Hox genes regulate digit patterning by controlling the wavelength of a Turing-type mechanism

Distinct ossification trade-offs illuminate the shoulder girdle reconfiguration at the water-to-land transition

The mechanisms of the pectoral girdle transformation at the origin of terrestrial locomotion in vertebrates remain an outstanding problem. The loss of intramembranous bones and the enlargement of endochondral bones resulted in the disarticulation of the pectoral girdle from the skull and the formation of the neck during the fish-to-tetrapod transition. Despite the functional implications of this skeletal shift in the emergence of terrestrial vertebrates, the underlying genetic-developmental alterations have remained enigmatic. Here, we show that in zebrafish pectoral girdle mesodermal cells expressing gli3, a transcription factor gene in the Hedgehog signaling pathway, differentiate into both intramembranous and endochondral bones. Intriguingly, Gli and Hedgehog compound knockout fish exhibited an unexpected combination of actinopterygian fish and stem-tetrapod pectoral girdle characteristics. These ontogenetic and anatomical data suggest that a trade-off between the two distinct ossification pathways is a deeply embedded developmental program in bony fishes and that tuning of this trade-off can generate novel pectoral girdle akin to those of stem-tetrapods at the dawn of vertebrate terrestrialization.

Development necessitates evolutionarily conserved factors

Early-stage generalised transcription factors in biological development are often evolutionarily conserved across species. Here, we find for the first time that similar factors functionally emerge in an alternative medium of development. Through comprehensively analysing a Neural Cellular Automata (NCA) model of morphogenesis, we find multiple properties of the hidden units that are functionally analogous to early factors in biological development. We test the generalisation abilities of our model through transfer learning of other morphologies and find that developmental strategies learnt by the model are reused to grow new body forms by conserving its early generalised factors. Our paper therefore provides evidence that nature did not become locked into one arbitrary method of developing multicellular organisms: the use of early generalised factors as fundamental control mechanisms and the resulting necessity for evolutionary conservation of those factors may be fundamental to development, regardless of the details of how development is implemented.

Unraveling the myths and mysteries of photon avalanching nanoparticles

Photon avalanching (PA) nanomaterials exhibit some of the most nonlinear optical phenomena reported for any material, allowing them to push the frontiers of applications ranging from nanoscale imaging and sensing to optical computing. But PA remains shrouded in mystery, with its underlying physics and limitations misunderstood. Photon avalanching is not, in fact, an avalanche of photons, at least not in the same way that snowballs beget more snowballing in an actual avalanche. In this focus article, we dispel these and other common myths surrounding PA in lanthanide-based nanoparticles and unravel the mysteries of this unique nonlinear optical effect. We hope that removing the misconceptions surrounding avalanching nanoparticles will inspire new interest and applications that harness the giant nonlinearity of PA across a broad range of scientific fields.

Optimal network sizes for most robust Turing patterns

Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor models and generally do not require fine-tuning of parameters as dictated by the Turing conditions. To address these issues, we employ random matrix theory to analyze the Jacobian matrices of larger networks with robust statistical properties. Our analysis reveals that Turing patterns are more likely to occur by chance than previously thought and that the most robust Turing networks have an optimal size, consisting of only a handful of molecular species, thus significantly increasing their identifiability in biological systems. Broadly speaking, this optimal size emerges from a trade-off between the highest stability in small networks and the greatest instability with diffusion in large networks. Furthermore, we find that with multiple immobile nodes, differential diffusion ceases to be important for Turing patterns. Our findings may inform future synthetic biology approaches and provide insights into bridging the gap to complex developmental pathways.

A three-node Turing gene circuit forms periodic spatial patterns in bacteria

Turing patterns are self-organizing systems that can form spots, stripes, or labyrinths. Proposed examples in tissue organization include zebrafish pigmentation, digit spacing, and many others. The theory of Turing patterns in biology has been debated because of their stringent fine-tuning requirements, where patterns only occur within a small subset of parameters. This has complicated the engineering of synthetic Turing gene circuits from first principles, although natural genetic Turing networks have been identified. Here, we engineered a synthetic genetic reaction-diffusion system where three nodes interact according to a non-classical Turing network with improved parametric robustness. The system reproducibly generated stationary, periodic, concentric stripe patterns in growing E. coli colonies. A partial differential equation model reproduced the patterns, with a Turing parameter regime obtained by fitting to experimental data. Our synthetic Turing system can contribute to nanotechnologies, such as patterned biomaterial deposition, and provide insights into developmental patterning programs. A record of this paper's transparent peer review process is included in the supplemental information.

Route to Measure Exact Parameters of Bio-Nanostructures Self-Assembly

Artificial bio-nanocoatings, primarily composed of proteins, offer a broad range of applications across various fields thanks to their unique properties. Proteins, as major components of these structures, enable a high degree of customization, such as mutations, conjugation with other molecules or nanoparticles, or the inclusion of an enzymatic activity. Their ability to self-assembly simplifies the production of bio-nanocoatings, making this process efficient and environment-friendly. Despite these advantages, a comprehensive understanding of the underlying self-assembly mechanism is lacking, and the reaction rates governing this process have not been characterized. In this article, we introduce a novel method to determine the key parameters describing the self-assembly mechanism of bio-nanostructures. For the first time, this approach enables an accurate calculation of the autocatalytic and self-inhibitory parameters controlling the process. Through mathematical modeling, our method enhances the understanding of how the protein-based nanocoatings form and opens new avenues for their application in nanotechnology and synthetic biology. Improved control over the self-assembly processes may enable the development of nanomaterials optimized for specific functions, such as drug delivery, biosensing, and bioactive surface fabrication.

Artificial cell system as a tool for investigating pattern formation mechanisms of intracellular reaction-diffusion waves

Intracellular positional information is crucial for the precise control of biological phenomena, including cell division, polarity, and motility. Intracellular reaction-diffusion (iRD) waves are responsible for regulating positional information within cells as morphogens in multicellular tissues. However, iRD waves are explained by the coupling of biochemical reactions and molecular diffusion which indicates nonlinear systems under far from equilibrium conditions. Because of this complexity, experiments using defined elements rather than living cells containing endogenous factors are necessary to elucidate their pattern formation mechanisms. In this review, we summarize the effectiveness of artificial cell systems for investigating iRD waves derived from their high controllability and ability to emulate cell-size space effects. We describe how artificial cell systems reveal the characteristics of iRD waves, including the mechanisms of wave generation, mode selection, and period regulation. Furthermore, we introduce remaining open questions and discuss future challenges even in Min waves and in applying artificial cell systems to various iRD waves.

Versatile system cores as a conceptual basis for generality in cell and developmental biology

The discovery of general principles underlying the complexity and diversity of cellular and developmental systems is a central and long-standing aim of biology. While new technologies collect data at an ever-accelerating rate, there is growing concern that conceptual progress is not keeping pace. We contend that this is due to a paucity of conceptual frameworks that support meaningful generalizations. This led us to develop the core and periphery (C&P) hypothesis, which posits that many biological systems can be decomposed into a highly versatile core with a large behavioral repertoire and a specific periphery that configures said core to perform one particular function. Versatile cores tend to be widely reused across biology, which confers generality to theories describing them. Here, we introduce this concept and describe examples at multiple scales, including Turing patterning, actomyosin dynamics, multi-cellular morphogenesis, and vertebrate gastrulation. We also sketch its evolutionary basis and discuss key implications and open questions. We propose that the C&P hypothesis could unlock new avenues of conceptual progress in mesoscale biology.

How the zebra got its stripes: Curvature-dependent diffusion orients Turing patterns on three-dimensional surfaces

Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate animal-like patterns for many species. When diffusion of the inhibitor is high enough relative to the activator, a diffusion-driven instability can spontaneously form patterns. However, it is not just the type of pattern but also the orientation that matters, and it remains unclear how patterns are oriented in practice. Here, we propose a mechanism by which the curvature of the surface influences the rate of diffusion, and can recapture the correct orientation of stripes on models of a zebra and of a cat in numerical simulations. Previous work has shown how anisotropic diffusion can give stripe forming reaction-diffusion systems a bias in orientation. From the observation that zebra stripes run around the direction of highest curvature, that is around the torso and legs, we apply this result by modifying the anisotropic diffusion rates based on the local curvature. These results show how local geometry can influence the reaction dynamics to give robust, global-scale patterns. Overall, this model proposes a coupling between the system geometry and reaction-diffusion dynamics that can give global control over the patterning by using only local curvature information. Such a model can give shape and positioning information in animal development without the need for spatially dependent morphogen gradients.

A fibronectin gradient remodels mixed-phase mesoderm

Physical processes ultimately shape tissue during development. Two emerging proposals are that cells migrate toward stiffer tissue (durotaxis) and that the extent of cell rearrangements reflects tissue phase, but it is unclear whether and how these concepts are related. Here, we identify fibronectin-dependent tissue stiffness as a control variable that underlies and unifies these phenomena in vivo. In murine limb bud mesoderm, cells are either caged, move directionally, or intercalate as a function of their location along a stiffness gradient. A modified Landau phase equation that incorporates tissue stiffness accurately predicts cell diffusivity upon loss or gain of fibronectin. Fibronectin is regulated by WNT5A-YAP feedback that controls cell movements, tissue shape, and skeletal pattern. The results identify a key determinant of phase transition and show how fibronectin-dependent directional cell movement emerges in a mixed-phase environment in vivo.

Unraveling biochemical spatial patterns: Machine learning approaches to the inverse problem of stationary Turing patterns

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is challenging. To address this, we aim to solve the inverse problem in artificial and experimental Turing patterns. This task is challenging since patterns are often corrupted by noise and slight changes in initial conditions can lead to different patterns. We used both least squares to explore the problem and physics-informed neural networks to build a noise-robust method. We elucidate the functionality of our network in scenarios mimicking biological noise levels and showcase its application using an experimentally obtained chemical pattern. The findings reveal the significant promise of machine learning in steering the creation of synthetic patterns in bioengineering, thereby advancing our grasp of morphological intricacies within biological systems while acknowledging existing limitations.

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.

Information content and optimization of self-organized developmental systems

A key feature of many developmental systems is their ability to self-organize spatial patterns of functionally distinct cell fates. To ensure proper biological function, such patterns must be established reproducibly, by controlling and even harnessing intrinsic and extrinsic fluctuations. While the relevant molecular processes are increasingly well understood, we lack a principled framework to quantify the performance of such stochastic self-organizing systems. To that end, we introduce an information-theoretic measure for self-organized fate specification during embryonic development. We show that the proposed measure assesses the total information content of fate patterns and decomposes it into interpretable contributions corresponding to the positional and correlational information. By optimizing the proposed measure, our framework provides a normative theory for developmental circuits, which we demonstrate on lateral inhibition, cell type proportioning, and reaction-diffusion models of self-organization. This paves a way toward a classification of developmental systems based on a common information-theoretic language, thereby organizing the zoo of implicated chemical and mechanical signaling processes.

Whole genome resequencing reveals candidate genes for postaxial polydactyly in Large White pigs

Polydactyly is a genetic abnormality that affects both pig welfare and industry profits. Despite efforts to explore the genetic basis of pig polydactyly, progress remains limited. In this study, we analyzed a group of Large White pigs with postaxial polydactyly, including 29 cases and 79 controls from 24 families. High-depth sequencing was performed on 20 pigs, while low-depth sequencing was improved through imputation for the remaining pigs. A genome-wide association study (GWAS) and genetic differentiation were conducted using the resequencing dataset, resulting in the identification of 48 significantly associated SNPs and 27 candidate regions. The genetic differentiation regions on chromosomes 5 and 18, which harbored GWAS-identified SNPs, were delineated as confidence regions. The confidence region at Chr18: 1.850-1.925 Mb covers the fifth intron of LMBR1, a gene that contains an important regulatory element for SHH, known as ZRS. Mutations in this ZRS have been found to cause polydactyly in animals and humans. Therefore, we propose LMBR1 as a prospective candidate gene for postaxial polydactyly. These findings emphasize the importance of exploring the role of ZRS within LMBR1 in the pathogenesis of polydactyly in pigs.

Twinning Engineering of Platinum/Iridium Nanonets as Turing-Type Catalysts for Efficient Water Splitting

The twin boundary, a common lattice plane of mirror-symmetric crystals, may have high reactivity due to special atomic coordination. However, twinning platinum and iridium nanocatalysts are grand challenges due to the high stacking fault energies that are nearly 1 order of magnitude larger than those of easy-twinning gold and silver. Here, we demonstrate that Turing structuring, realized by selective etching of superthin metal film, provides 14.3 and 18.9 times increases in twin-boundary densities for platinum and iridium nanonets, comparable to the highly twinned silver nanocatalysts. The Turing configurations with abundant low-coordination atoms contribute to the formation of nanotwins and create a large active surface area. Theoretical calculations reveal that the specific atom arrangement on the twin boundary changes the electronic structure and reduces the energy barrier of water dissociation. The optimal Turing-type platinum nanonets demonstrated excellent hydrogen-evolution-reaction performance with a 25.6 mV overpotential at 10.0 mA·cm-2 and a 14.8-fold increase in mass activity. And the bifunctional Turing iridium catalysts integrated in the water electrolyzer had a mass activity 23.0 times that of commercial iridium catalysts. This work opens a new avenue for nanocrystal twinning as a facile paradigm for designing high-performance nanocatalysts.

Periodic pattern formation during embryonic development

During embryonic development many organs and structures require the formation of series of repeating elements known as periodic patterns. Ranging from the digits of the limb to the feathers of the avian skin, the correct formation of these embryonic patterns is essential for the future form and function of these tissues. However, the mechanisms that produce these patterns are not fully understood due to the existence of several modes of pattern generation which often differ between organs and species. Here, we review the current state of the field and provide a perspective on future approaches to studying this fundamental process of embryonic development.

A mathematical framework for evo-devo dynamics

Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Classic evolutionary theory indicates that development affects evolution by modulating the genetic covariation upon which selection acts, thus affecting genetic constraints. However, whether genetic constraints are relative, thus diverting adaptation from the direction of steepest fitness ascent, or absolute, thus blocking adaptation in certain directions, remains uncertain. This limits understanding of long-term evolution of developmentally constructed phenotypes. Here we formulate a general, tractable mathematical framework that integrates age progression, explicit development (i.e., the construction of the phenotype across life subject to developmental constraints), and evolutionary dynamics, thus describing the evolutionary and developmental (evo-devo) dynamics. The framework yields simple equations that can be arranged in a layered structure that we call the evo-devo process, whereby five core elementary components generate all equations including those mechanistically describing genetic covariation and the evo-devo dynamics. The framework recovers evolutionary dynamic equations in gradient form and describes the evolution of genetic covariation from the evolution of genotype, phenotype, environment, and mutational covariation. This shows that genotypic and phenotypic evolution must be followed simultaneously to yield a dynamically sufficient description of long-term phenotypic evolution in gradient form, such that evolution described as the climbing of a fitness landscape occurs in "geno-phenotype" space. Genetic constraints in geno-phenotype space are necessarily absolute because the phenotype is related to the genotype by development. Thus, the long-term evolutionary dynamics of developed phenotypes is strongly non-standard: (1) evolutionary equilibria are either absent or infinite in number and depend on genetic covariation and hence on development; (2) developmental constraints determine the admissible evolutionary path and hence which evolutionary equilibria are admissible; and (3) evolutionary outcomes occur at admissible evolutionary equilibria, which do not generally occur at fitness landscape peaks in geno-phenotype space, but at peaks in the admissible evolutionary path where "total genotypic selection" vanishes if exogenous plastic response vanishes and mutational variation exists in all directions of genotype space. Hence, selection and development jointly define the evolutionary outcomes if absolute mutational constraints and exogenous plastic response are absent, rather than the outcomes being defined only by selection. Moreover, our framework provides formulas for the sensitivities of a recurrence and an alternative method to dynamic optimization (i.e., dynamic programming or optimal control) to identify evolutionary outcomes in models with developmentally dynamic traits. These results show that development has major evolutionary effects.

Perspectives on Principles of Cellular Behavior from the Biophysics of Protists

Cells are the fundamental unit of biological organization. Although it may be easy to think of them as little more than the simple building blocks of complex organisms such as animals, single cells are capable of behaviors of remarkable apparent sophistication. This is abundantly clear when considering the diversity of form and function among the microbial eukaryotes, the protists. How might we navigate this diversity in the search for general principles of cellular behavior? Here, we review cases in which the intensive study of protists from the perspective of cellular biophysics has driven insight into broad biological questions of morphogenesis, navigation and motility, and decision making. We argue that applying such approaches to questions of evolutionary cell biology presents rich, emerging opportunities. Integrating and expanding biophysical studies across protist diversity, exploiting the unique characteristics of each organism, will enrich our understanding of general underlying principles.

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.

Morphogenetic metasurfaces: unlocking the potential of turing patterns

The reaction-diffusion principle imagined by Alan Turing in an attempt to explain the structuring of living organisms is leveraged in this work for the procedural synthesis of radiating metasurfaces. The adaptation of this morphogenesis technique ensures the growth of anisotropic cellular patterns automatically arranged to satisfy local electromagnetic constraints, facilitating the radiation of waves controlled in frequency, space, and polarization. Experimental validations of this method are presented, designing morphogenetic metasurfaces radiating far-field circularly polarized beams and generating a polarization-multiplexed hologram in the radiative near-field zone. The exploitation of morphogenesis-inspired models proves particularly well suited for solving generative design problems, converting global physical constraints into local interactions of simulated chemical reactants ensuring the emergence of self-organizing meta-atoms.

Closing the loop on morphogenesis: a mathematical model of morphogenesis by closed-loop reaction-diffusion

Morphogenesis, the establishment and repair of emergent complex anatomy by groups of cells, is a fascinating and biomedically-relevant problem. One of its most fascinating aspects is that a developing embryo can reliably recover from disturbances, such as splitting into twins. While this reliability implies some type of goal-seeking error minimization over a morphogenic field, there are many gaps with respect to detailed, constructive models of such a process. A common way to achieve reliability is negative feedback, which requires characterizing the existing body shape to create an error signal-but measuring properties of a shape may not be simple. We show how cells communicating in a wave-like pattern could analyze properties of the current body shape. We then describe a closed-loop negative-feedback system for creating reaction-diffusion (RD) patterns with high reliability. Specifically, we use a wave to count the number of peaks in a RD pattern, letting us use a negative-feedback controller to create a pattern with N repetitions, where N can be altered over a wide range. Furthermore, the individual repetitions of the RD pattern can be easily stretched or shrunk under genetic control to create, e.g., some morphological features larger than others. This work contributes to the exciting effort of understanding design principles of morphological computation, which can be used to understand evolved developmental mechanisms, manipulate them in regenerative-medicine settings, or engineer novel synthetic morphology constructs with desired robust behavior.

Skeletal-Vascular Interactions in Bone Development, Homeostasis, and Pathological Destruction

Bone is a highly vascularized organ that not only plays multiple roles in supporting the body and organs but also endows the microstructure, enabling distinct cell lineages to reciprocally interact. Recent studies have uncovered relevant roles of the bone vasculature in bone patterning, morphogenesis, homeostasis, and pathological bone destruction, including osteoporosis and tumor metastasis. This review provides an overview of current topics in the interactive molecular events between endothelial cells and bone cells during bone ontogeny and discusses the future direction of this research area to find novel ways to treat bone diseases.

Self-organized collective cell behaviors as design principles for synthetic developmental biology

Over the past two decades, molecular cell biology has graduated from a mostly analytic science to one with substantial synthetic capability. This success is built on a deep understanding of the structure and function of biomolecules and molecular mechanisms. For synthetic biology to achieve similar success at the scale of tissues and organs, an equally deep understanding of the principles of development is required. Here, we review some of the central concepts and recent progress in tissue patterning, morphogenesis and collective cell migration and discuss their value for synthetic developmental biology, emphasizing in particular the power of (guided) self-organization and the role of theoretical advances in making developmental insights applicable in synthesis.

Growth of self-integrated atomic quantum wires and junctions of a Mott semiconductor

Continued advances in quantum technologies rely on producing nanometer-scale wires. Although several state-of-the-art nanolithographic technologies and bottom-up synthesis processes have been used to engineer these wires, critical challenges remain in growing uniform atomic-scale crystalline wires and constructing their network structures. Here, we discover a simple method to fabricate atomic-scale wires with various arrangements, including stripes, X-junctions, Y-junctions, and nanorings. Single-crystalline atomic-scale wires of a Mott insulator, whose bandgap is comparable to those of wide-gap semiconductors, are spontaneously grown on graphite substrates by pulsed-laser deposition. These wires are one unit cell thick and have an exact width of two and four unit cells (1.4 and 2.8 nm) and lengths up to a few micrometers. We show that the nonequilibrium reaction-diffusion processes may play an essential role in atomic pattern formation. Our findings offer a previously unknown perspective on the nonequilibrium self-organization phenomena on an atomic scale, paving a unique way for the quantum architecture of nano-network.

Natural selection and convergent evolution of the HOX gene family in Carnivora

HOX genes play a central role in the development and regulation of limb patterns. For mammals in the order Carnivora, limbs have evolved in different forms, and there are interesting cases of phenotypic convergence, such as the pseudothumb of the giant and red pandas, and the flippers or specialized limbs of the pinnipeds and sea otter. However, the molecular bases of limb development remain largely unclear. Here, we studied the molecular evolution of the HOX9 ~ 13 genes of 14 representative species in Carnivora and explored the molecular evolution of other HOX genes. We found that only one limb development gene, HOXC10, underwent convergent evolution between giant and red pandas and was thus an important candidate gene related to the development of pseudothumbs. No signals of amino acid convergence and natural selection were found in HOX9 ~ 13 genes between pinnipeds and sea otter, but there was evidence of positive selection and rapid evolution in four pinniped species. Overall, few HOX genes evolve via natural selection or convergent evolution, and these could be important candidate genes for further functional validation. Our findings provide insights into potential molecular mechanisms of the development of specialized pseudothumbs and flippers (or specialized limbs).

The developmental basis of fingerprint pattern formation and variation

Fingerprints are complex and individually unique patterns in the skin. Established prenatally, the molecular and cellular mechanisms that guide fingerprint ridge formation and their intricate arrangements are unknown. Here we show that fingerprint ridges are epithelial structures that undergo a truncated hair follicle developmental program and fail to recruit a mesenchymal condensate. Their spatial pattern is established by a Turing reaction-diffusion system, based on signaling between EDAR, WNT, and antagonistic BMP pathways. These signals resolve epithelial growth into bands of focalized proliferation under a precociously differentiated suprabasal layer. Ridge formation occurs as a set of waves spreading from variable initiation sites defined by the local signaling environments and anatomical intricacies of the digit, with the propagation and meeting of these waves determining the type of pattern that forms. Relying on a dynamic patterning system triggered at spatially distinct sites generates the characteristic types and unending variation of human fingerprint patterns.

Universal dynamics of biological pattern formation in spatio-temporal morphogen variations

In biological systems, chemical signals termed morphogens self-organize into patterns that are vital for many physiological processes. As observed by Turing in 1952, these patterns are in a state of continual development, and are usually transitioning from one pattern into another. How do cells robustly decode these spatio-temporal patterns into signals in the presence of confounding effects caused by unpredictable or heterogeneous environments? Here, we answer this question by developing a general theory of pattern formation in spatio-temporal variations of ‘pre-pattern’ morphogens, which determine gene-regulatory network parameters. Through mathematical analysis, we identify universal dynamical regimes that apply to wide classes of biological systems. We apply our theory to two paradigmatic pattern-forming systems, and predict that they are robust with respect to non-physiological morphogen variations. More broadly, our theoretical framework provides a general approach to classify the emergent dynamics of pattern-forming systems based on how the bifurcations in their governing equations are traversed.

Gene expression changes during the evolution of the tetrapod limb

Major changes in the vertebrate anatomy have preceded the conquest of land by the members of this taxon, and continuous changes in limb shape and use have occurred during the later radiation of tetrapods. While the main, conserved mechanisms of limb development have been discerned over the past century using a combination of classical embryological and molecular methods, only recent advances made it possible to identify and study the regulatory changes that have contributed to the evolution of the tetrapod appendage. These advances include the expansion of the model repertoire from traditional genetic model species to non-conventional ones, a proliferation of predictive mathematical models that describe gene interactions, an explosion in genomic data and the development of high-throughput methodologies. These revolutionary innovations make it possible to identify specific mutations that are behind specific transitions in limb evolution. Also, as we continue to apply them to more and more extant species, we can expect to gain a fine-grained view of this evolutionary transition that has been so consequential for our species as well.

Whole-genome identification and construction of the lncRNA-mRNA co-expression network in patients with actinic keratosis

BACKGROUND

Actinic keratosis (AK) is a common premalignant lesion induced by chronic exposure to ultraviolet radiation and may develop into invasive cutaneous squamous carcinoma (cSCC). The identification of specific biomarkers in AK are still unclear. Long non-coding RNAs (lncRNAs), as transcripts of more than 200 nucleotides, significantly involving in multiple biologic processes, especially in the development of tumors.

METHODS

In our study, we obtained data from RNA-sequencing analysis using two AK lesion tissues and three normal cutaneous tissues to comparatively analyze the differentially expressed (DE) lncRNAs and messenger RNAs (mRNAs). Firstly, we used microarray analyses to identify DE lncRNAs and DE mRNAs. Secondly, we performed Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) analysis to analyze the primary function and find out significant pathways of these DE mRNA and lncRNAs. Finally, we used the top ten DE lncRNAs to construct a lncRNA-mRNA co-expression network.

RESULTS

Our results showed that there were a total of 2,097 DE lncRNAs and 2,043 DE mRNAs identified. GO and KEGG analysis and the lncRNA-mRNA co-expression network (using the top 10 DE lncRNAs comprises 130 specific co-expressed mRNAs to construct) indicated that lncRNA uc011fnr.2 may negatively regulate SCIMP and Toll-like receptor 4 (TLR4) and play an important role in Janus kinase-signal transducer and activator of transcription 3 (JAK-STAT3) signaling pathway of AK.

CONCLUSIONS

lncRNA uc011fnr.2 may play an important role in JAK-STAT3 signaling pathway of AK by modulating SCIMP, TLR4 and IL-6. Further research is required to validate the value of lncRNA uc011fnr.2 in the progression of AK.

Cellular reaction gene regulation network for swarm robots with pattern formation maneuvering control

Self-organized pattern formation enables swarm robots to interact with local environments to self-organize into intricate structures generated by gene regulatory network (GRN) control methods without global knowledge. Previous studies have reported that it is challenging to maintain pattern formation stability during maneuvering in the environment due to local morphogenetic reaction rules. Motivated by the mechanism of the GRN in multi-cellular organisms, we propose a novel cellular reaction gene regulatory network (CR-GRN) for pattern formation maneuvering control. In CR-GRN, a cellular reaction network is creatively proposed to depict the robots, environment, virtual target pattern, and their interaction to generate emergent swarm behavior in multi-robot systems. A novel diffusion equation is proposed to simulate the process of morphogen diffusion among cells to ensure stable adaptive pattern generation. In addition, genes, proteins, and morphogens are used to define the internal and external states of cells and form a feedback regulation network. Simulation experiments are conducted to validate the proposed method. The results show that the CR-GRN can satisfy the requirements of turning curvature and maintain the robot's uniformity based on the proposed algorithm. This proves that robots using the CR-GRN can cooperate more effectively to cope in a complicated environment, and maintain a stable formation during maneuvering.

Spatial programming of self-organizing chemical systems using sustained physicochemical gradients from reaction, diffusion and hydrodynamics

Living organisms employ chemical self-organization to build structures, and inspire new strategies to design synthetic systems that spontaneously take a particular form, via a combination of integrated chemical reactions, assembly pathways and physicochemical processes. However, spatial programmability that is required to direct such self-organization is a challenge to control. Thermodynamic equilibrium typically brings about a homogeneous solution, or equilibrium structures such as supramolecular complexes and crystals. This perspective addresses out-of-equilibrium gradients that can be driven by coupling chemical reaction, diffusion and hydrodynamics, and provide spatial differentiation in the self-organization of molecular, ionic or colloidal building blocks in solution. These physicochemical gradients are required to (1) direct the organization from the starting conditions (e.g. a homogeneous solution), and (2) sustain the organization, to prevent it from decaying towards thermodynamic equilibrium. We highlight four different concepts that can be used as a design principle to establish such self-organization, using chemical reactions as a driving force to sustain the gradient and, ultimately, program the characteristics of the gradient: (1) reaction-diffusion coupling; (2) reaction-convection; (3) the Marangoni effect and (4) diffusiophoresis. Furthermore, we outline their potential as attractive pathways to translate chemical reactions and molecular/colloidal assembly into organization of patterns in solution, (dynamic) self-assembled architectures and collectively moving swarms at the micro-, meso- and macroscale, exemplified by recent demonstrations in the literature.

A degenerative process underlying hierarchic transitions in evolution

This paper describes an evolutionary process likely involved in hierarchic transitions in biological evolution at many levels, from genetics to social organization. It is related to the evolutionary process described as contingent neutral evolution (CNE). It involves a sequence of stages initiated by the spontaneous appearance of functional redundancy. This redundancy can be the result of gene duplication, symbiosis, cell-cell interactions, environmental supports, etc. The availability of redundant sources of biological functionality relaxes purifying selection and allows degenerative changes to accumulate in one or more of the duplicates, potentially degrading or otherwise fractionating its function. This degeneration will be effectively neutral so long as another maintains functional integrity. Sexual recombination can potentially sample different combinations of these sub functional alternatives, with the result that favorable synergistic interactions between independently degenerate duplicates will have a non-negligible probability of being uncovered. The expression of such a synergistic combinatorial effect will result in the irreversible degradation of any remaining autonomous functionality, thereby initiating selection to prevent breakup of co-dependency. This becomes relevant to the evolution of hierarchic transitions when two or more organisms reciprocally duplicate functions that each other requires. If the resulting relaxation of selection reliably persists for an extended evolutionary period it will tend to produce complementary degenerative effects in each organism, leading to their irreversible codependency and purifying selection to avoid loss of integrity of their higher order functional unity. This provides a partial inversion of Darwinian logic that explains how the potential costs of the loss of organism autonomy can be mitigated, enabling the incremental transition to a synergistic higher order unit of evolution.

Downregulation of Grem1 expression in the distal limb mesoderm is a necessary precondition for phalanx development

BACKGROUND

The phalanges are the final skeletal elements to form in the vertebrate limb and their identity is regulated by signaling at the phalanx forming region (PFR) located at the tip of the developing digit ray. Here, we seek to explore the relationship between PFR activity and phalanx morphogenesis, which define the most distal limb skeletal elements, and signals associated with termination of limb outgrowth.

RESULTS

As Grem1 is extinguished in the distal chick limb mesoderm, the chondrogenesis marker Aggrecan is up-regulated in the metatarsals and phalanges. Fate mapping confirms that subridge mesoderm cells contribute to the metatarsal and phalanges when subridge Grem1 is down-regulated. Grem1 overexpression specifically blocks chick phalanx development by inhibiting PFR activity. PFR activity and digit development are also disrupted following overexpression of a Gli3 repressor, which results in Grem1 expression in the distal limb and downregulation of Bmpr1b.

CONCLUSIONS

Based on expression and fate mapping studies, we propose that downregulation of Grem1 in the distal limb marks the transition from metatarsal to phalanx development. This suggests that downregulation of Grem1 in the distal limb mesoderm is necessary for phalanx development. Grem1 downregulation allows for full PFR activity and phalanx progenitor cell commitment to digit fate.

Boundary Conditions Cause Different Generic Bifurcation Structures in Turing Systems

Turing’s theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is true under zero-flux boundary conditions. However, under fixed boundary conditions, the Turing bifurcation becomes generically transcritical. We derive these algebraic results through weakly nonlinear analysis and apply them to the Schnakenberg kinetics. We observe that the combination of kinetics and boundary conditions produce their own uncommon boundary complexities that we explore numerically. Overall, this work demonstrates that it is not enough to only consider parameter perturbations in a sensitivity analysis of a specific application. Variations in boundary conditions should also be considered.

Turing patterns by supramolecular self-assembly of a single salphen building block

In the 1950s, Alan Turing showed that concerted reactions and diffusion of activating and inhibiting chemical species can autonomously generate patterns without previous positional information, thus providing a chemical basis for morphogenesis in Nature. However, access to these patterns from only one molecular component that contained all the necessary information to execute agonistic and antagonistic signaling is so far an elusive goal, since two or more participants with different diffusivities are a must. Here, we report on a single-molecule system that generates Turing patterns arrested in the solid state, where supramolecular interactions are used instead of chemical reactions, whereas diffusional differences arise from heterogeneously populated self-assembled products. We employ a family of hydroxylated organic salphen building blocks based on a bis-Schiff-base scaffold with portions responsible for either activation or inhibition of assemblies at different hierarchies through purely supramolecular reactions, only depending upon the solvent dielectric constant and evaporation as fuel.

A novel chromosome 2q24.3-q32.1 microdeletion in a fetus with multiple malformations

BACKGROUND

Terminal or interstitial deletion of chromosome 2q is rarely reported but clinically significant, which can result in developmental malformations and psychomotor retardation in humans. In the present study, we analyzed this deletion to comprehensively clarify the relationship between phenotype and microdeletion region.

METHODS

We collected clinical records of the fetus and summarized patient symptoms. Subsequently, genomic DNA was extracted from fetal tissue or peripheral blood collected from parents. In addition, whole-exome sequencing (WES) and copy number variation sequencing (CNV-seq) were performed.

RESULTS

The fetus presented a previously unreported interstitial deletion of 2q24.3-q32.1. WES and CNV-seq revealed a de novo 18.46 Mb deletion at 2q24.3-q32.1, a region involving 94 protein-coding genes, including HOXD13, MAP3K20, DLX1, DLX2, SCN2A, and SCN1A. The fetus had upper and lower limb malformations, including camptodactyly and syndactyly, along with congenital cardiac defects.

CONCLUSION

Herein, we report a fetus with a novel microdeletion of chromosome 2q24.3-q32.1, likely a heterozygous pathogenic variant. Haploinsufficiency of HOXD13 might be related to limb deformity in the fetus.

Synthetic spatial patterning in bacteria: advances based on novel diffusible signals

Engineering multicellular patterning may help in the understanding of some fundamental laws of pattern formation and thus may contribute to the field of developmental biology. Furthermore, advanced spatial control over gene expression may revolutionize fields such as medicine, through organoid or tissue engineering. To date, foundational advances in spatial synthetic biology have often been made in prokaryotes, using artificial gene circuits. In this review, engineered patterns are classified into four levels of increasing complexity, ranging from spatial systems with no diffusible signals to systems with complex multi-diffusor interactions. This classification highlights how the field was held back by a lack of diffusible components. Consequently, we provide a summary of both previously characterized and some new potential candidate small-molecule signals that can regulate gene expression in Escherichia coli. These diffusive signals will help synthetic biologists to successfully engineer increasingly intricate, robust and tuneable spatial structures.

Homogeneous solution assembled Turing structures with near zero strain semi-coherence interface

Turing structures typically emerge in reaction-diffusion processes far from thermodynamic equilibrium, involving at least two chemicals with different diffusion coefficients (inhibitors and activators) in the classic Turing systems. Constructing a Turing structure in homogeneous solutions is a large challenge because of the similar diffusion coefficients of most small molecule weight species. In this work, we show that Turing structure with near zero strain semi-coherence interfaces is constructed in homogeneous solutions subject to the diffusion kinetics. Experimental results combined with molecular dynamics and numerical simulations confirm the Turing structure in the spinel ferrite films. Furthermore, using the hard-soft acid-base theory, the design of coordination binding can improve the diffusion motion of molecules in homogeneous solutions, increasing the library of Turing structure designs, which provides a greater potential to develop advanced materials.

Patterning, From Conifers to Consciousness: Turing's Theory and Order From Fluctuations

This is a brief account of Turing's ideas on biological pattern and the events that led to their wider acceptance by biologists as a valid way to investigate developmental pattern, and of the value of theory more generally in biology. Periodic patterns have played a key role in this process, especially 2D arrays of oriented stripes, which proved a disappointment in theoretical terms in the case of Drosophila segmentation, but a boost to theory as applied to skin patterns in fish and model chemical reactions. The concept of "order from fluctuations" is a key component of Turing's theory, wherein pattern arises by selective amplification of spatial components concealed in the random disorder of molecular and/or cellular processes. For biological examples, a crucial point from an analytical standpoint is knowing the nature of the fluctuations, where the amplifier resides, and the timescale over which selective amplification occurs. The answer clarifies the difference between "inelegant" examples such as Drosophila segmentation, which is perhaps better understood as a programmatic assembly process, and "elegant" ones expressible in equations like Turing's: that the fluctuations and selection process occur predominantly in evolutionary time for the former, but in real time for the latter, and likewise for error suppression, which for Drosophila is historical, in being lodged firmly in past evolutionary events. The prospects for a further extension of Turing's ideas to the complexities of brain development and consciousness is discussed, where a case can be made that it could well be in neuroscience that his ideas find their most important application.

Mechanical feedback defines organizing centers to drive digit emergence

During embryonic development, digits gradually emerge in a periodic pattern. Although genetic evidence indicates that digit formation results from a self-organizing process, the underlying mechanisms are still unclear. Here, we find that convergent-extension tissue flows driven by active stresses underlie digit formation. These active stresses simultaneously shape cartilage condensations and lead to the emergence of a compressive stress region that promotes high activin/p-SMAD/SOX9 expression, thereby defining digit-organizing centers via a mechanical feedback. In Wnt5a mutants, such mechanical feedback is disrupted due to the loss of active stresses, organizing centers do not emerge, and digit formation is precluded. Thus, digit emergence does not result solely from molecular interactions, as was previously thought, but requires a mechanical feedback that ensures continuous coupling between phalanx specification and elongation. Our work, which links mechanical and molecular signals, provides a mechanistic context for the emergence of organizing centers that may underlie various developmental processes.

A single locus regulates a female-limited color pattern polymorphism in a reptile

Animal coloration is often expressed in periodic patterns that can arise from differential cell migration, yet how these processes are regulated remains elusive. We show that a female-limited polymorphism in dorsal patterning (diamond/chevron) in the brown anole is controlled by a single Mendelian locus. This locus contains the gene CCDC170 that is adjacent to, and coexpressed with, the Estrogen receptor-1 gene, explaining why the polymorphism is female limited. CCDC170 is an organizer of the Golgi-microtubule network underlying a cell's ability to migrate, and the two segregating alleles encode structurally different proteins. Our agent-based modeling of skin development demonstrates that, in principle, a change in cell migratory behaviors is sufficient to switch between the two morphs. These results suggest that CCDC170 might have been co-opted as a switch between color patterning morphs, likely by modulating cell migratory behaviors.

Computational Systems Biology of Morphogenesis

Extracting mechanistic knowledge from the spatial and temporal phenotypes of morphogenesis is a current challenge due to the complexity of biological regulation and their feedback loops. Furthermore, these regulatory interactions are also linked to the biophysical forces that shape a developing tissue, creating complex interactions responsible for emergent patterns and forms. Here we show how a computational systems biology approach can aid in the understanding of morphogenesis from a mechanistic perspective. This methodology integrates the modeling of tissues and whole-embryos with dynamical systems, the reverse engineering of parameters or even whole equations with machine learning, and the generation of precise computational predictions that can be tested at the bench. To implement and perform the computational steps in the methodology, we present user-friendly tools, computer code, and guidelines. The principles of this methodology are general and can be adapted to other model organisms to extract mechanistic knowledge of their 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'.

Rethinking positional information and digit identity: The role of late interdigit signaling

Seminal work from John Fallon's lab has illuminated how digit identity determination involves ongoing late regulation and occurs progressively during phalanx formation. Complementary genetic analyses in mice and several papers in this special issue have begun to flesh out how interdigit signaling accomplishes this, but major questions remain unaddressed, including how uncommitted progenitors from which phalanges arise are maintained, and what factors set limits on digit extension and phalanx number, particularly in mammals. This review summarizes what has been learned in the two decades since control of digit identity by late interdigit signals was first identified and what remains poorly understood, and will hopefully spark renewed interest in a process that is critical to evolutionary limb adaptations but nevertheless remains enigmatic.

The Shh/Gli3 gene regulatory network precedes the origin of paired fins and reveals the deep homology between distal fins and digits

In this study, we show that the inactivation of the gli3 gene in medaka fish results in the formation of larger dorsal and paired fins. These mutant fins display multiple radial bones and fin rays which resemble polydactyly in Gli3-deficient mice. Our molecular and genetic analyses indicate that the size of fish fins is controlled by an ancient mechanism mediated by SHH-GLI signaling that appeared prior to the evolutionary appearance of paired fins. We also show that the key regulatory networks that mediate the expansion of digit progenitor cells in tetrapods were already in place in the fins of the last common ancestor between ray and lobe-finned fishes, suggesting an ancient similarity between distal fins and digits.

One of the central problems of vertebrate evolution is understanding the relationship among the distal portions of fins and limbs. Lacking comparable morphological markers of these regions in fish and tetrapods, these relationships have remained uncertain for the past century and a half. Here we show that Gli3 functions in controlling the proliferative expansion of distal progenitors are shared among dorsal and paired fins as well as tetrapod limbs. Mutant knockout gli3 fins in medaka (Oryzias latipes) form multiple radials and rays, in a pattern reminiscent of the polydactyly observed in Gli3-null mutant mice. In limbs, Gli3 controls both anterior–posterior patterning and cell proliferation, two processes that can be genetically uncoupled. In situ hybridization, quantification of proliferation markers, and analysis of regulatory regions reveal that in paired and dorsal fins, gli3 plays a main role in controlling proliferation but not in patterning. Moreover, gli3 down-regulation in shh mutant fins rescues fin loss in a manner similar to how Gli3 deficiency restores digits in the limbs of Shh mutant mouse embryos. We hypothesize that the Gli3/Shh gene pathway preceded the origin of paired appendages and was originally involved in modulating cell proliferation. Accordingly, the distal regions of dorsal fins, paired fins, and limbs retain a deep regulatory and functional homology that predates the origin of paired appendages.

Systems of pattern formation within developmental biology

Applications of mathematical models to developmental biology have provided helpful insight into various subfields, ranging from the patterning of animal skin to the development of complex organ systems. Systems involved in patterning within morphology present a unique path to explain self-organizing systems. Current efforts show that patterning systems, notably Reaction-Diffusion and specific signaling pathways, provide insight for explaining morphology and could provide novel applications revolving around the formation of biological systems. Furthermore, the application of pattern formation provides a new perspective on understanding developmental biology and pathology research to study molecular mechanisms. The current review is to cover and take a more in-depth overlook at current applications of patterning systems while also building on the principles of patterning of future research in predictive medicine.

Computational biology: Turing's lessons in simplicity

Biophysical modeling of development started with Alan Turing. His two-morphogen reaction-diffusion model was a radical but powerful simplification. Despite its apparent limitations, the model captured real developmental processes that only recently have been validated at the molecular level in many systems. The precision and robustness of reaction-diffusion patterning, despite boundary condition-dependence, remain active areas of investigation in developmental biology.