Mathematical Models in Biology
Serving as a basic introduction to concepts in deterministic biological modeling, this text shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions.
TABLE OF CONTENTS Mathematical Models in Biology
Chapter 11: Models for Development and Pattern Formation in Biological Systems
It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.
A.M.Turing, (1952).
The chemical basis for morphogenesis.
Phil. Trans. Roy. Soc. Lond., 237, 37 72.
Simple interactions can have consequences that are not predictable by intuition based on biological experience alone.
L.A.Segel, (1980). ed.
Mathematical Models in Molecular and Cellular Biology,
Cambridge University Press, Cambridge, England.
This indicates a genuine developmental constraint, namely that it is not possible to have a striped animal with a spotted tail...
J.D.Murray (1981a).
OVERVIEW
The beauty of natural forms and the intricate shapes, structures, and patterns in living things have been a source of wonder for natural philosophers long before our time. Like the spiral arrangement of leaves or florets on a plant, the shapes of shells, horns, and tusks were thought to signify some underlying geometric concepts in Nature s designs. The teeming world of minute organisms was found to hold patterns no less amazing than those on the grander scales. Forms of living things were used from ancient times as a means of classifying relationships among organisms. The study of phenomena underlying such forms, although more recent, also dates back to previous centuries.
Initially, a primary fascination with static designs was characterized by attempts to fathom the secrets of natural forms with geometric concepts or simple physical analogies. Phyllotaxis (the study of the geometric arrangement of plant parts; e.g. leaves on a...
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