Model-Free or Not?

Abstract

Relaxation in nuclear magnetic resonance is a powerful method for obtaining spatially resolved, timescale-specific dynamics information about molecular systems. However, dynamics in biomolecular systems are generally too complex to be fully characterized based on NMR data alone. This is a familiar problem, addressed by the Lipari-Szabo model-free analysis, a method that captures the full information content of NMR relaxation data in case all internal motion of a molecule in solution is sufficiently fast. We investigate model-free analysis, as well as several other approaches, and find that model-free, spectral density mapping, LeMaster’s approach, and our detector analysis form a class of analysis methods, for which behavior of the fitted parameters has a well-defined relationship to the distribution of correlation times of motion, independent of the specific form of that distribution. In a sense, they are all “model-free.” Of these methods, only detectors are generally applicable to solid-state NMR relaxation data. We further discuss how detectors may be used for comparison of experimental data to data extracted from molecular dynamics simulation, and how simulation may be used to extract details of the dynamics that are not accessible via NMR, where detector analysis can be used to connect those details to experiments. We expect that combined methodology can eventually provide enough insight into complex dynamics to provide highly accurate models of motion, thus lending deeper insight into the nature of biomolecular dynamics.

Rotating Frame Relaxation in Magic Angle Spinning Solid State NMR, a Promising Tool for Characterizing Biopolymer Motion

“…For uniaxially symmetric tensors, it can be expressed simply as the scalar ratio of the thermally averaged anisotropy to the corresponding static value S = ⟨δ⟩/δ (angular brackets represent the time average). When generating a model free expression to represent a two-site hop Markov model with populations, p A and p B , and hop angle β, the following expression was used to compute the squared order parameter. , If the populations are assumed to be equal, as is the case for the numerical simulations here, the expression reduces to …”

“…Nuclear magnetic resonance, including measurements in solution and the solid state, has been a powerful experimental tool for probing biopolymer dynamics on time scales from minutes to picoseconds. Experimental strategies for characterizing dynamics using solid state NMR have been a particularly active area of research recently. − …”

Explicit models of motions to analyze NMR relaxation data in proteins

“…For the past 40 years, the Model Free approach has been prefered for the analysis of NMR relaxation data as it does not require a priori knowledge on the nature of motions of the bond vectors. The advances in MD simulations methods can now provide such information, for instance with the help of the detector analysis which can easily distinguish the contribution of motions originating from different times-scales [25,[64][65][66]93]. Explicit models of motions as presented here can be used to obtain a mechanistic picture of the motions from a combined NMR and MD analysis [94].…”

Experimental Characterization of the Hepatitis B Virus Capsid Dynamics by Solid-State NMR

“…However, the internal protein motions can be rather complex, and the description in terms of an extended model-free approach ( Clore et al, 1990 ; Chevelkov et al, 2009 ) with several correlation times τ c can be ambiguous ( Smith et al, 2017 ). To mitigate this, the detector analysis approach has been introduced to analyze such data with minimal bias ( Smith et al, 2018 ), as well as to facilitate comparison with molecular dynamics (MD) simulations ( Smith et al, 2019 ; Zumpfe and Smith, 2021 ).…”