Iridophores as a source of robustness in zebrafish stripes and variability in Danio patterns

Zebrafish (Danio rerio) feature black and yellow stripes, while related Danios display very different patterns. All these patterns form due to the interactions of pigment cells, which self-organize on the fish skin. Until recently, research focused on two cell types, but newer work has uncovered the leading role of a third type, called iridophores. By carefully-orchestrated transitions in shape, iridophores instruct the other cells, but little is known about what drives their shape changes. Here we address this question from a mathematical perspective: we develop a model (based on known interactions between the original two cell types) that allows us to assess potential iridophore behavior. We identify a series of mechanisms governing iridophore shape that is consistent across a range of empirical data. Our model also suggests that the complex cues iridophores receive may act as a key source of redundancy, enabling both robust patterning and variability within Danio. Characterized by stripes across its body and fins, the zebrafish (Danio rerio) has emerged as the archetype for studying pattern formation in vertebrates [1–3]. Zebrafish are amenable to experimental analysis, and numerous results (e.g. [4–6]) have shown that their namesake patterns emerge robustly because of the self-organizing interactions of pigment cells. Other members of the Danio genus display markedly different patterns, giving the study of cell interactions on zebrafish evolutionary and mathematical value [2, 7, 8]. Until recently, the biological community has focused on two cell types, but new work [2, 9–11] has uncovered the leading role of a third, iridophores [12]. The purpose of this work is to contribute to a better understanding of these newly-uncovered dynamics from a mathematical modeling perspective. Through an agent-based approach that works alongside the empirical literature [11], we conduct mutational analysis in silico to help elucidate cell behavior. Our results suggest that iridophores are more than the leaders of stripe formation on zebrafish: through built-in redundancy in the cues they receive from other cells, iridophores may also serve as a source of robustness and variability within Danio. As a zebrafish develops from a larva to an adult, 4-5 dark stripes and 4 light interstripes, represented by a layered mosaic of 3 main types of cells, emerge sequentially [2], Fig. 1. While melanophores are restricted to stripes, xanthophores and iridophores are spread across the skin, appearing in a loose (yellow or blue) shape in stripes and adopting a dense (orange or silver) form in interstripes [6, 13–15]. Thus, stripes consist of yellow xanthophores atop blue iridophores and a bottom layer of black melanophores; interstripes, in turn, are made up of orange xanthophores above silver iridophores [11, 13]. Until recently, empirical work (e.g. [4–6, 16]) focused on uncovering how melanophores and dense xanthophores interact through birth, competition, and movement. Iridophores were considered largely unnecessary, and a series of interactions in the form of short-range activation and long-range inhibition [17, 18] was deduced [19]. Past mathematical models, whether discrete [20–24] or continuum [4, 19, 20, 25–27], have also explored the interactions of melanophores and dense xanthophores. The empirical picture changed significantly in recent years: new experimental results [9, 10, 29] discovered that iridophores play a leading role in patterning. By changing shape between loose and dense, iridophores instruct the behavior of melanophores and xanthophores and drive the sequential appearance of body stripes [2, 9]. This governing behavior is particularly visible in shady, a mutation that lacks iridophores and instead features spots [11]. Recent research