Biological Growth and Spread: Mathematical Theories and by Renato Baserga (auth.), Willi Jäger, Hermann Rost, Petre

By Renato Baserga (auth.), Willi Jäger, Hermann Rost, Petre Tautu (eds.)

These lawsuits were assembled from papers provided on the convention on versions of organic progress and unfold, held on the German melanoma study Centre Heidelberg and on the Institute of utilized arithmetic of the college of Heidelberg, July 16-21, 1979. the most subject of the convention used to be the mathematical illustration of biolog­ ical populations with an underlying spatial constitution. a major characteristic of such populations is they and/or their person com­ ponents may perhaps engage with one another. Such interactions can be as a result of exterior disturbances, inner regulatory elements or a mixture of either. Many organic phenomena and strategies together with embryogenesis, phone development, chemotaxis, mobilephone adhesion, carcinogenesis, and the unfold of a virulent disease or of an helpful gene might be studied during this con­ textual content. therefore, difficulties of specific significance in medication (human and veterinary), agriculture, ecology, and so on. will be considered and a deeper perception received through the use of (more) sensible mathematical versions. because the intrinsic organic mechanisms may possibly vary significantly from one another, an outstanding number of mathematical ways, theories and strategies is needed. The goals of the convention have been (i) to supply an outline of crucial organic features. (ii) To survey and examine attainable stochastic and deterministic techniques. (iii) To inspire new examine through bringing jointly mathematicians drawn to difficulties of a organic nature and scientists actively engaged in constructing mathematical versions in biology.

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Extra resources for Biological Growth and Spread: Mathematical Theories and Applications, Proceedings of a Conference Held at Heidelberg, July 16 – 21, 1979

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Nature 255 Cheng, H. P. (1974) Origin, differentiation and renewal of the four main epithelial cell types in the mouse small intestine. V Unitarian theory of the origin of the four epithelial cell types. Am. J. Anat. 141 537-562 Christophers, E. (1971a) Derm. 56 165-169 Cellular architecture of the stratum corneum. Christophers, E. (197lb) Die Epidermale Columnarstruktur. J. i nvest. Z. Zellforsch. W. G. (1965) The importance of cell population kinetics in determining response to irradiation of normal and malignant tissue Cellular Radiation Biology.

Further studies are needed to clarify these points. Maturing CoIuRVlar . and Goblet tells I non-prolilntive I Fig. 11 Schematic representation of a small intestinal crypt. P, Paneth cells; S, stem cells; cells; E, enteroendocrine cells; M, mitosis; G, goblet F, pericryptal fibroblast Reproduced by courtesy of Elsevier North/Holland (Potten et aZ, 1979). CONCLUSIONS Biological modelling of surface epithelia can be achieved and these models provide working hypotheses for the proliferative cell organisation of the tissue.

A MODEL OF DEVELOPMENT OF A CELL R. R. Thompson, A. Michalowski and J. CWik. e. the fact that some cells die before reaching mitosis, and (2) the variability of the intermitotic time •• The central idea of the model is the assumption that within the cell there occur two stochastic processes. One of ~ hem, say X(t), is • birth and death process of some type of organellas. When X(t) reaches the value 0, the cell dies (perhaps not immediately). The organellas in question are assumed to be responsible for supplying energy to the cell.

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