Unraveling the complexity of protein backbone dynamics with combined ¹³C and ¹⁵N solid-state NMR relaxation measurements

Abstract

Typically, protein dynamics involve a complex hierarchy of motions occurring on different time scales between conformations separated by a range of different energy barriers. NMR relaxation can in principle provide a site-specific picture of both the time scales and amplitudes of these motions, but independent relaxation rates sensitive to fluctuations in different time scale ranges are required to obtain a faithful representation of the underlying dynamic complexity. This is especially pertinent for relaxation measurements in the solid state, which report on dynamics in a broader window of time scales by more than 3 orders of magnitudes compared to solution NMR relaxation. To aid in unraveling the intricacies of biomolecular dynamics we introduce (13)C spin-lattice relaxation in the rotating frame (R1ρ) as a probe of backbone nanosecond-microsecond motions in proteins in the solid state. We present measurements of (13)C'R1ρ rates in fully protonated crystalline protein GB1 at 600 and 850 MHz (1)H Larmor frequencies and compare them to (13)C'R1, (15)N R1 and R1ρ measured under the same conditions. The addition of carbon relaxation data to the model free analysis of nitrogen relaxation data leads to greatly improved characterization of time scales of protein backbone motions, minimizing the occurrence of fitting artifacts that may be present when (15)N data is used alone. We also discuss how internal motions characterized by different time scales contribute to (15)N and (13)C relaxation rates in the solid state and solution state, leading to fundamental differences between them, as well as phenomena such as underestimation of picosecond-range motions in the solid state and nanosecond-range motions in solution.

Optimized “detectors” for dynamics analysis in solid-state NMR

“…[29][30][31] Note that acquiring more than two R1 rate constants still provides considerable value to experimental data, as it is a good means of verifying the data quality and improves the overall experimental signal to noise, although it will not usually add much information that could not be extracted from the first two rate constants alone. Higher or lower fields than the example here with 400 and 850 MHz may also allow additional detection vectors, as would more (4-5) R1 measurements, or inclusion of different nuclei, for example backbone 15 N relaxation with 13 CO relaxation, 13 and inclusion of other experiments such as NOE measurement. 32…”

“…(13) An alternative way to understand this transformation is to note that the detector responses can be considered to be weights, such that the observed relaxation rate constants are given by a linear combination of the detection vectors.…”

“…13. 15 N R 1 (500-1000 MHz) 13 CO R 1 (500-1000 MHz) 15 N R 1 (100-1000 MHz) max. error for 1 τ c error for uni.…”

“…9(b)). This is done to test the importance of the width of the sensitivity of each R1 rate constants, where 13 CO R1 relaxation has a narrower sensitivity,…”

“…This was inspired by the success of the Lipari-Szabo modelfree approach 4 or extensions of that approach [5][6][7] in solution-state NMR, achieved by setting the correlation time of the overall tumbling in solids to infinity. While the validity of the LipariSzabo model-free approach in solution-state NMR was justified in detail (similar correlation functions are derived by Halle and Wennerström, 8 with the validity of this and the model-free approach discussed in detail 9 ), studies in solid-state NMR have investigated primarily the effects that the model selection [10][11][12] and the data included 13 have on the analysis of the experimental data. Although there are indications that modeling the correlation function with a sum of exponential functions is not always reliable, these studies do not directly consider modeling behavior in the case that the real motion is too complex to be fully characterized by the experimental data.…”