SRLS Analysis of ¹⁵N–¹H NMR Relaxation from the Protein S100A1: Dynamic Structure, Calcium Binding, and Related Changes in Conformational Entropy

Abstract

We report on amide (N−H) NMR relaxation from the protein S100A1 analyzed with the slowly relaxing local structure (SRLS) approach. S100A1 comprises two calcium-binding "EF-hands" (helixloop-helix motifs) connected by a linker. The dynamic structure of this protein, in both calcium-free and calcium-bound form, is described as the restricted local N−H motion coupled to isotropic protein tumbling. The restrictions are given by a rhombic potential, u (∼10 kT), the local motion by a diffusion tensor with rate constant D 2 (∼10 9 s −1 ), and principal axis tilted from the N−H bond at angle β (10−20°). This parameter combination provides a physically insightful picture of the dynamic structure of S100A1 from the N−H bond perspective. Calcium binding primarily affects the C-terminal EF-hand, among others slowing down the motion of helices III and IV approximately 10-fold. Overall, it brings about significant changes in the shape of the local potential, u, and the orientation of the local diffusion axis, β. Conformational entropy derived from u makes an unfavorable entropic contribution to the free energy of calcium binding estimated at 8.6 ± 0.5 kJ/mol. The N-terminal EF-hand undergoes moderate changes. These findings provide new insights into the calcium-binding process. The same data were analyzed previously with the extended model-free (EMF) method, which is a simple limit of SRLS. In that interpretation, the protein tumbles anisotropically. Locally, calcium binding increases ordering in the loops of S100A1 and conformational exchange (R ex ) in the helices of its N-terminal EF-hand. These are very unusual features. We show that they most likely stem from problematic data-fitting, oversimplifications inherent in EMF, and experimental imperfections. R ex is shown to be mainly a fit parameter. By reanalyzing the experimental data with SRLS, which is largely free of these deficiencies, we obtainas delineated abovephysically-relevant structural, kinetic, geometric, and binding information.

Structural Dynamics from NMR Relaxation by SRLS Analysis: Local Geometry, Potential Energy Landscapes, and Spectral Densities

“…c 0 2 evaluates the strength of the local potential, and c 2 2 evaluates its rhombicity . In previous work, we found that Z OF is typically pointing along the C α –C α axis. − ,− This ordering characteristic was also determined by other methods. − …”

“…Thus, R ex is likely to act as a fit parameter. As shown in a recent study, in such cases the results can be substantially impaired. This might be the reason for only S 2 being reported out of the four parameters comprising the five MF models.…”

“…On the contrary, the J DD (ω) and J CC (ω) functions comply with two different potential energy landscapes associated with preferential ordering along the N–H bond or the C α –C α axis. The former case is the naı̈vely expected ordering type; the latter was revealed in previous work by us − ,− and others. − The reasons for this geometrical ambiguity, its generality, and the relation between the two potential energy landscapes are delineated and discussed in the text; pictorial illustrations are also provided. In practice, only one of the two forms materializes for any given N–H bond in the protein.…”

“…Until now, our SRLS analyses provided the diffusion tensors, D 1 and D 2 , and the coupling/ordering potential, u . − ,− Here we enhance this description of structural dynamics as described below. The j KK ′ (ω) functions are unambiguous with regard to their information content.…”

Comment on mr-2021-28

“…Related approaches employ discrete or continuous distributions to more fully capture the range of intramolecular correlation times (Lemaster, 1995;Calandrini et al, 2010;Khan et al, 2015;Hsu et al, 2018Hsu et al, , 2020Smith et al, 2019). Other strategies employ physical models or atomistic molecular dynamics simulations for overall rotational diffusion and internal conformational fluctuations, to more directly link the NMR phenomena to underlying physical processes (Tugarinov et al, 2001;Zerbetto et al, 2013;Ollila et al, 2018;Polimeno et al, 2019a, b;Mendelman et al, 2020;Mendelman and Meirovitch, 2021). The availability of extended model-free formalisms, or other approaches with variable numbers of parameters, has created a further dilemma: should a data analysis protocol extract the most exacting information justified by the data or employ the model most robust to experimental variation?…”