Autocovariance function methods

FIGURE 4.8 Autocovariance function method computed on computer-generated 2D map. (a) Simulated disordered 2D maps containing 100 components, (b) Autocovariance function of the 2D map. Reproduced from Marchetti et al., (2004) with permission from the American Chemical Society. 

The applicability of the 2D autocovariance function method and the most relevant results obtained will be discussed in the next section. 

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). 

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). 

Moreover, the two procedures display different and complementary properties so that each of them is the method of choice to obtain specific information on the 2D separations. The SMO procedure is an unique tool to quantitatively estimate the degree of peak overlapping present in a map as well as to predict the influence of different experimental conditions on peak overlapping. The strength of the 2D autocovariance function method lies in its ability to simply single out ordered retention pattern hidden in the complex separation, which can be related to information on the chemical composition of the complex mixture. 

FIGURE 4.13 Identification of a train of spots by the 2D autocovariance function method. (See text for full caption.)... 

The statistical degree of overlapping (SDO) and 2D autocovariance function (ACVF) methods have been applied to 2D-PAGE maps (Marchetti et al., 2004 Pietrogrande et al., 2002, 2003, 2005, 2006a Campostrini et al., 2005) the means for extracting information from the experimental data and their relevance to proteomics are discussed in the following. The procedures were validated on computer-simulated maps. Their applicability to real samples was tested on reference maps obtained from literature sources. Application to experimental maps is also discussed. 

---