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 ¹⁵N relaxation data: longitudinal relaxation rate (R ₁), transverse relaxation rate (R ₂), and ¹⁵N–{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 R ₂/R ₁ 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.     

Unraveling protein dynamics through fast spectral density mapping

Spectral density mapping at multiple NMR field strengths is probably the best method to describe the dynamical behavior of a protein in solution through the analysis of ¹⁵N heteronuclear relaxation parameters. Nevertheless, such analyses are scarcely reported in the literature, probably because this method is excessively demanding in spectrometer measuring time. Indeed, when using n different magnetic fields and assuming the validity of the high frequency approximation, the discrete sampling of the spectral density function with 2n + 1 points needs the measurement of 3n ¹⁵N heteronuclear relaxation measurements (n R ₁, n R ₂, and n¹⁵N{¹H}NOEs). Based on further approximations, we proposed a new strategy that allows us to describe the spectral density with n + 2 points, with the measurement of a total of n + 2 heteronuclear relaxation parameters. Applied to the dynamics analysis of the protein p13 ^MTCP1 at three different NMR fields, this approach allowed us to divide by nearly a factor of two the total measuring time, without altering further results obtained by the “model free” analysis of the resulting spectral densities. Furthermore, simulations have shown that this strategy remains applicable to any low isotropically tumbling protein ( ns), and is valid for the types of motion generally envisaged for proteins.     

Protein-bound water molecule counting by resolution of (1)H spin-lattice relaxation mechanisms

Water proton spin-lattice relaxation is studied in dilute solutions of bovine serum albumin as a function of magnetic field strength, oxygen concentration, and solvent deuteration. In contrast to previous studies conducted at high protein concentrations, the observed relaxation dispersion is accurately Lorentzian with an effective correlation time of 41 +/- 3 ns when measured at low proton and low protein concentrations to minimize protein aggregation. Elimination of oxygen flattens the relaxation dispersion profile above the rotational inflection frequency, nearly eliminating the high field tail previously attributed to a distribution of exchange times for either whole water molecules or individual protons at the protein-water interface. The small high-field dispersion that remains is attributed to motion of the bound water molecules on the protein or to internal protein motions on a time scale of order one ns. Measurements as a function of isotope composition permit separation of intramolecular and intermolecular relaxation contributions. The magnitude of the intramolecular proton-proton relaxation rate constant is interpreted in terms of 25 +/- 4 water molecules that are bound rigidly to the protein for a time long compared with the rotational correlation time of 42 ns. This number of bound water molecules neglects the possibility of local motions of the water in the binding site; inclusion of these effects may increase the number of bound water molecules by 50%.     

Analysis of Sub-τc and Supra-τc Motions in Protein Gβ1 Using Molecular Dynamics Simulations

The functions of proteins depend on the dynamical behavior of their native states on a wide range of timescales. To investigate these dynamics in the case of the small protein Gβ1, we analyzed molecular dynamics simulations with the model-free approach of nuclear magnetic relaxation. We found amplitudes of fast timescale motions (sub-τ_c, where τ_c is the rotational correlation time) consistent with S² obtained from spin relaxation measurements as well as amplitudes of slow timescale motions (supra-τ_c) in quantitative agreement with S² order parameters derived from residual dipolar coupling measurements. The slow timescale motions are associated with the large variations of the ³J couplings that follow transitions between different conformational substates. These results provide further characterization of the large structural fluctuations in the native states of proteins that occur on timescales longer than the rotational correlation time.     

Direct determination of the heteronuclear T1/T2 ratio by off-resonance steady-state magnetization measurement: Investigation of the possible application to fast exchange characterization of 15N-labeled proteins

The ¹⁵N steady-state magnetization in the presence of off-resonance rf irradiation is an analytical function of the T₁/T₂ ratio and of the angle between the ¹⁵N effective field axis and the static magnetic field direction. This relation holds whatever the relaxation mechanisms due to motions on the nanosecond time scale, and the size of the spin system. If motions on the micro- to millisecond time scale are present (fast exchange), the same observable depends also on their spectral density at the frequency of the effective field. The cross-peak intensity in each 2D ¹⁵N-¹H correlation map is directly related to the dynamic parameters, so that the characterization of fast exchange phenomena by this method is in principle less time-consuming than the separate measurement of self-relaxation rates. The theory of this approach is described. Its practical validity is experimentally evaluated on a ¹⁵N-labeled 61 amino acid neurotoxin. It turns out that existing equipments lead to non-negligible biases. Their consequences for the accuracy attainable, at present, by this method are investigated in detail.     

High frequency dynamics in hemoglobin measured by magnetic relaxation dispersion

The magnetic relaxation dispersion profiles for formate, acetate, and water protons are reported for aqueous solutions of hemoglobin singly and doubly labeled with a nitroxide and mercury(II) ion at cysteines at beta-93. Using two spin labels, one nuclear and one electron spin, a long intramolecular vector is defined between the two beta-93 positions in the protein. The paramagnetic contributions to the observed 1H spin-lattice relaxation rate constant are isolated from the magnetic relaxation dispersion profiles obtained on a dual-magnet apparatus that provides spectral density functions characterizing fluctuations sensed by intermoment dipolar interactions in the time range from the tens of microseconds to approximately 1 ps. Both formate and acetate ions are found to bind specifically within 5 angstroms of the beta-93 spin-label position and the relaxation dispersion has inflection points corresponding to correlation times of 30 ps and 4 ns for both ions. The 4-ns motion is identified with exchange of the anions from the site, whereas the 30-ps correlation time is identified with relative motions of the spin label and the bound anion in the protein environment close to beta-93. The magnetic field dependence of the paramagnetic contributions in both cases is well described by a simple Lorentzian spectral density function; no peaks in the spectral density function are observed. Therefore, the high frequency motions of the protein monitored by the intramolecular vector defined by the electron and nuclear spin are well characterized by a stationary random function of time. Attempts to examine long vector fluctuations by employing electron spin and nuclear spin double-labeling techniques did not yield unambiguous characterization of the high frequency motions of the vector between beta-93 positions on different chains.     

In vivo High Angular Resolution Diffusion-Weighted Imaging of Mouse Brain at 16.4 Tesla

Magnetic Resonance Imaging (MRI) of the rodent brain at ultra-high magnetic fields (> 9.4 Tesla) offers a higher signal-to-noise ratio that can be exploited to reduce image acquisition time or provide higher spatial resolution. However, significant challenges are presented due to a combination of longer T ₁ and shorter T ₂/T₂* relaxation times and increased sensitivity to magnetic susceptibility resulting in severe local-field inhomogeneity artefacts from air pockets and bone/brain interfaces. The Stejskal-Tanner spin echo diffusion-weighted imaging (DWI) sequence is often used in high-field rodent brain MRI due to its immunity to these artefacts. To accurately determine diffusion-tensor or fibre-orientation distribution, high angular resolution diffusion imaging (HARDI) with strong diffusion weighting (b >3000 s/mm²) and at least 30 diffusion-encoding directions are required. However, this results in long image acquisition times unsuitable for live animal imaging. In this study, we describe the optimization of HARDI acquisition parameters at 16.4T using a Stejskal-Tanner sequence with echo-planar imaging (EPI) readout. EPI segmentation and partial Fourier encoding acceleration were applied to reduce the echo time (TE), thereby minimizing signal decay and distortion artefacts while maintaining a reasonably short acquisition time. The final HARDI acquisition protocol was achieved with the following parameters: 4 shot EPI, b = 3000 s/mm², 64 diffusion-encoding directions, 125×150 μm² in-plane resolution, 0.6 mm slice thickness, and 2h acquisition time. This protocol was used to image a cohort of adult C57BL/6 male mice, whereby the quality of the acquired data was assessed and diffusion tensor imaging (DTI) derived parameters were measured. High-quality images with high spatial and angular resolution, low distortion and low variability in DTI-derived parameters were obtained, indicating that EPI-DWI is feasible at 16.4T to study animal models of white matter (WM) diseases.     

Quantitative analysis of backbone motion in proteins using MAS solid-state NMR spectroscopy

We present a comprehensive analysis of protein dynamics for a micro-crystallin protein in the solid-state. Experimental data include ¹⁵N T ₁ relaxation times measured at two different magnetic fields as well as ¹H–¹⁵N dipole, ¹⁵N CSA cross correlated relaxation rates which are sensitive to the spectral density function J(0) and are thus a measure of T ₂ in the solid-state. In addition, global order parameters are included from a ¹H,¹⁵N dipolar recoupling experiment. The data are analyzed within the framework of the extended model-free Clore–Lipari–Szabo theory. We find slow motional correlation times in the range of 5 and 150 ns. Assuming a wobbling in a cone motion, the amplitude of motion of the respective amide moiety is on the order of 10° for the half-opening angle of the cone in most of the cases. The experiments are demonstrated using a perdeuterated sample of the chicken α-spectrin SH3 domain.     

Phospholipid Reorientation at the Lipid/Water Interface Measured by High Resolution P Field Cycling NMR Spectroscopy

The magnetic field dependence of the ³¹P spin-lattice relaxation rate, R₁, of phospholipids can be used to differentiate motions for these molecules in a variety of unilamellar vesicles. In particular, internal motion with a 5- to 10-ns correlation time has been attributed to diffusion-in-a-cone of the phosphodiester region, analogous to motion of a cylinder in a liquid hydrocarbon. We use the temperature dependence of ³¹P R₁ at low field (0.03-0.08 T), which reflects this correlation time, to explore the energy barriers associated with this motion. Most phospholipids exhibit a similar energy barrier of 13.2 ± 1.9 kJ/mol at temperatures above that associated with their gel-to-liquid-crystalline transition (T_m); at temperatures below T_m, this barrier increases dramatically to 68.5 ± 7.3 kJ/mol. This temperature dependence is broadly interpreted as arising from diffusive motion of the lipid axis in a spatially rough potential energy landscape. The inclusion of cholesterol in these vesicles has only moderate effects for phospholipids at temperatures above their T_m, but significantly reduces the energy barrier (to 17 ± 4 kJ/mol) at temperatures below the T_m of the pure lipid. Very-low-field R₁ data indicate that cholesterol inclusion alters the averaged disposition of the phosphorus-to-glycerol-proton vector (both its average length and its average angle with respect to the membrane normal) that determines the ³¹P relaxation.     

Temperature-dependent spectral density analysis applied to monitoring backbone dynamics of major urinary protein-I complexed with the pheromone 2-sec-butyl-4,5-dihydrothiazole*

Backbone dynamics of mouse major urinary protein I (MUP-I) was studied by (15)N NMR relaxation. Data were collected at multiple temperatures for a complex of MUP-I with its natural pheromonal ligand, 2- sec -4,5-dihydrothiazole, and for the free protein. The measured relaxation rates were analyzed using the reduced spectral density mapping. Graphical analysis of the spectral density values provided an unbiased qualitative picture of the internal motions. Varying temperature greatly increased the range of analyzed spectral density values and therefore improved reliability of the analysis. Quantitative parameters describing the dynamics on picosecond to nanosecond time scale were obtained using a novel method of simultaneous data fitting at multiple temperatures. Both methods showed that the backbone flexibility on the fast time scale is slightly increased upon pheromone binding, in accordance with the previously reported results. Zero-frequency spectral density values revealed conformational changes on the microsecond to millisecond time scale. Measurements at different temperatures allowed to monitor temperature dependence of the motional parameters.     

Dynamics of a truncated prion protein,PrP(113–231), from 15N NMR relaxation: Order parameters calculated and slow conformational fluctuations localized to a distinct region

Prion diseases are associated with the misfolding of the prion protein (PrP^C) from a largely α‐helical isoform to a β‐sheet rich oligomer (PrP^Sc). Flexibility of the polypeptide could contribute to the ability of PrP^C to undergo the conformational rearrangement during PrP^C–PrP^Sc interactions, which then leads to the misfolded isoform. We have therefore examined the molecular motions of mouse PrP^C, residues 113–231, in solution, using ¹⁵N NMR relaxation measurements. A truncated fragment has been used to eliminate the effect of the 90‐residue unstructured tail of PrP^C so the dynamics of the structured domain can be studied in isolation. ¹⁵N longitudinal (T₁) and transverse relaxation (T₂) times as well as the proton‐nitrogen nuclear Overhauser effects have been used to calculate the spectral density at three frequencies, 0, ω_N, and 0.87ω_H. Spectral densities at each residue indicate various time‐scale motions of the main‐chain. Even within the structured domain of PrP^C, a diverse range of motions are observed. We find that removal of the tail increases T₂ relaxation times significantly indicating that the tail is responsible for shortening of T₂ times in full‐length PrP^C. The truncated fragment of PrP has facilitated the determination of meaningful order parameters (S²) from the relaxation data and shows for the first time that all three helices in PrP^C have similar rigidity. Slow conformational fluctuations of mouse PrP^C are localized to a distinct region that involves residues 171 and 172. Interestingly, residues 170–175 have been identified as a segment within PrP that will form a steric zipper, believed to be the fundamental amyloid unit. The flexibility within these residues could facilitate the PrP^C–PrP^Sc recognition process during fibril elongation.     

Dynamics of the intrinsically disordered protein NUPR1 in isolation and in its fuzzy complexes with DNA and prothymosin α

Intrinsically disordered proteins (IDPs) explore diverse conformations in their free states and, a few of them, also in their molecular complexes. This functional plasticity is essential for the function of IDPs, although their dynamics in both free and bound states is poorly understood. NUPR1 is a protumoral multifunctional IDP, activated during the acute phases of pancreatitis. It interacts with DNA and other IDPs, such as prothymosin α (ProTα), with dissociation constants of ~0.5 μM, and a 1:1 stoichiometry. We studied the structure and picosecond-to-nanosecond (ps-ns) dynamics by using both NMR and SAXS in: (i) isolated NUPR1; (ii) the NUPR1/ProTα complex; and (iii) the NUPR1/double stranded (ds) GGGCGCGCCC complex. Our SAXS findings show that NUPR1 remained disordered when bound to either partner, adopting a worm-like conformation; the fuzziness of bound NUPR1 was also pinpointed by NMR. Residues with the largest values of the relaxation rates (R₁, R_1ρ, R₂ and η_xy), in the free and bound species, were mainly clustered around the 30s region of the sequence, which agree with one of the protein hot-spots already identified by site-directed mutagenesis. Not only residues in this region had larger relaxation rates, but they also moved slower than the rest of the molecule, as indicated by the reduced spectral density approach (RSDA). Upon binding, the energy landscape of NUPR1 was not funneled down to a specific, well-folded conformation, but rather its backbone flexibility was kept, with distinct motions occurring at the hot-spot region.     

Backbone dynamics of apocytochrome b5 in its native, partially folded state

The backbone dynamics in the native state of apocytochrome b5 were studied using 15N nuclear magnetic spin relaxation measurements. The field (11.7 and 14.1 T) and temperature (10-25 degrees C) dependence of the relaxation parameters (R1, R2, and R1rho) and the 1H-15N NOE established that the protein undergoes multiple time scale internal motions related to the secondary structure. The relaxation data were analyzed with the reduced spectral density mapping approach and within the extended model-free framework. The apoprotein was confirmed to contain a disordered heme-binding loop of approximately 30 residues with dynamics on the sub-nanosecond time scale (0.6 < S2 < 0.7, 100 ps < taue < 500 ps). This loop is attached to a structured hydrophobic core, rigid on the picosecond time scale (S2 > 0.75, taue < 50 ps). The inability to fit the data for several residues with the model-free protocol revealed the presence of correlated motion. An exchange contribution was detected in the transverse relaxation rate (R2) of all residues. The differential temperature response of R2 along the backbone supported slower exchange rates for residues in the loop (tauex > 300 micros) than for the folded polypeptide chain (tauex < 150 micros). The distribution of the reduced spectral densities at the 1H and 15N frequencies followed the dynamic trend and predicted the slowing of the internal motions at 10 degrees C. Comparison of the dynamics with those of the holoprotein [Dangi, B., Sarma, S., Yan, C., Banville, D. L., and Guiles, R. D. (1998) Biochemistry 37, 8289-8302] demonstrated that binding of the heme alters the time scale of motions both in the heme-binding loop and in the structured hydrophobic core.     

Backbone dynamics of the natively unfolded pro-peptide of subtilisin by heteronuclear NMR relaxation studies

The dynamics of the natively unfolded form of the pro-peptide of subtilisin (PPS) have been characterized at two different pHs (6.0 and 3.0) by ¹⁵N relaxation experiments. ¹⁵N relaxation data is obtained at multiple field strengths and a detailed comparison of spectral density mapping, the model free approach and the recently proposed Cole–Cole model free (CC-MF) analysis is presented. The CC-MF analysis provides a better fit to the observed magnetic field dependence of ¹⁵N relaxation data of unfolded PPS than conventional model free approaches and shows that fluctuations in R₂ may be accounted for by a distribution of correlation times on the nanosecond timescale. A new parameter derives from the analysis and represents the width of the distribution function and the heterogeneity of the dynamics on the nanosecond timescale at a particular site. Particularly interesting is the observation that is sensitive to pH changes and that PPS samples a wider distribution of nanosecond time scale motions at less acidic pHs than at more acidic pHs. These results suggest that PPS experiences a higher degree of correlated motion at pH 6.0 and that electrostatic interactions may be important for inducing correlated motions on the nanosecond timescale in unfolded PPS.     

Fast evaluation of protein dynamics from deficient <Superscript>15</Superscript>N relaxation data

Simple and convenient method of protein dynamics evaluation from the insufficient experimental ¹⁵N relaxation data is presented basing on the ratios, products, and differences of longitudinal and transverse ¹⁵N relaxation rates obtained at a single magnetic field. Firstly, the proposed approach allows evaluating overall tumbling correlation time (nanosecond time scale). Next, local parameters of the model-free approach characterizing local mobility of backbone amide N–H vectors on two different time scales, S² and R _ex , can be elucidated. The generalized order parameter, S², describes motions on the time scale faster than the overall tumbling correlation time (pico- to nanoseconds), while the chemical exchange term, R _ex , identifies processes slower than the overall tumbling correlation time (micro- to milliseconds). Advantages and disadvantages of different methods of data handling are thoroughly discussed.     

A Physical Picture of Protein Dynamics and Conformational Changes

A physical model is reviewed which explains different aspects of protein dynamics consistently. At low temperatures, the molecules are frozen in conformational substates. Their average energy is 3/2RT. Solid-state vibrations occur on a time scale of femtoseconds to nanoseconds. Above a characteristic temperature, often called the dynamical transition temperature, slow modes of motions can be observed occurring on a time scale between about 140 and 1 ns. These motions are overdamped, quasidiffusive, and involve collective motions of segments of the size of an α-helix. Molecules performing these types of motion are in the “flexible state”. This state is reached by thermal activation. It is shown that these motions are essential for conformational relaxation. Based on this picture, a new approach is proposed to understand conformational changes. It connects structural fluctuations and conformational transitions.     

Detection of internal motions in oligosaccharides by 1H relaxation measurements at different magnetic fields.

The effect of internal motions on proton relaxation data in oligosaccharides has been investigated experimentally. 1H steady-state and transient NOEs together with 13C T1's have been measured at two magnetic field strengths. The existence of internal motions leads to additional modulations of the dipolar interaction between proton pairs, thus producing a range of spectral density functions for these interactions. As a result, it is possible to show that protons relaxing through fixed distances have a different ratio of relaxation parameters, acquired at 500 and 300 MHz, compared to those relaxing through fluctuating distances. This approach has been used to unequivocally establish for two disaccharides the existence of internal motions on the time scale of the overall tumbling.     

Anisotropic rotational diffusion of perdeuterated HIV protease from 15N NMR relaxation measurements at two magnetic fields

Summary ¹⁵N NMR relaxation times in perdeuterated HIV-1 protease, complexed with the sub-nanomolar inhibitor DMP323, have been measured at 600 and 360 MHz ¹H frequency. The relative magnitudes of the principal components of the inertia tensor, calculated from the X-ray coordinates of the protein-drug complex, are 1.0:0.85:0.44. The relation between the T₁/T₂ ratios observed for the individual backbone amides and their N-H orientation within the 3D structure of the protease dimer yields a rotational diffusion tensor oriented nearly collinear to the inertia tensor. The relative magnitudes of its principal components (1.00:1.11:1.42) are also in good agreement with hydrodynamic modeling results. The orientation and magnitude of the diffusion tensors derived from relaxation data obtained at 360 and 600 MHz are nearly identical. The anisotropic nature of the rotational diffusion has little influence on the order parameters derived from the ¹⁵N T₁ and T₂ relaxation times; however, if anisotropy is ignored, this can result in erroneous identification of either exchange broadening or internal motions on a nanosecond time scale. The average ratio of the T₁ values measured at 360 and 600 MHz is 0.50±0.015, which is slightly larger than the value of 0.466 expected for an isotropic rigid rotor with _c = 10.7 ns. The average ratio of the T₂ values measured at 360 and 600 MHz is 1.14±0.04, which is also slightly larger than the expected ratio of 1.11. This magnetic field dependence of the T₁ and T₂ relaxation times suggests that the spectral density contribution from fast internal motions is not negligible, and that the chemical shift anisotropy of peptide backbone amides, on average, is larger than the 160 ppm value commonly used in ¹⁵N relaxation studies of proteins.