Prevalence of germ-line mutations in p16, p19ARF, and CDK4 in familial melanoma: analysis of a clinic-based population.

Five to ten percent of individuals with melanoma have another affected family member, suggesting familial predisposition. Germ-line mutations in the cyclin-dependent kinase (CDK) inhibitor p16 have been reported in a subset of melanoma pedigrees, but their prevalence is unknown in more common cases of familial melanoma that do not involve large families with multiple affected members. We screened for germ-line mutations in p16 and in two other candidate melanoma genes, p19ARF and CDK4, in 33 consecutive patients treated for melanoma; these patients had at least one affected first or second degree relative (28 independent families). Five independent, definitive p16 mutations were detected (18%, 95% confidence interval: 6%, 37%), including one nonsense, one disease-associated missense, and three small deletions. No mutations were detected in CDK4. Disease-associated mutations in p19ARF, whose transcript is derived in part from an alternative codon reading frame of p16, were only detected in patients who also had mutations inactivating p16. We conclude that germ-line p16 mutations are present in a significant fraction of individuals who have melanoma and a positive family history.

Hyperplane arrangements, interval orders, and trees.

A hyperplane arrangement is a finite set of hyperplanes in a real affine space. An especially important arrangement is the braid arrangement, which is the set of all hyperplanes xi - xj = 1, 1 interval orders and with the enumeration of trees. For instance, the number of labeled interval orders that can be obtained from n intervals I1,..., In of generic lengths is counted. There is also discussed an arrangement due to N. Linial whose number of regions is the number of alternating (or intransitive) trees, as defined by Gelfand, Graev, and Postnikov [Gelfand, I. M., Graev, M. I., and Postnikov, A. (1995), preprint]. Finally, a refinement is given, related to counting labeled trees by number of inversions, of a result of Shi [Shi, J.-Y. (1986), Lecture Notes in Mathematics, no. 1179, Springer-Verlag] that a certain deformation of the braid arrangement has (n + 1)n-1 regions.