Guiding self-organized pattern formation in cell polarity establishment

Quantitative perturbation-phenotype maps reveal nonlinear responses underlying robustness of PAR-dependent asymmetric cell division

A key challenge in the development of an organism is to maintain robust phenotypic outcomes in the face of perturbation. Yet, it is often unclear how such robust outcomes are encoded by developmental networks. Here, we use the Caenorhabditis elegans zygote as a model to understand sources of developmental robustness during PAR polarity-dependent asymmetric cell division. By quantitatively linking alterations in protein dosage to phenotype in individual embryos, we show that spatial information in the zygote is read out in a highly nonlinear fashion and, as a result, phenotypes are highly canalized against substantial variation in input signals. Our data point towards robustness of the conserved PAR polarity network that renders polarity axis specification resistant to variations in both the strength of upstream symmetry-breaking cues and PAR protein dosage. Analogously, downstream pathways involved in cell size and fate asymmetry are robust to dosage-dependent changes in the local concentrations of PAR proteins, implying nontrivial complexity in translating PAR concentration profiles into pathway outputs. We propose that these nonlinear signal-response dynamics between symmetry-breaking, PAR polarity, and asymmetric division modules effectively insulate each individual module from variation arising in others. This decoupling helps maintain the embryo along the correct developmental trajectory, thereby ensuring that asymmetric division is robust to perturbation. Such modular organization of developmental networks is likely to be a general mechanism to achieve robust developmental outcomes.

Quantitative determination of the spatial distribution of components in single cells with CellDetail

The distribution of biomolecules within cells changes upon aging and diseases. To quantitatively determine the spatial distribution of components inside cells, we built the user-friendly open-source 3D-cell-image analysis platform Cell Detection and Analysis of Intensity Lounge (CellDetail). The algorithm within CellDetail is based on the concept of the dipole moment. CellDetail provides quantitative values for the distribution of the polarity proteins Cdc42 and Tubulin in young and aged hematopoietic stem cells (HSCs). Septin proteins form networks within cells that are critical for cell compartmentalization. We uncover a reduced level of organization of the Septin network within aged HSCs and within senescent human fibroblasts. Changes in the Septin network structure might therefore be a common feature of aging. The level of organization of the network of Septin proteins in aged HSCs can be restored to a youthful level by pharmacological attenuation of the activity of the small RhoGTPase Cdc42.

Self-organized tissue mechanics underlie embryonic regulation

Early amniote development is highly self-organized, capable of adapting to interference through local and long-range cell-cell interactions. This process, called embryonic regulation1, has been well illustrated in experiments on avian embryos, in which subdividing the epiblast disk into different parts not only redirects cell fates to eventually form a complete and well-proportioned embryo at its original location, but also leads to the self-organization of additional, fully formed embryos2,3 in the other separated parts. The cellular interactions underlying embryonic self-organization are widely believed to be mediated by molecular signals, yet the identity of such signals is unclear. Here, by analysing intact and mechanically perturbed quail embryos, we show that the mechanical forces that drive embryogenesis self-organize, with contractility locally self-activating and the ensuing tension acting as a long-range inhibitor. This mechanical feedback governs the persistent pattern of tissue flows that shape the embryo4-6 and also steers the concomitant emergence of embryonic territories by modulating gene expression, ensuring the formation of a single embryo under normal conditions, yet allowing the emergence of multiple, well-proportioned embryos after perturbations. Thus, mechanical forces act at the core of embryonic self-organization, shaping both tissues and gene expression to robustly yet plastically canalize early development.

Oligomerization and positive feedback on membrane recruitment encode dynamically stable PAR-3 asymmetries in the C. elegans zygote

Studies of PAR polarity have emphasized a paradigm in which mutually antagonistic PAR proteins form complementary polar domains in response to transient cues. A growing body of work suggests that the oligomeric scaffold PAR-3 can form unipolar asymmetries without mutual antagonism, but how it does so is largely unknown. Here we combine single molecule analysis and modeling to show how the interplay of two positive feedback loops promote dynamically stable unipolar PAR-3 asymmetries in early C. elegans embryos. First, the intrinsic dynamics of PAR-3 membrane binding and oligomerization encode negative feedback on PAR-3 dissociation. Second, membrane-bound PAR-3 promotes its own recruitment through a mechanism that requires the anterior polarity proteins CDC-42, PAR-6 and PKC-3. Using a kinetic model tightly constrained by our experimental measurements, we show that these two feedback loops are individually required and jointly sufficient to encode dynamically stable and locally inducible unipolar PAR-3 asymmetries in the absence of posterior inhibition. Given the central role of PAR-3, and the conservation of PAR-3 membrane-binding, oligomerization, and core interactions with PAR-6/aPKC, these results have widespread implications for PAR-mediated polarity in metazoa.

Optimized PAR-2 RING dimerization mediates cooperative and selective membrane binding for robust cell polarity

Cell polarity networks are defined by quantitative features of their constituent feedback circuits, which must be tuned to enable robust and stable polarization, while also ensuring that networks remain responsive to dynamically changing cellular states and/or spatial cues during development. Using the PAR polarity network as a model, we demonstrate that these features are enabled by the dimerization of the polarity protein PAR-2 via its N-terminal RING domain. Combining theory and experiment, we show that dimer affinity is optimized to achieve dynamic, selective, and cooperative binding of PAR-2 to the plasma membrane during polarization. Reducing dimerization compromises positive feedback and robustness of polarization. Conversely, enhanced dimerization renders the network less responsive due to kinetic trapping of PAR-2 on internal membranes and reduced sensitivity of PAR-2 to the anterior polarity kinase, aPKC/PKC-3. Thus, our data reveal a key role for a dynamically oligomeric RING domain in optimizing interaction affinities to support a robust and responsive cell polarity network, and highlight how optimization of oligomerization kinetics can serve as a strategy for dynamic and cooperative intracellular targeting.

Atypical Protein Kinase C Promotes its own Asymmetric Localisation by Phosphorylating Cdc42 in the C. elegans zygote

Atypical protein kinase C (aPKC) is a major regulator of cell polarity. Acting in conjunction with Par6, Par3 and the small GTPase Cdc42, aPKC becomes asymmetrically localised and drives the polarisation of cells. aPKC activity is crucial for its own asymmetric localisation, suggesting a hitherto unknown feedback mechanism contributing to polarisation. Here we show in the C. elegans zygote that the feedback relies on aPKC phosphorylation of Cdc42 at serine 71. The turnover of CDC-42 phosphorylation ensures optimal aPKC asymmetry and activity throughout polarisation by tuning Par6/aPKC association with Par3 and Cdc42. Moreover, turnover of Cdc42 phosphorylation regulates actomyosin cortex dynamics that are known to drive aPKC asymmetry. Given the widespread role of aPKC and Cdc42 in cell polarity, this form of self-regulation of aPKC may be vital for the robust control of polarisation in many cell types.

Robust spatiotemporal organization of mitotic events in mechanically perturbed C. elegans embryos

Early embryogenesis of the nematode Caenorhabditis elegans progresses in an autonomous fashion within a protective chitin eggshell. Cell-division timing and the subsequent mechanically guided positioning of cells is virtually invariant between individuals, especially before gastrulation. Here, we have challenged this stereotypical developmental program in early stages by mechanically perturbing the embryo without breaking its eggshell. Compressing embryos to about two-thirds of their unperturbed diameter only resulted in markedly slower cell divisions. In contrast, compressing embryos to half of their native diameter frequently resulted in a loss of cytokinesis, yielding a non-natural syncytium that still allowed for multiple divisions of nuclei. Although the orientation of mitotic axes was strongly altered in the syncytium, key features of division timing and spatial arrangement of nuclei remained surprisingly similar to those of unperturbed embryos in the first few division cycles. This suggests that few, very robust mechanisms provide a basic and resilient program for safeguarding the early embryogenesis of C. elegans.

Order from chaos: cellular asymmetries explained with modelling

Molecules inside cells are subject to physical forces and undergo biochemical interactions, continuously changing their physical properties and dynamics. Despite this, cells achieve highly ordered molecular patterns that are crucial to regulate various cellular functions and to specify cell fate. In the Caenorhabditis elegans one-cell embryo, protein asymmetries are established in the narrow time window of a cell division. What are the mechanisms that allow molecules to establish asymmetries, defying the randomness imposed by Brownian motion? Mathematical and computational models have paved the way to the understanding of protein dynamics up to the 'single-molecule level' when resolution represents an issue for precise experimental measurements. Here we review the models that interpret cortical and cytoplasmic asymmetries in the one-cell C. elegans embryo.

Friction forces determine cytoplasmic reorganization and shape changes of ascidian oocytes upon fertilization

Contraction and flow of the actin cell cortex have emerged as a common principle by which cells reorganize their cytoplasm and take shape. However, how these cortical flows interact with adjacent cytoplasmic components, changing their form and localization, and how this affects cytoplasmic organization and cell shape remains unclear. Here we show that in ascidian oocytes, the cooperative activities of cortical actomyosin flows and deformation of the adjacent mitochondria-rich myoplasm drive oocyte cytoplasmic reorganization and shape changes following fertilization. We show that vegetal-directed cortical actomyosin flows, established upon oocyte fertilization, lead to both the accumulation of cortical actin at the vegetal pole of the zygote and compression and local buckling of the adjacent elastic solid-like myoplasm layer due to friction forces generated at their interface. Once cortical flows have ceased, the multiple myoplasm buckles resolve into one larger buckle, which again drives the formation of the contraction pole-a protuberance of the zygote's vegetal pole where maternal mRNAs accumulate. Thus, our findings reveal a mechanism where cortical actomyosin network flows determine cytoplasmic reorganization and cell shape by deforming adjacent cytoplasmic components through friction forces.

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.

Cleavage furrow-directed cortical flows bias PAR polarization pathways to link cell polarity to cell division

During development, the conserved PAR polarity network is continuously redeployed, requiring that it adapt to changing cellular contexts and environmental cues. In the early C. elegans embryo, polarity shifts from being a cell-autonomous process in the zygote to one that must be coordinated between neighbors as the embryo becomes multicellular. Here, we sought to explore how the PAR network adapts to this shift in the highly tractable C. elegans germline P lineage. We find that although P lineage blastomeres exhibit a distinct pattern of polarity emergence compared with the zygote, the underlying mechanochemical processes that drive polarity are largely conserved. However, changes in the symmetry-breaking cues of P lineage blastomeres ensure coordination of their polarity axis with neighboring cells. Specifically, we show that furrow-directed cortical flows associated with cytokinesis of the zygote induce symmetry breaking in the germline blastomere P1 by transporting PAR-3 into the nascent cell contact. This pool of PAR-3 then biases downstream PAR polarization pathways to establish the polarity axis of P1 with respect to the position of its anterior sister, AB. Thus, our data suggest that cytokinesis itself induces symmetry breaking through the advection of polarity proteins by furrow-directed flows. By directly linking cell polarity to cell division, furrow-directed cortical flows could be a general mechanism to ensure proper organization of cell polarity within actively dividing systems.

Design principles for selective polarization of PAR proteins by cortical flows

Clustering of membrane-associated molecules is thought to promote interactions with the actomyosin cortex, enabling size-dependent transport by actin flows. Consistent with this model, in the Caenorhabditis elegans zygote, efficient anterior segregation of the polarity protein PAR-3 requires oligomerization. However, through direct assessment of local coupling between motion of PAR proteins and the underlying cortex, we find no links between PAR-3 oligomer size and the degree of coupling. Indeed, both anterior and posterior PAR proteins experience similar advection velocities, at least over short distances. Consequently, differential cortex engagement cannot account for selectivity of PAR protein segregation by cortical flows. Combining experiment and theory, we demonstrate that a key determinant of differential segregation of PAR proteins by cortical flow is the stability of membrane association, which is enhanced by clustering and enables transport across cellular length scales. Thus, modulation of membrane binding dynamics allows cells to achieve selective transport by cortical flows despite widespread coupling between membrane-associated molecules and the cell cortex.

Geometry-induced patterns through mechanochemical coupling

Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic cell-shape changes. These changes in cell shape may in turn affect the dynamics of pattern-forming proteins, hence leading to an intricate feedback loop between cell shape and chemical dynamics. While several computational studies have examined the rich resulting dynamics, the underlying mechanisms are not yet fully understood. To elucidate some of these mechanisms, we explore a conceptual model for cell polarity on a dynamic one-dimensional manifold. Using concepts from differential geometry, we derive the equations governing mass-conserving reaction-diffusion systems on time-evolving manifolds. Analyzing these equations mathematically, we show that dynamic shape changes of the membrane can induce pattern-forming instabilities in parts of the membrane, which we refer to as regional instabilities. Deformations of the local membrane geometry can also (regionally) suppress pattern formation and spatially shift already existing patterns. We explain our findings by applying and generalizing the local equilibria theory of mass-conserving reaction-diffusion systems. This allows us to determine a simple onset criterion for geometry-induced pattern-forming instabilities, which is linked to the phase-space structure of the reaction-diffusion system. The feedback loop between membrane shape deformations and reaction-diffusion dynamics then leads to a surprisingly rich phenomenology of patterns, including oscillations, traveling waves, and standing waves, even if these patterns do not occur in systems with a fixed membrane shape. Our paper reveals that the local conformation of the membrane geometry acts as an important dynamical control parameter for pattern formation in mass-conserving reaction-diffusion systems.

Self-organized collective cell behaviors as design principles for synthetic developmental biology

Over the past two decades, molecular cell biology has graduated from a mostly analytic science to one with substantial synthetic capability. This success is built on a deep understanding of the structure and function of biomolecules and molecular mechanisms. For synthetic biology to achieve similar success at the scale of tissues and organs, an equally deep understanding of the principles of development is required. Here, we review some of the central concepts and recent progress in tissue patterning, morphogenesis and collective cell migration and discuss their value for synthetic developmental biology, emphasizing in particular the power of (guided) self-organization and the role of theoretical advances in making developmental insights applicable in synthesis.

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.

Self-organized intracellular twisters

Life in complex systems, such as cities and organisms, comes to a standstill when global coordination of mass, energy, and information flows is disrupted. Global coordination is no less important in single cells, especially in large oocytes and newly formed embryos, which commonly use fast fluid flows for dynamic reorganization of their cytoplasm. Here, we combine theory, computing, and imaging to investigate such flows in the Drosophila oocyte, where streaming has been proposed to spontaneously arise from hydrodynamic interactions among cortically anchored microtubules loaded with cargo-carrying molecular motors. We use a fast, accurate, and scalable numerical approach to investigate fluid-structure interactions of 1000s of flexible fibers and demonstrate the robust emergence and evolution of cell-spanning vortices, or twisters. Dominated by a rigid body rotation and secondary toroidal components, these flows are likely involved in rapid mixing and transport of ooplasmic components.

Exploring generic principles of compartmentalization in a developmental in vitro model

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

Liesegang Phenomenon of Liquid Metals on Au Film

Room temperature liquid metals (LM) such as gallium (Ga) own the potential to react with specific materials which would incubate new application categories. Here, diverse self-organized ring patterns due to nonequilibrium reaction-diffusion and spreading-limitation of Ga-based LM clusters on gold (Au) film are reported, among which diffusion is the controlling step and the self-limiting oxide layer plays the role of kinetic barrier. Such phenomena, classically known as the Liesegang rings, mainly occur in electrolyte media. Unlike existing systems, the present periodic crystallization mechanism enables highly symmetric spatiotemporal periodic Liesegang rings on a smaller scale under ambient conditions. Typically, the Ga-Au and eutectic gallium-indium alloy (EGaIn)-Au reaction-diffusion-spreading systems are constructed, obtaining the revert type and hybrid type concentric Liesegang patterns, respectively. The competitive patterning behavior of the intermediate phase products AuGa₂ and AuIn₂ in hybrid Liesegang patterns is further analyzed by altering the initial Ga/In mass ratio, first-principles calculations, and molecular dynamic simulations. When the mass ratio of In in GaIn alloy exceeds 15%, it will preferentially react with Au. The discovery of LM Liesegang phenomenon is expected to be a flashpoint for self-organized reaction-diffusion systems and offers promising rules for diverse areas such as materials synthesis and the jewelry design industry.

Directing Min protein patterns with advective bulk flow

The Min proteins constitute the best-studied model system for pattern formation in cell biology. We theoretically predict and experimentally show that the propagation direction of in vitro Min protein patterns can be controlled by a hydrodynamic flow of the bulk solution. We find downstream propagation of Min wave patterns for low MinE:MinD concentration ratios, upstream propagation for large ratios, but multistability of both propagation directions in between. Whereas downstream propagation can be described by a minimal model that disregards MinE conformational switching, upstream propagation can be reproduced by a reduced switch model, where increased MinD bulk concentrations on the upstream side promote protein attachment. Our study demonstrates that a differential flow, where bulk flow advects protein concentrations in the bulk, but not on the surface, can control surface-pattern propagation. This suggests that flow can be used to probe molecular features and to constrain mathematical models for pattern-forming systems.

Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking

A panoply of new tools for tracking single particles and molecules has led to an explosion of experimental data, leading to novel insights into physical properties of living matter governing cellular development and function, health and disease. In this Perspective, we present tools to investigate the dynamics and mechanics of living systems from the molecular to cellular scale via single-particle techniques. In particular, we focus on methods to measure, interpret, and analyse complex data sets that are associated with forces, materials properties, transport, and emergent organisation phenomena within biological and soft-matter systems. Current approaches, challenges, and existing solutions in the associated fields are outlined in order to support the growing community of researchers at the interface of physics and the life sciences. Each section focuses not only on the general physical principles and the potential for understanding living matter, but also on details of practical data extraction and analysis, discussing limitations, interpretation, and comparison across different experimental realisations and theoretical frameworks. Particularly relevant results are introduced as examples. While this Perspective describes living matter from a physical perspective, highlighting experimental and theoretical physics techniques relevant for such systems, it is also meant to serve as a solid starting point for researchers in the life sciences interested in the implementation of biophysical methods.

Mass Balance Imaging: A Phase Portrait Analysis for Characterizing Growth Kinetics of Biomolecular Condensates

Biomolecular condensation has emerged as a key organizing principle governing the formation of membraneless cellular assemblies. Revealing the mechanism of formation of biomolecular condensates requires the quantitative examination of their growth kinetics. Here, we introduce mass balance imaging (MBI) as a general method to study compositional growth dynamics based on fluorescent images of multicomponent clusters. MBI allows the visualization and measurement of composition-dependent growth rates of biomolecular condensates and other assemblies. We provide a computational pipeline and demonstrate the applicability of our method by investigating cortical assemblies containing N-WASP (WSP-1) and F-actin that appear during oocyte cortex activation in C. elegans. In general, the method can be broadly implemented to identify interactions that underlie growth kinetics of multicomponent assemblies in vivo and in vitro.

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.

Live imaging of echinoderm embryos to illuminate evo-devo

Echinoderm embryos have been model systems for cell and developmental biology for over 150 years, in good part because of their optical clarity. Discoveries that shaped our understanding of fertilization, cell division and cell differentiation were only possible because of the transparency of sea urchin eggs and embryos, which allowed direct observations of intracellular structures. More recently, live imaging of sea urchin embryos, coupled with fluorescence microscopy, has proven pivotal to uncovering mechanisms of epithelial to mesenchymal transition, cell migration and gastrulation. However, live imaging has mainly been performed on sea urchin embryos, while echinoderms include numerous experimentally tractable species that present interesting variation in key aspects of morphogenesis, including differences in embryo compaction and mechanisms of blastula formation. The study of such variation would allow us not only to understand how tissues are formed in echinoderms, but also to identify which changes in cell shape, cell-matrix and cell-cell contact formation are more likely to result in evolution of new embryonic shapes. Here we argue that adapting live imaging techniques to more echinoderm species will be fundamental to exploit such an evolutionary approach to the study of morphogenesis, as it will allow measuring differences in dynamic cellular behaviors - such as changes in cell shape and cell adhesion - between species. We briefly review existing methods for live imaging of echinoderm embryos and describe in detail how we adapted those methods to allow long-term live imaging of several species, namely the sea urchin Lytechinus pictus and the sea stars Patiria miniata and Patiriella regularis. We outline procedures to successfully label, mount and image early embryos for 10-16 h, from cleavage stages to early blastula. We show that data obtained with these methods allows 3D segmentation and tracking of individual cells over time, the first step to analyze how cell shape and cell contact differ among species. The methods presented here can be easily adopted by most cell and developmental biology laboratories and adapted to successfully image early embryos of additional species, therefore broadening our understanding of the evolution of morphogenesis.

A combined in silico and in vivo approach to the structure-function annotation of SPD-2 provides mechanistic insight into its functional diversity

Centrosomes are organelles that function as hubs of microtubule nucleation and organization, with key roles in organelle positioning, asymmetric cell division, ciliogenesis, and signaling. Aberrant centrosome number, structure or function is linked to neurodegenerative diseases, developmental abnormalities, ciliopathies, and tumor development. A major regulator of centrosome biogenesis and function in C. elegans is the conserved Spindle-defective protein 2 (SPD-2), a homolog of the human CEP-192 protein. CeSPD-2 is required for centrosome maturation, centriole duplication, spindle assembly and possibly cell polarity establishment. Despite its importance, the specific molecular mechanism of CeSPD-2 regulation and function is poorly understood. Here, we combined computational analysis with cell biology approaches to uncover possible structure-function relationships of CeSPD-2 that may shed mechanistic light on its function. Domain prediction analysis corroborated and refined previously identified coiled-coils and ASH (Aspm-SPD-2 Hydin) domains and identified new domains: a GEF domain, an Ig-like domain, and a PDZ-like domain. In addition to these predicted structural features, CeSPD-2 is also predicted to be intrinsically disordered. Surface electrostatic maps identified a large basic region unique to the ASH domain of CeSPD-2. This basic region overlaps with most of the residues predicted to be involved in protein-protein interactions. In vivo, ASH::GFP localized to centrosomes and centrosome-associated microtubules. Our analysis groups ASH domains, PapD, Usher chaperone domains, and Major Sperm Protein (MSP) domains into a single superfold within the larger Immunoglobulin superfamily. This study lays the groundwork for designing rational hypothesis-based experiments to uncover the mechanisms of CeSPD-2 function in vivo.Abbreviations: AIR, Aurora kinase; ASH, Aspm-SPD-2 Hydin; ASP, Abnormal Spindle Protein; ASPM, Abnormal Spindle-like Microcephaly-associated Protein; CC, coiled-coil; CDK, Cyclin-dependent Kinase; Ce, Caenorhabditis elegans; CEP, Centrosomal Protein; CPAP, centrosomal P4.1-associated protein; D, Drosophila; GAP, GTPase activating protein; GEF, GTPase guanine nucleotide exchange factor; Hs, Homo sapiens/Human; Ig, Immunoglobulin; MAP, Microtubule associated Protein; MSP, Major Sperm Protein; MDP, Major Sperm Domain-Containing Protein; OCRL-1, Golgi endocytic trafficking protein Inositol polyphosphate 5-phosphatase; PAR, abnormal embryonic PARtitioning of the cytosol; PCM, Pericentriolar material; PCMD, pericentriolar matrix deficient; PDZ, PSD95/Dlg-1/zo-1; PLK, Polo like kinase; RMSD, Root Mean Square Deviation; SAS, Spindle assembly abnormal proteins; SPD, Spindle-defective protein; TRAPP, TRAnsport Protein Particle; Xe, Xenopus; ZYG, zygote defective protein.

Delineating the mechanisms and design principles of Caenorhabditis elegans embryogenesis using in toto high-resolution imaging data and computational modeling

The nematode (roundworm) Caenorhabditis elegans is one of the most popular animal models for the study of developmental biology, as its invariant development and transparent body enable in toto cellular-resolution fluorescence microscopy imaging of developmental processes at 1-min intervals. This has led to the development of various computational tools for the systematic and automated analysis of imaging data to delineate the molecular and cellular processes throughout the embryogenesis of C. elegans, such as those associated with cell lineage, cell migration, cell morphology, and gene activity. In this review, we first introduce C. elegans embryogenesis and the development of techniques for tracking cell lineage and reconstructing cell morphology during this process. We then contrast the developmental modes of C. elegans and the customized technologies used for studying them with the ones of other animal models, highlighting its advantage for studying embryogenesis with exceptional spatial and temporal resolution. This is followed by an examination of the physical models that have been devised-based on accurate determinations of developmental processes afforded by analyses of imaging data-to interpret the early embryonic development of C. elegans from subcellular to intercellular levels of multiple cells, which focus on two key processes: cell polarization and morphogenesis. We subsequently discuss how quantitative data-based theoretical modeling has improved our understanding of the mechanisms of C. elegans embryogenesis. We conclude by summarizing the challenges associated with the acquisition of C. elegans embryogenesis data, the construction of algorithms to analyze them, and the theoretical interpretation.

An analog sensitive allele permits rapid and reversible chemical inhibition of PKC-3 activity in C. elegans

Engineered analog sensitive kinases provide a highly effective method for acute, controllable, and highly selective inhibition of kinase activity. Here we describe the design and characterization of an analog sensitive allele of the polarity kinase, PKC-3. This allele supports normal function as measured by its ability to exclude PAR-2 from the anterior membrane of zygotes, and is rapidly and reversibly inhibited in a dose-dependent manner by the ATP analog 1NA-PP1. This allele provides a new tool to explore the role of PKC-3 in diverse contexts within C. elegans , particularly those in which acute and reversible control of PKC-3 kinase activity may be desired.

Forced and spontaneous symmetry breaking in cell polarization

How does breaking the symmetry of an equation alter the symmetry of its solutions? Here, we systematically examine how reducing underlying symmetries from spherical to axisymmetric influences the dynamics of an archetypal model of cell polarization, a key process of biological spatial self-organization. Cell polarization is characterized by nonlinear and non-local dynamics, but we overcome the theory challenges these traits pose by introducing a broadly applicable numerical scheme allowing us to efficiently study continuum models in a wide range of geometries. Guided by numerical results, we discover a dynamical hierarchy of timescales that allows us to reduce relaxation to a purely geometric problem of area-preserving geodesic curvature flow. Through application of variational results, we analytically construct steady states on a number of biologically relevant shapes. In doing so, we reveal non-trivial solutions for symmetry breaking.

SAIBR: a simple, platform-independent method for spectral autofluorescence correction

Biological systems are increasingly viewed through a quantitative lens that demands accurate measures of gene expression and local protein concentrations. CRISPR/Cas9 gene tagging has enabled increased use of fluorescence to monitor proteins at or near endogenous levels under native regulatory control. However, owing to typically lower expression levels, experiments using endogenously tagged genes run into limits imposed by autofluorescence (AF). AF is often a particular challenge in wavelengths occupied by commonly used fluorescent proteins (GFP, mNeonGreen). Stimulated by our work in C. elegans, we describe and validate Spectral Autofluorescence Image Correction By Regression (SAIBR), a simple platform-independent protocol and FIJI plug-in to correct for autofluorescence using standard filter sets and illumination conditions. Validated for use in C. elegans embryos, starfish oocytes and fission yeast, SAIBR is ideal for samples with a single dominant AF source; it achieves accurate quantitation of fluorophore signal, and enables reliable detection and quantification of even weakly expressed proteins. Thus, SAIBR provides a highly accessible low-barrier way to incorporate AF correction as standard for researchers working on a broad variety of cell and developmental systems.

Orchestrating nonmuscle myosin II filament assembly at the onset of cytokinesis

Contractile forces in the actomyosin cortex are required for cellular morphogenesis. This includes the invagination of the cell membrane during division, where filaments of nonmuscle myosin II (NMII) are responsible for generating contractile forces in the cortex. However, how NMII heterohexamers form filaments in vivo is not well understood. To quantify NMII filament assembly dynamics, we imaged the cortex of Caenorhabditis elegans embryos at high spatial resolution around the time of the first division. We show that during the assembly of the cytokinetic ring, the number of NMII filaments in the cortex increases and more NMII motors are assembled into each filament. These dynamics are influenced by two proteins in the RhoA GTPase pathway, the RhoA-dependent kinase LET-502 and the myosin phosphatase MEL-11. We find that these two proteins differentially regulate NMII activity at the anterior and at the division site. We show that the coordinated action of these regulators generates a gradient of free NMII in the cytoplasm driving a net diffusive flux of NMII motors toward the cytokinetic ring. Our work highlights how NMII filament assembly and disassembly dynamics are orchestrated over space and time to facilitate the up-regulation of cortical contractility during cytokinesis.

Stability selection enables robust learning of differential equations from limited noisy data

We present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data. We address two issues that have so far limited the application of such methods, namely their robustness against noise and the need for manual parameter tuning, by proposing stability-based model selection to determine the level of regularization required for reproducible inference. This avoids manual parameter tuning and improves robustness against noise in the data. Our stability selection approach, termed PDE-STRIDE, can be combined with any sparsity-promoting regression method and provides an interpretable criterion for model component importance. We show that the particular combination of stability selection with the iterative hard-thresholding algorithm from compressed sensing provides a fast and robust framework for equation inference that outperforms previous approaches with respect to accuracy, amount of data required, and robustness. We illustrate the performance of PDE-STRIDE on a range of simulated benchmark problems, and we demonstrate the applicability of PDE-STRIDE on real-world data by considering purely data-driven inference of the protein interaction network for embryonic polarization in Caenorhabditis elegans. Using fluorescence microscopy images of C. elegans zygotes as input data, PDE-STRIDE is able to learn the molecular interactions of the proteins.

Advances and challenges in programming pattern formation using living cells

Spatial patterning of cell populations is a ubiquitous phenomenon in nature. Patterns occur at various length and time scales and exhibit immense diversity. In addition to offering a deeper understanding of the emergence of patterns in nature, the ability to program synthetic patterns using living cells has the potential for broad applications. To date, however, progress in engineering pattern formation has been hampered by technical challenges. In this Review, we discuss recent advances in programming pattern formation in terms of biological insights, experimental and computational tool development, and potential applications.

A particle size threshold governs diffusion and segregation of PAR-3 during cell polarization

The actomyosin cortex regulates the localization and function of proteins at the plasma membrane. Here, we study how membrane binding, cortical movements, and diffusion determine membrane protein distribution. In Caenorhabditis elegans zygotes, actomyosin flows transport PAR polarity proteins to establish the anterior-posterior axis. Oligomerization of a key scaffold protein, PAR-3, is required for polarization. PAR-3 oligomers are a heterogeneous population of many different sizes, and it remains unclear how oligomer size affects PAR-3 segregation. To address this question, we engineered PAR-3 to defined sizes. We report that PAR-3 trimers are necessary and sufficient for PAR-3 function during polarization and later embryo development. Quantitative analysis of PAR-3 diffusion shows that a threshold size of three subunits allows PAR-3 clusters to stably bind the membrane, where they are corralled and transported by the actomyosin cortex. Our study provides a quantitative model for size-dependent protein transportation of peripheral membrane proteins by cortical flow.

The actomyosin cytoskeleton is a major regulator of cellular organization. Chang and Dickinson develop protein-engineering and particle-tracking tools to study how clustered membrane-bound proteins are transported by actomyosin contractions in vivo. Data-driven modeling reveals how membrane binding, diffusion, and collisions with F-actin contribute to protein movement.

Counting fluorescently labeled proteins in tissues in the spinning disk microscope using single-molecule calibrations

Quantification of molecular numbers and concentrations in living cells is critical for testing models of complex biological phenomena. Counting molecules in cells requires estimation of the fluorescence intensity of single molecules, which is generally limited to imaging near cell surfaces, in isolated cells, or where motions are diffusive. To circumvent this difficulty, we have devised a calibration technique for spinning–disk confocal microscopy, commonly used for imaging in tissues, that uses single–step bleaching kinetics to estimate the single–fluorophore intensity. To cross–check our calibrations, we compared the brightness of fluorophores in the SDC microscope to those in the total internal reflection and epifluorescence microscopes. We applied this calibration method to quantify the number of end–binding protein 1 (EB1)–eGFP in the comets of growing microtubule ends and to measure the cytoplasmic concentration of EB1–eGFP in sensory neurons in fly larvae. These measurements allowed us to estimate the dissociation constant of EB1–eGFP from the microtubules as well as the GTP–tubulin cap size. Our results show the unexplored potential of single–molecule imaging using spinning–disk confocal microscopy and provide a straightforward method to count the absolute number of fluorophores in tissues that can be applied to a wide range of biological systems and imaging techniques.

Biophysical Models of PAR Cluster Transport by Cortical Flow in C. elegans Early Embryogenesis

The clustering of membrane-bound proteins facilitates their transport by cortical actin flow in early Caenorhabditis elegans embryo cell polarity. PAR-3 clustering is critical for this process, yet the biophysical processes that couple protein clusters to cortical flow remain unknown. We develop a discrete, stochastic agent-based model of protein clustering and test four hypothetical models for how clusters may interact with the flow. Results show that the canonical way to assess transport characteristics from single-particle tracking data used thus far in this area, the Péclet number, is insufficient to distinguish these hypotheses and that all models can account for transport characteristics quantified by this measure. However, using this model, we demonstrate that these different cluster-cortex interactions may be distinguished using a different metric, namely the scalar projection of cluster displacement on to the flow displacement vector. Our results thus provide a testable way to use existing single-particle tracking data to test how endogenous protein clusters may interact with the cortical flow to localize during polarity establishment. To facilitate this investigation, we also develop both improved simulation and semi-analytic methodologies to quantify motion summary statistics (e.g., Péclet number and scalar projection) for these stochastic models as a function of biophysical parameters.

Volume segregation programming in a nematode's early embryogenesis

Nematode species are well-known for their invariant cell lineage pattern during development. Combining knowledge about the fate specification induced by asymmetric division and the anti-correlation between cell cycle length and cell volume in Caenorhabditis elegans, we propose a minimal model to simulate lineage initiation by altering cell volume segregation ratio in each division, and quantify the derived pattern's performance in proliferation speed, fate diversity, and space robustness. The stereotypic pattern in C. elegans embryo is found to be one of the most optimal solutions taking minimum time to achieve the cell number before gastrulation, by programming asymmetric divisions as a strategy.

Cytoskeletal symmetry breaking in animal cells

Symmetry breaking is a crucial step in structure formation and function of all cells, necessary for cell movement, cell division, and polarity establishment. Although the mechanisms of symmetry breaking are diverse, they often share common characteristics. Here we review examples of nematic, polar, and chiral cytoskeletal symmetry breaking in animal cells, and analogous processes in simplified reconstituted systems. We discuss the origins of symmetry breaking, which can arise spontaneously, or involve amplification of a pre-existing external or internal bias to the whole cell level. The underlying mechanisms often involve both chemical and mechanical processes that cooperate to break symmetry in a robust manner, and typically depend on the shape, size, or properties of the cell's boundary.

Spatiotemporal model of cellular mechanotransduction via Rho and YAP

How cells sense and respond to mechanical stimuli remains an open question. Recent advances have identified the translocation of Yes-associated protein (YAP) between nucleus and cytoplasm as a central mechanism for sensing mechanical forces and regulating mechanotransduction. We formulate a spatiotemporal model of the mechanotransduction signalling pathway that includes coupling of YAP with the cell force-generation machinery through the Rho family of GTPases. Considering the active and inactive forms of a single Rho protein (GTP/GDP-bound) and of YAP (non-phosphorylated/phosphorylated), we study the cross-talk between cell polarization due to active Rho and YAP activation through its nuclear localization. For fixed mechanical stimuli, our model predicts stationary nuclear-to-cytoplasmic YAP ratios consistent with experimental data at varying adhesive cell area. We further predict damped and even sustained oscillations in the YAP nuclear-to-cytoplasmic ratio by accounting for recently reported positive and negative YAP-Rho feedback. Extending the framework to time-varying mechanical stimuli that simulate cyclic stretching and compression, we show that the YAP nuclear-to-cytoplasmic ratio's time dependence follows that of the cyclic mechanical stimulus. The model presents one of the first frameworks for understanding spatiotemporal YAP mechanotransduction, providing several predictions of possible YAP localization dynamics, and suggesting new directions for experimental and theoretical studies.

Mechanical Patterning in Animal Morphogenesis

Morphogenesis is one of the most remarkable examples of biological pattern formation. Despite substantial progress in the field, we still do not understand the organizational principles responsible for the robust convergence of the morphogenesis process across scales to form viable organisms under variable conditions. Achieving large-scale coordination requires feedback between mechanical and biochemical processes, spanning all levels of organization and relating the emerging patterns with the mechanisms driving their formation. In this review, we highlight the role of mechanics in the patterning process, emphasizing the active and synergistic manner in which mechanical processes participate in developmental patterning rather than merely following a program set by biochemical signals. We discuss the value of applying a coarse-grained approach toward understanding this complex interplay, which considers the large-scale dynamics and feedback as well as complementing the reductionist approach focused on molecular detail. A central challenge in this approach is identifying relevant coarse-grained variables and developing effective theories that can serve as a basis for an integrated framework for understanding this remarkable pattern-formation process. Expected final online publication date for the Annual Review of Cell and Developmental Biology, Volume 37 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

A balance between antagonizing PAR proteins specifies the pattern of asymmetric and symmetric divisions in C. elegans embryogenesis

Coordination between cell differentiation and proliferation during development requires the balance between asymmetric and symmetric modes of cell division. However, the cellular intrinsic cue underlying the choice between these two division modes remains elusive. Here, we show evidence in Caenorhabditis elegans that the invariable lineage of the division modes is specified by the balance between antagonizing complexes of partitioning-defective (PAR) proteins. By uncoupling unequal inheritance of PAR proteins from that of fate determinants during cell division, we demonstrate that changes in the balance between PAR-2 and PAR-6 can be sufficient to re-program the division modes from symmetric to asymmetric and vice versa in two daughter cells. The division mode adopted occurs independently of asymmetry in cytoplasmic fate determinants, cell-size asymmetry, and cell-cycle asynchrony between sister cells. We propose that the balance between PAR proteins represents an intrinsic self-organizing cue for the specification of the two division modes during development.

Orchestration of tissue-scale mechanics and fate decisions by polarity signalling

Eukaryotic development relies on dynamic cell shape changes and segregation of fate determinants to achieve coordinated compartmentalization at larger scale. Studies in invertebrates have identified polarity programmes essential for morphogenesis; however, less is known about their contribution to adult tissue maintenance. While polarity-dependent fate decisions in mammals utilize molecular machineries similar to invertebrates, the hierarchies and effectors can differ widely. Recent studies in epithelial systems disclosed an intriguing interplay of polarity proteins, adhesion molecules and mechanochemical pathways in tissue organization. Based on major advances in biophysics, genome editing, high-resolution imaging and mathematical modelling, the cell polarity field has evolved to a remarkably multidisciplinary ground. Here, we review emerging concepts how polarity and cell fate are coupled, with emphasis on tissue-scale mechanisms, mechanobiology and mammalian models. Recent findings on the role of polarity signalling for tissue mechanics, micro-environmental functions and fate choices in health and disease will be summarized.

Learning physically consistent differential equation models from data using group sparsity

We propose a statistical learning framework based on group-sparse regression that can be used to (i) enforce conservation laws, (ii) ensure model equivalence, and (iii) guarantee symmetries when learning or inferring differential-equation models from data. Directly learning interpretable mathematical models from data has emerged as a valuable modeling approach. However, in areas such as biology, high noise levels, sensor-induced correlations, and strong intersystem variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure. Hence, it is important to leverage prior knowledge from physical principles to learn biologically plausible and physically consistent models rather than models that simply fit the data best. We present the group iterative hard thresholding algorithm and use stability selection to infer physically consistent models with minimal parameter tuning. We show several applications from systems biology that demonstrate the benefits of enforcing priors in data-driven modeling.

Active Viscoelasticity of Odd Materials

The mechanical response of active media ranging from biological gels to living tissues is governed by a subtle interplay between viscosity and elasticity. We generalize the canonical Kelvin-Voigt and Maxwell models to active viscoelastic media that break both parity and time-reversal symmetries. The resulting continuum theories exhibit viscous and elastic tensors that are both antisymmetric, or odd, under exchange of pairs of indices. We analyze how these parity violating viscoelastic coefficients determine the relaxation mechanisms and wave-propagation properties of odd materials.

The first steps in the life of a worm: Themes and variations in asymmetric division in C. elegans and other nematodes

Starting with Boveri in the 1870s, microscopic investigation of early embryogenesis in a broad swath of nematode species revealed the central role of asymmetric cell division in embryonic axis specification, blastomere positioning, and cell fate specification. Notably, across the class Chromadorea, a conserved theme emerges-asymmetry is first established in the zygote and specifies its asymmetric division, giving rise to an anterior somatic daughter cell and a posterior germline daughter cell. Beginning in the 1980s, the emergence of Caenorhabditis elegans as a model organism saw the advent of genetic tools that enabled rapid progress in our understanding of the molecular mechanisms underlying asymmetric division, in many cases defining key paradigms that turn out to regulate asymmetric division in a wide range of systems. Yet, the consequence of this focus on C. elegans came at the expense of exploring the extant diversity of developmental variation exhibited across nematode species. Given the resurgent interest in evolutionary studies facilitated in part by new tools, here we revisit the diversity in this asymmetric first division, juxtaposing molecular insight into mechanisms of symmetry-breaking, spindle positioning and fate specification, with a consideration of plasticity and variability within and between species. In the process, we hope to highlight questions of evolutionary forces and molecular variation that may have shaped the extant diversity of developmental mechanisms observed across Nematoda.

Developmental clock and mechanism of de novo polarization of the mouse embryo

Embryo polarization is critical for mouse development; however, neither the regulatory clock nor the molecular trigger that it activates is known. Here, we show that the embryo polarization clock reflects the onset of zygotic genome activation, and we identify three factors required to trigger polarization. Advancing the timing of transcription factor AP-2 gamma (Tfap2c) and TEA domain transcription factor 4 (Tead4) expression in the presence of activated Ras homolog family member A (RhoA) induces precocious polarization as well as subsequent cell fate specification and morphogenesis. Tfap2c and Tead4 induce expression of actin regulators that control the recruitment of apical proteins on the membrane, whereas RhoA regulates their lateral mobility, allowing the emergence of the apical domain. Thus, Tfap2c, Tead4, and RhoA are regulators for the onset of polarization and cell fate segregation in the mouse.

Four different mechanisms for switching cell polarity

The mechanisms and design principles of regulatory systems establishing stable polarized protein patterns within cells are well studied. However, cells can also dynamically control their cell polarity. Here, we ask how an upstream signaling system can switch the orientation of a polarized pattern. We use a mathematical model of a core polarity system based on three proteins as the basis to study different mechanisms of signal-induced polarity switching. The analysis of this model reveals four general classes of switching mechanisms with qualitatively distinct behaviors: the transient oscillator switch, the reset switch, the prime-release switch, and the push switch. Each of these regulatory mechanisms effectively implements the function of a spatial toggle switch, however with different characteristics in their nonlinear and stochastic dynamics. We identify these characteristics and also discuss experimental signatures of each type of switching mechanism.

Mechanochemical Control of Symmetry Breaking in the Caenorhabditis elegans Zygote

Cell polarity is the asymmetric organization of cellular components along defined axes. A key requirement for polarization is the ability of the cell to break symmetry and achieve a spatially biased organization. Despite different triggering cues in various systems, symmetry breaking (SB) usually relies on mechanochemical modulation of the actin cytoskeleton, which allows for advected movement and reorganization of cellular components. Here, the mechanisms underlying SB in Caenorhabditis elegans zygote, one of the most popular models to study cell polarity, are reviewed. A zygote initiates SB through the centrosome, which modulates mechanics of the cell cortex to establish advective flow of cortical proteins including the actin cytoskeleton and partitioning defective (PAR) proteins. The chemical signaling underlying centrosomal control of the Aurora A kinase–mediated cascade to convert the organization of the contractile actomyosin network from an apolar to polar state is also discussed.

Coordinating cell polarization and morphogenesis through mechanical feedback

Many cellular processes require cell polarization to be maintained as the cell changes shape, grows or moves. Without feedback mechanisms relaying information about cell shape to the polarity molecular machinery, the coordination between cell polarization and morphogenesis, movement or growth would not be possible. Here we theoretically and computationally study the role of a genetically-encoded mechanical feedback (in the Cell Wall Integrity pathway) as a potential coordination mechanism between cell morphogenesis and polarity during budding yeast mating projection growth. We developed a coarse-grained continuum description of the coupled dynamics of cell polarization and morphogenesis as well as 3D stochastic simulations of the molecular polarization machinery in the evolving cell shape. Both theoretical approaches show that in the absence of mechanical feedback (or in the presence of weak feedback), cell polarity cannot be maintained at the projection tip during growth, with the polarization cap wandering off the projection tip, arresting morphogenesis. In contrast, for mechanical feedback strengths above a threshold, cells can robustly maintain cell polarization at the tip and simultaneously sustain mating projection growth. These results indicate that the mechanical feedback encoded in the Cell Wall Integrity pathway can provide important positional information to the molecular machinery in the cell, thereby enabling the coordination of cell polarization and morphogenesis.

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'.

Compete or Coexist? Why the Same Mechanisms of Symmetry Breaking Can Yield Distinct Outcomes

Cellular morphogenesis is governed by the prepattern based on the symmetry-breaking emergence of dense protein clusters. Thus, a cluster of active GTPase Cdc42 marks the site of nascent bud in the baker's yeast. An important biological question is which mechanisms control the number of pattern maxima (spots) and, thus, the number of nascent cellular structures. Distinct flavors of theoretical models seem to suggest different predictions. While the classical Turing scenario leads to an array of stably coexisting multiple structures, mass-conserved models predict formation of a single spot that emerges via the greedy competition between the pattern maxima for the common molecular resources. Both the outcome and the kinetics of this competition are of significant biological importance but remained poorly explored. Recent theoretical analyses largely addressed these questions, but their results have not yet been fully appreciated by the broad biological community. Keeping mathematical apparatus and jargon to the minimum, we review the main conclusions of these analyses with their biological implications in mind. Focusing on the specific example of pattern formation by small GTPases, we speculate on the features of the patterning mechanisms that bypass competition and favor formation of multiple coexisting structures and contrast them with those of the mechanisms that harness competition to form unique cellular structures.