Rocking motion in solid proteins studied by the 15N proton-decoupled R1ρ relaxometry.

Recently it has been revealed that proteins in solid samples undergo slow overall rocking. The parameters of this motion depend on intermolecular interactions. Therefore, the characterization of the rocking motion enables one to investigate protein-protein interactions. NMR R1ρ relaxometry is the most suitable tool to study slow molecular motions. However, the time scale of the rocking motion is on the edge of the dynamics window of the standard R1ρ experiment, precluding the R1ρ data analysis from being precise and reliable. In this work, we apply a modified R1ρ relaxation method to characterize the slow motion in solids with much higher precision and reliability. The modification is the simultaneous use of a strong 1H-CW pulse and a weak/moderate 15N spin-lock pulse. We demonstrate theoretically and experimentally that under this condition, R1ρ decays have a significantly better signal-to-noise ratio and a much shorter "dead time" caused by the initial oscillations compared to the conventional R1ρ experiment. Moreover, the proton-decoupled R1ρ's can be measured at a much smaller difference between the spin-lock and MAS frequencies; thus, much slower molecular motions can be sampled. The proton decoupling during the 15N spin-lock pulse also suppresses the interfering coherent spin-spin relaxation pathway at low spin-lock fields, which overlaps the Bloch-McConnell (chemical exchange) range of R1ρ dispersions. The proton-decoupled and standard R1ρ experiments were used to study the rocking motion of 15N,2H-enriched protein GB1 in two solid forms, microcrystals and lyophilized amorphous powder. The most striking finding is that the correlation function of this motion consists of two components with very different correlation times, 2-20 µs and a few hundred µs. The rocking motion parameters in microcrystals and powder are quite different, revealing the distinct nature of inter-protein interactions in these two samples.

Microsecond motions probed by near-rotary-resonance R1ρ15N MAS NMR experiments: the model case of protein overall-rocking in crystals.

Solid-state near-rotary-resonance measurements of the spin-lattice relaxation rate in the rotating frame (R1ρ) is a powerful NMR technique for studying molecular dynamics in the microsecond time scale. The small difference between the spin-lock (SL) and magic-angle-spinning (MAS) frequencies allows sampling very slow motions, at the same time it brings up some methodological challenges. In this work, several issues affecting correct measurements and analysis of 15N R1ρ data are considered in detail. Among them are signal amplitude as a function of the difference between SL and MAS frequencies, "dead time" in the initial part of the relaxation decay caused by transient spin-dynamic oscillations, measurements under HORROR condition and proper treatment of the multi-exponential relaxation decays. The multiple 15N R1ρ measurements at different SL fields and temperatures have been conducted in 1D mode (i.e. without site-specific resolution) for a set of four different microcrystalline protein samples (GB1, SH3, MPD-ubiquitin and cubic-PEG-ubiquitin) to study the overall protein rocking in a crystal. While the amplitude of this motion varies very significantly, its correlation time for all four sample is practically the same, 30-50 µs. The amplitude of the rocking motion correlates with the packing density of a protein crystal. It has been suggested that the rocking motion is not diffusive but likely a jump-like dynamic process.

Quantitative NMR study of heat-induced aggregation of eye-lens crystallin proteins under crowding conditions.

The eye lens contains a highly concentrated, polydisperse mixture of crystallins, and a loss in transparency during cataract formation is attributed to the aggregation of these proteins. Most biochemical and biophysical studies of crystallins have been performed in diluted samples because of various physical limitations of the respective method at physiological concentrations of up to 200-400 mg/mL. We introduce a straightforward proton NMR transverse relaxometry method to quantify simultaneously proteins in the dissolved and aggregated states at these elevated concentrations, because these states significantly differ in their transverse relaxation properties. The key feature of this method is a direct observation of the protein signal in a wide range of relaxation delays, from few microseconds up to few hundred milliseconds. We applied this method to follow heat-induced aggregation of bovine α- and γB-crystallin between 60 and 200 mg/mL. We find that at 60 °C, a temperature where both crystallins still comprise a native tertiary structure, γB-crystallin aggregated at these high protein concentrations with a time constant of about 30-40 h. α-crystallin remained soluble at 60 mg/mL but formed a transparent gel at 200 mg/mL. This quantitative NMR method can be applied to investigations of other proteins and their mixtures under various aggregation conditions.

Coupling and Decoupling of Rotational and Translational Diffusion of Proteins under Crowding Conditions.

Molecular motion of biopolymers in vivo is known to be strongly influenced by the high concentration of organic matter inside cells, usually referred to as crowding conditions. To elucidate the effect of intermolecular interactions on Brownian motion of proteins, we performed (1)H pulsed-field gradient NMR and fluorescence correlation spectroscopy (FCS) experiments combined with small-angle X-ray scattering (SAXS) and viscosity measurements for three proteins, αB-crystalline (αBc), bovine serum albumin, and hen egg-white lysozyme (HEWL) in aqueous solution. Our results demonstrate that long-time translational diffusion quantitatively follows the expected increase of macro-viscosity upon increasing the protein concentration in all cases, while rotational diffusion as assessed by polarized FCS and previous multi-frequency (1)H NMR relaxometry experiments reveals protein-specific behavior spanning the full range between the limiting cases of full decoupling from (αBc) and full coupling to (HEWL) the macro-viscosity. SAXS was used to study the interactions between the proteins in solution, whereby it is shown that the three cases cover the range between a weakly interacting hard-sphere system (αBc) and screened Coulomb repulsion combined with short-range attraction (HEWL). Our results, as well as insights from the recent literature, suggest that the unusual rotational-translational coupling may be due to anisotropic interactions originating from hydrodynamic shape effects combined with high charge and possibly a patchy charge distribution.

NMR-detected brownian dynamics of αB-crystallin over a wide range of concentrations.

Knowledge about the global translational and rotational motion of proteins under crowded conditions is highly relevant for understanding the function of proteins in vivo. This holds in particular for human αB-crystallin, which is strongly crowded in vivo and inter alia responsible for preventing cataracts. Quantitative information on translational and rotational diffusion is not readily available, and we here demonstrate an approach that combines pulsed-field-gradient NMR for translational diffusion and proton T1ρ/T2 relaxation-time measurements for rotational diffusion, thus overcoming obstacles encountered in previous studies. The relaxation times measured at variable temperature provide a quantitative measure of the correlation function of protein tumbling, which cannot be approximated by a single exponential, because two components are needed for a minimal and adequate description of the data. We find that at high protein concentrations, rotational diffusion is decoupled from translational diffusion, the latter following the macroscopic viscosity change almost quantitatively, resembling the behavior of spherical colloids. Analysis of data reported in the literature shows that well-packed globular proteins follow a scaling relation between the hydrodynamic radius and the molar mass, Rh ∼ M(1/d), with a fractal dimension of d ∼ 2.5 rather than 3. Despite its oligomeric nature, Rh of αB-crystallin as derived from both NMR methods is found to be fully consistent with this relation.

The "long tail" of the protein tumbling correlation function: observation by (1)H NMR relaxometry in a wide frequency and concentration range.

Inter-protein interactions in solution affect the auto-correlation function of Brownian tumbling not only in terms of a simple increase of the correlation time, they also lead to the appearance of a weak slow component ("long tail") of the correlation function due to a slowly changing local anisotropy of the microenvironment. The conventional protocol of correlation time estimation from the relaxation rate ratio R1/R2 assumes a single-component tumbling correlation function, and thus can provide incorrect results as soon as the "long tail" is of relevance. This effect, however, has been underestimated in many instances. In this work we present a detailed systematic study of the tumbling correlation function of two proteins, lysozyme and bovine serum albumin, at different concentrations and temperatures using proton field-cycling relaxometry combined with R1ρ and R2 measurements. Unlike high-field NMR relaxation methods, these techniques enable a detailed study of dynamics on a time scale longer than the normal protein tumbling correlation time and, thus, a reliable estimate of the parameters of the "long tail". In this work we analyze the concentration dependence of the intensity and correlation time of the slow component and perform simulations of high-field (15)N NMR relaxation data demonstrating the importance of taking the "long tail" in the analysis into account.

Solid-state NMR approaches to internal dynamics of proteins: from picoseconds to microseconds and seconds.

Solid-state nuclear magnetic resonance (NMR) spectroscopy has matured to the point that it is possible to determine the structure of proteins in immobilized states, such as within microcrystals or embedded in membranes. Currently, researchers continue to develop and apply NMR techniques that can deliver site-resolved dynamic information toward the goal of understanding protein function at the atomic scale. As a widely-used, natural approach, researchers have mostly measured longitudinal (T1) relaxation times, which, like in solution-state NMR, are sensitive to picosecond and nanosecond motions, and motionally averaged dipolar couplings, which provide an integral amplitude of all motions with a correlation time of up to a few microseconds. While overall Brownian tumbling in solution mostly precludes access to slower internal dynamics, dedicated solid-state NMR approaches are now emerging as powerful new options. In this Account, we give an overview of the classes of solid-state NMR experiments that have expanded the accessible range correlation times from microseconds to many milliseconds. The measurement of relaxation times in the rotating frame, T1ρ, now allows researchers to access the microsecond range. Using our recent theoretical work, researchers can now quantitatively analyze this data to distinguish relaxation due to chemical-shift anisotropy (CSA) from that due to dipole-dipole couplings. Off-resonance irradiation allows researchers to extend the frequency range of such experiments. We have built multidimensional analogues of T2-type or line shape experiments using variants of the dipolar-chemical shift correlation (DIPSHIFT) experiment that are particularly suited to extract intermediate time scale motions in the millisecond range. In addition, we have continuously improved variants of exchange experiments, mostly relying on the recoupling of anisotropic interactions to address ultraslow motions in the ms to s ranges. The NH dipolar coupling offers a useful probe of local dynamics, especially with proton-depleted samples that suppress the adverse effect of strong proton dipolar couplings. We demonstrate how these techniques have provided a concise picture of the internal dynamics in a popular model system, the SH3 domain of α-spectrin. T1-based methods have shown that large-amplitude bond orientation fluctuations in the picosecond range and slower 10 ns low-amplitude motions coexist in these structures. When we include T1ρ data, we observe that many residues undergo low amplitude motions slower than 100 ns. On the millisecond to second scale, mostly localized but potentially cooperative motions occur. Comparing different exchange experiments, we found that terminal NH2 groups in side chains can even undergo a combination of ultraslow large-angle two-site jumps accompanied by small-angle fluctuations that occur 10 times more quickly.

Internal protein dynamics on ps to µs timescales as studied by multi-frequency (15)N solid-state NMR relaxation.

A comprehensive analysis of the dynamics of the SH3 domain of chicken alpha-spectrin is presented, based upon (15)N T1 and on- and off-resonance T1ρ relaxation times obtained on deuterated samples with a partial back-exchange of labile protons under a variety of the experimental conditions, taking explicitly into account the dipolar order parameters calculated from (15)N-(1)H dipole-dipole couplings. It is demonstrated that such a multi-frequency approach enables access to motional correlation times spanning about 6 orders of magnitude. We asses the validity of different motional models based upon orientation autocorrelation functions with a different number of motional components. We find that for many residues a "two components" model is not sufficient for a good description of the data and more complicated fitting models must be considered. We show that slow motions with correlation times on the order of 1-10 µs can be determined reliably in spite of rather low apparent amplitudes (below 1 %), and demonstrate that the distribution of the protein backbone mobility along the time scale axis is pronouncedly non-uniform and non-monotonic: two domains of fast (τ < 10(-10) s) and intermediate (10(-9) s < τ < 10(-7) s) motions are separated by a gap of one order of magnitude in time with almost no motions. For slower motions (τ > 10(-6) s) we observe a sharp ~1 order of magnitude decrease of the apparent motional amplitudes. Such a distribution obviously reflects different nature of backbone motions on different time scales, where the slow end may be attributed to weakly populated "excited states." Surprisingly, our data reveal no clearly evident correlations between secondary structure of the protein and motional parameters. We also could not notice any unambiguous correlations between motions in different time scales along the protein backbone emphasizing the importance of the inter-residue interactions and the cooperative nature of protein dynamics.

The trehalose coating effect on the internal protein dynamics.

(15)N and (13)C NMR experiments were applied to conduct a comparative study of a cold shock protein (Csp) in two states-lyophilized powder and a protein embedded in a glassy trehalose matrix. Both samples were studied at various levels of rehydration. The experiments used (measuring relaxation rates R(1) and R(1ρ), motionally averaged dipolar couplings and solid state exchange method detecting reorientation of the chemical shift anisotropy tensor) allow obtaining abundant information on the protein structural features and internal motions in a range of correlation times from nanoseconds to seconds. The main results are: (a) the trehalose coating makes the protein structure more native in comparison with the dehydrated lyophilized powder, however, trehalose still cannot remove all non-native hydrogen bonds which are present in a dehydrated protein; (b) trehalose has an appreciable effect on the internal dynamics: the motion of the backbone N-H groups in the nanosecond and microsecond time scales becomes slower while the motional amplitude remains constant; (c) upon adding water to the Csp-trehalose mixture, water molecules accumulate around proteins forming a layer between the protein surface and the trehalose matrix. The protein dynamics become faster, however, not as fast as in the fully hydrated state; (d) the hydration response of dynamics of the NH and CH(CH(2)) groups in a protein is qualitatively different: upon increasing protein hydration, the correlation times of the N-H motions become shorter and the amplitude remains stable, and for CH(CH(2)) groups the motional amplitude increases and the correlation times do not change. This can be explained by a different ability of the NH and CH(CH(2)) groups to form hydrogen bonds.

The nuclear magnetic resonance relaxation data analysis in solids: general R1/R1(ρ) equations and the model-free approach.

The advantage of the solid state NMR for studying molecular dynamics is the capability to study slow motions without limitations: in the liquid state, if orienting media are not used, all anisotropic magnetic interactions are averaged out by fast overall Brownian tumbling of a molecule and thus investigation of slow internal conformational motions (e.g., of proteins) in solution can be conducted using only isotropic interactions. One of the main tools for obtaining amplitudes and correlation times of molecular motions in the µs time scale is measuring relaxation rate R(1)(ρ). Yet, there have been a couple of unresolved problems in the quantitative analysis of the relaxation rates. First, when the resonance offset of the spin-lock pulse is used, the spin-lock field can be oriented under an arbitrary angle in respect to B(0). Second, the spin-lock frequency can be comparable or even less than the magic angle spinning rate. Up to now, there have been no equations for R(1)(ρ) that would be applicable for any values of the spin-lock frequency, magic angle spinning rate and resonance offset of the spin-lock pulse. In this work such equations were derived for two most important relaxation mechanisms: heteronuclear dipolar coupling and chemical shift anisotropy. The validity of the equations was checked by numerical simulation of the R(1)(ρ) experiment using SPINEVOLUTION program. In addition to that, the applicability of the well-known model-free approach to the solid state NMR relaxation data analysis was considered. For the wobbling in a cone at 30° and 90° cone angles and two-site jump models, it has been demonstrated that the auto-correlation functions G(0)(t), G(1)(t), G(2)(t), corresponding to different spherical harmonics, for isotropic samples (powders, polycrystals, etc.) are practically the same regardless of the correlation time of motion. This means that the model-free approach which is widely used in liquids can be equally applied, at least assuming these two motional models, to the analysis of the solid state NMR relaxation data.

Microsecond time scale mobility in a solid protein as studied by the 15N R(1rho) site-specific NMR relaxation rates.

For the first time, we have demonstrated the site-resolved measurement of reliable (i.e., free of interfering effects) (15)N R(1rho) relaxation rates from a solid protein to extract dynamic information on the microsecond time scale. (15)N R(1rho) NMR relaxation rates were measured as a function of the residue number in a (15)N,(2)H-enriched (with 10-20% back-exchanged protons at labile sites) microcrystalline SH3 domain of chicken alpha-spectrin. The experiments were performed at different temperatures and at different spin-lock frequencies, which were realized by on- and off-resonance spin-lock irradiation. The results obtained indicate that the interfering spin-spin contribution to the R(1rho) rate in a perdeuterated protein is negligible even at low spin-lock fields, in contrast to the case for normal protonated samples. Through correlation plots, the R(1rho) rates were compared with previous data for the same protein characterizing different kinds of internal mobility.

Relaxation-induced dipolar exchange with recoupling (RIDER) distortions in CODEX experiments.

Chemical shift anisotropy (CSA) and dipolar CODEX (Cenralband Only Detection of EXchange) experiments enable abundant quantitative information on the reorientation of the CSA and dipolar tensors to be obtained on millisecond-second timescales. At the same time, proper performance of the experiments and data analysis can often be a challenge since CODEX is prone to some interfering effects that may lead to incorrect interpretation of the experimental results. One of the most important such effects is RIDER (relaxation-induced dipolar exchange with recoupling). It appears due to the dipolar interaction of the observed X nuclei with some other nuclei, which causes an apparent decay in the mixing time dependence of the signal intensity reflecting not molecular motion, but spin flips of the adjacent nuclei. This may hamper obtaining correct values of the parameters of molecular mobility. In this contribution we consider in detail the reasons why the RIDER distortions remain even under decoupling conditions and propose measures to eliminate them. That is, we suggest (1) using an additional Z filter between the cross-polarization (CP) section and the CODEX recoupling blocks that suppresses the interfering anti-phase coherence responsible for the X-H RIDER and (2) recording only the cosine component of the CODEX signal since it is less prone to the RIDER distortions in comparison to the sine component. The experiments were conducted on rigid model substances as well as microcrystalline 2H / 15N-enriched proteins (GB1 and SH3) with a partial back-exchange of labile protons. Standard CSA and dipolar CODEX experiments reveal a fast-decaying component in the mixing time dependence of 15N nuclei in proteins, which can be misinterpreted as a slow overall protein rocking motion. However, the RIDER-free experimental setup provides flat mixing time dependences, meaning that the studied proteins do not undergo global motions on the millisecond timescale.

Direct observation of millisecond to second motions in proteins by dipolar CODEX NMR spectroscopy.

We present a site-resolved study of slow (ms to s) motions in a protein in the solid (microcrystalline) state performed with the use of a modified version of the centerband-only detection of exchange (CODEX) NMR experiment. CODEX was originally based on measuring changes in molecular orientation by means of the chemical shift anisotropy (CSA) tensor, and in our modification, angular reorientations of internuclear vectors are observed. The experiment was applied to the study of slow (15)N-(1)H motions of the SH3 domain of chicken alpha-spectrin. The protein was perdeuterated with partial back-exchange of protons at labile sites. This allowed indirect (proton) detection of (15)N nuclei and thus a significant enhancement of sensitivity. The diluted proton system also made negligible proton-driven spin diffusion between (15)N nuclei, which interferes with the molecular exchange (motion) and hampers the acquisition of dynamic parameters. The experiment has shown that approximately half of the peaks in the 2D (15)N-(1)H correlation spectrum exhibit exchange in a different extent. The correlation time of the slow motion for most peaks is 1 to 3 s. This is the first NMR study of the internal dynamics of proteins in the solid state on the millisecond to second time scale with site-specific spectral resolution that provides both time-scale and geometry information about molecular motions.

Comparison of the internal dynamics of globular proteins in the microcrystalline and rehydrated lyophilized states.

Natural abundance solid-state 13C-NMR spin-lattice relaxation experiments in the laboratory (T1) and off-resonance rotating (T(1rho)) frames were applied for qualitative comparison of the internal molecular dynamics of barstar, hen egg white lysozyme and bacteriophage T4 lysozyme in both the microcrystalline and the rehydrated (water content is 50% of the protein mass) lyophilized states. The microcrystalline state of proteins provides a better spectral resolution; however, less is known about the local structure and dynamics in the different states. We found by visual comparison of both T1 and T(1rho) relaxation decays of various resonance bands of the CPMAS spectra that within the ns-mus range of correlation times there is no appreciable difference in the internal dynamics between rehydrated lyophilized and crystalline states for all three proteins tested. This suggests that the internal conformational dynamics depends weakly if at all on inter-protein interactions in the solid state. Hence, physical properties of globular proteins in a fully hydrated solid state seem to be similar to those in solution. This result at least partly removes concerns about biological relevance of studies of globular proteins in the solid state.

15N spin diffusion rate in solid-state NMR of totally enriched proteins: the magic angle spinning frequency effect.

As demonstrated by means of the one-dimensional solid-state MAS exchange experiment (CODEX), the rate of the proton driven spin diffusion between backbone (15)N nuclei in totally enriched protein depends strongly on the magic angle spinning (MAS) frequency: spin diffusion at MAS frequency 16 kHz is about 4-5 times slower as compared to that at MAS frequency 1 kHz which is due to the averaging of the homo- and hetero-nuclear dipolar interactions by MAS. It is important that even at the highest MAS frequencies used in our experiments the spin diffusion rate is comparable or larger than typical values of the spin-lattice relaxation rates of backbone nitrogens in solid proteins. Thus, the precise quantitative analysis of (15)N T(1)'s in totally enriched solid proteins may lead to wrong quantitative results. On the other hand, the effectiveness of the (15)N-(15)N correlation and structure determination experiments making use of (15)N-(15)N distances can be increased by decreasing the MAS frequency as far as possible, which is counter intuitive to the commonly applied fast MAS conditions in order to reduce the dipolar-broadened line widths for increased spectral resolution.

Simultaneous processing of solid-state NMR relaxation and 1D-MAS exchange data: the backbone dynamics of free vs. binase-bound barstar.

Two types of dynamic solid-state NMR experiments-relaxation and 1D-MAS exchange-were combined for the investigation of the backbone dynamics of a 15% randomly 15N-enriched protein barstar in both free and binase-bound states. The main novelty of this work is a simultaneous quantitative processing of the results of these two types of experiments that we call Simultaneous Relaxation and Exchange Data Analysis (SREDA) approach. It extends the well-known model-free approach such that it permits to discriminate between various motional models (jumps between different sites, wobbling in a cone, etc.). This objective cannot be achieved by analyzing the relaxation or exchange data separately. The SREDA approach was applied to probe a modification of the average backbone dynamics of barstar upon forming a complex with another protein binase. T(1) and off-resonance T(1rho) relaxation times of 15N backbone nuclei were measured at three temperatures between 0 and 45 degrees C, 1D-MAS exchange (CODEX) data were obtained at room temperature within the mixing time range from 0.3 to 200 ms. It has been found that the barstar backbone participates in two molecular processes with correlation times in the 10(-9)-10(-7) and 10(-3)-10(-2) s ranges. Forming the complex with binase results in a significant decrease of the amplitudes of both motions, suggesting that the complex is a more rigid and stable structure than free barstar.

Slow motions in microcrystalline proteins as observed by MAS-dependent 15N rotating-frame NMR relaxation.

(15)N NMR relaxation rate R1ρ measurements reveal that a substantial fraction of residues in the microcrystalline chicken alpha-spectrin SH3 domain protein undergoes dynamics in the µs-ms timescale range. On the basis of a comparison of 2D site-resolved with 1D integrated (15)N spectral intensities, we demonstrate that the significant fraction of broad signals in the 2D spectrum exhibits the most pronounced slow mobility. We show that (15)N R1ρ's in proton-diluted protein samples are practically free from the coherent spin-spin contribution even at low MAS rates, and thus can be analysed quantitatively. Moderate MAS rates (10-30 kHz) can be more advantageous in comparison with the rates >50-60 kHz when slow dynamics are to be identified and quantified by means of R1ρ experiments.

The relation of the X-ray B-factor to protein dynamics: insights from recent dynamic solid-state NMR data.

In addressing the potential use of B-factors derived from X-ray scattering data of proteins for the understanding the (functional) dynamics of proteins, we present a comparison of B-factors of five different proteins (SH3 domain, Crh, GB1, ubiquitin and thioredoxin) with data from recent solid-state nuclear magnetic resonance experiments reflecting true (rotational) dynamics on well-defined timescales. Apart from trivial correlations involving mobile loop regions and chain termini, we find no significant correlation of B-factors with the dynamic data on any of the investigated timescales, concluding that there is no unique and general correlation of B-factors with the internal reorientational dynamics of proteins.

Intermolecular electrostatic interactions and Brownian tumbling in protein solutions.

It is often implicitly assumed that the long-range intermolecular electrostatic interactions in homogeneous protein solutions either are negligible for affecting protein Brownian tumbling or cause its deceleration without changing the shape of rotational auto-correlation function. This review presents a wide set of experimental data (NMR relaxation, dielectric spectroscopy and Brownian dynamics simulations) demonstrating that the interprotein electrostatic steering leads to a complication of the rotational correlation function. The key point of this effect is the rotational anisotropy caused by the interaction of the electric dipole moment of a protein with the external electric field produced by charges of neighboring proteins. Taking this effect into account in some cases might be of critical importance for the correct interpretation of various experimental data.