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  • Featured in Physics
  • Open Access

Simple Reaction-Diffusion Modeling Predicts Inconspicuous Neighborhood-Dependent Color Subclustering of Lizard Scales

Szabolcs Zakany* and Michel C. Milinkovitch†

  • Laboratory of Artificial and Natural Evolution (LANE), Department of Genetics and Evolution, University of Geneva, 1211 Geneva, Switzerland and SIB Swiss Institute of Bioinformatics, 1211 Geneva, Switzerland

  • *szabolcs.zakany@unige.ch
  • †Author to whom correspondence should be addressed: michel.milinkovitch@unige.ch
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Phys. Rev. X 13, 041011 – Published 20 October, 2023

DOI: https://doi.org/10.1103/PhysRevX.13.041011

Abstract

Turing proposed a reaction-diffusion (RD) process as the chemical basis of morphogenesis. Despite the elegance of this model, its relevance for the precise description of morphogenesis in real organisms is largely disputed. Here, we show that a simple RD system, predicting the cellular-automaton-like patterning of ocellated lizards’ skin into green and black labyrinthine chains of scales, additionally predicts unsuspected subtle color subclustering that correlates with the colors of the scales’ neighbors. Hyperspectral imaging indicates that color subclustering is present in real lizards, confirming the numerical model nontrivial prediction. In addition, extensive histological analyses show that melanophores’ spatial distribution correlates with scale neighborhood, confirming that color subclustering is associated to the underlying microscopic system of chromatophore interactions. We then show that the observed subclustering is efficiently captured by RD models, irrespective of their form, discretization, and spatial dimensionality. We also show that sets of values can be identified in the 12-dimensional RD parameter space to yield the correct direction of correlation (i.e., observed in real lizards) between green-scale blackness and their neighborhood configuration, hence instructing the mathematical model. More generally, our results show that subtle mesoscopic properties of biological dynamical systems, as well as some of the underlying microscopic features, are quantitatively captured by simple RD models without integrating the unmanageable profusion of variables at lower scales.

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synopsis

Model Reveals Reptilian Scale Pattern

Published 20 October, 2023

Researchers have predicted—and confirmed—a secondary pattern on the ocellated lizard’s scales that is too subtle for our eyes to see.

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Popular Summary

Turing posited that morphological patterns in living organisms—a zebra’s stripes, a human’s digits—could emerge from the interplay between chemical reactions and particle diffusion. This reaction-diffusion mathematical model is still viewed today with suspicion by most developmental biologists. They regard it as an artificial mathematical toy because it does not incorporate the many cellular and molecular variables that underlie chemical-based patterning. Here, we show that reaction-diffusion modeling is highly effective in quantitatively predicting the skin color patterning process.

When superposed on the geometry of reptilian scaled skin, a simple system of reaction-diffusion equations not only describes the cellular automaton—like scale-by-scale skin color patterning observed in some lizards, but also predicts unsuspected and subtle color subclustering that correlates with the colors of the scales’ neighbors. Hyperspectral imaging and histological analyses indicate that this color subclustering, observed in numerical simulations, is present in real lizards and correlates with the behavior of colored cells in the skin. We also show that the quantitative correlation observed in real lizards can be leveraged to produce an improved mathematical model.

These results are important in advancing the field of biological pattern formation by raising the bar on how to move beyond simple qualitative comparisons between theory and experiments, and by showing that reaction-diffusion models can predict unobserved features of these systems. More generally, our study shows that biology, despite its “messy” nature, with its unmanageable profusion of cellular and molecular variables, can be efficiently and quantitatively investigated mathematically, including with simple phenomenological models.

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Phys. Rev. X 13, 041011– Published 20 October, 2023
  • Received 9 June 2023
  • Accepted 1 September 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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