Application of Wavelet Packet Transform to detect genetic polymorphisms by the analysis of inter-Alu PCR patterns

Abstract

Background: The analysis of Inter-Alu PCR patterns obtained from human genomic DNA samples is a promising technique for a simultaneous analysis of many genomic loci flanked by Alu repetitive sequences in order to detect the presence of genetic polymorphisms. Inter-Alu PCR products may be separated and analyzed by capillary electrophoresis using an automatic sequencer that generates a complex pattern of peaks. We propose an algorithmic method based on the Haar-Walsh Wavelet Packet Transformation (WPT) for an efficient detection of fingerprint-type patterns generated by PCR-based methodologies. We have tested our algorithmic approach on inter-Alu patterns obtained from the genomic DNA of three couples of monozygotic twins, expecting that the inter-Alu patterns of each twins couple will show differences due to unavoidable experimental variability. On the contrary the differences among samples of different twins are supposed to originate from genetic variability. Our goal is to automatically detect regions in the inter-Alu pattern likely associated to the presence of genetic polymorphisms.

Results: We show that the WPT algorithm provides a reliable tool to identify sample to sample differences in complex peak patterns, reducing the possible errors and limits associated to a subjective evaluation. The redundant decomposition of the WPT algorithm allows for a procedure of best basis selection which maximizes the pattern differences at the lowest possible scale. Our analysis points out few classifying signal regions that could indicate the presence of possible genetic polymorphisms.

Conclusions: The WPT algorithm based on the Haar-Walsh wavelet is an efficient tool for a non-supervised pattern classification of inter-ALU signals provided by a genetic analyzer, even if it was not possible to estimate the power and false positive rate due to the lacking of a suitable data base. The identification of non-reproducible peaks is usually accomplished comparing different experimental replicates of each sample. Moreover, we remark that, albeit we developed and optimized an algorithm able to analyze patterns obtained through inter-Alu PCR, the method is theoretically applicable to whatever fingerprint-type pattern obtained analyzing anonymous DNA fragments through capillary electrophoresis, and it could be usefully applied on a wide range of fingerprint-type methodologies.

Figure 1

Inter-Alu electrophoretic patterns. Example of the electrophoretic inter-Alu pattern obtained from 310 Genetic Analyzer (PE/ABI) using the two primers, 5'-AGCGAGACTCCG-3' (R12A/267) labeled with the "TET" fluorochrome and 5'-CAGAGCGAGACTCT (R14B/264) labeled with the "FAM" fluorochrome: the x-axis units are base-pairs whereas the peak amplitude is in arbitrary units. Green peaks represent TET-labeled PCR products, while blue peaks represent FAM-labeled PCR products.

Figure 2

Repeated signals. Scheme of the union procedure for the 4 repeated signals; the peak in the union signals are obtained using an "or" procedure with an average on the peak position.

Figure 3

Haar Walsh basis. The normalized signals are shown together with the Haar-Walsh basis function that provides a maximal classification; the four figures refer to different scale levels in a decreasing order from fig. 1 to 4. On the x-axis we report the position in bp of the selected region; in the y-axis we report the six signals of the three twin couples (denoted by Cn1, Cn2 and Cn3). The amplitude of the normalized Gaussian peaks is measured along the z-axis. The Haar function that performs the signal classification is also drawn. The level 4 allows an optimal classification of the selected region of the first twins couple. The selected region is not a global classifying region since it does not distinguish between the signals of the second and the third twin couples.

Figure 4

Signal Classification. Examples of global classifying regions. In the top picture the classification procedure based on WPT is applied on the interval 392-400 bp of the inter-Alu pattern. The classification is due to the presence of a single peak at different positions in the signals of the different twin couples Cn1, Cn2, Cn3, whereas it maintains the same position in the signals of a single twin couple. The wavelet function that performs the classification is positive in the interval 392-396 bp and negative in the interval 396-400 bp; therefore the convolution with the Gaussian peaks of the signal is the sum of positive and negative terms. The picture is obtained by multiplying the signals by the classifying wavelet function in order to illustrate the results of the WPT. The WPT coefficient is the sum of the positive and negative peak areas; therefore the WPT coefficient is positive for the couple Cn1, negative for the couple Cn2 and nearly zero for the couple Cn3 and a K value ≃1 is obtained in eq. (2). In the bottom picture the classification procedure is applied to a larger interval 120-160 bp. In such a case the WPT classification is due to the presence of a pattern of several peaks that have a significant variability among the signals of the different twin couples.