Characterization of NMR relaxation-active motions of a partially folded A-state analogue of ubiquitin

One touch is all it takes: the supramolecular interaction between ubiquitin and lanthanide complexes revisited by paramagnetic NMR and molecular dynamics

The supramolecular interaction between lanthanide complexes and proteins is at the heart of numerous chemical and biological studies. Some of these complexes have demonstrated remarkable interaction properties with proteins or peptides in solution and in the crystalline state. Here we have used the paramagnetism of lanthanide ions to characterize the affinity of two lanthanide complexes for ubiquitin. As the interaction process is dynamic, the acquired NMR data only reflect the time average of the different steps. We have used molecular dynamics (MD) simulations to get a deeper insight into the detailed interaction scenario at the microsecond scale. This NMR/MD approach enabled us to establish that the tris-dipicolinate complex interacts specifically with arginines and lysines, while the crystallophore explores the protein surface through weak interactions with carboxylates. These observations shed new light on the dynamic interaction properties of these complexes, which will ultimately enable us to propose a crystallization mechanism.

Quantitative prediction of ensemble dynamics, shapes and contact propensities of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are highly dynamic systems that play an important role in cell signaling processes and their misfunction often causes human disease. Proper understanding of IDP function not only requires the realistic characterization of their three-dimensional conformational ensembles at atomic-level resolution but also of the time scales of interconversion between their conformational substates. Large sets of experimental data are often used in combination with molecular modeling to restrain or bias models to improve agreement with experiment. It is shown here for the N-terminal transactivation domain of p53 (p53TAD) and Pup, which are two IDPs that fold upon binding to their targets, how the latest advancements in molecular dynamics (MD) simulations methodology produces native conformational ensembles by combining replica exchange with series of microsecond MD simulations. They closely reproduce experimental data at the global conformational ensemble level, in terms of the distribution properties of the radius of gyration tensor, and at the local level, in terms of NMR properties including 15N spin relaxation, without the need for reweighting. Further inspection revealed that 10-20% of the individual MD trajectories display the formation of secondary structures not observed in the experimental NMR data. The IDP ensembles were analyzed by graph theory to identify dominant inter-residue contact clusters and characteristic amino-acid contact propensities. These findings indicate that modern MD force fields with residue-specific backbone potentials can produce highly realistic IDP ensembles sampling a hierarchy of nano- and picosecond time scales providing new insights into their biological function.

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.

Atomic resolution conformational dynamics of intrinsically disordered proteins from NMR spin relaxation

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful experimental approaches for investigating the conformational behaviour of intrinsically disordered proteins (IDPs). IDPs represent a significant fraction of all proteomes, and, despite their importance for understanding fundamental biological processes, the molecular basis of their activity still remains largely unknown. The functional mechanisms exploited by IDPs in their interactions with other biomolecules are defined by their intrinsic dynamic modes and associated timescales, justifying the considerable interest over recent years in the development of technologies adapted to measure and describe this behaviour. NMR spin relaxation delivers information-rich, site-specific data reporting on conformational fluctuations occurring throughout the molecule. Here we review recent progress in the use of ¹⁵N relaxation to identify local backbone dynamics and long-range chain-like motions in unfolded proteins.

Action-FRET of a Gaseous Protein

Mass spectrometry is an extremely powerful technique for analysis of biological molecules, in particular proteins. One aspect that has been contentious is how much native solution-phase structure is preserved upon transposition to the gas phase by soft ionization methods such as electrospray ionization. To address this question-and thus further develop mass spectrometry as a tool for structural biology-structure-sensitive techniques must be developed to probe the gas-phase conformations of proteins. Here, we report Förster resonance energy transfer (FRET) measurements on a ubiquitin mutant using specific photofragmentation as a reporter of the FRET efficiency. The FRET data is interpreted in the context of circular dichroism, molecular dynamics simulation, and ion mobility data. Both the dependence of the FRET efficiency on the charge state-where a systematic decrease is observed-and on methanol concentration are considered. In the latter case, a decrease in FRET efficiency with methanol concentration is taken as evidence that the conformational ensemble of gaseous protein cations retains a memory of the solution phase conformational ensemble upon electrospray ionization. Graphical Abstract ᅟ.

Validation of Molecular Dynamics Simulations of Biomolecules Using NMR Spin Relaxation as Benchmarks: Application to the AMBER99SB Force Field

Biological function of biomolecules is accompanied by a wide range of motional behavior. Accurate modeling of dynamics by molecular dynamics (MD) computer simulations is therefore a useful approach toward the understanding of biomolecular function. NMR spin relaxation measurements provide rigorous benchmarks for assessing important aspects of MD simulations, such as the amount and time scales of conformational space sampling, which are intimately related to the underlying molecular mechanics force field. Until recently, most simulations produced trajectories that exhibited too much dynamics particularly in flexible loop regions. Recent modifications made to the backbone φ and ψ torsion angle potentials of the AMBER and CHARMM force fields indicate that these changes produce more realistic molecular dynamics behavior. To assess the consequences of these changes, we performed a series of 5-20 ns molecular dynamics trajectories of human ubiquitin using the AMBER99 and AMBER99SB force fields for different conditions and water models and compare the results with NMR experimental backbone N-H S(2) order parameters. A quantitative analysis of the trajectories shows significantly improved agreement with experimental NMR data for the AMBER99SB force field as compared to AMBER99. Because NMR spin relaxation data (T1, T2, NOE) reflect the combined effects of spatial and temporal fluctuations of bond vectors, it is found that comparison of experimental and back-calculated NMR spin-relaxation data provides a more objective way of assessing the quality of the trajectory than order parameters alone. Analysis of a key mobile β-hairpin in ubiquitin demonstrates that the dynamics of mobile sites are not only reduced by the modified force field, but the extent of motional correlations between amino acids is also markedly diminished.

Defining the nature of thermal intermediate in 3 state folding proteins: apoflavodoxin, a study case

The early stages of the thermal unfolding of apoflavodoxin have been determined by using atomistic multi microsecond-scale molecular dynamics (MD) simulations complemented with a variety of experimental techniques. Results strongly suggest that the intermediate is reached very early in the thermal unfolding process and that it has the properties of an “activated” form of the native state, where thermal fluctuations in the loops break loop-loop contacts. The unrestrained loops gain then kinetic energy corrupting short secondary structure elements without corrupting the core of the protein. The MD-derived ensembles agree with experimental observables and draw a picture of the intermediate state inconsistent with a well-defined structure and characteristic of a typical partially disordered protein. Our results allow us to speculate that proteins with a well packed core connected by long loops might behave as partially disordered proteins under native conditions, or alternatively behave as three state folders. Small details in the sequence, easily tunable by evolution, can yield to one or the other type of proteins.

A simplistic view of protein structure tends to emphasize the opposition between the native state and the denatured ensemble of unfolded conformations. In addition to these extreme conformations, proteins subjected to a variety of perturbations often populate alternative partly unfolded conformations, some of which are close in energy to the native state and, accordingly, can be populated under native or quasi-native conditions. There is increasing evidence that these “perturbed” conformations participate in protein function or, in some cases, are related to the outcome of folding diseases. We have used the “state of the art” molecular dynamics combined with a variety of experimental techniques to characterize for the first time, to our knowledge, the thermal intermediate of a three-state folding protein (apoflavodoxin). Based on our results we have been able to suggest a general mechanism of thermal unfolding in complex proteins and to determine interesting links between thermal intermediates and partially unfolded proteins.

Molecular dynamics simulations of the native and partially folded states of ubiquitin: influence of methanol cosolvent, pH, and temperature on the protein structure and dynamics

A series of explicit-solvent molecular dynamics simulations of the protein ubiquitin are reported, which investigate the effect of environmental factors (presence of methanol cosolvent in the aqueous solution, neutral or low pH value, room or elevated temperature) on the structure, stability, and dynamics of the protein. The simulations are initiated either from the native structure of the protein or from a model of a partially folded state (A-state) that is known to exist at low pH in methanol-water mixtures. The main results of the simulations are: (1) The ubiquitin native structure is remarkably stable at neutral pH in water; (2) the addition of the methanol cosolvent enhances the stability of the secondary structure but weakens tertiary interactions within the protein; (3) this influence of methanol on the protein structure is enhanced at low pH, while the effect of lowering the pH in pure water is limited; and (4) the A-state of ubiquitin can be described as a set of relatively rigid secondary structure elements (a native-like beta-sheet and native-like alpha-helix plus two nonnative alpha-helices) connected by flexible linkers.

Ubiquitin folds through a highly polarized transition state

The small alpha/beta protein ubiquitin has been used as a model system for experimental and computational studies on protein folding for many years. Here, we present a comprehensive phi-value analysis and characterize the structure and energetics of the transition state ensemble (TSE). Twenty-seven non-disruptive mutations are made throughout the structure and a range of phi-values from zero to one are observed. The values cluster such that medium and high values and found only in the N-terminal region of the protein, whilst the C-terminal region has consistently low phi-values. In the TSE, the main alpha-helix appears to be fully formed (two phi-values which specifically probe helical structure are one) and the helix is stabilized by packing against the first beta-turn, which is partially structured. In striking comparison, the phi-values in the C-terminal region are all very low, suggesting that this region of the protein is largely unstructured in the TSE. Data are consistent with a nucleation-condensation mechanism in which there is a highly polarized folding nucleus comprising the first beta-hairpin and the alpha-helix. Data presented from the protein engineering study and phi-value analysis are compared with results from other experimental studies and also computational studies.

Hyaluronan chain conformation and dynamics

An overview of the present state of research in the field of hyaluronan chain conformational aspects is presented. The relationship between structure and dynamics are illustrated for a series of hyaluronan oligomers. Conformational characteristics of hyaluronan chains are discussed, together with the dynamic chain patterns, evaluated by using a theoretical approach to diffusive polymer dynamics. The dependence of correlation times and NMR relaxation parameters from the chain dimension are investigated. Topological features and dimensional properties are related to the structural determinants by using classical computational methods of molecular mechanics and Monte Carlo simulation.

Quantitative comparison of the hydrogen bond network of A-state and native ubiquitin by hydrogen bond scalar couplings

The backbone hydrogen bond (H-bond) network of the partially folded A-state of ubiquitin (60% methanol, 40% water, pH 2) has been characterized quantitatively by (h3)J(NC)(') H-bond scalar couplings between the (15)N nuclei of amino acid H-bond donors and the (13)C carbonyl nuclei of the acceptors. Results on (h3)J(NC)(') couplings and the amide proton ((1)H(N)) chemical shifts for the A-state are compared quantitatively to the native state. The (h3)J(NC)(') correlations of the A-state show intact, nativelike H-bonds of the first beta-hairpin beta1/beta2 and the alpha-helix, albeit at lower strength, whereas the H-bonds in the C-terminal part change from a pure beta-structure to an all alpha-helical H(N)(i)-->O(i-4) connectivity pattern. A residue-specific analysis reveals that the conformations within the conserved secondary structure segments are much more homogeneous in the A-state than in the native state. Thus, the strong asymmetry of (h3)J(NC)(') couplings and (1)H(N) chemical shifts between the interior and exterior sides of the native state alpha-helix vanishes in the A-state. This indicates that the bend of this helix around the native state hydrophobic core is released in the homogeneous solvent environment of the A-state. Similarly, an irregularity in the behavior of H-bond I3-->L15 in hairpin beta1/beta2, which results from strong contacts to strand beta5 in the native state, is absent in the A-state. These findings rationalize the behavior of the (1)H(N) chemical shifts in both states and indicate that the A-state is in many aspects similar to the onset of thermal denaturation of the native state.

Increased rigidity of eglin c at acidic pH: evidence from NMR spin relaxation and MD simulations

To gain physical insights into how proteins respond to changes in pH, the picosecond to nanosecond time scale dynamics of the small serine protease inhibitor eglin c have been studied by NMR spin relaxation experiments and MD simulations under two pH solution conditions, pH 7 and 3. Like many proteins, eglin c is destabilized by a lowering of the pH, although it retains enough stability to maintain its native conformation at pH 3. Backbone (15)N relaxation results show comparable global tumbling times (tau(m)) and model-free order parameters (S(2)) under the two pH conditions, indicating that the molecule maintains its overall molecular shape and structure at low pH, although the backbone rigidity is slightly increased (<DeltaS(pH3-pH7)(2)>/<S(2)> = 0.6%). In contrast, the side-chain methyl dynamics, as measured from (2)H relaxation experiments, show a substantial increase in rigidity at lower pH (<DeltaS(axis,pH3-pH7)(2)>/<S(axis)(2)> = 14.8%). Molecular dynamics simulations performed at these pH states produce results consistent with NMR measurements, showing that the two methods are in qualitative agreement. Although a full accounting of the physical basis for the concurrent conformational rigidification and destabilization at low pH requires further investigation, the high level of detail in the MD simulations provides a potential molecular mechanism: the breaking of the hydrogen bond between the side chains of Asp46 and Arg53, and changes in electrostatic interactions, appear to allow the binding loop to move closer to the core part of the protein, resulting in a more compact structure at low pH. This more compact structure may be responsible for the increased level of restriction of molecular motion. As these findings show, the stability of a molecular structure is distinct from its conformational rigidity, and the two can even change in opposite directions, against naïve expectation.

Modeling the dynamics of the solvated SL1 domain of HIV-1 genomic RNA

A mode-coupling solution of the Smoluchowski diffusion equation (MCD theory), designed to describe the dynamics of wobbling macromolecules in water, is applied to a macromolecular bead model including water beads in the nearest layers. The necessary statistical averages are evaluated by time averaging along a molecular dynamics (MD) trajectory where both solute and water are introduced as atomistic models. The cross peaks in (1)H nuclear Overhauser effect spectroscopy (NOESY) NMR spectra that are routinely measured to determine biological structures are here calculated for the mutated 23 nucleotides stem-loop fragment of the SL1 domain in the HIV-1(Lai) genomic RNA. The calculations are in acceptable agreement with experiments without requiring any screening of the hydrodynamic interactions. The screening of hydrodynamics was necessary in previous MCD calculations obtained by using the same full atomistic MD trajectory, but a nonsolvated frictional model.

Efficient RMSD measures for the comparison of two molecular ensembles. Root-mean-square deviation

Quantitative measures are presented for comparing the conformations of two molecular ensembles. The measures are based on Kabsch's formula for the root-mean-square deviation (RMSD) and the covariance matrix of atomic positions of isotropically distributed ensembles (IDE). By using a Taylor series expansion, it is shown that the RMSD can be expressed solely in terms of the IDE matrices. A fast approximate method is introduced for the pairwise RMSD determination whose computational cost scales linearly with the number of structures. A similarity measure for two structural ensembles that is based on the trace metric of the differences of powers of the IDE matrices is presented. The measures are illustrated for conformational ensembles generated by a molecular dynamics computer simulation of a partially folded A-state analog of ubiquitin.

Protein unfolding transitions in an intrinsically unstable annexin domain: molecular dynamics simulation and comparison with nuclear magnetic resonance data

Unfolding transitions of an intrinsically unstable annexin domain and the unfolded state structure have been examined using multiple approximately 10-ns molecular dynamics simulations. Three main basins are observed in the configurational space: native-like state, compact partially unfolded or intermediate compact state, and the unfolded state. In the native-like state fluctuations are observed that are nonproductive for unfolding. During these fluctuations, after an initial loss of approximately 20% of the core residue native contacts, the core of the protein transiently completely refolds to the native state. The transition from the native-like basin to the partially unfolded compact state involves approximately 75% loss of native contacts but little change in the radius of gyration or core hydration properties. The intermediate state adopts for part of the time in one of the trajectories a novel highly compact salt-bridge stabilized structure that can be identified as a conformational trap. The intermediate-to-unfolded state transition is characterized by a large increase in the radius of gyration. After an initial relaxation the unfolded state recovers a native-like topology of the domain. The simulated unfolded state ensemble reproduces in detail experimental nuclear magnetic resonance data and leads to a convincing complete picture of the unfolded domain.

General framework for studying the dynamics of folded and nonfolded proteins by NMR relaxation spectroscopy and MD simulation

A general framework is presented for the interpretation of NMR relaxation data of proteins. The method, termed isotropic reorientational eigenmode dynamics (iRED), relies on a principal component analysis of the isotropically averaged covariance matrix of the lattice functions of the spin interactions responsible for spin relaxation. The covariance matrix, which is evaluated using a molecular dynamics (MD) simulation, is diagonalized yielding reorientational eigenmodes and amplitudes that reveal detailed information about correlated protein dynamics. The eigenvalue distribution allows one to quantitatively assess whether overall and internal motions are statistically separable. To each eigenmode belongs a correlation time that can be adjusted to optimally reproduce experimental relaxation parameters. A key feature of the method is that it does not require separability of overall tumbling and internal motions, which makes it applicable to a wide range of systems, such as folded, partially folded, and unfolded biomolecular systems and other macromolecules in solution. The approach was applied to NMR relaxation data of ubiquitin collected at multiple magnetic fields in the native form and in the partially folded A-state using MD trajectories with lengths of 6 and 70 ns. The relaxation data of native ubiquitin are well reproduced after adjustment of the correlation times of the 10 largest eigenmodes. For this state, a high degree of separability between internal and overall motions is present as is reflected in large amplitude and collectivity gaps between internal and overall reorientational modes. In contrast, no such separability exists for the A-state. Residual overall tumbling motion involving the N-terminal beta-sheet and the central helix is observed for two of the largest modes only. By adjusting the correlation times of the 10 largest modes, a high degree of consistency between the experimental relaxation data and the iRED model is reached for this highly flexible biomolecule.

Dynamic and structural analysis of isotropically distributed molecular ensembles

An efficient new method is presented for the characterization of motional correlations derived from a set of protein structures without requiring the separation of overall and internal motion. In this method, termed isotropically distributed ensemble (IDE) analysis, each structure is represented by an ensemble of isotropically distributed replicas corresponding to the situation found in an isotropic protein solution. This leads to a covariance matrix of the cartesian atomic positions with elements proportional to the ensemble average of scalar products of the position vectors with respect to the center of mass. Diagonalization of the covariance matrix yields eigenmodes and amplitudes that describe concerted motions of atoms, including overall rotational and intramolecular dynamics. It is demonstrated that this covariance matrix naturally distinguishes between "rigid" and "mobile" parts without necessitating a priori selection of a reference structure and an atom set for the orientational alignment process. The method was applied to the analysis of a 5-ns molecular dynamics trajectory of native ubiquitin and a 40-ns trajectory of a partially folded state of ubiquitin. The results were compared with essential dynamics analysis. By taking advantage of the spherical symmetry of the IDE covariance matrix, more than a 10-fold speed up is achieved for the computation of eigenmodes and mode amplitudes. IDE analysis is particularly suitable for studying the correlated dynamics of flexible and large molecules.

Temperature dependence of dynamics and thermodynamics of the regulatory domain of human cardiac troponin C

Binding of Ca(2+) to the regulatory domain of troponin C (TnC) in cardiac muscle initiates a series of protein conformational changes and modified protein-protein interactions that initiate contraction. Cardiac TnC contains two Ca(2+) binding sites, with one site being naturally defunct. Previously, binding of Ca(2+) to the functional site in the regulatory domain of TnC was shown to lead to a decrease in conformational entropy (TDeltaS) of 2 and 0.5 kcal mol(-1) for the functional and nonfunctional sites, respectively, using (15)N nuclear magnetic resonance (NMR) relaxation studies [Spyracopoulos, L., et al. (1998) Biochemistry 37, 18032-18044]. In this study, backbone dynamics of the Ca(2+)-free regulatory domain are investigated by backbone amide (15)N relaxation measurements at eight temperatures from 5 to 45 degrees C. Analysis of the relaxation measurements yields an order parameter (S(2)) indicating the degree of spatial restriction for a backbone amide H-N vector. The temperature dependence of S(2) allows estimation of the contribution to protein heat capacity from pico- to nanosecond time scale conformational fluctuations on a per residue basis. The average heat capacity contribution (C(p,j)) from backbone conformational fluctuations for regions of secondary structure for the regulatory domain of cardiac apo-TnC is 6 cal mol(-1) K(-1). The average heat capacity for Ca(2+) binding site 1 is larger than that for site 2 by 1.3 +/- 0.8 cal mol(-1) K(-1), and likely represents a mechanism where differences in affinity between Ca(2+) binding sites for EF hand proteins can be modulated.

Thermodynamic insights into proteins from NMR spin relaxation studies

NMR spin relaxation measurements of picosecond to nanosecond timescale backbone and sidechain fluctuations of protein molecules, and subsequent entropic interpretation yield interesting, but sometimes counterintuitive, insights into proteins. The stabilities of proteins and protein interactions are achieved through enthalpy-entropy compensation, which is partitioned between the backbone and sidechains depending on the nature of the system.

Reorientational eigenmode dynamics: a combined MD/NMR relaxation analysis method for flexible parts in globular proteins

An approach is presented for the interpretation of heteronuclear NMR spin relaxation data in mobile protein parts in terms of reorientational eigenmode dynamics. The method is based on the covariance matrix of the spatial functions of the nuclear spin interactions that cause relaxation expressed as spherical harmonics of rank 2. The approach was applied to characterize the dynamics of a loop region of ubiquitin. The covariance matrix was determined from a conformational ensemble generated by a 5 ns molecular dynamics simulation. It was found that the time correlation functions of the dominant eigenmodes decay in good approximation with a single correlation time. From the reorientational eigenmodes, their eigenvalues, and correlation times, NMR relaxation data were calculated in accordance with Bloch-Wangsness-Redfield relaxation theory and directly compared with experimental (15)N relaxation parameters. Using a fitting procedure, agreement between calculated and experimental data was improved significantly by adjusting eigenvalues and correlation times of the dominant modes. The presented procedure provides detailed information on correlated reorientational dynamics of flexible parts in globular proteins. The covariance matrix was linked to the covariance matrix of backbone dihedral angle fluctuations, allowing one to study the motional behavior of these degrees of freedom on nano- and subnanosecond time scales.

NMR relaxation studies of the role of conformational entropy in protein stability and ligand binding

Recent advances in the measurement and analysis of protein NMR relaxation data have made it possible to characterize the dynamical properties of many backbone and side chain groups. With certain caveats, changes in flexibility that occur upon ligand binding, mutation, or changes in sample conditions can be interpreted in terms of contributions to conformational entropy. Backbone and side chain flexibility can either decrease or increase upon ligand binding. Decreases are often associated with "enthalpy-entropy compensation" and "induced fit" binding, whereas increases in conformational entropy can contribute to stabilization of complexes. In certain cases, conformational entropy appears to play a role in cooperative binding and enzyme catalysis. In addition, variations in conformational entropy and heat capacity may both be important in stabilizing the folded structures of proteins.