W-curve Z-Axis view of complete HIV-1 Genome showing all points (A), points near origin with radius <.5 (B) and further out, with radius >.5 (C).

<p>The last group of points (C) is used to re-align the curves after a gap. CG dinucleotide deficiencies are seen in B and C.</p

The W-curve for “CG” showing both Cartesian & Cylindrical notation for the points.

<p>The curve is shown in blue, layout lines indicating the X-Y locations and line for half-distance rule between the points for C & G are shown in red.</p

Autoregression in the W-curve after a gap inserted into sequences.

<p>The gap (green, right panel) offsets the matching portion of the right curve by seven bases. After three bases for the curves to converge (shown in blue) the curves converge again. Comparing bases 1204 and 1211 (gap + convergence window) will show the curves aligning.</p

W-curves of a whole HIV-1 genome (A) and embedded pol gene sequence (B, C).

<p>A W-curve of an entire genome of HIV-1 01TH.OUR6091 (Accession number AY358040 is shown in panel A. Panel B shows a “zoomed in” projection of pol gene HIV-1 99^TH.OUR1991 (Accession number AY358039) with respect to base pair position in the whole genome. Panel C shows the same pol sequence extracted from the fasta file and renumbered with respect to base pair position. Sequences can be input into one of two graphical packages for the W-curve existing on the internet (10, 11).</p

Difference measure for W-curves stored in Cylindrical notation.

<p>Subtracting the projection of the smaller radius onto the larger one smooths out small differences after the curves have largely converged. For small angles (shown) the projection is subtracted and produces a small difference. As the angle increases the projection becomes small; points in opposite quadrants have obtuse angles with a negative cosine, adding the projection onto the larger radius.</p

W-curve nucleotide coordinate positions (left) and W-curve projection of each nucleotide (right).

<p>The W-curve is generated using a square centered at the origin with corners on the axes (left). Each moving point moves halfway from a starting point P to P' halfway to the corner for the next base in sequence (right). The numbers iterate within the square as follows: P'(T) = [(Px+1)/2, (Py)/2]; P'(A) = [(Px)/2, (Py+1)/2]; P'(G) = [(Px–1)/2], (Py)/2]; P'(C) = [(Px)/2, (Py–1)/2]</p

Benchmark results for sequence comparison using the W-curve.

<p>For each group, the number of sequences determines how many comparisons must be made, average number of bases in each sample can be used to estimate the processing rate in terms of the sequence lengths (vs. count of sequences). These times were taken from processing the upper-triangular distance matrices processed by neighbor and drawgram to produce the phenograms from the Mother/Infant study data <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0010829#pone.0010829-httpwwwbioinformaticsorgwcurve1" target="_blank">[11]</a>. Variations in rates are largely due to timesharing overhead, which reflects the likely environment of any clinical application. The data was measured using Perl-5.10.1 on linux-2.6.31 on an Asus M3N-HT (i.e., commodity desktop) motherboard with 4GB RAM and AMD Phenom 3.0 GHz processor.</p

Building a fragment library.

<p>Panels A, B, C, D describe the process of extracting curve fragments. Autoregression allows re-use of the curve fragments for comparisons between curves. Starting with the W-curve for a genome or gene (A), regions corresponding to the sequences of interest are found (B) and the remainder of the curve dropped (C), leaving a set of smaller curves (D). The set of curve fragments can be used to search for a list of regions in or score only part of a gene. For example, scoring only the conserved regions of gp120 may prove more effective for generating phenograms than using the entire gp120 sequence or <i>env</i> gene.</p

Clinical Chemistry reference ranges (median and 95th-percentile) derived from HIV-seronegative adults in Kericho, Kenya.

a<p>: P value of <0.05 using the Wilcoxon rank test.</p

Hematology reference ranges from Kericho, Kenya compared to other sources in Africa and the United States of America.

a<p>: NA-Not Available.</p