Reaction-diffusion in a growing 3D domain of skin scales generates a discrete cellular automaton

Fabric soft pneumatic actuators with programmable turing pattern textures

This paper presents a novel computational design and fabrication method for fabric-based soft pneumatic actuators (FSPAs) that use Turing patterns, inspired by Alan Turing's morphogenesis theory. These inflatable structures can adapt their shapes with simple pressure changes and are applicable in areas like soft robotics, airbags, and temporary shelters. Traditionally, the design of such structures relies on isotropic materials and the designer's expertise, often requiring a trial-and-error approach. The present study introduces a method to automate this process using advanced numerical optimization to design and manufacture fabric-based inflatable structures with programmable shape-morphing capabilities. Initially, an optimized distribution of the material orientation field on the surface membrane is achieved through gradient-based orientation optimization. This involves a comprehensive physical deployment simulation using the nonlinear shell finite element method, which is integrated into the inner loop of the optimization algorithm. This continuous adjustment of material orientations enhances the design objectives. These material orientation fields are transformed into discretized texture patterns that replicate the same anisotropic deformations. Anisotropic reaction-diffusion equations, using diffusion coefficients determined by local orientations from the optimization step, are then utilized to create space-filling Turing pattern textures. Furthermore, the fabrication methods of these optimized Turing pattern textures are explored using fabrics through heat bonding and embroidery. The performance of the fabricated FSPAs is evaluated through three different deformation shapes: C-shaped bending, S-shaped bending, and twisting.

Parsing patterns: Emerging roles of tissue self-organization in health and disease

Patterned morphologies, such as segments, spirals, stripes, and spots, frequently emerge during embryogenesis through self-organized coordination between cells. Yet, complex patterns also emerge in adults, suggesting that the capacity for spontaneous self-organization is a ubiquitous property of biological tissues. We review current knowledge on the principles and mechanisms of self-organized patterning in embryonic tissues and explore how these principles and mechanisms apply to adult tissues that exhibit features of patterning. We discuss how and why spontaneous pattern generation is integral to homeostasis and healing of tissues, illustrating it with examples from regenerative biology. We examine how aberrant self-organization underlies diverse pathological states, including inflammatory skin disorders and tumors. Lastly, we posit that based on such blueprints, targeted engineering of pattern-driving molecular circuits can be leveraged for synthetic biology and the generation of organoids with intricate patterns.

Learning spatio-temporal patterns with Neural Cellular Automata

Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and Partial Differential Equation (PDE) trajectories. Our method is designed to identify underlying local rules that govern large scale dynamic emergent behaviours. Previous work on NCA focuses on learning rules that give stationary emergent structures. We extend NCA to capture both transient and stable structures within the same system, as well as learning rules that capture the dynamics of Turing pattern formation in nonlinear PDEs. We demonstrate that NCA can generalise very well beyond their PDE training data, we show how to constrain NCA to respect given symmetries, and we explore the effects of associated hyperparameters on model performance and stability. Being able to learn arbitrary dynamics gives NCA great potential as a data driven modelling framework, especially for modelling biological pattern formation.

On the role of TFEC in reptilian coloration

Reptilian species, particularly snakes and lizards, are emerging models of animal coloration. Here, I focus on the role of the TFEC transcription factor in snake and lizard coloration based on a study on wild-type and piebald ball pythons. Genomic mapping previously identified a TFEC mutation linked to the piebald ball python phenotype. The association of TFEC with skin coloration was further supported by gene-editing experiments in the brown anole lizard. However, novel histological analyses presented here reveal discrepancies between the ball python and the anole TFEC mutants phenotype, cautioning against broad generalizations. Indeed, both wild-type and piebald ball pythons completely lack iridophores, whereas the TFEC anole lizard mutants lose their iridophores compared to the wild-type anole. Based on these findings, I discuss the potential role of the MiT/TFE family in skin pigmentation across vertebrate lineages and advocate the need for developmental analyses and additional gene-editing experiments to explore the reptilian coloration diversity.

Forceful patterning: theoretical principles of mechanochemical pattern formation

Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.

The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning

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 (a) recapitulate the diversity of actual skin patterns, (b) capture the underlying dynamics of cellular interactions, (c) interact with tissue size and shape, (d) can lead to ordered sequential patterning, (e) generate cellular automaton dynamics in lizards and snakes, (f) predict actual patterns beyond their statistical features, and (g) 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.

Cellular automata imbedded memristor-based recirculated logic in-memory computing

Memristor-based circuits offer low hardware costs and in-memory computing, but full-memristive circuit integration for different algorithm remains limited. Cellular automata (CA) has been noticed for its well-known parallel, bio-inspired, computational characteristics. Running CA on conventional chips suffers from low parallelism and high hardware costs. Establishing dedicated hardware for CA remains elusive. We propose a recirculated logic operation scheme (RLOS) using memristive hardware and 2D transistors for CA evolution, significantly reducing hardware complexity. RLOS's versatility supports multiple CA algorithms on a single circuit, including elementary CA rules and more complex majority classification and edge detection algorithms. Results demonstrate up to a 79-fold reduction in hardware costs compared to FPGA-based approaches. RLOS-based reservoir computing is proposed for edge computing development, boasting the lowest hardware cost (6 components/per cell) among existing implementations. This work advances efficient, low-cost CA hardware and encourages edge computing hardware exploration.

Vascularized organ bioprinting: From strategy to paradigm

Over the past two decades, bioprinting has become a popular research topic worldwide, as it is the most promising approach for manufacturing vascularized organ in vitro. However, transitioning bioprinting from simple tissue models to real biomedical applications is still a challenge due to the lack of interdisciplinary theoretical knowledge and perfect multitechnology integration. This review examines the goals of vasculature manufacturing and proposes the objectives in three stages. We then outline a bidirectional manufacturing strategy consisting of top-down reproduction (bioprinting) and bottom-up regeneration (cellular behaviour). We also provide an in-depth analysis of the views from the four aspects of design, ink, printing, and culture. Furthermore, we present the 'constructing-comprehension cycle' research paradigm in Strategic Priority Research Program and the 'math-model-based batch insights generator' research paradigm for the future, which have the potential to revolutionize the biomedical field.

Quantitative Image Processing for Three-Dimensional Episcopic Images of Biological Structures: Current State and Future Directions

Episcopic imaging using techniques such as High Resolution Episcopic Microscopy (HREM) and its variants, allows biological samples to be visualized in three dimensions over a large field of view. Quantitative analysis of episcopic image data is undertaken using a range of methods. In this systematic review, we look at trends in quantitative analysis of episcopic images and discuss avenues for further research. Papers published between 2011 and 2022 were analyzed for details about quantitative analysis approaches, methods of image annotation and choice of image processing software. It is shown that quantitative processing is becoming more common in episcopic microscopy and that manual annotation is the predominant method of image analysis. Our meta-analysis highlights where tools and methods require further development in this field, and we discuss what this means for the future of quantitative episcopic imaging, as well as how annotation and quantification may be automated and standardized across the field.

Turing pattern-based design and fabrication of inflatable shape-morphing structures

Turing patterns are self-organizing stripes or spots widely found in biological systems and nature. Although inspiring, their applications are limited. Inflatable shape-morphing structures have attracted substantial research attention. Traditional inflatable structures use isotropic materials with geometrical features to achieve shape morphing. Recently, gradient-based optimization methods have been used to design these structures. These methods assume anisotropic materials whose orientation can vary freely. However, this assumption makes fabrication a considerable challenge by methods such as additive manufacturing, which print isotropic materials. Here, we present a methodology of using Turing patterns to bridge this gap. Specifically, we use Turing patterns to convert a design with distributed anisotropic materials to a distribution with two materials, which can be fabricated by grayscale digital light processing 3D printing. This work suggests that it is possible to apply patterns in biological systems and nature to engineering composites and offers new concepts for future material design.

Colour patterns: Predicting patterns without knowing the details

A bewildering array of colour patterns occurs across animals. New work studying five lizard species reveals that reaction-diffusion models can be remarkably predictive of future adult skin patterning, even though molecular details are unknown. This has implications for understanding how complex patterns evolve.

Modeling convergent scale-by-scale skin color patterning in multiple species of lizards

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.

The macroevolutionary and developmental evolution of the turtle carapacial scutes

The scutes of the carapace of extant turtles exhibit common elements in a narrow range of topographical arrangements. The typical arrangement has remained constant since its origin in the clade Mesochelydia (Early Jurassic), after a period of apparent greater diversity in the Triassic. This contribution is a review of the development and evolutionary history of the scute patterns of the carapace, seen through the lens of recent developmental models. This yields insights on pattern variations in the fossil record. We reinterpret the “supracaudal” scute and propose that Proganochelys had five vertebral scutes. We discuss the relationship between supramarginal scutes and Turing processes, and we show how a simple change during embryogenesis could account for origin of the configuration of the caudal region of the carapace in mesochelydians. We also discuss the nature of the decrease in number of scutes over the course of evolution, and whether macroevolutionary trends can be discerned. We argue that turtles with complete loss of scutes (e.g., softshells) follow clade-specific macroevolutionary regimes, which are distinct from the majority of other turtles. Finally, we draw a parallel between the variation of scute patterns on the carapace of turtles and the scale patterns in the pileus region (roof of the head) of squamates. The size and numbers of scales in the pileus region can evolve over a wide range, but we recognized tentative evidence of convergence towards a typical configuration when the scales become larger and fewer. Thus, typical patterns could be a more general property of similar systems of integumentary appendages.

Lizard Skin Patterns and the Ising Model

The ocellated lizard (Timon lepidus) exhibits an intricate skin color pattern made of monochromatic black and green skin scales, whose dynamics of color flipping are known to be well modeled by a stochastic cellular automaton. We show that the late-time probability distribution of the pattern corresponds to the canonical probability distribution of the antiferromagnetic Ising model and can be generated by dynamics different from the commonly-used Glauber. We comment on skin scale patterns generated by the Ising model on the triangular lattice in the low-temperature limit.