A leopard can’t change its spots, but certain lizards change theirs as a matter of course. The scales of an ocellated lizard, for example, switch between black and green as the lizard matures, before settling on a labyrinthine arrangement with short-range order. By modeling the dynamics of this process with Turing’s Reaction-Diffusion (RD) framework, Milinkovitch's lab now discovered that the seemingly binary configurations of scales hide a secondary pattern based on color gradations too subtle to see with the naked eye. These results are important in advancing the field of biological pattern formation by moving beyond simple qualitative comparisons between theory and experiments, and by showing that RD models can predict unobserved features of these systems. More generally, the 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.
Alan 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, the team shows 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 colour sub-clustering that correlates with the colours of the scales’ neighbours.
Hyperspectral imaging indicates that colour sub-clustering is present in real lizards, confirming the numerical model non-trivial prediction. In addition, extensive histological analyses show that melanophores’ spatial distribution correlates with scale neighbourhood, confirming that colour sub-clustering is associated to the underlying microscopic system of chromatophore interactions.
Michel Milinkovitch's team then shows that the observed sub-clustering is efficiently captured by RD models, irrespective of their form, discretisation and spatial dimensionality. They 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 neighbourhood configuration, hence instructing the mathematical model.
More generally, the 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.
Additional information is provided in the original article
Simple reaction-diffusion modelling predicts inconspicuous neighbourhood-dependent colour sub-clustering of lizard scales
Szabolcs Zakany & Michel C. Milinkovitch*
Physical Review X 13, 041011 (2023)