Waves in Embryonic Development

Oscillatory phenomena in electrophysiological networks: The coupling between cell bioelectricity and transcription

Morphogenetic regulation during embryogenesis and regeneration rely on information transfer and coordination between different regions. Here, we explore theoretically the coupling between bioelectrical and transcriptional oscillations at the individual cell and multicellular levels. The simulations, based on a set of ion channels and intercellular gap junctions, show that bioelectrical and transcriptional waves can electrophysiologically couple distant regions of a model network in phase and antiphase oscillatory states that include synchronization phenomena. In this way, different multicellular regionalizations can be encoded by cell potentials that oscillate between depolarized and polarized states, thus allowing a spatio-temporal coding. Because the electric potential patterns characteristic of development and regeneration are correlated with the spatial distributions of signaling ions and molecules, bioelectricity can act as a template for slow biochemical signals following a hierarchy of experimental times. In particular, bioelectrical gradients that couple cell potentials to transcription rates give to each single cell a rough idea of its location in the multicellular ensemble, thus controlling local differentiation processes that switch on and off crucial parts of the genome.

ERK synchronizes embryonic cleavages in Drosophila

Extracellular-signal-regulated kinase (ERK) signaling controls development and homeostasis and is genetically deregulated in human diseases, including neurocognitive disorders and cancers. Although the list of ERK functions is vast and steadily growing, the full spectrum of processes controlled by any specific ERK activation event remains unknown. Here, we show how ERK functions can be systematically identified using targeted perturbations and global readouts of ERK activation. Our experimental model is the Drosophila embryo, where ERK signaling at the embryonic poles has thus far only been associated with the transcriptional patterning of the future larva. Through a combination of live imaging and phosphoproteomics, we demonstrated that ERK activation at the poles is also critical for maintaining the speed and synchrony of embryonic cleavages. The presented approach to interrogating phosphorylation networks identifies a hidden function of a well-studied signaling event and sets the stage for similar studies in other organisms.

Mechanical state transitions in the regulation of tissue form and function

From embryonic development, postnatal growth and adult homeostasis to reparative and disease states, cells and tissues undergo constant changes in genome activity, cell fate, proliferation, movement, metabolism and growth. Importantly, these biological state transitions are coupled to changes in the mechanical and material properties of cells and tissues, termed mechanical state transitions. These mechanical states share features with physical states of matter, liquids and solids. Tissues can switch between mechanical states by changing behavioural dynamics or connectivity between cells. Conversely, these changes in tissue mechanical properties are known to control cell and tissue function, most importantly the ability of cells to move or tissues to deform. Thus, tissue mechanical state transitions are implicated in transmitting information across biological length and time scales, especially during processes of early development, wound healing and diseases such as cancer. This Review will focus on the biological basis of tissue-scale mechanical state transitions, how they emerge from molecular and cellular interactions, and their roles in organismal development, homeostasis, regeneration and disease.

Mechanochemical dynamics of collective cells and hierarchical topological defects in multicellular lumens

Collective cell dynamics is essential for tissue morphogenesis and various biological functions. However, it remains incompletely understood how mechanical forces and chemical signaling are integrated to direct collective cell behaviors underlying tissue morphogenesis. Here, we propose a three-dimensional (3D) mechanochemical theory accounting for biochemical reaction-diffusion and cellular mechanotransduction to investigate the dynamics of multicellular lumens. We show that the interplay between biochemical signaling and mechanics can trigger either pitchfork or Hopf bifurcation to induce diverse static mechanochemical patterns or generate oscillations with multiple modes both involving marked mechanical deformations in lumens. We uncover the crucial role of mechanochemical feedback in emerging morphodynamics and identify the evolution and morphogenetic functions of hierarchical topological defects including cell-level hexatic defects and tissue-level orientational defects. Our theory captures the common mechanochemical traits of collective dynamics observed in experiments and could provide a mechanistic context for understanding morphological symmetry breaking in 3D lumen-like tissues.

Mitotic waves in frog egg extracts: Transition from phase waves to trigger waves

Cyclin-dependent kinase 1 (Cdk1) activity rises and falls throughout the cell cycle, a cell-autonomous process known as mitotic oscillations. These oscillators can synchronize when spatially coupled, providing a crucial foundation for rapid synchronous divisions in large early embryos like Drosophila (~ 0.5 mm) and Xenopus (~ 1.2 mm). While diffusion alone cannot achieve such long-range coordination, recent studies have proposed two types of mitotic waves, phase and trigger waves, to explain the phenomena. How the waves establish over time for efficient spatial coordination remains unclear. Using Xenopus laevis egg extracts and a Cdk1 FRET sensor, we observe a transition from phase waves to a trigger wave regime in an initially homogeneous cytosol. Adding nuclei accelerates such transition. Moreover, the system transitions almost immediately to this regime when externally driven by metaphase-arrested extracts from the boundary. Employing computational modeling, we pinpoint how wave nature, including speed-period relation, depends on transient dynamics and oscillator properties, suggesting that phase waves appear transiently due to the time required for trigger waves to entrain the system and that spatial heterogeneity promotes entrainment. Therefore, we show that both waves belong to a single biological process capable of coordinating the cell cycle over long distances.

[The Dynamic Model of the Active-Inactive Cell Interface]

Objective

To explore the morphodynamics of the active-inactive cell monolayer interfaces by using the active liquid crystal model.

Methods

A continuum mechanical model was established based on the active liquid crystal theory and the active-inactive cell monolayer interfaces were established by setting the activity difference of cell monolayers. The theoretical equations were solved numerically by the finite difference and the lattice Boltzmann method.

Results

The active-inactive cell interfaces displayed three typical morphologies, namely, flat interface, wavy interface, and finger-like interface. On the flat interfaces, the cells were oriented perpendicular to the interface, the -1/2 topological defects were clustered in the interfaces, and the interfaces were negatively charged. On the wavy interfaces, cells showed no obvious preference for orientation at the interfaces and the interfaces were neutrally charged. On the finger-like interfaces, cells were tangentially oriented at the interfaces, the +1/2 topological defects were collected at the interfaces, driving the growth of the finger-like structures, and the interfaces were positively charged.

Conclusion

The orientation of the cell alignment at the interface can significantly affect the morphologies of the active-inactive cell monolayer interfaces, which is closely associated with the dynamics of topological defects at the interfaces.

Spiking at the edge: Excitability at interfaces in reaction-diffusion systems

Excitable media, ranging from bioelectric tissues and chemical oscillators to forest fires and competing populations, are nonlinear, spatially extended systems capable of spiking. Most investigations of excitable media consider situations where the amplifying and suppressing forces necessary for spiking coexist at every point in space. In this case, spikes arise due to local bistabilities, which require a fine-tuned ratio between local amplification and suppression strengths. But, in nature and engineered systems, these forces can be segregated in space, forming structures like interfaces and boundaries. Here, we show how boundaries can generate and protect spiking when the reacting components can spread out: Even arbitrarily weak diffusion can cause spiking at the edge between two non-excitable media. This edge spiking arises due to a global bistability, which can occur even if amplification and suppression strengths do not allow spiking when mixed. We analytically derive a spiking phase diagram that depends on two parameters: i) the ratio between the system size and the characteristic diffusive length-scale and ii) the ratio between the amplification and suppression strengths. Our analysis explains recent experimental observations of action potentials at the interface between two non-excitable bioelectric tissues. Beyond electrophysiology, we highlight how edge spiking emerges in predator-prey dynamics and in oscillating chemical reactions. Our findings provide a theoretical blueprint for a class of interfacial excitations in reaction-diffusion systems, with potential implications for spatially controlled chemical reactions, nonlinear waveguides and neuromorphic computation, as well as spiking instabilities, such as cardiac arrhythmias, that naturally occur in heterogeneous biological media.

Direct measurement of dynamic attractant gradients reveals breakdown of the Patlak-Keller-Segel chemotaxis model

Chemotactic bacteria not only navigate chemical gradients, but also shape their environments by consuming and secreting attractants. Investigating how these processes influence the dynamics of bacterial populations has been challenging because of a lack of experimental methods for measuring spatial profiles of chemoattractants in real time. Here, we use a fluorescent sensor for aspartate to directly measure bacterially generated chemoattractant gradients during collective migration. Our measurements show that the standard Patlak-Keller-Segel model for collective chemotactic bacterial migration breaks down at high cell densities. To address this, we propose modifications to the model that consider the impact of cell density on bacterial chemotaxis and attractant consumption. With these changes, the model explains our experimental data across all cell densities, offering insight into chemotactic dynamics. Our findings highlight the significance of considering cell density effects on bacterial behavior, and the potential for fluorescent metabolite sensors to shed light on the complex emergent dynamics of bacterial communities.

Automatic detection of spatio-temporal signaling patterns in cell collectives

Increasing experimental evidence points to the physiological importance of space-time correlations in signaling of cell collectives. From wound healing to epithelial homeostasis to morphogenesis, coordinated activation of biomolecules between cells allows the collectives to perform more complex tasks and to better tackle environmental challenges. To capture this information exchange and to advance new theories of emergent phenomena, we created ARCOS, a computational method to detect and quantify collective signaling. We demonstrate ARCOS on cell and organism collectives with space-time correlations on different scales in 2D and 3D. We made a new observation that oncogenic mutations in the MAPK/ERK and PIK3CA/Akt pathways of MCF10A epithelial cells hyperstimulate intercellular ERK activity waves that are largely dependent on matrix metalloproteinase intercellular signaling. ARCOS is open-source and available as R and Python packages. It also includes a plugin for the napari image viewer to interactively quantify collective phenomena without prior programming experience.

An active traveling wave of Eda/NF-κB signaling controls the timing and hexagonal pattern of skin appendages in zebrafish

Periodic patterns drive the formation of a variety of tissues, including skin appendages such as feathers and scales. Skin appendages serve important and diverse functions across vertebrates, yet the mechanisms that regulate their patterning are not fully understood. Here, we have used live imaging to investigate dynamic signals regulating the ontogeny of zebrafish scales. Scales are bony skin appendages that develop sequentially along the anterior-posterior and dorsal-ventral axes to cover the fish in a hexagonal array. We have found that scale development requires cell-cell communication and is coordinated through an active wave mechanism. Using a live transcriptional reporter, we show that a wave of Eda/NF-κB activity precedes scale initiation and is required for scale formation. Experiments decoupling the propagation of the wave from dermal placode formation and osteoblast differentiation demonstrate that the Eda/NF-κB activity wavefront controls the timing of the sequential patterning of scales. Moreover, this decoupling resulted in defects in scale size and significant deviations in the hexagonal patterning of scales. Thus, our results demonstrate that a biochemical traveling wave coordinates scale initiation and proper hexagonal patterning across the fish body.

Force propagation between epithelial cells depends on active coupling and mechano-structural polarization

Cell-generated forces play a major role in coordinating the large-scale behavior of cell assemblies, in particular during development, wound healing, and cancer. Mechanical signals propagate faster than biochemical signals, but can have similar effects, especially in epithelial tissues with strong cell-cell adhesion. However, a quantitative description of the transmission chain from force generation in a sender cell, force propagation across cell-cell boundaries, and the concomitant response of receiver cells is missing. For a quantitative analysis of this important situation, here we propose a minimal model system of two epithelial cells on an H-pattern ('cell doublet'). After optogenetically activating RhoA, a major regulator of cell contractility, in the sender cell, we measure the mechanical response of the receiver cell by traction force and monolayer stress microscopies. In general, we find that the receiver cells show an active response so that the cell doublet forms a coherent unit. However, force propagation and response of the receiver cell also strongly depend on the mechano-structural polarization in the cell assembly, which is controlled by cell-matrix adhesion to the adhesive micropattern. We find that the response of the receiver cell is stronger when the mechano-structural polarization axis is oriented perpendicular to the direction of force propagation, reminiscent of the Poisson effect in passive materials. We finally show that the same effects are at work in small tissues. Our work demonstrates that cellular organization and active mechanical response of a tissue are key to maintain signal strength and lead to the emergence of elasticity, which means that signals are not dissipated like in a viscous system, but can propagate over large distances.

Direct measurement of dynamic attractant gradients reveals breakdown of the Patlak-Keller-Segel chemotaxis model

Chemotactic bacteria not only navigate chemical gradients, but also shape their environments by consuming and secreting attractants. Investigating how these processes influence the dynamics of bacterial populations has been challenging because of a lack of experimental methods for measuring spatial profiles of chemoattractants in real time. Here, we use a fluorescent sensor for aspartate to directly measure bacterially generated chemoattractant gradients during collective migration. Our measurements show that the standard Patlak-Keller-Segel model for collective chemotactic bacterial migration breaks down at high cell densities. To address this, we propose modifications to the model that consider the impact of cell density on bacterial chemotaxis and attractant consumption. With these changes, the model explains our experimental data across all cell densities, offering new insight into chemotactic dynamics. Our findings highlight the significance of considering cell density effects on bacterial behavior, and the potential for fluorescent metabolite sensors to shed light on the complex emergent dynamics of bacterial communities.

An active traveling wave of Eda/NF-kB signaling controls the timing and hexagonal pattern of skin appendages in zebrafish

Periodic patterns make up a variety of tissues, including skin appendages such as feathers and scales. Skin appendages serve important and diverse functions across vertebrates, yet the mechanisms that regulate their patterning are not fully understood. Here, we have used live imaging to investigate dynamic signals regulating the ontogeny of zebrafish scales. Scales are bony skin appendages which develop sequentially along the anterior-posterior and dorsal-ventral axes to cover the fish in a hexagonal array. We have found that scale development requires cell-cell communication and is coordinated through an active wave mechanism. Using a live transcriptional reporter, we show that a wave of Eda/NF-κB activity precedes scale initiation and is required for scale formation. Experiments decoupling the propagation of the wave from dermal placode formation and osteoblast differentiation demonstrate that the Eda/NF-kB activity wavefront times the sequential patterning of scales. Moreover, this decoupling resulted in defects in scale size and significant deviations in the hexagonal patterning of scales. Thus, our results demonstrate that a biochemical traveling wave coordinates scale initiation and proper hexagonal patterning across the fish body.

Hydrodynamics of a confined active Belousov-Zhabotinsky droplet

Self-sustained locomotion of synthetic droplet swimmers has been of great interest due to their ability to mimic the behavior of biological swimmers. Here we harness the Belousov-Zhabotinsky (BZ) reaction to induce Marangoni stresses on the fluid-droplet interface and elucidate the spontaneous locomotion of active BZ droplets in a confined two-dimensional channel. Our approach employs the lattice Boltzmann method to simulate a coupled system of multiphase hydrodynamics and BZ-reaction kinetics. Our investigation reveals the mechanism underlying the propulsion of active BZ droplets, in terms of convective and diffusive fluxes and deformation of the droplets. Furthermore, we demonstrate that by manipulating the degree of confinement, strength, and nature of coupling between surface tension and active species' concentration, the motion of the BZ droplet can be directed. In addition, we are able to capture two different kinds of droplet behaviors, namely, sustained and stationary, and establish conditions for the sustained long-time motion. We envisage that our findings can be used not only to understand the mechanics of biological swimmers but also to design reaction-driven self-propelled systems for a variety of biomimetic applications.

Manipulating the nature of embryonic mitotic waves

Early embryogenesis is characterized by rapid and synchronous cleavage divisions, which are often controlled by wave-like patterns of Cdk1 activity. Two mechanisms have been proposed for mitotic waves: sweep and trigger waves.1,2 The two mechanisms give rise to different wave speeds, dependencies on physical and molecular parameters, and spatial profiles of Cdk1 activity: upward sweeping gradients versus traveling wavefronts. Both mechanisms hinge on the transient bistability governing the cell cycle and are differentiated by the speed of the cell-cycle progression: sweep and trigger waves arise for rapid and slow drives, respectively. Here, using quantitative imaging of Cdk1 activity and theory, we illustrate that sweep waves are the dominant mechanism in Drosophila embryos and test two fundamental predictions on the transition from sweep to trigger waves. We demonstrate that sweep waves can be turned into trigger waves if the cell cycle is slowed down genetically or if significant delays in the cell-cycle progression are introduced across the embryo by altering nuclear density. Our genetic experiments demonstrate that Polo kinase is a major rate-limiting regulator of the blastoderm divisions, and genetic perturbations reducing its activity can induce the transition from sweep to trigger waves. Furthermore, we show that changes in temperature cause an essentially uniform slowdown of interphase and mitosis. That results in sweep waves being observed across a wide temperature range despite the cell-cycle durations being significantly different. Collectively, our combination of theory and experiments elucidates the nature of mitotic waves in Drosophila embryogenesis, their control mechanisms, and their mutual transitions.