Pattern blending enriches the diversity of animal colorations

A new paradigm considering multicellular adhesion, repulsion and attraction represent diverse cellular tile patterns

Cell sorting by differential adhesion is one of the basic mechanisms explaining spatial organization of neurons in early stage brain development of fruit flies. The columnar arrangements of neurons determine the large-scale patterns in the fly visual center. Experimental studies indicate that hexagonal configurations regularly appear in the fly compound eye, which is connected to the visual center by photoreceptor axons, while tetragonal configurations can be induced in mutants. We need a mathematical framework to study the mechanisms of such a transition between hexagonal and tetragonal arrangements. Here, we propose a new mathematical model based on macroscopic approximations of agent-based models that produces a similar behavior changing from hexagonal to tetragonal steady configurations when medium-range repulsion and longer-range attraction between individuals are incorporated in previous successful models for cell sorting based on adhesion and volume constraints. We analyze the angular configurations of these patterns based on angle summary statistics and compare between experimental data and parameter fitted ARA (Adhesion-Repulsion-Attraction) models showing that intermediate patterns between hexagonal and tetragonal configuration are common in experimental data as well as in our ARA mathematical model. Our studies indicate an overall qualitative agreement of ARA models in tile patterning and pave the way for their quantitative studies. Our study opens up a new avenue to explore tile pattern transitions, found not only in the column arrangement in the brain, but also in the other related biological processes.

Linking discrete and continuous models of cell birth and migration

Self-organization of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of biological intuition. Discrete models provide straightforward interpretations by tracking each individual yet can be computationally expensive. Alternatively, continuous models supply a large-scale perspective by representing the 'effective' dynamics of infinite agents, but their results are often difficult to translate into experimentally relevant insights. We address this challenge by quantitatively linking spatio-temporal dynamics of continuous models and individual-based data in settings with biologically realistic, time-varying cell numbers. Specifically, we introduce and fit scaling parameters in continuous models to account for discrepancies that can arise from low cell numbers and localized interactions. We illustrate our approach on an example motivated by zebrafish-skin pattern formation, in which we create a continuous framework describing the movement and proliferation of a single cell population by upscaling rules from a discrete model. Our resulting continuous models accurately depict ensemble average agent-based solutions when migration or proliferation act alone. Interestingly, the same parameters are not optimal when both processes act simultaneously, highlighting a rich difference in how combining migration and proliferation affects discrete and continuous dynamics.

Photochemical Design for Diverse Controllable Patterns in Self-Wrinkling Films

Harnessing the spontaneous surface instability of pliable substances to create intricate, well-ordered, and on-demand controlled surface patterns holds great potential for advancing applications in optical, electrical, and biological processes. However, the current limitations stem from challenges in modulating multidirectional stress fields and diverse boundary environments. Herein, this work proposes a universal strategy to achieve arbitrarily controllable wrinkle patterns via the spatiotemporal photochemical boundaries. Utilizing constraints and inductive effects of the photochemical boundaries, the multiple coupling relationship is accomplished among the light fields, stress fields, and morphology of wrinkles in photosensitive polyurethane (PSPU) film. Moreover, employing sequential light-irradiation with photomask enables the attainment of a diverse array of controllable patterns, ranging from highly ordered 2D patterns to periodic or intricate designs. The fundamental mechanics of underlying buckling and the formation of surface features are comprehensively elucidated through theoretical stimulation and finite element analysis. The results reveal the evolution laws of wrinkles under photochemical boundaries and represent a new effective toolkit for fabricating intricate and captivating patterns in single-layer films.

recolorize: An R package for flexible colour segmentation of biological images

Colour pattern variation provides biological information in fields ranging from disease ecology to speciation dynamics. Comparing colour pattern geometries across images requires colour segmentation, where pixels in an image are assigned to one of a set of colour classes shared by all images. Manual methods for colour segmentation are slow and subjective, while automated methods can struggle with high technical variation in aggregate image sets. We present recolorize, an R package toolbox for human-subjective colour segmentation with functions for batch-processing low-variation image sets and additional tools for handling images from diverse (high-variation) sources. The package also includes export options for a variety of formats and colour analysis packages. This paper illustrates recolorize for three example datasets, including high variation, batch processing and combining with reflectance spectra, and demonstrates the downstream use of methods that rely on this output.

Mechanisms Underlying the Formation and Evolution of Vertebrate Color Patterns

Vertebrates exhibit a wide range of color patterns, which play critical roles in mediating intra- and interspecific communication. Because of their diversity and visual accessibility, color patterns offer a unique and fascinating window into the processes underlying biological organization. In this review, we focus on describing many of the general principles governing the formation and evolution of color patterns in different vertebrate groups. We characterize the types of patterns, review the molecular and developmental mechanisms by which they originate, and discuss their role in constraining or facilitating evolutionary change. Lastly, we outline outstanding questions in the field and discuss different approaches that can be used to address them. Overall, we provide a unifying conceptual framework among vertebrate systems that may guide research into naturally evolved mechanisms underlying color pattern formation and evolution.

Development shapes the evolutionary diversification of rodent stripe patterns

Vertebrate groups have evolved strikingly diverse color patterns. However, it remains unknown to what extent the diversification of such patterns has been shaped by the proximate, developmental mechanisms that regulate their formation. While these developmental mechanisms have long been inaccessible empirically, here we take advantage of recent insights into rodent pattern formation to investigate the role of development in shaping pattern diversification across rodents. Based on a broad survey of museum specimens, we first establish that various rodents have independently evolved diverse patterns consisting of longitudinal stripes, varying across species in number, color, and relative positioning. We then interrogate this diversity using a simple model that incorporates recent molecular and developmental insights into stripe formation in African striped mice. Our results suggest that, on the one hand, development has facilitated pattern diversification: The diversity of patterns seen across species can be generated by a single developmental process, and small changes in this process suffice to recapitulate observed evolutionary changes in pattern organization. On the other hand, development has constrained diversification: Constraints on stripe positioning limit the scope of evolvable patterns, and although pattern organization appears at first glance phylogenetically unconstrained, development turns out to impose a cryptic constraint. Altogether, this work reveals that pattern diversification in rodents can in part be explained by the underlying development and illustrates how pattern formation models can be leveraged to interpret pattern evolution.

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.

Studies of Turing pattern formation in zebrafish skin

Skin patterns are the first example of the existence of Turing patterns in living organisms. Extensive research on zebrafish, a model organism with stripes on its skin, has revealed the principles of pattern formation at the molecular and cellular levels. Surprisingly, although the networks of cell-cell interactions have been observed to satisfy the 'short-range activation and long-range inhibition' prerequisites for Turing pattern formation, numerous individual reactions were not envisioned based on the classical reaction-diffusion model. For example, in real skin, it is not an alteration in concentrations of chemicals, but autonomous migration and proliferation of pigment cells that establish patterns, and cell-cell interactions are mediated via direct contact through cell protrusions. Therefore, the classical reaction-diffusion mechanism cannot be used as it is for modelling skin pattern formation. Various studies are underway to adapt mathematical models to the experimental findings on research into skin patterns, and the purpose of this review is to organize and present them. These novel theoretical methods could be applied to autonomous pattern formation phenomena other than skin patterns. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

The beneficial roles of poisonous skin secretions in survival strategies of the odorous frog Odorrana andersonii

The evolution of predatory, anti-predatory, and defensive strategies regarding environmental adaptation in animals is of significant research interest. In particular, amphibians, who represent a transition between aquatic and terrestrial vertebrates, play an important role in animal evolution. The bioactive skin secretions of amphibians are of specific interest due to their involvement in the crucial physiological functions of amphibian skin. We previously isolated and identified several bioactive peptides, including those showing antioxidant, antimicrobial, and wound-healing properties, from the skin secretions of the odorous frog species Odorrana andersonii. Currently, however, the biological significance of skin secretions in O. andersonii survival remains unclear. Here, we studied the biological significance of skin glands and secretions in regard to environmental adaptations of O. andersonii. Our research found that O. andersonii may secrete and excrete bioactive secretions through many glands (peptides and proteins as the main components in glands) distributed in the skin. The skin secretions not only displayed toxicity but also showed antioxidant, antibacterial, and repair promoting activities, suggesting that they play a protective role in O. andersonii when facing environmental threats. These bioactive skin secretions appear to act as a chemical survival strategy in O. andersonii, allowing the species to gain advantages in survival behavior.

Evolution of pigment cells and patterns: recent insights from teleost fishes

Skin pigment patterns of vertebrates are stunningly diverse, and nowhere more so than in teleost fishes. Several species, including relatives of zebrafish, recently evolved cichlid fishes of East Africa, clownfishes, deep sea fishes, and others are providing insights into pigment pattern evolution. This overview describes recent advances in understanding periodic patterns, like stripes and spots, the loss of patterns, and the role of cell-type diversification in generating pigmentation phenotypes. Advances in this area are being facilitated by the application of modern methods of gene editing, genomics, computational analysis, and other approaches to non-traditional model organisms having interesting pigmentary phenotypes. Several topics worthy of future attention are outlined as well.