Statistical indicators of fitting significance

Standard error or T-value

The significance of the parameter values returned by the fitting procedure is indicated by the standard error or T-value, which broadly speaking represents the degree to which the value can be varied without significantly affecting the closeness of fit. The T-value is the standard error divided by the parameter value. A high standard error or low T-value indicates that the fitting is insensitive to changes in the parameter value: in other words, the value returned for the parameter has little significance. T-values for fitted parameters are listed in the table view of the fitting results.

It is important to examine the significance of returned values, to avoid the trap or reporting “constants” that have no significance. In the example of completely mass transport limited interactions, the rate constants will have a high standard error (low T-value), since it does not matter for the fitting result what value will be returned.

For ease of comparison between parameters with widely different absolute values (e.g. k_a and k_d), the standard error may be expressed as a T-value, which is obtained by dividing the value of the parameter by the standard error. A high T-value corresponds to a low standard error. As a general guideline, parameters with a T-value greater than about 10 should be regarded as significant.

The significance of a parameter is a measure of how much a change in the parameter value affects the closeness of fit. A parameter with low significance can have a wide range of values without affecting the fit. Typically (but not always), parameters with a low significance have unreasonable values: for example typical values for the mass transfer constant for proteins are around 10⁸ RU·M^-1s^-1, but evaluation of data with no mass transfer limitation might return a value of 10¹² or higher. Similarly, rate constants that lack significance are often assigned values outside the reasonable range for biomolecular interactions, or outside the range that can be measured with Biacore.

Note: Even if the significance of a parameter is low, so that any value within a wide range will give the same fit to the experimental data, the fitting algorithm will always return the same value from the same starting data. Consistency of returned values is not an indication of significance.

U-value

The U-value is one of the statistical parameters provided to indicate whether you can rely on the values reported from kinetic analysis. Fitting sensorgram data to an interaction model is a purely mathematical procedure, and there is no inherent guarantee that the results reported from the fitting will be meaningful.

The U-value is an estimate of the uniqueness of calculated parameters, determined by testing the dependence of the fit on correlated variations in pairs of values. If parameters are correlated, the fitting procedure cannot determine their absolute values, although it may sometimes be possible to determine the relative magnitudes. A common example is the association and dissociation rate constants: if these are correlated, the affinity (which is the ratio of the rate constants) can be determined but the rate constants themselves are uncertain. The fitting procedure will return apparently exact values for the rate constants, but the same fit could be obtained with different values provided that the ratio between them is unchanged.

For fitting to a 1:1 interaction model, the U-value is based on correlations between the three parameters k_a, k_d and R_max. A single U-value is reported for the whole fitting. U-values above 25 indicate that absolute values for two or more of the parameters (rate constants and R_max) are correlated and cannot be determined as absolute values. If the U-value is below about 15 the parameter values are not significantly correlated. Note however that a low value does not guarantee that the results are correct.

The U-value is calculated on the basis of the data used for evaluation, and can therefore vary if you exclude regions of the sensorgrams. U-values are not calculated for fitting to interaction models other than the predefined 1:1 binding model.

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