Spatial trigger waves: positive feedback gets you a long way

Robust trigger wave speed in Xenopus cytoplasmic extracts

Self-regenerating trigger waves can spread rapidly through the crowded cytoplasm without diminishing in amplitude or speed, providing consistent, reliable, long-range communication. The macromolecular concentration of the cytoplasm varies in response to physiological and environmental fluctuations, raising the question of how or if trigger waves can robustly operate in the face of such fluctuations. Using Xenopus extracts, we find that mitotic and apoptotic trigger wave speeds are remarkably invariant. We derive a model that accounts for this robustness and for the eventual slowing at extremely high and low cytoplasmic concentrations. The model implies that the positive and negative effects of cytoplasmic concentration (increased reactant concentration vs. increased viscosity) are nearly precisely balanced. Accordingly, artificially maintaining a constant cytoplasmic viscosity during dilution abrogates this robustness. The robustness in trigger wave speeds may contribute to the reliability of the extremely rapid embryonic cell cycle.

Self-extinguishing relay waves enable homeostatic control of human neutrophil swarming

Neutrophils collectively migrate to sites of injury and infection. How these swarms are coordinated to ensure the proper level of recruitment is unknown. Using an ex vivo model of infection, we show that human neutrophil swarming is organized by multiple pulsatile chemoattractant waves. These waves propagate through active relay in which stimulated neutrophils trigger their neighbors to release additional swarming cues. Unlike canonical active relays, we find these waves to be self-terminating, limiting the spatial range of cell recruitment. We identify an NADPH-oxidase-based negative feedback loop that is needed for this self-terminating behavior. We observe near-constant levels of neutrophil recruitment over a wide range of starting conditions, revealing surprising robustness in the swarming process. This homeostatic control is achieved by larger and more numerous swarming waves at lower cell densities. We link defective wave termination to a broken recruitment homeostat in the context of human chronic granulomatous disease.

Emergence of large-scale cell death through ferroptotic trigger waves

Large-scale cell death is commonly observed during organismal development and in human pathologies1-5. These cell death events extend over great distances to eliminate large populations of cells, raising the question of how cell death can be coordinated in space and time. One mechanism that enables long-range signal transmission is trigger waves6, but how this mechanism might be used for death events in cell populations remains unclear. Here we demonstrate that ferroptosis, an iron- and lipid-peroxidation-dependent form of cell death, can propagate across human cells over long distances (≥5 mm) at constant speeds (around 5.5 μm min-1) through trigger waves of reactive oxygen species (ROS). Chemical and genetic perturbations indicate a primary role of ROS feedback loops (Fenton reaction, NADPH oxidase signalling and glutathione synthesis) in controlling the progression of ferroptotic trigger waves. We show that introducing ferroptotic stress through suppression of cystine uptake activates these ROS feedback loops, converting cellular redox systems from being monostable to being bistable and thereby priming cell populations to become bistable media over which ROS propagate. Furthermore, we demonstrate that ferroptosis and its propagation accompany the massive, yet spatially restricted, cell death events during muscle remodelling of the embryonic avian limb, substantiating its use as a tissue-sculpting strategy during embryogenesis. Our findings highlight the role of ferroptosis in coordinating global cell death events, providing a paradigm for investigating large-scale cell death in embryonic development and human pathologies.

Dietary Amino Acids Promote Glucagon-like Hormone Release to Generate Novel Calcium Waves in Adipose Tissues

Nutrient sensing and the subsequent metabolic responses are fundamental functions of animals, closely linked to diseases such as type 2 diabetes and various obesity-related morbidities. Among different metabolic regulatory signals, cytosolic Ca2+ plays pivotal roles in metabolic regulation, including glycolysis, gluconeogenesis, and lipolysis. Recently, intercellular calcium waves (ICWs), the propagation of Ca2+ signaling through tissues, have been found in different systems to coordinate multicellular responses. Nevertheless, our understanding of how ICWs are modulated and operate within living organisms remains limited. In this study, we explore the real-time dynamics, both in organ culture and free-behaving animals, of ICWs in Drosophila larval and adult adipose tissues. We identified Adipokinetic hormone (AKH), the fly functional homolog of mammalian glucagon, as the key factor driving Ca2+ activities in adipose tissue. Interestingly, we found that AKH, which is released in a pulsatile manner into the circulating hemolymph from the AKH-producing neurosecretory cells (APCs) in the brain, stimulates ICWs in the larval fat by a previously unrecognized gap-junction-independent mechanism to promote lipolysis. In the adult fat body, however, gap-junction-dependent random ICWs are triggered by a presumably uniformly diffused AKH. This highlights the stage-specific interplay of hormone secretion, extracellular diffusion, and intercellular communication in the regulation of Ca2+ dynamics. Additionally, we discovered that specific dietary amino acids activate the APCs, leading to increased intracellular Ca2+ and subsequent AKH secretion. Altogether, our findings identify that dietary amino acids regulate the release of AKH peptides from the APCs, which subsequently stimulates novel gap-junction-independent ICWs in adipose tissues, thereby enhancing lipid metabolism.

Modeling the reactive oxygen species (ROS) wave in Chlamydomonas reinhardtii colonies

Reactive oxygen species (ROS) play a crucial role as signaling molecules in both plant and animal cells, enabling rapid responses to various stimuli. Among the many cellular mechanisms used to generate and transduce ROS signals, ROS-induced-ROS release (RIRR) is emerging as an important pathway involved in the responses of various multicellular and unicellular organisms to environmental stresses. In RIRR, one cellular compartment, organelle, or cell generates or releases ROS, triggering an increased ROS production and release by another compartment, organelle, or cell, thereby giving rise to a fast propagating ROS wave. This RIRR-based signal relay has been demonstrated to facilitate mitochondria-to-mitochondria communication in animal cells and long-distance systemic signaling in plants in response to biotic and abiotic stresses. More recently, it has been discovered that different unicellular microorganism communities also exhibit a RIRR cell-to-cell signaling process triggered by a localized stress treatment. However, the precise mechanism underlying the propagation of the ROS signal among cells within these unicellular communities remained elusive. In this study, we employed a reaction-diffusion model incorporating the RIRR mechanism to analyze the propagation of ROS-mediated signals. By effectively balancing production and scavenging processes, our model successfully reproduces the experimental ROS signal velocities observed in unicellular green algae (Chlamydomonas reinhardtii) colonies grown on agar plates, furthering our understanding of intercellular ROS communication.

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.

A mechanical wave travels along a genetic guide to drive the formation of an epithelial furrow during Drosophila gastrulation

Epithelial furrowing is a fundamental morphogenetic process during gastrulation, neurulation, and body shaping. A furrow often results from a fold that propagates along a line. How fold formation and propagation are controlled and driven is poorly understood. To shed light on this, we study the formation of the cephalic furrow, a fold that runs along the embryo dorsal-ventral axis during Drosophila gastrulation and the developmental role of which is still unknown. We provide evidence of its function and show that epithelial furrowing is initiated by a group of cells. This cellular cluster works as a pacemaker, triggering a bidirectional morphogenetic wave powered by actomyosin contractions and sustained by de novo medial apex-to-apex cell adhesion. The pacemaker's Cartesian position is under the crossed control of the anterior-posterior and dorsal-ventral gene patterning systems. Thus, furrow formation is driven by a mechanical trigger wave that travels under the control of a multidimensional genetic guide.

Robust trigger wave speed in Xenopus cytoplasmic extracts

Self-regenerating trigger waves can spread rapidly through the crowded cytoplasm without diminishing in amplitude or speed, providing consistent, reliable, long-range communication. The macromolecular concentration of the cytoplasm varies in response to physiological and environmental fluctuations, raising the question of how or if trigger waves can robustly operate in the face of such fluctuations. Using Xenopus extracts, we found that mitotic and apoptotic trigger wave speeds are remarkably invariant. We derived a model that accounts for this robustness and for the eventual slowing at extremely high and low cytoplasmic concentrations. The model implies that the positive and negative effects of cytoplasmic concentration (increased reactant concentration vs. increased viscosity) are nearly precisely balanced. Accordingly, artificially maintaining a constant cytoplasmic viscosity during dilution abrogates this robustness. The robustness in trigger wave speeds may contribute to the reliability of the extremely rapid embryonic cell cycle.

Coarsening and wavelength selection far from equilibrium: A unifying framework based on singular perturbation theory

Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory exists for the dynamics of fully nonlinear patterns. We develop a unifying theory for nonlinear wavelength-selection dynamics in (nearly) mass-conserving two-component reaction-diffusion systems independent of the specific mathematical model chosen. Previous work has shown that these systems support an extremely broad band of stable wavelengths, but the mechanism by which a specific wavelength is selected has remained unclear. We show that an interrupted coarsening process selects the wavelength at the threshold to stability. Based on the physical intuition that coarsening is driven by competition for mass and interrupted by weak source terms that break strict mass conservation, we develop a singular perturbation theory for the stability of stationary patterns. The resulting closed-form analytical expressions enable us to quantitatively predict the coarsening dynamics and the final pattern wavelength. We find excellent agreement with numerical results throughout the diffusion- and reaction-limited regimes of the dynamics, including the crossover region. Further, we show how, in these limits, the two-component reaction-diffusion systems map to generalized Cahn-Hilliard and conserved Allen-Cahn dynamics, therefore providing a link to these two fundamental scalar field theories. The systematic understanding of the length-scale dynamics of fully nonlinear patterns in two-component systems provided here builds the basis to reveal the mechanisms underlying wavelength selection in multicomponent systems with potentially several conservation laws.

A model of replicating coupled oscillators generates naturally occurring cell networks

When a founder cell and its progeny divide with incomplete cytokinesis, a network forms in which each intercellular bridge corresponds to a past mitotic event. Such networks are required for gamete production in many animals, and different species have evolved diverse final network topologies. Although mechanisms regulating network assembly have been identified in particular organisms, we lack a quantitative framework to understand network assembly and inter-species variability. Motivated by cell networks responsible for oocyte production in invertebrates, where the final topology is typically invariant within each species, we devised a mathematical model for generating cell networks, in which each node is an oscillator and, after a full cycle, the node produces a daughter to which it remains connected. These cell cycle oscillations are transient and coupled via diffusion over the edges of the network. By variation of three biologically motivated parameters, our model generates nearly all such networks currently reported across invertebrates. Furthermore, small parameter variations can rationalize cases of intra-species variation. Because cell networks outside of the ovary often form less deterministically, we propose model generalizations to account for sources of stochasticity.

ERK signaling waves via body-wall muscles guide planarian whole-body regeneration across long distances

Whole-body regeneration is a multifaceted process that reinstates a body to its initial three-dimension size and structure after resection injury. It is well-known that signaling waves such as calcium and extracellular signal-related kinase (ERK) signaling waves can efficiently transmit information between tissues or cells. However, the mechanisms responsible for coordinating wound responses over long distances are largely unexplored. A recent study has reported that the propagation of ERK signaling waves via longitudinal body-wall muscles play an essential role in wound response and whole-body regeneration in planarians, underscoring the significance of feedback interactions between spatially distinct tissues during whole-body regeneration over long distances. These findings not only address the central questions of regenerative biology but also have potential implications for regenerative medicine.

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.

Ultrafast distant wound response is essential for whole-body regeneration

Injury induces systemic responses, but their functions remain elusive. Mechanisms that can rapidly synchronize wound responses through long distances are also mostly unknown. Using planarian flatworms capable of whole-body regeneration, we report that injury induces extracellular signal-regulated kinase (Erk) activity waves to travel at a speed 10-100 times faster than those in other multicellular tissues. This ultrafast propagation requires longitudinal body-wall muscles, elongated cells forming dense parallel tracks running the length of the organism. The morphological properties of muscles allow them to act as superhighways for propagating and disseminating wound signals. Inhibiting Erk propagation prevents tissues distant to the wound from responding and blocks regeneration, which can be rescued by a second injury to distal tissues shortly after the first injury. Our findings provide a mechanism for long-range signal propagation in large, complex tissues to coordinate responses across cell types and highlight the function of feedback between spatially separated tissues during whole-body regeneration.

Self-extinguishing relay waves enable homeostatic control of human neutrophil swarming

Neutrophils exhibit self-amplified swarming to sites of injury and infection. How swarming is controlled to ensure the proper level of neutrophil recruitment is unknown. Using an ex vivo model of infection, we find that human neutrophils use active relay to generate multiple pulsatile waves of swarming signals. Unlike classic active relay systems such as action potentials, neutrophil swarming relay waves are self-extinguishing, limiting the spatial range of cell recruitment. We identify an NADPH-oxidase-based negative feedback loop that is needed for this self-extinguishing behavior. Through this circuit, neutrophils adjust the number and size of swarming waves for homeostatic levels of cell recruitment over a wide range of initial cell densities. We link a broken homeostat to neutrophil over-recruitment in the context of human chronic granulomatous disease.

Waves in a Stochastic Cell Motility Model

In Bhattacharya et al. (Sci Adv 6(32):7682, 2020), a set of chemical reactions involved in the dynamics of actin waves in cells was studied at two levels. The microscopic level, where the individual chemical reactions are directly modelled using Gillespie-type algorithms, and on a macroscopic level where a deterministic reaction-diffusion equation arises as the large-scale limit of the underlying chemical reactions. In this work, we derive, and subsequently study, the related mesoscopic stochastic reaction-diffusion system, or chemical Langevin equation, that arises from the same set of chemical reactions. We explain how the stochastic patterns that arise from this equation can be used to understand the experimentally observed dynamics from Bhattacharya et al. In particular, we argue that the mesoscopic stochastic model better captures the microscopic behaviour than the deterministic reaction-diffusion equation, while being more amenable for mathematical analysis and numerical simulations than the microscopic model.

Microbial models of development: Inspiration for engineering self-assembled synthetic multicellularity

While the field of synthetic developmental biology has traditionally focused on the study of the rich developmental processes seen in metazoan systems, an attractive alternate source of inspiration comes from microbial developmental models. Microbes face unique lifestyle challenges when forming emergent multicellular collectives. As a result, the solutions they employ can inspire the design of novel multicellular systems. In this review, we dissect the strategies employed in multicellular development by two model microbial systems: the cellular slime mold Dictyostelium discoideum and the biofilm-forming bacterium Bacillus subtilis. Both microbes face similar challenges but often have different solutions, both from metazoan systems and from each other, to create emergent multicellularity. These challenges include assembling and sustaining a critical mass of participating individuals to support development, regulating entry into development, and assigning cell fates. The mechanisms these microbial systems exploit to robustly coordinate development under a wide range of conditions offer inspiration for a new toolbox of solutions to the synthetic development community. Additionally, recreating these phenomena synthetically offers a pathway to understanding the key principles underlying how these behaviors are coordinated naturally.

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.

Ultrafast and long-range coordination of wound responses is essential for whole-body regeneration

Injury induces systemic, global responses whose functions remain elusive. In addition, mechanisms that rapidly synchronize wound responses through long distances across the organismal scale are mostly unknown. Using planarians, which have extreme regenerative ability, we report that injury induces Erk activity to travel in a wave-like manner at an unexpected speed (∼1 mm/h), 10-100 times faster than those measured in other multicellular tissues. This ultrafast signal propagation requires longitudinal body-wall muscles, elongated cells forming dense parallel tracks running the length of the organism. Combining experiments and computational models, we show that the morphological properties of muscles allow them to minimize the number of slow intercellular signaling steps and act as bidirectional superhighways for propagating wound signals and instructing responses in other cell types. Inhibiting Erk propagation prevents cells distant to the wound from responding and blocks regeneration, which can be rescued by a second injury to distal tissues within a narrow time window after the first injury. These results suggest that rapid responses in uninjured tissues far from wounds are essential for regeneration. Our findings provide a mechanism for long-range signal propagation in large and complex tissues to coordinate cellular responses across diverse cell types, and highlights the function of feedback between spatially separated tissues during whole-body regeneration.

Computational analysis of synergism in small networks with different logic

Cell fate decision processes are regulated by networks which contain different molecules and interactions. Different network topologies may exhibit synergistic or antagonistic effects on cellular functions. Here, we analyze six most common small networks with regulatory logic AND or OR, trying to clarify the relationship between network topologies and synergism (or antagonism) related to cell fate decisions. We systematically examine the contribution of both network topologies and regulatory logic to the cell fate synergism by bifurcation and combinatorial perturbation analysis. Initially, under a single set of parameters, the synergism of three types of networks with AND and OR logic is compared. Furthermore, to consider whether these results depend on the choices of parameter values, statistics on the synergism of five hundred parameter sets is performed. It is shown that the results are not sensitive to parameter variations, indicating that the synergy or antagonism mainly depends on the network topologies rather than the choices of parameter values. The results indicate that the topology with "Dual Inhibition" shows good synergism, while the topology with "Dual Promotion" or "Hybrid" shows antagonism. The results presented here may help us to design synergistic networks based on network structure and regulation combinations, which has promising implications for cell fate decisions and drug combinations.

Controlling periodic long-range signalling to drive a morphogenetic transition

Cells use signal relay to transmit information across tissue scales. However, the production of information carried by signal relay remains poorly characterised. To determine how the coding features of signal relay are generated, we used the classic system for long-range signalling: the periodic cAMP waves that drive Dictyostelium collective migration. Combining imaging and optogenetic perturbation of cell signalling states, we find that migration is triggered by an increase in wave frequency generated at the signalling centre. Wave frequency is regulated by cAMP wave circulation, which organises the long-range signal. To determine the mechanisms modulating wave circulation, we combined mathematical modelling, the general theory of excitable media, and mechanical perturbations to test competing models. Models in which cell density and spatial patterning modulate the wave frequency cannot explain the temporal evolution of signalling waves. Instead, our evidence leads to a model where wave circulation increases the ability for cells to relay the signal, causing further increase in the circulation rate. This positive feedback between cell state and signalling pattern regulates the long-range signal coding that drives morphogenesis.

Periodic spatial patterning with a single morphogen

During multicellular development, periodic spatial patterning systems generate repetitive structures, such as digits, vertebrae, and teeth. Turing patterning provides a foundational paradigm for understanding such systems. The simplest Turing systems are believed to require at least two morphogens to generate periodic patterns. Here, using mathematical modeling, we show that a simpler circuit, including only a single diffusible morphogen, is sufficient to generate long-range, spatially periodic patterns that propagate outward from transient initiating perturbations and remain stable after the perturbation is removed. Furthermore, an additional bistable intracellular feedback or operation on a growing cell lattice can make patterning robust to noise. Together, these results show that a single morphogen can be sufficient for robust spatial pattern formation and should provide a foundation for engineering pattern formation in the emerging field of synthetic developmental biology.

Regulation of Papillary Muscle Contractility by NAD and Ammonia Interplay: Contribution of Ion Channels and Exchangers

Various models, including stem cells derived and isolated cardiomyocytes with overexpressed channels, are utilized to analyze the functional interplay of diverse ion currents involved in cardiac automaticity and excitation-contraction coupling control. Here, we used β-NAD and ammonia, known hyperpolarizing and depolarizing agents, respectively, and applied inhibitory analysis to reveal the interplay of several ion channels implicated in rat papillary muscle contractility control. We demonstrated that: 4 mM β-NAD, having no strong impact on resting membrane potential (RMP) and action potential duration (APD90) of ventricular cardiomyocytes, evoked significant suppression of isometric force (F) of paced papillary muscle. Reactive blue 2 restored F to control values, suggesting the involvement of P2Y-receptor-dependent signaling in β-NAD effects. Meantime, 5 mM NH₄Cl did not show any effect on F of papillary muscle but resulted in significant RMP depolarization, APD90 shortening, and a rightward shift of I-V relationship for total steady state currents in cardiomyocytes. Paradoxically, NH₄Cl, being added after β-NAD and having no effect on RMP, APD, and I-V curve, recovered F to the control values, indicating β-NAD/ammonia antagonism. Blocking of HCN, Kir2.x, and L-type calcium channels, Ca²⁺-activated K⁺ channels (SK, IK, and BK), or NCX exchanger reverse mode prevented this effect, indicating consistent cooperation of all currents mediated by these channels and NCX. We suggest that the activation of Kir2.x and HCN channels by extracellular K⁺, that creates positive and negative feedback, and known ammonia and K⁺ resemblance, may provide conditions required for the activation of all the chain of channels involved in the interplay. Here, we present a mechanistic model describing an interplay of channels and second messengers, which may explain discovered antagonism of β-NAD and ammonia on rat papillary muscle contractile activity.

Three-dimensional chiral morphodynamics of chemomechanical active shells

Morphogenesis of active shells such as cells is a fundamental chemomechanical process that often exhibits three-dimensional (3D) large deformations and chemical pattern dynamics simultaneously. Here, we establish a chemomechanical active shell theory accounting for mechanical feedback and biochemical regulation to investigate the symmetry-breaking and 3D chiral morphodynamics emerging in the cell cortex. The active bending and stretching of the elastic shells are regulated by biochemical signals like actomyosin and RhoA, which, in turn, exert mechanical feedback on the biochemical events via deformation-dependent diffusion and inhibition. We show that active deformations can trigger chemomechanical bifurcations, yielding pulse spiral waves and global oscillations, which, with increasing mechanical feedback, give way to traveling or standing waves subsequently. Mechanical feedback is also found to contribute to stabilizing the polarity of emerging patterns, thus ensuring robust morphogenesis. Our results reproduce and unravel the experimentally observed solitary and multiple spiral patterns, which initiate asymmetric cleavage in Xenopus and starfish embryogenesis. This study underscores the crucial roles of mechanical feedback in cell development and also suggests a chemomechanical framework allowing for 3D large deformation and chemical signaling to explore complex morphogenesis in living shell-like structures.

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.

Cytoplasmic organization promotes protein diffusion in Xenopus extracts

The cytoplasm is highly organized. However, the extent to which this organization influences the dynamics of cytoplasmic proteins is not well understood. Here, we use Xenopus laevis egg extracts as a model system to study diffusion dynamics in organized versus disorganized cytoplasm. Such extracts are initially homogenized and disorganized, and self-organize into cell-like units over the course of tens of minutes. Using fluorescence correlation spectroscopy, we observe that as the cytoplasm organizes, protein diffusion speeds up by about a factor of two over a length scale of a few hundred nanometers, eventually approaching the diffusion time measured in organelle-depleted cytosol. Even though the ordered cytoplasm contained organelles and cytoskeletal elements that might interfere with diffusion, the convergence of protein diffusion in the cytoplasm toward that in organelle-depleted cytosol suggests that subcellular organization maximizes protein diffusivity. The effect of organization on diffusion varies with molecular size, with the effects being largest for protein-sized molecules, and with the time scale of the measurement. These results show that cytoplasmic organization promotes the efficient diffusion of protein molecules in a densely packed environment.

Cytoplasmic organization is a hallmark of living cells. Here, the authors make use of self-organizing cell extracts to examine how the emergence of large-scale organizations influences the microscopic diffusion of protein molecules in the cytoplasm.

Programmable, Spatiotemporal Control of Colloidal Motion Waves via Structured Light

Traveling waves in a reaction-diffusion system are essential for long-range communication in living organisms and inspire biomimetic materials of similar capabilities. One recent example is the traveling motion waves among photochemically oscillating, silver (Ag)-containing colloids. Being able to manipulate these colloidal waves holds the key for potential applications. Here, we have discovered that these motion waves can be confined by light patterns and that the chemical clocks of silver particles are moved forward by reducing local light intensity. Using these discoveries as design principles, we have applied structured light technology for the precise and programmable control of colloidal motion waves, including their origins, propagation directions, paths, shapes, annihilation, frequency, and speeds. We have also used the controlled propagation of colloidal waves to guide chemical messages along a predefined path to activate a population of micromotors located far from the signal. Our demonstrated capabilities in manipulating colloidal waves in space and time offer physical insights on their operation and expand their usefulness in the fundamental study of reaction-diffusion processes. Moreover, our findings inspire biomimetic strategies for the directional transport of mass, energy, and information at micro- or even nanoscales.

Quantitative models for building and growing fated small cell networks

Small cell clusters exhibit numerous phenomena typically associated with complex systems, such as division of labour and programmed cell death. A conserved class of such clusters occurs during oogenesis in the form of germline cysts that give rise to oocytes. Germline cysts form through cell divisions with incomplete cytokinesis, leaving cells intimately connected through intercellular bridges that facilitate cyst generation, cell fate determination and collective growth dynamics. Using the well-characterized Drosophila melanogaster female germline cyst as a foundation, we present mathematical models rooted in the dynamics of cell cycle proteins and their interactions to explain the generation of germline cell lineage trees (CLTs) and highlight the diversity of observed CLT sizes and topologies across species. We analyse competing models of symmetry breaking in CLTs to rationalize the observed dynamics and robustness of oocyte fate specification, and highlight remaining gaps in knowledge. We also explore how CLT topology affects cell cycle dynamics and synchronization and highlight mechanisms of intercellular coupling that underlie the observed collective growth patterns during oogenesis. Throughout, we point to similarities across organisms that warrant further investigation and comment on the extent to which experimental and theoretical findings made in model systems extend to other species.

Nonmodular oscillator and switch based on RNA decay drive regeneration of multimodal gene expression

Periodic gene expression dynamics are key to cell and organism physiology. Studies of oscillatory expression have focused on networks with intuitive regulatory negative feedback loops, leaving unknown whether other common biochemical reactions can produce oscillations. Oscillation and noise have been proposed to support mammalian progenitor cells’ capacity to restore heterogenous, multimodal expression from extreme subpopulations, but underlying networks and specific roles of noise remained elusive. We use mass-action-based models to show that regulated RNA degradation involving as few as two RNA species—applicable to nearly half of human protein-coding genes—can generate sustained oscillations without explicit feedback. Diverging oscillation periods synergize with noise to robustly restore cell populations’ bimodal expression on timescales of days. The global bifurcation organizing this divergence relies on an oscillator and bistable switch which cannot be decomposed into two structural modules. Our work reveals surprisingly rich dynamics of post-transcriptional reactions and a potentially widespread mechanism underlying development, tissue regeneration, and cancer cell heterogeneity.

Waves in Embryonic Development

Embryonic development hinges on effective coordination of molecular events across space and time. Waves have recently emerged as constituting an ubiquitous mechanism that ensures rapid spreading of regulatory signals across embryos, as well as reliable control of their patterning, namely, for the emergence of body plan structures. In this article, we review a selection of recent quantitative work on signaling waves and present an overview of the theory of waves. Our aim is to provide a succinct yet comprehensive guiding reference for the theoretical frameworks by which signaling waves can arise in embryos. We start, then, from reaction-diffusion systems, both static and time dependent; move to excitable dynamics; and conclude with systems of coupled oscillators. We link these theoretical models to molecular mechanisms recently elucidated for the control of mitotic waves in early embryos, patterning of the vertebrate body axis, micropattern cultures, and bone regeneration. Our goal is to inspire experimental work that will advance theory in development and connect its predictions to quantitative biological observations. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Deciphering cell signaling networks with massively multiplexed biosensor barcoding

Genetically encoded fluorescent biosensors are powerful tools for monitoring biochemical activities in live cells, but their multiplexing capacity is limited by the available spectral space. We overcome this problem by developing a set of barcoding proteins that can generate over 100 barcodes and are spectrally separable from commonly used biosensors. Mixtures of barcoded cells expressing different biosensors are simultaneously imaged and analyzed by deep learning models to achieve massively multiplexed tracking of signaling events. Importantly, different biosensors in cell mixtures show highly coordinated activities, thus facilitating the delineation of their temporal relationship. Simultaneous tracking of multiple biosensors in the receptor tyrosine kinase signaling network reveals distinct mechanisms of effector adaptation, cell autonomous and non-autonomous effects of KRAS mutations, as well as complex interactions in the network. Biosensor barcoding presents a scalable method to expand multiplexing capabilities for deciphering the complexity of signaling networks and their interactions between cells.

Reversible and spatiotemporal control of colloidal structure formation

Tuning colloidal structure formation is a powerful approach to building functional materials, as a wide range of optical and viscoelastic properties can be accessed by the choice of individual building blocks and their interactions. Precise control is achieved by DNA specificity, depletion forces, or geometric constraints and results in a variety of complex structures. Due to the lack of control and reversibility of the interactions, an autonomous oscillating system on a mesoscale without external driving was not feasible until now. Here, we show that tunable DNA reaction circuits controlling linker strand concentrations can drive the dynamic and fully reversible assembly of DNA-functionalized micron-sized particles. The versatility of this approach is demonstrated by programming colloidal interactions in sequential and spatial order to obtain an oscillatory structure formation process on a mesoscopic scale. The experimental results represent an approach for the development of active materials by using DNA reaction networks to scale up the dynamic control of colloidal self-organization.

Identification, visualization, statistical analysis and mathematical modeling of high-feedback loops in gene regulatory networks

Background

Feedback loops in gene regulatory networks play pivotal roles in governing functional dynamics of cells. Systems approaches demonstrated characteristic dynamical features, including multistability and oscillation, of positive and negative feedback loops. Recent experiments and theories have implicated highly interconnected feedback loops (high-feedback loops) in additional nonintuitive functions, such as controlling cell differentiation rate and multistep cell lineage progression. However, it remains challenging to identify and visualize high-feedback loops in complex gene regulatory networks due to the myriad of ways in which the loops can be combined. Furthermore, it is unclear whether the high-feedback loop structures with these potential functions are widespread in biological systems. Finally, it remains challenging to understand diverse dynamical features, such as high-order multistability and oscillation, generated by individual networks containing high-feedback loops. To address these problems, we developed HiLoop, a toolkit that enables discovery, visualization, and analysis of several types of high-feedback loops in large biological networks.

Results

HiLoop not only extracts high-feedback structures and visualize them in intuitive ways, but also quantifies the enrichment of overrepresented structures. Through random parameterization of mathematical models derived from target networks, HiLoop presents characteristic features of the underlying systems, including complex multistability and oscillations, in a unifying framework. Using HiLoop, we were able to analyze realistic gene regulatory networks containing dozens to hundreds of genes, and to identify many small high-feedback systems. We found more than a 100 human transcription factors involved in high-feedback loops that were not studied previously. In addition, HiLoop enabled the discovery of an enrichment of high feedback in pathways related to epithelial-mesenchymal transition.

Conclusions

HiLoop makes the study of complex networks accessible without significant computational demands. It can serve as a hypothesis generator through identification and modeling of high-feedback subnetworks, or as a quantification method for motif enrichment analysis. As an example of discovery, we found that multistep cell lineage progression may be driven by either specific instances of high-feedback loops with sparse appearances, or generally enriched topologies in gene regulatory networks. We expect HiLoop’s usefulness to increase as experimental data of regulatory networks accumulate. Code is freely available for use or extension at https://github.com/BenNordick/HiLoop.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04405-z.

Light-sheet fluorescence microscopy for the in vivo study of microtubule dynamics in the zebrafish embryo

During its first hours of development, the zebrafish embryo presents a large microtubule array in the yolk region, essential for its development. Despite of its size and dynamic behavior, this network has been studied only in limited field of views or in fixed samples. We designed and implemented different strategies in Light Sheet Fluorescence microscopy for imaging the entire yolk microtubule (MT) network in vivo. These have allowed us to develop a novel image analysis from which we clearly observe a cyclical re-arrangement of the entire MT network in synchrony with blastoderm mitotic waves. These dynamics also affect a previously unreported microtubule array deep within the yolk, here described. These findings provide a new vision of the zebrafish yolk microtubules arrangement, and offers novel insights in the interaction between mitotic events and microtubules reorganization.

Analytical approximations for the speed of pacemaker-generated waves

In oscillatory media, waves can be generated by pacemaker regions which oscillate faster than their surroundings. In many chemical and biological systems, such waves can synchronize the whole medium and as such they are a means of transmitting information at a fixed speed over large distances. In this paper, we apply analytical tools to investigate the factors that determine the speed of these waves. More precisely, we apply singular perturbation and phase reduction methods to two types of negative-feedback oscillators, one built on underlying bistability and one including a time delay in the negative feedback. In both systems, we investigate the influence of time-scale separation on the resulting wave speed, as well as the effect of size and frequency of the pacemaker region. We compare our analytical estimates to numerical simulations which we described previously [J. Rombouts and L. Gelens, Phys. Rev. Research 2, 043038 (2020)2643-156410.1103/PhysRevResearch.2.043038].

Shedding light on developmental ERK signaling with genetically encoded biosensors

The extracellular signal-regulated kinase (ERK) pathway governs cell proliferation, differentiation and migration, and therefore plays key roles in various developmental and regenerative processes. Recent advances in genetically encoded fluorescent biosensors have unveiled hitherto unrecognized ERK activation dynamics in space and time and their functional importance mainly in cultured cells. However, ERK dynamics during embryonic development have still only been visualized in limited numbers of model organisms, and we are far from a sufficient understanding of the roles played by developmental ERK dynamics. In this Review, we first provide an overview of the biosensors used for visualization of ERK activity in live cells. Second, we highlight the applications of the biosensors to developmental studies of model organisms and discuss the current understanding of how ERK dynamics are encoded and decoded for cell fate decision-making.

Liquid-liquid phase separation as a common organizing principle of intracellular space and biomembranes providing dynamic adaptive responses

This work is devoted to the phenomenon of liquid-liquid phase separation (LLPS), which has come to be recognized as fundamental organizing principle of living cells. We distinguish separation processes with different dimensions. Well-known 3D-condensation occurs in aqueous solution and leads to membraneless organelle (MLOs) formation. 2D-films may be formed near membrane surfaces and lateral phase separation (membrane rafts) occurs within the membranes themselves. LLPS may also occur on 1D structures like DNA and the cyto- and nucleoskeleton. Phase separation provides efficient transport and sorting of proteins and metabolites, accelerates the assembly of metabolic and signaling complexes, and mediates stress responses. In this work, we propose a model in which the processes of polymerization (1D structures), phase separation in membranes (2D structures), and LLPS in the volume (3D structures) influence each other. Disordered proteins and whole condensates may provide membrane raft separation or polymerization of specific proteins. On the other hand, 1D and 2D structures with special composition or embedded IDRs can nucleate condensates. We hypothesized that environmental change may trigger a LLPS which can propagate within the cell interior moving along the cytoskeleton or as an autowave. New phase propagation quickly and using a low amount of energy adjusts cell signaling and metabolic systems to new demands. Cumulatively, the interconnected phase separation phenomena in different dimensions represent a previously unexplored system of intracellular communication and regulation which cannot be ignored when considering both physiological and pathological cell processes.

Mitotic waves in an import-diffusion model with multiple nuclei in a shared cytoplasm

Nuclei import and export proteins, including cell cycle regulators. These import-export processes are modulated periodically by the cell cycle, for example due to the periodic assembly and breakdown of the nuclear envelope. As such, replicated DNA can be segregated between the two daughter cells and the proteins that were localized in the nucleus are free to diffuse throughout the cytoplasm. Here, we study a mathematical import-diffusion model to show how proteins, i.e. cell cycle regulators, could be redistributed in the cytoplasm by nuclei that periodically toggle between interphase and mitosis. We show that when the cell cycle period depends on the local concentration of regulators, the model exhibits mitotic waves. We discuss how the velocity and spatial origin of these mitotic waves depend on the different model parameters. This work is motivated by recent in vitro experiments reporting on mitotic waves in cycling cell-free extracts made with Xenopus laevis frog eggs, where multiple nuclei share the same cytoplasm. Such experiments have shown that nuclei act as pacemakers for the cell cycle and thus play an important role in collectively defining the spatial origin of mitotic waves.

Cell cycle control during early embryogenesis

Understanding the mechanisms of embryonic cell cycles is a central goal of developmental biology, as the regulation of the cell cycle must be closely coordinated with other events during early embryogenesis. Quantitative imaging approaches have recently begun to reveal how the cell cycle oscillator is controlled in space and time, and how it is integrated with mechanical signals to drive morphogenesis. Here, we discuss how the Drosophila embryo has served as an excellent model for addressing the molecular and physical mechanisms of embryonic cell cycles, with comparisons to other model systems to highlight conserved and species-specific mechanisms. We describe how the rapid cleavage divisions characteristic of most metazoan embryos require chemical waves and cytoplasmic flows to coordinate morphogenesis across the large expanse of the embryo. We also outline how, in the late cleavage divisions, the cell cycle is inter-regulated with the activation of gene expression to ensure a reliable maternal-to-zygotic transition. Finally, we discuss how precise transcriptional regulation of the timing of mitosis ensures that tissue morphogenesis and cell proliferation are tightly controlled during gastrulation.

Mathematical modeling of Erk activity waves in regenerating zebrafish scales

Erk signaling regulates cellular decisions in many biological contexts. Recently, we have reported a series of Erk activity traveling waves that coordinate regeneration of osteoblast tissue in zebrafish scales. These waves originate from a central source region, propagate as expanding rings, and impart cell growth, thus controlling tissue morphogenesis. Here, we present a minimal reaction-diffusion model for Erk activity waves. The model considers three components: Erk, a diffusible Erk activator, and an Erk inhibitor. Erk stimulates both its activator and inhibitor, forming a positive and negative feedback loop, respectively. Our model shows that this system can be excitable and propagate Erk activity waves. Waves originate from a pulsatile source that is modeled by adding a localized basal production of the activator, which turns the source region from an excitable to an oscillatory state. As Erk activity periodically rises in the source, it can trigger an excitable wave that travels across the entire tissue. Analysis of the model finds that positive feedback controls the properties of the traveling wavefront and that negative feedback controls the duration of Erk activity peak and the period of Erk activity waves. The geometrical properties of the waves facilitate constraints on the effective diffusivity of the activator, indicating that waves are an efficient mechanism to transfer growth factor signaling rapidly across a large tissue.

Programmed and self-organized flow of information during morphogenesis

How the shape of embryos and organs emerges during development is a fundamental question that has fascinated scientists for centuries. Tissue dynamics arise from a small set of cell behaviours, including shape changes, cell contact remodelling, cell migration, cell division and cell extrusion. These behaviours require control over cell mechanics, namely active stresses associated with protrusive, contractile and adhesive forces, and hydrostatic pressure, as well as material properties of cells that dictate how cells respond to active stresses. In this Review, we address how cell mechanics and the associated cell behaviours are robustly organized in space and time during tissue morphogenesis. We first outline how not only gene expression and the resulting biochemical cues, but also mechanics and geometry act as sources of morphogenetic information to ultimately define the time and length scales of the cell behaviours driving morphogenesis. Next, we present two idealized modes of how this information flows - how it is read out and translated into a biological effect - during morphogenesis. The first, akin to a programme, follows deterministic rules and is hierarchical. The second follows the principles of self-organization, which rests on statistical rules characterizing the system's composition and configuration, local interactions and feedback. We discuss the contribution of these two modes to the mechanisms of four very general classes of tissue deformation, namely tissue folding and invagination, tissue flow and extension, tissue hollowing and, finally, tissue branching. Overall, we suggest a conceptual framework for understanding morphogenetic information that encapsulates genetics and biochemistry as well as mechanics and geometry as information modules, and the interplay of deterministic and self-organized mechanisms of their deployment, thereby diverging considerably from the traditional notion that shape is fully encoded and determined by genes.

Dynamic bistable switches enhance robustness and accuracy of cell cycle transitions

Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent.

Many systems in nature show bistability, which means they can evolve to one of two stable steady states under exactly the same conditions. Which state they evolve to depends on where the system comes from. Such bistability underlies the switching behavior that is essential for cells to progress in the cell division cycle. A quick switch happens when the cell jumps from one steady state to another steady state. Typical of this switching behavior is its robustness and irreversibility. In this paper, we expand this viewpoint of the dynamics of the cell cycle by considering bistable switches which themselves are changing in time. This gives the cell an extra layer of control over transitions both in time and in space, and can make those transitions more robust. Such dynamically changing bistability can appear very naturally. We show this in a model of mitotic entry, in which we include a nuclear and cytoplasmic compartment. The activity of a crucial cell cycle protein follows a bistable switch in each compartment, but the shape of its response is changing in time as proteins are imported into and exported from the nucleus.

Control of osteoblast regeneration by a train of Erk activity waves

Regeneration is a complex chain of events that restores a tissue to its original size and shape. The tissue-wide coordination of cellular dynamics needed for proper morphogenesis is challenged by the large dimensions of regenerating body parts. Feedback mechanisms in biochemical pathways can provide effective communication across great distances^1-5, but how they might regulate growth during tissue regeneration is unresolved^6,7. Here, we report that rhythmic traveling waves of Erk activity control the growth of bone in time and space in regenerating zebrafish scales, millimetre-sized discs of protective body armour. We find that Erk activity waves travel as expanding concentric rings, broadcast from a central source, inducing ring-like patterns of osteoblast tissue growth. Using a combination of theoretical and experimental analyses, we show that Erk activity propagates as excitable trigger waves able to traverse the entire scale in approximately two days, with the frequency of wave generation controlling the rate of scale regeneration. Furthermore, periodic induction of synchronous, tissue-wide Erk activation in place of travelling waves impairs tissue growth, indicating that wave-distributed Erk activation is key to regeneration. Our findings reveal trigger waves as a regulatory strategy to coordinate cell behaviour and instruct tissue form during regeneration.

The nucleus serves as the pacemaker for the cell cycle

Mitosis is a dramatic process that affects all parts of the cell. It is driven by an oscillator whose various components are localized in the nucleus, centrosome, and cytoplasm. In principle, the cellular location with the fastest intrinsic rhythm should act as a pacemaker for the process. Here we traced the waves of tubulin polymerization and depolymerization that occur at mitotic entry and exit in Xenopus egg extracts back to their origins. We found that mitosis was commonly initiated at sperm-derived nuclei and their accompanying centrosomes. The cell cycle was ~20% faster at these initiation points than in the slowest regions of the extract. Nuclei produced from phage DNA, which did not possess centrosomes, also acted as trigger wave sources, but purified centrosomes in the absence of nuclei did not. We conclude that the nucleus accelerates mitotic entry and propose that it acts as a pacemaker for cell cycle.

Dynamics of diffusive cell signaling relays

In biological contexts as diverse as development, apoptosis, and synthetic microbial consortia, collections of cells or subcellular components have been shown to overcome the slow signaling speed of simple diffusion by utilizing diffusive relays, in which the presence of one type of diffusible signaling molecule triggers participation in the emission of the same type of molecule. This collective effect gives rise to fast-traveling diffusive waves. Here, in the context of cell signaling, we show that system dimensionality – the shape of the extracellular medium and the distribution of cells within it – can dramatically affect the wave dynamics, but that these dynamics are insensitive to details of cellular activation. As an example, we show that neutrophil swarming experiments exhibit dynamical signatures consistent with the proposed signaling motif. We further show that cell signaling relays generate much steeper concentration profiles than does simple diffusion, which may facilitate neutrophil chemotaxis.

Integrating cellular dimensions with cell differentiation during early development

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

Getting around the cell: physical transport in the intracellular world

Eukaryotic cells face the challenging task of transporting a variety of particles through the complex intracellular milieu in order to deliver, distribute, and mix the many components that support cell function. In this review, we explore the biological objectives and physical mechanisms of intracellular transport. Our focus is on cytoplasmic and intra-organelle transport at the whole-cell scale. We outline several key biological functions that depend on physically transporting components across the cell, including the delivery of secreted proteins, support of cell growth and repair, propagation of intracellular signals, establishment of organelle contacts, and spatial organization of metabolic gradients. We then review the three primary physical modes of transport in eukaryotic cells: diffusive motion, motor-driven transport, and advection by cytoplasmic flow. For each mechanism, we identify the main factors that determine speed and directionality. We also highlight the efficiency of each transport mode in fulfilling various key objectives of transport, such as particle mixing, directed delivery, and rapid target search. Taken together, the interplay of diffusion, molecular motors, and flows supports the intracellular transport needs that underlie a broad variety of biological phenomena.

Design principles of tissue organisation: How single cells coordinate across scales

Cells act as building blocks of multicellular organisms, forming higher-order structures at different biological scales. Niches, tissues and, ultimately, entire organisms consist of single cells that remain in constant communication. Emergence of developmental patterns and tissue architecture thus relies on single cells acting as a collective, coordinating growth, migration, cell fate transitions and cell type sorting. For this, information has to be transmitted forward from cells to tissues and fed back to the individual cell to allow dynamic and robust coordination. Here, we define the design principles of tissue organisation integrating chemical, genetic and mechanical cues. We also review the state-of-the-art technologies used for dissecting collective cellular behaviours at single cell- and tissue-level resolution. We finally outline future challenges that lie in a comprehensive understanding of how single cells coordinate across biological scales to insure robust development, homoeostasis and regeneration of tissues.

Nuclei determine the spatial origin of mitotic waves

Traveling waves play an essential role in coordinating mitosis over large distances, but what determines the spatial origin of mitotic waves remains unclear. Here, we show that such waves initiate at pacemakers, regions that oscillate faster than their surroundings. In cell-free extracts of Xenopus laevis eggs, we find that nuclei define such pacemakers by concentrating cell cycle regulators. In computational models of diffusively coupled oscillators that account for nuclear import, nuclear positioning determines the pacemaker location. Furthermore, we find that the spatial dimensions of the oscillatory medium change the nuclear positioning and strongly influence whether a pacemaker is more likely to be at a boundary or an internal region. Finally, we confirm experimentally that increasing the system width increases the proportion of pacemakers at the boundary. Our work provides insight into how nuclei and spatial system dimensions can control local concentrations of regulators and influence the emergent behavior of mitotic waves.