Mitotic Cortical Waves Predict Future Division Sites by Encoding Positional and Size Information

Generative frame interpolation enhances tracking of biological objects in time-lapse microscopy

Object tracking in microscopy videos is crucial for understanding biological processes. While existing methods often require fine-tuning tracking algorithms to fit the image dataset, here we explored an alternative paradigm: augmenting the image time-lapse dataset to fit the tracking algorithm. To test this approach, we evaluated whether generative video frame interpolation can augment the temporal resolution of time-lapse microscopy and facilitate object tracking in multiple biological contexts. We systematically compared the capacity of Latent Diffusion Model for Video Frame Interpolation (LDMVFI), Real-time Intermediate Flow Estimation (RIFE), Compression-Driven Frame Interpolation (CDFI), and Frame Interpolation for Large Motion (FILM) to generate synthetic microscopy images derived from interpolating real images. Our testing image time series ranged from fluorescently labeled nuclei to bacteria, yeast, cancer cells, and organoids. We showed that the off-the-shelf frame interpolation algorithms produced bio-realistic image interpolation even without dataset-specific retraining, as judged by high structural image similarity and the capacity to produce segmentations that closely resemble results from real images. Using a simple tracking algorithm based on mask overlap, we confirmed that frame interpolation significantly improved tracking across several datasets without requiring extensive parameter tuning and capturing complex trajectories that were difficult to resolve in the original image time series. Taken together, our findings highlight the potential of generative frame interpolation to improve tracking in time-lapse microscopy across diverse scenarios, suggesting that a generalist tracking algorithm for microscopy could be developed by combining deep learning segmentation models with generative frame interpolation.

Rho GTPase dynamics distinguish between models of cortical excitability

The Rho GTPases pattern the cell cortex in a variety of fundamental cell-morphogenetic processes, including division, wound repair, and locomotion. It has recently become apparent that this patterning arises from the ability of the Rho GTPases to self-organize into static and migrating spots, contractile pulses, and propagating waves in cells from yeasts to mammals.1 These self-organizing Rho GTPase patterns have been explained by a variety of theoretical models that require multiple interacting positive and negative feedback loops. However, it is often difficult, if not impossible, to discriminate between different models simply because the available experimental data do not simultaneously capture the dynamics of multiple molecular concentrations and biomechanical variables at fine spatial and temporal resolution. Specifically, most studies typically provide either the total Rho GTPase signal or the Rho GTPase activity, as reported by various sensors, but not both. Therefore, it remains largely unknown how membrane accumulation of Rho GTPases (i.e., Rho membrane enrichment) is related to Rho activity. Here, we dissect the dynamics of RhoA by simultaneously imaging both total RhoA and active RhoA in propagating waves of Rho activity and F-actin polymerization.2,3,4,5 We find that within nascent waves, accumulation of active RhoA precedes that of total RhoA, and we exploit this finding to distinguish between two popular theoretical models previously used to explain propagating cortical Rho waves.

Competition and synergy of Arp2/3 and formins in nucleating actin waves

Actin assembly and dynamics are crucial for maintaining cell structure and changing physiological states. The broad impact of actin on various cellular processes makes it challenging to dissect the specific role of actin regulatory proteins. Using actin waves that propagate on the cortex of mast cells as a model, we discovered that formins (FMNL1 and mDia3) are recruited before the Arp2/3 complex in actin waves. GTPase Cdc42 interactions drive FMNL1 oscillations, with active Cdc42 and the constitutively active mutant of FMNL1 capable of forming waves on the plasma membrane independently of actin waves. Additionally, the delayed recruitment of Arp2/3 antagonizes FMNL1 and active Cdc42. This antagonism is not due to competition for monomeric actin but rather for their common upstream regulator, active Cdc42, whose levels are negatively regulated by Arp2/3 via SHIP1 recruitment. Collectively, our study highlights the complex feedback loops in the dynamic control of the actin cytoskeletal network.

Actomyosin cortex: Inherently oscillatory?

A new analysis of cytokinetic furrow ingression in the Caenorhabditis elegans zygote at high spatiotemporal resolution demonstrates that, rather than being a process of steady, spatially uniform constriction, furrow ingression is modulated by complex contractile oscillations that move around the furrow, possibly in the form of propagating waves.

Mechanical and biochemical feedback combine to generate complex contractile oscillations in cytokinesis

The actomyosin cortex is an active material that generates force to drive shape changes via cytoskeletal remodeling. Cytokinesis is the essential cell division event during which a cortical actomyosin ring closes to separate two daughter cells. Our active gel theory predicted that actomyosin systems controlled by a biochemical oscillator and experiencing mechanical strain would exhibit complex spatiotemporal behavior. To test whether active materials in vivo exhibit spatiotemporally complex kinetics, we imaged the C. elegans embryo with unprecedented temporal resolution and discovered that sections of the cytokinetic cortex undergo periodic phases of acceleration and deceleration. Contractile oscillations exhibited a range of periodicities, including those much longer periods than the timescale of RhoA pulses, which was shorter in cytokinesis than in any other biological context. Modifying mechanical feedback in vivo or in silico revealed that the period of contractile oscillation is prolonged as a function of the intensity of mechanical feedback. Fast local ring ingression occurs where speed oscillations have long periods, likely due to increased local stresses and, therefore, mechanical feedback. Fast ingression also occurs where material turnover is high, in vivo and in silico. We propose that downstream of initiation by pulsed RhoA activity, mechanical feedback, including but not limited to material advection, extends the timescale of contractility beyond that of biochemical input and, therefore, makes it robust to fluctuations in activation. Circumferential propagation of contractility likely allows for sustained contractility despite cytoskeletal remodeling necessary to recover from compaction. Thus, like biochemical feedback, mechanical feedback affords active materials responsiveness and robustness.

Patterning of the cell cortex by Rho GTPases

The Rho GTPases - RHOA, RAC1 and CDC42 - are small GTP binding proteins that regulate basic biological processes such as cell locomotion, cell division and morphogenesis by promoting cytoskeleton-based changes in the cell cortex. This regulation results from active (GTP-bound) Rho GTPases stimulating target proteins that, in turn, promote actin assembly and myosin 2-based contraction to organize the cortex. This basic regulatory scheme, well supported by in vitro studies, led to the natural assumption that Rho GTPases function in vivo in an essentially linear matter, with a given process being initiated by GTPase activation and terminated by GTPase inactivation. However, a growing body of evidence based on live cell imaging, modelling and experimental manipulation indicates that Rho GTPase activation and inactivation are often tightly coupled in space and time via signalling circuits and networks based on positive and negative feedback. In this Review, we present and discuss this evidence, and we address one of the fundamental consequences of coupled activation and inactivation: the ability of the Rho GTPases to self-organize, that is, direct their own transition from states of low order to states of high order. We discuss how Rho GTPase self-organization results in the formation of diverse spatiotemporal cortical patterns such as static clusters, oscillatory pulses, travelling wave trains and ring-like waves. Finally, we discuss the advantages of Rho GTPase self-organization and pattern formation for cell function.

Collective dynamics of actin and microtubule and its crosstalk mediated by FHDC1

The coordination between actin and microtubule network is crucial, yet this remains a challenging problem to dissect and our understanding of the underlying mechanisms remains limited. In this study, we used travelling waves in the cell cortex to characterize the collective dynamics of cytoskeletal networks. Our findings show that Cdc42 and F-BAR-dependent actin waves in mast cells are mainly driven by formin-mediated actin polymerization, with the microtubule-binding formin FH2 domain-containing protein 1 (FHDC1) as an early regulator. Knocking down FHDC1 inhibits actin wave formation, and this inhibition require FHDC1's interaction with both microtubule and actin. The phase of microtubule depolymerization coincides with the nucleation of actin waves and microtubule stabilization inhibit actin waves, leading us to propose that microtubule shrinking and the concurrent release of FHDC1 locally regulate actin nucleation. Lastly, we show that FHDC1 is crucial for multiple cellular processes such as cell division and migration. Our data provided molecular insights into the nucleation mechanisms of actin waves and uncover an antagonistic interplay between microtubule and actin polymerization in their collective dynamics.

Bring the pain: wounding reveals a transition from cortical excitability to epithelial excitability in Xenopus embryos

The cell cortex plays many critical roles, including interpreting and responding to internal and external signals. One behavior which supports a cell's ability to respond to both internal and externally-derived signaling is cortical excitability, wherein coupled positive and negative feedback loops generate waves of actin polymerization and depolymerization at the cortex. Cortical excitability is a highly conserved behavior, having been demonstrated in many cell types and organisms. One system well-suited to studying cortical excitability is Xenopus laevis, in which cortical excitability is easily monitored for many hours after fertilization. Indeed, recent investigations using X. laevis have furthered our understanding of the circuitry underlying cortical excitability and how it contributes to cytokinesis. Here, we describe the impact of wounding, which represents both a chemical and a physical signal, on cortical excitability. In early embryos (zygotes to early blastulae), we find that wounding results in a transient cessation ("freezing") of wave propagation followed by transport of frozen waves toward the wound site. We also find that wounding near cell-cell junctions results in the formation of an F-actin (actin filament)-based structure that pulls the junction toward the wound; at least part of this structure is based on frozen waves. In later embryos (late blastulae to gastrulae), we find that cortical excitability diminishes and is progressively replaced by epithelial excitability, a process in which wounded cells communicate with other cells via wave-like increases of calcium and apical F-actin. While the F-actin waves closely follow the calcium waves in space and time, under some conditions the actin wave can be uncoupled from the calcium wave, suggesting that they may be independently regulated by a common upstream signal. We conclude that as cortical excitability disappears from the level of the individual cell within the embryo, it is replaced by excitability at the level of the embryonic epithelium itself.

Mechanical positive feedback and biochemical negative feedback combine to generate complex contractile oscillations in cytokinesis

Contractile force generation by the cortical actomyosin cytoskeleton is essential for a multitude of biological processes. The actomyosin cortex behaves as an active material that drives local and large-scale shape changes via cytoskeletal remodeling in response to biochemical cues and feedback loops. Cytokinesis is the essential cell division event during which a cortical actomyosin ring generates contractile force to change cell shape and separate two daughter cells. Our recent work with active gel theory predicts that actomyosin systems under the control of a biochemical oscillator and experiencing mechanical strain will exhibit complex spatiotemporal behavior, but cytokinetic contractility was thought to be kinetically simple. To test whether active materials in vivo exhibit spatiotemporally complex kinetics, we used 4-dimensional imaging with unprecedented temporal resolution and discovered sections of the cytokinetic cortex undergo periodic phases of acceleration and deceleration. Quantification of ingression speed oscillations revealed wide ranges of oscillation period and amplitude. In the cytokinetic ring, activity of the master regulator RhoA pulsed with a timescale of approximately 20 seconds, shorter than that reported for any other biological context. Contractility oscillated with 20-second periodicity and with much longer periods. A combination of in vivo and in silico approaches to modify mechanical feedback revealed that the period of contractile oscillation is prolonged as a function of the intensity of mechanical feedback. Effective local ring ingression is characterized by slower speed oscillations, likely due to increased local stresses and therefore mechanical feedback. Fast ingression also occurs where material turnover is high, in vivo and in silico . We propose that downstream of initiation by pulsed RhoA activity, mechanical positive feedback, including but not limited to material advection, extends the timescale of contractility beyond that of biochemical input and therefore makes it robust to fluctuations in activation. Circumferential propagation of contractility likely allows sustained contractility despite cytoskeletal remodeling necessary to recover from compaction. Our work demonstrates that while biochemical feedback loops afford systems responsiveness and robustness, mechanical feedback must also be considered to describe and understand the behaviors of active materials in vivo .

Competition and Synergy of Arp2/3 and Formins in Nucleating Actin Waves

The assembly and disassembly of actin filaments and their regulatory proteins are crucial for maintaining cell structure or changing physiological state. However, because of the tremendous global impact of actin on diverse cellular processes, dissecting the specific role of actin regulatory proteins remains challenging. In this study, we employ actin waves that propagate on the cortex of mast cell to investigate the interplay between formins and the Arp2/3 complex in the nucleating and turnover of cortical actin. Our findings reveal that the recruitment of FMNL1 and mDia3 precedes the Arp2/3 complex in cortical actin waves. Membrane and GTPase-interaction can drive oscillations of FMNL1 in an actin-dependent manner, but active Cdc42 waves or constitutively-active FMNL1 mutant can form without actin waves. In addition to the apparent coordinated assembly of formins and Arp2/3, we further reveal their antagonism, where inhibition of Arp2/3 complex by CK-666 led to a transient increase in the recruitment of formins and actin polymerization. Our analysis suggest that the antagonism could not be explained for the competition between FMNL1 and Arp2/3 for monomeric actin. Rather, it is regulated by a limited pool of their common upstream regulator, Cdc42, whose level is negatively regulated by Arp2/3. Collectively, our study highlights the multifaceted interactions, cooperative or competitive, between formins and Arp2/3 complex, in the intricate and dynamic control of actin cytoskeletal network.

Periodicity, mixed-mode oscillations, and multiple timescales in a phosphoinositide-Rho GTPase network

While rhythmic contractile behavior is commonly observed at the cellular cortex, the primary focus has been on excitable or periodic events described by simple activator-delayed inhibitor mechanisms. We show that Rho GTPase activation in nocodazole-treated mitotic cells exhibits both simple oscillations and complex mixed-mode oscillations. Rho oscillations with a 20- to 30-s period are regulated by phosphatidylinositol (3,4,5)-trisphosphate (PIP3) via an activator-delayed inhibitor mechanism, while a slow reaction with period of minutes is regulated by phosphatidylinositol 4-kinase via an activator-substrate depletion mechanism. Conversion from simple to complex oscillations can be induced by modulating PIP3 metabolism or altering membrane contact site protein E-Syt1. PTEN depletion results in a period-doubling intermediate, which, like mixed-mode oscillations, is an intermediate state toward chaos. In sum, this system operates at the edge of chaos. Small changes in phosphoinositide metabolism can confer cells with the flexibility to rapidly enter ordered states with different periodicities.

Fluctuations of formin binding in the generation of membrane patterns

Circular actin waves that propagate on the substrate-attached membrane of Dictyostelium cells separate two distinct membrane domains from each other: an inner territory rich in phosphatidyl-(3,4,5) trisphosphate (PIP3) and an external area decorated with the PIP3-degrading 3-phosphatase PTEN. During wave propagation, the inner territory increases at the expense of the external area. Beyond a size limit, the inner territory becomes unstable, breaking into an inner and an external domain. The sharp boundary between these domains is demarcated by the insertion of an actin wave. During the conversion of inner territory to external area, the state of the membrane fluctuates, as visualized by dynamic landscapes of formin B binding. Here we analyze the formin B fluctuations in relation to three markers of the membrane state: activated Ras, PIP3, and PTEN.

Chemo-mechanical diffusion waves explain collective dynamics of immune cell podosomes

Immune cells, such as macrophages and dendritic cells, can utilize podosomes, mechanosensitive actin-rich protrusions, to generate forces, migrate, and patrol for foreign antigens. Individual podosomes probe their microenvironment through periodic protrusion and retraction cycles (height oscillations), while oscillations of multiple podosomes in a cluster are coordinated in a wave-like fashion. However, the mechanisms governing both the individual oscillations and the collective wave-like dynamics remain unclear. Here, by integrating actin polymerization, myosin contractility, actin diffusion, and mechanosensitive signaling, we develop a chemo-mechanical model for podosome dynamics in clusters. Our model reveals that podosomes show oscillatory growth when actin polymerization-driven protrusion and signaling-associated myosin contraction occur at similar rates, while the diffusion of actin monomers drives wave-like coordination of podosome oscillations. Our theoretical predictions are validated by different pharmacological treatments and the impact of microenvironment stiffness on chemo-mechanical waves. Our proposed framework can shed light on the role of podosomes in immune cell mechanosensing within the context of wound healing and cancer immunotherapy.

Reliable and robust control of nucleus centering is contingent on nonequilibrium force patterns

Cell centers their division apparatus to ensure symmetric cell division, a challenging task when the governing dynamics is stochastic. Using fission yeast, we show that the patterning of nonequilibrium polymerization forces of microtubule (MT) bundles controls the precise localization of spindle pole body (SPB), and hence the division septum, at the onset of mitosis. We define two cellular objectives, reliability, the mean SPB position relative to the geometric center, and robustness, the variance of the SPB position, which are sensitive to genetic perturbations that change cell length, MT bundle number/orientation, and MT dynamics. We show that simultaneous control of reliability and robustness is required to minimize septum positioning error achieved by the wild type (WT). A stochastic model for the MT-based nucleus centering, with parameters measured directly or estimated using Bayesian inference, recapitulates the maximum fidelity of WT. Using this, we perform a sensitivity analysis of the parameters that control nuclear centering.

A versatile cortical pattern-forming circuit based on Rho, F-actin, Ect2, and RGA-3/4

Many cells can generate complementary traveling waves of actin filaments (F-actin) and cytoskeletal regulators. This phenomenon, termed cortical excitability, results from coupled positive and negative feedback loops of cytoskeletal regulators. The nature of these feedback loops, however, remains poorly understood. We assessed the role of the Rho GAP RGA-3/4 in the cortical excitability that accompanies cytokinesis in both frog and starfish. RGA-3/4 localizes to the cytokinetic apparatus, "chases" Rho waves in an F-actin-dependent manner, and when coexpressed with the Rho GEF Ect2, is sufficient to convert the normally quiescent, immature Xenopus oocyte cortex into a dramatically excited state. Experiments and modeling show that changing the ratio of RGA-3/4 to Ect2 produces cortical behaviors ranging from pulses to complex waves of Rho activity. We conclude that RGA-3/4, Ect2, Rho, and F-actin form the core of a versatile circuit that drives a diverse range of cortical behaviors, and we demonstrate that the immature oocyte is a powerful model for characterizing these dynamics.

Excitable reaction-diffusion waves of curvature-inducing proteins on deformable membrane tubes

Living cells employ excitable reaction-diffusion waves for internal cellular functions, in which curvature-inducing proteins are often involved. However, the role of their mechanochemical coupling is not well understood. Here, we report the membrane deformation induced by the excitable reaction-diffusion waves of curvature-inducing proteins and the alternation in the waves due to the deformation, using a coarse-grained simulation of tubular membranes with a modified FitzHugh-Nagumo model. Protein-propagating waves deform tubular membranes and large deformations induce budding and erase waves. The wave speed and shape are determined by a combination of membrane deformation and spatial distribution of the curvature-inducing protein. Waves are also undulated in the azimuthal direction depending on the condition. Rotationally symmetric waves locally deform the tubes into a symmetric shape but maintain a straight shape on average. Our simulation method can be applied to other chemical reaction models and used to investigate various biomembrane phenomena.

Cell cycle and developmental control of cortical excitability in Xenopus laevis

Interest in cortical excitability—the ability of the cell cortex to generate traveling waves of protein activity—has grown considerably over the past 20 years. Attributing biological functions to cortical excitability requires an understanding of the natural behavior of excitable waves and the ability to accurately quantify wave properties. Here we have investigated and quantified the onset of cortical excitability in Xenopus laevis eggs and embryos and the changes in cortical excitability throughout early development. We found that cortical excitability begins to manifest shortly after egg activation. Further, we identified a close relationship between wave properties—such as wave frequency and amplitude—and cell cycle progression as well as cell size. Finally, we identified quantitative differences between cortical excitability in the cleavage furrow relative to nonfurrow cortical excitability and showed that these wave regimes are mutually exclusive.

Seeing is believing: tools to study the role of Rho GTPases during cytokinesis

Cytokinesis is required to cleave the daughter cells at the end of mitosis and relies on the spatiotemporal control of RhoA GTPase. Cytokinesis failure can lead to changes in cell fate or aneuploidy, which can be detrimental during development and/or can lead to cancer. However, our knowledge of the pathways that regulate RhoA during cytokinesis is limited, and the role of other Rho family GTPases is not clear. This is largely because the study of Rho GTPases presents unique challenges using traditional cell biological and biochemical methods, and they have pleiotropic functions making genetic studies difficult to interpret. The recent generation of optogenetic tools and biosensors that control and detect active Rho has overcome some of these challenges and is helping to elucidate the role of RhoA in cytokinesis. However, improvements are needed to reveal the role of other Rho GTPases in cytokinesis, and to identify the molecular mechanisms that control Rho activity. This review examines some of the outstanding questions in cytokinesis, and explores tools for the imaging and control of Rho GTPases.

Reaction-diffusion waves coupled with membrane curvature

The reaction-diffusion waves of proteins are known to be involved in fundamental cellular functions, such as cell migration, cell division, and vesicular transportation. In some of these phenomena, pattern formation on the membranes is induced by the coupling between membrane deformation and the reaction-diffusion system through curvature-inducing proteins that bend the biological membranes. Although the membrane shape and the dynamics of the curvature-inducing proteins affect each other in these systems, the effect of such mechanochemical feedback loops on the waves has not been studied in detail. In this study, reaction-diffusion waves coupled with membrane deformation are investigated using simulations combining a dynamically triangulated membrane model with the Brusselator model extended to include the effect of membrane curvature. It is found that the propagating wave patterns change into nonpropageting patterns and spiral wave patterns due to the mechanochemical effects. Moreover, the wave speed is positively or negatively correlated with the local membrane curvature depending on the spontaneous curvature and bending rigidity. In addition, self-oscillation of the vesicle shape occurs, associated with the reaction-diffusion waves of curvature-inducing proteins. This agrees with the experimental observation of GUVs with a reconstituted Min system, which plays a key role in the cell division of Escherichia coli. The findings of this study demonstrate the importance of mechanochemical coupling in biological phenomena.

Cortical excitability and cell division

As the interface between the cell and its environment, the cell cortex must be able to respond to a variety of external stimuli. This is made possible in part by cortical excitability, a behavior driven by coupled positive and negative feedback loops that generate propagating waves of actin assembly in the cell cortex. Cortical excitability is best known for promoting cell protrusion and allowing the interpretation of and response to chemoattractant gradients in migrating cells. It has recently become apparent, however, that cortical excitability is involved in the response of the cortex to internal signals from the cell-cycle regulatory machinery and the spindle during cell division. Two overlapping functions have been ascribed to cortical excitability in cell division: control of cell division plane placement, and amplification of the activity of the small GTPase Rho at the equatorial cortex during cytokinesis. Here, we propose that cortical excitability explains several important yet poorly understood features of signaling during cell division. We also consider the potential advantages that arise from the use of cortical excitability as a signaling mechanism to regulate cortical dynamics in cell division.

Pattern formation in reaction-diffusion system on membrane with mechanochemical feedback

Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently, chemical reaction propagation has been experimentally observed in plasma membranes. Thus, it is important to understand how the reaction-diffusion dynamics are modified on deformable curved membranes. Here, we investigated nonequilibrium pattern formation on vesicles induced by mechanochemical feedback between membrane deformation and chemical reactions, using dynamically triangulated membrane simulations combined with the Brusselator model. We found that membrane deformation changes stable patterns relative to those that occur on a non-deformable curved surface, as determined by linear stability analysis. We further found that budding and multi-spindle shapes are induced by Turing patterns, and we also observed the transition from oscillation patterns to stable spot patterns. Our results demonstrate the importance of mechanochemical feedback in pattern formation on deforming membranes.

Comparative Study of Curvature Sensing Mediated by F-BAR and an Intrinsically Disordered Region of FBP17

Membrane curvature has emerged as an intriguing physical principle underlying biological signaling and membrane trafficking. The CIP4/FBP17/Toca-1 F-BAR subfamily is unique in the BAR family because its structurally folded F-BAR domain does not contain any hydrophobic motifs that insert into membrane. Although widely assumed so, whether the banana-shaped F-BAR domain alone can sense curvature has never been experimentally demonstrated. Using a nanobar-supported lipid bilayer system, we found that the F-BAR domain of FBP17 displayed minimal curvature sensing in vitro. In comparison, an alternatively spliced intrinsically disordered region (IDR) adjacent to the F-BAR domain has the membrane curvature-sensing ability greatly exceeding that of F-BAR domain alone. In living cells, the presence of the IDR delayed the recruitment of FBP17 in curvature-coupled cortical waves. Collectively, we propose that contrary to the common belief, FBP17's curvature-sensing capability largely originates from IDR, and not the F-BAR domain alone.

Mechanobiology in cortical waves and oscillations

Cortical actin waves have emerged as a widely prevalent phenomena and brought pattern formation to many fields of cell biology. Cortical excitabilities, reminiscent of the electric excitability in neurons, are likely fundamental property of the cell cortex. Although they have been mostly considered to be biochemical in nature, accumulating evidence support the role of mechanics in the pattern formation process. Both pattern formation and mechanobiology approach biological phenomena at the collective level, either by looking at the mesoscale dynamical behavior of molecular networks or by using collective physical properties to characterize biological systems. As such they are very different from the traditional reductionist, bottom-up view of biology, which brings new challenges and potential opportunities. In this essay, we aim to provide our perspectives on what the proposed mechanochemical feedbacks are and open questions regarding their role in cortical excitable and oscillatory dynamics.

Multiscale morphogenesis of the mouse blastocyst by actomyosin contractility

During preimplantation development, the mouse embryo forms the blastocyst, which consists of a squamous epithelium enveloping a fluid-filled lumen and a cluster of pluripotent cells. The shaping of the blastocyst into its specific architecture is a prerequisite to implantation and further development of the embryo. Recent studies identified the central role of the actomyosin cortex in generating the forces driving the successive steps of blastocyst morphogenesis. As seen in other developing animals, actomyosin functions across spatial scales from the subcellular to the tissue levels. In addition, the slow development of the mouse embryo reveals that actomyosin contractility operates at multiple timescales with periodic cortical waves of contraction every ∼80 s and tissue remodeling over hours.

Why a Large-Scale Mode Can Be Essential for Understanding Intracellular Actin Waves

During the last decade, intracellular actin waves have attracted much attention due to their essential role in various cellular functions, ranging from motility to cytokinesis. Experimental methods have advanced significantly and can capture the dynamics of actin waves over a large range of spatio-temporal scales. However, the corresponding coarse-grained theory mostly avoids the full complexity of this multi-scale phenomenon. In this perspective, we focus on a minimal continuum model of activator-inhibitor type and highlight the qualitative role of mass conservation, which is typically overlooked. Specifically, our interest is to connect between the mathematical mechanisms of pattern formation in the presence of a large-scale mode, due to mass conservation, and distinct behaviors of actin waves.

Organelle size scaling over embryonic development

Cell division without growth results in progressive cell size reductions during early embryonic development. How do the sizes of intracellular structures and organelles scale with cell size and what are the functional implications of such scaling relationships? Model organisms, in particular Caenorhabditis elegans worms, Drosophila melanogaster flies, Xenopus laevis frogs, and Mus musculus mice, have provided insights into developmental size scaling of the nucleus, mitotic spindle, and chromosomes. Nuclear size is regulated by nucleocytoplasmic transport, nuclear envelope proteins, and the cytoskeleton. Regulators of microtubule dynamics and chromatin compaction modulate spindle and mitotic chromosome size scaling, respectively. Developmental scaling relationships for membrane-bound organelles, like the endoplasmic reticulum, Golgi, mitochondria, and lysosomes, have been less studied, although new imaging approaches promise to rectify this deficiency. While models that invoke limiting components and dynamic regulation of assembly and disassembly can account for some size scaling relationships in early embryos, it will be exciting to investigate the contribution of newer concepts in cell biology such as phase separation and interorganellar contacts. With a growing understanding of the underlying mechanisms of organelle size scaling, future studies promise to uncover the significance of proper scaling for cell function and embryonic development, as well as how aberrant scaling contributes to disease. This article is categorized under: Establishment of Spatial and Temporal Patterns > Regulation of Size, Proportion, and Timing Early Embryonic Development > Fertilization to Gastrulation Comparative Development and Evolution > Model Systems.

Rhythmicity and waves in the cortex of single cells

Emergence of dynamic patterns in the form of oscillations and waves on the cortex of single cells is a fascinating and enigmatic phenomenon. Here we outline various theoretical frameworks used to model pattern formation with the goal of reducing complex, heterogeneous patterns into key parameters that are biologically tractable. We also review progress made in recent years on the quantitative and molecular definitions of these terms, which we believe have begun to transform single-cell dynamic patterns from a purely observational and descriptive subject to more mechanistic studies. Specifically, we focus on the nature of local excitable and oscillation events, their spatial couplings leading to propagating waves and the role of active membrane. Instead of arguing for their functional importance, we prefer to consider such patterns as basic properties of dynamic systems. We discuss how knowledge of these patterns could be used to dissect the structure of cellular organization and how the network-centric view could help define cellular functions as transitions between different dynamical states. Last, we speculate on how these patterns could encode temporal and spatial information.

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

Exploratory cell dynamics: a sense of touch for cells?

Cells need to process multifaceted external cues to steer their dynamic behavior. To efficiently perform this task, cells implement several exploratory mechanisms to actively sample their environment. In particular, cells can use exploratory actin-based cell protrusions and contractions to engage and squeeze the environment and to actively probe its chemical and mechanical properties. Multiple excitable signal networks were identified that can generate local activity pulses to control these exploratory processes. Such excitable signal networks offer particularly efficient mechanisms to process chemical or mechanical signals to steer dynamic cell behavior, such as directional migration, tissue morphogenesis and cell fate decisions.

Chemical waves in cell and developmental biology

Many biological events, such as the propagation of nerve impulses, the synchronized cell cycles of early embryogenesis, and collective cell migration, must be coordinated with remarkable speed across very large distances. Such rapid coordination cannot be achieved by simple diffusion of molecules alone and requires specialized mechanisms. Although active transport can provide a directed and efficient way to travel across subcellular structures, it cannot account for the most rapid examples of coordination found in biology. Rather, these appear to be driven by mechanisms involving traveling waves of chemical activities that are able to propagate information rapidly across biological or physical systems. Indeed, recent advances in our ability to probe the dynamics of signaling pathways are revealing many examples of coordination of cellular and developmental processes through traveling chemical waves. Here, we will review the theoretical principles underlying such waves; highlight recent literature on their role in different contexts, ranging from chemotaxis to development; and discuss open questions and future perspectives on the study of chemical waves as an essential feature of cell and tissue physiology.

How cells sense their own shape - mechanisms to probe cell geometry and their implications in cellular organization and function

Cells come in a variety of shapes that most often underlie their functions. Regulation of cell morphogenesis implies that there are mechanisms for shape sensing that still remain poorly appreciated. Global and local cell geometry features, such as aspect ratio, size or membrane curvature, may be probed by intracellular modules, such as the cytoskeleton, reaction-diffusion systems or molecular complexes. In multicellular tissues, cell shape emerges as an important means to transduce tissue-inherent chemical and mechanical cues into intracellular organization. One emergent paradigm is that cell-shape sensing is most often based upon mechanisms of self-organization, rather than determinism. Here, we review relevant work that has elucidated some of the core principles of how cellular geometry may be conveyed into spatial information to guide processes, such as polarity, signaling, morphogenesis and division-plane positioning.

Clathrin Assembly Defines the Onset and Geometry of Cortical Patterning

Assembly of the endocytic machinery is a constitutively active process that is important for the organization of the plasma membrane, signal transduction, and membrane trafficking. Existing research has focused on the stochastic nature of endocytosis. Here, we report the emergence of the collective dynamics of endocytic proteins as periodic traveling waves on the cell surface. Coordinated clathrin assembly provides the earliest spatial cue for cortical waves and sets the direction of propagation. Surprisingly, the onset of clathrin waves, but not individual endocytic events, requires feedback from downstream factors, including FBP17, Cdc42, and N-WASP. In addition to the localized endocytic assembly at the plasma membrane, intracellular clathrin and phosphatidylinositol-3,4-bisphosphate predict the excitability of the plasma membrane and modulate the geometry of traveling waves. Collectively, our data demonstrate the multiplicity of clathrin functions in cortical pattern formation and provide important insights regarding the nucleation and propagation of single-cell patterns.