Mechanisms of scaling in pattern formation

Information integration during bioelectric regulation of morphogenesis of the embryonic frog brain

Spatiotemporal patterns of cellular resting potential regulate several aspects of development. One key aspect of the bioelectric code is that transcriptional and morphogenetic states are determined not by local, single-cell, voltage levels but by specific distributions of voltage across cell sheets. We constructed and analyzed a minimal dynamical model of collective gene expression in cells based on inputs of multicellular voltage patterns. Causal integration analysis revealed a higher-order mechanism by which information about the voltage pattern was spatiotemporally integrated into gene activity, as well as a division of labor among and between the bioelectric and genetic components. We tested and confirmed predictions of this model in a system in which bioelectric control of morphogenesis regulates gene expression and organogenesis: the embryonic brain of the frog Xenopus laevis. This study demonstrates that machine learning and computational integration approaches can advance our understanding of the information-processing underlying morphogenetic decision-making, with a potential for other applications in developmental biology and regenerative medicine.

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.

Stability of Pattern Formation in Systems with Dynamic Source Regions

We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with a step-function production term, we identify the phase transition between low-precision indeterminate patterning and the phase in which a traveling, well-defined contact zone between two domains is formed. Our model analytically explains single- and two-gene domain dynamics and provides pattern stability conditions for all possible two-gene regulatory network motifs.

Shaping the scaling characteristics of gap gene expression patterns in Drosophila

How patterns are formed to scale with tissue size remains an unresolved problem. Here we investigate embryonic patterns of gap gene expression along the anterior-posterior (AP) axis in Drosophila. We use embryos that greatly differ in length and, importantly, possess distinct length-scaling characteristics of the Bicoid (Bcd) gradient. We systematically analyze the dynamic movements of gap gene expression boundaries in relation to both embryo length and Bcd input as a function of time. We document the process through which such dynamic movements drive both an emergence of a global scaling landscape and evolution of boundary-specific scaling characteristics. We show that, despite initial differences in pattern scaling characteristics that mimic those of Bcd in the anterior, such characteristics of final patterns converge. Our study thus partitions the contributions of Bcd input and regulatory dynamics inherent to the AP patterning network in shaping embryonic pattern's scaling characteristics.

A group theoretic approach to model comparison with simplicial representations

The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. Because biological systems are generally not well understood, most mathematical models of these systems are based on experimental data, resulting in a seemingly heterogeneous collection of models that ostensibly represent the same system. To understand the system we therefore need to understand how the different models are related to each other, with a view to obtaining a unified mathematical description. This goal is complicated by the fact that a number of distinct mathematical formalisms may be employed to represent the same system, making direct comparison of the models very difficult. A methodology for comparing mathematical models based on their underlying conceptual structure is therefore required. In previous work we developed an appropriate framework for model comparison where we represent models, specifically the conceptual structure of the models, as labelled simplicial complexes and compare them with the two general methodologies of comparison by distance and comparison by equivalence. In this article we continue the development of our model comparison methodology in two directions. First, we present a rigorous and automatable methodology for the core process of comparison by equivalence, namely determining the vertices in a simplicial representation, corresponding to model components, that are conceptually related and the identification of these vertices via simplicial operations. Our methodology is based on considerations of vertex symmetry in the simplicial representation, for which we develop the required mathematical theory of group actions on simplicial complexes. This methodology greatly simplifies and expedites the process of determining model equivalence. Second, we provide an alternative mathematical framework for our model-comparison methodology by representing models as groups, which allows for the direct application of group-theoretic techniques within our model-comparison methodology.

Patterning principles of morphogen gradients

Metazoan embryos develop from a single cell into three-dimensional structured organisms while groups of genetically identical cells attain specialized identities. Cells of the developing embryo both create and accurately interpret morphogen gradients to determine their positions and make specific decisions in response. Here, we first cover intellectual roots of morphogen and positional information concepts. Focusing on animal embryos, we then provide a review of current understanding on how morphogen gradients are established and how their spans are controlled. Lastly, we cover how gradients evolve in time and space during development, and how they encode information to control patterning. In sum, we provide a list of patterning principles for morphogen gradients and review recent advances in quantitative methodologies elucidating information provided by morphogens.

Archetypal Architecture Construction, Patterning, and Scaling Invariance in a 3D Embryoid Body Differentiation Model

Self-organized patterning and architecture construction studying is a priority goal for fundamental developmental and stem cell biology. To study the spatiotemporal patterning of pluripotent stem cells of different origins, we developed a three-dimensional embryoid body (EB) differentiation model quantifying volumetric parameters and investigated how the EB architecture formation, patterning, and scaling depend on the proliferation, cavitation, and differentiation dynamics, external environmental factors, and cell numbers. We identified three similar spatiotemporal patterns in the EB architectures, regardless of cell origin, which constitute the EB archetype and mimick the pre-gastrulation embryonic patterns. We found that the EB patterning depends strongly on cellular positional information, culture media factor/morphogen content, and free diffusion from the external environment and between EB cell layers. However, the EB archetype formation is independent of the EB size and initial cell numbers forming EBs; therefore, it is capable of scaling invariance and patterning regulation. Our findings indicate that the underlying principles of reaction-diffusion and positional information concepts can serve as the basis for EB architecture construction, patterning, and scaling. Thus, the 3D EB differentiation model represents a highly reproducible and reliable platform for experimental and theoretical research on developmental and stem cell biology issues.

Temporal scaling in C. elegans larval development

An enduring mystery of development is how its timing is controlled, particularly for development after birth, where timing is highly flexible and depends on environmental conditions, such as food availability and diet. We followed timing of cell- and organism-level events in individual Caenorhabditis elegans larvae developing from hatching to adulthood, uncovering widespread variations in event timing, both between isogenic individuals in the same environment and when changing conditions and genotypes. However, in almost all cases, we found that events occurred at the same time, when time was rescaled by the duration of development measured in each individual. This observation of “temporal scaling” poses strong constraints on models to explain timing of larval development.

It is essential that correct temporal order of cellular events is maintained during animal development. During postembryonic development, the rate of development depends on external conditions, such as food availability, diet, and temperature. How timing of cellular events is impacted when the rate of development is changed at the organism level is not known. We used a unique time-lapse microscopy approach to simultaneously measure timing of oscillatory gene expression, hypodermal stem cell divisions, and cuticle shedding in individual Caenorhabditis elegans larvae, as they developed from hatching to adulthood. This revealed strong variability in timing between isogenic individuals under the same conditions. However, this variability obeyed “temporal scaling,” meaning that events occurred at the same time when measured relative to the total duration of development in each individual. We also observed pervasive changes in timing when temperature, diet, or genotype were varied, but with larval development divided in “epochs” that differed in how event timing was impacted. Yet, these variations in timing were still explained by temporal scaling when time was rescaled by the duration of the respective epochs in each individual. Surprisingly, timing obeyed temporal scaling even in mutants lacking lin-42/Period, presumed a core regulator of timing of larval development, that exhibited strongly delayed, heterogeneous timing. However, shifting conditions middevelopment perturbed temporal scaling and changed event order in a highly condition-specific manner, indicating that a complex machinery is responsible for temporal scaling under constant conditions.

Targeted search for scaling genes reveals matrixmetalloproteinase 3 as a scaler of the dorsal-ventral pattern in Xenopus laevis embryos

How embryos scale patterning according to size is still not fully understood. Through in silico screening and analysis of reaction-diffusion systems that could be responsible for scaling, we predicted the existence of genes whose expression is sensitive to embryo size and which regulate the scaling of embryonic patterning. To find these scalers, we identified genes with strongly altered expression in half-size Xenopus laevis embryos compared with full-size siblings at the gastrula stage. Among found genes, we investigated the role of matrix metalloproteinase-3 (mmp3), which was most strongly downregulated in half-size embryos. We show that Mmp3 scales dorsal-ventral patterning by degrading the slowly diffusing embryonic inducers Noggin1 and Noggin2 but preventing cleavage of the more rapidly diffusing inducer Chordin via degradation of a Tolloid-type proteinase. In addition to unraveling the mechanism underlying the scaling of dorsal-ventral patterning, this work provides proof of principal for scalers identification in embryos of other species.

Molecular and Mechanical Cues for Somite Periodicity

Somitogenesis refers to the segmentation of the paraxial mesoderm, a tissue located on the back of the embryo, into regularly spaced and sized pieces, i.e., the somites. This periodicity is important to assure, for example, the formation of a functional vertebral column. Prevailing models of somitogenesis are based on the existence of a gene regulatory network capable of generating a striped pattern of gene expression, which is subsequently translated into periodic tissue boundaries. An alternative view is that the pre-pattern that guides somitogenesis is not chemical, but of a mechanical origin. A striped pattern of mechanical strain can be formed in physically connected tissues expanding at different rates, as it occurs in the embryo. Here we argue that both molecular and mechanical cues could drive somite periodicity and suggest how they could be integrated.

Scaling of internal organs during Drosophila embryonic development

Many species show a diverse range of sizes; for example, domestic dogs have large variation in body mass. Yet, the internal structure of the organism remains similar, i.e., the system scales to organism size. Drosophila melanogaster has been a powerful model system for exploring scaling mechanisms. In the early embryo, gene expression boundaries scale very precisely to embryo length. Later in development, the adult wings grow with remarkable symmetry and scale well with animal size. Yet, our knowledge of whether internal organs initially scale to embryo size remains largely unknown. Here, we utilize artificially small Drosophila embryos to explore how three critical internal organs-the heart, hindgut, and ventral nerve cord (VNC)-adapt to changes in embryo morphology. We find that the heart scales precisely with embryo length. Intriguingly, reduction in cardiac cell length, rather than number, appears to be important in controlling heart length. The hindgut, which is the first chiral organ to form, displays scaling with embryo size under large-scale changes in the artificially smaller embryos but shows few hallmarks of scaling within wild-type size variation. Finally, the VNC only displays weak scaling behavior; even large changes in embryo geometry result in only small shifts in VNC length. This suggests that the VNC may have an intrinsic minimal length that is largely independent of embryo length. Overall, our work shows that internal organs can adapt to embryo size changes in Drosophila, but the extent to which they scale varies significantly between organs.

Morphology changes induced by intercellular gap junction blocking: A reaction-diffusion mechanism

Complex anatomical form is regulated in part by endogenous physiological communication between cells; however, the dynamics by which gap junctional (GJ) states across tissues regulate morphology are still poorly understood. We employed a biophysical modeling approach combining different signaling molecules (morphogens) to qualitatively describe the anteroposterior and lateral morphology changes in model multicellular systems due to intercellular GJ blockade. The model is based on two assumptions for blocking-induced patterning: (i) the local concentrations of two small antagonistic morphogens diffusing through the GJs along the axial direction, together with that of an independent, uncoupled morphogen concentration along an orthogonal direction, constitute the instructive patterns that modulate the morphological outcomes, and (ii) the addition of an external agent partially blocks the intercellular GJs between neighboring cells and modifies thus the establishment of these patterns. As an illustrative example, we study how the different connectivity and morphogen patterns obtained in presence of a GJ blocker can give rise to novel head morphologies in regenerating planaria. We note that the ability of GJs to regulate the permeability of morphogens post-translationally suggests a mechanism by which different anatomies can be produced from the same genome without the modification of gene-regulatory networks. Conceptually, our model biosystem constitutes a reaction-diffusion information processing mechanism that allows reprogramming of biological morphologies through the external manipulation of the intercellular GJs and the resulting changes in instructive biochemical signals.

Signaling gradients in surface dynamics as basis for planarian regeneration

Based on experimental data, we introduce and analyze a system of reaction-diffusion equations for the regeneration of planarian flatworms. We model dynamics of head and tail cells expressing positional control genes that translate into localized signals which in turn guide stem cell differentiation. Tissue orientation and positional information are encoded in a long range wnt-related signaling gradient. Our system correctly reproduces typical cut and graft experiments, and improves on previous models by preserving polarity in regeneration over orders of magnitude in body size during growth phases. Key to polarity preservation in our model flatworm is the sensitivity of cell differentiation to gradients of wnt-related signals relative to the tissue surface. This process is particularly relevant in small tissue layers close to cuts during their healing, and modeled in a robust fashion through dynamic boundary conditions.

Diversity and robustness of bone morphogenetic protein pattern formation

Pattern formation by bone morphogenetic proteins (BMPs) demonstrates remarkable plasticity and utility in several contexts, such as early embryonic development, tissue patterning and the maintenance of stem cell niches. BMPs pattern tissues over many temporal and spatial scales: BMP gradients as short as 1-2 cell diameters maintain the stem cell niche of the Drosophila germarium over a 24-h cycle, and BMP gradients of several hundred microns establish dorsal-ventral tissue specification in Drosophila, zebrafish and Xenopus embryos in timescales between 30 min and several hours. The mechanisms that shape BMP signaling gradients are also incredibly diverse. Although ligand diffusion plays a dominant role in forming the gradient, a cast of diffusible and non-diffusible regulators modulate gradient formation and confer robustness, including scale invariance and adaptability to perturbations in gene expression and growth. In this Review, we document the diverse ways that BMP gradients are formed and refined, and we identify the core principles that they share to achieve reliable performance.

Growing Up in a Changing World: Environmental Regulation of Development in Insects

All organisms are exposed to changes in their environment throughout their life cycle. When confronted with these changes, they adjust their development and physiology to ensure that they can produce the functional structures necessary for survival and reproduction. While some traits are remarkably invariant, or robust, across environmental conditions, others show high degrees of variation, known as plasticity. Generally, developmental processes that establish cell identity are thought to be robust to environmental perturbation, while those relating to body and organ growth show greater degrees of plasticity. However, examples of plastic patterning and robust organ growth demonstrate that this is not a hard-and-fast rule.In this review, we explore how the developmental context and the gene regulatory mechanisms underlying trait formation determine the impacts of the environment on development in insects. Furthermore, we outline future issues that need to be resolved to understand how the structure of signaling networks defines whether a trait displays plasticity or robustness.

Scaling a Dpp Morphogen Gradient through Feedback Control of Receptors and Co-receptors

Gradients of decapentaplegic (Dpp) pattern Drosophila wing imaginal discs, establishing gene expression boundaries at specific locations. As discs grow, Dpp gradients expand, keeping relative boundary positions approximately stationary. Such scaling fails in mutants for Pentagone (pent), a gene repressed by Dpp that encodes a diffusible protein that expands Dpp gradients. Although these properties fit a recent mathematical model of automatic gradient scaling, that model requires an expander that spreads with minimal loss throughout a morphogen field. Here, we show that Pent's actions are confined to within just a few cell diameters of its site of synthesis and can be phenocopied by manipulating non-diffusible Pent targets strictly within the Pent expression domain. Using genetics and mathematical modeling, we develop an alternative model of scaling driven by feedback downregulation of Dpp receptors and co-receptors. Among the model's predictions is a size beyond which scaling fails-something we observe directly in wing discs.

Integrating cellular dimensions with cell differentiation during early development

Early embryo development is characterized by alteration of cellular dimensions and fating of blastomeres. An emerging concept is that cell size and shape drive cellular differentiation during early embryogenesis in a variety of model organisms. In this review, we summarize recent advances that elucidate the contribution of the physical dimensions of a cell to major embryonic transitions and cell fate specification in vivo. We also highlight techniques and newly evolving methods for manipulating the sizes and shapes of cells and whole embryos in situ and ex vivo. Finally, we provide an outlook for addressing fundamental questions in the field and more broadly uncovering how changes to cell size control decision making in a variety of biological contexts.

Shaping Organs: Shared Structural Principles Across Kingdoms

Development encapsulates the morphogenesis of an organism from a single fertilized cell to a functional adult. A critical part of development is the specification of organ forms. Beyond the molecular control of morphogenesis, shape in essence entails structural constraints and thus mechanics. Revisiting recent results in biophysics and development, and comparing animal and plant model systems, we derive key overarching principles behind the formation of organs across kingdoms. In particular, we highlight how growing organs are active rather than passive systems and how such behavior plays a role in shaping the organ. We discuss the importance of considering different scales in understanding how organs form. Such an integrative view of organ development generates new questions while calling for more cross-fertilization between scientific fields and model system communities.

Pattern formation mechanisms of self-organizing reaction-diffusion systems

Embryonic development is a largely self-organizing process, in which the adult body plan arises from a ball of cells with initially nearly equal potency. The reaction-diffusion theory first proposed by Alan Turing states that the initial symmetry in embryos can be broken by the interplay between two diffusible molecules, whose interactions lead to the formation of patterns. The reaction-diffusion theory provides a valuable framework for self-organized pattern formation, but it has been difficult to relate simple two-component models to real biological systems with multiple interacting molecular species. Recent studies have addressed this shortcoming and extended the reaction-diffusion theory to realistic multi-component networks. These efforts have challenged the generality of previous central tenets derived from the analysis of simplified systems and guide the way to a new understanding of self-organizing processes. Here, we discuss the challenges in modeling multi-component reaction-diffusion systems and how these have recently been addressed. We present a synthesis of new pattern formation mechanisms derived from these analyses, and we highlight the significance of reaction-diffusion principles for developmental and synthetic pattern formation.

Interplay between morphogen-directed positional information systems and physiological signaling

The development of an organism from an undifferentiated single cell into a spatially complex structure requires spatial patterning of cell fates across tissues. Positional information, proposed by Lewis Wolpert in 1969, has led to the characterization of many components involved in regulating morphogen signaling activity. However, how morphogen gradients are established, maintained, and interpreted by cells still is not fully understood. Quantitative and systems-based approaches are increasingly needed to define general biological design rules that govern positional information systems in developing organisms. This short review highlights a selective set of studies that have investigated the roles of physiological signaling in modulating and mediating morphogen-based pattern formation. Similarities between neural transmission and morphogen-based pattern formation mechanisms suggest underlying shared principles of active cell-based communication. Within larger tissues, neural networks provide directed information, via physiological signaling, that supplements positional information through diffusion. Further, mounting evidence demonstrates that physiological signaling plays a role in ensuring robustness of morphogen-based signaling. We conclude by highlighting several outstanding questions regarding the role of physiological signaling in morphogen-based pattern formation. Elucidating how physiological signaling impacts positional information is critical for understanding the close coupling of developmental and cellular processes in the context of development, disease, and regeneration.

Growth control in the Drosophila wing disk

The regulation of size and shape is a fundamental requirement of biological development and has been a subject of scientific study for centuries, but we still lack an understanding of how organisms know when to stop growing. Imaginal wing disks of the fruit fly Drosophila melanogaster, which are precursors of the adult wings, are an archetypal tissue for studying growth control. The growth of the disks is dependent on many inter- and intra-organ factors such as morphogens, mechanical forces, nutrient levels, and hormones that influence gene expression and cell growth. Extracellular signals are transduced into gene-control signals via complex signal transduction networks, and since cells typically receive many different signals, a mechanism for integrating the signals is needed. Our understanding of the effect of morphogens on tissue-level growth regulation via individual pathways has increased significantly in the last half century, but our understanding of how multiple biochemical and mechanical signals are integrated to determine whether or not a cell decides to divide is still rudimentary. Numerous fundamental questions are involved in understanding the decision-making process, and here we review the major biochemical and mechanical pathways involved in disk development with a view toward providing a basis for beginning to understand how multiple signals can be integrated at the cell level, and how this translates into growth control at the level of the imaginal disk. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Cellular Models.

Positional information and tissue scaling during development and regeneration

In order to contribute to the appropriate tissues during development, cells need to know their position within the embryo. This positional information is conveyed by gradients of signaling molecules, termed morphogens, that are produced in specific regions of the embryo and induce concentration-dependent responses in target tissues. Positional information is remarkably robust, and embryos often develop with the correct proportions even if large parts of the embryo are removed. In this Review, we discuss classical embryological experiments and modern quantitative analyses that have led to mechanistic insights into how morphogen gradients adapt, scale and properly pattern differently sized domains. We analyze these experimental findings in the context of mathematical models and synthesize general principles that apply to multiple systems across species and developmental stages.

Integrated K+ channel and K+Cl- cotransporter functions are required for the coordination of size and proportion during development

The coordination of growth during development establishes proportionality within and among the different anatomic structures of organisms. Innate memory of this proportionality is preserved, as shown in the ability of regenerating structures to return to their original size. Although the regulation of this coordination is incompletely understood, mutant analyses of zebrafish with long-finned phenotypes have uncovered important roles for bioelectric signaling in modulating growth and size of the fins and barbs. To date, long-finned mutants identified are caused by hypermorphic mutations, leaving unresolved whether such signaling is required for normal development. We isolated a new zebrafish mutant, schleier, with proportional overgrowth phenotypes caused by a missense mutation and loss of function in the K+-Cl- cotransporter Kcc4a. Creation of dominant negative Kcc4a in wild-type fish leads to loss of growth restriction in fins and barbs, supporting a requirement for Kcc4a in regulation of proportion. Epistasis experiments suggest that Kcc4a and the two-pore potassium channel Kcnk5b both contribute to a common bioelectrical signaling response in the fin. These data suggest that an integrated bioelectric signaling pathway is required for the coordination of size and proportion during development.

Communication codes in developmental signaling pathways

A handful of core intercellular signaling pathways play pivotal roles in a broad variety of developmental processes. It has remained puzzling how so few pathways can provide the precision and specificity of cell-cell communication required for multicellular development. Solving this requires us to quantitatively understand how developmentally relevant signaling information is actively sensed, transformed and spatially distributed by signaling pathways. Recently, single cell analysis and cell-based reconstitution, among other approaches, have begun to reveal the 'communication codes' through which information is represented in the identities, concentrations, combinations and dynamics of extracellular ligands. They have also revealed how signaling pathways decipher these features and control the spatial distribution of signaling in multicellular contexts. Here, we review recent work reporting the discovery and analysis of communication codes and discuss their implications for diverse developmental processes.

Microfluidics on the fly: Inexpensive rapid fabrication of thermally laminated microfluidic devices for live imaging and multimodal perturbations of multicellular systems

Microfluidic devices provide a platform for analyzing both natural and synthetic multicellular systems. Currently, substantial capital investment and expertise are required for creating microfluidic devices using standard soft-lithography. These requirements present barriers to entry for many nontraditional users of microfluidics, including developmental biology laboratories. Therefore, fabrication methodologies that enable rapid device iteration and work "out-of-the-box" can accelerate the integration of microfluidics with developmental biology. Here, we have created and characterized low-cost hybrid polyethylene terephthalate laminate (PETL) microfluidic devices that are suitable for cell and micro-organ culture assays. These devices were validated with mammalian cell lines and the Drosophila wing imaginal disc as a model micro-organ. First, we developed and tested PETLs that are compatible with both long-term cultures and high-resolution imaging of cells and organs. Further, we achieved spatiotemporal control of chemical gradients across the wing discs with a multilayered microfluidic device. Finally, we created a multilayered device that enables controllable mechanical loading of micro-organs. This mechanical actuation assay was used to characterize the response of larval wing discs at different developmental stages. Interestingly, increased deformation of the older wing discs for the same mechanical loading suggests that the compliance of the organ is increased in preparation for subsequent morphogenesis. Together, these results demonstrate the applicability of hybrid PETL devices for biochemical and mechanobiology studies on micro-organs and provide new insights into the mechanics of organ development.

Coordinating Development: How Do Animals Integrate Plastic and Robust Developmental Processes?

Our developmental environment significantly affects myriad aspects of our biology, including key life history traits, morphology, physiology, and our susceptibility to disease. This environmentally-induced variation in phenotype is known as plasticity. In many cases, plasticity results from alterations in the rate of synthesis of important developmental hormones. However, while developmental processes like organ growth are sensitive to environmental conditions, others like patterning - the process that generates distinct cell identities - remain robust to perturbation. This is particularly surprising given that the same hormones that regulate organ growth also regulate organ patterning. In this review, we revisit the current approaches that address how organs coordinate their growth and pattern, and outline our hypotheses for understanding how organs achieve correct pattern across a range of sizes.

A model of neocortical area patterning in the lissencephalic mouse may hold for larger gyrencephalic brains

In the mouse, two telencephalic signaling centers orchestrate embryonic patterning of the cerebral cortex. From the rostral patterning center in the telencephalon, the Fibroblast Growth Factor, FGF8, disperses as a morphogen to establish the rostral to caudal axis of the neocortical area map. FGF8 coordinates with Wnt3a from the cortical hem to regulate graded expression of transcription factors that position neocortical areas, and control hippocampal development. Whether similar signaling centers pattern the much larger cortices of carnivore and primate species, however, is unclear. The limited dispersion range of FGF8 and Wnt3a is inconsistent with patterning larger cortical primordia. Yet the implication that different mechanisms organize cortex in different mammals flies in the face of the tenet that developmental patterning mechanisms are conserved across vertebrate species. In the present study, both signaling centers were identified in the ferret telencephalon, as were expression gradients of the patterning transcription factor genes regulated by FGF8 and Wnt3a. Notably, at the stage corresponding to the peak period of FGF8 signaling in the mouse neocortical primordium (NP), the NP was the same size in ferret and mouse, which would allow morphogen patterning of the ferret NP. Subsequently, the size of ferret neocortex shot past that of the mouse. Images from online databases further suggest that NP growth in humans, too, is slowed in early cortical development. We propose that if early growth in larger brains is held back, mechanisms that pattern the neocortical area map in the mouse could be conserved across mammalian species.

Scale-invariant patterning by size-dependent inhibition of Nodal signalling

Individuals can vary significantly in size, but the proportions of their body plans are often maintained. We generated smaller zebrafish by removing 30% of their cells at blastula stages and found that these embryos developed into normally patterned individuals. Strikingly, the proportions of all germ layers adjusted to the new embryo size within two hours after cell removal. Since Nodal/Lefty signalling controls germ layer patterning, we performed a computational screen for scale-invariant models of this activator/inhibitor system. This analysis predicted that the concentration of the highly diffusive inhibitor Lefty increases in smaller embryos, leading to a decreased Nodal activity range and contracted germ layer dimensions. In vivo studies confirmed that Lefty concentration increased in smaller embryos, and embryos with reduced Lefty levels or with diffusion-hindered Lefty failed to scale their tissue proportions. These results reveal that size-dependent inhibition of Nodal signalling allows scale-invariant patterning.

Scale invariance in natural and artificial collective systems: a review

Self-organized collective coordinated behaviour is an impressive phenomenon, observed in a variety of natural and artificial systems, in which coherent global structures or dynamics emerge from local interactions between individual parts. If the degree of collective integration of a system does not depend on size, its level of robustness and adaptivity is typically increased and we refer to it as scale-invariant. In this review, we first identify three main types of self-organized scale-invariant systems: scale-invariant spatial structures, scale-invariant topologies and scale-invariant dynamics. We then provide examples of scale invariance from different domains in science, describe their origins and main features and discuss potential challenges and approaches for designing and engineering artificial systems with scale-invariant properties.

Growth and size control during development

The size and shape of organs are characteristic for each species. Even when organisms develop to different sizes due to varying environmental conditions, such as nutrition, organ size follows species-specific rules of proportionality to the rest of the body, a phenomenon referred to as allometry. Therefore, for a given environment, organs stop growth at a predictable size set by the species's genotype. How do organs stop growth? How can related species give rise to organs of strikingly different size? No definitive answer has been given to date. One of the major models for the studies of growth termination is the vinegar fly Drosophila melanogaster. Therefore, this review will focus mostly on work carried out in Drosophila to try to tease apart potential mechanisms and identify routes for further investigation. One general rule, found across the animal kingdom, is that the rate of growth declines with developmental time. Therefore, answers to the problem of growth termination should explain this seemingly universal fact. In addition, growth termination is intimately related to the problems of robustness (i.e. precision) and plasticity in organ size, symmetric and asymmetric organ development, and of how the ‘target’ size depends on extrinsic, environmental factors.

Size-reduced embryos reveal a gradient scaling-based mechanism for zebrafish somite formation

Little is known about how the sizes of animal tissues are controlled. A prominent example is somite size, which varies widely both within an individual and across species. Despite intense study of the segmentation clock governing the timing of somite generation, how it relates to somite size is poorly understood. Here, we examine somite scaling and find that somite size at specification scales with the length of the presomitic mesoderm (PSM) despite considerable variation in PSM length across developmental stages and in surgically size-reduced embryos. Measurement of clock period, axis elongation speed and clock gene expression patterns demonstrate that existing models fail to explain scaling. We posit a 'clock and scaled gradient' model, in which somite boundaries are set by a dynamically scaling signaling gradient across the PSM. Our model not only explains existing data, but also makes a unique prediction that we confirm experimentally - the formation of periodic 'echoes' in somite size following perturbation of the size of one somite. Our findings demonstrate that gradient scaling plays a central role in both progression and size control of somitogenesis.

Proliferation of cells with aggregation and communication

Cell proliferation is often considered to occur via front propagation with constant velocity. This scenario proposed by Fisher, Kolmogorov, Petrovsky, and Piskunov is based on the solution of the corresponding mean-field reaction-diffusion equations and does not take into account that due to adhesion the cells have tendency to aggregate and that the rate of cell division may depend on the cell-cell communication. Herein, the author presents extensive Monte Carlo simulations taking both these factors into account and illustrating that the former factor can dramatically modify the spatio-temporal kinetics of cell proliferation. In particular, the conventional relation between the front velocity and diffusion coefficient may fail, the front velocity may appreciably increase with increasing time, and/or the front may be partly or fully smeared on the realistic length scales.

Scaling of Morphogenetic Patterns

Mathematical studies of morphogenetic pattern formation are commonly performed by using reaction-diffusion equations that describe the dynamics of morphogen concentration. Various features of the modeled patterns, including their ability to scale, are analyzed to justify constructed models and to understand the processes responsible for these features in nature. In this chapter, we introduce a method for evaluation of scaling for patterns arising in mathematical models and demonstrate its use by applying it to a set of different models. We introduce a quantity representing the sensitivity of a pattern to changes in the size of the domain, where it forms, and we show how to use it to perform a formal analysis of scaling for chemical patterns forming in continuous systems.

Simulation of Morphogen and Tissue Dynamics

Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modeling this process can provide novel insights into development and the principles that orchestrate the developmental processes. This chapter focuses on the mathematical description and numerical simulation of developmental processes. In particular, we discuss the mathematical representation of morphogen and tissue dynamics on static and growing domains, as well as the corresponding tissue mechanics. In addition, we give an overview of numerical methods that are routinely used to solve the resulting systems of partial differential equations. These include the finite element method and the Lattice Boltzmann method for the discretization as well as the arbitrary Lagrangian-Eulerian method and the Diffuse-Domain method to numerically treat deforming domains.

Mechanisms and Measurements of Scale Invariance of Morphogen Gradients

Morphogen gradients provide positional information to underlying cells that translate the information into differential gene expression and eventually different cell fates. Scale invariance is the property where the gradients of the morphogen adjust proportionately to the size of the domain. Scale invariance of morphogen gradients or patterns of differentiation is a common phenomenon observed between individuals within the same species and between homologous tissues or structures in different species. To determine whether or not a pattern is scale invariant, others and we have developed definitions and measurements of gradient scaling. These include point-wise and global scaling errors as well as global scaling power. Furthermore, there are a number of mathematical conditions for scale invariance of advection-diffusion-reaction models that inform mechanisms of scaling. Herein we provide a deeper perspective on modeling and measurement of scale invariance of morphogen gradients.

A critical-like collective state leads to long-range cell communication in Dictyostelium discoideum aggregation

The transition from single-cell to multicellular behavior is important in early development but rarely studied. The starvation-induced aggregation of the social amoeba Dictyostelium discoideum into a multicellular slug is known to result from single-cell chemotaxis towards emitted pulses of cyclic adenosine monophosphate (cAMP). However, how exactly do transient, short-range chemical gradients lead to coherent collective movement at a macroscopic scale? Here, we developed a multiscale model verified by quantitative microscopy to describe behaviors ranging widely from chemotaxis and excitability of individual cells to aggregation of thousands of cells. To better understand the mechanism of long-range cell—cell communication and hence aggregation, we analyzed cell—cell correlations, showing evidence of self-organization at the onset of aggregation (as opposed to following a leader cell). Surprisingly, cell collectives, despite their finite size, show features of criticality known from phase transitions in physical systems. By comparing wild-type and mutant cells with impaired aggregation, we found the longest cell—cell communication distance in wild-type cells, suggesting that criticality provides an adaptive advantage and optimally sized aggregates for the dispersal of spores.

A multiscale model and imaging data show that cells of the slime mold Dictyostelium discoideum maximize their cell—cell communication range during aggregation by a critical-like state known from phase transitions in physical systems.

Cells are often coupled to each other in cell collectives, such as aggregates during early development, tissues in the developed organism, and tumors in disease. How do cells communicate over macroscopic distances much larger than the typical cell—cell distance to decide how they should behave? Here, we developed a multiscale model of social amoeba, spanning behavior from individuals to thousands of cells. We show that local cell—cell coupling via secreted chemicals may be tuned to a critical value, resulting in emergent long-range communication and heightened sensitivity. Hence, these aggregates are remarkably similar to bacterial biofilms and neuronal networks, all communicating in a pulselike fashion. Similar organizing principles may also aid our understanding of the remarkable robustness in cancer development.

Repeated removal of developing limb buds permanently reduces appendage size in the highly-regenerative axolotl

Matching appendage size to body size is fundamental to animal function. Generating an appropriately-sized appendage is a robust process executed during development which is also critical for regeneration. When challenged, larger animals are programmed to regenerate larger limbs than smaller animals within a single species. Understanding this process has important implications for regenerative medicine. To approach this complex question, models with altered appendage size:body size ratios are required. We hypothesized that repeatedly challenging axolotls to regrow limb buds would affect their developmental program resulting in altered target morphology. We discovered that after 10 months following this experimental procedure, limbs that developed were permanently miniaturized. This altered target morphology was preserved upon amputation and regeneration. Future experiments using this platform should provide critical information about how target limb size is encoded within limb progenitors.

Robustness of spatial patterns in buffered reaction-diffusion systems and its reciprocity with phase plasticity

The robustness of spatial patterns against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively investigated, little is known about a general mechanism for achieving robustness in reaction-diffusion systems. Here, we propose a buffered reaction-diffusion system, in which active states of chemicals mediated by buffer molecules contribute to reactions, and demonstrate that robustness of the pattern wavelength is achieved by the dynamics of the buffer molecule. This robustness is analytically explained as a result of the scaling properties of the buffered system, which also lead to a reciprocal relationship between the wavelength's robustness and the plasticity of the spatial phase upon external perturbations. Finally, we explore the relevance of this reciprocity to biological systems.

Embryoids, organoids and gastruloids: new approaches to understanding embryogenesis

Cells have an intrinsic ability to self-assemble and self-organize into complex and functional tissues and organs. By taking advantage of this ability, embryoids, organoids and gastruloids have recently been generated in vitro, providing a unique opportunity to explore complex embryological events in a detailed and highly quantitative manner. Here, we examine how such approaches are being used to answer fundamental questions in embryology, such as how cells self-organize and assemble, how the embryo breaks symmetry, and what controls timing and size in development. We also highlight how further improvements to these exciting technologies, based on the development of quantitative platforms to precisely follow and measure subcellular and molecular events, are paving the way for a more complete understanding of the complex events that help build the human embryo.

Gene expression boundary scaling and organ size regulation in the Drosophila embryo

How the shape and size of tissues and organs is regulated during development is a major question in developmental biology. Such regulation relies upon both intrinsic cues (such as signaling networks) and extrinsic inputs (such as from neighboring tissues). Here, we focus on pattern formation and organ development during Drosophila embryogenesis. In particular, we outline the importance of both biochemical and mechanical tissue-tissue interactions in size regulation. We describe how the Drosophila embryo can potentially provide novel insights into how shape and size are regulated during development. We focus on gene expression boundary scaling in the early embryo and how size is regulated in three organs (hindgut, trachea, and ventral nerve cord) later in development, with particular focus on the role of tissue-tissue interactions. Overall, we demonstrate that Drosophila embryogenesis provides a suitable model system for studying spatial and temporal scaling and size control in vivo.

Spatial pattern formation in microtubule post-translational modifications and the tight localization of motor-driven cargo

Microtubule (MT) "age" can be interpreted as nucleotide state, lattice defects, or post-translational modification (PTM) such as acetylation and detyrosination. In all three cases, these have been recently shown to have functionally-important effects on the dynamics of MT arrays, and can present spatial and temporal heterogeneity. While mathematical models for MT array densities are well-established, here we present equations describing MT age, defined as the mean time since the MT's building blocks (tubulin) were polymerized from their soluble dimer state. We derive the age equations using a mean first-passage time calculation and two complementary approaches: The continuum limit of spatial discretization model, and an adjoint operator approach. These equations can recapitulate the observation that the oldest (most de-tyrosinated) tubulin in axons is near the middle of axons during neuronal development in chick embryos. Furthermore, PTMs influence motor kinetics up to approximately twofold for off-rates and velocities. Our simulations demonstrate that this relatively weak dependence of motor kinetics is sufficient to target motor cargo to a specific location along the array. This localization is tightly peaked in a way that magnifies the relatively small signal of PTM spatial heterogeneity. Thus, MT age can produce long-range spatial patterning without feedbacks or diffusing signals.

Scaling Pattern to Variations in Size during Development of the Vertebrate Neural Tube

Anatomical proportions are robustly maintained in individuals that vary enormously in size, both within a species and between members of related taxa. However, the mechanisms underlying scaling are still poorly understood. We have examined this phenomenon in the context of the patterning of the ventral neural tube in response to a gradient of the morphogen Sonic hedgehog (SHH) in the chick and zebra finch, two species that differ in size during the time of neural tube patterning. We find that scaling is achieved, at least in part, by altering the sensitivity of the target cells to SHH and appears to be achieved by modulating the ratio of the repressive and activating transcriptional regulators, GLI2 and GLI3. This mechanism contrasts with previous experimental and theoretical analyses of morphogenic scaling that have focused on compensatory changes in the morphogen gradient itself.

Emerging developmental genetic model systems in holometabolous insects

The number of insect species that are amenable to functional genetic studies is growing rapidly and provides many new research opportunities in developmental and evolutionary biology. The holometabolous insects represent a disproportionate percentage of animal diversity and are thus well positioned to provide model species for a wide variety of developmental processes. Here we discuss emerging holometabolous models, and review some recent breakthroughs. For example, flies and midges were found to use structurally unrelated long-range pattern organizers, butterflies and moths revealed extensive pattern formation during oogenesis, new imaging possibilities in the flour beetle Tribolium castaneum showed how embryos break free of their extraembryonic membranes, and the complex genetics governing interspecies difference in head shape were revealed in Nasonia wasps.

Developmental Pattern Formation in Phases

Cells in developing organs undergo a series of changes in their transcriptional state until a complete repertoire of cell types is specified. These changes in cell identity, together with the control of tissue growth, determine the pattern of gene expression in the tissue. Recent studies explore the dynamics of pattern formation during development and provide new insights into the control mechanisms. Changes in morphogen signalling and transcriptional networks control the specification of cell types. This is often followed by a distinct second phase, where pattern is elaborated by tissue growth. Here, we discuss the transitions between distinct phases in pattern formation. We consider the implications of the underlying mechanisms for understanding how reproducible patterns form during development.

Maternal AP determinants in the Drosophila oocyte and embryo

An animal embryo cannot initiate its journey of forming a new life on its own. It must rely on maternally provided resources and inputs to kick-start its developmental process. In Drosophila, the initial polarities of the embryo along both the anterior-posterior (AP) and dorsal-ventral (DV) axes are also specified by maternal determinants. Over the past several decades, genetic and molecular studies have identified and characterized such determinants, as well as the zygotic genetic regulatory networks that control patterning in the early embryo. Extensive studies of oogenesis have also led to a detailed knowledge of the cellular and molecular interactions that control the formation of a mature egg. Despite these efforts, oogenesis and embryogenesis have been studied largely as separate problems, except for qualitative aspects with regard to maternal regulation of the asymmetric localization of maternal determinants. Can oogenesis and embryogenesis be viewed from a unified perspective at a quantitative level, and can that improve our understanding of how robust embryonic patterning is achieved? Here, we discuss the basic knowledge of the regulatory mechanisms controlling oogenesis and embryonic patterning along the AP axis. We explore properties of the maternal Bicoid gradient in relation to embryo size in search for a unified framework for robust AP patterning. WIREs Dev Biol 2016, 5:562-581. doi: 10.1002/wdev.235 For further resources related to this article, please visit the WIREs website.

Scaling of morphogenetic patterns in reaction-diffusion systems

Development of multicellular organisms is commonly associated with the response of individual cells to concentrations of chemical substances called morphogens. Concentration fields of morphogens form a basis for biological patterning and ensure its properties including ability to scale with the size of the organism. While mechanisms underlying the formation of morphogen gradients are reasonably well understood, little is known about processes responsible for their scaling. Here, we perform a formal analysis of scaling for chemical patterns forming in continuous systems. We introduce a quantity representing the sensitivity of systems to changes in their size and use it to analyse scaling properties of patterns forming in a few different systems. Particularly, we consider how scaling properties of morphogen gradients forming in diffusion-decay systems depend on boundary conditions and how the scaling can be improved by passive modulation of morphogens or active transport in the system. We also analyse scaling of morphogenetic signal caused by two opposing gradients and consider scaling properties of patterns forming in activator-inhibitor systems. We conclude with a few possible mechanisms which allow scaling of morphogenetic patterns.