Influence of survival, promotion, and growth on pattern formation in zebrafish skin

Abstract

The coloring of zebrafish skin is often used as a model system to study biological pattern formation. However, the small number and lack of movement of chromatophores defies traditional Turing-type pattern generating mechanisms. Recent models invoke discrete short-range competition and long-range promotion between different pigment cells as an alternative to a reaction-diffusion scheme. In this work, we propose a lattice-based “Survival model,” which is inspired by recent experimental findings on the nature of long-range chromatophore interactions. The Survival model produces stationary patterns with diffuse stripes and undergoes a Turing instability. We also examine the effect that domain growth, ubiquitous in biological systems, has on the patterns in both the Survival model and an earlier “Promotion” model. In both cases, domain growth alone is capable of orienting Turing patterns above a threshold wavelength and can reorient the stripes in ablated cells, though the wavelength for which the patterns orient is much larger for the Survival model. While the Survival model is a simplified representation of the multifaceted interactions between pigment cells, it reveals complex organizational behavior and may help to guide future studies.

Correspondences Between Parameters in a Reaction-Diffusion Model and Connexin Functions During Zebrafish Stripe Formation

“…Most other models for pigmentpattern formation are based on interactions at a cellular level. These models implement different effects depending on the distance from each pigment cell by agent-based models [17,18] and by minimal lattice models [19,20]. Several attempts were made to explain the observed patterns in zebrafish mutants by a general Turing model [21,22]; however, they were not supported experimentally even though there are several paths to cause the expected pattern changes in mutants.…”

Recombinant COL6 α2 as a Self-Organization Factor That Triggers Orderly Nerve Regeneration Without Guidance Cues

“…Self-organization, on the contrary, refers to a process in which the system spontaneously forms an internal orderly structure through interactions among its components rather than through external intervention or instruction (Haken and Portugali, 2017 ). Examples of this process include the generation of patterns on animal furs, fish skins, and butterfly wings (Liu et al, 2006 ; Werner et al, 2010 ; Konow et al, 2021 ); the development of fertilized eggs and embryos (Niu et al, 2019 ; Xiang et al, 2020 ); and the orderly axon bundle formation in the homogeneous, COL6- or COL6 α2-containing microenvironment without any guidance cues. This concept greatly simplifies the strategy for ordering nerve regeneration; however, it also has some limitations in precisely guiding the direction of axonal regeneration.…”

Emergence of Diverse Epidermal Patterns via the Integration of the Turing Pattern Model with the Majority Voting Model

“…Moreira and Deutsch [28] presented a model depicting pigment-cell pattern formation in zebrafish based on the local interaction cellular automata (CA) model, demonstrating the importance of differential intercellular adhesion and the mechanisms of stem cell regulation. Konow et al [29] proposed a lattice-based "survival model" based on recent findings on the nature of longrange chromatophore interactions and found that the model produces stationary patterns using diffuse stripes and undergoes Turing instability. Owen et al [30] constructed an individual-based mathematical lattice model of the zebrafish skin pattern that incorporated all important cell types and known interactions.…”