Results from 2D Autocovariance Function Method

The 2D autocovariance function was computed on the digitized map signal using Equation 4.28 and the separation parameters were estimated according to Equation 4.30. The results obtained are reported in the following table (Pietrogrande et al., 2005). 

It must be emphasized that the availability of the SMO and 2D autocovariance function methods as two independent statistical procedures to estimate the same parameter, in, the number of proteins, is a helpful tool to verify the reliability of the results obtained. In the case of the 2D PAGE map of colorectal adenocarcinoma cell line (DL-1) an excellent agreement was found between the values obtained from the SMO method—m = 101 10 and m = 105 10—and the 2D autocovariance function procedure—m = 104 10 (Pietrogrande et al., 2006a). 

The 2D autocovariance function was computed on the selected map region that contains the spot train (eight proteins) in addition to 53 proteins randomly located (4.5-7 p7 and 0.65-0.68 log Mr values, enlarged inset in Fig. 4.13a). From the 2D autocovariance function, the number of proteins present in this map region, m, can be correctly estimated m = 53 7 for the original computer-generated map containing 53 SCs (blue line in inset in Fig. 4.13b) and m = 62 8 for the map where the spot train was added (red line in inset in Fig. 4.13b). 

In the 2D autocovariance function plot (Fig. 4.13b) well defined deterministic cones are evident along the Ap7 axis at values ApH 0.2, 0.4, 0.6 pH they are related to the constant interdistances repeated in the spot trains. This behavior is more clearly shown by the intersection of the 2D autocovariance function with the Ap7 separation axis. The inset in Fig. 4.13b reports the 2D autocovariance function plots computed on the same map with (red line) and without (blue line) the spot train. A comparison between the two lines shows that the 2D autocovariance function peaks at 0.2, 0.4, 0.6 ApH (red line) clearly identifying the presence of the spot train singling out this ordered pattern from the random complexity of the map (blue line, from map without the spot train). The difference between the two lines identifies the contribution of the two components to the complex separation the blue line corresponds to the random separation pattern present in the map the red line describes the order in the 2D map due to the superimposed spot train. The high sensitivity of the 2D autocovariance function method in detecting order is noted in fact it is able to detect the presence of only sevenfold repetitiveness hidden in a random pattern of 200 proteins (Pietrogrande et al., 2005). 

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