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Cell Surface as a Fractal: Normal and Cancerous Cervical Cells Demonstrate Different Fractal Behavior of Surface Adhesion Maps at the Nanoscale

Abstract:

Here we show that the surface of human cervical epithelial cells demonstrates substantially different fractal behavior when the cell becomes cancerous. Analyzing the adhesion maps of individual cervical cells, which were obtained using the atomic force microscopy operating in the HarmoniX mode, we found that cancerous cells demonstrate simple fractal behavior, whereas normal cells can only be approximated at best as multifractal. Tested on ~ 300 cells collected from 12 humans, the fractal dimensionality of cancerous cells is found to be unambiguously higher than that for normal cells.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.028101
#abstract
A living mesoscopic cellular automaton made of skin scales

Abstract:

In vertebrates, skin colour patterns emerge from nonlinear dynamical microscopic systems of cell interactions. Here we show that in ocellated lizards a quasi-hexagonal lattice of skin scales, rather than individual chromatophore cells, establishes a green and black labyrinthine pattern of skin colour. We analysed time series of lizard scale colour dynamics over four years of their development and demonstrate that this pattern is produced by a cellular automaton (a grid of elements whose states are iterated according to a set of rules based on the states of neighbouring elements) that dynamically computes the colour states of individual mesoscopic skin scales to produce the corresponding macroscopic colour pattern. Using numerical simulations and mathematical derivation, we identify how a discrete von Neumann cellular automaton emerges from a continuous Turing reaction–diffusion system. Skin thickness variation generated by three-dimensional morphogenesis of skin scales causes the underlying reaction–diffusion dynamics to separate into microscopic and mesoscopic spatial scales, the latter generating a cellular automaton. Our study indicates that cellular automata are not merely abstract computational systems, but can directly correspond to processes generated by biological evolution.

https://www.nature.com/articles/nature22031
#abstract