Form, function, mind: What doesn't compute (and what might)

The applicability of computational and dynamical systems models to organisms is scrutinized, using examples from developmental biology and cognition. Developmental morphogenesis is dependent on the inherent material properties of developing animal (metazoan) tissues, a non-computational modality, but cell differentiation, which utilizes chromatin-based revisable memory banks and program-like function-calling, via the developmental gene co-expression system unique to the metazoans, has a quasi-computational basis. Multi-attractor dynamical models are argued to be misapplied to global properties of development, and it is suggested that along with computationalism, classic forms of dynamicism are similarly unsuitable to accounting for cognitive phenomena. Proposals are made for treating brains and other nervous tissues as novel forms of excitable matter with inherent properties which enable the intensification of cell-based basal cognition capabilities present throughout the tree of life. Finally, some connections are drawn between the viewpoint described here and active inference models of cognition, such as the Free Energy Principle.

An emerging role for tissue plasticity in developmental precision

Reproducible tissue morphology is a fundamental feature of embryonic development. To ensure such robustness during tissue morphogenesis, inherent noise in biological processes must be buffered. While redundant genes, parallel signaling pathways and intricate network topologies are known to reduce noise, over the last few years, mechanical properties of tissues have been shown to play a vital role. Here, taking the example of somite shape changes, I will discuss how tissues are highly plastic in their ability to change shapes leading to increased precision and reproducibility.

Emergent dynamics due to chemo-hydrodynamic self-interactions in active polymers

The field of synthetic active matter has, thus far, been led by efforts to create point-like, isolated (yet interacting) self-propelled objects (e.g. colloids, droplets, microrobots) and understanding their collective dynamics. The design of flexible, freely jointed active assemblies from autonomously powered sub-components remains a challenge. Here, we report freely-jointed active polymers created using self-propelled droplets as monomeric units. Our experiments reveal that the self-shaping chemo-hydrodynamic interactions between the monomeric droplets give rise to an emergent rigidity (the acquisition of a stereotypical asymmetric C-shape) and associated ballistic propulsion of the active polymers. The rigidity and propulsion of the chains vary systematically with their lengths. Using simulations of a minimal model, we establish that the emergent polymer dynamics are a generic consequence of quasi two-dimensional confinement and auto-repulsive trail-mediated chemical interactions between the freely jointed active droplets. Finally, we tune the interplay between the chemical and hydrodynamic fields to experimentally demonstrate oscillatory dynamics of the rigid polymer propulsion. Altogether, our work highlights the possible first steps towards synthetic self-morphic active matter.

Clonal dynamics of surface-driven growing tissues

The self-organization of cells into complex tissues relies on a tight coordination of cell behavior. Identifying the cellular processes driving tissue growth is key to understanding the emergence of tissue forms and devising targeted therapies for aberrant growth, such as in cancer. Inferring the mode of tissue growth, whether it is driven by cells on the surface or by cells in the bulk, is possible in cell culture experiments but difficult in most tissues in living organisms (in vivo). Genetic tracing experiments, where a subset of cells is labeled with inheritable markers, have become important experimental tools to study cell fate in vivo. Here we show that the mode of tissue growth is reflected in the size distribution of the progeny of marked cells. To this end, we derive the clone size distributions using analytical calculations in the limit of negligible cell migration and cell death, and we test our predictions with an agent-based stochastic sampling technique. We show that for surface-driven growth the clone size distribution takes a characteristic power-law form with an exponent determined by fluctuations of the tissue surface. Our results propose a possible way of determining the mode of tissue growth from genetic tracing experiments.

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

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

Forceful patterning: theoretical principles of mechanochemical pattern formation

Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.

Axis convergence in C. elegans embryos

Embryos develop in a surrounding that guides key aspects of their development. For example, the anteroposterior (AP) body axis is always aligned with the geometric long axis of the surrounding eggshell in fruit flies and worms. The mechanisms that ensure convergence of the AP axis with the long axis of the eggshell remain unresolved. We investigate axis convergence in early C. elegans development, where the nascent AP axis, when misaligned, actively re-aligns to converge with the long axis of the egg. We identify two physical mechanisms that underlie axis convergence. First, bulk cytoplasmic flows, driven by actomyosin cortical flows, can directly reposition the AP axis. Second, active forces generated within the pseudocleavage furrow, a transient actomyosin structure similar to a contractile ring, can drive a mechanical re-orientation such that it becomes positioned perpendicular to the long axis of the egg. This in turn ensures AP axis convergence. Numerical simulations, together with experiments that either abolish the pseudocleavage furrow or change the shape of the egg, demonstrate that the pseudocleavage-furrow-dependent mechanism is a major driver of axis convergence. We conclude that active force generation within the actomyosin cortical layer drives axis convergence in the early nematode.

Calcium regulates cortex contraction inPhysarum polycephalum

The tubular network-forming slime moldPhysarum polycephalumis able to maintain long-scale contraction patterns driven by an actomyosin cortex. The resulting shuttle streaming in the network is crucial for the organism to respond to external stimuli and reorganize its body mass giving rise to complex behaviors. However, the chemical basis of the self-organized flow pattern is not fully understood. Here, we present ratiometric measurements of free intracellular calcium in simple morphologies ofPhysarumnetworks. The spatiotemporal patterns of the free calcium concentration reveal a nearly anti-correlated relation to the tube radius, suggesting that calcium is indeed a key regulator of the actomyosin activity. We compare the experimentally observed phase relation between the radius and the calcium concentration to the predictions of a theoretical model including calcium as an inhibitor. Numerical simulations of the model suggest that calcium indeed inhibits the contractions inPhysarum, although a quantitative difference to the experimentally measured phase relation remains. Unraveling the mechanism underlying the contraction patterns is a key step in gaining further insight into the principles ofPhysarum's complex behavior.

Patterning and dynamics of membrane adhesion under hydraulic stress

Hydraulic fracturing plays a major role in cavity formation during embryonic development, when pressurized fluid opens microlumens at cell-cell contacts, which evolve to form a single large lumen. However, the fundamental physical mechanisms behind these processes remain masked by the complexity and specificity of biological systems. Here, we show that adhered lipid vesicles subjected to osmotic stress form hydraulic microlumens similar to those in cells. Combining vesicle experiments with theoretical modelling and numerical simulations, we provide a physical framework for the hydraulic reconfiguration of cell-cell adhesions. We map the conditions for microlumen formation from a pristine adhesion, the emerging dynamical patterns and their subsequent maturation. We demonstrate control of the fracturing process depending on the applied pressure gradients and the type and density of membrane bonds. Our experiments further reveal an unexpected, passive transition of microlumens to closed buds that suggests a physical route to adhesion remodeling by endocytosis.

Design principles of Cdr2 node patterns in fission yeast cells

Pattern-forming networks have diverse roles in cell biology. Rod-shaped fission yeast cells use pattern formation to control the localization of mitotic signaling proteins and the cytokinetic ring. During interphase, the kinase Cdr2 forms membrane-bound multiprotein complexes termed nodes, which are positioned in the cell middle due in part to the node inhibitor Pom1 enriched at cell tips. Node positioning is important for timely cell cycle progression and positioning of the cytokinetic ring. Here, we combined experimental and modeling approaches to investigate pattern formation by the Pom1-Cdr2 system. We found that Cdr2 nodes accumulate near the nucleus, and Cdr2 undergoes nucleocytoplasmic shuttling when cortical anchoring is reduced. We generated particle-based simulations based on tip inhibition, nuclear positioning, and cortical anchoring. We tested model predictions by investigating Pom1-Cdr2 localization patterns after perturbing each positioning mechanism, including in both anucleate and multinucleated cells. Experiments show that tip inhibition and cortical anchoring alone are sufficient for the assembly and positioning of nodes in the absence of the nucleus, but that the nucleus and Pom1 facilitate the formation of unexpected node patterns in multinucleated cells. These findings have implications for spatial control of cytokinesis by nodes and for spatial patterning in other biological systems.

Design principles of Cdr2 node patterns in fission yeast cells

Pattern forming networks have diverse roles in cell biology. Rod-shaped fission yeast cells use pattern formation to control the localization of mitotic signaling proteins and the cytokinetic ring. During interphase, the kinase Cdr2 forms membrane-bound multiprotein complexes termed nodes, which are positioned in the cell middle due in part to the node inhibitor Pom1 enriched at cell tips. Node positioning is important for timely cell cycle progression and positioning of the cytokinetic ring. Here, we combined experimental and modeling approaches to investigate pattern formation by the Pom1-Cdr2 system. We found that Cdr2 nodes accumulate near the nucleus, and Cdr2 undergoes nucleocytoplasmic shuttling when cortical anchoring is reduced. We generated particle-based simulations based on tip inhibition, nuclear positioning, and cortical anchoring. We tested model predictions by investigating Pom1-Cdr2 localization patterns after perturbing each positioning mechanism, including in both anucleate and multinucleated cells. Experiments show that tip inhibition and cortical anchoring alone are sufficient for the assembly and positioning of nodes in the absence of the nucleus, but that the nucleus and Pom1 facilitate the formation of unexpected node patterns in multinucleated cells. These findings have implications for spatial control of cytokinesis by nodes and for spatial patterning in other biological systems.

Flow-driven control of pulse width in excitable media

Models of pulse formation in nerve conduction have provided manifold insight not only into neuronal dynamics but also the nonlinear dynamics of pulse formation in general. Recent observation of neuronal electrochemical pulses also driving mechanical deformation of the tubular neuronal wall, and thereby generating ensuing cytoplasmic flow, now question the impact of flow on the electrochemical dynamics of pulse formation. Here, we theoretically investigate the classical Fitzhugh-Nagumo model, now accounting for advective coupling between the pulse propagator typically describing membrane potential and triggering mechanical deformations, and thus governing flow magnitude, and the pulse controller, a chemical species advected with the ensuing fluid flow. Employing analytical calculations and numerical simulations, we find that advective coupling allows for a linear control of pulse width while leaving pulse velocity unchanged. We therefore uncover an independent control of pulse width by fluid flow coupling.

Active Nematic Defects and Epithelial Morphogenesis

Inspired by recent experiments that highlight the role of nematic defects in the morphogenesis of epithelial tissues, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture. Allowing the surface to evolve via relaxational dynamics leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects. In an ex-vivo setting of cultured murine neural progenitor cells, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting, we show that the defect configuration consisting of a bound +1 defect state, which is stabilized by activity, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles, consistent with observations of a basal marine invertebrate Hydra.

Pulsatile contractions and pattern formation in excitable actomyosin cortex

The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense, generate, and transmit mechanical forces. The cortex exhibits a wide range of dynamic behaviours, from generating pulsatory contractions and travelling waves to forming organised structures. Despite the progress in characterising the biochemical and mechanical components of the actin cortex, the emergent dynamics of this mechanochemical system is poorly understood. Here we develop a reaction-diffusion model for the RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an active actomyosin gel, to investigate how the interplay between chemical signalling and mechanical forces regulates stresses and patterns in the cortex. We demonstrate that mechanochemical feedback in the cortex acts to destabilise homogeneous states and robustly generate pulsatile contractions. By tuning active stress in the system, we show that the cortex can generate propagating contraction pulses, form network structures, or exhibit topological turbulence.

The cellular actin cortex is a dynamic sub-membranous network of filamentous actin, myosin motors, and other accessory proteins that regulates the ability of cells to maintain or change shapes. While the key molecular components and mechanical properties of the actin cortex have been characterized, the ways in which biochemical signalling and mechanical forces interact to regulate cortex behaviours remain poorly understood. In this article, we develop a mathematical model for the actomyosin cortex that combines the reaction-diffusion dynamics of signalling proteins with active force generation by actomyosin networks. Using this model, we investigate how the feedback between mechanics and biochemical signalling regulates the propagation of actomyosin flows, mechanical stresses, and pattern formation in the cortex. Our work reveals a variety of ways in which the cortex can tune the dynamic coupling between biochemical activity, force production, and advective transport to control mechanical behaviours.

Front speed and pattern selection of a propagating chemical front in an active fluid

Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly understood in general. In this analytical and numerical paper, we study an experimentally motivated minimal model of coupling between reaction-diffusion and active matter: a propagating front of an autocatalytic and stress-generating species. In the absence of activity, the front is described by the well-studied Kolmogorov, Petrovsky, and Piskunov equation. We find that front propagation is maintained even in active systems, with crucial differences: an extensile stress increases the front speed beyond a critical magnitude of the stress, while a contractile stress has no effect on the front speed but can generate a periodic instability in the high-concentration region behind the front. We expect our results to be useful in interpreting pattern formation in active systems with mechanochemical coupling in vivo and in vitro.

Programmed mechano-chemical coupling in reaction-diffusion active matter

Embryo morphogenesis involves a complex combination of self-organization mechanisms that generate a great diversity of patterns. However, classical in vitro patterning experiments explore only one self-organization mechanism at a time, thus missing coupling effects. Here, we conjugate two major out-of-equilibrium patterning mechanisms—reaction-diffusion and active matter—by integrating dissipative DNA/enzyme reaction networks within an active gel composed of cytoskeletal motors and filaments. We show that the strength of the flow generated by the active gel controls the mechano-chemical coupling between the two subsystems. This property was used to engineer a synthetic material where contractions trigger chemical reaction networks both in time and space, thus mimicking key aspects of the polarization mechanism observed in C. elegans oocytes. We anticipate that reaction-diffusion active matter will promote the investigation of mechano-chemical transduction and the design of new materials with life-like properties.

Coupling Turing stripes to active flows

We numerically solve the active nematohydrodynamic equations of motion, coupled to a Turing reaction-diffusion model, to study the effect of active nematic flow on the stripe patterns resulting from a Turing instability. If the activity is uniform across the system, the Turing patterns dissociate when the flux from active advection balances that from the reaction-diffusion process. If the activity is coupled to the concentration of Turing morphogens, and neighbouring stripes have equal and opposite activity, the system self organises into a pattern of shearing flows, with stripes tending to fracture and slip sideways to join their neighbours. We discuss the role of active instabilities in controlling the crossover between these limits. Our results are of relevance to mechanochemical coupling in biological systems.

Establishment of the vertebrate body plan: Rethinking gastrulation through stem cell models of early embryogenesis

A striking property of vertebrate embryos is the emergence of a conserved body plan across a wide range of organisms through the process of gastrulation. As the body plan unfolds, gene regulatory networks (GRNs) and multicellular interactions (cell regulatory networks, CRNs) combine to generate a conserved set of morphogenetic events that lead to the phylotypic stage. Interrogation of these multilevel interactions requires manipulation of the mechanical environment, which is difficult in vivo. We review recent studies of stem cell models of early embryogenesis from different species showing that, independent of species origin, cells in culture form similar structures. The main difference between embryos and in vitro models is the boundary conditions of the multicellular ensembles. We discuss these observations and suggest that the mechanical and geometric boundary conditions of different embryos before gastrulation hide a morphogenetic ground state that is revealed in the stem-cell-based models of embryo development.

Inferring simple but precise quantitative models of human oocyte and early embryo development

Macroscopic, phenomenological models are useful as concise framings of our understandings in fields from statistical physics to finance to biology. Constructing a phenomenological model for development would provide a framework for understanding the complicated, regulatory nature of oogenesis and embryogenesis. Here, we use a data-driven approach to infer quantitative, precise models of human oocyte maturation and pre-implantation embryo development, by analysing clinical in-vitro fertilization (IVF) data on 7399 IVF cycles resulting in 57 827 embryos. Surprisingly, we find that both oocyte maturation and early embryo development are quantitatively described by simple models with minimal interactions. This simplicity suggests that oogenesis and embryogenesis are composed of modular processes that are relatively siloed from one another. In particular, our analysis provides strong evidence that (i) pre-antral follicles produce anti-Müllerian hormone independently of effects from other follicles, (ii) oocytes mature to metaphase-II independently of the woman's age, her BMI and other factors, (iii) early embryo development is memoryless for the variables assessed here, in that the probability of an embryo transitioning from its current developmental stage to the next is independent of its previous stage. Our results both provide insight into the fundamentals of oogenesis and embryogenesis and have implications for the clinical IVF.

The cell in the age of the genomic revolution: Cell Regulatory Networks

Over the last few years an intense activity in the areas of advanced microscopy and quantitative cell biology has put the focus on the morphogenetic events that shape embryos. The interest in these processes is taking place against the backdrop of genomic studies, particularly of global patterns of gene expression at the level of single cells, which cannot fully account for the way cells build tissues and organs. Here we discuss the need to integrate the activity of genes with that of cells and propose the need to develop a framework, based on cellular processes and cell interactions, that parallels that which has been created for gene activity in the form of Gene Regulatory Networks (GRNs). We begin to do this by suggesting elements for building Cell Regulatory Networks (CRNs). In the same manner that GRNs create schedules of gene expression that result in the emergence of cell fates over time, CRNs create tissues and organs i.e. space. We also suggest how GRNs and CRNs might interact in the building of embryos through feedback loops involving mechanics and tissue tectonics.

Spatiotemporal dynamics of single cell stiffness in the early developing ascidian chordate embryo

During the developmental processes of embryos, cells undergo massive deformation and division that are regulated by mechanical cues. However, little is known about how embryonic cells change their mechanical properties during different cleavage stages. Here, using atomic force microscopy, we investigated the stiffness of cells in ascidian embryos from the fertilised egg to the stage before gastrulation. In both animal and vegetal hemispheres, we observed a Rho kinase (ROCK)-independent cell stiffening that the cell stiffness exhibited a remarkable increase at the timing of cell division where cortical actin filaments were organized. Furthermore, in the vegetal hemisphere, we observed another mechanical behaviour, i.e., a ROCK-associated cell stiffening, which was retained even after cell division or occurred without division and propagated sequentially toward adjacent cells, displaying a characteristic cell-to-cell mechanical variation. The results indicate that the mechanical properties of embryonic cells are regulated at the single cell level in different germ layers.

Fujii et al. investigate the stiffness of cells in ascidian embryos from the fertilised egg to the stage before gastrulation. They find two types of cell stiffening, occurring during cell division and in the interphase, the latter of which is associated with the Rho kinase pathway. They conclude that the mechanical properties of early embryonic cells are regulated specifically at the single cell level.

Role of cell polarity dynamics and motility in pattern formation due to contact-dependent signalling

A key challenge in biology is to understand how spatio-temporal patterns and structures arise during the development of an organism. An initial aggregate of spatially uniform cells develops and forms the differentiated structures of a fully developed organism. On the one hand, contact-dependent cell-cell signalling is responsible for generating a large number of complex, self-organized, spatial patterns in the distribution of the signalling molecules. On the other hand, the motility of cells coupled with their polarity can independently lead to collective motion patterns that depend on mechanical parameters influencing tissue deformation, such as cellular elasticity, cell-cell adhesion and active forces generated by actin and myosin dynamics. Although modelling efforts have, thus far, treated cell motility and cell-cell signalling separately, experiments in recent years suggest that these processes could be tightly coupled. Hence, in this paper, we study how the dynamics of cell polarity and migration influence the spatiotemporal patterning of signalling molecules. Such signalling interactions can occur only between cells that are in physical contact, either directly at the junctions of adjacent cells or through cellular protrusional contacts. We present a vertex model which accounts for contact-dependent signalling between adjacent cells and between non-adjacent neighbours through long protrusional contacts that occur along the orientation of cell polarization. We observe a rich variety of spatiotemporal patterns of signalling molecules that is influenced by polarity dynamics of the cells, relative strengths of adjacent and non-adjacent signalling interactions, range of polarized interaction, signalling activation threshold, relative time scales of signalling and polarity orientation, and cell motility. Though our results are developed in the context of Delta-Notch signalling, they are sufficiently general and can be extended to other contact dependent morpho-mechanical dynamics.

The Relative Densities of Cytoplasm and Nuclear Compartments Are Robust against Strong Perturbation

The cell nucleus is a compartment in which essential processes such as gene transcription and DNA replication occur. Although the large amount of chromatin confined in the finite nuclear space could install the picture of a particularly dense organelle surrounded by less dense cytoplasm, recent studies have begun to report the opposite. However, the generality of this newly emerging, opposite picture has so far not been tested. Here, we used combined optical diffraction tomography and epi-fluorescence microscopy to systematically quantify the mass densities of cytoplasm, nucleoplasm, and nucleoli of human cell lines, challenged by various perturbations. We found that the nucleoplasm maintains a lower mass density than cytoplasm during cell cycle progression by scaling its volume to match the increase of dry mass during cell growth. At the same time, nucleoli exhibited a significantly higher mass density than the cytoplasm. Moreover, actin and microtubule depolymerization and changing chromatin condensation altered volume, shape, and dry mass of those compartments, whereas the relative distribution of mass densities was generally unchanged. Our findings suggest that the relative mass densities across membrane-bound and membraneless compartments are robustly conserved, likely by different as-of-yet unknown mechanisms, which hints at an underlying functional relevance. This surprising robustness of mass densities contributes to an increasing recognition of the importance of physico-chemical properties in determining cellular characteristics and compartments.

Chromatin as an active polymeric material

The patterns of the large-scale spatial organization of chromatin in interphase human somatic cells are not random. Such patterns include the radial separation of euchromatin and heterochromatin, the territorial organization of individual chromosomes, the non-random locations of chromosome territories and the differential positioning of the two X chromosomes in female cells. These features of large-scale nuclear architecture follow naturally from the hypothesis that ATP-consuming non-equilibrium processes associated with highly transcribed regions of chromosomes are a source of 'active' forces. These forces are in excess of those that arise from Brownian motion. Simulations of model chromosomes that incorporate such activity recapitulate these features. In addition, they reproduce many other aspects of the spatial organization of chromatin at large scales that are known from experiments. Our results, reviewed here, suggest that the distribution of transcriptional activity across chromosomes underlies many aspects of large-scale nuclear architecture that were hitherto believed to be unrelated.

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.

Going with the flow: insights from Caenorhabditis elegans zygote polarization

Cell polarity is the asymmetric distribution of cellular components along a defined axis. Polarity relies on complex signalling networks between conserved patterning proteins, including the PAR (partitioning defective) proteins, which become segregated in response to upstream symmetry breaking cues. Although the mechanisms that drive the asymmetric localization of these proteins are dependent upon cell type and context, in many cases the regulation of actomyosin cytoskeleton dynamics is central to the transport, recruitment and/or stabilization of these polarity effectors into defined subcellular domains. The transport or advection of PAR proteins by an actomyosin flow was first observed in the Caenorhabditis elegans zygote more than a decade ago. Since then a multifaceted approach, using molecular methods, high-throughput screens, and biophysical and computational models, has revealed further aspects of this flow and how polarity regulators respond to and modulate it. Here, we review recent findings on the interplay between actomyosin flow and the PAR patterning networks in the polarization of the C. elegans zygote. We also discuss how these discoveries and developed methods are shaping our understanding of other flow-dependent polarizing systems. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.

Dynamic morphoskeletons in development

Morphogenetic flows in developmental biology are characterized by the coordinated motion of thousands of cells that organize into tissues, naturally raising the question of how this collective organization arises. Using only the kinematics of tissue deformation, which naturally integrates local and global mechanisms along cell paths, we identify the dynamic morphoskeletons behind morphogenesis, i.e., the evolving centerpieces of multicellular trajectory patterns. These features are model- and parameter-free, frame-invariant, and robust to measurement errors and can be computed from unfiltered cell-velocity data. We reveal the spatial attractors and repellers of the embryo by quantifying its Lagrangian deformation, information that is inaccessible to simple trajectory inspection or Eulerian methods that are local and typically frame-dependent. Computing these dynamic morphoskeletons in wild-type and mutant chick and fly embryos, we find that they capture the early footprint of known morphogenetic features, reveal new ones, and quantitatively distinguish between different phenotypes.

Caenorhabditis elegans Gastrulation: A Model for Understanding How Cells Polarize, Change Shape, and Journey Toward the Center of an Embryo

Gastrulation is fundamental to the development of multicellular animals. Along with neurulation, gastrulation is one of the major processes of morphogenesis in which cells or whole tissues move from the surface of an embryo to its interior. Cell internalization mechanisms that have been discovered to date in Caenorhabditis elegans gastrulation bear some similarity to internalization mechanisms of other systems including Drosophila, Xenopus, and mouse, suggesting that ancient and conserved mechanisms internalize cells in diverse organisms. C. elegans gastrulation occurs at an early stage, beginning when the embryo is composed of just 26 cells, suggesting some promise for connecting the rich array of developmental mechanisms that establish polarity and pattern in embryos to the force-producing mechanisms that change cell shapes and move cells interiorly. Here, we review our current understanding of C. elegans gastrulation mechanisms. We address how cells determine which direction is the interior and polarize with respect to that direction, how cells change shape by apical constriction and internalize, and how the embryo specifies which cells will internalize and when. We summarize future prospects for using this system to discover some of the general principles by which animal cells change shape and internalize during development.

Light-Sheet Microscopy and Its Potential for Understanding Developmental Processes

The ability to visualize and quantitatively measure dynamic biological processes in vivo and at high spatiotemporal resolution is of fundamental importance to experimental investigations in developmental biology. Light-sheet microscopy is particularly well suited to providing such data, since it offers exceptionally high imaging speed and good spatial resolution while minimizing light-induced damage to the specimen. We review core principles and recent advances in light-sheet microscopy, with a focus on concepts and implementations relevant for applications in developmental biology. We discuss how light-sheet microcopy has helped advance our understanding of developmental processes from single-molecule to whole-organism studies, assess the potential for synergies with other state-of-the-art technologies, and introduce methods for computational image and data analysis. Finally, we explore the future trajectory of light-sheet microscopy, discuss key efforts to disseminate new light-sheet technology, and identify exciting opportunities for further advances.

Active poroelastic two-phase model for the motion of physarum microplasmodia

The onset of self-organized motion is studied in a poroelastic two-phase model with free boundaries for Physarum microplasmodia (MP). In the model, an active gel phase is assumed to be interpenetrated by a passive fluid phase on small length scales. A feedback loop between calcium kinetics, mechanical deformations, and induced fluid flow gives rise to pattern formation and the establishment of an axis of polarity. Altogether, we find that the calcium kinetics that breaks the conservation of the total calcium concentration in the model and a nonlinear friction between MP and substrate are both necessary ingredients to obtain an oscillatory movement with net motion of the MP. By numerical simulations in one spatial dimension, we find two different types of oscillations with net motion as well as modes with time-periodic or irregular switching of the axis of polarity. The more frequent type of net motion is characterized by mechano-chemical waves traveling from the front towards the rear. The second type is characterized by mechano-chemical waves that appear alternating from the front and the back. While both types exhibit oscillatory forward and backward movement with net motion in each cycle, the trajectory and gel flow pattern of the second type are also similar to recent experimental measurements of peristaltic MP motion. We found moving MPs in extended regions of experimentally accessible parameters, such as length, period and substrate friction strength. Simulations of the model show that the net speed increases with the length, provided that MPs are longer than a critical length of ≈ 120 μm. Both predictions are in line with recent experimental observations.

Guiding self-organized pattern formation in cell polarity establishment

Spontaneous pattern formation in Turing systems relies on feedback. Patterns in cells and tissues however often do not form spontaneously, but are under control of upstream pathways that provide molecular guiding cues. The relationship between guiding cues and feedback in controlled biological pattern formation remains unclear. We explored this relationship during cell polarity establishment in the one-cell-stage C. elegans embryo. We quantified the strength of two feedback systems that operate during polarity establishment, feedback between polarity proteins and the actomyosin cortex, and mutual antagonism amongst polarity proteins. We characterized how these feedback systems are modulated by guiding cues from the centrosome. By coupling a mass-conserved Turing-like reaction-diffusion system for polarity proteins to an active gel description of the actomyosin cortex, we reveal a transition point beyond which feedback ensures self-organized polarization even when cues are removed. Notably, the baton is passed from a guide-dominated to a feedback-dominated regime significantly beyond this transition point, which ensures robustness. Together, this reveals a general criterion for controlling biological pattern forming systems: feedback remains subcritical to avoid unstable behaviour, and molecular guiding cues drive the system beyond a transition point for pattern formation.

Spheroid Culture of Mesenchymal Stromal Cells Results in Morphorheological Properties Appropriate for Improved Microcirculation

Human bone marrow mesenchymal stromal cells (MSCs) are used in clinical trials for the treatment of systemic inflammatory diseases due to their regenerative and immunomodulatory properties. However, intravenous administration of MSCs is hampered by cell trapping within the pulmonary capillary networks. Here, it is hypothesized that traditional 2D plastic-adherent cell expansion fails to result in appropriate morphorheological properties required for successful cell circulation. To address this issue, a method to culture MSCs in nonadherent 3D spheroids (mesenspheres) is adapted. The biological properties of mesensphere-cultured MSCs remain identical to conventional 2D cultures. However, morphorheological analyses reveal a smaller size and lower stiffness of mesensphere-derived MSCs compared to plastic-adherent MSCs, measured using real-time deformability cytometry and atomic force microscopy. These properties result in an increased ability to pass through microconstrictions in an ex vivo microcirculation assay. This ability is confirmed in vivo by comparison of cell accumulation in various organ capillary networks after intravenous injection of both types of MSCs in mouse. The findings generally identify cellular morphorheological properties as attractive targets for improving microcirculation and specifically suggest mesensphere culture as a promising approach for optimized MSC-based therapies.

Self-Organized Nuclear Positioning Synchronizes the Cell Cycle in Drosophila Embryos

The synchronous cleavage divisions of early embryogenesis require coordination of the cell-cycle oscillator, the dynamics of the cytoskeleton, and the cytoplasm. Yet, it remains unclear how spatially restricted biochemical signals are integrated with physical properties of the embryo to generate collective dynamics. Here, we show that synchronization of the cell cycle in Drosophila embryos requires accurate nuclear positioning, which is regulated by the cell-cycle oscillator through cortical contractility and cytoplasmic flows. We demonstrate that biochemical oscillations are initiated by local Cdk1 inactivation and spread through the activity of phosphatase PP1 to generate cortical myosin II gradients. These gradients cause cortical and cytoplasmic flows that control proper nuclear positioning. Perturbations of PP1 activity and optogenetic manipulations of cortical actomyosin disrupt nuclear spreading, resulting in loss of cell-cycle synchrony. We conclude that mitotic synchrony is established by a self-organized mechanism that integrates the cell-cycle oscillator and embryo mechanics.

Joining forces: crosstalk between biochemical signalling and physical forces orchestrates cellular polarity and dynamics

Dynamic processes like cell migration and morphogenesis emerge from the self-organized interaction between signalling and cytoskeletal rearrangements. How are these molecular to sub-cellular scale processes integrated to enable cell-wide responses? A growing body of recent studies suggest that forces generated by cytoskeletal dynamics and motor activity at the cellular or tissue scale can organize processes ranging from cell movement, polarity and division to the coordination of responses across fields of cells. To do so, forces not only act mechanically but also engage with biochemical signalling. Here, we review recent advances in our understanding of this dynamic crosstalk between biochemical signalling, self-organized cortical actomyosin dynamics and physical forces with a special focus on the role of membrane tension in integrating cellular motility.This article is part of the theme issue 'Self-organization in cell biology'.

Continuum Models of Collective Cell Migration

Collective cell migration plays a central role in tissue development, morphogenesis, wound repair and cancer progression. With the growing realization that physical forces mediate cell motility in development and physiology, a key biological question is how cells integrate molecular activities for force generation on multicellular scales. In this review we discuss recent advances in modeling collective cell migration using quantitative tools and approaches rooted in soft matter physics. We focus on theoretical models of cell aggregates as continuous active media, where the feedback between mechanical forces and regulatory biochemistry gives rise to rich collective dynamical behavior. This class of models provides a powerful predictive framework for the physiological dynamics that underlies many developmental processes, where cells need to collectively migrate like a viscous fluid to reach a target region, and then stiffen to support mechanical stresses and maintain tissue cohesion.

Cell-cell adhesion interface: orthogonal and parallel forces from contraction, protrusion, and retraction

The epithelial lateral membrane plays a central role in the integration of intercellular signals and, by doing so, is a principal determinant in the emerging properties of epithelial tissues. Mechanical force, when applied to the lateral cell-cell interface, can modulate the strength of adhesion and influence intercellular dynamics. Yet the relationship between mechanical force and epithelial cell behavior is complex and not completely understood. This commentary aims to provide an investigative look at the usage of cellular forces at the epithelial cell-cell adhesion interface.

Symmetry Breaking in the Mammalian Embryo

We present an overview of symmetry breaking in early mammalian development as a continuous process from compaction to specification of the body axes. While earlier studies have focused on individual symmetry-breaking events, recent advances enable us to explore progressive symmetry breaking during early mammalian development. Although we primarily discuss embryonic development of the mouse, as it is the best-studied mammalian model system to date, we also highlight the shared and distinct aspects between different mammalian species. Finally, we discuss how insights gained from studying mammalian development can be generalized in light of self-organization principles. With this review, we hope to highlight new perspectives in studying symmetry breaking and self-organization in multicellular systems.

The devil is in the mesoscale: Mechanical and behavioural heterogeneity in collective cell movement

Heterogeneity within cell populations can be an important aspect affecting their collective movement and tissue-mechanical properties, determining for example their effective viscoelasticity. Differences in cell-level properties and behaviour within a group of moving cells can give rise to unexpected and non-intuitive behaviours at the tissue level. Such emergent phenomena often manifest themselves through spatiotemporal patterns at an intermediate 'mesoscale' between cell and tissue scales, typically involving tens of cells. Focussing on the development of embryonic animal tissues, we review recent evidence for the importance of heterogeneity at the mesoscale for collective cell migration and convergence and extension movements. We further discuss approaches to incorporate heterogeneity into computational models to complement experimental investigations.

Fluid flows shaping organism morphology

A dynamic self-organized morphology is the hallmark of network-shaped organisms like slime moulds and fungi. Organisms continuously reorganize their flexible, undifferentiated body plans to forage for food. Among these organisms the slime mould Physarum polycephalum has emerged as a model to investigate how an organism can self-organize their extensive networks and act as a coordinated whole. Cytoplasmic fluid flows flowing through the tubular networks have been identified as the key driver of morphological dynamics. Inquiring how fluid flows can shape living matter from small to large scales opens up many new avenues for research. This article is part of the theme issue 'Self-organization in cell biology'.

Local control of globally competing patterns in coupled Swift-Hohenberg equations

We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turing-wave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.