Estimation of dynamic parameters from NMR relaxation data using the Lipari-Szabo model-free approach and Bayesian statistical methods

Effects of Excipients on the Structure and Dynamics of Filgrastim Monitored by Thermal Unfolding Studies by CD and NMR Spectroscopy

Product excipients are used to confer a number of desirable properties on the drug substance to maintain or improve stability and facilitate drug delivery. This is especially important for products where the active pharmaceutical ingredient (API) is a recombinant protein. In this study, we aimed to determine if excipients and formulation conditions affect the structure and/or modulate the dynamics of the protein API of filgrastim products. Samples of uniformly labeled ¹⁵N-Met-granulocyte-colony stimulating factor (GCSF) were prepared at 100 μM (near formulation concentration) with various concentrations of individual components (polysorbate-20 and -80, sorbitol) and three pH values. Nuclear magnetic resonance (NMR) spectroscopy techniques were applied to measure chemical shift perturbation (CSP) to detect structural changes, and relaxation parameters (T ₁, T ₂, and heteronuclear Overhauser effect) were measured to probe the effects on protein backbone motions. In parallel, the same solution conditions were subjected to protein thermal unfolding studies monitored by circular dichroism spectropolarimetry (CD). Detergents (polysorbate-20 and 80) do not induce any observable changes on the protein structure and do not modify its dynamics at formulation concentration. Lowering pH to 4.0, a condition known to stabilize the conformation of filgrastim, as well as the addition of sorbitol produced changes of the fast motion dynamics in the nanosecond and picosecond timescale. NMR-derived order parameters, which measure the local conformational entropy of the protein backbone, show that lowering pH leads to a compaction of the four-helix bundle while the addition of sorbitol relaxes helices B and C, thereby reducing the mobility of loop CD. CSPs and measurements of protein dynamics via NMR-derived order parameters provide a description in structural and motional terms at an atomic resolution on how formulation components contribute to the stabilization of filgrastim products.

Surface impact on nanoparticle-based magnetic resonance imaging contrast agents

Magnetic resonance imaging (MRI) is one of the most widely used diagnostic tools in the clinic. To improve imaging quality, MRI contrast agents, which can modulate local T1 and T2 relaxation times, are often injected prior to or during MRI scans. However, clinically used contrast agents, including Gd3+-based chelates and iron oxide nanoparticles (IONPs), afford mediocre contrast abilities. To address this issue, there has been extensive research on developing alternative MRI contrast agents with superior r1 and r2 relaxivities. These efforts are facilitated by the fast progress in nanotechnology, which allows for preparation of magnetic nanoparticles (NPs) with varied size, shape, crystallinity, and composition. Studies suggest that surface coatings can also largely affect T1 and T2 relaxations and can be tailored in favor of a high r1 or r2. However, the surface impact of NPs has been less emphasized. Herein, we review recent progress on developing NP-based T1 and T2 contrast agents, with a focus on the surface impact.

Dynamic domain arrangement of CheA-CheY complex regulates bacterial thermotaxis, as revealed by NMR

Bacteria utilize thermotaxis signal transduction proteins, including CheA, and CheY, to switch the direction of the cell movement. However, the thermally responsive machinery enabling warm-seeking behavior has not been identified. Here we examined the effects of temperature on the structure and dynamics of the full-length CheA and CheY complex, by NMR. Our studies revealed that the CheA-CheY complex exists in equilibrium between multiple states, including one state that is preferable for the autophosphorylation of CheA, and another state that is preferable for the phosphotransfer from CheA to CheY. With increasing temperature, the equilibrium shifts toward the latter state. The temperature-dependent population shift of the dynamic domain arrangement of the CheA-CheY complex induced changes in the concentrations of phosphorylated CheY that are comparable to those induced by chemical attractants or repellents. Therefore, the dynamic domain arrangement of the CheA-CheY complex functions as the primary thermally responsive machinery in warm-seeking behavior.

Dynamic Allostery Modulates Catalytic Activity by Modifying the Hydrogen Bonding Network in the Catalytic Site of Human Pin1

Allosteric communication among domains in modular proteins consisting of flexibly linked domains with complimentary roles remains poorly understood. To understand how complementary domains communicate, we have studied human Pin1, a representative modular protein with two domains mutually tethered by a flexible linker: a WW domain for substrate recognition and a peptidyl-prolyl isomerase (PPIase) domain. Previous studies of Pin1 showed that physical contact between the domains causes dynamic allostery by reducing conformation dynamics in the catalytic domain, which compensates for the entropy costs of substrate binding to the catalytic site and thus increases catalytic activity. In this study, the S138A mutant PPIase domain, a mutation that mimics the structural impact of the interdomain contact, was demonstrated to display dynamic allostery by rigidification of the α2-α3 loop that harbors the key catalytic residue C113. The reduced dynamics of the α2-α3 loop stabilizes the C113-H59 hydrogen bond in the hydrogen-bonding network of the catalytic site. The stabilized hydrogen bond between C113 and H59 retards initiation of isomerization, which explains the reduced isomerization rate by ~20% caused by the S138A mutation. These results provide new insight into the interdomain allosteric communication of Pin1.

Gd-AAZTA-MADEC, an improved blood pool agent for DCE-MRI studies on mice on 1 T scanners

A novel MRI blood-pool contrast agent (Gd-AAZTA-MADEC) has been compared with established blood pool agents for tumor contrast enhanced images and angiography. Synthesis, relaxometric properties, albumin binding affinity and pharmacokinetic profiles are reported. For in vivo studies, angiographic images and tumor contrast enhanced images were acquired on mice with benchtop 1T-MRI scanners and compared with MS-325, B22956/1 and B25716/1. The design of this contrast agent involved the elongation of the spacer between the targeting deoxycholic acid moiety and the Gd-AAZTA imaging reporting unit that drastically changed either the binding affinity to albumin (KA(HSA) = 8.3 × 10(5) M(-1)) and the hydration state of the Gd ion (q = 2) in comparison to the recently reported B25716/1. The very markedly high binding affinity towards mouse and human serum albumins resulted in peculiar pharmacokinetics and relaxometric properties. The NMRD profiles clearly indicated that maximum efficiency is attainable at magnetic field strength of 1 T. In vivo studies showed high enhancement of the vasculature and a prolonged accumulation inside tumor. The herein reported pre-clinical imaging studies show that a great benefit arises from the combination of a benchtop MRI scanner operating at 1 T and the albumin-binding Gd-AAZTA-MADEC complex, for pursuing enhanced angiography and improved characterization of tumor vascular microenvironment.

Opsin Effect on the Electronic Structure of the Retinylidene Chromophore in Rhodopsin

Direct examination of experimental NMR parameters combined with electronic structure analysis was used to provide a first-principle interpretation of NMR experiments and give a precise evaluation of how the electronic perturbation of the protein environment affects the electronic properties of the retinylidene chromophere in rhodopsin. To this end, we pursued a theoretical analysis using a combination of tools including quantum mechanics/molecular mechanics (QM/MM) at the Density Functional Theory (DFT) level, in conjunction with gauge independent atomic orbital (GIAO) calculations of (13)C NMR chemical shieldings and (1)J(CC) spin-spin coupling constants obtained with the Coupled Perturbed DFT (CPDFT) method. The opsin effect on the retinylidene chromophere is interpreted as an inductive effect of Glu-113 which readjusts the weighting factors of resonance substructures of the conjugated chain of the chromophere. These changes give a rationalization to the alternating effect of the (13)C chemical shifts magnitudes when comparing the retinylidene chromophere in the presence and absence of the protein environment. Conversely, perturbation of π orbitals has little to no effect over (1)J (13)C-(13)C spin-spin coupling constants, as they are mainly dominated by the Fermi contact term, and hence the counteraion effect is restricted to the vicinity of the perturbation. Thus, the apparent contradiction between experimental findings based on chemical shifts (deep penetration) and one-bond J-couplings (localized effects of the protonated Schiff base at the chain terminus) is in fact a consequence of different properties responding differently to the same external perturbation.

On the reliability of NMR relaxation data analyses: a Markov Chain Monte Carlo approach

The analysis of NMR relaxation data is revisited along the lines of a Bayesian approach. Using a Markov Chain Monte Carlo strategy of data fitting, we investigate conditions under which relaxation data can be effectively interpreted in terms of internal dynamics. The limitations to the extraction of kinetic parameters that characterize internal dynamics are analyzed, and we show that extracting characteristic time scales shorter than a few tens of ps is very unlikely. However, using MCMC methods, reliable estimates of the marginal probability distributions and estimators (average, standard deviations, etc.) can still be obtained for subsets of the model parameters. Thus, unlike more conventional strategies of data analysis, the method avoids a model selection process. In addition, it indicates what information may be extracted from the data, but also what cannot.

Proton-decoupled CPMG: a better experiment for measuring (15)N R2 relaxation in disordered proteins

(15)N R2 relaxation is one of the most informative experiments for characterization of intrinsically disordered proteins (IDPs). Small changes in nitrogen R2 rates are often used to determine how IDPs respond to various biologically relevant perturbations such as point mutations, posttranslational modifications and weak ligand interactions. However collecting high-quality (15)N relaxation data can be difficult. Of necessity, the samples of IDPs are often prepared with low protein concentration and the measurement time can be limited because of rapid sample degradation. Furthermore, due to hardware limitations standard experiments such as (15)N spin-lock and CPMG can sample the relaxation decay only to ca. 150ms. This is much shorter than (15)N T2 times in disordered proteins at or near physiological temperature. As a result, the sampling of relaxation decay profiles in these experiments is suboptimal, which further lowers the precision of the measurements. Here we report a new implementation of the proton-decoupled (PD) CPMG experiment which allows one to sample (15)N R2 relaxation decay up to ca. 0.5-1s. The new experiment has been validated through comparison with the well-established spin-lock measurement. Using dilute samples of denatured ubiquitin, we have demonstrated that PD-CPMG produces up to 3-fold improvement in the precision of the data. It is expected that for intrinsically disordered proteins the gains may be even more substantial. We have also shown that this sequence has a number of favorable properties: (i) the spectra are recorded with narrow linewidth in nitrogen dimension; (ii) (15)N offset correction is small and easy to calculate; (iii) the experiment is immune to various spurious effects arising from solvent exchange; (iv) the results are stable with respect to pulse miscalibration and rf field inhomogeneity; (v) with minimal change, the pulse sequence can also be used to measure R2 relaxation of (15)N(ε) spins in arginine side chains. We anticipate that the new experiment will be a valuable addition to the NMR toolbox for studies of IDPs.

A probe to monitor performance of ¹⁵N longitudinal relaxation experiments for proteins in solution

The magnitude of the ¹⁵N longitudinal relaxation rate typically decreases as magnetic field strength increases in globular proteins in solution. Thus, it is important to test the performance of ¹⁵N longitudinal relaxation experiments at high field strength. Herein, a tool to investigate systematic errors in ¹⁵N longitudinal relaxation rate, R₁, is introduced. The tool, a difference in R₁ values between the two components of the ¹H-coupled ¹⁵N magnetizations, R₁(1)-R₁(2), conveniently detects inefficiencies in cancellation of cross correlation between ¹H-¹⁵N dipolar coupling and ¹⁵N chemical shift anisotropy. Experiments, in varying conditions, and simulations of a two-spin system indicate that insufficient cancellation of the cross correlation is due to (1) ¹H pulse imperfection and (2) ¹H off-resonance effect, and (3) is further amplified by residual ¹⁵N transverse magnetization that is caused by the ¹⁵N off-resonance effect. Results also show that this problem can be easily and practically remedied by discarding the initial decay points when recording ¹⁵N longitudinal relaxation in proteins.

Hydrogen skeleton, mobility and protein architecture

The mobility of the proton-proton radial vectors is introduced as a quantitative measure for the structural dynamics of organic materials, especially protein molecules. As defined for the entire molecule, the hydrogen mobility (HM) is proposed as an "order parameter," which describes the effect of motional narrowing on inter-proton dipole-dipole interactions. HM satisfies all requirements of an order parameter in the Landau molecular field theory of phase transitions. The wide-line NMR second moments needed to obtain HM are exactly defined and measurable physical quantities, which are not produced by mathematical fitting and do not carry the limitations and restrictions of any model (theoretical formalism). We first demonstrate the usefulness of HM on small organic molecules with data taken form the literature. We outline its link with structural and functional characteristics on a range of proteins: HM provides a model-free parameter based on first principles that can clearly distinguish between globular and intrinsically disordered proteins, and can also provide insight into the behavior of disease-related mutants.

Gramicidin A backbone and side chain dynamics evaluated by molecular dynamics simulations and nuclear magnetic resonance experiments. II: nuclear magnetic resonance experiments

Motional properties are important for understanding protein function and are accessible to NMR relaxation measurements. The goal of this study is to investigate the internal dynamics occurring in gramicidin A (gA) channels in order to provide benchmark experimental data for comparison with the results of molecular dynamics simulations. We therefore synthesized several (15)N isotope-enriched gA samples, covering all backbone residues as well as the Trp indole side chains for NMR relaxation experiments. On the basis of the (15)N NMR spectra for labeled gA samples incorporated in sodium dodecylsulfate (SDS) micelles, we determined T(1), T(2), and heteronuclear NOE values for backbone and indole (15)NH groups. The results indicate that the SDS-incorporated gA channel is a constrained structure without an especially "floppy" region. The NMR observables, particularly those for backbone groups, are predicted well by the molecular dynamics simulations in the accompanying article (DOI 10.1021/jp200904d ).

Recent developments in (15)N NMR relaxation studies that probe protein backbone dynamics

Nuclear Magnetic Resonance (NMR) relaxation is a powerful technique that provides information about internal dynamics associated with configurational energetics in proteins, as well as site-specific information involved in conformational equilibria. In particular, (15)N relaxation is a useful probe to characterize overall and internal backbone dynamics of proteins because the relaxation mainly reflects reorientational motion of the N-H bond vector. Over the past 20 years, experiments and protocols for analysis of (15)N R (1), R 2, and the heteronuclear (15)N-{(1)H} NOE data have been well established. The development of these methods has kept pace with the increase in the available static-magnetic field strength, providing dynamic parameters optimized from data fitting at multiple field strengths. Using these methodological advances, correlation times for global tumbling and order parameters and correlation times for internal motions of many proteins have been determined. More recently, transverse relaxation dispersion experiments have extended the range of NMR relaxation studies to the milli- to microsecond time scale, and have provided quantitative information about functional conformational exchange in proteins. Here, we present an overview of recent advances in (15)N relaxation experiments to characterize protein backbone dynamics.

Model-free analysis for large proteins at high magnetic field strengths

Protein backbone dynamics is often characterized using model-free analysis of three sets of (15)N relaxation data: longitudinal relaxation rate (R1), transverse relaxation rate (R2), and (15)N-{H} NOE values. Since the experimental data is limited, a simplified model-free spectral density function is often used that contains one Lorentzian describing overall rotational correlation but not one describing internal motion. The simplified spectral density function may be also used in estimating the overall rotational correlation time, by making the R2/R1 largely insensitive to internal motions, as well as used as one of the choices in the model selection protocol. However, such approximation may not be valid for analysis of relaxation data of large proteins recorded at high magnetic field strengths since the contribution to longitudinal relaxation from the Lorentzian describing the overall rotational diffusion of the molecule is comparably small relative to that describing internal motion. Here, we quantitatively estimate the errors introduced by the use of the simplified spectral density in model-free analysis for large proteins at high magnetic field strength.

Bayesian and information theory analysis of MAS sideband patterns in spin 1/2 systems

Bayesian statistics and information theory are used to analyze the reliability of extracting chemical shift parameters from spinning sideband patterns of spin 1/2 systems. Efficient code has been written to calculate the two-dimensional posterior probability as a function of the chemical shift anisotropy, delta, and the asymmetry parameter, eta, given the sideband intensities and the signal-to-noise ratio. This method has the advantage of assuming only that the noise in the sideband intensities is distributed as a Gaussian. It assumes nothing about the distribution of the values of parameters delta and eta, which are shown in some cases to be highly non-Gaussian. The utility of Bayesian analysis is demonstrated on 1D slow-spinning MAS spectra and on sideband patterns extracted from 2D PASS spectra. Previous investigations have shown that there is an optimal range of spinning frequencies for determining delta. In this study, information theory is used to determine the signal-to-noise ratio dependence of the entropy in delta, eta, and total entropy in spinning sideband spectra. The entropy is a measure of the information content of a probability distribution. When the entropy is zero, there is perfect information on a system, while if it is infinite, there is no information on the system. It is found that for all values of eta and for signal-to-noise ratios in the range 50-1000, an entropy minimum in nudelta/nur occurs for values 1.5<or=nudelta/nur<or=3. In the same range of signal-to-noise ratios, the entropy in eta is a monotonically decreasing function of nudelta/nur. The global information content of a spinning sideband pattern (i.e., the total entropy) is dependent on the signal-to-noise ratio and has an optimal value at nudelta/nur approximately 2 at a signal-to-noise ratio of 50 and increasing to approximately 2.5 for signal-to-noise ratios of 1000. Finally, the increase of information in a sideband pattern as a function of the number of sidebands used in the analysis is examined. Most of the information about delta and eta is contained in the five central sidebands; i.e., sidebands -2 to 2.

Quantifying Lipari-Szabo modelfree parameters from 13CO NMR relaxation experiments

It is proposed to obtain effective Lipari-Szabo order parameters and local correlation times for relaxation vectors of protein (13)CO nuclei by carrying out a (13)CO-R(1) auto relaxation experiment, a transverse (13)CO CSA/13CO-13Calpha CSA/dipolar cross correlation and a transverse (13)CO CSA/(13)CO-(15)N CSA/dipolar cross correlation experiment. Given the global rotational correlation time from (15)N relaxation experiments, a new program COMFORD (CO-Modelfree Fitting Of Relaxation Data) is presented to fit the (13)CO data to an effective order parameter S2CO, an effective local correlation time and the orientation of the CSA tensor with respect to the molecular frame. It is shown that the effective S2CO is least sensitive to rotational fluctuations about an imaginary Calpha-Calpha axis and most sensitive to rotational fluctuations about an imaginary axis parallel to the NH bond direction. As such, the Calpha-Calpha information is fully complementary to the (15)N relaxation order parameter, which is least sensitive to fluctuations about the NH axis and most sensitive to fluctuations about the Calpha-Calpha axis. The new paradigm is applied on data of Ca(2+) saturated Calmodulin, and on available literature data for Ubiquitin. Our data indicate that the S2CO order parameters rapport on slower, and sometimes different, motions than the (15)N relaxation order parameters. The CO local correlation times correlate well with the calmodulin's secondary structure.

Backbone Dynamics of TEM-1 Determined by NMR: Evidence for a Highly Ordered Protein†

Backbone dynamics of TEM-1 beta-lactamase (263 amino acids, 28.9 kDa) were studied by 15N nuclear magnetic resonance relaxation at 11.7, 14.1, and 18.8 T. The high quality of the spectra allowed us to measure the longitudinal relaxation rate (R1), the transverse relaxation rate (R2), and the {1H}-15N NOE for up to 227 of the 250 potentially observable backbone amide groups. The model-free formalism was used to determine internal motional parameters using an axially anisotropic model. TEM-1 exhibits a small prolate axial anisotropy (D(parallel)/D(perpendicular) = 1.23 +/- 0.01) and a global correlation time (tau(m)) of 12.41 +/- 0.01 ns. The unusually high average generalized order parameter (S2) of 0.90 +/- 0.02 indicates that TEM-1 is one of the most ordered proteins studied by liquid-state NMR to date. Although the omega-loop has a high degree of order in the picosecond-to-nanosecond time scale (mean S2 value of 0.90 +/- 0.02), we observed the presence of microsecond-to-millisecond time scale motions for this loop, as for the vicinity of the active site. These motions could be relevant for the catalytic function of TEM-1. Amide exchange experiments were also performed, and several amide groups were not exchanged after 12 days, an indication that global motions in TEM-1 are also very limited. Although detailed dynamics characterization by NMR cannot be readily applied to TEM-1 in the presence of relevant substrates, the unusual picosecond-to-nanosecond dynamics behavior of TEM-1 presented here will be essential to the validation and improvement of future molecular dynamics simulations of TEM-1 in the presence of functionally relevant substrates.

Structure and dynamics of ASC2, a pyrin domain-only protein that regulates inflammatory signaling

Pyrin domain (PYD)-containing proteins are key components of pathways that regulate inflammation, apoptosis, and cytokine processing. Their importance is further evidenced by the consequences of mutations in these proteins that give rise to autoimmune and hyperinflammatory syndromes. PYDs, like other members of the death domain (DD) superfamily, are postulated to mediate homotypic interactions that assemble and regulate the activity of signaling complexes. However, PYDs are presently the least well characterized of all four DD subfamilies. Here we report the three-dimensional structure and dynamic properties of ASC2, a PYD-only protein that functions as a modulator of multidomain PYD-containing proteins involved in NF-kappaB and caspase-1 activation. ASC2 adopts a six-helix bundle structure with a prominent loop, comprising 13 amino acid residues, between helices two and three. This loop represents a divergent feature of PYDs from other domains with the DD fold. Detailed analysis of backbone 15N NMR relaxation data using both the Lipari-Szabo model-free and reduced spectral density function formalisms revealed no evidence of contiguous stretches of polypeptide chain with dramatically increased internal motion, except at the extreme N and C termini. Some mobility in the fast, picosecond to nanosecond timescale, was seen in helix 3 and the preceding alpha2-alpha3 loop, in stark contrast to the complete disorder seen in the corresponding region of the NALP1 PYD. Our results suggest that extensive conformational flexibility in helix 3 and the alpha2-alpha3 loop is not a general feature of pyrin domains. Further, a transition from complete disorder to order of the alpha2-alpha3 loop upon binding, as suggested for NALP1, is unlikely to be a common attribute of pyrin domain interactions.

Model-free model elimination: a new step in the model-free dynamic analysis of NMR relaxation data

Model-free analysis is a technique commonly used within the field of NMR spectroscopy to extract atomic resolution, interpretable dynamic information on multiple timescales from the R1, R2, and steady state NOE. Model-free approaches employ two disparate areas of data analysis, the discipline of mathematical optimisation, specifically the minimisation of a chi2 function, and the statistical field of model selection. By searching through a large number of model-free minimisations, which were setup using synthetic relaxation data whereby the true underlying dynamics is known, certain model-free models have been identified to, at times, fail. This has been characterised as either the internal correlation times, tau(e), tau(f), or tau(s), or the global correlation time parameter, local tau(m), heading towards infinity, the result being that the final parameter values are far from the true values. In a number of cases the minimised chi2 value of the failed model is significantly lower than that of all other models and, hence, will be the model which is chosen by model selection techniques. If these models are not removed prior to model selection the final model-free results could be far from the truth. By implementing a series of empirical rules involving inequalities these models can be specifically isolated and removed. Model-free analysis should therefore consist of three distinct steps: model-free minimisation, model-free model elimination, and finally model-free model selection. Failure has also been identified to affect the individual Monte Carlo simulations used within error analysis. Each simulation involves an independent randomised relaxation data set and model-free minimisation, thus simulations suffer from exactly the same types of failure as model-free models. Therefore, to prevent these outliers from causing a significant overestimation of the errors the failed Monte Carlo simulations need to be culled prior to calculating the parameter standard deviations.

HIV-1 Tat Is a Natively Unfolded Protein

Tat (transactivator of transcription) is a small RNA-binding protein that plays a central role in the regulation of human immunodeficiency virus type 1 replication and in approaches to treating latently infected cells. Its interactions with a wide variety of both intracellular and extracellular molecules is well documented. A molecular understanding of the multitude of Tat activities requires a determination of its structure and interactions with cellular and viral partners. To increase the dispersion of NMR signals and permit dynamics analysis by multinuclear NMR spectroscopy, we have prepared uniformly 15N- and 15N/13C-labeled Tat-(1-72) protein. The cysteine-rich protein is unambiguously reduced at pH 4.1, and NMR chemical shifts and coupling constants suggest that it exists in a random coil conformation. Line broadening and multiple peaks in the Cys-rich and core regions suggest that transient folding occurs in two of the five sequence domains. NMR relaxation parameters were measured and analyzed by spectral density and Lipari-Szabo approaches, both confirming the lack of structure throughout the length of the molecule. The absence of a fixed conformation and the observation of fast dynamics are consistent with the ability of Tat protein to interact with a wide variety of proteins and nucleic acid and support the concept of a natively unfolded protein.

Bayesian estimation of Karplus parameters and torsion angles from three-bond scalar couplings constants

We apply Bayesian inference to analyze three-bond scalar coupling constants in an objective and consistent way. The Karplus curve and a Gaussian error law are used to model scalar coupling measurements. By applying Bayes' theorem, we obtain a probability distribution for all unknowns, i.e., the torsion angles, the Karplus parameters, and the standard deviation of the Gaussian. We infer all these unknowns from scalar coupling data using Markov chain Monte Carlo sampling and analytically derive a probability distribution that only involves the torsion angles.

Inferential structure determination

Macromolecular structures calculated from nuclear magnetic resonance data are not fully determined by experimental data but depend on subjective choices in data treatment and parameter settings. This makes it difficult to objectively judge the precision of the structures. We used Bayesian inference to derive a probability distribution that represents the unknown structure and its precision. This probability distribution also determines additional unknowns, such as theory parameters, that previously had to be chosen empirically. We implemented this approach by using Markov chain Monte Carlo techniques. Our method provides an objective figure of merit and improves structural quality.

Protein and RNA Dynamics Play Key Roles in Determining the Specific Recognition of GU-rich Polyadenylation Regulatory Elements by Human Cstf-64 Protein

The N-terminal domain of the 64 kDa subunit of the cleavage stimulation factor (CstF-64) recognizes GU-rich elements within the 3'-untranslated region of eukaryotic mRNAs. This interaction is essential for mRNA 3' end processing and transcription termination, and its strength affects the efficiency of utilization of different polyadenylation sites. The structure of the RNA-binding N-terminal domain of CstF-64 showed how the N-terminal RNA recognition motif of CstF-64 recognizes GU-rich RNAs. However, it is still perplexing how this protein can bind selectively to RNAs that are rich in G and U residues regardless of their detailed sequence composition, yet discriminate effectively against non-GU-RNAs. We investigated by NMR the dynamics of the CstF-64 RNA-binding domain, both free and bound to two GU-rich RNA sequences that represent polyadenylation regulatory elements. While the free protein displays the motional properties typical of a well-folded protein domain and is uniformly rigid, the protein-RNA interface acquires significant mobility on the micro- to millisecond time-scale once GU-rich RNAs binds to it. These motional features, we propose, are intrinsic to the functional requirement to bind all GU-rich sequences and yet to discriminate against non-GU-rich RNAs. This behavior may be a general mechanism by which some RNA-binding proteins are able to bind to classes of sequences, as opposed to a well-defined sequence or consensus.

Dynamics of Ca2+-saturated calmodulin D129N mutant studied by multiple molecular dynamics simulations

Fifteen independent 1-nsec MD simulations of fully solvated Ca(2+) saturated calmodulin (CaM) mutant D129N were performed from different initial conditions to provide a sufficient statistical basis to gauge the significance of observed dynamical properties. In all MD simulations the four Ca(2+) ions remained in their binding sites, and retained a single water ligand as observed in the crystal structure. The coordination of Ca(2+) ions in EF-hands I, II, and III was sevenfold. In EF-hand IV, which was perturbed by the mutation of a highly conserved Asp129, an anomalous eightfold Ca(2+) coordination was observed. The Ca(2+) binding loop in EF-hand II was observed to dynamically sample conformations related to the Ca(2+)-free form. Repeated MD simulations implicate two well-defined conformations of Ca(2+) binding loop II, whereas similar effect was not observed for loops I, III, and IV. In 8 out of 15 MD simulations Ca(2+) binding loop II adopted an alternative conformation in which the Thr62 >C=O group was displaced from the Ca(2+) coordination by a water molecule, resulting in the Ca(2+) ion ligated by two water molecules. The alternative conformation of the Ca(2+) binding loop II appears related to the "closed" state involved in conformational exchange previously detected by NMR in the N-terminal domain fragment of CaM and the C-terminal domain fragment of the mutant E140Q. MD simulations suggest that conformations involved in microsecond exchange exist partially preformed on the nanosecond time scale.

Comparison of (13)C(alpha)H and (15)NH backbone dynamics in protein GB1

This study presents a site-resolved experimental view of backbone C(alpha)H and NH internal motions in the 56-residue immunoglobulin-binding domain of streptococcal protein G, GB1. Using (13)C(alpha)H and (15)NH NMR relaxation data [T(1), T(2), and NOE] acquired at three resonance frequencies ((1)H frequencies of 500, 600, and 800 MHz), spectral density functions were calculated as F(omega) = 2omegaJ(omega) to provide a model-independent way to visualize and analyze internal motional correlation time distributions for backbone groups in GB1. Line broadening in F(omega) curves indicates the presence of nanosecond time scale internal motions (0.8 to 5 nsec) for all C(alpha)H and NH groups. Deconvolution of F(omega) curves effectively separates overall tumbling and internal motional correlation time distributions to yield more accurate order parameters than determined by using standard model free approaches. Compared to NH groups, C(alpha)H internal motions are more broadly distributed on the nanosecond time scale, and larger C(alpha)H order parameters are related to correlated bond rotations for C(alpha)H fluctuations. Motional parameters for NH groups are more structurally correlated, with NH order parameters, for example, being larger for residues in more structured regions of beta-sheet and helix and generally smaller for residues in the loop and turns. This is most likely related to the observation that NH order parameters are correlated to hydrogen bonding. This study contributes to the general understanding of protein dynamics and exemplifies an alternative and easier way to analyze NMR relaxation data.

Protein dynamics using frequency-dependent order parameters from analysis of NMR relaxation data

A novel approach is described to analyze NMR relaxation data on proteins. This method introduces the frequency-dependent order parameter, S(2)(omega), in order to estimate contributions to the generalized order parameter S(2) from different motional frequencies occurring on the picosecond to nanosecond time scales. S(2)(omega) is defined as the sum of a specified set of weighting coefficients from the Lorentzian expansion of the spectral density function. 15N NMR relaxation data (500, 600, and 800 MHz) on protein GB1 exemplify the method. Using this approach provides information on motional restrictions over specific frequency or time scale ranges and provides a normalized comparison of motional restrictions between proteins having different overall tumbling correlation times.

Heat capacities and a snapshot of the energy landscape in protein GB1 from the pre-denaturation temperature dependence of backbone NH nanosecond fluctuations

Protein stability is usually characterized calorimetrically by a melting temperature and related thermodynamic parameters. Despite its importance, the microscopic origin of the melting transition and the relationship between thermodynamic stability and dynamics remains a mystery. Here, NMR relaxation parameters were acquired for backbone 15NH groups of the 56 residue immunoglobulin-binding domain of streptococcal protein G over a pre-denaturation temperature range of 5-50 degrees C. Relaxation data were analyzed using three methods: the standard three-Lorentzian model free approach; the F(omega)=2omegaJ(omega) spectral density approach that yields motional correlation time distributions, and a new approach that determines frequency-dependent order parameters. Regardless of the method of analysis, the temperature dependence of internal motional correlation times and order parameters is essentially the same. Nanosecond time-scale internal motions are found for all NHs in the protein, and their temperature dependence yields activation energies ranging up to about 33kJ/mol residue. NH motional barrier heights are structurally correlated, with the largest energy barriers being found for residues in the most "rigid" segments of the fold: beta-strands 1 and 4 and the alpha-helix. Trends in this landscape also parallel the free energy of folding-unfolding derived from hydrogen-deuterium (H-D) exchange measurements, indicating that the energetics for internal motions occurring on the nanosecond time-scale mirror those occurring on the much slower time-scale of H-D exchange. Residual heat capacities, derived from the temperature dependence of order parameters, range from near zero to near 100J/mol K residue and correlate with this energy landscape. These results provide a unique picture of this protein's energy landscape and a relationship between thermodynamic stability and dynamics that suggests thermosensitive regions in the fold that could initiate the melting process.

Molecular dynamics and NMR spin relaxation in proteins

Molecular dynamics simulations often play a central role in the analysis of biomolecular NMR data. The focus here is on NMR spin-relaxation, which can provide unique insights into the time-dependence of conformational fluctuations, especially on picosecond to nanosecond time scales which can be directly probed by simulations. A great deal has been learned from such simulations about the general nature of such motions and their impact on NMR observables. In principle, relaxation measurements should also provide valuable benchmarks for judging the quantitative accuracy of simulations, but there are a variety of experimental and computational obstacles to making useful direct comparisons. It seems likely that simulations on time scales that are just now becoming generally feasible may provide important new information on internal motions, overall rotational diffusion, and the coupling between internal and rotational motion. Such information could provide a sound foundation for a new generation of detailed interpretation of NMR spin-relaxation results.

Structure, dynamics, and thermodynamics of the structural domain of troponin C in complex with the regulatory peptide 1-40 of troponin I

The structure of the calcium-saturated C-domain of skeletal troponin C (CTnC) in complex with a regulatory peptide comprising residues 1-40 (Rp40) of troponin I (TnI) was determined using nuclear magnetic resonance (NMR) spectroscopy. The solution structure determined by NMR is similar to the structure of the C-domain from intact TnC in complex with TnI(1)(-)(47) determined by X-ray crystallography [Vassylyev, D. G., Takeda, S., Wakatsuki, S., Maeda, K., and Maeda, Y. (1998) Proc. Natl. Acad. Sci. U.S.A. 95, 4847-4852]. Changes in the dynamic properties of CTnC.2Ca2+ induced by Rp40 binding were investigated using backbone amide (15)N NMR relaxation measurements. Analysis of NMR relaxation data allows for extraction of motional order parameters on a per residue basis, from which the contribution of changes in picosecond to nanosecond time scale motions to the conformational entropy associated with complex formation can be estimated. The results indicate that binding of Rp40 decreases backbone flexibility in CTnC, particularly at the end of the C-terminal helix. The backbone conformational entropy change (-TDeltaS) associated with binding of Rp40 to CTnC.2Ca2+ determined from (15)N relaxation data is 9.6 +/- 0.7 kcal mol(-1) at 30 degrees C. However, estimation of thermodynamic quantities using a structural approach [Lavigne, P., Bagu, J. R., Boyko, R., Willard, L., Holmes, C. F., and Sykes, B. D. (2000) Protein Sci. 9, 252-264] reveals that the change in solvation entropy upon complex formation is dominant and overcomes the thermodynamic "cost" associated with "stiffening" of the protein backbone upon Rp40 binding. Additionally, backbone amide (15)N relaxation data measured at different concentrations of CTnC.2Ca2+.Rp40 reveal that the complex dimerizes in solution. Fitting of the apparent global rotational correlation time as a function of concentration to a monomer-dimer equilibrium yields a dimerization constant of approximately 8.3 mM.

Nmr probes of molecular dynamics: overview and comparison with other techniques

NMR spin relaxation spectroscopy is a powerful approach for characterizing intramolecular and overall rotational motions in proteins. This review describes experimental methods for measuring laboratory frame spin relaxation rate constants by high-resolution solution-state NMR spectroscopy, together with theoretical approaches for interpreting spin relaxation data in order to quantify protein conformational dynamics on picosecond-nanosecond time scales. Recent applications of these techniques to proteins are surveyed, and investigations of the contribution of conformational chain entropy to protein function are highlighted. Insights into the dynamical properties of proteins obtained from NMR spin relaxation spectroscopy are compared with results derived from other experimental and theoretical techniques.

Backbone dynamics of the channel-forming antibiotic zervamicin IIB studied by 15N NMR relaxation

The backbone dynamics of the channel-forming peptide antibiotic zervamicin IIB (Zrv-IIB) in methanol were studied by 15N nuclear magnetic resonance relaxation measurements at 11.7, 14.1 and 18.8 T magnetic fields. The anisotropic overall rotation of the peptide was characterized based on 15N relaxation data and by hydrodynamic calculations. 'Model-free' analysis of the relaxation data showed that the peptide is fairly rigid on a sub-nanosecond time-scale. The residues from the polar side of Zrv-IIB helix are involved in micro-millisecond time-scale conformational exchange. The conformational exchange observed might indicate intramolecular processes or specific intermolecular interactions of potential relevance to Zrv-IIB ion channel formation.

A Bayesian statistical method for the detection and quantification of rotational diffusion anisotropy from NMR relaxation data

It has recently become more widely appreciated that the presence of rotational diffusional anisotropy in proteins and other macromolecules can have a significant affect on the interpretation of NMR relaxation data in terms of molecular motion. In this paper, we show how commonly used NMR relaxation data (R(1), R(2), and NOE) obtained at two spectrometer frequencies can be analyzed using a Bayesian statistical approach to reliably detect and quantify the degree of rotational diffusion anisotropy. Our approach differs from previous methods in that it does not make assumptions concerning the internal motions experienced by the residues which are used to quantify the diffusion anisotropy, but rather averages the results over all internal motions consistent with the data. We demonstrate our method using synthetic data corresponding to isotropic, axially symmetric anisotropic, and fully asymmetric anisotropic rotational diffusion, as well as experimental NMR data. We compare the Bayesian statistical approach with a widely used method for extracting tumbling parameters using both synthetic and experimental data. While it can be difficult to separate the effects of chemical exchange from rotational anisotropy using this "standard" method, these effects are readily separated using Bayesian statistics. In addition, we find that the Bayesian statistical approach requires considerably less CPU time than an equivalent standard analysis.

The effects of ligand binding on the backbone dynamics of the kringle 1 domain of human plasminogen

The internal motions of the backbone nitrogen atoms of the kringle 1 domain of human plasminogen (K1(Pg)) were examined in the absence and presence of the ligand, epsilon-aminocaproic acid. These dynamic properties were determined from (15)N NMR relaxation data in terms of the extended model-free parameters. The model of isotropic reorientation was found sufficient to account for overall molecular tumbling for both apo and EACA-bound K1(Pg). The global rotational correlation time (tau(m)) for apo-K1(Pg) was 5.87(+/-0.01) ns, while the tau(m) for ligand-bound K1(Pg) was 5.20(+/-0.01) ns, suggesting that perhaps some small degree of aggregation occurred in the apo form of the kringle module. Complexation of K1(Pg) with ligand mainly reduced those internal motions that occurred on a 100 ps to 5 ns time-scale. The magnitude of the chemical exchange was also attenuated upon ligand binding. These data are consistent with studies employing other approaches that suggest that the binding pocket is preformed in K1(Pg).

Backbone dynamics of the C-terminal SH2 domain of the p85alpha subunit of phosphoinositide 3-kinase: effect of phosphotyrosine-peptide binding and characterization of slow conformational exchange processes

The backbone dynamics of the C-terminal SH2 domain from the regulatory subunit p85alpha (p85alpha C-SH2) of phosphoinositide 3-kinase has been investigated in the absence of, and in complex with, a high-affinity phosphotyrosine-containing peptide ligand derived from the platelet-derived growth-factor receptor. (15)N R(1) and R(2) relaxation rates and steady-state [(1)H]-(15)N NOE values were measured by means of (1)H-(15)N correlated two-dimensional methods and were analyzed within the framework of the model-free formalism. Several residues in the BC loop and in the neighbouring secondary structural elements display fast local dynamics in the absence of phosphotyrosine peptide ligand as evidenced by below-average [(1)H]-(15)N NOE values. Furthermore, residue Gln41 (BC3) displays conformational exchange phenomena as indicated by an above-average R(2) relaxation rate. Upon binding of the phosphotyrosine peptide, the NOE values increase to values observed for regular secondary structure and the exchange contribution to the R(2) relaxation rate for Gln41 (BC3) vanishes. These observations indicate a loss of backbone flexibility upon ligand binding. Substantial exchange contributions for His56 (betaD4) and Cys57 (betaD5), which are known to make important interactions with the ligand, are attenuated upon ligand binding. Several residues in the betaD'-FB region and the BG loop, which contribute to the ligand binding surface of the protein, exhibit exchange terms which are reduced or vanish when the ligand is bound. Together, these observations suggest that ligand binding is accompanied by a loss of conformational flexibility on the ligand binding face of the protein. However, comparison with other SH2 domains reveals an apparent lack of consensus in the changes in dynamics induced by ligand binding. Exchange rates for individual residues were quantified in peptide-complexed p85alpha C-SH2 from the dependence of the exchange contributions on the CPMG delay in an R(2) series and show that peptide-complexed p85alpha C-SH2 is affected by multiple conformational exchange processes with exchange rate constants from 10(2) s(-1) to 7.10(3) s(-1). Mapping of the exchange-rate constants on the protein surface show a clustering of residues with similar exchange-rate constants and suggests that clustered residues are affected by a common predominant exchange process.

Simple and accurate determination of global tau(R) in proteins using (13)C or (15)N relaxation data

In the study of protein dynamics by (13)C or (15)N relaxation measurements different models from the Lipari-Szabo formalism are used in order to determine the motion parameters. The global rotational correlation time tau(R) of the molecule must be estimated prior to the analysis. In this Communication, the authors propose a new approach in determining an accurate value for tau(R) in order to realize the best fit of R(2) for the whole sequence of the protein, regardless of the different type of motions atoms may experience. The method first determines the highly structured regions of the sequence. For each corresponding site, the Lipari-Szabo parameters are calculated for R(1) and NOE, using an arbitrary value for tau(R). The chi(2) for R(2), summed over the selected sites, shows a clear minimum, as a function of tau(R). This minimum is used to better estimate a proper value for tau(R).