Fast time scale dynamics of protein backbones: NMR relaxation methods, applications, and functional consequences

The entropic nature of protein thermal stabilization

We performed thermodynamic analysis of temperature-induced unfolding of mesophilic and thermophilic proteins. It was shown that the variability in protein thermostability associated with pH-dependent unfolding or linked to the substitution of amino acid residues on the protein surface is evidence of the governing role of the entropy factor. Numerical values of conformational components in enthalpy, entropy and free energy which characterize protein unfolding in the "gas phase" were obtained. Based on the calculated absolute values of entropy and free energy, a model of protein unfolding is proposed in which the driving force is the conformational entropy of native protein, as an energy of the heat motion (T·S(NC)) increasing with temperature and acting as an factor devaluating the energy of intramolecular weak bonds in the transition state.

Thermodynamic and structural determinants of differential Pdx1 binding to elements from the insulin and IAPP promoters

In adult mammals, the production of insulin and other peptide hormones, such as the islet amyloid polypeptide (IAPP), is limited to β-cells due to tissue-specific expression of a set of transcription factors, the best known of which is pancreatic duodenal homeobox protein 1 (Pdx1). Like many homeodomain transcription factors, Pdx1 binds to a core DNA recognition sequence containing the tetranucleotide 5'-TAAT-3'; its consensus recognition element is 5'-CTCTAAT(T/G)AG-3'. Currently, a complete thermodynamic profile of Pdx1 binding to near-consensus and native promoter sequences has not been established, obscuring the mechanism of target site selection by this critical transcription factor. Strikingly, while Pdx1 responsive elements in the human insulin promoter conform to the pentanucleotide 5'-CTAAT-3' sequence, the Pdx1 responsive elements in the human iapp promoter all contain a substitution to 5'-TTAAT-3'. The crystal structure of Pdx1 bound to the consensus nucleotide sequence does not explain how Pdx1 identifies this natural variation, if it does at all. Here we report a combination of isothermal calorimetric titrations, NMR spectroscopy, and extensive multi-microsecond molecular dynamics calculations of Pdx1 that define its interactions with a panel of natural promoter elements and consensus-derived sequences. Our results show a small preference of Pdx1 for a C base 5' relative to the core TAAT promoter element. Molecular mechanics calculations, corroborated by experimental NMR data, lead to a rational explanation for sequence discrimination at this position. Taken together, our results suggest a molecular mechanism for differential Pdx1 affinity to elements from the insulin and iapp promoter sequences.

A 13C labeling strategy reveals a range of aromatic side chain motion in calmodulin

NMR relaxation experiments often require site-specific isotopic enrichment schemes in order to allow for quantitative interpretation. Here we describe a new labeling scheme for site-specific (13)C-(1)H enrichment of a single ortho position of aromatic amino acid side chains in an otherwise perdeuterated background by employing a combination of [4-(13)C]erythrose and deuterated pyruvate during growth on deuterium oxide. This labeling scheme largely eliminates undesired contributions to (13)C relaxation and greatly simplifies the fitting of relaxation data using the Lipari-Szabo model-free formalism. This approach is illustrated with calcium-saturated vertebrate calmodulin and oxidized flavodoxin from Cyanobacterium anabaena . Analysis of (13)C relaxation in the aromatic groups of calcium-saturated calmodulin indicates a wide range of motion in the subnanosecond time regime.

The C-terminal V5 domain of Protein Kinase Cα is intrinsically disordered, with propensity to associate with a membrane mimetic

The C-terminal V5 domain is one of the most variable domains in Protein Kinase C isoforms (PKCs). V5 confers isoform specificity on its parent enzyme through interactions with isoform-specific adaptor proteins and possibly through specific intra-molecular interactions with other PKC domains. The structural information about V5 domains in solution is sparse. The objective of this work was to determine the conformational preferences of the V5 domain from the α isoform of PKC (V5α) and evaluate its ability to associate with membrane mimetics. We show that V5α and its phosphorylation-mimicking variant, dmV5α, are intrinsically disordered protein domains. Phosphorylation-mimicking mutations do not alter the overall conformation of the polypeptide backbone, as evidenced by the local nature of chemical shift perturbations and the secondary structure propensity scores. However, the population of the “cis-trans” conformer of the Thr⁶³⁸-Pro⁶³⁹-Pro⁶⁴⁰ turn motif, which has been implicated in the down-regulation of PKCα via peptidyl-prolyl isomerase Pin1, increases in dmV5α, along with the conformational flexibility of the region between the turn and hydrophobic motifs. Both wild type and dmV5α associate with micelles made of a zwitterionic detergent, n-dodecylphosphocholine. Upon micelle binding, V5α acquires a higher propensity to form helical structures at the conserved “NFD” motif and the entire C-terminal third of the domain. The ability of V5α to partition into the hydrophobic micellar environment suggests that it may serve as a membrane anchor during the PKC maturation process.

Solution structure, dynamics and binding studies of a family 11 carbohydrate-binding module from Clostridium thermocellum (CtCBM11)

Non-catalytic cellulosomal CBMs (carbohydrate-binding modules) are responsible for increasing the catalytic efficiency of cellulosic enzymes by selectively putting the substrate (a wide range of poly- and oligo-saccharides) and enzyme into close contact. In the present study we carried out an atomistic rationalization of the molecular determinants of ligand specificity for a family 11 CBM from thermophilic Clostridium thermocellum [CtCBM11 (C. thermocellum CBM11)], based on a NMR and molecular modelling approach. We have determined the NMR solution structure of CtCBM11 at 25°C and 50°C and derived information on the residues of the protein that are involved in ligand recognition and on the influence of the length of the saccharide chain on binding. We obtained models of the CtCBM11-cellohexaose and CtCBM11-cellotetraose complexes by docking in accordance with the NMR experimental data. Specific ligand-protein CH-π and Van der Waals interactions were found to be determinant for the stability of the complexes and for defining specificity. Using the order parameters derived from backbone dynamics analysis in the presence and absence of ligand and at 25°C and 50°C, we determined that the protein's backbone conformational entropy is slightly positive. This data in combination with the negative binding entropy calculated from ITC (isothermal titration calorimetry) studies supports a selection mechanism where a rigid protein selects a defined oligosaccharide conformation.

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.

Structural and dynamics characterization of norovirus protease

Norovirus protease is an essential enzyme for proteolytic maturation of norovirus nonstructural proteins and has been implicated as a potential target for antiviral drug development. Although X-ray structural studies of the protease give us wealth of structural information including interactions of the protease with its substrate and dimeric overall structure, the role of protein dynamics in the substrate recognition and the biological relevance of the protease dimer remain unclear. Here we determined the solution NMR structure of the 3C-like protease from Norwalk virus (NV 3CLpro), a prototype strain of norovirus, and analyzed its backbone dynamics and hydrodynamic behavior in solution. ¹⁵N spin relaxation and analytical ultracentrifugation analyses demonstrate that NV 3CLpro is predominantly a monomer in solution. Solution structure of NV 3CLpro shows significant structural variation in C-terminal domain compared with crystal structures and among lower energy structure ensembles. Also, ¹⁵N spin relaxation and Carr-Purcell-Meiboom-Gill (CPMG)-based relaxation dispersion analyses reveal the dynamic properties of residues in the C-terminal domain over a wide range of timescales. In particular, the long loop spanning residues T123-G133 show fast motion (ps-ns), and the residues in the bII-cII region forming the large hydrophobic pocket (S2 site) undergo conformational exchanges on slower timescales (μs-ms), suggesting their important role in substrate recognition.

Protein dynamics in living cells studied by in-cell NMR spectroscopy

Most proteins function in cells where protein concentrations can reach 400 g/l. However, most quantitative studies of protein properties are performed in idealized, dilute conditions. Recently developed in-cell NMR techniques can provide protein structure and other biophysical properties inside living cells at atomic resolution. Here we review how protein dynamics, including global and internal motions have been characterized by in-cell NMR, and then discuss the remaining challenges and future directions.

Analysis of 15N-1H NMR relaxation in proteins by a combined experimental and molecular dynamics simulation approach: picosecond-nanosecond dynamics of the Rho GTPase binding domain of plexin-B1 in the dimeric state indicates allosteric pathways

We investigate picosecond–nanosecond dynamics of the Rho-GTPase Binding Domain (RBD) of plexin-B1, which plays a key role in plexin-mediated cell signaling. Backbone 15N relaxation data of the dimeric RBD are analyzed with the model-free (MF) method, and with the slowly relaxing local structure/molecular dynamics (SRLS-MD) approach. Independent analysis of the MD trajectories, based on the MF paradigm, is also carried out. MF is a widely popular and simple method, SRLS is a general approach, and SRLS-MD is an integrated approach we developed recently. Corresponding parameters from the RBD dimer, a previously studied RBD monomer mutant, and the previously studied complex of the latter with the GTPase Rac1, are compared. The L2, L3, and L4 loops of the plexin-B1 RBD are involved in interactions with other plexin domains, GTPase binding, and RBD dimerization, respectively. Peptide groups in the loops of both the monomeric and dimeric RBD are found to experience weak and moderately asymmetric local ordering centered approximately at the C(i–1)(α)–C(i)(α) axes, and nanosecond backbone motion. Peptide groups in the α-helices and the β-strands of the dimer (the β-strands of the monomer) experience strong and highly asymmetric local ordering centered approximately at the C(i–1)(α)–C(i)(α) axes (N–H bonds). N–H fluctuations occur on the picosecond time scale. An allosteric pathway for GTPase binding, providing new insights into plexin function, is delineated.

A surprising role for conformational entropy in protein function

Formation of high-affinity complexes is critical for the majority of enzymatic reactions involving proteins. The creation of the family of Michaelis and other intermediate complexes during catalysis clearly involves a complicated manifold of interactions that are diverse and complex. Indeed, computing the energetics of interactions between proteins and small molecule ligands using molecular structure alone remains a great challenge. One of the most difficult contributions to the free energy of protein-ligand complexes to access experimentally is that due to changes in protein conformational entropy. Fortunately, recent advances in solution nuclear magnetic resonance (NMR) relaxation methods have enabled the use of measures-of-motion between conformational states of a protein as a proxy for conformational entropy. This review briefly summarizes the experimental approaches currently employed to characterize fast internal motion in proteins, how this information is used to gain insight into conformational entropy, what has been learned, and what the future may hold for this emerging view of protein function.

2H-13C HETCOR MAS NMR for indirect detection of 2H quadrupole patterns and spin-lattice relaxation rates

Two-dimensional (2D) cross-polarization magic angle spinning (CP-MAS) (2)H-(13)C heteronuclear correlation (HETCOR) experiments were utilized to indirectly detect site-specific deuterium MAS powder patterns. The (2)H-(13)C cross-polarization efficiency is orientation-dependent and non-uniform for all crystallites. This leads to difficulty in extracting the correct (2)H MAS quadrupole powder patterns. In order to obtain accurate deuterium line shapes, (13)C spin lock rf field, spin lock rf ramp and CP contact time were carefully calibrated with the assistance of theoretical simulations. The extracted quadrupole patterns for U-[(2)H/(13)C/(15)N]-alanine indicate that the methyl deuterium undergoes classic, three-site jumping in the fast motion regime (10(-8)-10(-12)s) and the methine deuterium has a rigid deuterium powder pattern. For U-[(2)H/(13)C/(15)N]-phenylalanine, indirectly detected deuterium line shapes illustrate that the aromatic ring undergoes 180° flips in the fast motion regime while (2)Hβ and (2)Hα are completely rigid. The experimental deuterium line shapes for U-[(2)H/(13)C/(15)N]-proline reflect that (2)Hβ, (2)Hγ and (2)Hδ are subjected to fast, two-site reorientations at an angle of (15±5)°, (30±5)° and (25±10)° respectively. In addition, an approach that combines a composite inversion pulse with (2)H-(13)C CP-MAS is applied to measure (2)H spin-lattice relaxation times in a site-specific, (13)C-detected fashion.

Starting-structure dependence of nanosecond timescale intersubstate transitions and reproducibility of MD-derived order parameters

Factors affecting the accuracy of molecular dynamics (MD) simulations are investigated by comparing generalized order parameters for backbone NH vectors of the B3 immunoglobulin-binding domain of streptococcal protein G (GB3) derived from simulations with values obtained from NMR spin relaxation (Yao L, Grishaev A, Cornilescu G, Bax A, J Am Chem Soc 2010;132:4295-4309.). Choices for many parameters of the simulations, such as buffer volume, water model, or salt concentration, have only minor influences on the resulting order parameters. In contrast, seemingly minor conformational differences in starting structures, such as orientations of sidechain hydroxyl groups, resulting from applying different protonation algorithms to the same structure, have major effects on backbone dynamics. Some, but not all, of these effects are mitigated by increased sampling in simulations. Most discrepancies between simulated and experimental results occur for residues located at the ends of secondary structures and involve large amplitude nanosecond timescale transitions between distinct conformational substates. These transitions result in autocorrelation functions for bond vector reorientation that do not converge when calculated over individual simulation blocks, typically of length similar to the overall rotational diffusion time. A test for convergence before averaging the order parameters from different blocks results in better agreement between order parameters calculated from different sets of simulations and with NMR-derived order parameters. Thus, MD-derived order parameters are more strongly affected by transitions between conformational substates than by fluctuations within individual substates themselves, while conformational differences in the starting structures affect the frequency and scale of such transitions.

The role of human Dicer-dsRBD in processing small regulatory RNAs

One of the most exciting recent developments in RNA biology has been the discovery of small non-coding RNAs that affect gene expression through the RNA interference (RNAi) mechanism. Two major classes of RNAs involved in RNAi are small interfering RNA (siRNA) and microRNA (miRNA). Dicer, an RNase III enzyme, plays a central role in the RNAi pathway by cleaving precursors of both of these classes of RNAs to form mature siRNAs and miRNAs, which are then loaded into the RNA-induced silencing complex (RISC). miRNA and siRNA precursors are quite structurally distinct; miRNA precursors are short, imperfect hairpins while siRNA precursors are long, perfect duplexes. Nonetheless, Dicer is able to process both. Dicer, like the majority of RNase III enzymes, contains a dsRNA binding domain (dsRBD), but the data are sparse on the exact role this domain plays in the mechanism of Dicer binding and cleavage. To further explore the role of human Dicer-dsRBD in the RNAi pathway, we determined its binding affinity to various RNAs modeling both miRNA and siRNA precursors. Our study shows that Dicer-dsRBD is an avid binder of dsRNA, but its binding is only minimally influenced by a single-stranded – double-stranded junction caused by large terminal loops observed in miRNA precursors. Thus, the Dicer-dsRBD contributes directly to substrate binding but not to the mechanism of differentiating between pre-miRNA and pre-siRNA. In addition, NMR spin relaxation and MD simulations provide an overview of the role that dynamics contribute to the binding mechanism. We compare this current study with our previous studies of the dsRBDs from Drosha and DGCR8 to give a dynamic profile of dsRBDs in their apo-state and a mechanistic view of dsRNA binding by dsRBDs in general.

The dynamic structure of thrombin in solution

The backbone dynamics of human α-thrombin inhibited at the active site serine were analyzed using R(1), R(2), and heteronuclear NOE experiments, variable temperature TROSY 2D [(1)H-(15)N] correlation spectra, and R(ex) measurements. The N-terminus of the heavy chain, which is formed upon zymogen activation and inserts into the protein core, is highly ordered, as is much of the double beta-barrel core. Some of the surface loops, by contrast, remain very dynamic with order parameters as low as 0.5 indicating significant motions on the ps-ns timescale. Regions of the protein that were thought to be dynamic in the zymogen and to become rigid upon activation, in particular the γ-loop, the 180s loop, and the Na(+) binding site have order parameters below 0.8. Significant R(ex) was observed in most of the γ-loop, in regions proximal to the light chain, and in the β-sheet core. Accelerated molecular dynamics simulations yielded a molecular ensemble consistent with measured residual dipolar couplings that revealed dynamic motions up to milliseconds. Several regions, including the light chain and two proximal loops, did not appear highly dynamic on the ps-ns timescale, but had significant motions on slower timescales.

Conservation of flexible residue clusters among structural and functional enzyme homologues

Conformational flexibility between structural ensembles is an essential component of enzyme function. Although the broad dynamical landscape of proteins is known to promote a number of functional events on multiple time scales, it is yet unknown whether structural and functional enzyme homologues rely on the same concerted residue motions to perform their catalytic function. It is hypothesized that networks of contiguous and flexible residue motions occurring on the biologically relevant millisecond time scale evolved to promote and/or preserve optimal enzyme catalysis. In this study, we use a combination of NMR relaxation dispersion, model-free analysis, and ligand titration experiments to successfully capture and compare the role of conformational flexibility between two structural homologues of the pancreatic ribonuclease family: RNase A and eosinophil cationic protein (or RNase 3). In addition to conserving the same catalytic residues and structural fold, both homologues show similar yet functionally distinct clusters of millisecond dynamics, suggesting that conformational flexibility can be conserved among analogous protein folds displaying low sequence identity. Our work shows that the reduced conformational flexibility of eosinophil cationic protein can be dynamically and functionally reproduced in the RNase A scaffold upon creation of a chimeric hybrid between the two proteins. These results support the hypothesis that conformational flexibility is partly required for catalytic function in homologous enzyme folds, further highlighting the importance of dynamic residue sectors in the structural organization of proteins.

Site-specific coupling of hydration water and protein flexibility studied in solution with ultrafast 2D-IR spectroscopy

There is considerable evidence for the slaving of biomolecular dynamics to the motions of the surrounding solvent environment, but to date there have been few direct experimental measurements capable of site-selectively probing both the dynamics of the water and the protein with ultrafast time resolution. Here, two-dimensional infrared spectroscopy (2D-IR) is used to study the ultrafast hydration and protein dynamics sensed by a metal carbonyl vibrational probe covalently attached to the surface of hen egg white lysozyme dissolved in D(2)O/glycerol solutions. Surface labeling provides direct access to the dynamics at the protein-water interface, where both the hydration and the protein dynamics can be observed simultaneously through the vibrational probe's frequency-frequency correlation function. In pure D(2)O, the correlation function shows a fast initial 3 ps decay corresponding to fluctuations of the hydration water, followed by a significant static offset attributed to fluctuations of the protein that are not sampled within the <20 ps experimental window. Adding glycerol increases the bulk solvent viscosity while leaving the protein structurally intact and hydrated. The hydration dynamics exhibit a greater than 3-fold slowdown between 0 and 80% glycerol (v/v), and the contribution from the protein's dynamics is found to slow in a nearly identical fashion. In addition, the magnitude of the dynamic slowdown associated with hydrophobic hydration is directly measured and shows quantitative agreement with predictions from molecular dynamics simulations.

Solution structural analysis of the single-domain parvulin TbPin1

Background

Pin1-type parvulins are phosphorylation-dependent peptidyl-prolyl cis-trans isomerases. Their functions have been widely reported to be involved in a variety of cellular responses or processes, such as cell division, transcription, and apoptosis, as well as in human diseases including Alzheimer's disease and cancers. TbPin1 was identified as a novel class of Pin1-type parvulins from Trypanosoma brucei, containing a unique PPIase domain, which can catalyze the isomerization of phosphorylated Ser/Thr-Pro peptide bond.

Methodology/Principal Findings

We determined the solution structure of TbPin1 and performed ¹⁵N relaxation measurements to analyze its backbone dynamics using multi-dimensional heteronuclear NMR spectroscopy. The average RMSD values of the 20 lowest energy structures are 0.50±0.05 Å for backbone heavy atoms and 0.85±0.08 Å for all heavy atoms. TbPin1 adopts the typical catalytic tertiary structure of Pin1-type parvulins, which comprises a globular fold with a four-stranded anti-parallel β-sheet core surrounded by three α-helices and one 3₁₀-helix. The global structure of TbPin1 is relatively rigid except the active site. The 2D EXSY spectra illustrate that TbPin1 possesses a phosphorylation-dependent PPIase activity. The binding sites of TbPin1 for a phosphorylated peptide substrate {SSYFSG[p]TPLEDDSD} were determined by the chemical shift perturbation approach. Residues Ser15, Arg18, Asn19, Val21, Ser22, Val32, Gly66, Ser67, Met83, Asp105 and Gly107 are involved in substantial contact with the substrate.

Conclusions/Significance

The solution structure of TbPin1 and the binding sites of the phosphorylated peptide substrate on TbPin1 were determined. The work is helpful for further understanding the molecular basis of the substrate specificity for Pin1-type parvulin family and enzyme catalysis.

¹³C relaxation experiments for aromatic side chains employing longitudinal- and transverse-relaxation optimized NMR spectroscopy

Aromatic side chains are prevalent in protein binding sites, perform functional roles in enzymatic catalysis, and form an integral part of the hydrophobic core of proteins. Thus, it is of great interest to probe the conformational dynamics of aromatic side chains and its response to biologically relevant events. Indeed, measurements of (13)C relaxation rates in aromatic moieties have a long history in biomolecular NMR, primarily in the context of samples without isotope enrichment that avoid complications due to the strong coupling between neighboring (13)C spins present in uniformly enriched proteins. Recently established protocols for specific (13)C labeling of aromatic side chains enable measurement of (13)C relaxation that can be analyzed in a straightforward manner. Here we present longitudinal- and transverse-relaxation optimized pulse sequences for measuring R (1), R (2), and {(1)H}-(13)C NOE in specifically (13)C-labeled aromatic side chains. The optimized R (1) and R (2) experiments offer an increase in sensitivity of up to 35 % for medium-sized proteins, and increasingly greater gains are expected with increasing molecular weight and higher static magnetic field strengths. Our results highlight the importance of controlling the magnetizations of water and aliphatic protons during the relaxation period in order to obtain accurate relaxation rate measurements and achieve full sensitivity enhancement. We further demonstrate that potential complications due to residual two-bond (13)C-(13)C scalar couplings or dipolar interactions with neighboring (1)H spins do not significantly affect the experiments. The approach presented here should serve as a valuable complement to methods developed for other types of protein side chains.

The dynamical response of hen egg white lysozyme to the binding of a carbohydrate ligand

It has become clear that the binding of small and large ligands to proteins can invoke significant changes in side chain and main chain motion in the fast picosecond to nanosecond timescale. Recently, the use of a "dynamical proxy" has indicated that changes in these motions often reflect significant changes in conformational entropy. These entropic contributions are sometimes of the same order as the total entropy of binding. Thus, it is important to understand the connections amongst motion between the manifold of states accessible to the native state of proteins, the corresponding entropy, and how this impacts the overall energetics of protein function. The interaction of proteins with carbohydrate ligands is central to a range of biological functions. Here, we examine a classic carbohydrate interaction with an enzyme: the binding of wild-type hen egg white lysozyme (HEWL) to the natural, competitive inhibitor chitotriose. Using NMR relaxation experiments, backbone amide and side chain methyl axial order parameters were obtained across apo and chitotriose-bound HEWL. Upon binding, changes in the apparent amplitude of picosecond to nanosecond main chain and side chain motions are seen across the protein. Indeed, binding of chitotriose renders a large contiguous fraction of HEWL effectively completely rigid. Changes in methyl flexibility are most pronounced closest to the binding site, but average to only a small overall change in the dynamics across the protein. The corresponding change in conformational entropy is unfavorable and estimated to be a significant fraction of the total binding entropy.

SRLS analysis of 15N relaxation from bacteriophage T4 lysozyme: a tensorial perspective that features domain motion

Bacteriophage T4L lysozyme (T4L) comprises two domains connected by a helical linker. Several methods detected ns domain motion associated with the binding of the peptidoglycan substrate. An ESR study of nitroxide-labeled T4L, based on the slowly relaxing local structure (SRLS) approach, detected ns local motion involving the nitroxide and the helix housing it. (15)N−H spin relaxation data from T4L acquired at magnetic fields of 11.7 and 18.8 T, and 298 K, were analyzed previously with the model-free (MF) method. The results did not detect domain motion. SRLS is the generalization of MF. Here, we apply it to the same data analyzed previously with MF. The restricted local N−H motion is described in terms of tilted axial local ordering (S) and local diffusion (D(2)) tensors; dynamical coupling to the global tumbling is accounted for. We find that D(2,⊥) is 1.62 × 10(7) (1.56 × 10(7)) s(−1) for the N-terminal (C-terminal) domain. This dynamic mode represents domain motion. For the linker D(2,⊥) is the same as the rate of global tumbling, given by (1.46 ± 0.04) × 10(7) s(−1). D(2,∥) is 1.3 × 10(9), 1.8 × 10(9) and 5.3 × 10(9) s(−1) for the N-terminal domain, the C-terminal domain, and the linker, respectively. This dynamic mode represents N−H bond vector fluctuations. The principal axis of D(2) is virtually parallel to the N−H bond. The order parameter, S(0)(2), is 0.910 ± 0.046 for most N−H bonds. The principal axis of S is tilted from the C(i−1)(α) −C(i)(α) axis by −2° to 6° for the N-, and C-terminal domains, and by 2.5° for the linker. The tensorial-perspective-based and mode-coupling-based SRLS picture provides new insights into the structural dynamics of bacteriophage T4 lysozyme.

Will molecular dynamics simulations of proteins ever reach equilibrium?

We show that conformational entropies calculated for five proteins and protein-ligand complexes with dihedral-distribution histogramming, the von Mises approach, or quasi-harmonic analysis do not converge to any useful precision even if molecular dynamics (MD) simulations of 380-500 ns length are employed (the uncertainty is 12-89 kJ mol(-1)). To explain this, we suggest a simple protein model involving dihedrals with effective barriers forming a uniform distribution and show that for such a model, the entropy increases logarithmically with time until all significantly populated dihedral states have been sampled, in agreement with the simulations (during the simulations, 52-70% of the available dihedral phase space has been visited). This is also confirmed by the analysis of the trajectories of a 1 ms simulation of bovine pancreatic trypsin inhibitor (31 kJ mol(-1) difference in the entropy between the first and second part of the simulation). Strictly speaking, this means that it is practically impossible to equilibrate MD simulations of proteins. We discuss the implications of such a lack of strict equilibration of protein MD simulations and show that ligand-binding free energies estimated with the MM/GBSA method (molecular mechanics with generalised Born and surface-area solvation) vary by 3-15 kJ mol(-1) during a 500 ns simulation (the higher estimate is caused by rare conformational changes), although they involve a questionable but well-converged normal-mode entropy estimate, whereas free energies estimated by free-energy perturbation vary by less than 0.6 kJ mol(-1) for the same simulation.

Standard tensorial analysis of local ordering in proteins from residual dipolar couplings

Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and internal protein-related ordering of the spin-bearing probe. Griesinger et al. developed a method for treating RDCs in proteins. The global ordering is given in the standard manner by a rank 2 tensor specified in a known molecular frame, MF. The local ordering is described by the spherical harmonic ensemble averages, <Y(2m)(θ, φ)>, m = 0, ±1, ±2, also given in MF. From these quantities, a method we call mf-RDC derives the squared generalized order parameter (S(rdc)(2)), the amplitude (direction) of the anisotropic disorder, η (Φ′), and an approximation, (N−H)(eff), to the average probe orientation, i.e., to the local director. (N−H)(eff) is determined through a frame transformation where <Y(20)> is maximized. Φ′ is associated with a subsequent frame transformation where <Y(22) + Y(2−2)> is maximized. The mf-RDC method was applied previously to N−H and C−C(methyl) sites in ubiquitin. In this study, we convert the respective <Y(2m)(θ, φ)>'s into a Saupe tensor, which is diagonalized. This is the standard procedure. It yields the eigenvalues, S(xx), S(yy), and S(zz), and the Principal Axis System (PAS) of the rank 2 local ordering tensor, S(l). S(rdc)(2), η, and Φ′ can be recast as S(xx), S(yy), and S(zz). The mf-RDC frame transformations are not the same as the conventional Wigner rotation. The standard tensorial analysis provides new information. The contribution of local ordering rhombicity to S(rdc)(2) is evaluated. For the α-helix of ubiquitin, the main local ordering axis is assigned as C(i−1)(α) − C(i)(α); for the methyl sites, it is associated with the C−C(methyl) axis, as in mf-RDC. Ordering strength correlates with methyl type. The strength (rhombicity) of S(l) associated with picosecond−nanosecond local motions is reduced moderately (substantially) by nanosecond−millisecond local motions. A scheme for analyzing experimental RDCs based on the standard tensorial perspective, which allows for arbitrary orientation of the local director in the protein and of the PAS of S(l) in the probe, is formulated.

Quantitative comparison of errors in 15N transverse relaxation rates measured using various CPMG phasing schemes

Nitrogen-15 Carr-Purcell-Meiboom-Gill (CPMG) transverse relaxation experiment are widely used to characterize protein backbone dynamics and chemical exchange parameters. Although an accurate value of the transverse relaxation rate, R(2), is needed for accurate characterization of dynamics, the uncertainty in the R(2) value depends on the experimental settings and the details of the data analysis itself. Here, we present an analysis of the impact of CPMG pulse phase alternation on the accuracy of the (15)N CPMG R(2). Our simulations show that R(2) can be obtained accurately for a relatively wide spectral width, either using the conventional phase cycle or using phase alternation when the r.f. pulse power is accurately calibrated. However, when the r.f. pulse is miscalibrated, the conventional CPMG experiment exhibits more significant uncertainties in R(2) caused by the off-resonance effect than does the phase alternation experiment. Our experiments show that this effect becomes manifest under the circumstance that the systematic error exceeds that arising from experimental noise. Furthermore, our results provide the means to estimate practical parameter settings that yield accurate values of (15)N transverse relaxation rates in the both CPMG experiments.

Exposing the Moving Parts of Proteins with NMR Spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful tool for investigating the dynamics of biomolecules since it provides a description of motion that is comprehensive, site-specific, and relatively non-invasive. In particular, the study of protein dynamics has benefited from sustained methodological advances in NMR that have expanded the scope and time scales of accessible motion. Yet, many of these advances may not be well known to the more general physical chemistry community. Accordingly, this Perspective provides a glimpse of some of the more powerful methods in liquid state NMR that are helping reshape our understanding of functional motions of proteins.

Conformational dynamics and thermodynamics of protein–ligand binding studied by NMR relaxation

Protein conformational dynamics can be critical for ligand binding in two ways that relate to kinetics and thermodynamics respectively. First, conformational transitions between different substates can control access to the binding site (kinetics). Secondly, differences between free and ligand-bound states in their conformational fluctuations contribute to the entropy of ligand binding (thermodynamics). In the present paper, I focus on the second topic, summarizing our recent results on the role of conformational entropy in ligand binding to Gal3C (the carbohydrate-recognition domain of galectin-3). NMR relaxation experiments provide a unique probe of conformational entropy by characterizing bond-vector fluctuations at atomic resolution. By monitoring differences between the free and ligand-bound states in their backbone and side chain order parameters, we have estimated the contributions from conformational entropy to the free energy of binding. Overall, the conformational entropy of Gal3C increases upon ligand binding, thereby contributing favourably to the binding affinity. Comparisons with the results from isothermal titration calorimetry indicate that the conformational entropy is comparable in magnitude to the enthalpy of binding. Furthermore, there are significant differences in the dynamic response to binding of different ligands, despite the fact that the protein structure is virtually identical in the different protein–ligand complexes. Thus both affinity and specificity of ligand binding to Gal3C appear to depend in part on subtle differences in the conformational fluctuations that reflect the complex interplay between structure, dynamics and ligand interactions.

Selectivity of stop codon recognition in translation termination is modulated by multiple conformations of GTS loop in eRF1

Translation termination in eukaryotes is catalyzed by two release factors eRF1 and eRF3 in a cooperative manner. The precise mechanism of stop codon discrimination by eRF1 remains obscure, hindering drug development targeting aberrations at translation termination. By solving the solution structures of the wild-type N-domain of human eRF1 exhibited omnipotent specificity, i.e. recognition of all three stop codons, and its unipotent mutant with UGA-only specificity, we found the conserved GTS loop adopting alternate conformations. We propose that structural variability in the GTS loop may underline the switching between omnipotency and unipotency of eRF1, implying the direct access of the GTS loop to the stop codon. To explore such feasibility, we positioned N-domain in a pre-termination ribosomal complex using the binding interface between N-domain and model RNA oligonucleotides mimicking Helix 44 of 18S rRNA. NMR analysis revealed that those duplex RNA containing 2-nt internal loops interact specifically with helix α1 of N-domain, and displace C-domain from a non-covalent complex of N-domain and C-domain, suggesting domain rearrangement in eRF1 that accompanies N-domain accommodation into the ribosomal A site.

The projection analysis of NMR chemical shifts reveals extended EPAC autoinhibition determinants

EPAC is a cAMP-dependent guanine nucleotide exchange factor that serves as a prototypical molecular switch for the regulation of essential cellular processes. Although EPAC activation by cAMP has been extensively investigated, the mechanism of EPAC autoinhibition is still not fully understood. The steric clash between the side chains of two conserved residues, L273 and F300 in EPAC1, has been previously shown to oppose the inactive-to-active conformational transition in the absence of cAMP. However, it has also been hypothesized that autoinhibition is assisted by entropic losses caused by quenching of dynamics that occurs if the inactive-to-active transition takes place in the absence of cAMP. Here, we test this hypothesis through the comparative NMR analysis of several EPAC1 mutants that target different allosteric sites of the cAMP-binding domain (CBD). Using what to our knowledge is a novel projection analysis of NMR chemical shifts to probe the effect of the mutations on the autoinhibition equilibrium of the CBD, we find that whenever the apo/active state is stabilized relative to the apo/inactive state, dynamics are consistently quenched in a conserved loop (β2-β3) and helix (α5) of the CBD. Overall, our results point to the presence of conserved and nondegenerate determinants of CBD autoinhibition that extends beyond the originally proposed L273/F300 residue pair, suggesting that complete activation necessitates the simultaneous suppression of multiple autoinhibitory mechanisms, which in turn confers added specificity for the cAMP allosteric effector.

Protein function and allostery: a dynamic relationship

Allostery is a fundamental process by which distant sites within a protein system sense each other. Allosteric regulation is such an efficient mechanism that it is used to control protein activity in most biological processes, including signal transduction, metabolism, catalysis, and gene regulation. Over recent years, our view and understanding of the fundamental principles underlying allostery have been enriched and often utterly reshaped. This has been especially so for powerful techniques such as nuclear magnetic resonance spectroscopy, which offers an atomic view of the intrinsic motions of proteins. Here, I discuss recent results on the catabolite activator protein (CAP) that have drastically revised our view about how allosteric interactions are modulated. CAP has provided the first experimentally identified system showing that (i) allostery can be mediated through changes in protein motions, in the absence of changes in the mean structure of the protein, and (ii) favorable changes in protein motions may activate allosteric proteins that are otherwise structurally inactive.

Temperature dependence of molecular interactions involved in defining stability of glutamine binding protein and its complex with L-glutamine

The temperature dependence of dynamic parameters derived from nuclear magnetic resonance (NMR) relaxation data is related to conformational entropy of the system under study. This provides information such as macromolecules stability and thermodynamics of ligand binding. We studied the temperature dependence of NMR order parameter of glutamine binding protein (GlnBP), a periplasmic binding protein (PBP) highly specific to L-glutamine associated with its ABC transporter, with the goal of elucidating the dynamical differences between the respective ligand bound and free forms. We found that the protein-ligand interaction, which is stabilized at higher temperature, has a striking effect on the stability of the hydrophobic core of the large domain of GlnBP. Moreover, in contrast to what was found for less specific PBPs, the decreasing backbone motion of the hinge region at increasing temperature supports the idea that the likelihood that GlnBP can adopt a ligand free closed conformation in solution diminishes at higher temperatures. Our results support the induced-fit model as mode of action for GlnBP. In addition, we found that the backbones of residues involved in a salt bridge do not necessarily become more rigid as the temperature rises as it was previously suggested [Vinther, J. M., et al. (2011) J. Am. Chem. Soc., 133, 271-278]. Our results show that for this to happen these residues have to also directly interact with a region of the protein that is becoming more rigid as the temperature increases.

Allostery and binding cooperativity of the catalytic subunit of protein kinase A by NMR spectroscopy and molecular dynamics simulations

The catalytic subunit of cAMP-dependent protein kinase A (PKA-C) is an exquisite example of a single molecule allosteric enzyme, where classical and modern views of allosteric signaling merge. In this chapter, we describe the mapping of PKA-C conformational dynamics and allosteric signaling in the free and bound states using a combination of NMR spectroscopy and molecular dynamics simulations. We show that ligand binding affects the enzyme's conformational dynamics, shaping the free-energy landscape toward the next stage of the catalytic cycle. While nucleotide and substrate binding enhance the enzyme's conformational entropy and define dynamically committed states, inhibitor binding attenuates the internal dynamics in favor of enthalpic interactions and delineates dynamically quenched states. These studies support a central role of conformational dynamics in many aspects of enzymatic turnover and suggest future avenues for controlling enzymatic function.

Are ambivalent α-helices entropically driven?

This work is a first attempt to characterise the conformational preference of structurally ambivalent helices in terms of their backbone conformational entropy. Ambivalent sequences conform to two different secondary structures (helix-sheet or helix-random coil or sheet-random coil, etc.) in two different proteins. For variable ambivalent helices, the helical conformations are found to possess less conformational entropy as compared with their non-helical counterparts when the ϕ-ψ dihedral angle range of the entire peptide segment is used to calculate the backbone conformational entropy. The favourable number of native contacts is a primary stabilising factor for these helical conformations. However, an opposite trend is observed when the ϕ-ψ angles of the individual amino acids are used to calculate the backbone conformational entropy. The results show that these peptide segments are rather reluctant to form helices, but are driven to form helices due to the favourable number of native contacts and optimum range of ϕ-ψ angle of the segments. Both procedures are validated by applying on conserved helices in the non-redundant database and their corresponding counterparts in the Structural Classification of Proteins database. Although context is a major determinant in deciding conformations of ambivalent sequences, no significant difference in the conformational entropy of sequences flanking ambivalent helical sequences in helical and non-helical forms is observed in this study. The results may be useful in understanding the structural context and environmental factors which leads to the formation of ambivalent helices and designing de novo proteins.

Probing side-chain dynamics in proteins by the measurement of nine deuterium relaxation rates per methyl group

We demonstrate the feasibility of the measurement of up to nine deuterium spin relaxation rates in 13CHD2 and 13CH2D methyl isotopomers of small proteins. In addition to five measurable 2H relaxation rates in a 13CH2D methyl group (Millet, O.; Muhandiram, D. R.; Skrynnikov, N. R.; Kay, L. E. J. Am. Chem. Soc. 2002, 124, 6439-48), the measurement of additional four rates of (nearly) single-exponentially decaying magnetization terms in methyl groups of the 13CHD2 variety is reported. Consistency relationships between 2H spin relaxation rates measured in the two different types of methyl groups are derived and verified experimentally for a subset of methyl-containing side chains in the protein ubiquitin. A detailed comparison of methyl-bearing side-chain dynamics parameters obtained from relaxation measurements in 13CH2D and 13CHD2 methyls of ubiquitin at 10, 27, and 40 °C reveals that transverse 2H relaxation rates in 13CHD2 groups are reliable and accurate reporters of the amplitudes of methyl 3-fold axis motions (S(axis)2) for protein molecules with global molecular tumbling times τ(C) >~9 ns. For smaller molecules, simple correction of transverse 2H relaxation rates in 13CHD2 groups is sufficient for the derivation of robust measures of order. Residue-specific distributions of S(axis)2 are consistent with atomic-detail molecular dynamics (MD) results. Both 13CHD2- and 13CH2D-derived S(axis)2 values are in good overall agreement with those obtained from 1 μs MD simulations at all the three temperatures, although some differences in the site-specific temperature dependence between MD- and 2H-relaxation-derived S(axis)2 values are observed.

Protein conformational dynamics in the mechanism of HIV-1 protease catalysis

We have used chemical protein synthesis and advanced physical methods to probe dynamics-function correlations for the HIV-1 protease, an enzyme that has received considerable attention as a target for the treatment of AIDS. Chemical synthesis was used to prepare a series of unique analogues of the HIV-1 protease in which the flexibility of the "flap" structures (residues 37-61 in each monomer of the homodimeric protein molecule) was systematically varied. These analogue enzymes were further studied by X-ray crystallography, NMR relaxation, and pulse-EPR methods, in conjunction with molecular dynamics simulations. We show that conformational isomerization in the flaps is correlated with structural reorganization of residues in the active site, and that it is preorganization of the active site that is a rate-limiting factor in catalysis.

NMR studies of protein structure and dynamics - a look backwards and forwards

NMR spectroscopy has evolved to become one of the most powerful tools for the study of protein structure and dynamics. Advances over the past decade have greatly extended the methodology to studies of molecules of ever increasing complexity. Herein I provide a short perspective relating the circumstances that led to some of the contributions from my laboratory in this area and highlight how these original experiments, summarized in a Journal of Magnetic Resonance article in 2005 (JMR, 173 193–207), have influenced the current focus of my research.

Analytic treatment of nuclear spin-lattice relaxation for diffusion in a cone model

We consider nuclear spin-lattice relaxation rate resulted from a diffusion equation for rotational wobbling in a cone. We show that the widespread point of view that there are no analytical expressions for correlation functions for wobbling in a cone model is invalid and prove that nuclear spin-lattice relaxation in this model is exactly tractable and amenable to full analytical description. The mechanism of relaxation is assumed to be due to dipole-dipole interaction of nuclear spins and is treated within the framework of the standard Bloemberger, Purcell, Pound-Solomon scheme. We consider the general case of arbitrary orientation of the cone axis relative the magnetic field. The BPP-Solomon scheme is shown to remain valid for systems with the distribution of the cone axes depending only on the tilt relative the magnetic field but otherwise being isotropic. We consider the case of random isotropic orientation of cone axes relative the magnetic field taking place in powders. Also we consider the cases of their predominant orientation along or opposite the magnetic field and that of their predominant orientation transverse to the magnetic field which may be relevant for, e.g., liquid crystals. Besides we treat in details the model case of the cone axis directed along the magnetic field. The latter provides direct comparison of the limiting case of our formulas with the textbook formulas for free isotropic rotational diffusion. The dependence of the spin-lattice relaxation rate on the cone half-width yields results similar to those predicted by the model-free approach.

Understanding biomolecular motion, recognition, and allostery by use of conformational ensembles

We review the role conformational ensembles can play in the analysis of biomolecular dynamics, molecular recognition, and allostery. We introduce currently available methods for generating ensembles of biomolecules and illustrate their application with relevant examples from the literature. We show how, for binding, conformational ensembles provide a way of distinguishing the competing models of induced fit and conformational selection. For allostery we review the classic models and show how conformational ensembles can play a role in unravelling the intricate pathways of communication that enable allostery to occur. Finally, we discuss the limitations of conformational ensembles and highlight some potential applications for the future.

Achieving broad molecular insights into dynamic protein interactions by integrated structural-kinetic approaches

A network of dynamic protein interactions with their protein partners, substrates, and ligands is known to be crucial for biological function. Revealing molecular and structural-based mechanisms at atomic resolution and in real-time is fundamental for achieving a basic understanding of cellular processes. These technically challenging goals may be achieved by combining time-resolved spectroscopic and structural-kinetic tools, thus providing broad insights into specific molecular events over a wide range of timescales. Here we review representative studies utilizing such an integrated real-time structural approach designed to reveal molecular mechanisms underlying protein interactions at atomic resolution.

Active site dynamics in NADH oxidase from Thermus thermophilus studied by NMR spin relaxation

We have characterized the backbone dynamics of NADH oxidase from Thermus thermophilus (NOX) using a recently-developed suite of NMR experiments designed to isolate exchange broadening, together with (15)N R (1), R (1ρ ), and {(1)H}-(15)N steady-state NOE relaxation measurements performed at 11.7 and 18.8 T. NOX is a 54 kDa homodimeric enzyme that belongs to a family of structurally homologous flavin reductases and nitroreductases with many potential biotechnology applications. Prior studies have suggested that flexibility is involved in the catalytic mechanism of the enzyme. The active site residue W47 was previously identified as being particularly important, as its level of solvent exposure correlates with enzyme activity, and it was observed to undergo "gating" motions in computer simulations. The NMR data are consistent with these findings. Signals from W47 are dynamically broadened beyond detection and several other residues in the active site have significant R ( ex ) contributions to transverse relaxation rates. In addition, the backbone of S193, whose side chain hydroxyl proton hydrogen bonds directly with the FMN cofactor, exhibits extensive mobility on the ns-ps timescale. We hypothesize that these motions may facilitate structural rearrangements of the active site that allow NOX to accept both FMN and FAD as cofactors.

Structural basis for the interaction of lipopolysaccharide with outer membrane protein H (OprH) from Pseudomonas aeruginosa

Pseudomonas aeruginosa is a major nosocomial pathogen that infects cystic fibrosis and immunocompromised patients. The impermeability of the P. aeruginosa outer membrane contributes substantially to the notorious antibiotic resistance of this human pathogen. This impermeability is partially imparted by the outer membrane protein H (OprH). Here we have solved the structure of OprH in a lipid environment by solution NMR. The structure reveals an eight-stranded β-barrel protein with four extracellular loops of unequal size. Fast time-scale dynamics measurements show that the extracellular loops are disordered and unstructured. It was previously suggested that the function of OprH is to provide increased stability to the outer membranes of P. aeruginosa by directly interacting with lipopolysaccharide (LPS) molecules. Using in vivo and in vitro biochemical assays, we show that OprH indeed interacts with LPS in P. aeruginosa outer membranes. Based upon NMR chemical shift perturbations observed upon the addition of LPS to OprH in lipid micelles, we conclude that the interaction is predominantly electrostatic and localized to charged regions near both rims of the barrel, but also through two conspicuous tyrosines in the middle of the bilayer. These results provide the first molecular structure of OprH and offer evidence for multiple interactions between OprH and LPS that likely contribute to the antibiotic resistance of P. aeruginosa.

Increased hydrophobicity and decreased backbone flexibility explain the lower solubility of a cataract-linked mutant of γD-crystallin

A number of point mutations in γD-crystallin are associated with human cataract. The Pro23-to-Thr (P23T) mutation is perhaps the most common, is geographically widespread, and presents itself in a variety of phenotypes. It is therefore important to understand the molecular basis of lens opacity due to this mutation. In our earlier studies, we noted that P23T shows retrograde and sharply lowered solubility, most likely due to the emergence of hydrophobic patches involved in protein aggregation. Binding of 4,4'-dianilino-1,1'-binaphthyl-5,5'-disulfonate (Bis-ANS) dye (a probe commonly used for detecting surface hydrophobicity) competed with aggregation, suggesting that the residues involved in Bis-ANS binding are also involved in protein aggregation. Here, using NMR spectroscopy in conjunction with Bis-ANS binding, we identify three residues (Y16, D21, and Y50) in P23T that are involved in binding the dye. Furthermore, using (15)N NMR relaxation experiments, we show that, in the mutant protein, backbone fluctuations are restricted to the picosecond-to-nanosecond and microsecond timescales relative to the wild type. Our present studies specify the residues involved in these two pivotal characteristics of the mutant protein, namely increased surface hydrophobicity and restricted mobility of the protein backbone, which can explain the nucleation and further propagation of protein aggregates. Thus, we have now identified the residues in the P23T mutant that give rise to novel hydrophobic surfaces, as well as those regions of the protein backbone where fluctuations in different timescales are restricted, providing a comprehensive understanding of how lens opacity could result from this mutation.