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Mathematics of cell physiology and proliferation | ||||||
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Summer School LIFASTRObiomat980483/EW/jg Scientist in charge: Andrea DeGaetano CNR Centro Fisiopatologia Shock, Biomath Lab UCSC L.go Gemelli, 8 Rome 00168 ITALY Tel.: +39-06-338-5446 Fax.: +39-06-338-5446 Email : biomath@tin.it Contractor : Contract N°: |
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Biomathematics is an interdisciplinary field in rapid expansion, where the availability of cheap computing power now makes quantitative analyses important and useful for biological disciplines like Medicine, Biology and Ecology. The importance of mathematical models for these disciplines lies not only in the possibility they offer to obtain numerical answers, but also in the depth of understanding that their qualitative study has for structuring further biological research. A problem which is always present in this field is the relative difficulty, for highly skilled biological professionals, to understand the concepts, jargon and methods of mathematicians, and viceversa. This often translates in ineffective or missed cooperation. The goal of the school was to bring young researchers from biological disciplines and from the several mathematical specialties together, describing a wide range of applications and methods and fostering an atmosphere of dialogue and exchange of problems and solutions. The school offered seven main courses. Some were centered on biological domains and research areas, others were centered on fundamental mathematical methods for the study of biological problems, some were attempting to elucidate material directly used to connect mathematical tools and biological applications. In addition to the classroom courses, laboratory demonstrations of currently studied biological questions, where mathematical help would be welcome, were carried out at the Mario Negri Sud biological research institute. The course on Tumor Cell Biology considered mechanisms of cell cycle control, tumor cell growth, cell adhesion and angiogenesis from the biologist’s perspective, offering descriptions of the mechanisms of regulation of the multiplication of tumor cells, and highlighting some methods currently under study to affect such regulations. The angiogenesis segment of the course stressed the recent advances in the field of inhibition of the development of the vascular supply to tumor masses. Theoretical models and simulation techniques in the study of the Control of Haemopoiesis have proved useful in explaining the occurrence and development of diseases of the blood cell lines like cyclical neutropenia or periodic immune hemolytic anemia. The qualitative analysis of models of reproduction of blood cells looks at the existence of normal equilibria, their stability, the possible loss of stability and the creation of stable periodic oscillations. Flow cytometry is a laboratory technique used to detect and quantitate cells or cell constituents. The basic concepts of cytometry were described, and theoretical aspects like the concept of asynchronous exponential growth were illustrated. One of the important issues in Cytometry is the estimation of kinetic parameters like the population doubling time from measured quantities like cell cycle phase percentages. The more biological part on cytometry was then supplemented with a more general theoretical discussion on Parameter Estimation in nonlinear models. The assessment of the degree of curvature of the expectation surface in case space, that is of the degree of nonlinearity, allows the experimenter to make an informed decision on the reliability of the obtained estimates. The course in Cytoskeleton and the Regulation of Cell Function introduced several aspects of the cellular mechanical structure as well as techniques of image analysis for exploring the cytoskeleton and simulations of the cytoskeletal formation. The possible link provided by the cytoskeleton between the cell environment and the nuclear machinery may explain the role of cellular structures in the regulation of gene expression. The modelling of the geometry and movements of small filaments, as well as the problem of identifying their 3D geometry from 2D sections were discussed. The course on Structured Cell Populations dealt with the classical mathematical theory of cell population dynamics. The linear theory presented included elements of the theory of positive operators needed in the proof of asynchronous exponential growth, semigroup theory, and the mathematical treatment of a general class of cell population models. Examples with different nonlinearities were discussed from the point of view of their dynamical features like stability, the onset of instability, bifurcation and chaotic behavior. An introduction to the numerical analysis of equations of age and size structured populations was also provided. In the Modelling of Cancer Chemotherapy the regulation of the cell-cycle clock was presented, using a theoretical model where the clock is modeled as a single limit cycle.The wealth of behavior of morphogenetic tissues may correspond to the richness of behavior of this model, which can exhibit a strange attractor. These concepts translate to the design of protocols for the treatment of cancers, where it may be possible to control host toxicity by rational drug scheduling. In this course, a formal introduction to optimal control theory was offered, together with applications to various problems of cell population dynamics. Stochastic optimization problems were also introduced and some applications of optimal control theory to cancer chemotherapy scheduling were presented. The Population Genetics of Organisms and Cells course introduced very recent developments on population genetics, with several applications to the history of growth and migrations of modern humans, or cancer induced by somatic mutations. The biology of genetics was introduced, with lectures on the genome, satellite DNA, mini- and microsatellites, mitochondrial DNA. The mathematical concept of coalescence was expounded and several aspects of the theory of branching processes were presented in detail. The effect of the expansion of DNA triplet repeats in the development of such diseases as the fragile X syndrome and Huntington’s diseases, the concept of genetic drift and the neutral theory of evolution, cancer cell genetics and carcinogenesis, were discussed. The main lectures were supplemented by invited talks, exercise sessions, laboratory demonstrations and tutorials. In all, 30 instructors and 77 participants shared 107 teaching units of 40 minutes duration each over two weeks. The breadth of topics, the excellent community spirit and the continuous interaction between younger and older researchers made the school a memorable educational experience. The end results are a better preparation of the participants to tackle real-life problems in the application of mathematical techniques to biological problems, a heightened sensitivity of mathematicians and biologists for each other’s peculiar set of goals and constraints, and a reinforcement of the european network of collaborations in this increasingly important field. Finally, a project of a book to be published by Wiley, Publ. in its Biomathematics Series (ed. S.Levin), based on the lecture notes of the courses, is under way. The book will be a collective work, uniting the efforts of the instructors, and will be edited by Z.Agur, an associate editor of the Wiley series. | ||||||
| A more detailed scientific summary of the school may be found at the school's WWW site: Termoli 1999 Biomath Summer School Page | ||||||
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PROGRAMME OF EVENT
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