The diffusion seeded paradigm

Ever since the original Lipari and Szabo papers (Lipari and Szabo, 1982a,b), the question of how to obtain the model-free description of the system has followed the route in which the diffusion tensor is initially estimated. Using this rough estimate, the model-free models are optimised for each spin system i, the best model selected, and then the global model $\mathfrak{S}$ of the diffusion model $\mathfrak{D}$ with each model-free model $\mathfrak{F}_i$ is optimised. This procedure is then repeated using the diffusion tensor parameters of $\mathfrak{S}$ as the initial input. Finally the global model is selected. The full protocol, when combined with AIC model selection (d'Auvergne and Gooley, 2003), is illustrated in Figure 7.2.

Figure 7.2: A schematic of model-free analysis using the diffusion seeded paradigm - the initial diffusion tensor estimate - together with AIC model selection and model elimination. The initial estimates of the parameters of $\mathfrak{D}$ are held constant while model-free models m0 to m9 (7.22.0-7.22.9) of the set $\mathfrak{F}_i$ for each spin system i are optimised, model elimination applied to remove failed models, and AIC model selection used to determine the best model. The global model $\mathfrak{S}$, the union of $\mathfrak{D}$ and all $\mathfrak{F}_i$, is then optimised. These steps are repeated until convergence of the global model. The entire iterative process is repeated for each of the Brownian diffusion models. Finally AIC model selection is used to determine the best description of the dynamics of the molecule by selecting between the global models $\mathfrak{S}$ including the sphere, oblate spheroid, prolate spheroid, and ellipsoid. Once the solution has been found, Monte Carlo simulations can be utilised for error analysis.

Again this protocol is not implemented in the relax sample scripts. This would have to be implemented in exactly the same manner as described in the previous section, but using the AIC model selection build into relax. Constructing this set of scripts, or a single master script, would be much easier than the Mandel et al. (1995) protocol as Modelfree4 would not need to be used, and the handling of F-tests and chi-squared tests is avoided.