'Big frog, small frog'--maintaining proportions in embryonic development: delivered on 2 July 2008 at the 33rd FEBS Congress in Athens, Greece

The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning

In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying the foundations of morphogenesis as a self-organized process emerging from physicochemical first principles. Regrettably, this approach has been widely doubted in the field of developmental biology. First, we summarize Turing's line of thoughts to alleviate the misconception that RD is an artificial mathematical construct. Second, we discuss why phenomenological RD models are particularly effective for understanding skin color patterning at the meso/macroscopic scales, without the need to parameterize the profusion of variables at lower scales. More specifically, we discuss how RD models (a) recapitulate the diversity of actual skin patterns, (b) capture the underlying dynamics of cellular interactions, (c) interact with tissue size and shape, (d) can lead to ordered sequential patterning, (e) generate cellular automaton dynamics in lizards and snakes, (f) predict actual patterns beyond their statistical features, and (g) are robust to model variations. Third, we discuss the utility of linear stability analysis and perform numerical simulations to demonstrate how deterministic RD emerges from the underlying chaotic microscopic agents.

Long-range morphogen gradient formation by cell-to-cell signal propagation

Morphogen gradients are a central concept in developmental biology. Their formation often involves the secretion of morphogens from a local source, that spread by diffusion in the cell field, where molecules eventually get degraded. This implies limits to both the time and length scales over which morphogen gradients can form which are set by diffusion coefficients and degradation rates. Towards the goal of identifying plausible mechanisms capable of extending the gradient range, we here use theory to explore properties of a cell-to-cell signaling relay. Inspired by the millimeter-scale Wnt-expression and signaling gradients in flatworms, we consider morphogen-mediated morphogen production in the cell field. We show that such a relay can generate stable morphogen and signaling gradients that are oriented by a local, morphogen-independent source of morphogen at a boundary. This gradient formation can be related to an effective diffusion and an effective degradation that result from morphogen production due to signaling relay. If the secretion of morphogen produced in response to the relay is polarized, it further gives rise to an effective drift. We find that signaling relay can generate long-ranged gradients in relevant times without relying on extreme choices of diffusion coefficients or degradation rates, thus exceeding the limits set by physiological diffusion coefficients and degradation rates. A signaling relay is hence an attractive principle to conceptualize long-range gradient formation by slowly diffusing morphogens that are relevant for patterning in adult contexts such as regeneration and tissue turn-over.

A role for Flower and cell death in controlling morphogen gradient scaling

During development, morphogen gradients encode positional information to pattern morphological structures during organogenesis¹. Some gradients, like that of Dpp in the fly wing, remain proportional to the size of growing organs-that is, they scale. Gradient scaling keeps morphological patterns proportioned in organs of different sizes^2,3. Here we show a mechanism of scaling that ensures that, when the gradient is smaller than the organ, cell death trims the developing tissue to match the size of the gradient. Scaling is controlled by molecular associations between Dally and Pentagone, known factors involved in scaling, and a key factor that mediates cell death, Flower^4-6. We show that Flower activity in gradient expansion is not dominated by cell death, but by the activity of Dally/Pentagone on scaling. Here we show a potential connection between scaling and cell death that may uncover a molecular toolbox hijacked by tumours.

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.

The Biophysics of Regenerative Repair Suggests New Perspectives on Biological Causation

Evolution exploits the physics of non-neural bioelectricity to implement anatomical homeostasis: a process in which embryonic patterning, remodeling, and regeneration achieve invariant anatomical outcomes despite external interventions. Linear "developmental pathways" are often inadequate explanations for dynamic large-scale pattern regulation, even when they accurately capture relationships between molecular components. Biophysical and computational aspects of collective cell activity toward a target morphology reveal interesting aspects of causation in biology. This is critical not only for unraveling evolutionary and developmental events, but also for the design of effective strategies for biomedical intervention. Bioelectrical controls of growth and form, including stochastic behavior in such circuits, highlight the need for the formulation of nuanced views of pathways, drivers of system-level outcomes, and modularity, borrowing from concepts in related disciplines such as cybernetics, control theory, computational neuroscience, and information theory. This approach has numerous practical implications for basic research and for applications in regenerative medicine and synthetic bioengineering.

The Cognitive Lens: a primer on conceptual tools for analysing information processing in developmental and regenerative morphogenesis

Brains exhibit plasticity, multi-scale integration of information, computation and memory, having evolved by specialization of non-neural cells that already possessed many of the same molecular components and functions. The emerging field of basal cognition provides many examples of decision-making throughout a wide range of non-neural systems. How can biological information processing across scales of size and complexity be quantitatively characterized and exploited in biomedical settings? We use pattern regulation as a context in which to introduce the Cognitive Lens-a strategy using well-established concepts from cognitive and computer science to complement mechanistic investigation in biology. To facilitate the assimilation and application of these approaches across biology, we review tools from various quantitative disciplines, including dynamical systems, information theory and least-action principles. We propose that these tools can be extended beyond neural settings to predict and control systems-level outcomes, and to understand biological patterning as a form of primitive cognition. We hypothesize that a cognitive-level information-processing view of the functions of living systems can complement reductive perspectives, improving efficient top-down control of organism-level outcomes. Exploration of the deep parallels across diverse quantitative paradigms will drive integrative advances in evolutionary biology, regenerative medicine, synthetic bioengineering, cognitive neuroscience and artificial intelligence. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Critical Point in Self-Organized Tissue Growth

We present a theory of pattern formation in growing domains inspired by biological examples of tissue development. Gradients of signaling molecules regulate growth, while growth changes these graded chemical patterns by dilution and advection. We identify a critical point of this feedback dynamics, which is characterized by spatially homogeneous growth and proportional scaling of patterns with tissue length. We apply this theory to the biological model system of the developing wing of the fruit fly Drosophila melanogaster and quantitatively identify signatures of the critical point.

The bioelectric code: An ancient computational medium for dynamic control of growth and form

What determines large-scale anatomy? DNA does not directly specify geometrical arrangements of tissues and organs, and a process of encoding and decoding for morphogenesis is required. Moreover, many species can regenerate and remodel their structure despite drastic injury. The ability to obtain the correct target morphology from a diversity of initial conditions reveals that the morphogenetic code implements a rich system of pattern-homeostatic processes. Here, we describe an important mechanism by which cellular networks implement pattern regulation and plasticity: bioelectricity. All cells, not only nerves and muscles, produce and sense electrical signals; in vivo, these processes form bioelectric circuits that harness individual cell behaviors toward specific anatomical endpoints. We review emerging progress in reading and re-writing anatomical information encoded in bioelectrical states, and discuss the approaches to this problem from the perspectives of information theory, dynamical systems, and computational neuroscience. Cracking the bioelectric code will enable much-improved control over biological patterning, advancing basic evolutionary developmental biology as well as enabling numerous applications in regenerative medicine and synthetic bioengineering.

Dynamics of BMP signaling and distribution during zebrafish dorsal-ventral patterning

During vertebrate embryogenesis, dorsal-ventral patterning is controlled by the BMP/Chordin activator/inhibitor system. BMP induces ventral fates, whereas Chordin inhibits BMP signaling on the dorsal side. Several theories can explain how the distributions of BMP and Chordin are regulated to achieve patterning, but the assumptions regarding activator/inhibitor diffusion and stability differ between models. Notably, ‘shuttling’ models in which the BMP distribution is modulated by a Chordin-mediated increase in BMP diffusivity have gained recent prominence. Here, we directly test five major models by measuring the biophysical properties of fluorescently tagged BMP2b and Chordin in zebrafish embryos. We found that BMP2b and Chordin diffuse and rapidly form extracellular protein gradients, Chordin does not modulate the diffusivity or distribution of BMP2b, and Chordin is not required to establish peak levels of BMP signaling. Our findings challenge current self-regulating reaction-diffusion and shuttling models and provide support for a graded source-sink mechanism underlying zebrafish dorsal-ventral patterning.

Animals start life as clumps of cells that ultimately give rise to complex structures and organs. Over a century of research has revealed a small number of proteins that are crucial for complex structures to form from these clumps, including one protein called BMP. Different levels of BMP instruct cells to give rise to different tissues. In zebrafish, BMP is more abundant on one side of the embryo than the other. This gradient in BMP levels causes different tissues to form at distinct positions and helps coordinate embryo development.

Several theories have been proposed to explain how the BMP gradient is established. They all suggest that a second protein – Chordin – plays an important role in influencing how cells sense the BMP gradient by blocking BMP’s activity. However, the exact role of Chordin in the formation of the BMP gradient is disputed. To address this, Pomreinke, Soh, Rogers et al. directly tested five theories of how BMP and Chordin molecules spread through embryos.

The experiments used microscopy to track the movements of fluorescent versions of both molecules in zebrafish embryos. The measurements contradict one theory stating that BMP does not move, and another in which Chordin increases the mobility of BMP. Pomreinke, Soh, Rogers et al. also found that embryos that lack Chordin have increased BMP signaling levels only on the side where Chordin is normally made but not on the opposite side where BMP is made, ruling out several of the theories. The findings are most consistent with the idea that the BMP gradient forms mainly as a result of higher production of BMP on one side of the embryo combined with movement of BMP away from where it is made. Chordin produced at the opposite end of the embryo helps to ensure that only the correct cells receive instructions from BMP.

In the future, two approaches could further clarify how the BMP gradient is formed. First, better techniques to directly observe the BMP gradient in normally developing embryos would be useful. Second, new theories that take into account additional players other than BMP and Chordin might help explain some features of development that current theories cannot address. Uncovering the mechanisms that control the formation of BMP gradients will improve our understanding of how clumps of cells can develop into animals.

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.

Collective Space-Sensing Coordinates Pattern Scaling in Engineered Bacteria

Scale invariance refers to the maintenance of a constant ratio of developing organ size to body size. Although common, its underlying mechanisms remain poorly understood. Here, we examined scaling in engineered Escherichia coli that can form self-organized core-ring patterns in colonies. We found that the ring width exhibits perfect scale invariance to the colony size. Our analysis revealed a collective space-sensing mechanism, which entails sequential actions of an integral feedback loop and an incoherent feedforward loop. The integral feedback is implemented by the accumulation of a diffusive chemical produced by a colony. This accumulation, combined with nutrient consumption, sets the timing for ring initiation. The incoherent feedforward is implemented by the opposing effects of the domain size on the rate and duration of ring maturation. This mechanism emphasizes a role of timing control in achieving robust pattern scaling and provides a new perspective in examining the phenomenon in natural systems.

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.

Inferring regulatory networks from experimental morphological phenotypes: a computational method reverse-engineers planarian regeneration

Transformative applications in biomedicine require the discovery of complex regulatory networks that explain the development and regeneration of anatomical structures, and reveal what external signals will trigger desired changes of large-scale pattern. Despite recent advances in bioinformatics, extracting mechanistic pathway models from experimental morphological data is a key open challenge that has resisted automation. The fundamental difficulty of manually predicting emergent behavior of even simple networks has limited the models invented by human scientists to pathway diagrams that show necessary subunit interactions but do not reveal the dynamics that are sufficient for complex, self-regulating pattern to emerge. To finally bridge the gap between high-resolution genetic data and the ability to understand and control patterning, it is critical to develop computational tools to efficiently extract regulatory pathways from the resultant experimental shape phenotypes. For example, planarian regeneration has been studied for over a century, but despite increasing insight into the pathways that control its stem cells, no constructive, mechanistic model has yet been found by human scientists that explains more than one or two key features of its remarkable ability to regenerate its correct anatomical pattern after drastic perturbations. We present a method to infer the molecular products, topology, and spatial and temporal non-linear dynamics of regulatory networks recapitulating in silico the rich dataset of morphological phenotypes resulting from genetic, surgical, and pharmacological experiments. We demonstrated our approach by inferring complete regulatory networks explaining the outcomes of the main functional regeneration experiments in the planarian literature; By analyzing all the datasets together, our system inferred the first systems-biology comprehensive dynamical model explaining patterning in planarian regeneration. This method provides an automated, highly generalizable framework for identifying the underlying control mechanisms responsible for the dynamic regulation of growth and form.

Developmental and regenerative biology experiments are producing a huge number of morphological phenotypes from functional perturbation experiments. However, existing pathway models do not generally explain the dynamic regulation of anatomical shape due to the difficulty of inferring and testing non-linear regulatory networks responsible for appropriate form, shape, and pattern. We present a method that automates the discovery and testing of regulatory networks explaining morphological outcomes directly from the resultant phenotypes, producing network models as testable hypotheses explaining regeneration data. Our system integrates a formalization of the published results in planarian regeneration, an in silico simulator in which the patterning properties of regulatory networks can be quantitatively tested in a regeneration assay, and a machine learning module that evolves networks whose behavior in this assay optimally matches the database of planarian results. We applied our method to explain the key experiments in planarian regeneration, and discovered the first comprehensive model of anterior-posterior patterning in planaria under surgical, pharmacological, and genetic manipulations. Beyond the planarian data, our approach is readily generalizable to facilitate the discovery of testable regulatory networks in developmental biology and biomedicine, and represents the first developmental model discovered de novo from morphological outcomes by an automated system.

Scaling morphogen gradients during tissue growth by a cell division rule

Morphogen gradients guide the patterning of tissues and organs during the development of multicellular organisms. In many cases, morphogen signaling is also required for tissue growth. The consequences of this interplay between growth and patterning are not well understood. In the Drosophila wing imaginal disc, the morphogen Dpp guides patterning and is also required for tissue growth. In particular, it was recently reported that cell division in the disc correlates with the temporal increase in Dpp signaling. Here we mathematically model morphogen gradient formation in a growing tissue, accounting also for morphogen advection and dilution. Our analysis defines a new scaling mechanism, which we term the morphogen-dependent division rule (MDDR): when cell division depends on the temporal increase in morphogen signaling, the morphogen gradient scales with the growing tissue size, tissue growth becomes spatially uniform and the tissue naturally attains a finite size. This model is consistent with many properties of the wing disc. However, we find that the MDDR is not consistent with the phenotype of scaling-defective mutants, supporting the view that temporal increase in Dpp signaling is not the driver of cell division during late phases of disc development. More generally, our results show that local coupling of cell division with morphogen signaling can lead to gradient scaling and uniform growth even in the absence of global feedbacks. The MDDR scaling mechanism might be particularly beneficial during rapid proliferation, when global feedbacks are hard to implement.

Reprogramming cells and tissue patterning via bioelectrical pathways: molecular mechanisms and biomedical opportunities

Transformative impact in regenerative medicine requires more than the reprogramming of individual cells: advances in repair strategies for birth defects or injuries, tumor normalization, and the construction of bioengineered organs and tissues all require the ability to control large-scale anatomical shape. Much recent work has focused on the transcriptional and biochemical regulation of cell behavior and morphogenesis. However, exciting new data reveal that bioelectrical properties of cells and their microenvironment exert a profound influence on cell differentiation, proliferation, and migration. Ion channels and pumps expressed in all cells, not just excitable nerve and muscle, establish resting potentials that vary across tissues and change with significant developmental events. Most importantly, the spatiotemporal gradients of these endogenous transmembrane voltage potentials (Vmem ) serve as instructive patterning cues for large-scale anatomy, providing organ identity, positional information, and prepattern template cues for morphogenesis. New genetic and pharmacological techniques for molecular modulation of bioelectric gradients in vivo have revealed the ability to initiate complex organogenesis, change tissue identity, and trigger regeneration of whole vertebrate appendages. A large segment of the spatial information processing that orchestrates individual cells' programs toward the anatomical needs of the host organism is electrical; this blurs the line between memory and decision-making in neural networks and morphogenesis in nonneural tissues. Advances in cracking this bioelectric code will enable the rational reprogramming of shape in whole tissues and organs, revolutionizing regenerative medicine, developmental biology, and synthetic bioengineering.

Experiments, measurements, and mathematical modeling to decipher time signals in development

Good progress has been made in identifying key signaling molecules and explaining how they are used to generate spatial patterns during embryonic development. In contrast, little is known about the control of timing or how cells use time signals in the developing embryo. In this review, I describe how direct measurements from the embryo combined with mathematical modeling could bring new insights. To illustrate this point, I discuss three examples: the Dpp gradient during growth of the Drosophila wing imaginal disc; the Polycomb-based epigenetic silencing during vernalization in plants; and the Notch-dependent somite segmentation clock.

Dpp signaling activity requires Pentagone to scale with tissue size in the growing Drosophila wing imaginal disc

The activity of the Dpp morphogen adapts to tissue size in the growing Drosophila wing imaginal disc, and Pentagone, an important secreted feedback regulator of the Dpp pathway, is required for this adaptation.

The wing of the fruit fly, Drosophila melanogaster, with its simple, two-dimensional structure, is a model organ well suited for a systems biology approach. The wing arises from an epithelial sac referred to as the wing imaginal disc, which undergoes a phase of massive growth and concomitant patterning during larval stages. The Decapentaplegic (Dpp) morphogen plays a central role in wing formation with its ability to co-coordinately regulate patterning and growth. Here, we asked whether the Dpp signaling activity scales, i.e. expands proportionally, with the growing wing imaginal disc. Using new methods for spatial and temporal quantification of Dpp activity and its scaling properties, we found that the Dpp response scales with the size of the growing tissue. Notably, scaling is not perfect at all positions in the field and the scaling of target gene domains is ensured specifically where they define vein positions. We also found that the target gene domains are not defined at constant concentration thresholds of the downstream Dpp activity gradients P-Mad and Brinker. Most interestingly, Pentagone, an important secreted feedback regulator of the pathway, plays a central role in scaling and acts as an expander of the Dpp gradient during disc growth.

Scaling, the fitting of pattern to size, manifests itself in numerous examples around us. During development, individual body parts scale up to fit the overall body size. Starved animals form smaller adults with proportionally smaller parts, and amphibian embryos can form normally proportioned adults after extreme surgical operations. How scaling is achieved is not well understood. Here, we establish the Drosophila wing imaginal disc, the precursor tissue of the adult wing, as a model to study scaling quantitatively during growth. In this model, we define scaling as the preservation of proportions of gene expression domains with tissue size during disc growth. The Decapentaplegic (Dpp) morphogen is known to play a central role in Drosophila wing formation and co-coordinately regulates growth and patterning. We found that as the disc grows, the Dpp response expands and scales with the tissue size. Interestingly, scaling is not perfect at all positions in the field. The scaling of the target gene domains is best where they have a function; Spalt, for example, scales best at the position in the anterior compartment where it helps to form one of the anterior veins of the wing. Analysis of mutants for pentagone, a transcriptional target of Dpp that encodes a secreted feedback regulator of the pathway, indicates that Pentagone plays a key role in scaling the Dpp gradient activity.

Understanding morphogenetic growth control -- lessons from flies

Morphogens are secreted signalling molecules that control the patterning and growth of developing organs. How morphogens regulate patterning is fairly well understood; however, how they control growth is less clear. Four principal models have been proposed to explain how the morphogenetic protein Decapentaplegic (DPP) controls the growth of the wing imaginal disc in the fly. Recent studies in this model system have provided a wealth of experimental data on growth and DPP gradient properties, as well as on the interactions of DPP with other signalling pathways. These findings have allowed a more precise formulation and evaluation of morphogenetic growth models. The insights into growth control by the DPP gradient will also be useful for understanding other morphogenetic growth systems.

Expansion-repression mechanism for scaling the Dpp activation gradient in Drosophila wing imaginal discs

Maintaining a proportionate body plan requires the adjustment or scaling of organ pattern with organ size. Scaling is a general property of developmental systems, yet little is known about its underlying molecular mechanisms. Using theoretical modeling, we examine how the Dpp activation gradient in the Drosophila wing imaginal disc scales with disc size. We predict that scaling is achieved through an expansion-repression mechanism [1] whose mediator is the widely diffusible protein Pentagone (Pent). Central to this mechanism is the repression of pent expression by Dpp signaling, which provides an effective size measurement, and the Pent-dependent expansion of the Dpp gradient, which adjusts the gradient with tissue size. We validate this mechanism experimentally by demonstrating that scaling requires Pent and further, that scaling is abolished when pent is ubiquitously expressed. The expansion-repression circuit can be readily implemented by a variety of molecular interactions, suggesting its general utilization for scaling morphogen gradients during development.

Conservation and diversification of an ancestral chordate gene regulatory network for dorsoventral patterning

Formation of a dorsoventral axis is a key event in the early development of most animal embryos. It is well established that bone morphogenetic proteins (Bmps) and Wnts are key mediators of dorsoventral patterning in vertebrates. In the cephalochordate amphioxus, genes encoding Bmps and transcription factors downstream of Bmp signaling such as Vent are expressed in patterns reminiscent of those of their vertebrate orthologues. However, the key question is whether the conservation of expression patterns of network constituents implies conservation of functional network interactions, and if so, how an increased functional complexity can evolve. Using heterologous systems, namely by reporter gene assays in mammalian cell lines and by transgenesis in medaka fish, we have compared the gene regulatory network implicated in dorsoventral patterning of the basal chordate amphioxus and vertebrates. We found that Bmp but not canonical Wnt signaling regulates promoters of genes encoding homeodomain proteins AmphiVent1 and AmphiVent2. Furthermore, AmphiVent1 and AmphiVent2 promoters appear to be correctly regulated in the context of a vertebrate embryo. Finally, we show that AmphiVent1 is able to directly repress promoters of AmphiGoosecoid and AmphiChordin genes. Repression of genes encoding dorsal-specific signaling molecule Chordin and transcription factor Goosecoid by Xenopus and zebrafish Vent genes represents a key regulatory interaction during vertebrate axis formation. Our data indicate high evolutionary conservation of a core Bmp-triggered gene regulatory network for dorsoventral patterning in chordates and suggest that co-option of the canonical Wnt signaling pathway for dorsoventral patterning in vertebrates represents one of the innovations through which an increased morphological complexity of vertebrate embryo is achieved.

Robust generation and decoding of morphogen gradients

Morphogen gradients play a key role in multiple differentiation processes. Both the formation of the gradient and its interpretation by the receiving cells need to occur at high precision to ensure reproducible patterning. This need for quantitative precision is challenged by fluctuations in the environmental conditions and by variations in the genetic makeup of the developing embryos. We discuss mechanisms that buffer morphogen profiles against variations in gene dosage. Self-enhanced morphogen degradation and pre-steady-state decoding provide general means for buffering the morphogen profile against fluctuations in morphogen production rate. A more specific "shuttling" mechanism, which establishes a sharp and robust activation profile of a widely expressed morphogen, and enables the adjustment of morphogen profile with embryo size, is also described. Finally, we consider the transformation of the smooth gradient profile into sharp borders of gene expression in the signal-receiving cells. The integration theory and experiments are increasingly used, providing key insights into the system-level functioning of the developmental system.

Scaling of morphogen gradients by an expansion-repression integral feedback control

Despite substantial size variations, proportions of the developing body plan are maintained with a remarkable precision. Little is known about the mechanisms that ensure this adaptation (scaling) of pattern with size. Most models of patterning by morphogen gradients do not support scaling. In contrast, we show that scaling arises naturally in a general feedback topology, in which the range of the morphogen gradient increases with the abundance of some diffusible molecule, whose production, in turn, is repressed by morphogen signaling. We term this mechanism "expansion-repression" and show that it can function within a wide range of biological scenarios. The expansion-repression scaling mechanism is analogous to an integral-feedback controller, a key concept in engineering that is likely to be instrumental also in maintaining biological homeostasis.

Particle tracking model of electrophoretic morphogen movement reveals stochastic dynamics of embryonic gradient

Some developmental events rely on an electrophoretic force to produce morphogenetic gradients. To quantitatively explore the dynamics of this process, we constructed a stochastic model of an early phase of left-right patterning: serotonin movement through the gap junction-coupled blastomeres of the Xenopus embryo. Particle-tracking simulations showed that a left-right gradient is formed rapidly, quickly reaching a final stable level. The voltage difference was critical for producing a morphogen gradient of the right steepness; gap junctional connectivity and morphogen mass determined the timing of the gradient. Endogenous electrophoresis drives approximately 50% of the particles across more than one cell width, and approximately 20% can travel across half the embryo. The stochastic behavior of the resulting gradients exhibited unexpected complexity among blastomeres' morphogen content, and showed how spatiotemporal variability within individual cells resulted in robust and consistent gradients across the embryonic left-right axis. Analysis of the distribution profile of gradient gain values made quantitative predictions about the conditions that result in the observed background level of laterality defects in unperturbed frog embryos. This work provides a general model that can be used to quantitatively analyze the unexpectedly complex dynamics of morphogens in a wide variety of systems.

Bioelectric mechanisms in regeneration: Unique aspects and future perspectives

Regenerative biology has focused largely on chemical factors and transcriptional networks. However, endogenous ion flows serve as key epigenetic regulators of cell behavior. Bioelectric signaling involves feedback loops, long-range communication, polarity, and information transfer over multiple size scales. Understanding the roles of endogenous voltage gradients, ion flows, and electric fields will contribute to the basic understanding of numerous morphogenetic processes and the means by which they can robustly restore pattern after perturbation. By learning to modulate the bioelectrical signals that control cell proliferation, migration, and differentiation, we gain a powerful set of new techniques with which to manipulate growth and patterning in biomedical contexts. This chapter reviews the unique properties of bioelectric signaling, surveys molecular strategies and reagents for its investigation, and discusses the opportunities made available for regenerative medicine.