Coreceptor usage is warranted as it determines the clinical outcomes in HIV-afflicted patients. The coreceptor usage is determined, in part, by the V3 (V for variable) sequence in gp120 -- a protein of HIV. Bozed et al. (2009) characterized the V3 distribution in a distance-defined sequence space. Their distance measurement is done according to the 'Blosum62 matrix'. However, measuring distances in exotic spaces -- such as the V3 loop space -- is a hurdle not easily surmounted, especially when using non-kernel distances. For example, V3 sequences can not be processed as constant-size vectors as their length varies greatly (31-40 residues). A kernel is, in essence, a dot product. Akin to the computation 3 * 8 (= 24), we can compute CTRPNNNTRKSIRIQRGPGRAFVTIGKIGNMRQAHC * CTRPSNNTRTGITIGPGQVWYRTGDIIGDIRKAYC with the so-called 'string kernels'. Leslie et al. (2002) proposed the spectrum kernel -- a similarity measurement based on the composition in fixed-length substrings. Leslie et al. (2004) revisited the spectrum approach, but this time allowed mismatches. Vert et al. (2004) introduced the (now famous) local alignment kernel -- an alignment-based string kernel which satisfies the conditions of a Mercer kernel. Boisvert et al. (2008) introduced the distant segments kernel, which uses paired segments in strings. Boisvert et al. (2008) actually defined a feature space, using the distant segments kernel, to evaluate the distribution and separability of CCR5- and CXCR4-binding sequences. Given a kernel k, two objects x and y, we can define a kernel distance with d(x,y,k)=(k(x,x)+k(y,y)-2k(x,y))^0.5, regardless of the class (integer, graph, string, vector) of x and y.

References

V3 loop sequence space analysis suggests different evolutionary patterns of CCR5- and CXCR4-tropic HIV.
Bozek K, Thielen A, Sierra S, Kaiser R, Lengauer T.
PLoS One. 2009 Oct 9;4(10):e7387. http://dx.doi.org/10.1371...

HIV-1 coreceptor usage prediction without multiple alignments: an application of string kernels.
Boisvert S, Marchand M, Laviolette F, Corbeil J.
Retrovirology. 2008 Dec 4;5:110. http://dx.doi.org/doi:10....

Protein homology detection using string alignment kernels.
Saigo H, Vert JP, Ueda N, Akutsu T.
Bioinformatics. 2004 Jul 22;20(11):1682-9. http://dx.doi.org/doi:10....

Mismatch string kernels for discriminative protein classification.
Leslie C, Eskin E, Cohen A, Weston J, Noble W.
Bioinformatics 2004, 20:467-476. http://dx.doi.org/doi:10....

The spectrum kernel: a string kernel for SVM protein classification.
Leslie C, Eskin E, Noble W.
Pac Symp Biocomput 2002, 564-575. http://books.nips.cc/pape...