The recent dramatic advances inbiotechnology have led to an explosion of data in the life sciences at the molecular level as well as more detailed observation and ch- acterization at the cellular and tissue levels. Itis now absolutely clear that one needs a theoretical framework inwhich to place this data to gain from it as much information as possible. Mathematical and computational modelling approaches are the obvious waytodothis. Heeding lessons from the physical sciences, one might expect that all areas in the life sciences would be actively pursuing quantitative methods to c- solidate the vast bodies of data that exist and to integrate rapidly accumulating new information. Remarkably, with a few notable exceptions, quite the contrary situation exists. However, things are now beginning to change and there is the sense that we are at the beginning of an exciting new era of research inwhich the novel problems posed by biologists will challenge the mathematicians and computer scientists, who, in turn, will use their tools to inform the experimentalists, who will verify model predictions. Only through such a tight interaction among disciplines will we have the opportunity to solve many of the major problems in the life sciences. One such problem, central to developmental biology, is the understanding of how various processes interact to produce spatio-temporal patterns in the embryo.
Mục lục
General Principles, Theories, and Models of Pattern Formation.- and Outline.- On the Origin of Patterns.- Mathematical Modeling of Biological Pattern Formation.- Cellular Automaton Modeling.- Cellular Automata.- Applications.- Random Movement.- Growth Processes.- Adhesive Cell Interaction.- Alignment and Cellular Swarming.- Pigment Cell Pattern Formation.- Tissue and Tumor Development.- Turing Patterns and Excitable Media.- Discussion and Outlook.
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