Atypical Protein Kinase C Promotes its own Asymmetric Localisation by Phosphorylating Cdc42 in Polarising Cells

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.

Robust cytoplasmic partitioning by solving an intrinsic cytoskeletal instability

Early development across vertebrates and insects critically relies on robustly reorganizing the cytoplasm of fertilized eggs into individualized cells. This intricate process is orchestrated by large microtubule structures that traverse the embryo, partitioning the cytoplasm into physically distinct and stable compartments. Despite the robustness of embryonic development, here we uncover an intrinsic instability in cytoplasmic partitioning driven by the microtubule cytoskeleton. We reveal that embryos circumvent this instability through two distinct mechanisms: either by matching the cell cycle duration to the time needed for the instability to unfold or by limiting microtubule nucleation. These regulatory mechanisms give rise to two possible strategies to fill the cytoplasm, which we experimentally demonstrate in zebrafish and Drosophila embryos, respectively. In zebrafish embryos, unstable microtubule waves fill the geometry of the entire embryo from the first division. Conversely, in Drosophila embryos, stable microtubule asters resulting from reduced microtubule nucleation gradually fill the cytoplasm throughout multiple divisions. Our results indicate that the temporal control of microtubule dynamics could have driven the evolutionary emergence of species-specific mechanisms for effective cytoplasmic organization. Furthermore, our study unveils a fundamental synergy between physical instabilities and biological clocks, uncovering universal strategies for rapid, robust, and efficient spatial ordering in biological systems.

From Homogeneity to Turing Pattern: Kinetically Controlled Self-Organization of Transmembrane Protein

Understanding the spatial organization of membrane proteins is crucial for unraveling key principles in cell biology. The reaction-diffusion model is commonly used to understand biochemical patterning; however, applying reaction-diffusion models to subcellular phenomena is challenging because of the difficulty in measuring protein diffusivity and interaction kinetics in the living cell. In this work, we investigated the self-organization of the plasmalemma vesicle-associated protein (PLVAP), which creates regular arrangements of fenestrated ultrastructures, using single-molecule tracking. We demonstrated that the spatial organization of the ultrastructures is associated with a decrease in the association rate by actin destabilization. We also constructed a reaction-diffusion model that accurately generates a hexagonal array with the same 130 nm spacing as the actual scale and informs the stoichiometry of the ultrastructure, which can be discerned only through electron microscopy. Through this study, we integrated single-molecule experiments and reaction-diffusion modeling to surpass the limitations of static imaging tools and proposed emergent properties of the PLVAP ultrastructure.

Origin and development of primary animal epithelia

Epithelia are the first organized tissues that appear during development. In many animal embryos, early divisions give rise to a polarized monolayer, the primary epithelium, rather than a random aggregate of cells. Here, we review the mechanisms by which cells organize into primary epithelia in various developmental contexts. We discuss how cells acquire polarity while undergoing early divisions. We describe cases where oriented divisions constrain cell arrangement to monolayers including organization on top of yolk surfaces. We finally discuss how epithelia emerge in embryos from animals that branched early during evolution and provide examples of epithelia-like arrangements encountered in single-celled eukaryotes. Although divergent and context-dependent mechanisms give rise to primary epithelia, here we trace the unifying principles underlying their formation.

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.

Kinesin-1 patterns Par-1 and Rho signaling at the cortex of syncytial embryos of Drosophila

The cell cortex of syncytial Drosophila embryos is patterned into cap and intercap regions by centrosomes, specific sets of proteins that are restricted to their respective regions by unknown mechanisms. Here, we found that Kinesin-1 is required for the restriction of plus- and minus-ends of centrosomal and non-centrosomal microtubules to the cap region, marked by EB1 and Patronin/Shot, respectively. Kinesin-1 also directly or indirectly restricts proteins and Rho signaling to the intercap, including the RhoGEF Pebble, Dia, Myosin II, Capping protein-α, and the polarity protein Par-1. Furthermore, we found that Par-1 is required for cap restriction of Patronin/Shot, and vice versa Patronin, for Par-1 enrichment at the intercap. In summary, our data support a model that Kinesin-1 would mediate the restriction of centrosomal and non-centrosomal microtubules to a region close to the centrosomes and exclude Rho signaling and Par-1. In addition, mutual antagonistic interactions would refine and maintain the boundary between cap and intercap and thus generate a distinct cortical pattern.

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.

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

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

Membrane extraction in native lipid nanodiscs reveals dynamic regulation of Cdc42 complexes during cell polarization

Embryonic development requires the establishment of cell polarity to enable cell fate segregation and tissue morphogenesis. This process is regulated by Par complex proteins, which partition into polarized membrane domains and direct downstream polarized cell behaviors. The kinase aPKC (along with its cofactor Par6) is a key member of this network and can be recruited to the plasma membrane by either the small GTPase Cdc42 or the scaffolding protein Par3. Although in vitro interactions among these proteins are well established, much is still unknown about the complexes they form during development. Here, to enable the study of membrane-associated complexes ex vivo, we used a maleic acid copolymer to rapidly isolate membrane proteins from single C. elegans zygotes into lipid nanodiscs. We show that native lipid nanodisc formation enables detection of endogenous complexes involving Cdc42, which are undetectable when cells are lysed in detergent. We found that Cdc42 interacts more strongly with aPKC/Par6 during polarity maintenance than polarity establishment, two developmental stages that are separated by only a few minutes. We further show that Cdc42 and Par3 do not bind aPKC/Par6 simultaneously, confirming recent in vitro findings in an ex vivo context. Our findings establish a new tool for studying membrane-associated signaling complexes and reveal an unexpected mode of polarity regulation via Cdc42.

Temporally distinct roles of Aurora A in polarization of the C. elegans zygote

During asymmetric cell division, coordination of cell polarity and the cell cycle is critical for proper inheritance of cell fate determinants and generation of cellular diversity. In Caenorhabditis elegans (C. elegans), polarity is established in the zygote and is governed by evolutionarily conserved Partitioning defective (PAR) proteins that localize to distinct cortical domains. At the time of polarity establishment, anterior and posterior PARs segregate to opposing cortical domains that specify asymmetric cell fates. Timely establishment of these PAR domains requires a cell cycle kinase, Aurora A (AIR-1 in C.elegans). Aurora A depletion by RNAi causes a spectrum of phenotypes including no posterior domain, reversed polarity, and excess posterior domains. How depletion of a single kinase can cause seemingly opposite phenotypes remains obscure. Using an auxin-inducible degradation system, drug treatments, and high-resolution microscopy, we found that AIR-1 regulates polarity via distinct mechanisms at different times of the cell cycle. During meiosis I, AIR-1 acts to prevent the formation of bipolar domains, while in meiosis II, AIR-1 is necessary to recruit PAR-2 onto the membrane. Together these data clarify the origin of the multiple polarization phenotypes observed in RNAi experiments and reveal multiple roles of AIR-1 in coordinating PAR protein localization with the progression of the cell cycle.

Apical PAR protein caps orient the mitotic spindle in C. elegans early embryos

During embryonic development, oriented cell divisions are important for patterned tissue growth and cell fate specification. Cell division orientation is controlled in part by asymmetrically localized polarity proteins, which establish functional domains of the cell membrane and interact with microtubule regulators to position the mitotic spindle. For example, in the 8-cell mouse embryo, apical polarity proteins form caps on the outside, contact-free surface of the embryo that position the mitotic spindle to execute asymmetric cell division. A similar radial or "inside-outside" polarity is established at an early stage in many other animal embryos, but in most cases, it remains unclear how inside-outside polarity is established and how it influences downstream cell behaviors. Here, we explore inside-outside polarity in C. elegans somatic blastomeres using spatiotemporally controlled protein degradation and live embryo imaging. We show that PAR polarity proteins, which form apical caps at the center of the contact-free membrane, localize dynamically during the cell cycle and contribute to spindle orientation and proper cell positioning. Surprisingly, isolated single blastomeres lacking cell contacts are able to break symmetry and form PAR-3/atypical protein kinase C (aPKC) caps. Polarity caps form independently of actomyosin flows and microtubules and can regulate spindle orientation in cooperation with the key polarity kinase aPKC. Together, our results reveal a role for apical polarity caps in regulating spindle orientation in symmetrically dividing cells and provide novel insights into how these structures are formed.

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.

Apical polarity and actomyosin dynamics control Kibra subcellular localization and function in Drosophila Hippo signaling

The Hippo pathway is an evolutionarily conserved regulator of tissue growth that integrates inputs from both polarity and actomyosin networks. An upstream activator of the Hippo pathway, Kibra, localizes at the junctional and medial regions of the apical cortex in epithelial cells, and medial accumulation promotes Kibra activity. Here, we demonstrate that cortical Kibra distribution is controlled by a tug-of-war between apical polarity and actomyosin dynamics. We show that while the apical polarity network, in part via atypical protein kinase C (aPKC), tethers Kibra at the junctional cortex to silence its activity, medial actomyosin flows promote Kibra-mediated Hippo complex formation at the medial cortex, thereby activating the Hippo pathway. This study provides a mechanistic understanding of the relationship between the Hippo pathway, polarity, and actomyosin cytoskeleton, and it offers novel insights into how fundamental features of epithelial tissue architecture can serve as inputs into signaling cascades that control tissue growth, patterning, and morphogenesis.

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.

Simulation of microtubule-cytoplasm interaction revealed the importance of fluid dynamics in determining the organization of microtubules

Although microtubules in plant cells have been extensively studied, the mechanisms that regulate the spatial organization of microtubules are poorly understood. We hypothesize that the interaction between microtubules and cytoplasmic flow plays an important role in the assembly and orientation of microtubules. To test this hypothesis, we developed a new computational modeling framework for microtubules based on theory and methods from the fluid-structure interaction. We employed the immersed boundary method to track the movement of microtubules in cytoplasmic flow. We also incorporated details of the encounter dynamics when two microtubules collide with each other. We verified our computational model through several numerical tests before applying it to the simulation of the microtubule-cytoplasm interaction in a growing plant cell. Our computational investigation demonstrated that microtubules are primarily oriented in the direction orthogonal to the axis of cell elongation. We validated the simulation results through a comparison with the measurement from laboratory experiments. We found that our computational model, with further calibration, was capable of generating microtubule orientation patterns that were qualitatively and quantitatively consistent with the experimental results. The computational model proposed in this study can be naturally extended to many other cellular systems that involve the interaction between microstructures and the intracellular fluid.

Go with the flow - bulk transport by molecular motors

Cells are the smallest building blocks of all living eukaryotic organisms, usually ranging from a couple of micrometers (for example, platelets) to hundreds of micrometers (for example, neurons and oocytes) in size. In eukaryotic cells that are more than 100 µm in diameter, very often a self-organized large-scale movement of cytoplasmic contents, known as cytoplasmic streaming, occurs to compensate for the physical constraints of large cells. In this Review, we discuss cytoplasmic streaming in multiple cell types and the mechanisms driving this event. We particularly focus on the molecular motors responsible for cytoplasmic movements and the biological roles of cytoplasmic streaming in cells. Finally, we describe bulk intercellular flow that transports cytoplasmic materials to the oocyte from its sister germline cells to drive rapid oocyte growth.

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.

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.

Using Optogenetics to Investigate the Shared Mechanisms of Apical-Basal Polarity and Mitosis

The initiation of apical-basal (AB) polarity and the process of mitotic cell division are both characterised by the generation of specialised plasma membrane and cortical domains. These are generated using shared mechanisms, such as asymmetric protein accumulation, Rho GTPase signalling, cytoskeletal reorganisation, vesicle trafficking, and asymmetric phosphoinositide distribution. In epithelial tissue, the coordination of AB polarity and mitosis in space and time is important both during initial epithelial development and to maintain tissue integrity and ensure appropriate cell differentiation at later stages. Whilst significant progress has been made in understanding the mechanisms underlying cell division and AB polarity, it has so far been challenging to fully unpick the complex interrelationship between polarity, signalling, morphogenesis, and cell division. However, the recent emergence of optogenetic protein localisation techniques is now allowing researchers to reversibly control protein activation, localisation, and signalling with high spatiotemporal resolution. This has the potential to revolutionise our understanding of how subcellular processes such as AB polarity are integrated with cell behaviours such as mitosis and how these processes impact whole tissue morphogenesis. So far, these techniques have been used to investigate processes such as cleavage furrow ingression, mitotic spindle positioning, and in vivo epithelial morphogenesis. This review describes some of the key shared mechanisms of cell division and AB polarity establishment, how they are coordinated during development and how the advance of optogenetic techniques is furthering this research field.

Polarity and axis formation in the Drosophila female germ line

By the time a Drosophila egg is laid, both major body axes have already been defined and it contains all the nutrients needed to develop into a free-living larva in 24 h. By contrast, it takes almost a week to make an egg from a female germline stem cell, during the complex process of oogenesis. This review will discuss key symmetry-breaking steps in Drosophila oogenesis that lead to the polarisation of both body axes: the asymmetric divisions of the germline stem cells; the selection of the oocyte from the 16-cell germline cyst; the positioning of the oocyte at the posterior of the cyst; Gurken signalling from the oocyte to polarise the anterior-posterior axis of the somatic follicle cell epithelium around the developing germline cyst; the signalling back from the posterior follicle cells to polarise the anterior-posterior axis of the oocyte; and the migration of the oocyte nucleus that specifies the dorsal-ventral axis. Since each event creates the preconditions for the next, I will focus on the mechanisms that drive these symmetry-breaking steps, how they are linked and the outstanding questions that remain to be answered.

Oligomerization of peripheral membrane proteins provides tunable control of cell surface polarity

Asymmetric distributions of peripheral membrane proteins define cell polarity across all kingdoms of life. Non-linear positive feedback on membrane binding is essential to amplify and stabilize these asymmetries, but how specific molecular sources of non-linearity shape polarization dynamics remains poorly understood. Here we show that the ability to oligomerize, which is common to many peripheral membrane proteins, can play a profound role in shaping polarization dynamics in simple feedback circuits. We show that size-dependent binding avidity and mobility of membrane-bound oligomers endow polarity circuits with several key properties. Size-dependent membrane binding avidity confers a form of positive feedback on the accumulation of oligomer subunits. Although insufficient by itself, this sharply reduces the amount of additional feedback required for spontaneous emergence and stable maintenance of polarized states. Size-dependent oligomer mobility makes symmetry breaking and stable polarity more robust with respect to variation in subunit diffusivities and cell sizes, and slows the approach to a final stable spatial distribution, allowing cells to "remember" polarity boundaries imposed by transient external cues. Together, these findings reveal how oligomerization of peripheral membrane proteins can provide powerful and highly tunable sources of non-linear feedback in biochemical circuits that govern cell surface polarity. Given its prevalence and widespread involvement in cell polarity, we speculate that self-oligomerization may have provided an accessible path to evolving simple polarity circuits.

Follicle cell contact maintains main body axis polarity in the Drosophila melanogaster oocyte

In Drosophila melanogaster, the anterior-posterior body axis is maternally established and governed by differential localization of partitioning defective (Par) proteins within the oocyte. At mid-oogenesis, Par-1 accumulates at the oocyte posterior end, while Par-3/Bazooka is excluded there but maintains its localization along the remaining oocyte cortex. Past studies have proposed the need for somatic cells at the posterior end to initiate oocyte polarization by providing a trigger signal. To date, neither the molecular identity nor the nature of the signal is known. Here, we provide evidence that mechanical contact of posterior follicle cells (PFCs) with the oocyte cortex causes the posterior exclusion of Bazooka and maintains oocyte polarity. We show that Bazooka prematurely accumulates exclusively where posterior follicle cells have been mechanically detached or ablated. Furthermore, we provide evidence that PFC contact maintains Par-1 and oskar mRNA localization and microtubule cytoskeleton polarity in the oocyte. Our observations suggest that cell-cell contact mechanics modulates Par protein binding sites at the oocyte cortex.

A Gaussian jump process formulation of the reaction–diffusion master equation enables faster exact stochastic simulations

We propose a Gaussian jump process model on a regular Cartesian lattice for the diffusion part of the Reaction–Diffusion Master Equation (RDME). We derive the resulting Gaussian RDME (GRDME) formulation from analogy with a kernel-based discretization scheme for continuous diffusion processes and quantify the limits of its validity relative to the classic RDME. We then present an exact stochastic simulation algorithm for the GRDME, showing that the accuracies of GRDME and RDME are comparable, but exact simulations of the GRDME require only a fraction of the computational cost of exact RDME simulations. We analyze the origin of this speedup and its scaling with problem dimension. The benchmarks suggest that the GRDME is a particularly beneficial model for diffusion-dominated systems in three dimensional spaces, often occurring in systems biology and cell biology.

Separable mechanisms drive local and global polarity establishment in the Caenorhabditiselegans intestinal epithelium

Apico-basolateral polarization is essential for epithelial cells to function as selective barriers and transporters, and to provide mechanical resilience to organs. Epithelial polarity is established locally, within individual cells to establish distinct apical, junctional and basolateral domains, and globally, within a tissue where cells coordinately orient their apico-basolateral axes. Using live imaging of endogenously tagged proteins and tissue-specific protein depletion in the Caenorhabditiselegans embryonic intestine, we found that local and global polarity establishment are temporally and genetically separable. Local polarity is initiated prior to global polarity and is robust to perturbation. PAR-3 is required for global polarization across the intestine but local polarity can arise in its absence, as small groups of cells eventually established polarized domains in PAR-3-depleted intestines in a HMR-1 (E-cadherin)-dependent manner. Despite the role of PAR-3 in localizing PKC-3 to the apical surface, we additionally found that PAR-3 and PKC-3/aPKC have distinct roles in the establishment and maintenance of local and global polarity. Taken together, our results indicate that different mechanisms are required for local and global polarity establishment in vivo.

Chemical Kinetics and Mass Action in Coexisting Phases

The kinetics of chemical reactions are determined by the law of mass action, which has been successfully applied to homogeneous, dilute mixtures. At nondilute conditions, interactions among the components can give rise to coexisting phases, which can significantly alter the kinetics of chemical reactions. Here, we derive a theory for chemical reactions in coexisting phases at phase equilibrium. We show that phase equilibrium couples the rates of chemical reactions of components with their diffusive exchanges between the phases. Strikingly, the chemical relaxation kinetics can be represented as a flow along the phase equilibrium line in the phase diagram. A key finding of our theory is that differences in reaction rates between coexisting phases stem solely from phase-dependent reaction rate coefficients. Our theory is key to interpreting how concentration levels of reactive components in condensed phases control chemical reaction rates in synthetic and biological systems.

Design centering enables robustness screening of pattern formation models

MOTIVATION

Access to unprecedented amounts of quantitative biological data allows us to build and test biochemically accurate reaction-diffusion models of intracellular processes. However, any increase in model complexity increases the number of unknown parameters and, thus, the computational cost of model analysis. To efficiently characterize the behavior and robustness of models with many unknown parameters remains, therefore, a key challenge in systems biology.

RESULTS

We propose a novel computational framework for efficient high-dimensional parameter space characterization of reaction-diffusion models in systems biology. The method leverages the Lp-Adaptation algorithm, an adaptive-proposal statistical method for approximate design centering and robustness estimation. Our approach is based on an oracle function, which predicts for any given point in parameter space whether the model fulfills given specifications. We propose specific oracles to efficiently predict four characteristics of Turing-type reaction-diffusion models: bistability, instability, capability of spontaneous pattern formation and capability of pattern maintenance. We benchmark the method and demonstrate that it enables global exploration of a model's ability to undergo pattern-forming instabilities and to quantify robustness for model selection in polynomial time with dimensionality. We present an application of the framework to pattern formation on the endosomal membrane by the small GTPase Rab5 and its effectors, and we propose molecular mechanisms underlying this system.

AVAILABILITY AND IMPLEMENTATION

Our code is implemented in MATLAB and is available as open source under https://git.mpi-cbg.de/mosaic/software/black-box-optimization/rd-parameter-space-screening.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Cell Repolarization: A Bifurcation Study of Spatio-Temporal Perturbations of Polar Cells

The intrinsic polarity of migrating cells is regulated by spatial distributions of protein activity. Those proteins (Rho-family GTPases, such as Rac and Rho) redistribute in response to stimuli, determining the cell front and back. Reaction-diffusion equations with mass conservation and positive feedback have been used to explain initial polarization of a cell. However, the sensitivity of a polar cell to a reversal stimulus has not yet been fully understood. We carry out a PDE bifurcation analysis of two polarity models to investigate routes to repolarization: (1) a single-GTPase ("wave-pinning") model and (2) a mutually antagonistic Rac-Rho model. We find distinct routes to reversal in (1) vs. (2). We show numerical simulations of full PDE solutions for the RD equations, demonstrating agreement with predictions of the bifurcation results. Finally, we show that simulations of the polarity models in deforming 1D model cells are consistent with biological experiments.

Sensing the shape of a cell with reaction diffusion and energy minimization

Some dividing cells sense their shape by becoming polarized along their long axis. Cell polarity is controlled in part by polarity proteins, like Rho GTPases, cycling between active membrane-bound forms and inactive cytosolic forms, modeled as a "wave-pinning" reaction-diffusion process. Does shape sensing emerge from wave pinning? We show that wave pinning senses the cell's long axis. Simulating wave pinning on a curved surface, we find that high-activity domains migrate to peaks and troughs of the surface. For smooth surfaces, a simple rule of minimizing the domain perimeter while keeping its area fixed predicts the final position of the domain and its shape. However, when we introduce roughness to our surfaces, shape sensing can be disrupted, and high-activity domains can become localized to locations other than the global peaks and valleys of the surface. On rough surfaces, the domains of the wave-pinning model are more robust in finding the peaks and troughs than the minimization rule, although both can become trapped in steady states away from the peaks and valleys. We can control the robustness of shape sensing by altering the Rho GTPase diffusivity and the domain size. We also find that the shape-sensing properties of cell polarity models can explain how domains localize to curved regions of deformed cells. Our results help to understand the factors that allow cells to sense their shape-and the limits that membrane roughness can place on this process.

Delineating 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.

A two-step search and run response to gradients shapes leukocyte navigation in vivo

Migrating cells must interpret chemical gradients to guide themselves within tissues. A long-held principle is that gradients guide cells via reorientation of leading-edge protrusions. However, recent evidence indicates that protrusions can be dispensable for locomotion in some contexts, raising questions about how cells interpret endogenous gradients in vivo and whether other mechanisms are involved. Using laser wound assays in zebrafish to elicit acute endogenous gradients and quantitative analyses, we demonstrate a two-stage process for leukocyte chemotaxis in vivo: first a “search” phase, with stimulation of actin networks at the leading edge, cell deceleration, and turning. This is followed by a “run” phase, with fast actin flows, cell acceleration, and persistence. When actin dynamics are perturbed, cells fail to resolve the gradient, suggesting that pure spatial sensing of the gradient is insufficient for navigation. Our data suggest that cell contractility and actin flows provide memory for temporal sensing, while expansion of the leading edge serves to enhance gradient sampling.

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.

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.

Modeling protein dynamics in Caenorhabditis elegans embryos reveals that the PLK-1 gradient relies on weakly coupled reaction-diffusion mechanisms

Intracellular gradients have essential roles in cell and developmental biology, but their formation is not fully understood. We have developed a computational approach facilitating interpretation of protein dynamics and gradient formation. We have combined this computational approach with experiments to understand how Polo-Like Kinase 1 (PLK-1) forms a cytoplasmic gradient in Caenorhabditis elegans embryos. Although the PLK-1 gradient depends on the Muscle EXcess-5/6 (MEX-5/6) proteins, we reveal differences in PLK-1 and MEX-5 gradient formation that can be explained by a model with two components, PLK-1 bound to MEX-5 and unbound PLK-1. Our combined approach suggests that a weak coupling between PLK-1 and MEX-5 reaction–diffusion mechanisms dictates the dynamic exchange of PLK-1 with the cytoplasm, explaining PLK-1 high diffusivity and smooth gradient.

Protein gradients have fundamental roles in cell and developmental biology. In the one-cell Caenorhabditis elegans embryo, the mitotic Polo-Like Kinase 1 (PLK-1) forms an anterior-rich cytoplasmic gradient, which is crucial for asymmetric cell division and embryonic development. The PLK-1 gradient depends on the RNA-binding Muscle-EXcess-5 protein (MEX-5), whose slow-diffusing complexes accumulate in the anterior via a reaction–diffusion mechanism. Here, we combine experiments and a computational approach to investigate the dynamics of PLK-1 gradient formation. We find that the gradient of PLK-1 initiates later, is less steep, and forms with slower dynamics than does the MEX-5 gradient. The data show that PLK-1 diffuses faster than MEX-5 in both anterior and posterior cytoplasmic regions. Our simulations suggest that binding to slow-diffusing MEX-5 is required for PLK-1 gradient formation, but that a significant fraction of unbound PLK-1 is necessary to justify the different gradient dynamics. We provide a computational tool able to predict gradient establishment prior to cell division and show that a two-component, bound and unbound, model of PLK-1 dynamics recapitulates the experimental observations.

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.

Generation, Transmission, and Regulation of Mechanical Forces in Embryonic Morphogenesis

Embryonic morphogenesis is a biological process which depicts shape forming of tissues and organs during development. Unveiling the roles of mechanical forces generated, transmitted, and regulated in cells and tissues through these processes is key to understanding the biophysical mechanisms governing morphogenesis. To this end, it is imperative to measure, simulate, and predict the regulation and control of these mechanical forces during morphogenesis. This article aims to provide a comprehensive review of the recent advances on mechanical properties of cells and tissues, generation of mechanical forces in cells and tissues, the transmission processes of these generated forces during cells and tissues, the tools and methods used to measure and predict these mechanical forces in vivo, in vitro, or in silico, and to better understand the corresponding regulation and control of generated forces. Understanding the biomechanics and mechanobiology of morphogenesis will not only shed light on the fundamental physical mechanisms underlying these concerted biological processes during normal development, but also uncover new information that will benefit biomedical research in preventing and treating congenital defects or tissue engineering and regeneration.

The Drosophila anterior-posterior axis is polarized by asymmetric myosin activation

The Drosophila anterior-posterior axis is specified at mid-oogenesis when the Par-1 kinase is recruited to the posterior cortex of the oocyte, where it polarizes the microtubule cytoskeleton to define where the axis determinants, bicoid and oskar mRNAs, localize. This polarity is established in response to an unknown signal from the follicle cells, but how this occurs is unclear. Here we show that the myosin chaperone Unc-45 and non-muscle myosin II (MyoII) are required upstream of Par-1 in polarity establishment. Furthermore, the myosin regulatory light chain (MRLC) is di-phosphorylated at the oocyte posterior in response to the follicle cell signal, inducing longer pulses of myosin contractility at the posterior that may increase cortical tension. Overexpression of MRLC-T21A that cannot be di-phosphorylated or treatment with the myosin light-chain kinase inhibitor ML-7 abolishes Par-1 localization, indicating that the posterior of MRLC di-phosphorylation is essential for both polarity establishment and maintenance. Thus, asymmetric myosin activation polarizes the anterior-posterior axis by recruiting and maintaining Par-1 at the posterior cortex. This raises an intriguing parallel with anterior-posterior axis formation in C. elegans, where MyoII also acts upstream of the PAR proteins to establish polarity, but to localize the anterior PAR proteins rather than Par-1.

Pole position: How plant cells polarize along the axes

Having a sense of direction is a fundamental cellular trait that can determine cell shape, division orientation, or function, and ultimately the formation of a functional, multicellular body. Cells acquire and integrate directional information by establishing discrete subcellular domains along an axis with distinct molecular profiles, a process known as cell polarization. Insight into the principles and mechanisms underlying cell polarity has been propelled by decades of extensive research mostly in yeast and animal models. Our understanding of cell polarity establishment in plants, which lack most of the regulatory molecules identified in other eukaryotes, is more limited, but significant progress has been made in recent years. In this review, we explore how plant cells coordinately establish stable polarity axes aligned with the organ axes, highlighting similarities in the molecular logic used to polarize both plant and animal cells. We propose a classification system for plant cell polarity events and nomenclature guidelines. Finally, we provide a deep phylogenetic analysis of polar proteins and discuss the evolution of polarity machineries in plants.

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.

Autonomous epithelial folding induced by an intracellular mechano-polarity feedback loop

Epithelial tissues form folded structures during embryonic development and organogenesis. Whereas substantial efforts have been devoted to identifying mechanical and biochemical mechanisms that induce folding, whether and how their interplay synergistically shapes epithelial folds remains poorly understood. Here we propose a mechano-biochemical model for dorsal fold formation in the early Drosophila embryo, an epithelial folding event induced by shifts of cell polarity. Based on experimentally observed apical domain homeostasis, we couple cell mechanics to polarity and find that mechanical changes following the initial polarity shifts alter cell geometry, which in turn influences the reaction-diffusion of polarity proteins, thus forming a feedback loop between cell mechanics and polarity. This model can induce spontaneous fold formation in silico, recapitulate polarity and shape changes observed in vivo, and confer robustness to tissue shape change against small fluctuations in mechanics and polarity. These findings reveal emergent properties of a developing epithelium under control of intracellular mechano-polarity coupling.

Phases of cortical actomyosin dynamics coupled to the neuroblast polarity cycle

The Par complex dynamically polarizes to the apical cortex of asymmetrically dividing Drosophila neuroblasts where it directs fate determinant segregation. Previously, we showed that apically directed cortical movements that polarize the Par complex require F-actin (Oon and Prehoda, 2019). Here, we report the discovery of cortical actomyosin dynamics that begin in interphase when the Par complex is cytoplasmic but ultimately become tightly coupled to cortical Par dynamics. Interphase cortical actomyosin dynamics are unoriented and pulsatile but rapidly become sustained and apically-directed in early mitosis when the Par protein aPKC accumulates on the cortex. Apical actomyosin flows drive the coalescence of aPKC into an apical cap that depolarizes in anaphase when the flow reverses direction. Together with the previously characterized role of anaphase flows in specifying daughter cell size asymmetry, our results indicate that multiple phases of cortical actomyosin dynamics regulate asymmetric cell division.

A theoretical understanding of mammalian preimplantation development

The blastocyst has long been a hallmark system of study in developmental biology due to its importance in mammalian development and clinical relevance for assisted reproductive technologies. In recent years, the blastocyst is emerging as a system of study for mathematical modelling. In this review, we compile, to our knowledge, all models describing preimplantation development. Coupled with experiments, these models have provided insight regarding the morphogenesis and cell-fate specification throughout preimplantation development. In the case of cell-fate specification, theoretical models have provided mechanisms explaining how proportion of cell types are established and maintained when confronted to perturbations. For cell-shape based models, they have described quantitatively how mechanical forces sculpt the blastocyst and even predicted how morphogenesis could be manipulated. As theoretical biology develops, we believe the next critical stage in modelling involves an integration of cell fate and mechanics to provide integrative models of development at distinct spatiotemporal scales. We discuss how, building on a balanced base of mechanical and chemical models, the preimplantation embryo will play a key role in integrating these two faces of the same coin.

A C++ expression system for partial differential equations enables generic simulations of biological hydrodynamics

We present a user-friendly and intuitive C++ expression system to implement numerical simulations of continuum biological hydrodynamics. The expression system allows writing simulation programs in near-mathematical notation and makes codes more readable, more compact, and less error-prone. It also cleanly separates the implementation of the partial differential equation model from the implementation of the numerical methods used to discretize it. This allows changing either of them with minimal changes to the source code. The presented expression system is implemented in the high-performance computing platform OpenFPM, supporting simulations that transparently parallelize on multi-processor computer systems. We demonstrate that our expression system makes it easier to write scalable codes for simulating biological hydrodynamics in space and time. We showcase the present framework in numerical simulations of active polar fluids, as well as in classic simulations of fluid dynamics from the incompressible Navier-Stokes equations to Stokes flow in a ball. The presented expression system accelerates scalable simulations of spatio-temporal models that encode the physics and material properties of tissues in order to algorithmically study morphogenesis.

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.

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 picket fence function for adherens junctions in epithelial cell polarity

Adherens junctions are a defining feature of all epithelial cells, providing cell-cell adhesion and contractile ring formation that is essential for cell and tissue morphology. In Drosophila, adherens junctions are concentrated between the apical and basolateral plasma membrane domains, defined by aPKC-Par6-Baz and Lgl/Dlg/Scrib, respectively. Whether adherens junctions contribute to apical-basal polarization itself has been unclear because neuroblasts exhibit apical-basal polarization of aPKC-Par6-Baz and Lgl in the absence of adherens junctions. Here we show that, upon disruption of adherens junctions in epithelial cells, apical polarity determinants such as aPKC can still segregate from basolateral Lgl, but lose their sharp boundaries and also overlap with Dlg and Scrib - similar to neuroblasts. In addition, control of apical versus basolateral domain size is lost, along with control of cell shape, in the absence of adherens junctions. Manipulating the levels of apical Par3/Baz or basolateral Lgl polarity determinants in experiments and in computer simulations confirms that adherens junctions provide a 'picket fence' diffusion barrier that restricts the spread of polarity determinants along the membrane to enable precise domain size control. Movement of adherens junctions in response to mechanical forces during morphogenetic change thus enables spontaneous adjustment of apical versus basolateral domain size as an emergent property of the polarising system.