Protein Dynamics from NMR:  The Slowly Relaxing Local Structure Analysis Compared with Model-Free Analysis

Abstract

(15)N-(1)H spin relaxation is a powerful method for deriving information on protein dynamics. The traditional method of data analysis is model-free (MF), where the global and local N-H motions are independent and the local geometry is simplified. The common MF analysis consists of fitting single-field data. The results are typically field-dependent, and multifield data cannot be fit with standard fitting schemes. Cases where known functional dynamics has not been detected by MF were identified by us and others. Recently we applied to spin relaxation in proteins the slowly relaxing local structure (SRLS) approach, which accounts rigorously for mode mixing and general features of local geometry. SRLS was shown to yield MF in appropriate asymptotic limits. We found that the experimental spectral density corresponds quite well to the SRLS spectral density. The MF formulas are often used outside of their validity ranges, allowing small data sets to be force-fitted with good statistics but inaccurate best-fit parameters. This paper focuses on the mechanism of force-fitting and its implications. It is shown that MF analysis force-fits the experimental data because mode mixing, the rhombic symmetry of the local ordering and general features of local geometry are not accounted for. Combined multifield multitemperature data analyzed with the MF approach may lead to the detection of incorrect phenomena, and conformational entropy derived from MF order parameters may be highly inaccurate. On the other hand, fitting to more appropriate models can yield consistent physically insightful information. This requires that the complexity of the theoretical spectral densities matches the integrity of the experimental data. As shown herein, the SRLS spectral densities comply with this requirement.

An Improved Picture of Methyl Dynamics in Proteins from Slowly Relaxing Local Structure Analysis of 2H Spin Relaxation

“…[16][17][18][19][20][21][22][23] Two rotators, representing the global motion of the protein, R C , and the local motion of the probe (C-D bond in this case), R L , are treated. The motions of the protein and the probe are coupled by a local potential, U(Ω C'M ), where C' denotes the local director fixed in the protein, and M the local ordering/local diffusion frame fixed in the probe.…”

“…The Euler angles Ω C'M are modulated by the local motion whereas the Euler angles Ω LC' , with L denoting the fixed laboratory frame, are modulated by the overall tumbling of the protein. 21 If the protein is considered axially symmetric then a global diffusion frame C tilted relative to the C' frame will be defined. The site-specific angles, β CC' , are fixed in the protein.…”

“…L = 2, terms being preserved. 21,23,25,26 The coefficient (given in units of kB T) is a measure of the orientational ordering of the C-D bond with respect to the local director, C', whereas measures the asymmetry of the ordering around the director. Time correlation functions are calculated as: (6) Their Fourier-Laplace transforms yield the spectral densities j J MKK' (ω).…”

“…[16][17][18][19][20][21][22][23] This has been accomplished by applying to NMR spin relaxation in proteins 16 the Slowly Relaxing Local Structure (SRLS) approach of Freed and co-workers. [24][25][26] SRLS can be considered the generalization of MF, yielding the latter in asymptotic limits.…”

“…It features explicitly local motional modes parallel and perpendicular to the methyl rotation axis. [16][17][18][19][20][21][22][23]25,26 and accounts rigorously for the tilt between a rhombic local ordering frame, M, and the magnetic frame, Q. The Euler angles Ω C'M , which relate the M frame to a local director frame, C' (e.g., the equilibrium C-CH 3 orientation), are governed by the coupling/ ordering potential.…”