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.

Pollen Cell Wall Patterns Form from Modulated Phases.

The ornately geometric walls of pollen grains have inspired scientists for decades. We show that the evolved diversity of these patterns is entirely recapitulated by a biophysical model in which an initially uniform polysaccharide layer in the extracellular space, mechanically coupled to the cell membrane, phase separates to a spatially modulated state. Experiments reveal this process occurring in living cells. We observe that in ∼10% of extant species, this phase separation reaches equilibrium during development such that individual pollen grains are identical and perfectly reproducible. About 90% of species undergo an arrest of this process prior to equilibrium such that individual grains are similar but inexact copies. Equilibrium patterns have appeared multiple times during the evolution of seed plants, but selection does not favor these states. This framework for pattern development provides a route to rationalizing the surface textures of other secreted structures, such as cell walls and insect cuticle.

Diverse Spatial Expression Patterns Emerge from Unified Kinetics of Transcriptional Bursting.

How transcriptional bursting relates to gene regulation is a central question that has persisted for more than a decade. Here, we measure nascent transcriptional activity in early Drosophila embryos and characterize the variability in absolute activity levels across expression boundaries. We demonstrate that boundary formation follows a common transcription principle: a single control parameter determines the distribution of transcriptional activity, regardless of gene identity, boundary position, or enhancer-promoter architecture. We infer the underlying bursting kinetics and identify the key regulatory parameter as the fraction of time a gene is in a transcriptionally active state. Unexpectedly, both the rate of polymerase initiation and the switching rates are tightly constrained across all expression levels, predicting synchronous patterning outcomes at all positions in the embryo. These results point to a shared simplicity underlying the apparently complex transcriptional processes of early embryonic patterning and indicate a path to general rules in transcriptional regulation.

Development of Concurrent Retinotopic Maps in the Fly Motion Detection Circuit.

Understanding how complex brain wiring is produced during development is a daunting challenge. In Drosophila, information from 800 retinal ommatidia is processed in distinct brain neuropiles, each subdivided into 800 matching retinotopic columns. The lobula plate comprises four T4 and four T5 neuronal subtypes. T4 neurons respond to bright edge motion, whereas T5 neurons respond to dark edge motion. Each is tuned to motion in one of the four cardinal directions, effectively establishing eight concurrent retinotopic maps to support wide-field motion. We discovered a mode of neurogenesis where two sequential Notch-dependent divisions of either a horizontal or a vertical progenitor produce matching sets of two T4 and two T5 neurons retinotopically coincident with pairwise opposite direction selectivity. We show that retinotopy is an emergent characteristic of this neurogenic program and derives directly from neuronal birth order. Our work illustrates how simple developmental rules can implement complex neural organization.

Mechanisms Underlying the Formation and Evolution of Vertebrate Color Patterns.

Vertebrates exhibit a wide range of color patterns, which play critical roles in mediating intra- and interspecific communication. Because of their diversity and visual accessibility, color patterns offer a unique and fascinating window into the processes underlying biological organization. In this review, we focus on describing many of the general principles governing the formation and evolution of color patterns in different vertebrate groups. We characterize the types of patterns, review the molecular and developmental mechanisms by which they originate, and discuss their role in constraining or facilitating evolutionary change. Lastly, we outline outstanding questions in the field and discuss different approaches that can be used to address them. Overall, we provide a unifying conceptual framework among vertebrate systems that may guide research into naturally evolved mechanisms underlying color pattern formation and evolution.

The Heidelberg Screen for Pattern Mutants of Drosophila: A Personal Account.

In large-scale mutagenesis screens performed in 1979-1980 at the EMBL in Heidelberg, we isolated mutations affecting the pattern or structure of the larval cuticle in Drosophila. The 600 mutants we characterized could be assigned to 120 genes and represent the majority of such genes in the genome. These mutants subsequently provided a rich resource for understanding many fundamental developmental processes, such as the transcriptional hierarchies controlling segmentation, the establishment of cell states by signaling pathways, and the differentiation of epithelial cells. Most of the Heidelberg genes are now molecularly known, and many of them are conserved in other animals, including humans. Although the screens were initially driven entirely by curiosity, the mutants now serve as models for many human diseases. In this review, we describe the rationale of the screening procedures and provide a classification of the genes on the basis of their initial phenotypes and the subsequent molecular analyses.

Genetic Screens to Analyze Pattern Formation of Egg and Embryo in Drosophila: A Personal History.

In Drosophila development, the axes of the egg and future embryo are established during oogenesis. To learn about the underlying genetic and molecular pathways that lead to axis formation, I conducted a large-scale genetic screen at the beginning of my independent career. This led to the eventual understanding that both anterior-posterior and dorsal-ventral pattern information is transmitted from the oocyte to the surrounding follicle cells and in turn from the follicle cells back to the oocyte. How I came to conduct this screen and what further insights were gained by studying the mutants isolated in the screen are the topics of this autobiographical article.

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.

Integrating chemistry, fluid flow, and mechanics to drive spontaneous formation of three-dimensional (3D) patterns in anchored microstructures.

Enzymatic reactions in solution drive the convection of confined fluids throughout the enclosing chambers and thereby couple the processes of reaction and convection. In these systems, the energy released from the chemical reactions generates a force, which propels the fluids' spontaneous motion. Here, we use theoretical and computational modeling to determine how reaction-convection can be harnessed to tailor and control the dynamic behavior of soft matter immersed in solution. Our model system encompasses an array of surface-anchored, flexible posts in a millimeter-sized, fluid-filled chamber. Selected posts are coated with enzymes, which react with dissolved chemicals to produce buoyancy-driven fluid flows. We show that these chemically generated flows exert a force on both the coated (active) and passive posts and thus produce regular, self-organized patterns. Due to the specificity of enzymatic reactions, the posts display controllable kaleidoscopic behavior where one regular pattern is smoothly morphed into another with the addition of certain reactants. These spatiotemporal patterns also form "fingerprints" that distinctly characterize the system, reflecting the type of enzymes used, placement of the enzyme-coated posts, height of the chamber, and bending modulus of the elastic posts. The results reveal how reaction-convection provides concepts for designing soft matter that readily switches among multiple morphologies. This behavior enables microfluidic devices to be spontaneously reconfigured for specific applications without construction of new chambers and the fabrication of standalone sensors that operate without extraneous power sources.

On the mechanical origins of waving, coiling and skewing in Arabidopsis thaliana roots.

By masterfully balancing directed growth and passive mechanics, plant roots are remarkably capable of navigating complex heterogeneous environments to find resources. Here, we present a theoretical and numerical framework which allows us to interrogate and simulate the mechanical impact of solid interfaces on the growth pattern of plant organs. We focus on the well-known waving, coiling, and skewing patterns exhibited by roots of Arabidopsis thaliana when grown on inclined surfaces, serving as a minimal model of the intricate interplay with solid substrates. By modeling growing slender organs as Cosserat rods that mechanically interact with the environment, our simulations verify hypotheses of waving and coiling arising from the combination of active gravitropism and passive root-plane responses. Skewing is instead related to intrinsic twist due to cell file rotation. Numerical investigations are outfitted with an analytical framework that consistently relates transitions between straight, waving, coiling, and skewing patterns with substrate tilt angle. Simulations are found to corroborate theory and recapitulate a host of reported experimental observations, thus providing a systematic approach for studying in silico plant organs behavior in relation to their environment.

Chemical composition from photos: Dried solution drops reveal a morphogenetic tree.

Under nonequilibrium conditions, inorganic systems can produce a wealth of life-like shapes and patterns which, compared to well-formed crystalline materials, remain widely unexplored. A seemingly simple example is the formation of salt deposits during the evaporation of sessile droplets. These evaporites show great variations in their specific patterns including single rings, creep, small crystals, fractals, and featureless disks. We have explored the patterns of 42 different salts at otherwise constant conditions. Based on 7,500 images, we show that distinct pattern families can be identified and that some salts (e.g., Na2SO4 and NH4NO3) are bifurcated creating two distinct motifs. Family affiliations cannot be predicted a priori from composition alone but rather emerge from the complex interplay of evaporation, crystallization, thermodynamics, capillarity, and fluid flow. Nonetheless, chemical composition can be predicted from the deposit pattern with surprisingly high accuracy even if the set of reference images is small. These findings suggest possible applications including smartphone-based analyses and lightweight tools for space missions.

Voltage-gated sodium channel activity mediates sea urchin larval skeletal patterning through spatial regulation of Wnt5 expression.

Defining pattern formation mechanisms during embryonic development is important for understanding the etiology of birth defects and to inform tissue engineering approaches. In this study, we used tricaine, a voltage-gated sodium channel (VGSC) inhibitor, to show that VGSC activity is required for normal skeletal patterning in Lytechinus variegatus sea urchin larvae. We demonstrate that tricaine-mediated patterning defects are rescued by an anesthetic-insensitive version of the VGSC LvScn5a. Expression of this channel is enriched in the ventrolateral ectoderm, where it spatially overlaps with posterolaterally expressed Wnt5. We show that VGSC activity is required to spatially restrict Wnt5 expression to this ectodermal region that is adjacent and instructive to clusters of primary mesenchymal cells that initiate secretion of the larval skeleton as triradiates. Tricaine-mediated Wnt5 spatial expansion correlates with the formation of ectopic PMC clusters and triradiates. These defects are rescued by Wnt5 knockdown, indicating that the spatial expansion of Wnt5 is responsible for the patterning defects induced by VGSC inhibition. These results demonstrate a previously unreported connection between bioelectrical status and the spatial control of patterning cue expression during embryonic pattern formation.

Exploring generic principles of compartmentalization in a developmental in vitro model.

Self-organization of cells into higher-order structures is key for multicellular organisms, for example via repetitive replication of template-like founder cells or syncytial energids. Yet, very similar spatial arrangements of cell-like compartments ('protocells') are also seen in a minimal model system of Xenopus egg extracts in the absence of template structures and chromatin, with dynamic microtubule assemblies driving the self-organization process. Quantifying geometrical features over time, we show here that protocell patterns are highly organized with a spatial arrangement and coarsening dynamics similar to that of two-dimensional foams but without the long-range ordering expected for hexagonal patterns. These features remain invariant when enforcing smaller protocells by adding taxol, i.e. patterns are dominated by a single, microtubule-derived length scale. Comparing our data to generic models, we conclude that protocell patterns emerge by simultaneous formation of randomly assembling protocells that grow at a uniform rate towards a frustrated arrangement before fusion of adjacent protocells eventually drives coarsening. The similarity of protocell patterns to arrays of energids and cells in developing organisms, but also to epithelial monolayers, suggests generic mechanical cues to drive self-organized space compartmentalization.

Frizzled2 receives WntA signaling during butterfly wing pattern formation.

Butterfly color patterns provide visible and biodiverse phenotypic readouts of the patterning processes. Although the secreted ligand WntA has been shown to instruct the color pattern formation in butterflies, its mode of reception remains elusive. Butterfly genomes encode four homologs of the Frizzled-family of Wnt receptors. Here, we show that CRISPR mosaic knockouts of frizzled2 (fz2) phenocopy the color pattern effects of WntA loss of function in multiple nymphalids. Whereas WntA mosaic clones result in intermediate patterns of reduced size, fz2 clones are cell-autonomous, consistent with a morphogen function. Shifts in expression of WntA and fz2 in WntA crispant pupae show that they are under positive and negative feedback, respectively. Fz1 is required for Wnt-independent planar cell polarity in the wing epithelium. Fz3 and Fz4 show phenotypes consistent with Wnt competitive-antagonist functions in vein formation (Fz3 and Fz4), wing margin specification (Fz3), and color patterning in the Discalis and Marginal Band Systems (Fz4). Overall, these data show that the WntA/Frizzled2 morphogen-receptor pair forms a signaling axis that instructs butterfly color patterning and shed light on the functional diversity of insect Frizzled receptors.

Migration and division in cell monolayers on substrates with topological defects.

Collective movement and organization of cell monolayers are important for wound healing and tissue development. Recent experiments highlighted the importance of liquid crystal order within these layers, suggesting that +1 topological defects have a role in organizing tissue morphogenesis. We study fibroblast organization, motion, and proliferation on a substrate with micron-sized ridges that induce +1 and -1 topological defects using simulation and experiment. We model cells as self-propelled deformable ellipses that interact via a Gay-Berne potential. Unlike earlier work on other cell types, we see that density variation near defects is not explained by collective migration. We propose instead that fibroblasts have different division rates depending on their area and aspect ratio. This model captures key features of our previous experiments: the alignment quality worsens at high cell density and, at the center of the +1 defects, cells can adopt either highly anisotropic or primarily isotropic morphologies. Experiments performed with different ridge heights confirm a prediction of this model: Suppressing migration across ridges promotes higher cell density at the +1 defect. Our work enables a mechanism for tissue patterning using topological defects without relying on cell migration.

Phase-separation physics underlies new theory for the resilience of patchy ecosystems.

Spatial self-organization of ecosystems into large-scale (from micron to meters) patterns is an important phenomenon in ecology, enabling organisms to cope with harsh environmental conditions and buffering ecosystem degradation. Scale-dependent feedbacks provide the predominant conceptual framework for self-organized spatial patterns, explaining regular patterns observed in, e.g., arid ecosystems or mussel beds. Here, we highlight an alternative mechanism for self-organized patterns, based on the aggregation of a biotic or abiotic species, such as herbivores, sediment, or nutrients. Using a generalized mathematical model, we demonstrate that ecosystems with aggregation-driven patterns have fundamentally different dynamics and resilience properties than ecosystems with patterns that formed through scale-dependent feedbacks. Building on the physics theory for phase-separation dynamics, we show that patchy ecosystems with aggregation patterns are more vulnerable than systems with patterns formed through scale-dependent feedbacks, especially at small spatial scales. This is because local disturbances can trigger large-scale redistribution of resources, amplifying local degradation. Finally, we show that insights from physics, by providing mechanistic understanding of the initiation of aggregation patterns and their tendency to coarsen, provide a new indicator framework to signal proximity to ecological tipping points and subsequent ecosystem degradation for this class of patchy ecosystems.

Pattern selection by material aging: Modeling chemical gardens in two and three dimensions.

Chemical gardens are complex, often macroscopic, structures formed by precipitation reactions. Their thin walls compartmentalize the system and adjust in size and shape if the volume of the interior reactant solution is increased by osmosis or active injection. Spatial confinement to a thin layer is known to result in various patterns including self-extending filaments and flower-like patterns organized around a continuous, expanding front. Here, we describe a cellular automaton model for this type of self-organization, in which each lattice site is occupied by one of the two reactants or the precipitate. Reactant injection causes the random replacement of precipitate and generates an expanding near-circular precipitate front. If this process includes an age bias favoring the replacement of fresh precipitate, thin-walled filaments arise and grow-like in the experiments-at the leading tip. In addition, the inclusion of a buoyancy effect allows the model to capture various branched and unbranched chemical garden shapes in two and three dimensions. Our results provide a model of chemical garden structures and highlight the importance of temporal changes in the self-healing membrane material.

Wetting transition and fluid trapping in a microfluidic fracture.

Immiscible fluid-fluid displacement in confined geometries is a fundamental process occurring in many natural phenomena and technological applications, from geological CO2 sequestration to microfluidics. Due to the interactions between the fluids and the solid walls, fluid invasion undergoes a wetting transition from complete displacement at low displacement rates to leaving a film of the defending fluid on the confining surfaces at high displacement rates. While most real surfaces are rough, fundamental questions remain about the type of fluid-fluid displacement that can emerge in a confined, rough geometry. Here, we study immiscible displacement in a microfluidic device with a precisely controlled structured surface as an analogue for a rough fracture. We analyze the influence of the degree of surface roughness on the wetting transition and the formation of thin films of the defending liquid. We show experimentally, and rationalize theoretically, that roughness affects both the stability and dewetting dynamics of thin films, leading to distinct late-time morphologies of the undisplaced (trapped) fluid. Finally, we discuss the implications of our observations for geologic and technological applications.

Emergence of tip singularities in dissolution patterns.

Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock-like salt, gypsum, or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the mass transfer, and the flow leads to the formation of remarkable patterns, like scallop patterns in caves. We emphasize the common presence of very sharp shapes and spikes, despite the diversity of hydrodynamic conditions and the nature of the soluble materials. We explain the generic emergence of such spikes in dissolution processes by a geometrical approach. Singularities at the interface emerge as a consequence of the erosion directed in the normal direction, when the surface displays curvature variations, like those associated with a dissolution pattern. First, we demonstrate the presence of singular structures in natural interfaces shaped by dissolution. Then, we propose simple surface evolution models of increasing complexity demonstrating the emergence of spikes and allowing us to explain at long term by coarsening the formation of cellular structures. Finally, we perform a dissolution pattern experiment driven by solutal convection, and we report the emergence of a cellular pattern following well the model predictions. Although the precise prediction of dissolution shapes necessitates performing a complete hydrodynamic study, we show that the characteristic spikes which are reported ultimately for dissolution shapes are explained generically by geometrical arguments due to the surface evolution. These findings can be applied to other ablation patterns, reported for example in melting ice.

Geometrical control of interface patterning underlies active matter invasion.

Interaction between active materials and the boundaries of geometrical confinement is key to many emergent phenomena in active systems. For living active matter consisting of animal cells or motile bacteria, the confinement boundary is often a deformable interface, and it has been unclear how activity-induced interface dynamics might lead to morphogenesis and pattern formation. Here, we studied the evolution of bacterial active matter confined by a deformable boundary. We found that an ordered morphological pattern emerged at the interface characterized by periodically spaced interfacial protrusions; behind the interfacial protrusions, bacterial swimmers self-organized into multicellular clusters displaying +1/2 nematic defects. Subsequently, a hierarchical sequence of transitions from interfacial protrusions to creeping branches allowed the bacterial active drop to rapidly invade surrounding space with a striking self-similar branch pattern. We found that this interface patterning is geometrically controlled by the local curvature of the interface, a phenomenon we denote as collective curvature sensing. Using a continuum active model, we revealed that the collective curvature sensing arises from enhanced active stresses near high-curvature regions, with the active length scale setting the characteristic distance between the interfacial protrusions. Our findings reveal a protrusion-to-branch transition as a unique mode of active matter invasion and suggest a strategy to engineer pattern formation of active materials.