Forging patterns and making waves from biology to geology: a commentary on Turing (1952) 'The chemical basis of morphogenesis'

The Clock and Wavefront Self-Organizing model recreates the dynamics of mouse somitogenesis in vivo and in vitro

During mouse development, presomitic mesoderm cells synchronize Wnt and Notch oscillations, creating sequential phase waves that pattern somites. Traditional somitogenesis models attribute phase waves to a global modulation of the oscillation frequency. However, increasing evidence suggests that they could arise in a self-organizing manner. Here, we introduce the Sevilletor, a novel reaction-diffusion system that serves as a framework to compare different somitogenesis patterning hypotheses. Using this framework, we propose the Clock and Wavefront Self-Organizing model that considers an excitable self-organizing region where phase waves form independent of global frequency gradients. The model recapitulates the change in relative phase of Wnt and Notch observed during mouse somitogenesis and provides a theoretical basis for understanding the excitability of mouse presomitic mesoderm cells in vitro.

A neural network-based model framework for cell-fate decisions and development

Gene regulatory networks (GRNs) fulfill the essential function of maintaining the stability of cellular differentiation states by sustaining lineage-specific gene expression, while driving the progression of development. However, accounting for the relative stability of intermediate differentiation stages and their divergent trajectories remains a major challenge for models of developmental biology. Here, we develop an empirical data-based associative GRN model (AGRN) in which regulatory networks store multilineage stage-specific gene expression profiles as associative memory patterns. These networks are capable of responding to multiple instructive signals and, depending on signal timing and identity, can dynamically drive the differentiation of multipotent cells toward different cell state attractors. The AGRN dynamics can thus generate diverse lineage-committed cell populations in a robust yet flexible manner, providing an attractor-based explanation for signal-driven cell fate decisions during differentiation and offering a readily generalizable modelling tool that can be applied to a wide variety of cell specification systems.

Exploring the complex dynamics of a diffusive epidemic model: Stability and bifurcation analysis

The recent pandemic has highlighted the need to understand how we resist infections and their causes, which may differ from the ways we often think about treating epidemic diseases. The current study presents an improved version of the susceptible-infected-recovered (SIR) epidemic model, to better comprehend the community's overall dynamics of diseases, involving numerous infectious agents. The model deals with a non-monotone incidence rate that exhibits psychological or inhibitory influence and a saturation treatment rate. It has been identified that depending on the measure of medical resources and the effectiveness of their supply, the model exposes both forward and backward bifurcations where two endemic equilibria coexist with infection-free equilibrium. The model also experiences local and global bifurcations of codimension two, including saddle-node, Hopf, and Bogdanov-Takens bifurcations. Additionally, the stability of equilibrium points is investigated. For a spatially extended SIR model system, we have shown that cross-diffusion allows S and I populations to coexist in a habitat. Also, the Turing instability requirements and Turing bifurcation regime are derived. The relationship between distinct role-playing model parameters and various pattern formations like spot and stripe patterns is validated by carrying out in-depth numerical simulations. The findings in the vicinity of the endemic equilibrium solution demonstrate the significance of positive and negative valued cross-diffusion coefficients in regulating the genesis of spatial patterns in susceptible as well as diseased individuals. The discussion of the findings of epidemiological ramifications concludes the manuscript.

Minimal reaction schemes for pattern formation

We link continuum models of reaction-diffusion systems that exhibit diffusion-driven instability to constraints on the particle-scale interactions underpinning this instability. While innumerable biological, chemical and physical patterns have been studied through the lens of Alan Turing's reaction-diffusion pattern-forming mechanism, the connections between models of pattern formation and the nature of the particle interactions generating them have been relatively understudied in comparison with the substantial efforts that have been focused on understanding proposed continuum systems. To derive the necessary reactant combinations for the most parsimonious reaction schemes, we analyse the emergent continuum models in terms of possible generating elementary reaction schemes. This analysis results in the complete list of such schemes containing the fewest reactions; these are the simplest possible hypothetical mass-action models for a pattern-forming system of two interacting species.

Pudgy mouse rib deformities emanate from abnormal paravertebral longitudinal cartilage/bone accumulations

The pudgy (pu/pu) mouse, caused by a recessive mutation in the Notch family Delta like-3 gene (Dll3), has severe rib, vertebral body and intervertebral disc abnormalities. Using whole-mount preparations and serial histologic sections we demonstrate: 1) localized paravertebral longitudinal cartilage/bone accumulations (PVLC/BAs) invariably associated with branched, fused and asymmetrically spaced ribs that emanate from it laterally; 2) abnormal rib formation immediately adjacent to abnormal vertebral body and intervertebral disc formation in asymmetric right/left fashion; and 3) patterns of rib deformation that differ in each mouse. Normal BALB/c embryo and age-matched non-affected pu/+ mice assessments allow for pu/pu comparisons. The Dll3 Notch family gene is involved in normal somitogenesis via the segmentation clock mechanism. Although pathogenesis of rib deformation is initially triggered by the Dll3 gene mutation, these findings of abnormal asymmetric costo-vertebral region structure imply that differing patterns cannot be attributed to this single gene mutation alone. All findings implicate a dual mechanism of malformation: the Dll3 gene mutation leading to subtle timing differences in traveling oscillation waves of the segmentation clock and further subsequent misdirection of tissue formation by altered chemical reaction-diffusion and epigenetic landscape responses. PVLC/BAs appear as primary supramolecular structures underlying severe rib malformation associated both with time-sensitive segmentation clock mutations and subsequent reactions.

Diffusive mediator feedbacks control the health-to-disease transition of skin inflammation

The spatiotemporal dynamics of inflammation provide vital insights into the understanding of skin inflammation. Skin inflammation primarily depends on the regulatory feedback between pro- and anti-inflammatory mediators. Healthy skin exhibits fading erythema. In contrast, diseased skin exhibits expanding erythema with diverse patterns, which are clinically classified into five types: circular, annular, arcuate, gyrate, and polycyclic. Inflammatory diseases with expanding erythema are speculated to result from the overproduction of pro-inflammatory mediators. However, the mechanism by which feedback selectively drives the transition from a healthy fading erythema to each of the five types of diseased expanding erythema remains unclear. This study theoretically elucidates the imbalanced production between pro- and anti-inflammatory mediators and prospective treatment strategies for each expanding pattern. Our literature survey showed that eleven diseases exhibit some of the five expanding erythema, thereby suggesting a common spatiotemporal regulation underlying different patterns and diseases. Accordingly, a reaction-diffusion model incorporating mediator feedback reproduced the five observed types of diseased expanding and healthy fading patterns. Importantly, the fading pattern transitioned to the arcuate, gyrate, and polycyclic patterns when the productions of anti-inflammatory and pro-inflammatory mediators were lower and higher, respectively than in the healthy condition. Further depletion of anti-inflammatory mediators caused a circular pattern, whereas further overproduction of pro-inflammatory mediators caused an annular pattern. Mechanistically, the bistability due to stabilization of the diseased state exhibits circular and annular patterns, whereas the excitability exhibits the gyrate, polycyclic, arcuate, and fading patterns as the threshold of pro-inflammatory mediator concentration relative to the healthy state increases. These dynamic regulations of diffusive mediator feedback provide effective treatment strategies for mediator production wherein skins recover from each expanding pattern toward a fading pattern. Thus, these strategies can estimate disease severity and risk based on erythema patterns, paving the way for developing noninvasive and personalized treatments for inflammatory skin diseases.

The primacy of temporal dynamics in driving spatial self-organization of soil iron redox patterns

This study investigates mechanisms that generate regularly spaced iron-rich bands in upland soils. These striking features appear in soils worldwide, but beyond a generalized association with changing redox, their genesis is yet to be explained. Upland soils exhibit significant redox fluctuations driven by rainfall, groundwater changes, or irrigation. Pattern formation in such systems provides an opportunity to investigate the temporal aspects of spatial self-organization, which have been heretofore understudied. By comparing multiple alternative mechanisms, we found that regular iron banding in upland soils is explained by coupling two sets of scale-dependent feedbacks, the general principle of Turing morphogenesis. First, clay dispersion and coagulation in iron redox fluctuations amplify soil Fe(III) aggregation and crystal growth to a level that negatively affects root growth. Second, the activation of this negative root response to highly crystalline Fe(III) leads to the formation of rhythmic iron bands. In forming iron bands, environmental variability plays a critical role. It creates alternating anoxic and oxic conditions for required pattern-forming processes to occur in distinctly separated times and determines durations of anoxic and oxic episodes, thereby controlling relative rates of processes accompanying oxidation and reduction reactions. As Turing morphogenesis requires ratios of certain process rates to be within a specific range, environmental variability thus modifies the likelihood that pattern formation will occur. Projected changes of climatic regime could significantly alter many spatially self-organized systems, as well as the ecological functioning associated with the striking patterns they present. This temporal dimension of pattern formation merits close attention in the future.

Optogenetic control of Wnt signaling models cell-intrinsic embryogenic patterning using 2D human pluripotent stem cell culture

In embryonic stem cell (ESC) models for early development, spatially and temporally varying patterns of signaling and cell types emerge spontaneously. However, mechanistic insight into this dynamic self-organization is limited by a lack of methods for spatiotemporal control of signaling, and the relevance of signal dynamics and cell-to-cell variability to pattern emergence remains unknown. Here, we combine optogenetic stimulation, imaging and transcriptomic approaches to study self-organization of human ESCs (hESC) in two-dimensional (2D) culture. Morphogen dynamics were controlled via optogenetic activation of canonical Wnt/β-catenin signaling (optoWnt), which drove broad transcriptional changes and mesendoderm differentiation at high efficiency (>99% cells). When activated within cell subpopulations, optoWnt induced cell self-organization into distinct epithelial and mesenchymal domains, mediated by changes in cell migration, an epithelial to mesenchymal-like transition and TGFβ signaling. Furthermore, we demonstrate that such optogenetic control of cell subpopulations can be used to uncover signaling feedback mechanisms between neighboring cell types. These findings reveal that cell-to-cell variability in Wnt signaling is sufficient to generate tissue-scale patterning and establish a hESC model system for investigating feedback mechanisms relevant to early human embryogenesis.

Physical interactions in non-ideal fluids promote Turing patterns

Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the inhibiting species, and the involved reactions are highly nonlinear. Such reactions can originate from cooperativity, whose physical interactions should also affect diffusion. We here take direct interactions into account and show that they strongly affect Turing patterns. We find that weak repulsion between the activator and inhibitor can substantially lower the required differential diffusivity and reaction nonlinearity. By contrast, strong interactions can induce phase separation, but the resulting length scale is still typically governed by the fundamental reaction-diffusion length scale. Taken together, our theory connects traditional Turing patterns with chemically active phase separation, thus describing a wider range of systems. Moreover, we demonstrate that even weak interactions affect patterns substantially, so they should be incorporated when modelling realistic systems.

Incubation temperature alters stripe formation and head colouration in American alligator hatchlings and is unaffected by estradiol-induced sex reversal

Considerations of the impact climate change has on reptiles are typically focused on habitat change or loss, range shifts and skewed sex ratios in species with temperature-dependent sex determination. Here, we show that incubation temperature alters stripe number and head colouration of hatchling American alligators (Alligator mississippiensis). Animals incubated at higher temperatures (33.5°C) had, on average, one more stripe than those at lower temperatures (29.5°C), and also had significantly lighter heads. These patterns were not affected by estradiol-induced sex reversal, suggesting independence from hatchling sex. Therefore, increases in nest temperatures as a result of climate change have the potential to alter pigmentation patterning, which may have implications for offspring fitness.

Goldilocks mushrooms: How ballistospory has shaped basidiomycete evolution

Ballistospory has been a governing factor in mushroom diversification. Modifications to fruit body morphology are subject to a series of fundamental constraints imposed by this uniquely fungal mechanism. Gill spacing in lamellate mushrooms, tube width in poroid species, and other configurations of the hymenium must comply with the distance that spores shoot themselves from their basidia. This reciprocal relationship between the development of fruit bodies and spores may have been maintained by a form of evolutionary seesaw proposed in this article. The necessity of the accurate gravitropic orientation of gills and tubes is another constraint on mushroom development and physiology, along with the importance of evaporative cooling of the hymenium for successful spore discharge and the aerodynamic shaping of the fruit body to aid dispersal. Ballistospory has been lost in secotioid and gasteroid basidiomycetes whose spores are dispersed by animal vectors and has been replaced by alterative mechanisms of active spore discharge in some species. Partnered with the conclusions drawn from molecular phylogenetic research, the biomechanical themes discussed in this review afford new ways to think about the evolution of basidiomycetes.

Turing's cascade instability supports the coordination of the mind, brain, and behavior

Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor-that of the cascade. The time has come to confront Turing's cascading instability, which suggests a geometrical framework driven by power laws and can be studied using multifractal formalism and multiscale probability density function analysis. Here, we review a rapidly growing body of scientific investigations revealing signatures of cascade instability and their consequences for a perceiving, acting, and thinking organism. We review work related to executive functioning (planning to act), postural control (bodily poise for turning plans into action), and effortful perception (action to gather information in a single modality and action to blend multimodal information). We also review findings on neuronal avalanches in the brain, specifically about neural participation in body-wide cascades. Turing's cascade instability blends the mind, brain, and behavior across space and time scales and provides an alternative to the dominant computer metaphor.

Effect of obstructions on growing Turing patterns

We study how Turing pattern formation on a growing domain is affected by discrete domain discontinuities. We use the Lengyel-Epstein reaction-diffusion model to numerically simulate Turing pattern formation on radially expanding circular domains containing a variety of obstruction geometries, including obstructions spanning the length of the domain, such as walls and slits, and local obstructions, such as small blocks. The pattern formation is significantly affected by the obstructions, leading to novel pattern morphologies. We show that obstructions can induce growth mode switching and disrupt local pattern formation and that these effects depend on the shape and placement of the objects as well as the domain growth rate. This work provides a customizable framework to perform numerical simulations on different types of obstructions and other heterogeneous domains, which may guide future numerical and experimental studies. These results may also provide new insights into biological pattern growth and formation, especially in non-idealized domains containing noise or discontinuities.

The mechanical forces that shape our senses

Developing organs are shaped, in part, by physical interaction with their environment in the embryo. In recent years, technical advances in live-cell imaging and material science have greatly expanded our understanding of the mechanical forces driving organ formation. Here, we provide a broad overview of the types of forces generated during embryonic development and then focus on a subset of organs underlying our senses: the eyes, inner ears, nose and skin. The epithelia in these organs emerge from a common origin: the ectoderm germ layer; yet, they arrive at unique and complex forms over developmental time. We discuss exciting recent animal studies that show a crucial role for mechanical forces in, for example, the thickening of sensory placodes, the coiling of the cochlea and the lengthening of hair. Finally, we discuss how microfabricated organoid systems can now provide unprecedented insights into the physical principles of human development.

Introduction to 'Recent progress and open frontiers in Turing's theory of morphogenesis'

Elucidating pattern forming processes is an important problem in the physical, chemical and biological sciences. Turing's contribution, after being initially neglected, eventually catalysed a huge amount of work from mathematicians, physicists, chemists and biologists aimed towards understanding how steady spatial patterns can emerge from homogeneous chemical mixtures due to the reaction and diffusion of different chemical species. While this theory has been developed mathematically and investigated experimentally for over half a century, many questions still remain unresolved. This theme issue places Turing's theory of pattern formation in a modern context, discussing the current frontiers in foundational aspects of pattern formation in reaction-diffusion and related systems. It highlights ongoing work in chemical, synthetic and developmental settings which is helping to elucidate how important Turing's mechanism is for real morphogenesis, while highlighting gaps that remain in matching theory to reality. The theme issue also surveys a variety of recent mathematical research pushing the boundaries of Turing's original theory to more realistic and complicated settings, as well as discussing open theoretical challenges in the analysis of such models. It aims to consolidate current research frontiers and highlight some of the most promising future directions. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Modern perspectives on near-equilibrium analysis of Turing systems

In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction-diffusion theory. Some of these developments were nascent in Turing's paper, and others have been due to new insights from modern mathematical techniques, advances in numerical simulations and extensive biological experiments. Despite such progress, there are still important gaps between theory and experiment, with many examples of biological patterning where the underlying mechanisms are still unclear. Here, we review modern developments in the mathematical theory pioneered by Turing, showing how his approach has been generalized to a range of settings beyond the classical two-species reaction-diffusion framework, including evolving and complex manifolds, systems heterogeneous in space and time, and more general reaction-transport equations. While substantial progress has been made in understanding these more complicated models, there are many remaining challenges that we highlight throughout. We focus on the mathematical theory, and in particular linear stability analysis of 'trivial' base states. We emphasize important open questions in developing this theory further, and discuss obstacles in using these techniques to understand biological reality. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Insights from chemical systems into Turing-type morphogenesis

In 1952, Alan Turing proposed a theory showing how morphogenesis could occur from a simple two morphogen reaction-diffusion system [Turing, A. M. (1952) Phil. Trans. R. Soc. Lond. A 237, 37-72. (doi:10.1098/rstb.1952.0012)]. While the model is simple, it has found diverse applications in fields such as biology, ecology, behavioural science, mathematics and chemistry. Chemistry in particular has made significant contributions to the study of Turing-type morphogenesis, providing multiple reproducible experimental methods to both predict and study new behaviours and dynamics generated in reaction-diffusion systems. In this review, we highlight the historical role chemistry has played in the study of the Turing mechanism, summarize the numerous insights chemical systems have yielded into both the dynamics and the morphological behaviour of Turing patterns, and suggest future directions for chemical studies into Turing-type morphogenesis. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

The regulatory network for petal anthocyanin pigmentation is shaped by the MYB5a/NEGAN transcription factor in Mimulus

Much of the visual diversity of angiosperms is due to the frequent evolution of novel pigmentation patterns in flowers. The gene network responsible for anthocyanin pigmentation, in particular, has become a model for investigating how genetic changes give rise to phenotypic innovation. In the monkeyflower genus Mimulus, an evolutionarily recent gain of petal lobe anthocyanin pigmentation in M. luteus var. variegatus was previously mapped to genomic region pla2. Here, we use sequence and expression analysis, followed by transgenic manipulation of gene expression, to identify MYB5a—orthologous to the NEGAN transcriptional activator from M. lewisii—as the gene responsible for the transition to anthocyanin-pigmented petals in M. l. variegatus. In other monkeyflower taxa, MYB5a/NEGAN is part of a reaction-diffusion network that produces semi-repeating spotting patterns, such as the array of spots in the nectar guides of both M. lewisii and M. guttatus. Its co-option for the evolution of an apparently non-patterned trait—the solid petal lobe pigmentation of M. l. variegatus—illustrates how reaction-diffusion can contribute to evolutionary novelty in non-obvious ways. Transcriptome sequencing of a MYB5a RNAi line of M. l. variegatus reveals that this genetically simple change, which we hypothesize to be a regulatory mutation in cis to MYB5a, has cascading effects on gene expression, not only on the enzyme-encoding genes traditionally thought of as the targets of MYB5a but also on all of its known partners in the anthocyanin regulatory network.

Influence of survival, promotion, and growth on pattern formation in zebrafish skin

The coloring of zebrafish skin is often used as a model system to study biological pattern formation. However, the small number and lack of movement of chromatophores defies traditional Turing-type pattern generating mechanisms. Recent models invoke discrete short-range competition and long-range promotion between different pigment cells as an alternative to a reaction-diffusion scheme. In this work, we propose a lattice-based “Survival model,” which is inspired by recent experimental findings on the nature of long-range chromatophore interactions. The Survival model produces stationary patterns with diffuse stripes and undergoes a Turing instability. We also examine the effect that domain growth, ubiquitous in biological systems, has on the patterns in both the Survival model and an earlier “Promotion” model. In both cases, domain growth alone is capable of orienting Turing patterns above a threshold wavelength and can reorient the stripes in ablated cells, though the wavelength for which the patterns orient is much larger for the Survival model. While the Survival model is a simplified representation of the multifaceted interactions between pigment cells, it reveals complex organizational behavior and may help to guide future studies.

Fundamental functional differences between gyri and sulci: implications for brain function, cognition, and behavior

Folding of the cerebral cortex is a prominent characteristic of mammalian brains. Alterations or deficits in cortical folding are strongly correlated with abnormal brain function, cognition, and behavior. Therefore, a precise mapping between the anatomy and function of the brain is critical to our understanding of the mechanisms of brain structural architecture in both health and diseases. Gyri and sulci, the standard nomenclature for cortical anatomy, serve as building blocks to make up complex folding patterns, providing a window to decipher cortical anatomy and its relation with brain functions. Huge efforts have been devoted to this research topic from a variety of disciplines including genetics, cell biology, anatomy, neuroimaging, and neurology, as well as involving computational approaches based on machine learning and artificial intelligence algorithms. However, despite increasing progress, our understanding of the functional anatomy of gyro-sulcal patterns is still in its infancy. In this review, we present the current state of this field and provide our perspectives of the methodologies and conclusions concerning functional differentiation between gyri and sulci, as well as the supporting information from genetic, cell biology, and brain structure research. In particular, we will further present a proposed framework for attempting to interpret the dynamic mechanisms of the functional interplay between gyri and sulci. Hopefully, this review will provide a comprehensive summary of anatomo-functional relationships in the cortical gyro-sulcal system together with a consideration of how these contribute to brain function, cognition, and behavior, as well as to mental disorders.

Synthetic Lateral Inhibition in Periodic Pattern Forming Microbial Colonies

Multicellular entities are characterized by intricate spatial patterns, intimately related to the functions they perform. These patterns are often created from isotropic embryonic structures, without external information cues guiding the symmetry breaking process. Mature biological structures also display characteristic scales with repeating distributions of signals or chemical species across space. Many candidate patterning modules have been used to explain processes during development and typically include a set of interacting and diffusing chemicals or agents known as morphogens. Great effort has been put forward to better understand the conditions in which pattern-forming processes can occur in the biological domain. However, evidence and practical knowledge allowing us to engineer symmetry-breaking is still lacking. Here we follow a different approach by designing a synthetic gene circuit in E. coli that implements a local activation long-range inhibition mechanism. The synthetic gene network implements an artificial differentiation process that changes the physicochemical properties of the agents. Using both experimental results and modeling, we show that the proposed system is capable of symmetry-breaking leading to regular spatial patterns during colony growth. Studying how these patterns emerge is fundamental to further our understanding of the evolution of biocomplexity and the role played by self-organization. The artificial system studied here and the engineering perspective on embryogenic processes can help validate developmental theories and identify universal properties underpinning biological pattern formation, with special interest for the area of synthetic developmental biology.

Varieties Of Evolved Forms Of Consciousness, Including Mathematical Consciousness

I shall introduce a complex, apparently unique, cross-disciplinary approach to understanding consciousness, especially ancient forms of mathematical consciousness, based on joint work with Jackie Chappell (Birmingham Biosciences) on the Meta-Configured Genome (MCG) theory. All known forms of consciousness (apart from recent very simple AI forms) are products of biological evolution, in some cases augmented by products of social, or technological evolution. Forms of consciousness differ between organisms with different sensory mechanisms, needs and abilities; and in complex animals can vary across different stages of development before and after birth or hatching or pupation, and before or after sexual and other kinds of maturity (or senility). Those forms can differ across individuals with different natural talents and environments, some with and some without fully functional sense organs or motor control functions (in humans: hearing, sight, touch, taste, smell, proprioception and other senses), along with mechanisms supporting meta-cognitive functions such as recollection, expectation, foreboding, error correction, and so forth, and varying forms of conscious control differing partly because of physical differences, such as conjoined twins sharing body parts. Forms of consciousness can also differ across individuals in different cultures with different shared theories, and social practices (e.g., art-forms, musical traditions, religions, etc.). There are many unanswered questions about such varieties of consciousness in products of biological evolution. Most of the details are completely ignored by most philosophers and scientists who focus only on a small subset of types of human consciousness-resulting in shallow theories. Immanuel Kant was deeper than most, though his insights, especially insights into mathematical consciousness tend to be ignored by recent philosophers and scientists, for bad reasons. This paper, partly inspired by Turing's 1952 paper on chemistry-based morphogenesis, supporting William James' observation that all known forms of consciousness must have been products of biological evolution in combination with other influences, attempts to provide (still tentative and incomplete) foundations for a proper study of the variety of biological and non-biological forms of consciousness, including the types of mathematical consciousness identified by Kant in 1781.

Non-uniform curvature and anisotropic deformation control wrinkling patterns on tori

We investigate wrinkling patterns in a tri-layer torus consisting of an expanding thin outer layer, an intermediate soft layer and an inner core with a tunable shear modulus, inspired by pattern formation in developmental biology, such as follicle pattern formation during the development of chicken embryos. We show from large-scale finite element simulations that hexagonal wrinkling patterns form for stiff cores whereas stripe wrinkling patterns develop for soft cores. Hexagons and stripes co-exist to form hybrid patterns for cores with intermediate stiffness. The governing mechanism for the pattern transition is that the stiffness of the inner core controls the degree to which the major radius of the torus expands - this has a greater effect on deformation in the long direction as compared to the short direction of the torus. This anisotropic deformation alters stress states in the outer layer which change from biaxial (preferred hexagons) to uniaxial (preferred stripes) compression as the core stiffness is reduced. As the outer layer continues to expand, stripe and hexagon patterns will evolve into zigzags and segmented labyrinths, respectively. Stripe wrinkles are observed to initiate at the inner surface of the torus while hexagon wrinkles start from the outer surface as a result of curvature-dependent stresses in the torus. We further discuss the effects of elasticities and geometries of the torus on the wrinkling patterns.

Astromimetics: The dawn of a new era for (bio)materials science?

Composite, multifunctional fine particles are likely to be at the frontier of materials science in the foreseeable future. Here we present a submicron composite particle that mimics the stratified structure of the Earth by having a zero-valent iron core, a silicate/silicide mantle, and a thin carbonaceous crust resembling the biosphere and its biotic deposits. Particles were formulated in a stable colloidal form and made to interact with various types of healthy and cancer cells in vitro. A selective anticancer activity was observed, promising from the point of view of the intended use of the particles for tumor targeting across the blood–brain barrier. As an extension of the idea underlying the fabrication of a particle mimicking the planet Earth, we propose a new field of mimetics within materials science: astromimetics. The astromimetic approach in the context of materials science consists of the design of particles after the structure of celestial bodies. With Earth being the most chemically diverse and fertile out of all the astral bodies known, it is anticipated that the great majority of astromimetic material models will fall in the domain of geo-inspired ones.

Pair correlation functions for identifying spatial correlation in discrete domains

Identifying and quantifying spatial correlation are important aspects of studying the collective behavior of multiagent systems. Pair correlation functions (PCFs) are powerful statistical tools that can provide qualitative and quantitative information about correlation between pairs of agents. Despite the numerous PCFs defined for off-lattice domains, only a few recent studies have considered a PCF for discrete domains. Our work extends the study of spatial correlation in discrete domains by defining a new set of PCFs using two natural and intuitive definitions of distance for a square lattice: the taxicab and uniform metric. We show how these PCFs improve upon previous attempts and compare between the quantitative data acquired. We also extend our definitions of the PCF to other types of regular tessellation that have not been studied before, including hexagonal, triangular, and cuboidal. Finally, we provide a comprehensive PCF for any tessellation and metric, allowing investigation of spatial correlation in irregular lattices for which recognizing correlation is less intuitive.

Emulsion patterns in the wake of a liquid-liquid phase separation front

Miscible liquids can phase separate in response to a composition change. In bulk fluids, the demixing begins on molecular-length scales, which coarsen into macroscopic phases. By contrast, confining a mixture in microfluidic droplets causes sequential phase separation bursts, which self-organize into rings of oil and water to make multilayered emulsions. The spacing in these nonequilibrium patterns is self-similar and scale-free over a range of droplet sizes. We develop a modified Cahn-Hilliard model, in which an immiscibility front with stretched exponential dynamics quantitatively predicts the spacing of the layers. In addition, a scaling law predicts the lifetime of each layer, giving rise to a stepwise release of inner droplets. Analogously, in long rectangular capillaries, a diffusive front yields large-scale oil and water stripes on the time scale of hours. The same theory relates their characteristic length scale to the speed of the front and the rate of mass transport. Control over liquid-liquid phase separation into large-scale patterns finds potential material applications in living cells, encapsulation, particulate design, and surface patterning.

Nonlinear Oscillatory Dynamics of the Hardening of Calcium Phosphate Bone Cements

Here we report on the nonlinear, oscillatory dynamics detected in the evolution of phase composition during the setting of different calcium phosphate cements, two of which evolved toward brushite and one toward hydroxyapatite as the final product. Whereas both brushite-forming cements contained ion-doped β-tricalcium phosphate as the initial phase, the zinc-containing one yielded scholzite as an additional phase during setting and the oscillations between these two products were pronounced throughout the entire 80 h setting period, long after the hardening processes was over from the mechanical standpoint. Oscillations in the copper-containing system involved the amount of brushite as the main product of the hardening reaction and they progressed faster toward an equilibrium point than in the zinc-containing system. Initially detected with the use of in situ energy-dispersive X-ray diffractometry, the oscillations were confirmed with a sufficient level of temporal matching in an in situ Fourier transform infrared spectroscopic analysis. The kinetic reaction analysis based on the Johnson-Mehl-Avrami-Kolmogorov model indicated an edge-controlled nucleation mechanism for brushite. The hydroxyapatite-forming cement comprised gelatin as an additional phase with a role of slowing down diffusion and allowing the detection of otherwise rapid oscillations in crystallinity and in the amount of the apatitic phase on the timescale of minutes. A number of possible causes for these dynamic instabilities were discussed. The classical chemical oscillatory model should not apply to these systems unless in combination with less exotic mechanisms of physicochemical nature. One possibility is that the variations in viscosity, directly affecting diffusion and nucleation rates and accompanying growth and transformation from the lower to the higher interfacial energy per the Ostwald-Lussac rule, are responsible for the oscillatory dynamics. The conception of bone replacement materials and tissue engineering constructs capable of engaging in the dynamics of integration with the natural tissues in compliance with this oscillatory nature may open a new avenue for the future of this type of medical devices. To succeed in this goal, the mechanism of these and similar instabilities must be better understood.

Generation of animal form by the Chordin/Tolloid/BMP gradient: 100 years after D'Arcy Thompson

The classic book "On Growth and Form" by naturalist D'Arcy Thompson was published 100 years ago. To celebrate this landmark, we present experiments in the Xenopus embryo that provide a framework for understanding how simple, quantitative transformations of a morphogen gradient might have affected evolution and morphological diversity of organisms. D'Arcy Thompson proposed that different morphologies might be generated by modifying physical parameters in an underlying system of Cartesian coordinates that pre-existed in Nature and arose during evolutionary history. Chordin is a BMP antagonist secreted by the Spemann organizer located on the dorsal side of the gastrula. Chordin generates a morphogen gradient as first proposed by mathematician Alan Turing. The rate-limiting step of this dorsal-ventral (D-V) morphogen is the degradation of Chordin by the Tolloid metalloproteinase in the ventral side. Chordin is expressed at gastrula on the dorsal side where BMP signaling is low, while at the opposite side peak levels of BMP signaling are reached. In fishes, amphibians, reptiles and birds, high BMP signaling in the ventral region induces transcription of a secreted inhibitor of Tolloid called Sizzled. By depleting Sizzled exclusively in the ventral half of the embryo we were able to expand the ventro-posterior region in an otherwise normal embryo. Conversely, ventral depletion of Tolloid, which stabilizes Chordin, decreased ventral and tail structures, phenocopying the tolloid zebrafish mutation. We explain how historical constraints recorded in the language of DNA become subject to the universal laws of physics when an ancestral reaction-diffusion morphogen gradient dictates form.

Antimicrobial Hydroxyapatite-Gelatin-Silica Composite Pastes with Tunable Setting Properties

Bone grafting is one of the commonest surgical procedures, yet all bone substitutes developed so far suffer from specific weaknesses and the search for a bone graft material with ideal physical and biological properties is still ongoing. Calcium phosphate pastes are the most frequently used synthetic bone grafts, yet they (a) often take an impractically long time to set, (b) release the drug content too fast, and (c) do not form pores large enough to accommodate host cells and foster osseointegration. To make up for these deficiencies, we introduced gelatin and silica to pastes composed of 5-15 nm sized hydroxyapatite nanoparticles and yielded a bioresorbable composite that is compact, yet flowing upon injection; that prevents setting at room temperature, but sets promptly, in minutes, at 37 °C; that displays an increase in surface porosity following immersion in physiological fluids; that allows for sustained release of antibiotics; and that sets in a tunable manner and in clinically relevant time windows: 1-3 minutes at its fastest. Timelapse, in situ X-ray diffraction analysis demonstrated that the setting process is accompanied by an increase in crystallinity of the initially amorphous hydroxyapatite, involving no polymorphic phase transitions in its course. Setting time can be tuned by controlling the weight content of gelatin or powder-to-liquid ratio. The release of vancomycin was slow, ~ 8 % after 2 weeks, and unaffected by the gelatin content. While vancomycin-loaded pastes were effective in reducing the concentration of all bacterial species analyzed, the bacteriostatic effects of the antibiotic-free pastes were pronounced against S. liquefaciens and E. coli. S. liquefaciens bacilli underwent beading and filamentation during the treatment, suggesting that the antimicrobial effects are attributable to cell wall disruption by hydroxyapatite nanoparticles. Vancomycin-loaded pastes augmented the activity of the antibiotic against P. aeruginosa and S. liquefaciens, while exhibiting no negative effects against human mesenchymal stem cells. They were also uptaken three times more abundantly than pure hydroxyapatite, indicating the theoretical favorability of their use for intracellular delivery of therapeutics. This selectivity, toxic for bacteria and harmless for primary stem cells, is promising for application as bone grafts for osteomyelitis.

Earthicle: The Design of a Conceptually New Type of Particle

The conception and the steps made in the design of a conceptually new type of composite particle, so-called "earthicle", are being described. This particle is meant to roughly mimic the layered structure of the Earth, having zerovalent iron core, silicate mantle, and a thin carbonaceous crust resembling the biosphere and its geological remnants. Particles are made in a stable colloidal form in an aqueous medium, involving chemical precipitation and pyrolysis of citric acid in the solution. The effects of various synthesis parameters were studied, including borohydride and oleate concentrations, APTES/TEOS molar ratio, chemical nature of the carbon precursors, and others. XRD analysis confirmed the predominantly zerovalent iron composition of the core, amorphous silica and crystalline iron silicate/silicide composition of the mesolayer, and the carbonaceous, amorphous graphitic composition of the surface coating. The atomically thin carbon shell was also detected as a distinct shoulder on the broad n-π* absorption resonance and the peak at ∼300 nm, a signature of sp² hybridized electronic orbitals and the result of the interband π-π* transition characteristic of graphitic structures. The irregularity of the shape of generally round Fe⁰ particles has caused the uniformity of the silica shell to be directly proportional to the particle size. The size of the earthicles ranged from 60 to 500 nm depending on the ionic concentration of the precursors and additives. Silica layer effectively prevented the aggregation of the iron core and increased the biocompatibility of the particles. The point of zero charge first increased from the acidic to the neutral range after coating Fe⁰ core with the APTES-functionalized, aminated silica shell and then restored its low value after depositing the carboxylated carbonic crust in a charge-reversal process designed to facilitate the formation of core-multishell structures. Tested on K7M2 osteosarcoma cell line and primary kidney and lung fibroblasts, cytotoxicity was cell-line dependent; however, the trend assessed in both planar and 3D cell culture with respect to the three types of particles, Fe⁰, Fe/SiO₂, and Fe/SiO₂/C, was general and independent of the cell line. Thus, the pronounced toxicity of Fe⁰ alone became neutralized after the silica layer was coated around Fe⁰. The further addition of the carbonic layer reduced the viability as compared to Fe/SiO₂, albeit in a statistically significant manner only for K7M2 cell line when compared against the untreated control. Cell response also varied depending on the formulation: while some formulations exhibited lethal effects on kidney fibroblasts, were harmless to lung fibroblasts, and boosted the proliferation of K7M2 osteosarcoma cells, other formulations exhibited the opposite behavior despite being similar in terms of their core/double-shell structure. Compared across three different cancerous cell lines, K7M2 osteosarcoma and U87 and E297 glioblastoma, a similar cell-line dependency in response was observed, yet the viability reduction was consistent for all Fe/SiO₂/C particles, ranging from 80% to 85% of the untreated control. Carbon surface layer, albeit of graphitic structural nature, was of a markedly more viable character than that of nanosized graphene oxide. The viability of lung fibroblasts incubated with Fe/SiO₂/C particles was reduced in the presence of the alternating magnetic field of 312.75 A/m and 1 MHz, while the viability reduction caused by Fe/SiO₂/C particles in kidney fibroblasts and K7M2 cells was converted from statistically insignificant to significant, suggesting that the composite particles could be used for hyperthermia treatments, although their properties should be optimized for a more intense effect. A single-cell immunofluorescent analysis of the interaction of primary kidney fibroblasts and K7M2 osteosarcoma cells with Fe/SiO₂/C particles demonstrated that the cell uptake and perinuclear localization may be responsible for the necrotic effects. This analysis also showed that composite Fe/SiO₂/C particles may have the ability to cause the rupture of the cancer cell nucleus while having a harmless effect on the primary cells. Such a promising and selective anticancer activity will be investigated in more detail in future studies.

The heterocyst regulatory protein HetP and its homologs modulate heterocyst commitment in Anabaena sp. strain PCC 7120

The commitment of differentiating cells to a specialized fate is fundamental to the correct assembly of tissues within a multicellular organism. Because commitment is often irreversible, entry into and progression through this phase of development must be tightly regulated. Under nitrogen-limiting conditions, the multicellular cyanobacterium Anabaena sp. strain PCC 7120 terminally commits ∼10% of its cells to become specialized nitrogen-fixing heterocysts. Although commitment is known to occur 9-14 h after the induction of differentiation, the factors that regulate the initiation and duration of this phase have yet to be elucidated. Here, we report the identification of four genes that share a functional domain and modulate heterocyst commitment: hetP (alr2818), asl1930, alr2902, and alr3234 Epistatic relationships between all four genes relating to commitment were revealed by deleting them individually and in combination; asl1930 and alr3234 acted most upstream to delay commitment, alr2902 acted next in the pathway to inhibit development, and hetP acted most downstream to drive commitment forward. Possible protein-protein interactions between HetP, its homologs, and the heterocyst master regulator, HetR, were assessed, and interaction partners were defined. Finally, patterns of gene expression for each homolog, as determined by promoter fusions to gfp and reverse transcription-quantitative PCR, were distinct from that of hetP in both spatiotemporal organization and regulation. We posit that a dynamic succession of protein-protein interactions modulates the timing and efficiency of the commitment phase of development and note that this work highlights the utility of a multicellular cyanobacterium as a model for the study of developmental processes.

Toward Synthetic Spatial Patterns in Engineered Cell Populations with Chemotaxis

A major force shaping form and patterns in biology is based in the presence of amplification mechanisms able to generate ordered, large-scale spatial structures out of local interactions and random initial conditions. Turing patterns are one of the best known candidates for such ordering dynamics, and their existence has been proven in both chemical and physical systems. Their relevance in biology, although strongly supported by indirect evidence, is still under discussion. Extensive modeling approaches have stemmed from Turing's pioneering ideas, but further confirmation from experimental biology is required. An alternative possibility is to engineer cells so that self-organized patterns emerge from local communication. Here we propose a potential synthetic design based on the interaction between population density and a diffusing signal, including also directed motion in the form of chemotaxis. The feasibility of engineering such a system and its implications for developmental biology are also assessed.

Where to Go: Breaking the Symmetry in Cell Motility

Cell migration in the “correct” direction is pivotal for many biological processes. Although most work is devoted to its molecular mechanisms, the cell’s preference for one direction over others, thus overcoming intrinsic random motility, epitomizes a profound principle that underlies all complex systems: the choice of one axis, in structure or motion, from a uniform or symmetric set of options. Explaining directional motility by an external chemo-attractant gradient does not solve but only shifts the problem of causation: whence the gradient? A new study in PLOS Biology shows cell migration in a self-generated gradient, offering an opportunity to take a broader look at the old dualism of extrinsic instruction versus intrinsic symmetry-breaking in cell biology.

Directional cell motility is enabled by chemoattractant gradient and symmetry-breaking. This Primer argues that the recent observation of cells generating a gradient in a uniformly distributed nutrient reveals the multilayered nature of symmetry-breaking in cell locomotion.

Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment

This citizen science study evaluates the occurrence of Fibonacci structure in the spirals of sunflower (Helianthus annuus) seedheads. This phenomenon has competing biomathematical explanations, and our core premise is that observation of both Fibonacci and non-Fibonacci structure is informative for challenging such models. We collected data on 657 sunflowers. In our most reliable data subset, we evaluated 768 clockwise or anticlockwise parastichy numbers of which 565 were Fibonacci numbers, and a further 67 had Fibonacci structure of a predefined type. We also found more complex Fibonacci structures not previously reported in sunflowers. This is the third, and largest, study in the literature, although the first with explicit and independently checkable inclusion and analysis criteria and fully accessible data. This study systematically reports for the first time, to the best of our knowledge, seedheads without Fibonacci structure. Some of these are approximately Fibonacci, and we found in particular that parastichy numbers equal to one less than a Fibonacci number were present significantly more often than those one more than a Fibonacci number. An unexpected further result of this study was the existence of quasi-regular heads, in which no parastichy number could be definitively assigned.

2- and 3-dimensional synthetic large-scale de novo patterning by mammalian cells through phase separation

Synthetic biology provides an opportunity for the construction and exploration of alternative solutions to biological problems - solutions different from those chosen by natural life. To this end, synthetic biologists have built new sensory systems, cellular memories, and alternative genetic codes. There is a growing interest in applying synthetic approaches to multicellular systems, especially in relation to multicellular self-organization. Here we describe a synthetic biological system that confers large-scale de novo patterning activity on 2-D and 3-D populations of mammalian cells. Instead of using the reaction-diffusion mechanisms common in real embryos, our system uses cadherin-mediated phase separation, inspired by the known phenomenon of cadherin-based sorting. An engineered self-organizing, large-scale patterning system requiring no prior spatial cue may be a significant step towards the construction of self-assembling synthetic tissues.

Organoids and the genetically encoded self-assembly of embryonic stem cells

Understanding the mechanisms of early embryonic patterning and the timely allocation of specific cells to embryonic regions and fates as well as their development into tissues and organs, is a fundamental problem in Developmental Biology. The classical explanation for this process had been built around the notion of positional information. Accordingly the programmed appearance of sources of Morphogens at localized positions within a field of cells directs their differentiation. Recently, the development of organs and tissues from unpatterned and initially identical stem cells (adult and embryonic) has challenged the need for positional information and even the integrity of the embryo, for pattern formation. Here we review the emerging area of organoid biology from the perspective of Developmental Biology. We argue that the events underlying the development of these systems are not purely linked to self-organization, as often suggested, but rather to a process of genetically encoded self-assembly where genetic programs encode and control the emergence of biological structures.

The mechanisms of spatial and temporal patterning of cell-edge dynamics

Adherent cells migrate and change their shape by means of protrusion and retraction at their edges. When and where these activities occur defines the shape of the cell and the way it moves. Despite a great deal of knowledge about the structural organization, components, and biochemical reactions involved in protrusion and retraction, the origins of their spatial and temporal patterns are still poorly understood. Chemical signaling circuitry is believed to be an important source of patterning, but recent studies highlighted mechanisms based on physical forces, motion, and mechanical feedback.