Discrete mathematics in primary and secondary schools in the United States

This article provides a status report on discrete mathematics in America's schools, including an overview of publications and programs that have had major impact. It discusses why discrete mathematics should be introduced in the schools and the authors' efforts to advocate, facilitate, and support the adoption of discrete mathematics topics in the schools. Their perspective is that discrete mathematics should be viewed not only as a collection of new and interesting mathematical topics, but, more importantly, as a vehicle for providing teachers with a new way to think about traditional mathematical topics and new strategies for engaging their students in the study of mathematics.     

p53 mutations in basal cell carcinomas arising in routine users of sunscreens

Sun exposure histories were obtained from a series of patients age 35 or younger following diagnosis and removal of a basal cell carcinoma (BCC). The DNA was extracted from tumor biopsy samples derived from BCC of 10 patients who reported that they did not use sunscreens during youth (age 18 or younger) and 10 patients who routinely employed sunscreens during this age period. Exons 5-9 of the p53 gene were then amplified in three fragments from these samples using a nested polymerase chain reaction (PCR) approach and screened for mutations using an RNA heteroduplex assay. All PCR products displaying evidence of a mutation were sequenced. It was found that 6 of the 10 patients who were not routine sunscreen users displayed mutations in these p53 exons. All of the mutations were located at dipyrimidine sites, five of the six were C-->T transitions and one mutation was a tandem double mutation, consistent with a role for solar UVB in BCC formation. In contrast, only one p53 mutation was detected in the group of 10 patients who routinely employed sunscreens during childhood and adolescence. Hence, a significantly (P = 0.029) lower level of p53 mutations was detected in the BCC obtained from sunscreen users compared with tumors derived from nonusers. These findings suggest that the mechanisms involved in the etiology of skin carcinogenesis differ in sunscreen users compared with people who did not routinely employ sunscreens. These data are also indicative of a protective effect associated with sunscreen use against the formation of p53 mutations. It is possible that the patients who were diagnosed with BCC despite their use of sunscreens possessed a genetic susceptibility for skin cancer formation and developed BCC through a p53-independent pathway. Alternatively, solar UVA wavelengths, that were generally not blocked by the suncare products employed by the sunscreen users, may have played a significant role in BCC development through induction of a mutation(s) in an oncogene and/or a tumor suppressor gene, other than p53, for these patients.     

INDUCTION OF CHROMOSOME ABERRATIONS IN ICR 2A FROG CELLS EXPOSED TO265–313 nm MONOCHROMATIC ULTRAVIOLET WAVELENGTHS and PHOTOREACTIVATING LIGHT

Abstract— Exposure of ICR 2A cells to either 265, 289, 302 or 313 nm monochromatic UV wavelengths caused the induction of chromosome aberrations with chromatid gaps and breaks being the most common type of aberration detected. Treatment of U V-irradiated cells with photoreactivating light (PRL) resulted in a lower yield of aberrations demonstrating that pyrimidine dimers are involved in the formation of chromosome aberrations induced by the UV wavelengths tested. However, the decrease in the level of aberrations resulting from PRL treatment of 313 nm-irradiated cells was significantly less than for the other wavelengths indicating that non-dimer photoproducts may have played an important additional role in the induction of chromosome aberrations by this UV wavelength.     

DNA-PROTEIN CROSSLINKING IN NORMAL HUMAN SKIN FIBROBLASTS EXPOSED TO SOLAR ULTRAVIOLET WAVELENGTHS

Three normal human skin fibroblast cell lines were exposed to the simulated solar UV radiation produced by a fluorescent sunlamp under conditions in which the wavelength components shorter than either 295, 305 or 315 nm were excluded. The level of DNA-protein crosslinks (DPC) was then measured in those cells using the alkaline elution technique either immediately after irradiation or following a 24 h incubation. In each case, cells were exposed to fluences that induce similar levels of DPC. For cells exposed to 10 kJ m(-2) of sunlamp UV > 295 nm, the level of DPC exhibited a 2-5-fold increase following incubation. In contrast, 40-100% of the DPC were removed upon incubation of cells irradiated with either 100 kJ m(-2) of sunlamp UV > 305 nm or 150 kJ m(-2) of sunlamp UV > 315 nm. A major difference between the effects induced by these wavelength regions is that, in addition to DPC, a very high level of pyrimidine dimers is also produced by sunlamp UV > 295 nm, whereas much lower dimer yields result from treatment with either sunlamp UV > 305 nm or sunlamp UV > 315 nm. A potential role for type II DNA topoisomerase in the formation of these DPC resulting from either the change in conformational structure caused by the presence of a high level of dimers or an involvement of this enzyme in dimer excision repair is discussed.     

PHOTOREACTIVATION OF ULTRAVIOLET IRRADIATED NON-DIVIDING POPULATIONS OF ICR 2A FROG CELLS

Abstract— Ultraviolet (UV) irradiation of non-dividing populations of ICR 2A frog cells led to their detachment from the surface of the culture dish and eventual lysis. Exposure of the cells to photoreactivating light after UV irradiation prevented cell killing and was accompanied by a loss of endonuclease sensitive sites from DNA. This photoreversal did not take place when the cells were exposed at 4°C to photoreactivating light indicating that the reversal was the result of photoenzymatic repair. As the action of photoreactivating enzyme is specific for the repair of pyrimidine dimers in DNA, these results suggest that pyrimidine dimers in DNA are the critical lesions leading to the death of non-dividing populations of UV irradiated cells.     

PHOTOREACTIVATION OF ICR 2A FROG CELLS AFTER EXPOSURE TO MONOCHROMATIC ULTRAVIOLET RADIATION IN THE 252–313 nm RANGE

Abstract— Exposure of ICR 2A frog cells to photoreactivating light after treatment with monochromatic ultraviolet (UV) radiation in the 252–313 nm range resulted in an increase in survival with similar photoreactivable sectors for each of the wavelengths tested. As photoreactivating enzyme is specific for the repair of pyrimidine dimers in DNA, these findings support the hypothesis that these are critical lesions responsible for killing of cells exposed to UV radiation in this wavelength range. The action spectra for cell killing and production of UV-endonuclease sensitive sites were similar to the DNA absorption spectrum though not identical. Because the number of endonuclease sensitive sites is a reflection of the yield of pyrimidine dimers, these data also suggest that the induction of dimers in DNA by UV radiation in the 252–313 nm range is the principal event leading to cell death.