Biological pattern formation: from basic mechanisms to complex structures

Abstract

The reliable development of highly complex organisms is an intriguing and fascinating problem. The genetic material is, as a rule, the same in each cell of an organism. How then do cells, under the influence of their common genes, produce spatial patterns' Simple models are discussed that describe the generation of patterns out of an initially nearly homogeneous state. They are based on nonlinear interactions of at least two chemicals and on their diffusion. The concepts of local autocatalysis and of long-range inhibition play a fundamental role. Numerical simulations show that the models account for many basic biological observations such as the regeneration of a pattern after excision of tissue or the production of regular (or nearly regular) arrays of organs during (or after) completion of growth. Very complex patterns can be generated in a reproducible way by hierarchical coupling of several such elementary reactions. Applications to animal coats and to the generation of polygonally shaped patterns are provided. It is further shown how to generate a strictly periodic pattern of units that themselves exhibit a complex and polar fine structure. This is illustrated by two examples: the assembly of photoreceptor cells in the eye of Drosophila and the positioning of leaves and axillary buds in a growing shoot. In both cases, the substructures have to achieve an internal polarity under the influence of some primary pattern-forming system existing in the fly s eye or in the plant. The fact that similar models can describe essential steps in organisms as distantly related as animals and plants suggests that they reveal some universal mechanisms. CONTENTS I. Introduction II. Gradients in Biological Systems III. Simple Models for Pattern Formation A. Activator-inhibitor systems B. Activator-substrate systems C. Biochemical switches D. Other realizations of local autocatalysis and long-range inhibition IV. Some Regulatory Properties of Pattern-Forming Reactions A. Insertion of new maxima during isotropic growth B. Strictly periodic patterns C. Regeneration properties and polarity V. Prom Simple Gradients to Complex Structures A. Animal coat patterns B. Reticulated structures C. The faceted eye of Dv osophila flies 1. The morphogenetic furrow

A dynamical model of ommatidial crystal formation

“…This mechanism implies that R8s are chosen earlier than previously thought, during the initial process of induction. Unlike previous scenarios (8,9), the switch and template mechanism predicts that genetically identical tissue can readily sustain different patterns depending on initial conditions, as we verify experimentally.…”

Size-dependent symmetry breaking in models for morphogenesis

“…This could explain why the symmetry is robustly kept when it is generated starting from a disk-like embryological structure, as in the case of the sea urchins. On the contrary, when the primordia grow starting from a symmetry breaking along a string-like one-dimensional structure, as in the case of leaf and flower initiation during plant growth [17], the final symmetry could not be controlled in an unique way. For instance, a single strawberry plant can produce flowers with a variable number of petals (see below).…”

“…The pattern with spots exhibiting hexagonal symmetry is ubiquitous in Turing models for biological morphogenesis [14,[17][18][19]. A weakly nonlinear theory based on corresponding amplitude equations has been recently developed to study the stability of this unavoidable hexagonal pattern [20].…”

Origin of directionality in the fish stripe pattern

“…An RD mechanism provides an effective solution to this problem. Many mathematical studies have shown that the RD system is able to account for most of the animal coat pattern (Murray, 1989;Koch and Meinhardt, 1994).…”