Introduction to the consistency testing of relaxation data

In spin relaxation, datasets are often recorded at different magnetic fields. This is especially important when R₂ values are to be used since μs-ms motions contribute to R₂. This contribution being scaled quadratically with the strength of the magnetic field, recording at multiple magnetic fields helps extract it. Also, acquiring data at multiple magnetic fields allows over-determination of the mathematical problems, e.g. in the model-free approach.

Recording at multiple magnetic fields is a good practice. However, it can cause artifacts if those different datasets are inconsistent. Inconsistencies can originate from, inter alia, the sample or the acquisition. Sample variations can be linked to changes in temperature, concentration, pH, etc. Water suppression is the main cause of acquisition variations as it affect relaxation parameters (especially NOE) of exposed and exchangeable moieties (e.g. the NH moiety).

It is thus a good idea to assess consistency of datasets acquired at different magnetic fields. For this purpose, three tests are implemented in relax. They are all based on the same principle - calculate a field independent value and compare it from one field to another.

The three tests are:

J(0)

The spectral density at the zero frequency calculated using the reduced spectral density approach.

F_η

A consistency function proposed by Fushman et al. (1998).

F_R2

A consistency function proposed by Fushman et al. (1998).

These three tests are very similar (all probing consistency of R₂ data and all suffering from the same limitations) and any of them can be used for consistency testing. In the example below, the J(0) values are used for consistency testing.

Different methods exist to compare tests values calculated from one field to another. These include correlation plots and histograms, and calculation of correlation, skewness and kurtosis coefficients. The details of how to interpret such analyses are avaliable at the end of this chapter in Section 9.7.

For more details on the tests and their implementation within relax, see:

• Morin and Gagné (2009a)

Or for the origin of the tests themselves:

• Fushman et al. (1999)

In addition, see the following review which includes a discussion on how to evaluate the reliability of recorded relaxation data:

• Morin (2011)