Self-similarity, distortion waves, and the essence of morphogenesis: A generalized view of color pattern formation in butterfly wings

Abstract

The morphology of multicellular organisms can be viewed as structuresof three-dimensional bulges and dents of an otherwise nearly two-dimensionalepithelial sheet. Morphogenesis is thus a process to stably form those physicaldistortions over time through differential cellular adhesion, contraction, and aggregationand through cellular changes in size, shape, and number. Such physicaldistortions may be hierarchically repeated with modifications, which is suggestedby self-similar structures in organisms. Butterfly wings are nearly two-dimensionalbut contain three-dimensional bulges and dents that correspond to organizingcenters for color pattern elements. Importantly, an eyespot and its correspondingparafocal element on a wing, constituting the border symmetry system, are selfsimilar.From this perspective, I review here the color pattern rules and severalformal models that have been proposed, clarifying their relationships with theinduction model for positional information. To reinforce the induction model, Ipropose the distortion hypothesis, in which dynamic epithelial distortion forces atorganizing centers, such as the center of a presumptive eyespot, that are producedthrough changes in cell size spread to surrounding immature cells over distances asmorphogenic signals in developing butterfly wings. The physical distortion forcesopen stretch-activated calcium channels that cause calcium signals in the cell andactivate the expression of regulatory genes. These regulatory gene products initiate a cascade of structural genes that eventually produce eyespot black rings. Calciumwaves also activate a process of genome duplication, resulting in an increase in cellsize, as the ploidy hypothesis states. A new distortion of epithelial cells is induced atthe center of a presumptive parafocal element through an increase in cell size,producing self-similarity of the eyespot and the parafocal element. The self-similarconfiguration of the border symmetry system further suggests the essence ofmorphogenesis as the DCG cycle: repeated sequential events of epithelial distortions(D), calcium waves (C), and gene expression changes (G). Future studiesshould examine these hypotheses and speculations that constitute the inductionmodel in butterfly wings and the generality of the DCG cycle in other organisms.