staff

Ebrahim Jahanbakhsh

Postdoctoral fellow in Artificial & Natural Evolution

  • T: +41 22 379 31 22
  • office 4024a (Sciences III)

  • The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning. Annu Rev Cell Dev Biol 2023 Oct;39():145-174. 10.1146/annurev-cellbio-120319-024414.

    abstract

    In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying the foundations of morphogenesis as a self-organized process emerging from physicochemical first principles. Regrettably, this approach has been widely doubted in the field of developmental biology. First, we summarize Turing's line of thoughts to alleviate the misconception that RD is an artificial mathematical construct. Second, we discuss why phenomenological RD models are particularly effective for understanding skin color patterning at the meso/macroscopic scales, without the need to parameterize the profusion of variables at lower scales. More specifically, we discuss how RD models () recapitulate the diversity of actual skin patterns, () capture the underlying dynamics of cellular interactions, () interact with tissue size and shape, () can lead to ordered sequential patterning, () generate cellular automaton dynamics in lizards and snakes, () predict actual patterns beyond their statistical features, and () are robust to model variations. Third, we discuss the utility of linear stability analysis and perform numerical simulations to demonstrate how deterministic RD emerges from the underlying chaotic microscopic agents.

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  • Modeling convergent scale-by-scale skin color patterning in multiple species of lizards. Curr Biol 2022 Nov;():. S0960-9822(22)01692-X. 10.1016/j.cub.2022.10.044.

    abstract

    Skin color patterning in vertebrates emerges at the macroscale from microscopic cell-cell interactions among chromatophores. Taking advantage of the convergent scale-by-scale skin color patterning dynamics in five divergent species of lizards, we quantify the respective efficiencies of stochastic (Lenz-Ising and cellular automata, sCA) and deterministic reaction-diffusion (RD) models to predict individual patterns and their statistical attributes. First, we show that all models capture the underlying microscopic system well enough to predict, with similar efficiencies, neighborhood statistics of adult patterns. Second, we show that RD robustly generates, in all species, a substantial gain in scale-by-scale predictability of individual adult patterns without the need to parametrize the system down to its many cellular and molecular variables. Third, using 3D numerical simulations and Lyapunov spectrum analyses, we quantitatively demonstrate that, given the non-linearity of the dynamical system, uncertainties in color measurements at the juvenile stage and in skin geometry variation explain most, if not all, of the residual unpredictability of adult individual scale-by-scale patterns. We suggest that the efficiency of RD is due to its intrinsic ability to exploit mesoscopic information such as continuous scale colors and the relations among growth, scales geometries, and the pattern length scale. Our results indicate that convergent evolution of CA patterning dynamics, leading to dissimilar macroscopic patterns in different species, is facilitated by their spontaneous emergence under a large range of RD parameters, as long as a Turing instability occurs in a skin domain with periodic thickness. VIDEO ABSTRACT.

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