Amino-acid side-chain properties in proteins are key determinants of protein function. NMR spin relaxation of side chains is an important source of information about local protein dynamics and flexibility. However, traditional solution NMR relaxation methods are most sensitive to sub-nanosecond dynamics lacking information on slower ns−μs time-scale motions. Nanoparticle-assisted NMR spin relaxation (NASR) of methyl-side chains is introduced here as a window into these ns−μs dynamics. NASR utilizes the transient and nonspecific interactions between folded proteins and slowly tumbling spherical nanoparticles (NPs), whereby the increase of the relaxation rates reflects motions on time scales from ps all the way to the overall tumbling correlation time of the NPs ranging from hundreds of ns to μs. The observed motional amplitude of each methyl group can then be expressed by a model-free NASR S 2 order parameter. The method is demonstrated for 2H-relaxation of CH2D methyl moieties and cross-correlated relaxation of CH3 groups for proteins Im7 and ubiquitin in the presence of anionic silica-nanoparticles. Both types of relaxation experiments, dominated by either quadrupolar or dipolar interactions, yield highly consistent results. Im7 shows additional dynamics on the intermediate time scales taking place in a functionally important loop, whereas ubiquitin visits the majority of its conformational substates on the sub-ns time scale. These experimental observations are in good agreement with 4–10 μs all-atom molecular dynamics trajectories. NASR probes side-chain dynamics on a much wider range of motional time scales than previously possible, thereby providing new insights into the interplay between protein structure, dynamics, and molecular interactions that govern protein function.

The transient interactions of proteins and other molecules with much larger structures, such as synthetic or biological nanoparticles, lead to certain types of enhanced nuclear magnetic resonance (NMR) spin relaxation effects, which can be accurately measured by multidimensional solution NMR techniques. These relaxation effects provide new information about the nanostructures and the protein, their interactions, internal dynamics, and associated kinetic and thermodynamic parameters, such as exchange rates and populations. Although theoretical treatments exist that cover either the fast or slow exchange limits, a theoretical treatment that applies to all practically relevant exchange processes is still missing. A unified theoretical framework is presented for this purpose based on a stochastic Liouville equation (SLE). It covers nuclear spin dynamics, overall rotational diffusion of both the protein and the nanostructure, the exchange process between a free state and a bound state, and internal protein dynamics. Although the numerical implementation of the SLE typically involves large matrices, it is shown here that it is computationally still tractable for situations relevant in practice. Application of the theory demonstrates how transverse relaxation is substantially impacted by the kinetics of binding on a wide range of exchange timescales. It is further shown that when exchange occurs on the appropriate timescale, transverse relaxation is able to report on internal dynamics far slower than observable by traditional transverse relaxation experiments. The SLE will allow the realistic and quantitative interpretation of experimental NMR data reporting about transient protein−nanoparticle interactions, thereby providing a powerful tool for the characterization of protein dynamics modes on a vast range of timescales including motions that may be functionally relevant.

NMR spectroscopy is an extraordinarily rich source of quantitative dynamics of proteins in solution using spin relaxation or chemical exchange saturation transfer (CEST) experiments. However, 15 N-CEST measurements require prolonged multidimensional, so-called pseudo-3D HSQC experiments where the pseudo dimension is a radio frequency offset Δω of a weak 15 N saturation field. Nonuniform sampling (NUS) approaches have the potential to significantly speed up these measurements, but they also carry the risk of introducing serious artifacts and the systematic optimization of nonuniform sampling schedules has remained elusive. It is demonstrated here how this challenge can be addressed by using fitted cross-peaks of a reference 2D HSQC experiment as footprints, which are subsequently used to reconstruct cross-peak amplitudes of a pseudo-3D data set as a function of Δω by a linear least-squares fit. It is shown for protein Im7 how the approach can yield highly accurate CEST profiles based on an absolutely minimally sampled (AMS) data set allowing a speed-up of a factor 20−30. Spectrum-specific optimized nonuniform sampling (SONUS) schemes based on the Cramer−Rao lower bound metric were critical to achieve such a performance, revealing also more general properties of optimal sampling schedules. This is the first systematic exploration and optimization of NUS schedules for the dramatic speed-up of quantitative multidimensional NMR measurements that minimize unwanted errors.

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Nanoparticle-assisted NMR spin relaxation (NASR), which makes internal protein dynamics in solution directly observable on nanosecond to microsecond time scales, has been applied to different nuclei and relaxation processes of the same protein system. A model is presented describing the transient interaction between ubiquitin and anionic silica nanoparticles for the unified interpretation of a wealth of experimental data including 2H, 13C, and 15N relaxation of methyl side chain and backbone moieties. The best model, implemented using a stochastic Liouville equation, describes the exchange process via an intermediary encounter state between free and fully nanoparticle-bound protein. The implication of the three-state binding model on the interpretation of NASR data is discussed.