The use of model selection in the model-free analysis of protein dynamics

Model-free analysis of NMR relaxation data, which is widely used for the study of protein dynamics, consists of the separation of the global rotational diffusion from internal motions relative to the diffusion frame and the description of these internal motions by amplitude and timescale. Five model-free models exist, each of which describes a different type of motion. Model-free analysis requires the selection of the model which best describes the dynamics of the NH bond. It will be demonstrated that the model selection technique currently used has two significant flaws, under-fitting, and not selecting a model when one ought to be selected. Under-fitting breaks the principle of parsimony causing bias in the final model-free results, visible as an overestimation of S2 and an underestimation of τe and Rex. As a consequence the protein falsely appears to be more rigid than it actually is. Model selection has been extensively developed in other fields. The techniques known as Akaike's Information Criteria (AIC), small sample size corrected AIC (AICc), Bayesian Information Criteria (BIC), bootstrap methods, and cross-validation will be compared to the currently used technique. To analyse the variety of techniques, synthetic noisy data covering all model-free motions was created. The data consists of two types of three-dimensional grid, the Rex grids covering single motions with chemical exchange {S2,τe,Rex}, and the Double Motion grids covering two internal motions {Sf2,Ss2,τs}. The conclusion of the comparison is that for accurate model-free results, AIC model selection is essential. As the method neither under, nor over-fits, AIC is the best tool for applying Occam's razor and has the additional benefits of simplifying and speeding up model-free analysis.