Pattern formation

The science of pattern formation deals with the visible, (statistically) orderly outcomes of self-organization and the common principles behind similar patterns in nature. The science of pattern formation deals with the visible, (statistically) orderly outcomes of self-organization and the common principles behind similar patterns in nature. In developmental biology, pattern formation refers to the generation of complex organizations of cell fates in space and time. Pattern formation is controlled by genes. The role of genes in pattern formation is an aspect of morphogenesis, the creation of diverse anatomies from similar genes, now being explored in the science of evolutionary developmental biology or evo-devo. The mechanisms involved are well seen in the anterior-posterior patterning of embryos from the model organism Drosophila melanogaster (a fruit fly), one of the first organisms to have its morphogenesis studied, and in the eyespots of butterflies, whose development is a variant of the standard (fruit fly) mechanism. Examples of pattern formation can be found in Biology, Chemistry, Physics and Mathematics, and can readily be simulated with Computer graphics, as described in turn below. Biological patterns such as animal markings, the segmentation of animals, and phyllotaxis are formed in different ways. In developmental biology, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue in an embryo assume complex forms and functions. Embryogenesis, such as of the fruit fly Drosophila, involves coordinated control of cell fates. Pattern formation is genetically controlled, and often involves each cell in a field sensing and responding to its position along a morphogen gradient, followed by short distance cell-to-cell communication through cell signaling pathways to refine the initial pattern. In this context, a field of cells is the group of cells whose fates are affected by responding to the same set positional information cues. This conceptual model was first described as the French flag model in the 1960s. More generally, the morphology of organisms is patterned by the mechanisms of evolutionary developmental biology, such as changing the timing and positioning of specific developmental events in the embryo. Possible mechanisms of pattern formation in biological systems include the classical reaction-diffusion model proposed by Alan Turing and the more recently found elastic instability mechanism which is thought to be responsible for the fold patterns on the cerebral cortex of higher animals, among other things. Bacterial colonies show a large variety of patterns formed during colony growth. The resulting shapes depend on the growth conditions. In particular, stresses (hardness of the culture medium, lack of nutrients, etc.) enhance the complexity of the resulting patterns. Other organisms such as slime moulds display remarkable patterns caused by the dynamics of chemical signalling. Vegetation patterns such as tiger bush and fir waves form for different reasons. Tiger bush consists of stripes of bushes on arid slopes in countries such as Niger where plant growth is limited by rainfall. Each roughly horizontal stripe of vegetation absorbs rainwater from the bare zone immediately above it. In contrast, fir waves occur in forests on mountain slopes after wind disturbance, during regeneration. When trees fall, the trees that they had sheltered become exposed and are in turn more likely to be damaged, so gaps tend to expand downwind. Meanwhile, on the windward side, young trees grow, protected by the wind shadow of the remaining tall trees. Pattern formation has been well studied in chemistry and chemical engineering, including both temperature and concentration patterns. The Brusselator model developed by Ilya Prigogine and collaborators is one such example that exhibits Turing instability. Pattern formation in chemical systems often involve oscillatory chemical kinetics or autocatalytic reactions such as Belousov-Zhabotinsky reaction or Briggs-Rauscher reaction. In industrial applications such as chemical reactors, pattern formation can lead to temperature hot spots which can reduce the yield or create hazardous safety problems such as a thermal runaway. The emergence of pattern formation can be studied by mathematical modeling and simulation of the underlying reaction-diffusion system.