Results and Discussion Principle and Design of gGCSI The original GCSI required the use of 4096 windows for optimal computation in bacterial genomes, but this fixed number of windows made GCSI only applicable to genomes larger than approximately 400 kbp; thus, each window contained at least 100 bp. The use of sliding win- dows is a simple means for increasing the number of win- dows, but this is technically just the moving average, which therefore diminishes the degree of GC skew and is not a solution to the problem. The limitations of the orig- inal GCSI were derived from the dependence of SR and dist on the number of windows; therefore, in order to gen- eralise the GCSI to be applicable for smaller genomic ele- ments, such as plasmids, we have made three modifications. First, SR and dist were replaced with the normalised meas- ure SA (spectral amplitude) and the normalised distance of the maximum and minimum vertices in the cumulative GC skew graph, dist(norm). Window-size dependence of SR was primarily due to the variation in basal noise levels depending on the number of windows, so the gGCSI is calculated simply using the amplitude of the 1-Hz Fourier power spectrum, without taking the S/N ratio. Because the distribution of spectral amplitude is non-linear, unlike SR, the exponentially regressed and thus linearised value for the 1-Hz spectrum is defined as SA. The other measure, dist, proportionally changes according to the number of windows, so it is linearly normalised as dist(norm). Second, the gGCSI is defined as the geometric mean of SA and dist(norm), instead of the arithmetic mean utilised in the original GCSI. The arithmetic mean results in a rela- tively large value when only one of the two indices exhib- its a large value; the use of a geometric mean instead ensures a balance between them. number of windows 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 BMC Genomics 2009, 10:640 http://www.biomedcentral.com/1471-2164/10/640 Third, the statistical significance of the calculated gGCSI can be tested using the z-score and the p-value. Although the gGCSI is independent of the number of windows, the use of very few windows produces more uncertain results compared with when a sufficient number of windows are used for the calculation. In order to provide confidence measures in such cases, the p value of the gGCSI is obtained by repeatedly calculating the gGCSI using ran- domly shuffled input GC skew data series. Because the randomised iterations were statistically confirmed to be normal, a z-score and a corresponding p-value are given to the gGCSI to indicate its significance. Performance validation of the gGCSI In order to test the applicability of the gGCSI to genomes of different sizes, we investigated the effects of the number of windows on the resulting values of the GCSI. First, we checked the effects in detail using the complete genome sequence of Escherichia coli K12 MG1655 (NC_000913), as shown in Table 1. The old GCSI, as well as the values of its contributing variables, SR and dist, increase propor- tionally with the number of windows, whereas the new gGCSI, SA, and dist(norm) show only small changes (standard deviation of 0.003 for gGCSI) as the number of windows changes, especially when more than 32 win- dows are used. Window independence of the gGCSI was further tested using bacterial chromosomes and plasmids of different sizes. Randomly sampled genomes, including the Bacillus subtilis chromosome (4.2 Mbp), Mycoplasma genitalium chromosome (0.58 Mbp), Borrelia burgdorferi cp32 plasmid (31 Kbp), Staphylococcus aureus pT181 plas- mid (4.4 Kbp), and Lactobacillus plantarum pWCFS102 plasmid (2.3 Kbp), are shown in Table 2. In all of these genomes, the gGCSI showed only negligible changes when different numbers of windows from 8 to 32768 were used. The standard deviation of gGCSI values calcu- lated with these windows was consistently low in all 1448 Table 1: Comparison of GCSI and gGCSI values with different numbers of windows in the Escherichia coli K12 genome mean ± SD 0.0978 ± 0.156 319 ± 271 85 ± 162 0.0964 ± 0.003 485 ± 5 GCSI 0.0059 0.0069 0.0063 0.0091 0.0139 0.0183 0.0258 0.0368 0.0573 0.0953 0.1648 0.2932 0.5380 SR 69.65 80.82 70.77 99.03 145.27 176.85 223.43 269.47 342.96 453.39 594.02 744.70 881.89 dist 0.11 0.24 0.52 1.05 2.13 4.27 8.61 17.16 34.49 69.04 138.34 277.35 557.37 gGCSI 0.0884 0.0902 0.0963 0.0965 0.0971 0.0973 0.0978 0.0976 0.0980 0.0981 0.0984 0.0987 0.0989 SA 472.84 478.82 483.45 484.12 483.97 483.97 485.00 485.07 486.53 487.22 488.97 490.72 490.30 dist(norm) 58.77 60.33 67.16 67.35 68.11 68.40 68.90 68.64 68.97 69.04 69.17 69.34 69.67 67 ± 3 Page 3 of 10 (page number not for citation purposes)