Fixing the model-free analysis of protein dynamics

Edward d'Auvergne and Paul Gooley
Russell Grimwade Department of Biochemistry, University of Melbourne, VIC, 3010 Australia.

NMR is a powerful technique for the study of protein dynamics which can reveal motional details on an atomic level.  The NMR data commonly collected includes the 15N R1 and R2 relaxation rates and the {1H}-15N steady-state NOE.  Model-free theory, the most widely used method for the analysis of this relaxation data, permits the separation of pico to nanosecond motional amplitudes (S2) and time-scales (?e).  Model-free refers to the theory being independent from a mechanical model of motion.  Slower micro to millisecond motions can be resolved by the extraction of chemical exchange relaxation (Rex).  Motions on two time-scales may also be extracted, when they occur, using the parameters Sf2 and ?f for the faster motion and Ss2 and ?s for the slower.  Multiple mathematical models, usually five, can be constructed using various combinations of these parameters.  Model-free analysis consists of fitting the model-free parameters to the collected relaxation data using chi-squared minimisation.  The data is fitted multiple times, once for each model-free model, and the best of these models is selected.

Two problems have been identified with the implementation of model-free data analysis.  The first is with the use of model selection, the second is with minimisation.  The current implementation of model-free model selection consists of hypothesis testing using chi-squared and F-tests.  It has been found that this approach has two flaws, under-fitting, and not selecting a model when one ought to be selected.  The consequence is that the protein falsely appears to be more rigid than reality.  It was found that AIC model selection, a standard and widely used statistical tool, increases the speed, simplicity, and accuracy of model-free analysis (1).

The second problem, due to the implementation of minimisation, results in the extraction of incorrect parameter values.  The program Modelfree is almost universally used for model-free analysis and minimisation, however other major programs include Dasha, DYNAMICS, and Tensor.  A few of the issues found in these programs include a programming bug, poor constraint algorithms, minimisation terminating far too early, and poorly performing minimisation algorithms.  The effects include incorrect results effecting a large proportion of the data, parameters stuck at the limits, inaccurate parameter values, and minimisation not occuring.  To solve these problems a new program, relax, is currently under development.  Both synthetic and real data will be used to identify the best minimisation methods, to verify the program, and to demonstrate the improvements over current analysis.


References
1.	E. J. d'Auvergne and P. R. Gooley, Journal of Biomolecular NMR, 2003, 25, 25-39.