Chemical waves in open flows of active media: Their relevance to axial segmentation in biology

The boundary forcing of open flows of active media can lead to a variety of spatiotemporal structures, depending on the local kinetics of the medium and on the characteristics of the forcing. Here, we demonstrate that regardless of the local kinetics, the combination of flow and boundary forcing is a powerful method for replacing intrinsic modes with extrinsic ones. This entrainment of dynamics has important implications for biological morphogenesis. During early embryonic development it is frequently observed that stripes of gene expression and segments arise one after the other along a growth-axis. We show that axial growth can be viewed as an open flow of cells away from a growth zone. Based on this realisation, we demonstrate using three generic reaction-diffusion-advection schemes how a space-periodic structure is induced, one segment at a time along the growth/flow axis, by a segmental clock that is synchronised within the growth zone. The schemes are investigated in the context of an abrupt and a gradual change in the properties of the segmental clock. Experimental observations provide evidence that the latter is involved in the early development of many vertebrates.