFF20 tends to lose some well-defined secondary structural elements and increases the percentage of coil regions, indicating that the perfect balance of all interactions remains elusive. Nevertheless, we argue that KBFF20 is an improvement over recently modified force fields that require ad hoc interventions to prevent the collapse of intrinsically disordered proteins.

Segmental structural dynamics in Aβ42 globulomers

Aβ42 aggregation plays a central role in the pathogenesis of Alzheimer's disease. In addition to the insoluble fibrils that comprise the amyloid plaques, Aβ42 also forms soluble aggregates collectively called oligomers, which are more toxic and pathogenic than fibrils. Understanding the structure and dynamics of Aβ42 oligomers is critical for developing effective therapeutic interventions against these oligomers. Here we studied the structural dynamics of Aβ42 globulomers, a type of Aβ42 oligomers prepared in the presence of sodium dodecyl sulfate, using site-directed spin labeling. Spin labels were introduced, one at a time, at all 42 residue positions of Aβ42 sequence. Electron paramagnetic resonance spectra of spin-labeled samples reveal four structural segments based on site-dependent spin label mobility pattern. Segment-1 consists of residues 1-6, which have the highest mobility that is consistent with complete disorder. Segment-3 is the most immobilized region, including residues 31-34. Segment-2 and -4 have intermediate mobility and are composed of residues 7-30 and 35-42, respectively. Considering the inverse relationship between protein dynamics and stability, our results suggest that residues 31-34 are the most stable segment in Aβ42 oligomers. At the same time, the EPR spectral lineshape suggests that Aβ42 globulomers lack a well-packed structural core akin to that of globular proteins.

Leiomodin creates a leaky cap at the pointed end of actin-thin filaments

Improper lengths of actin-thin filaments are associated with altered contractile activity and lethal myopathies. Leiomodin, a member of the tropomodulin family of proteins, is critical in thin filament assembly and maintenance; however, its role is under dispute. Using nuclear magnetic resonance data and molecular dynamics simulations, we generated the first atomic structural model of the binding interface between the tropomyosin-binding site of cardiac leiomodin and the N-terminus of striated muscle tropomyosin. Our structural data indicate that the leiomodin/tropomyosin complex only forms at the pointed end of thin filaments, where the tropomyosin N-terminus is not blocked by an adjacent tropomyosin protomer. This discovery provides evidence supporting the debated mechanism where leiomodin and tropomodulin regulate thin filament lengths by competing for thin filament binding. Data from experiments performed in cardiomyocytes provide additional support for the competition model; specifically, expression of a leiomodin mutant that is unable to interact with tropomyosin fails to displace tropomodulin at thin filament pointed ends and fails to elongate thin filaments. Together with previous structural and biochemical data, we now propose a molecular mechanism of actin polymerization at the pointed end in the presence of bound leiomodin. In the proposed model, the N-terminal actin-binding site of leiomodin can act as a "swinging gate" allowing limited actin polymerization, thus making leiomodin a leaky pointed-end cap. Results presented in this work answer long-standing questions about the role of leiomodin in thin filament length regulation and maintenance.

Mathematical aspects of molecular replacement. V. Isolating feasible regions in motion spaces

This paper mathematically characterizes the tiny feasible regions within the vast 6D rotation–translation space in a full molecular replacement (MR) search. The capability to a priori isolate such regions is potentially important for enhancing robustness and efficiency in computational phasing in macromolecular crystallography (MX). The previous four papers in this series have concentrated on the properties of the full configuration space of rigid bodies that move relative to each other with crystallographic symmetry constraints. In particular, it was shown that the configuration space of interest in this problem is the right-coset space Γ\G, where Γ is the space group of the chiral macromolecular crystal and G is the group of rigid-body motions, and that fundamental domains F Γ\G can be realized in many ways that have interesting algebraic and geometric properties. The cost function in MR methods can be viewed as a function on these fundamental domains. This, the fifth and final paper in this series, articulates the constraints that bodies packed with crystallographic symmetry must obey. It is shown that these constraints define a thin feasible set inside a motion space and that they fall into two categories: (i) the bodies must not interpenetrate, thereby excluding so-called `collision zones' from consideration in MR searches; (ii) the bodies must be in contact with a sufficient number of neighbors so as to form a rigid network leading to a physically realizable crystal. In this paper, these constraints are applied using ellipsoidal proxies for proteins to bound the feasible regions. It is shown that the volume of these feasible regions is small relative to the total volume of the motion space, which justifies the use of ellipsoids as proxies for complex proteins in MR searches, and this is demonstrated with P1 (the simplest space group) and with P212121 (the most common space group in MX).

Evaluating rotation diffusion properties of molecules from short trajectories

We show that under proper assumptions it is possible to estimate with good precision the principal values of the rotational diffusion tensor of proteins from the analysis of short (up to 2-3 ns) molecular dynamics trajectories. We apply this analysis to a few model cases: three polyalanine peptides (2, 5, and 10 aminoacids), the fragment B3 of protein G (GB3), the bovine pancreatic trypsin inhibitor (BPTI), the hen egg-white lysozyme (LYS), the B1 domain of plexin (PB1), and thrombin. The protocol is based on the analysis of the global angular momentum autocorrelation functions, complementing the standard approach based on rotational autocorrelation functions, which requires much longer trajectories. A comparison with values predicted by hydrodynamic modeling and available experimental data is presented.

Accurate Electron-Nucleus Distances from Paramagnetic Relaxation Enhancements

Measurements of paramagnetic relaxation enhancements (PREs) in ¹H NMR spectra are an important tool to obtain long-range distance information in proteins, but quantitative interpretation is easily compromised by nonspecific intermolecular PREs. Here we show that PREs generated by lanthanides with anisotropic magnetic susceptibilities offer a route to accurate calibration-free distance measurements. As these lanthanides change ¹H chemical shifts due to pseudocontact shifts, the relaxation rates in the paramagnetic and diamagnetic state can be measured with a single sample that simultaneously contains the protein labeled with a paramagnetic and a diamagnetic lanthanide ion. Nonspecific intermolecular PREs are thus automatically subtracted when calculating the PREs as the difference in nuclear relaxation rates between paramagnetic and diamagnetic protein. Although PREs from lanthanides with anisotropic magnetic susceptibilities are complicated by additional cross-correlation effects and residual dipolar couplings (RDCs) in the paramagnetic state, these effects can be controlled by the choice of lanthanide ion and experimental conditions. Using calbindin D_9k with erbium, we succeeded in measuring intramolecular PREs with unprecedented accuracy, resulting in distance predictions with a root-mean-square-deviation of <0.9 Å in the range 11-24 Å.

HullRad: Fast Calculations of Folded and Disordered Protein and Nucleic Acid Hydrodynamic Properties

Hydrodynamic properties are useful parameters for estimating the size and shape of proteins and nucleic acids in solution. The calculation of such properties from structural models informs on the solution properties of these molecules and complements corresponding structural studies. Here we report, to our knowledge, a new method to accurately predict the hydrodynamic properties of molecular structures. This method uses a convex hull model to estimate the hydrodynamic volume of the molecule and is orders of magnitude faster than common methods. It works well for both folded proteins and ensembles of conformationally heterogeneous proteins and for nucleic acids. Because of its simplicity and speed, the method should be useful for the modification of computer-generated, intrinsically disordered protein ensembles and ensembles of flexible, but folded, molecules in which rapid calculation of experimental parameters is needed. The convex hull method is implemented in a Python script called HullRad. The use of the method is facilitated by a web server and the code is freely available for batch applications.

Narrowing the gap between experimental and computational determination of methyl group dynamics in proteins

A synergistic analysis of methyl NMR relaxation data and MD simulations identifies ways to improve studies of protein dynamics.

In silico characterization of protein partial molecular volumes and hydration shells

In this paper we present a computational approach, based on NVT molecular dynamics trajectories, that allows the direct evaluation of the protein partial molecular volume. The results obtained for five different globular proteins demonstrate the accuracy of this computational procedure in reproducing protein partial molecular volumes, providing quantitative characterization of the hydration shell in terms of the protein excluded volume, hydration shell ellipsoidal volume and related solvent density. Remarkably, our data indicate for the hydration shell a ≈10% solvent density increase with respect to the liquid water bulk density, in excellent agreement with the available experimental data.

Dissipative self-assembly of vesicular nanoreactors

Dissipative self-assembly is exploited by nature to control important biological functions, such as cell division, motility and signal transduction. The ability to construct synthetic supramolecular assemblies that require the continuous consumption of energy to remain in the functional state is an essential premise for the design of synthetic systems with lifelike properties. Here, we show a new strategy for the dissipative self-assembly of functional supramolecular structures with high structural complexity. It relies on the transient stabilization of vesicles through noncovalent interactions between the surfactants and adenosine triphosphate (ATP), which acts as the chemical fuel. It is shown that the lifetime of the vesicles can be regulated by controlling the hydrolysis rate of ATP. The vesicles sustain a chemical reaction but only as long as chemical fuel is present to keep the system in the out-of-equilibrium state. The lifetime of the vesicles determines the amount of reaction product produced by the system.

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.

O-tert-Butyltyrosine, an NMR tag for high-molecular-weight systems and measurements of submicromolar ligand binding affinities

O-tert-Butyltyrosine (Tby) is an unnatural amino acid that can be site-specifically incorporated into proteins using established orthogonal aminoacyl-tRNA synthetase/tRNA systems. Here we show that the tert-butyl group presents an outstanding NMR tag that can readily be observed in one-dimensional (1)H NMR spectra without any isotope labeling. Owing to rapid bond rotations and the chemical equivalence of the protons of a solvent-exposed tert-butyl group from Tby, the singlet resonance from the tert-butyl group generates an easily detectable narrow signal in a spectral region with limited overlap with other methyl resonances. The potential of the tert-butyl (1)H NMR signal in protein research is illustrated by the observation and assignment of two resonances in the Bacillus stearothermophilus DnaB hexamer (320 kDa), demonstrating that this protein preferentially assumes a 3-fold rather than 6-fold symmetry in solution, and by the quantitative measurement of the submicromolar dissociation constant Kd (0.2 μM) of the complex between glutamate and the Escherichia coli aspartate/glutamate binding protein (DEBP, 32 kDa). The outstanding signal height of the (1)H NMR signal of the Tby tert-butyl group allows Kd measurements using less concentrated protein solutions than usual, providing access to Kd values 1 order of magnitude lower than established NMR methods that employ direct protein detection for Kd measurements.

ADP-Ribosylargininyl reaction of cholix toxin is mediated through diffusible intermediates

Background

Cholix toxin is an ADP-ribosyltransferase found in non-O1/non-O139 strains of Vibrio cholera. The catalytic fragment of cholix toxin was characterized as a diphthamide dependent ADP-ribosyltransferase.

Results

Our studies on the enzymatic activity of cholix toxin catalytic fragment show that the transfer of ADP-ribose to toxin takes place by a predominantly intramolecular mechanism and results in the preferential alkylation of arginine residues proximal to the NAD⁺ binding pocket. Multiple arginine residues, located near the catalytic site and at distal sites, can be the ADP-ribose acceptor in the auto-reaction. Kinetic studies of a model enzyme, M8, showed that a diffusible intermediate preferentially reacted with arginine residues in proximity to the NAD⁺ binding pocket. ADP-ribosylarginine activity of cholix toxin catalytic fragment could also modify exogenous substrates. Auto-ADP-ribosylation of cholix toxin appears to have negatively regulatory effect on ADP-ribosylation of exogenous substrate. However, at the presence of both endogenous and exogenous substrates, ADP-ribosylation of exogenous substrates occurred more efficiently than that of endogenous substrates.

Conclusions

We discovered an ADP-ribosylargininyl activity of cholix toxin catalytic fragment from our studies in auto-ADP-ribosylation, which is mediated through diffusible intermediates. The lifetime of the hypothetical intermediate exceeds recorded and predicted lifetimes for the cognate oxocarbenium ion. Therefore, a diffusible strained form of NAD⁺ intermediate was proposed to react with arginine residues in a proximity dependent manner.

Electronic supplementary material

The online version of this article (doi:10.1186/s12858-014-0026-1) contains supplementary material, which is available to authorized users.

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.

An FFT-based method for modeling protein folding and binding under crowding: benchmarking on ellipsoidal and all-atom crowders

It is now well recognized that macromolecular crowding can exert significant effects on protein folding and binding stability. In order to calculate such effects in direct simulations of proteins mixed with bystander macromolecules, the latter (referred to as crowders) are usually modeled as spheres and the proteins represented at a coarse-grained level. Our recently developed postprocessing approach allows the proteins to be represented at the all-atom level but, for computational efficiency, has only been implemented for spherical crowders. Modeling crowder molecules in cellular environments and in vitro experiments as spheres may distort their effects on protein stability. Here we present a new method that is capable for treating aspherical crowders. The idea, borrowed from protein-protein docking, is to calculate the excess chemical potential of the proteins in crowded solution by fast Fourier transform (FFT). As the first application, we studied the effects of ellipsoidal crowders on the folding and binding free energies of all-atom proteins, and found, in agreement with previous direct simulations with coarse-grained protein models, that the aspherical crowders exert greater stabilization effects than spherical crowders of the same volume. Moreover, as demonstrated here, the FFT-based method has the important property that its computational cost does not increase strongly even when the level of details in representing the crowders is increased all the way to all-atom, thus significantly accelerating realistic modeling of protein folding and binding in cell-like environments.

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.

Parameterization of solvent-protein interaction and its use on NMR protein structure determination

NMR structure determination is frequently hindered by an insufficient amount of distance information for determining the correct fold of the protein in its early stages. In response we introduce a simple and general structure-based metric that can be used to incorporate NMR-based restraints on protein surface accessibility. This metric is inversely proportional to the sum of the inverse square distances to neighboring heavy atoms. We demonstrate the use of this restraint using a dataset from the water to protein magnetization transfer experiment on the protein Bax and the solvent paramagnetic relaxation enhancement experiment on the protein ubiquitin and Qua1 homodimer. The calculated solvent accessibility values using the new empirical function are well correlated with the experimental data. By incorporating an associated energy term into Xplor-NIH, we show that structure calculation with a limited number of additional experimental restraints, improves both the precision and accuracy of the resulting structures. This new empirical energy term will have general applicability to other types of solvent accessibility data.

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.

Determining protein dynamics from ¹⁵N relaxation data by using DYNAMICS

Motions are essential for protein function, and knowledge of protein dynamics is a key to our understanding the mechanisms underlying protein folding and stability, ligand recognition, allostery, and catalysis. In the last two decades, NMR relaxation measurements have become a powerful tool for characterizing backbone and side chain dynamics in complex biological macromolecules such as proteins and nucleic acids. Accurate analysis of the experimental data in terms of motional parameters is an essential prerequisite for developing physical models of motions to paint an adequate picture of protein dynamics. Here, I describe in detail how to use the software package DYNAMICS that was developed for accurate characterization of the overall tumbling and local dynamics in a protein from nuclear spin-relaxation rates measured by NMR. Step-by-step instructions are provided and illustrated through an analysis of (15)N relaxation data for protein G.

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

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

Impact of 15N R2/R1 relaxation restraints on molecular size, shape, and bond vector orientation for NMR protein structure determination with sparse distance restraints

(15)N R(2)/R(1) relaxation data contain information on molecular shape and size as well as on bond vector orientations relative to the diffusion tensor. Since the diffusion tensor can be directly calculated from the molecular coordinates, direct inclusion of (15)N R(2)/R(1) restraints in NMR structure calculations without any a priori assumptions is possible. Here we show that (15)N R(2)/R(1) restraints are particularly valuable when only sparse distance restraints are available. Using three examples of proteins of varying size, namely, GB3 (56 residues), ubiquitin (76 residues), and the N-terminal domain of enzyme I (EIN, 249 residues), we show that incorporation of (15)N R(2)/R(1) restraints results in large and significant increases in coordinate accuracy that can make the difference between being able or unable to determine an approximate global fold. For GB3 and ubiquitin, good coordinate accuracy was obtained using only backbone hydrogen-bond restraints supplemented by (15)N R(2)/R(1) relaxation restraints. For EIN, the global fold could be determined using sparse nuclear Overhauser enhancement (NOE) distance restraints involving only NH and methyl groups in conjunction with (15)N R(2)/R(1) restraints. These results are of practical significance in the study of larger and more complex systems, where the increasing spectral complexity and number of chemical shift degeneracies reduce the number of unambiguous NOE assignments that can be readily obtained, resulting in progressively reduced NOE coverage as the size of the protein increases.

Integrated computational approach to the analysis of NMR relaxation in proteins: application to ps-ns main chain 15N-1H and global dynamics of the Rho GTPase binding domain of plexin-B1

An integrated computational methodology for interpreting NMR spin relaxation in proteins has been developed. It combines a two-body coupled-rotator stochastic model with a hydrodynamics-based approach for protein diffusion, together with molecular dynamics based calculations for the evaluation of the coupling potential of mean force. The method is applied to ¹⁵N relaxation of N-H bonds in the Rho GTPase binding (RBD) domain of plexin-B1, which exhibits intricate internal mobility. Bond vector dynamics are characterized by a rhombic local ordering tensor, S, with principal values S₀² and S₂², and an axial local diffusion tensor, D₂, with principal values D(2,||) and D(2,⊥). For α-helices and β-sheets we find that S₀² ~ -0.5 (strong local ordering), -1.2 < S₂² < -0.8 (large S tensor anisotropy), D(2,⊥) ~ D₁ = 1.93 × 10⁷ s⁻¹ (D₁ is the global diffusion rate), and log(D(2,||)/D₁) ~ 4. For α-helices the z-axis of the local ordering frame is parallel to the C(α)-C(α) axis. For β-sheets the z-axes of the S and D₂ tensors are parallel to the N-H bond. For loops and terminal chain segments the local ordering is generally weaker and more isotropic. On average, D(2,⊥) ~ D₁ also, but log(D(2,||)/D₁) is on the order of 1-2. The tensor orientations are diversified. This study sets forth an integrated computational approach for treating NMR relaxation in proteins by combining stochastic modeling and molecular dynamics. The approach developed provides new insights by its application to a protein that experiences complex dynamics.

Direct use of 15N relaxation rates as experimental restraints on molecular shape and orientation for docking of protein-protein complexes

(15)N relaxation rates contain information on overall molecular shape and size, as well as residue specific orientations of N-H bond vectors relative to the axes of the diffusion tensor. Here we describe a pseudopotential E(relax) that permits direct use of (15)N relaxation rates, in the form of R(2)/R(1) ratios, as experimental restraints in structure calculations without requiring prior information to be extracted from a known molecular structure. The elements of the rotational diffusion tensor are calculated from the atomic coordinates at each step of the structure calculation and then used together with the N-H bond vector orientations to compute the (15)N R(2)/R(1) ratios. We show that the E(relax) term can be reliably used for protein-protein docking of complexes and illustrate its applicability to the 40 kDa complex of the N-terminal domain of enzyme I and the histidine phosphocarrier protein HPr and to the symmetric HIV-1 protease dimer.

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

We describe a new, computationally efficient method for computing the molecular alignment tensor based on the molecular shape. The increase in speed is achieved by re-expressing the problem as one of numerical integration, rather than a simple uniform sampling (as in the PALES method), and by using a convex hull rather than a detailed representation of the surface of a molecule. This method is applicable to bicelles, PEG/hexanol, and other alignment media that can be modeled by steric restrictions introduced by a planar barrier. This method is used to further explore and compare various representations of protein shape by an equivalent ellipsoid. We also examine the accuracy of the alignment tensor and residual dipolar couplings (RDC) prediction using various ab initio methods. We separately quantify the inaccuracy in RDC prediction caused by the inaccuracy in the orientation and in the magnitude of the alignment tensor, concluding that orientation accuracy is much more important in accurate prediction of RDCs.

Using the experimentally determined components of the overall rotational diffusion tensor to restrain molecular shape and size in NMR structure determination of globular proteins and protein-protein complexes

This paper describes an approach for making use of the components of the experimentally determined rotational diffusion tensor derived from NMR relaxation measurements in macromolecular structure determination. The parameters of the rotational diffusion tensor describe the shape and size of the macromolecule or macromolecular complex, and are therefore complementary to traditional NMR restraints. The structural information contained in the rotational diffusion tensor is not dissimilar to that present in the small-angle region of solution X-ray scattering profiles. We demonstrate the utility of rotational diffusion tensor restraints for protein structure refinement using the N-terminal domain of enzyme I (EIN) as an example and validate the results by solution small-angle X-ray scattering. We also show how rotational diffusion tensor restraints can be used for docking complexes using the dimeric HIV-1 protease and the EIN-HPr complexes as examples. In the former case, the rotational diffusion tensor restraints are sufficient in their own right to determine the position of one subunit relative to another. In the latter case, rotational diffusion tensor restraints complemented by highly ambiguous distance restraints derived from chemical shift perturbation mapping and a hydrophobic contact potential are sufficient to correctly dock EIN to HPr. In each case, the cluster containing the lowest-energy structure corresponds to the correct solution.

Evidence for domain motion in proteins affecting global diffusion properties: a nuclear magnetic resonance study

The rotational diffusion of proteins is an important hydrodynamic property. Compact protein structures were found previously to exhibit hydration layer viscosity, etaloc, higher than the viscosity of bulk water, eta. This implies an apparent activation energy for rotational diffusion higher than the activation energy of water viscosity, Eeta=15.4+/-0.3 kJ/mol. In this study we examine etaloc of internally mobile proteins using 15N spin relaxation methods. We also examine the activation enthalpy, DeltaH#, and activation entropy, DeltaS#, for rotational diffusion. Of particular relevance are internally mobile ligand-free forms and compact ligand-bound forms of multidomain proteins. Adenylate kinase (AKeco) and Ca2+-calmodulin (Ca2+-CaM) are typical examples. For AKeco (Ca2+-CaM) we find that DeltaH# is 14.5+/-0.5 (15.7+/-0.4) kJ/mol. For the complex of AKeco with the inhibitor AP5A (the complex of Ca2+-CaM with the peptide smMLCKp), we find that DeltaH# is 18.1+/-0.7 (18.2+/-0.5) kJ/mol. The internally mobile outer surface protein A has DeltaH#=12.6+/-0.8 kJ/mol, and the compact protein Staphylococcal nuclease has DeltaH#=18.8+/-0.6 kJ/mol. For the internally mobile and compact proteins studied, <|DeltaS(|> equals 62+/-7 J/(mol K) and 44+/-5 J/(mol K), respectively. The fact is that etaloc>eta (DeltaH#>Eeta) for compact proteins was ascribed previously to electrostatic interactions between surface sites and water rigidifying the hydration layer. We find herein that obliteration of these interactions by domain motion leads to etaloc approximately eta, DeltaH# approximately Eeta, and large activation entropy for internally mobile protein structures.

Effect of knotting on polymer shapes and their enveloping ellipsoids

We simulate freely jointed chains to investigate how knotting affects the overall shapes of freely fluctuating circular polymeric chains. To characterize the shapes of knotted polygons, we construct enveloping ellipsoids that minimize volume while containing the entire polygon. The lengths of the three principal axes of the enveloping ellipsoids are used to define universal size and shape descriptors analogous to the squared radius of gyration and the inertial asphericity and prolateness. We observe that polymeric chains forming more complex knots are more spherical and also more prolate than chains forming less complex knots with the same number of edges. We compare the shape measures, determined by the enveloping ellipsoids, with those based on constructing inertial ellipsoids and explain the differences between these two measures of polymer shape.

Influence of the coupling of interdomain and overall motions on NMR relaxation

Most theoretical models for NMR relaxation in liquids assume that overall rotational motion can be described as rotational diffusion with a single diffusion tensor. Such models cannot handle motions (such as between "closed" and "open" states of an enzyme, or between conformers of a partially disordered system) where the shape of the molecule (and hence its rotational diffusion behavior) fluctuates. We provide here a formalism for dealing with such problems. The model involves jumps between discrete conformers with different overall diffusion tensors, and a master (rate) equation to describe the transitions between these conformers. Numerical examples are given for a two-site jump model where global and local motions are concerted, showing how the rate of conformational transitions (relative to the rate of rotational diffusion) affects the observed relaxation parameters.

Hydrodynamic modeling of diffusion tensor properties of flexible molecules

We present a computationally efficient implementation of hydrodynamic modeling for the evaluation of diffusion tensors of molecules with internal degrees of freedom, adapted to take into account information from linear scaling computations of solvent accessible surfaces implemented in the framework of last generation continuum solvent models. Torsional angles are taken also explicitly into account, while retaining correct hydrodynamic interactions. A comparison with literature data is presented to prove the effectiveness of the approach for a wide range of molecular dimensions and solvent environments.

Description of the low-affinity interaction between nociceptin and the second extracellular loop of its receptor by fluorescence and NMR spectroscopies

The second extracellular loop (ECL2) of the Noc receptor has been proposed to be involved in ligand binding and selectivity. The interaction of Noc with a constrained cyclic synthetic peptide, mimicking the ECL2, has been studied using fluorescence and NMR spectroscopies. Selective binding was shown with a dissociation constant of approximately 10 microM (observed with the constrained cyclic loop and not with the open chain), and residues involved in ligand binding and selectivity have been identified. This bimolecular complex is stabilized by (i) ionic interactions between the two Noc basic motives and the ECL2 acidic residues; (ii) hydrophobic contacts involving Noc FGGF N-terminal sequence and an ECL2 tryptophane residue. Our data confirm that Noc receptor's ECL2 contributes actively to ligand binding and selectivity by providing the peptidic ligand with a low affinity-binding site.

An overview of recent developments in the interpretation and prediction of fast internal protein dynamics

During the past decades, NMR spectroscopy has emerged as a unique tool for the study of protein dynamics. Indeed, relaxation studies on isotopically labeled proteins can provide information on the overall motions as well as the internal fast, sub-nanosecond, dynamics. Therefore, the interpretation and the prediction of spin relaxation rates in proteins are important issues that have motivated numerous theoretical and methodological developments, including the description of overall dynamics and its possible coupling to internal mobility, the introduction of models of internal dynamics, the determination of correlation functions from experimental data, and the relationship between relaxation and thermodynamical quantities. A brief account of recent developments that have proven useful in this domain are presented.

Structural assembly of multidomain proteins and protein complexes guided by the overall rotational diffusion tensor

We present a simple and robust approach that uses the overall rotational diffusion tensor as a structural constraint for domain positioning in multidomain proteins and protein-protein complexes. This method offers the possibility to use NMR relaxation data for detailed structure characterization of such systems provided the structures of individual domains are available. The proposed approach extends the concept of using long-range information contained in the overall rotational diffusion tensor. In contrast to the existing approaches, we use both the principal axes and principal values of protein's rotational diffusion tensor to determine not only the orientation but also the relative positioning of the individual domains in a protein. This is achieved by finding the domain arrangement in a molecule that provides the best possible agreement with all components of the overall rotational diffusion tensor derived from experimental data. The accuracy of the proposed approach is demonstrated for two protein systems with known domain arrangement and parameters of the overall tumbling: the HIV-1 protease homodimer and Maltose Binding Protein. The accuracy of the method and its sensitivity to domain positioning are also tested using computer-generated data for three protein complexes, for which the experimental diffusion tensors are not available. In addition, the proposed method is applied here to determine, for the first time, the structure of both open and closed conformations of a Lys48-linked diubiquitin chain, where domain motions render impossible accurate structure determination by other methods. The proposed method opens new avenues for improving structure characterization of proteins in solution.

Measurement of dissociation constants of high-molecular weight protein-protein complexes by transferred 15N-relaxation

The use of (15)N-relaxation data for determination of the dissociation constant of a protein-protein complex is proposed for the situation where a (15)N-labeled protein is bound to an unlabeled protein of high molecular weight, and the chemical exchange between bound and free protein is fast on the NMR time scale. The approach is shown to be suitable for estimating dissociation constants in the micromolar to millimolar range, using protein solutions at relatively low concentration. An example is shown for the interaction between two subunits from the Escherichia coli DNA polymerase III complex, involving a (15)N-labeled fragment of the C-terminal domain of the tau subunit (15 kDa) and the unlabeled alpha subunit (130 kDa).