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A stochastic model of cancer initiation is considered. The model is used to evaluate whether a bystander effect may be important in the pre-malignant and malignant stages of carcinogenesis, and furthermore, on the basis of epidemiological data, to estimate the mutation rates of genes involved in the development of oral leukoplakias. The bystander effect is defined here as the capability of oncogenic mutations to increase the mutation probability of neighbouring (bystander) cells, thus leading potentially to a cascade of neighbouring mutated and neoplastic cells as a pre-stage in the development to leukoplakias and cancer. We find that incidence data for oral cancer are indeed in accordance with a significant bystander effect, operating either alone or in combination with genomic instability in the early stages of carcinogenesis, i.e. the development of neoplasia. Simulations performed gave a picture of how mutations and neoplasia may spread in a tissue, to form characteristic leukoplakias with a core of neoplastic cells. The model also showed that the probability of finding at least one neoplastic cell in the tissue after a given number of years is more sensitive to changes in genomic instability within the cell itself than to changes in a bystander effect. Based on epidemiological data we also calculate the maximum number of oncogenic genes that may be involved in the bystander effect and development of genomic instability. Even if capable of explaining the initial development of oncogenic mutations towards neoplastic cells, the bystander model could not reproduce the observed incidence rates of leukoplakia without assuming a carcinogen mutation probability per cell per year of neoplastic cells practically equal to one. This means that the bystander effect, to be of substantial importance in the final development of neoplastic cells towards leukoplakias, requires a very significant increase in mutation probabilities for bystanders to neoplastic cells. Alternatively, additional mechanisms such as abnormal cell differentiation and uncontrolled proliferation and apoptotis in the neoplastic stage may be of major importance during the development to cancerization.

Melanin produced in follicular melanocytes is the major basis for pigmentation of hair and wool in mammals. Two major types of melanin may be synthesized, the black/brown eumelanin and the reddish/yellow pheomelanin. Based on available cell biological evidence and reasonable assumptions, a mathematical model is developed to improve our understanding of melanogenic switching, i.e. the switching between eumelanin and pheomelanin production depending on the extracellular signalling context. In 1993, Ito proposed that melanogenic switching is due to the covalent binding of the intermediate DOPAquinone to the enzyme glutathione reductase. We were only able to obtain a good fit to available experimental data on the relation between pheomelanin levels and the activity of the key enzyme tyrosinase by taking Ito's hypothesis into account. Thus, our results support Ito's hypothesis, and suggest that melanogenic switching may be due to a jump between two stable production pattern states when the tyrosinase activity varies between two bifurcation levels. This implies that small changes in the levels of external regulatory factors may cause an accentuated change in the proportion of the produced colour pigments and may explain the fact that mammalian coat patterns often exhibit sharply delimited patches of either black or reddish colour., (Copyright 2002 Elsevier Science Ltd. All rights reserved.)