Models of Biological Pattern Formation: From Elementary Steps to the Organization of Embryonic Axes

Deciphering the functional specialization of whole-brain spatiomolecular gradients in the adult brain

Cortical arealization arises during neurodevelopment from the confluence of molecular gradients representing patterned expression of morphogens and transcription factors. However, whether similar gradients are maintained in the adult brain remains unknown. Here, we uncover three axes of topographic variation in gene expression in the adult human brain that specifically capture previously identified rostral-caudal, dorsal-ventral, and medial-lateral axes of early developmental patterning. The interaction of these spatiomolecular gradients i) accurately reconstructs the position of brain tissue samples, ii) delineates known functional territories, and iii) can model the topographical variation of diverse cortical features. The spatiomolecular gradients are distinct from canonical cortical axes differentiating the primary sensory cortex from the association cortex, but radiate in parallel with the axes traversed by local field potentials along the cortex. We replicate all three molecular gradients in three independent human datasets as well as two nonhuman primate datasets and find that each gradient shows a distinct developmental trajectory across the lifespan. The gradients are composed of several well-known transcription factors (e.g., PAX6 and SIX3), and a small set of genes shared across gradients are strongly enriched for multiple diseases. Together, these results provide insight into the developmental sculpting of functionally distinct brain regions, governed by three robust transcriptomic axes embedded within brain parenchyma.

Preparation of surgical meshes using self-regulating technology based on reaction-diffusion processes

While reaction-diffusion processes are utilized in multiple scientific fields, these phenomena have seen limited practical application in the polymer industry. Although self-regulating processes driven by parallel reaction and diffusion can lead to patterned structures, most polymeric products with repeating subunits are still prepared by methods that require complex and expensive instrumentation. A notable, high-added-value example is surgical mesh, which is often manufactured by weaving or knitting. In our present work, we demonstrate how the polymer and the biomedical industry can benefit from the pattern-forming capabilities of reaction-diffusion. We would like to propose a self-regulating method that facilitates the creation of surgical meshes from biocompatible polymers. Since the control of the process assumes a thorough understanding of the underlying phenomena, the theoretical background, as well as a mathematical model that can accurately describe the empirical data, is also introduced and explained. Our method offers the benefits of conventional techniques while introducing additional advantages not attainable with them. Most importantly, the method proposed in this paper enables the rapid creation of meshes with an average pore size that can be adjusted easily and tailored to fit the intended area of application.

The WIP6 transcription factor TOO MANY LATERALS specifies vein type in C4 and C3 grass leaves

Grass leaves are invariantly strap shaped with an elongated distal blade and a proximal sheath that wraps around the stem. Underpinning this shape is a scaffold of leaf veins, most of which extend in parallel along the proximo-distal leaf axis. Differences between species are apparent both in the vein types that develop and in the distance between veins across the medio-lateral leaf axis. A prominent engineering goal is to increase vein density in leaves of C3 photosynthesizing species to facilitate the introduction of the more efficient C4 pathway. Here, we discover that the WIP6 transcription factor TOO MANY LATERALS (TML) specifies vein rank in both maize (C4) and rice (C3). Loss-of-function tml mutations cause large lateral veins to develop in positions normally occupied by smaller intermediate veins, and TML transcript localization in wild-type leaves is consistent with a role in suppressing lateral vein development in procambial cells that form intermediate veins. Attempts to manipulate TML function in rice were unsuccessful because transgene expression was silenced, suggesting that precise TML expression is essential for shoot viability. This finding may reflect the need to prevent the inappropriate activation of downstream targets or, given that transcriptome analysis revealed altered cytokinin and auxin signaling profiles in maize tml mutants, the need to prevent local or general hormonal imbalances. Importantly, rice tml mutants display an increased occupancy of veins in the leaf, providing a step toward an anatomical chassis for C4 engineering. Collectively, a conserved mechanism of vein rank specification in grass leaves has been revealed.

Spatiotemporal Coordination of Rac1 and Cdc42 at the Whole Cell Level during Cell Ruffling

Rho-GTPases are central regulators within a complex signaling network that controls cytoskeletal organization and cell movement. The network includes multiple GTPases, such as the most studied Rac1, Cdc42, and RhoA, along with their numerous effectors that provide mutual regulation through feedback loops. Here we investigate the temporal and spatial relationship between Rac1 and Cdc42 during membrane ruffling, using a simulation model that couples GTPase signaling with cell morphodynamics and captures the GTPase behavior observed with FRET-based biosensors. We show that membrane velocity is regulated by the kinetic rate of GTPase activation rather than the concentration of active GTPase. Our model captures both uniform and polarized ruffling. We also show that cell-type specific time delays between Rac1 and Cdc42 activation can be reproduced with a single signaling motif, in which the delay is controlled by feedback from Cdc42 to Rac1. The resolution of our simulation output matches those of time-lapsed recordings of cell dynamics and GTPase activity. Our data-driven modeling approach allows us to validate simulation results with quantitative precision using the same pipeline for the analysis of simulated and experimental data.

Spatiotemporal coordination of Rac1 and Cdc42 at the whole cell level during cell ruffling

Rho-GTPases are central regulators within a complex signaling network that controls the cytoskeletal organization and cell movement. This network includes multiple GTPases, such as the most studied Rac1, Cdc42, and RhoA, and their numerous effectors that provide mutual regulation and feedback loops. Here we investigate the temporal and spatial relationship between Rac1 and Cdc42 during membrane ruffling using a simulation model which couples GTPase signaling with cell morphodynamics to capture the GTPase behavior observed with FRET-based biosensors. We show that membrane velocity is regulated by the kinetic rate of GTPase activation rather than the concentration of active GTPase. Our model captures both uniform and polarized ruffling. We also show that cell-type specific time delays between Rac1 and Cdc42 activation can be reproduced with a single signaling motif, in which the delay is controlled by feedback from Cdc42 to Rac1. The resolution of our simulation output matches those of the time-lapsed recordings of cell dynamics and GTPase activity. This approach allows us to validate simulation results with quantitative precision using the same pipeline for the analysis of simulated and experimental data.

Transplantation of fragments from different planaria: A bioelectrical model for head regeneration

Head-tail planaria morphologies are influenced by the electric potential differences across the animal's primary axis, as evidenced e.g. by voltage-sensitive dyes and functional experiments that create permanent lines of 2-headed but genetically wild-type animals. However, bioelectrical and biochemical models that make predictions on what would happen in the case of spatial chimeras made by tissue transplantation from different planaria (different species and head shapes) are lacking. Here, we use a bioelectrical model to qualitatively describe the effects of tissue transplantation on the shape of the regenerated head. To this end, we assume that the cells may have distinct sets of ion channels and ascribe the system outcome to the axial distributions of average cell potentials over morphologically relevant regions. Our rationale is that the distributions of signaling ions and molecules are spatially coupled with multicellular electric potentials. Thus, long-time downstream transcriptional events should be triggered by short-time bioelectrical processes. We show that relatively small differences between the ion channel characteristics of the cells could eventually give noticeable changes in the electric potential profiles and the expected morphological deviations, which suggests that small but timely bioelectrical actions may have significant morphological effects. Our approach is based on the observed relationships between bioelectrical regionalization and biochemical gradients in body-plan studies. Such models are relevant to regenerative, developmental, and cancer biology in which cells with distinct properties and morphogenetic target states confront each other in the same tissue.

Mathematical models of nitrogen-fixing cell patterns in filamentous cyanobacteria

The Anabaena genus is a model organism of filamentous cyanobacteria whose vegetative cells can differentiate under nitrogen-limited conditions into a type of cell called a heterocyst. These heterocysts lose the possibility to divide and are necessary for the filament because they can fix and share environmental nitrogen. In order to distribute the nitrogen efficiently, heterocysts are arranged to form a quasi-regular pattern whose features are maintained as the filament grows. Recent efforts have allowed advances in the understanding of the interactions and genetic mechanisms underlying this dynamic pattern. Here, we present a systematic review of the existing theoretical models of nitrogen-fixing cell differentiation in filamentous cyanobacteria. These filaments constitute one of the simplest forms of multicellular organization, and this allows for several modeling scales of this emergent pattern. The system has been approached at three different levels. From bigger to smaller scale, the system has been considered as follows: at the population level, by defining a mean-field simplified system to study the ratio of heterocysts and vegetative cells; at the filament level, with a continuous simplification as a reaction-diffusion system; and at the cellular level, by studying the genetic regulation that produces the patterning for each cell. In this review, we compare these different approaches noting both the virtues and shortcomings of each one of them.

Terminal heterocyst differentiation in the Anabaena patA mutant as a result of post-transcriptional modifications and molecular leakage

The Anabaena genus is a model organism of filamentous cyanobacteria whose vegetative cells can differentiate under nitrogen-limited conditions into a type of cell called heterocyst. These heterocysts lose the possibility to divide and are necessary for the colony because they can fix and share environmental nitrogen. In order to distribute the nitrogen efficiently, heterocysts are arranged to form a quasi-regular pattern whose features are maintained as the filament grows. Recent efforts have allowed advances in the understanding of the interactions and genetic mechanisms underlying this dynamic pattern. However, the main role of the patA and hetF genes are yet to be clarified; in particular, the patA mutant forms heterocysts almost exclusively in the terminal cells of the filament. In this work, we investigate the function of these genes and provide a theoretical model that explains how they interact within the broader genetic network, reproducing their knock-out phenotypes in several genetic backgrounds, including a nearly uniform concentration of HetR along the filament for the patA mutant. Our results suggest a role of hetF and patA in a post-transcriptional modification of HetR which is essential for its regulatory function. In addition, the existence of molecular leakage out of the filament in its boundary cells is enough to explain the preferential appearance of terminal heterocysts, without any need for a distinct regulatory pathway.

Understanding multicellular pattern formation is key for the study of both natural and synthetic developmental processes. Arguably one of the simplest model systems for this is the filamentous cyanobacterium Anabaena, that in conditions of nitrogen deprivation undergoes a dynamical differentiation process that differentiates roughly one in every ten cells into nitrogen-fixing heterocysts, in a quasi-regular pattern that is maintained as the filament keeps growing. One of the most characteristic mutations affecting this process forms heterocysts mostly constrained to the terminal cells of the filament. We have used experimental observations to propose a mathematical model of heterocyst differentiation able to reproduce this striking phenotype. The model extends our understanding of the regulations in this pattern-forming system and makes several predictions on molecular interactions. Importantly, a key aspect is the boundary condition at the filament’s ends: inhibitors of differentiation should be able to leak out of the filament, or otherwise the terminal cells would not differentiate. This highlights, in a very clear example, the importance of considering physical constraints in developmental processes.

The Hippo pathway regulates axis formation and morphogenesis in Hydra

How did cells of early metazoan organisms first organize themselves to form a body axis? The canonical Wnt pathway has been shown to be sufficient for induction of axis in Cnidaria, a sister group to Bilateria, and is important in bilaterian axis formation. Here, we provide experimental evidence that in cnidarian Hydra the Hippo pathway regulates the formation of a new axis during budding upstream of the Wnt pathway. The transcriptional target of the Hippo pathway, the transcriptional coactivator YAP, inhibits the initiation of budding in Hydra and is regulated by Hydra LATS. In addition, we show functions of the Hippo pathway in regulation of actin organization and cell proliferation in Hydra. We hypothesize that the Hippo pathway served as a link between continuous cell division, cell density, and axis formation early in metazoan evolution.

The Making of a Heterocyst in Cyanobacteria

Heterocyst differentiation that occurs in some filamentous cyanobacteria, such as Anabaena sp. PCC 7120, provides a unique model for prokaryotic developmental biology. Heterocyst cells are formed in response to combined-nitrogen deprivation and possess a microoxic environment suitable for nitrogen fixation following extensive morphological and physiological reorganization. A filament of Anabaena is a true multicellular organism, as nitrogen and carbon sources are exchanged among different cells and cell types through septal junctions to ensure filament growth. Because heterocysts are terminally differentiated cells and unable to divide, their activity is an altruistic behavior dedicated to providing fixed nitrogen for neighboring vegetative cells. Heterocyst development is also a process of one-dimensional pattern formation, as heterocysts are semiregularly intercalated among vegetative cells. Morphogens form gradients along the filament and interact with each other in a fashion that fits well into the Turing model, a mathematical framework to explain biological pattern formation. Expected final online publication date for the Annual Review of Microbiology, Volume 76 is September 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Emerging spatiotemporal patterns in cyclic predator-prey systems with habitats

Three-species cyclic predator-prey systems are known to establish spiral waves that allow species to coexist. In this study, we analyze a structured heterogeneous system which gives one species an advantage to escape predation in an area that we refer to as a habitat and study the effect on species coexistence and emerging spatiotemporal patterns. Counterintuitively, the predator of the advantaged species emerges as dominant species with the highest average density inside the habitat. The species given the advantage in the form of an escape rate has the lowest average density until some threshold value for the escape rate is exceeded, after which the density of the species with the advantage overtakes that of its prey. Numerical analysis of the spatial density of each species as well as of the spatial two-point correlation function for both inside and outside the habitats allow a detailed quantitative discussion. Our analysis is extended to a six-species game that exhibits spontaneous spiral waves, which displays similar but more complicated results.

A segmentation clock patterns cellular differentiation in a bacterial biofilm

Contrary to multicellular organisms that display segmentation during development, communities of unicellular organisms are believed to be devoid of such sophisticated patterning. Unexpectedly, we find that the gene expression underlying the nitrogen stress response of a developing Bacillus subtilis biofilm becomes organized into a ring-like pattern. Mathematical modeling and genetic probing of the underlying circuit indicate that this patterning is generated by a clock and wavefront mechanism, similar to that driving vertebrate somitogenesis. We experimentally validated this hypothesis by showing that predicted nutrient conditions can even lead to multiple concentric rings, resembling segments. We additionally confirmed that this patterning mechanism is driven by cell-autonomous oscillations. Importantly, we show that the clock and wavefront process also spatially patterns sporulation within the biofilm. Together, these findings reveal a biofilm segmentation clock that organizes cellular differentiation in space and time, thereby challenging the paradigm that such patterning mechanisms are exclusive to plant and animal development.

Sculpting with stem cells: how models of embryo development take shape

During embryogenesis, organisms acquire their shape given boundary conditions that impose geometrical, mechanical and biochemical constraints. A detailed integrative understanding how these morphogenetic information modules pattern and shape the mammalian embryo is still lacking, mostly owing to the inaccessibility of the embryo in vivo for direct observation and manipulation. These impediments are circumvented by the developmental engineering of embryo-like structures (stembryos) from pluripotent stem cells that are easy to access, track, manipulate and scale. Here, we explain how unlocking distinct levels of embryo-like architecture through controlled modulations of the cellular environment enables the identification of minimal sets of mechanical and biochemical inputs necessary to pattern and shape the mammalian embryo. We detail how this can be complemented with precise measurements and manipulations of tissue biochemistry, mechanics and geometry across spatial and temporal scales to provide insights into the mechanochemical feedback loops governing embryo morphogenesis. Finally, we discuss how, even in the absence of active manipulations, stembryos display intrinsic phenotypic variability that can be leveraged to define the constraints that ensure reproducible morphogenesis in vivo.

Spatiotemporal patterns emerging from a spatially localized time-delayed feedback scheme

In attempts to manage spatiotemporal transient chaos in spatially extended systems, these systems are often subjected to protocols that perturb them as a whole and stabilize globally a new dynamic regime, as, for example, a uniform steady state. In this work we show that selectively perturbing only part of a system can generate space-time patterns that are not observed when controlling the whole system. Depending on the protocol used, these new patterns can emerge either in the perturbed or the unperturbed region. Specifically, we use a spatially localized time-delayed feedback scheme on the one-dimensional Gray-Scott reaction-diffusion system in the transient chaotic regime and demonstrate, through the numerical integration of the resulting kinetic equations, the stabilization of spatially localized space-time patterns that can be perfectly periodic. The mechanism underlying the observed pattern generation is related to diffusion across the interfaces separating the perturbed and unperturbed regions.

Systems of pattern formation within developmental biology

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

The dynamics of morphogenesis in stem cell-based embryology: Novel insights for symmetry breaking

Breaking embryonic symmetry is an essential prerequisite to shape the initially symmetric embryo into a highly organized body plan that serves as the blueprint of the adult organism. This critical process is driven by morphogen signaling gradients that instruct anteroposterior axis specification. Despite its fundamental importance, what triggers symmetry breaking and how the signaling gradients are established in time and space in the mammalian embryo remain largely unknown. Stem cell-based in vitro models of embryogenesis offer an unprecedented opportunity to quantitatively dissect the multiple physical and molecular processes that shape the mammalian embryo. Here we review biochemical mechanisms governing early mammalian patterning in vivo and highlight recent advances to recreate this in vitro using stem cells. We discuss how the novel insights from these model systems extend previously proposed concepts to illuminate the extent to which embryonic cells have the intrinsic capability to generate specific, reproducible patterns during embryogenesis.

How cells determine the number of polarity sites

The diversity of cell morphologies arises, in part, through regulation of cell polarity by Rho-family GTPases. A poorly understood but fundamental question concerns the regulatory mechanisms by which different cells generate different numbers of polarity sites. Mass-conserved activator-substrate (MCAS) models that describe polarity circuits develop multiple initial polarity sites, but then those sites engage in competition, leaving a single winner. Theoretical analyses predicted that competition would slow dramatically as GTPase concentrations at different polarity sites increase toward a 'saturation point', allowing polarity sites to coexist. Here, we test this prediction using budding yeast cells, and confirm that increasing the amount of key polarity proteins results in multiple polarity sites and simultaneous budding. Further, we elucidate a novel design principle whereby cells can switch from competition to equalization among polarity sites. These findings provide insight into how cells with diverse morphologies may determine the number of polarity sites.

Roadmap for the multiscale coupling of biochemical and mechanical signals during development

The way in which interactions between mechanics and biochemistry lead to the emergence of complex cell and tissue organization is an old question that has recently attracted renewed interest from biologists, physicists, mathematicians and computer scientists. Rapid advances in optical physics, microscopy and computational image analysis have greatly enhanced our ability to observe and quantify spatiotemporal patterns of signalling, force generation, deformation, and flow in living cells and tissues. Powerful new tools for genetic, biophysical and optogenetic manipulation are allowing us to perturb the underlying machinery that generates these patterns in increasingly sophisticated ways. Rapid advances in theory and computing have made it possible to construct predictive models that describe how cell and tissue organization and dynamics emerge from the local coupling of biochemistry and mechanics. Together, these advances have opened up a wealth of new opportunities to explore how mechanochemical patterning shapes organismal development. In this roadmap, we present a series of forward-looking case studies on mechanochemical patterning in development, written by scientists working at the interface between the physical and biological sciences, and covering a wide range of spatial and temporal scales, organisms, and modes of development. Together, these contributions highlight the many ways in which the dynamic coupling of mechanics and biochemistry shapes biological dynamics: from mechanoenzymes that sense force to tune their activity and motor output, to collectives of cells in tissues that flow and redistribute biochemical signals during development.

Screwed up: Spirality of segments and other iterated structures suggest an underlying principle of seriality in bilaterians

This review deals with helicomery, that is, the specific malformation of a spiral arrangement of segments and other serial structures. Helicomery was first described in annelid and arthropod body segments. However, corresponding patterns occur in arthropod appendages and other bilaterians with serially arranged body parts, such as tapeworms, nematodes, vertebrates, and probably chitons. The specifics of the spirals such as length, orientation, and handedness are described. Most spirals are dorsal and comprise only a few loops. Helicomery is formed by a shift of cells during development or in adults caused by changes in cell adhesion or mechanical impacts such as lesions. A model for the formation of helicomery is proposed, which is based on medieval church labyrinths. These complex spiral structures are derived from concentric lines by the shift of relatively few tiles. This principle of "small causes, great effect" also applies to "spiral segments," because helicomery dissolves segmental patterns and questions the concept of segments as distinct structures. The widespread occurrence of helicomery in nonhomologous serial structures might indirectly indicate an underlying principle of seriality among Bilateria.

Whole-Body Regeneration in Sponges: Diversity, Fine Mechanisms, and Future Prospects

While virtually all animals show certain abilities for regeneration after an injury, these abilities vary greatly among metazoans. Porifera (Sponges) is basal metazoans characterized by a wide variety of different regenerative processes, including whole-body regeneration (WBR). Considering phylogenetic position and unique body organization, sponges are highly promising models, as they can shed light on the origin and early evolution of regeneration in general and WBR in particular. The present review summarizes available data on the morphogenetic and cellular mechanisms accompanying different types of WBR in sponges. Sponges show a high diversity of WBR, which principally could be divided into (1) WBR from a body fragment and (2) WBR by aggregation of dissociated cells. Sponges belonging to different phylogenetic clades and even to different species and/or differing in the anatomical structure undergo different morphogeneses after similar operations. A common characteristic feature of WBR in sponges is the instability of the main body axis: a change of the organism polarity is described during all types of WBR. The cellular mechanisms of WBR are different across sponge classes, while cell dedifferentiations and transdifferentiations are involved in regeneration processes in all sponges. Data considering molecular regulation of WBR in sponges are extremely scarce. However, the possibility to achieve various types of WBR ensured by common morphogenetic and cellular basis in a single species makes sponges highly accessible for future comprehensive physiological, biochemical, and molecular studies of regeneration processes.

Morphometric and allometric rules of polyp's landscape in regular and chimeric coral colonies of the branching species Stylophora pistillata

BACKGROUND

Most studies on architectural rules in corals have focused on the branch and the colony level, unveiling a variety of allometric rules. Working on the branching coral Stylophora pistillata, here we further extend the astogenic directives of this species at the polyp level, to reveal allometric and morphometric rules dictating polyps' arrangement.

RESULTS

We identified a basic morphometric landscape as a six-polyp circlet developed around a founder polyp, with established distances between polyps (six equilateral triangles), reflecting a strong genetic-based background vs high plasticity on the population level. Testing these rules in regular and chimeric S. pistillata colonies, we revealed similar morphometric/allometric rules developed via a single astogenic pathway. In regular colonies, this pathway was driven by the presence/absence of intra-circlet budding polyps, while in chimeras, by the distances between the two founder polyps. In addition, we identified the intra-circlet budding as the origin of first branching, if BPC distances are kept <1.09 ± 0.25 mm.

CONCLUSIONS

The emerged allometric/morphometric rules indicate the existence of a positional information paradigm for polyps' landscape distribution, where each polyp creates its own positional field of morphogen gradients through six inductive sites, thus forming six positional fields for the development of the archetypal "six-polyp crown".

A postlarval instar of Phoxichilidium femoratum (Pycnogonida, Phoxichilidiidae) with an exceptional malformation

Individuals of the marine chelicerate lineage Pycnogonida (sea spiders) show considerable regenerative capabilities after appendage injury or loss. In their natural habitats, especially the long legs of sea spiders are commonly lost and regenerated, as is evidenced by the frequent encounter of specimens with missing or miniature legs. In contrast to this, the collection of individuals with abnormally developed appendages or trunk regions is comparably rare. Here, we studied a remarkable malformation in a postlarval instar of the species Phoxichilidium femoratum (Rathke, 1799) and describe the external morphology and internal organization of the specimen using a combination of fluorescent histochemistry and scanning electron microscopy. The individual completely lacks the last trunk segment with leg pair 4 and the normally penultimate trunk segment bears only a single aberrant appendage resembling an extension of the anteroposterior body axis. Externally, the proximal units of the articulated appendage are unpaired, but further distally a bifurcation into two equally developed leg-like branches is found. Three-dimensional reconstruction of the musculature reveals components of two regular leg muscle sets in several of the proximal articles. This confirms interpretation of the entire appendage as a malformed leg and reveals an externally hidden paired organization along its entire proximodistal axis. To explain the origin of this unique malformation, early pioneering studies on the regenerative potential of pycnogonids are evaluated and (a) an injury-induced partial fusion of the developing limb buds of leg pair 3, as well as (b) irregular leg regeneration following near complete loss of trunk segments 3 and 4 are discussed. Which of the two hypotheses is more realistic remains to be tested by dedicated experimental approaches. These will have to rely on pycnogonid species with established laboratory husbandry in order to overcome the limitations of the few short-term regeneration studies performed to date.

Size-Regulated Symmetry Breaking in Reaction-Diffusion Models of Developmental Transitions

The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organisation. Many of these transitions are achieved by spontaneous symmetry breaking mechanisms, allowing cells and tissues to acquire pattern and polarity by virtue of local interactions without an upstream supply of information. The combined work of theory and experiment has elucidated how these systems break symmetry during developmental transitions. Given that such transitions are multiple and their temporal ordering is crucial, an equally important question is how these developmental transitions are coordinated in time. Using a minimal mass-conserved substrate-depletion model for symmetry breaking as our case study, we elucidate mechanisms by which cells and tissues can couple reaction-diffusion-driven symmetry breaking to the timing of developmental transitions, arguing that the dependence of patterning mode on system size may be a generic principle by which developing organisms measure time. By analysing different regimes of our model, simulated on growing domains, we elaborate three distinct behaviours, allowing for clock-, timer- or switch-like dynamics. Relating these behaviours to experimentally documented case studies of developmental timing, we provide a minimal conceptual framework to interrogate how developing organisms coordinate developmental transitions.

Cyp1B1 expression patterns in the developing chick inner ear

BACKGROUND

Retinoic acid (RA) plays an important role in organogenesis as a paracrine signal through transcriptional regulation of an increasing number of known downstream target genes, regulating cell proliferation, and differentiation. During the development of the inner ear, RA directly governs the morphogenesis and specification processes mainly by means of RA-synthesizing retinaldehyde dehydrogenase (RALDH) enzymes. Interestingly, CYP1B1, a cytochrome P450 enzyme, is able to mediate the oxidative metabolisms also leading to RA generation, its expression patterns being associated with many known sites of RA activity.

RESULTS

This study describes for the first time the presence of CYP1B1 in the developing chick inner ear as a RALDH-independent RA-signaling mechanism. In our in situ hybridization analysis, Cyp1B1 expression was first observed in a domain located in the ventromedial wall of the otic anlagen, being included within the rostralmost aspect of an Fgf10-positive pan-sensory domain. As development proceeds, all identified Fgf10-positive areas were Cyp1B1 stained, with all sensory patches being Cyp1B1 positive at stage HH34, except the macula neglecta.

CONCLUSIONS

Cyp1B1 expression suggested a possible contribution of CYP1B1 action in the specification of the lateral-to-medial and dorsal-to-ventral axes of the developing chick inner ear.

A 3D model of a human epiblast reveals BMP4-driven symmetry breaking

Breaking the anterior-posterior symmetry in mammals occurs at gastrulation. Much of the signalling network underlying this process has been elucidated in the mouse; however, there is no direct molecular evidence of events driving axis formation in humans. Here, we use human embryonic stem cells to generate an in vitro three-dimensional model of a human epiblast whose size, cell polarity and gene expression are similar to a day 10 human epiblast. A defined dose of BMP4 spontaneously breaks axial symmetry, and induces markers of the primitive streak and epithelial-to-mesenchymal transition. We show that WNT signalling and its inhibitor DKK1 play key roles in this process downstream of BMP4. Our work demonstrates that a model human epiblast can break axial symmetry despite the absence of asymmetry in the initial signal and of extra-embryonic tissues or maternal cues. Our three-dimensional model is an assay for the molecular events underlying human axial symmetry breaking.

Self-organization of stem cells into embryos: A window on early mammalian development

Embryonic development is orchestrated by robust and complex regulatory mechanisms acting at different scales of organization. In vivo studies are particularly challenging for mammals after implantation, owing to the small size and inaccessibility of the embryo. The generation of stem cell models of the embryo represents a powerful system with which to dissect this complexity. Control of geometry, modulation of the physical environment, and priming with chemical signals reveal the intrinsic capacity of embryonic stem cells to make patterns. Adding the stem cells for the extraembryonic lineages generates three-dimensional models that are more autonomous from the environment and recapitulate many features of the pre- and postimplantation mouse embryo, including gastrulation. Here, we review the principles of self-organization and how they set cells in motion to create an embryo.

Isolating and quantifying the role of developmental noise in generating phenotypic variation

Genotypic variation, environmental variation, and their interaction may produce variation in the developmental process and cause phenotypic differences among individuals. Developmental noise, which arises during development from stochasticity in cellular and molecular processes when genotype and environment are fixed, also contributes to phenotypic variation. While evolutionary biology has long focused on teasing apart the relative contribution of genes and environment to phenotypic variation, our understanding of the role of developmental noise has lagged due to technical difficulties in directly measuring the contribution of developmental noise. The influence of developmental noise is likely underestimated in studies of phenotypic variation due to intrinsic mechanisms within organisms that stabilize phenotypes and decrease variation. Since we are just beginning to appreciate the extent to which phenotypic variation due to stochasticity is potentially adaptive, the contribution of developmental noise to phenotypic variation must be separated and measured to fully understand its role in evolution. Here, we show that variation in the component of the developmental process corresponding to environmental and genetic factors (here treated together as a unit called the LALI-type) versus the contribution of developmental noise, can be distinguished for leopard gecko (Eublepharis macularius) head color patterns using mathematical simulations that model the role of random variation (corresponding to developmental noise) in patterning. Specifically, we modified the parameters of simulations corresponding to variation in the LALI-type to generate the full range of phenotypic variation in color pattern seen on the heads of eight leopard geckos. We observed that over the range of these parameters, variation in color pattern due to LALI-type variation exceeds that due to developmental noise in the studied gecko cohort. However, the effect of developmental noise on patterning is also substantial. Our approach addresses one of the major goals of evolutionary biology: to quantify the role of stochasticity in shaping phenotypic variation.

Self-organization principles of intracellular pattern formation

Dynamic patterning of specific proteins is essential for the spatio-temporal regulation of many important intracellular processes in prokaryotes, eukaryotes and multicellular organisms. The emergence of patterns generated by interactions of diffusing proteins is a paradigmatic example for self-organization. In this article, we review quantitative models for intracellular Min protein patterns in Escherichia coli, Cdc42 polarization in Saccharomyces cerevisiae and the bipolar PAR protein patterns found in Caenorhabditis elegans. By analysing the molecular processes driving these systems we derive a theoretical perspective on general principles underlying self-organized pattern formation. We argue that intracellular pattern formation is not captured by concepts such as ‘activators’, ‘inhibitors’ or ‘substrate depletion’. Instead, intracellular pattern formation is based on the redistribution of proteins by cytosolic diffusion, and the cycling of proteins between distinct conformational states. Therefore, mass-conserving reaction–diffusion equations provide the most appropriate framework to study intracellular pattern formation. We conclude that directed transport, e.g. cytosolic diffusion along an actively maintained cytosolic gradient, is the key process underlying pattern formation. Thus the basic principle of self-organization is the establishment and maintenance of directed transport by intracellular protein dynamics.

This article is part of the theme issue ‘Self-organization in cell biology’.

Planarian regeneration as a model of anatomical homeostasis: Recent progress in biophysical and computational approaches

Planarian behavior, physiology, and pattern control offer profound lessons for regenerative medicine, evolutionary biology, morphogenetic engineering, robotics, and unconventional computation. Despite recent advances in the molecular genetics of stem cell differentiation, this model organism's remarkable anatomical homeostasis provokes us with truly fundamental puzzles about the origin of large-scale shape and its relationship to the genome. In this review article, we first highlight several deep mysteries about planarian regeneration in the context of the current paradigm in this field. We then review recent progress in understanding of the physiological control of an endogenous, bioelectric pattern memory that guides regeneration, and how modulating this memory can permanently alter the flatworm's target morphology. Finally, we focus on computational approaches that complement reductive pathway analysis with synthetic, systems-level understanding of morphological decision-making. We analyze existing models of planarian pattern control and highlight recent successes and remaining knowledge gaps in this interdisciplinary frontier field.

SPATIAL ASPECT OF HUNTING COOPERATION IN PREDATORS WITH HOLLING TYPE II FUNCTIONAL RESPONSE

In this paper, we have investigated a spatial predator–prey model with hunting cooperation in predators. Using linear stability analysis, we obtain the condition for diffusive instability and identify the corresponding domain in the space of controlling parameters. Using extensive numerical simulations, we obtain complex patterns, namely, spotted pattern, stripe pattern and mixed pattern in the Turing domain, by varying the hunting cooperation parameter in predators and carrying capacity of preys. The results focus on the effect of hunting cooperation in pattern dynamics of a diffusive predator–prey model and help us in better understanding of the dynamics of the predator–prey interaction in real environments.

Ancient association of cyanobacterial multicellularity with the regulator HetR and an RGSGR pentapeptide-containing protein (PatX)

One simple model to explain biological pattern postulates the existence of a stationary regulator of differentiation that positively affects its own expression, coupled with a diffusible suppressor of differentiation that inhibits the regulator's expression. The first has been identified in the filamentous, heterocyst-forming cyanobacterium, Anabaena PCC 7120 as the transcriptional regulator, HetR and the second as the small protein, PatS, which contains a critical RGSGR motif that binds to HetR. HetR is present in almost all filamentous cyanobacteria, but only a subset of heterocyst-forming strains carry proteins similar to PatS. We identified a third protein, PatX that also carries the RGSGR motif and is coextensive with HetR. Amino acid sequences of PatX contain two conserved regions: the RGSGR motif and a hydrophobic N-terminus. Within 69 nt upstream from all instances of the gene is a DIF1 motif correlated in Anabaena with promoter induction in developing heterocysts, preceded in heterocyst-forming strains by an apparent NtcA-binding site, associated with regulation by nitrogen-status. Consistent with a role in the simple model, PatX is expressed dependent on HetR and acts to inhibit differentiation. The acquisition of the PatX/HetR pair preceded the appearance of both PatS and heterocysts, dating back to the beginnings of multicellularity.

Bioelectrical control of positional information in development and regeneration: A review of conceptual and computational advances

Positional information describes pre-patterns of morphogenetic substances that alter spatio-temporal gene expression to instruct development of growth and form. A wealth of recent data indicate bioelectrical properties, such as the transmembrane potential (Vmem), are involved as instructive signals in the spatiotemporal regulation of morphogenesis. However, the mechanistic relationships between Vmem and molecular positional information are only beginning to be understood. Recent advances in computational modeling are assisting in the development of comprehensive frameworks for mechanistically understanding how endogenous bioelectricity can guide anatomy in a broad range of systems. Vmem represents an extraordinarily strong electric field (∼1.0 × 106 V/m) active over the thin expanse of the plasma membrane, with the capacity to influence a variety of downstream molecular signaling cascades. Moreover, in multicellular networks, intercellular coupling facilitated by gap junction channels may induce directed, electrodiffusive transport of charged molecules between cells of the network to generate new positional information patterning possibilities and characteristics. Given the demonstrated role of Vmem in morphogenesis, here we review current understanding of how Vmem can integrate with molecular regulatory networks to control single cell state, and the unique properties bioelectricity adds to transport phenomena in gap junction-coupled cell networks to facilitate self-assembly of morphogen gradients and other patterns. Understanding how Vmem integrates with biochemical regulatory networks at the level of a single cell, and mechanisms through which Vmem shapes molecular positional information in multicellular networks, are essential for a deep understanding of body plan control in development, regeneration and disease.

Phenotypic Assessment Suggests Multiple Start Codons for HetN, an Inhibitor of Heterocyst Differentiation, in Anabaena sp. Strain PCC 7120

Multicellular organisms must carefully regulate the timing, number, and location of specialized cellular development. In the filamentous cyanobacterium Anabaena sp. strain PCC 7120, nitrogen-fixing heterocysts are interspersed between vegetative cells in a periodic pattern to achieve an optimal exchange of bioavailable nitrogen and reduced carbon. The spacing between heterocysts is regulated by the activity of two developmental inhibitors, PatS and HetN. PatS functions to create a de novo pattern from a homogenous field of undifferentiated cells, while HetN maintains the pattern throughout subsequent growth. Both PatS and HetN harbor the peptide motif ERGSGR, which is sufficient to inhibit development. While the small size of PatS makes the interpretation of inhibitory domains relatively simple, HetN is a 287-amino-acid protein with multiple functional regions. Previous work suggested the possibility of a truncated form of HetN containing the ERGSGR motif as the source of the HetN-derived inhibitory signal. In this work, we present evidence that the glutamate of the ERGSGR motif is required for proper HetN inhibition of heterocysts. Mutational analysis and subcellular localization indicate that the gene encoding HetN uses two methionine start codons (M1 and M119) to encode two protein forms: M1 is required for protein localization, while M119 is primarily responsible for inhibitory function. Finally, we demonstrate that patS and hetN are not functionally equivalent when expressed from the other gene's regulatory sequences. Taken together, these results help clarify the functional forms of HetN and will help refine future work defining a HetN-derived inhibitory signal in this model of one-dimensional periodic patterning.IMPORTANCE The proper placement of different cell types during a developmental program requires the creation and maintenance of a biological pattern to define the cells that will differentiate. Here we show that the HetN inhibitor, responsible for pattern maintenance of specialized nitrogen-fixing heterocyst cells in the filamentous cyanobacterium Anabaena, may be produced from two different start methionine codons. This work demonstrates that the two start sites are individually involved in a different HetN function, either membrane localization or inhibition of cellular differentiation.

A general framework dedicated to computational morphogenesis Part I - Constitutive equations

In order to understand living organisms, considerable experimental efforts and resources have been devoted to correlate genes and their expressions with cell, tissue, organ and whole organisms' phenotypes. This data driven approach to knowledge discovery has led to many breakthrough in our understanding of healthy and diseased states, and is paving the way to improve the diagnosis and treatment of diseases. Complementary to this data-driven approach, computational models of biological systems based on first principles have been developed in order to deepen our understanding of the multi-scale dynamics that drives normal and pathological biological functions. In this paper we describe the biological, physical and mathematical concepts that led to the design of a Computational Morphogenesis (CM) platform baptized Generic Modeling and Simulating Platform (GMSP). Its role is to generate realistic 3D multi-scale biological tissues from virtual stem cells and the intended target applications include in virtuo studies of normal and abnormal tissue (re)generation as well as the development of complex diseases such as carcinogenesis. At all space-scales of interest, biological agents interact with each other via biochemical, bioelectrical, and mechanical fields that operate in concert during embryogenesis, growth and adult life. The spatio-temporal dependencies of these fields can be modeled by physics-based constitutive equations that we propose to examine in relation to the landmark biological events that occur during embryogenesis.

The hetZ gene indirectly regulates heterocyst development at the level of pattern formation in Anabaena sp. strain PCC 7120

Multicellular development requires the careful orchestration of gene expression to correctly create and position specialized cells. In the filamentous cyanobacterium Anabaena sp. strain PCC 7120, nitrogen-fixing heterocysts are differentiated from vegetative cells in a reproducibly periodic and physiologically relevant pattern. While many genetic factors required for heterocyst development have been identified, the role of HetZ has remained unclear. Here, we present evidence to clarify the requirement of hetZ for heterocyst production and support a model where HetZ functions in the patterning stage of differentiation. We show that a clean, nonpolar deletion of hetZ fails to express the developmental genes hetR, patS, hetP and hetZ correctly and fails to produce heterocysts. Complementation and overexpression of hetZ in a hetP mutant revealed that hetZ was incapable of bypassing hetP, suggesting that it acts upstream of hetP. Complementation and overexpression of hetZ in a hetR mutant, however, demonstrated bypass of hetR, suggesting that it acts downstream of hetR and is capable of bypassing the need for hetR for differentiation irrespective of nitrogen status. Finally, protein-protein interactions were observed between HetZ and HetR, Alr2902 and HetZ itself. Collectively, this work suggests a regulatory role for HetZ in the patterning phase of cellular differentiation in Anabaena.

Modeling Mammalian Gastrulation With Embryonic Stem Cells

Understanding cell fate patterning and morphogenesis in the mammalian embryo remains a formidable challenge. Recently, in vivo models based on embryonic stem cells (ESCs) have emerged as complementary methods to quantitatively dissect the physical and molecular processes that shape the embryo. Here we review recent developments in using ESCs to create both two- and three-dimensional culture models that shed light on mammalian gastrulation.

Nodal and BMP dispersal during early zebrafish development

The secreted TGF-β superfamily signals Nodal and BMP coordinate the patterning of vertebrate embryos. Nodal specifies endoderm and mesoderm during germ layer formation, and BMP specifies ventral fates and patterns the dorsal/ventral axis. Five major models have been proposed to explain how the correct distributions of Nodal and BMP are achieved within tissues to orchestrate embryogenesis: source/sink, transcriptional determination, relay, self-regulation, and shuttling. Here, we discuss recent experiments probing these signal dispersal models, focusing on early zebrafish development.

Role of the boundary in feather bud formation on one-dimensional bioengineered skin

The role of a boundary in pattern formation from a homogenous state in Turing's reaction–diffusion equations is important, particularly when the domain size is comparable to the pattern scale. Such experimental conditions may be achieved for in vitro regeneration of ectodermal appendages such as feathers, via reconstruction of embryonic single cells. This procedure can eliminate a predefined genetic map, such as the midline of chick feather bud formation, leaving uniformly distributed identical cells as a bioengineered skin. Here, the self-organizing nature of multiple feather bud formation was examined in bioengineered 1D-skin samples. Primal formation of feather buds occurred at a fixed length from the skin edge. This formation was numerically recapitulated by a standard two-component reaction-diffusion model, suggesting that the boundary effect caused this observation. The proper boundary conditions were nonstandard, either mixed Dirichlet–Neumann or partial-flux. In addition, the model implies imperfect or hindered bud formation as well as nearly equal distances between buds. In contrast, experimental observations indicated that the skin curvature, which was not included in our model, also strongly affected bud formation. Thus, bioengineered skin may provide an ideal template for modeling a self-organized process from a homogenous state. This study will examine the possible diffusion activities of activator or inhibitor molecular candidates and mechanical activities during cell aggregation, which will advance our understanding of skin appendage regeneration from pluripotent or embryonic stem cells.

Modeling the Notch Response

NOTCH signaling regulates developmental processes in all tissues and all organisms across the animal kingdom. It is often involved in coordinating the differentiation of neighboring cells into different cell types. As our knowledge on the structural, molecular and cellular properties of the NOTCH pathway expands, there is a greater need for quantitative methodologies to get a better understanding of the processes controlled by NOTCH signaling. In recent years, theoretical and computational approaches to NOTCH signaling and NOTCH mediated patterning are gaining popularity. Mathematical models of NOTCH mediated patterning provide insight into complex and counterintuitive behaviors and can help generate predictions that can guide experiments. In this chapter, we review the recent advances in modeling NOTCH mediated patterning processes. We discuss new modeling approaches to lateral inhibition patterning that take into account cis-interactions between NOTCH receptors and ligands, signaling through long cellular protrusions, cell division processes, and coupling to external signals. We also describe models of somitogenesis, where NOTCH signaling is used for synchronizing cellular oscillations. We then discuss modeling approaches that consider the effect of cell morphology on NOTCH signaling and NOTCH mediated patterning. Finally, we consider models of boundary formation and how they are influenced by the combinatorial action of multiple ligands. Together, these topics cover the main advances in the field of modeling the NOTCH response.

Why we need mechanics to understand animal regeneration

Mechanical forces are an important contributor to cell fate specification and cell migration during embryonic development in animals. Similarities between embryogenesis and regeneration, particularly with regards to pattern formation and large-scale tissue movements, suggest similarly important roles for physical forces during regeneration. While the influence of the mechanical environment on stem cell differentiation in vitro is being actively exploited in the fields of tissue engineering and regenerative medicine, comparatively little is known about the role of stresses and strains acting during animal regeneration. In this review, we summarize published work on the role of physical principles and mechanical forces in animal regeneration. Novel experimental techniques aimed at addressing the role of mechanics in embryogenesis have greatly enhanced our understanding at scales from the subcellular to the macroscopic - we believe the time is ripe for the field of regeneration to similarly leverage the tools of the mechanobiological research community.

Emergence of epithelial cell density waves

Epithelial cell monolayers exhibit traveling mechanical waves. We rationalize this observation thanks to a hydrodynamic description of the monolayer as a compressible, active and polar material. We show that propagating waves of the cell density, polarity, velocity and stress fields may be due to a Hopf bifurcation occurring above threshold values of active coupling coefficients.

On the evolution of bilaterality

Bilaterality – the possession of two orthogonal body axes – is the name-giving trait of all bilaterian animals. These body axes are established during early embryogenesis and serve as a three-dimensional coordinate system that provides crucial spatial cues for developing cells, tissues, organs and appendages. The emergence of bilaterality was a major evolutionary transition, as it allowed animals to evolve more complex body plans. Therefore, how bilaterality evolved and whether it evolved once or several times independently is a fundamental issue in evolutionary developmental biology. Recent findings from non-bilaterian animals, in particular from Cnidaria, the sister group to Bilateria, have shed new light into the evolutionary origin of bilaterality. Here, we compare the molecular control of body axes in radially and bilaterally symmetric cnidarians and bilaterians, identify the minimal set of traits common for Bilateria, and evaluate whether bilaterality arose once or more than once during evolution.

Bioelectric gene and reaction networks: computational modelling of genetic, biochemical and bioelectrical dynamics in pattern regulation

Gene regulatory networks (GRNs) describe interactions between gene products and transcription factors that control gene expression. In combination with reaction-diffusion models, GRNs have enhanced comprehension of biological pattern formation. However, although it is well known that biological systems exploit an interplay of genetic and physical mechanisms, instructive factors such as transmembrane potential (Vmem) have not been integrated into full GRN models. Here we extend regulatory networks to include bioelectric signalling, developing a novel synthesis: the bioelectricity-integrated gene and reaction (BIGR) network. Using in silico simulations, we highlight the capacity for Vmem to alter steady-state concentrations of key signalling molecules inside and out of cells. We characterize fundamental feedbacks where Vmem both controls, and is in turn regulated by, biochemical signals and thereby demonstrate Vmem homeostatic control, Vmem memory and Vmem controlled state switching. BIGR networks demonstrating hysteresis are identified as a mechanisms through which more complex patterns of stable Vmem spots and stripes, along with correlated concentration patterns, can spontaneously emerge. As further proof of principle, we present and analyse a BIGR network model that mechanistically explains key aspects of the remarkable regenerative powers of creatures such as planarian flatworms. The functional properties of BIGR networks generate the first testable, quantitative hypotheses for biophysical mechanisms underlying the stability and adaptive regulation of anatomical bioelectric pattern.

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

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

Brg1 chromatin remodeling ATPase balances germ layer patterning by amplifying the transcriptional burst at midblastula transition

Zygotic gene expression programs control cell differentiation in vertebrate development. In Xenopus, these programs are initiated by local induction of regulatory genes through maternal signaling activities in the wake of zygotic genome activation (ZGA) at the midblastula transition (MBT). These programs lay down the vertebrate body plan through gastrulation and neurulation, and are accompanied by massive changes in chromatin structure, which increasingly constrain cellular plasticity. Here we report on developmental functions for Brahma related gene 1 (Brg1), a key component of embyronic SWI/SNF chromatin remodeling complexes. Carefully controlled, global Brg1 protein depletion in X. tropicalis and X. laevis causes embryonic lethality or developmental arrest from gastrulation on. Transcriptome analysis at late blastula, before development becomes arrested, indicates predominantly a role for Brg1 in transcriptional activation of a limited set of genes involved in pattern specification processes and nervous system development. Mosaic analysis by targeted microinjection defines Brg1 as an essential amplifier of gene expression in dorsal (BCNE/Nieuwkoop Center) and ventral (BMP/Vent) signaling centers. Moreover, Brg1 is required and sufficient for initiating axial patterning in cooperation with maternal Wnt signaling. In search for a common denominator of Brg1 impact on development, we have quantitatively filtered global mRNA fluctuations at MBT. The results indicate that Brg1 is predominantly required for genes with the highest burst of transcriptional activity. Since this group contains many key developmental regulators, we propose Brg1 to be responsible for raising their expression above threshold levels in preparation for embryonic patterning.

Brahma-related-gene-1 (Brg1) is a catalytic subunit of mammalian SWI/SNF chromatin remodeling complexes. Loss of maternal Brg1 protein arrests development in mice at the 2-cell stage, while null homozygotes die at the blastocyst stage. These early requirements have precluded any analysis of Brg1’s embryonic functions. Here we present data from X. laevis and X. tropicalis, which for the first time describe a role for Brg1 during germ layer patterning and axis formation. Brg1-depleted embryos fail to develop past gastrulation. Genome-wide transcriptome analysis at late blastula stage, before the developmental arrest, shows that Brg1 is required predominantly for transcriptional activation of a limited set of genes involved in pattern specification processes and nervous system development shortly after midblastula transition. Mosaic analysis by targeted microinjection defines Brg1 as an essential amplifier of gene expression in dorsal (BCNE and Nieuwkoop center) and ventral (BMP/Vent) signaling centers, being required and sufficient to initiate axial patterning by cooperating with canonical Wnt signaling. Since Brg1-dependent genes share a high burst of transcriptional activation before gastrulation, we propose a systemic role for Brg1 as transcriptional amplifier, which balances the embryonic patterning process.

Automated numerical simulation of biological pattern formation based on visual feedback simulation framework

There are various fantastic biological phenomena in biological pattern formation. Mathematical modeling using reaction-diffusion partial differential equation systems is employed to study the mechanism of pattern formation. However, model parameter selection is both difficult and time consuming. In this paper, a visual feedback simulation framework is proposed to calculate the parameters of a mathematical model automatically based on the basic principle of feedback control. In the simulation framework, the simulation results are visualized, and the image features are extracted as the system feedback. Then, the unknown model parameters are obtained by comparing the image features of the simulation image and the target biological pattern. Considering two typical applications, the visual feedback simulation framework is applied to fulfill pattern formation simulations for vascular mesenchymal cells and lung development. In the simulation framework, the spot, stripe, labyrinthine patterns of vascular mesenchymal cells, the normal branching pattern and the branching pattern lacking side branching for lung branching are obtained in a finite number of iterations. The simulation results indicate that it is easy to achieve the simulation targets, especially when the simulation patterns are sensitive to the model parameters. Moreover, this simulation framework can expand to other types of biological pattern formation.