Symmetry breaking in biology

Synthetic control of actin polymerization and symmetry breaking in active protocells

Nonlinear biomolecular interactions on membranes drive membrane remodeling crucial for biological processes including chemotaxis, cytokinesis, and endocytosis. The complexity of biomolecular interactions, their redundancy, and the importance of spatiotemporal context in membrane organization impede understanding of the physical principles governing membrane mechanics. Developing a minimal in vitro system that mimics molecular signaling and membrane remodeling while maintaining physiological fidelity poses a major challenge. Inspired by chemotaxis, we reconstructed chemically regulated actin polymerization inside vesicles, guiding membrane self-organization. An external, undirected chemical input induced directed actin polymerization and membrane deformation uncorrelated with upstream biochemical cues, suggesting symmetry breaking. A biophysical model incorporating actin dynamics and membrane mechanics proposes that uneven actin distributions cause nonlinear membrane deformations, consistent with experimental findings. This protocellular system illuminates the interplay between actin dynamics and membrane shape during symmetry breaking, offering insights into chemotaxis and other cell biological processes.

Uniaxial Symmetry Breaking in Bacteriorhodopsin at the Thermal Phase Transition of Lipids of Purple Membranes

The article correlates between symmetry breaking and phase transition. An analogy, extending from physics to biology, is known to exist between these two topics. Bacteriorhodopsin (bR) as a paradigm of membrane proteins has been used as a case study in the present work. The bR, as the sole protein embedded in what is called a purple membrane (PM), has attracted widespread interest in bionanotechnological applications. The lipids of PM have a crucial role in maintaining the crystal lattice of bR inside PM. For this reason, the present work has been concerned with elucidating the thermal phase transition properties of the PM lipids in orthogonal directions. The results indicated that the axial symmetry of bR exhibits considerable changes occurring at the thermal phase transition of lipids. These changes are brought by an anomaly observed in the time course of orthogonal electric responses during the application of thermal fields on PM. The observed anomaly may bear on symmetry breaking in bR occurring at the phase transition of lipids based on such analogy found between symmetry breaking and phase transition. Lipid-protein interactions may underlie the broken axial symmetry of bR at such lipid thermal transition of PM. Accordingly, thermally perturbed axial symmetry of bR may be of biological relevance relying on the essence of the crystal lattice of bR. Most importantly, a question has to be raised in the present study: Can bR, as a helical protein with broken axial symmetry, affect the symmetry breaking of helical light? This may be of potential technical applications based on a recent discovery that bR breaks the symmetry of helical light.

Patterning of the cell cortex by Rho GTPases

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

Engineering DNA-based cytoskeletons for synthetic cells

The development and bottom-up assembly of synthetic cells with a functional cytoskeleton sets a major milestone to understand cell mechanics and to develop man-made machines on the nano- and microscale. However, natural cytoskeletal components can be difficult to purify, deliberately engineer and reconstitute within synthetic cells which therefore limits the realization of multifaceted functions of modern cytoskeletons in synthetic cells. Here, we review recent progress in the development of synthetic cytoskeletons made from deoxyribonucleic acid (DNA) as a complementary strategy. In particular, we explore the capabilities and limitations of DNA cytoskeletons to mimic functions of natural cystoskeletons like reversible assembly, cargo transport, force generation, mechanical support and guided polymerization. With recent examples, we showcase the power of rationally designed DNA cytoskeletons for bottom-up assembled synthetic cells as fully engineerable entities. Nevertheless, the realization of dynamic instability, self-replication and genetic encoding as well as contractile force generating motors remains a fruitful challenge for the complete integration of multifunctional DNA-based cytoskeletons into synthetic cells.

Synthetic control of actin polymerization and symmetry breaking in active protocells

Non-linear biomolecular interactions on the membranes drive membrane remodeling that underlies fundamental biological processes including chemotaxis, cytokinesis, and endocytosis. The multitude of biomolecules, the redundancy in their interactions, and the importance of spatiotemporal context in membrane organization hampers understanding the physical principles governing membrane mechanics. A minimal, in vitro system that models the functional interactions between molecular signaling and membrane remodeling, while remaining faithful to cellular physiology and geometry is powerful yet remains unachieved. Here, inspired by the biophysical processes underpinning chemotaxis, we reconstituted externally-controlled actin polymerization inside giant unilamellar vesicles, guiding self-organization on the membrane. We show that applying undirected external chemical inputs to this system results in directed actin polymerization and membrane deformation that are uncorrelated with upstream biochemical cues, indicating symmetry breaking. A biophysical model of the dynamics and mechanics of both actin polymerization and membrane shape suggests that inhomogeneous distributions of actin generate membrane shape deformations in a non-linear fashion, a prediction consistent with experimental measurements and subsequent local perturbations. The active protocellular system demonstrates the interplay between actin dynamics and membrane shape in a symmetry breaking context that is relevant to chemotaxis and a suite of other biological processes.

Synthetic symmetry breaking and programmable multicellular structure formation

During development, cells undergo symmetry breaking into differentiated subpopulations that self-organize into complex structures.1,2,3,4,5 However, few tools exist to recapitulate these behaviors in a controllable and coupled manner.6,7,8,9 Here, we engineer a stochastic recombinase genetic switch tunable by small molecules to induce programmable symmetry breaking, commitment to downstream cell fates, and morphological self-organization. Inducers determine commitment probabilities, generating tunable subpopulations as a function of inducer dosage. We use this switch to control the cell-cell adhesion properties of cells committed to each fate.10,11 We generate a wide variety of 3D morphologies from a monoclonal population and develop a computational model showing high concordance with experimental results, yielding new quantitative insights into the relationship between cell-cell adhesion strengths and downstream morphologies. We expect that programmable symmetry breaking, generating precise and tunable subpopulation ratios and coupled to structure formation, will serve as an integral component of the toolbox for complex tissue and organoid engineering.

On-Demand Breaking of Action-Reaction Reciprocity between Magnetic Microdisks Using Global Stimuli

Coupled physical interactions induce emergent collective behaviors of many interacting objects. Nonreciprocity in the interactions generates unexpected behaviors. There is a lack of experimental model system that switches between the reciprocal and nonreciprocal regime on demand. Here, we study a system of magnetic microdisks that breaks action-reaction reciprocity via fluid-mediated hydrodynamic interactions, on demand. Via experiments and simulations, we demonstrate that nonreciprocal interactions generate self-propulsion-like behaviors of a pair of disks; group separation in collective of magnetically nonidentical disks; and decouples a part of the group from the rest. Our results could help in developing controllable microrobot collectives. Our approach highlights the effect of global stimuli in generating nonreciprocal interactions.

Complexity and self-organization in the evolution of cell polarization

Cellular life exhibits order and complexity, which typically increase over the course of evolution. Cell polarization is a well-studied example of an ordering process that breaks the internal symmetry of a cell by establishing a preferential axis. Like many cellular processes, polarization is driven by self-organization, meaning that the macroscopic pattern emerges as a consequence of microscopic molecular interactions at the biophysical level. However, the role of self-organization in the evolution of complex protein networks remains obscure. In this Review, we provide an overview of the evolution of polarization as a self-organizing process, focusing on the model species Saccharomyces cerevisiae and its fungal relatives. Moreover, we use this model system to discuss how self-organization might relate to evolutionary change, offering a shift in perspective on evolution at the microscopic scale.

Symmetry-breaking rhythms in coupled, identical fast-slow oscillators

Symmetry-breaking in coupled, identical, fast-slow systems produces a rich, dramatic variety of dynamical behavior-such as amplitudes and frequencies differing by an order of magnitude or more and qualitatively different rhythms between oscillators, corresponding to different functional states. We present a novel method for analyzing these systems. It identifies the key geometric structures responsible for this new symmetry-breaking, and it shows that many different types of symmetry-breaking rhythms arise robustly. We find symmetry-breaking rhythms in which one oscillator exhibits small-amplitude oscillations, while the other exhibits phase-shifted small-amplitude oscillations, large-amplitude oscillations, mixed-mode oscillations, or even undergoes an explosion of limit cycle canards. Two prototypical fast-slow systems illustrate the method: the van der Pol equation that describes electrical circuits and the Lengyel-Epstein model of chemical oscillators.

More is different with a vengeance

In his 1972 landmark paper "More is Different," Philip W. Anderson established "complexity" as a fundamentally important subject of inquiry. He highlighted the profound limitations of reductionist approaches in understanding nature's complexity, and he set in motion new lines of investigation that have, among other things, led to systems biology.

Odd dynamics of living chiral crystals

Active crystals are highly ordered structures that emerge from the self-organization of motile objects, and have been widely studied in synthetic^1,2 and bacterial^3,4 active matter. Whether persistent  crystalline order can emerge  in groups of autonomously developing multicellular organisms is currently unknown. Here we show that swimming starfish embryos spontaneously assemble into chiral crystals that span thousands of spinning organisms and persist for tens of hours. Combining experiments, theory and simulations, we demonstrate that the formation, dynamics and dissolution of these living crystals are controlled by the hydrodynamic properties and the natural development of embryos. Remarkably, living chiral crystals exhibit self-sustained chiral oscillations as well as various unconventional deformation response behaviours recently predicted for odd elastic materials^5,6. Our results provide direct experimental evidence for how non-reciprocal interactions between autonomous multicellular components may facilitate non-equilibrium phases of chiral active matter.

Spacer prioritization in CRISPR-Cas9 immunity is enabled by the leader RNA

CRISPR-Cas systems store fragments of foreign DNA called spacers as immunological recordings used to combat future infections. Of the many spacers stored in a CRISPR array, the newest spacers are known to be prioritized for immune defense. However, the underlying mechanism remains unclear. Here we show that the leader region upstream of CRISPR arrays in CRISPR-Cas9 systems enhances CRISPR RNA (crRNA) processing from the newest spacer, prioritizing defense against the matching invader. Using the CRISPR-Cas9 system from Streptococcus pyogenes as a model, we found that the transcribed leader interacts with the conserved repeats bordering the newest spacer. The resulting interaction promotes tracrRNA hybridization with the second repeat, accelerating crRNA processing. Accordingly, disrupting this structure reduces the abundance of the associated crRNA and immune defense against targeted plasmids and bacteriophages. Beyond the S. pyogenes system, bioinformatics analyses revealed that leader-repeat structures appear across CRISPR-Cas9 systems. CRISPR-Cas systems thus possess an RNA-based mechanism to prioritize defense against the most recently encountered invaders.

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.

Studying Cell Division Plane Positioning in Early-Stage Embryos

Unraveling the mechanisms that govern division plane orientation is a major challenge to understand plant development. In this respect, the Arabidopsis early embryo is a model system of choice since embryogenesis is relatively simple and cell division planes orientation is highly predictable. Here we present an integrated set of protocols to study 3D cell division patterns in early-stage Arabidopsis embryos that combine both cellular and sub-cellular localization of selected protein markers with spatial organization of cells, cytoskeleton, and nuclei.

RhoA- and Cdc42-induced antagonistic forces underlie symmetry breaking and spindle rotation in mouse oocytes

Mammalian oocyte meiotic divisions are highly asymmetric and produce a large haploid gamete and 2 small polar bodies. This relies on the ability of the cell to break symmetry and position its spindle close to the cortex before anaphase occurs. In metaphase II–arrested mouse oocytes, the spindle is actively maintained close and parallel to the cortex, until fertilization triggers sister chromatid segregation and the rotation of the spindle. The latter must indeed reorient perpendicular to the cortex to enable cytokinesis ring closure at the base of the polar body. However, the mechanisms underlying symmetry breaking and spindle rotation have remained elusive. In this study, we show that spindle rotation results from 2 antagonistic forces. First, an inward contraction of the cytokinesis furrow dependent on RhoA signaling, and second, an outward attraction exerted on both sets of chromatids by a Ran/Cdc42-dependent polarization of the actomyosin cortex. By combining live segmentation and tracking with numerical modeling, we demonstrate that this configuration becomes unstable as the ingression progresses. This leads to spontaneous symmetry breaking, which implies that neither the rotation direction nor the set of chromatids that eventually gets discarded are biologically predetermined.

Mammalian oocyte meiotic divisions are highly asymmetric and produce a large haploid gamete and two small polar bodies, but the mechanisms underlying the required symmetry breaking and spindle rotation have remained elusive. This study shows that spindle rotation in activated mouse oocytes relies on spontaneous symmetry breaking resulting from an unstable configuration generated by cleavage furrow ingression and cortical chromosome attraction.

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.

A general principle for spontaneous genetic symmetry breaking and pattern formation within cell populations

Elements within biological systems interact and frequently self-organize from initially disordered states into highly structured patterns. The local self-activation and lateral inhibition mechanism, derived from the coupling between two reacting and diffusing chemicals, has been believed to be one of the main causes for biological pattern formation. Graded positional information can be produced by the limited diffusion of one single signaling molecule through cell populations with no pre-patterns being required. We demonstrate, using multiscale computations, that spontaneous symmetry breaking can be driven within expanding and non-expanding cell populations, without local self-enhancement of activators and long-range inhibition. Instead, cells can self-organize into structured gene patterns via a combination of timing gene expression in cells and the graded positional information which has been coupled to the gene expression. We show that the genetic symmetry breaking in expanding E. coli populations occurs at a critical colony size, which is independent of the cell doubling time but scales with the diffusion speed of the signaling molecule. We also show the quasi-3D structure of gene patterns, and observe that the wave length of periodic genetic stripes is in proportion to the genetic oscillation cycle time and in inverse proportion to cell doubling time. Our results provide insights into relevant biological development processes.

Physics of compartmentalization: How phase separation and signaling shape membrane and organelle identity

Compartmentalization of cellular functions is at the core of the physiology of eukaryotic cells. Recent evidences indicate that a universal organizing process - phase separation - supports the partitioning of biomolecules in distinct phases from a single homogeneous mixture, a landmark event in both the biogenesis and the maintenance of membrane and non-membrane-bound organelles. In the cell, 'passive' (non energy-consuming) mechanisms are flanked by 'active' mechanisms of separation into phases of distinct density and stoichiometry, that allow for increased partitioning flexibility and programmability. A convergence of physical and biological approaches is leading to new insights into the inner functioning of this driver of intracellular order, holding promises for future advances in both biological research and biotechnological applications.

Morphometric analysis of nuclear symmetry in urothelial carcinoma for predicting tumor recurrence

Urothelial carcinoma is the ninth most common cancer in the world. Cytological analysis of the urine is used for screening, as well as for cases suspected for neoplasia of the urinary tract. However, the sensitivity of urine cytology examination is low. The golden standard for diagnosing bladder cancer relies upon cystoscopy followed by a biopsy, which is microscopically assessed by the pathologist. Treatment decisions are based on the histological grade and stage of the tumor. Posttreatment tumor recurrence is 50%. The purpose of this study is to predict recurrence of urothelial carcinoma using a novel morphometric method of nuclear symmetry analysis. This method may help tailor the appropriate treatment and may reduce the need of invasive surgical procedures in patients. Computerized morphometry was applied to develop multiple symmetry indices of the nuclei of the tumor cells as follows: each nucleus was physically divided along its digital axis in two segments that were separately analyzed for their shape, size, optical density, and texture. Subsequently, ratios were obtained by mathematically dividing between the morphometric values of the two nuclear segments where the denominator contained the largest value of the two. These ratios were named symmetry indices and were included as variables to predict the recurrence time of the tumors. The change in the symmetry indices (loss of symmetry) of the nuclear roundness, fractal dimension and margination were the only independent predictors of recurrence time. Computerized morphometry of nuclear symmetry indices may help to predict tumor recurrence in urothelial carcinomas.

The Emergence of the Bilateral Symmetry in Animals: A Review and a New Hypothesis

Most biological organisms exhibit different kinds of symmetry; an Animal (Metazoa), which is our Darwinist ancestor, has bilateral symmetry, and many plants exhibit rotational symmetry. It raises some questions: I. How can the evolution from an undifferentiated cell without bilateral symmetry to a complex biological organism with symmetry, which is based on asymmetric DNA and enzymes, lead to the bilateral symmetry? II. Is this evolution to an organism with bilateral symmetry obtained by other factors than DNA and enzymatic reactions? The existing literature about the evolution of the bilateral symmetry has been reviewed, and a new hypothesis has been formulated based on these reviews. The hypothesis is that the morphogenesis of biosystems is connected with the metabolism and that the oscillating kinetics in the Glycolysis have played a role in the polarity of the biological cells and in the establishment of the bilateral symmetry in Animals.

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.

Emergence of multistability and strongly asymmetric collective modes in two quorum sensing coupled identical ring oscillators

The simplest ring oscillator is made from three strongly nonlinear elements repressing each other unidirectionally, resulting in the emergence of a limit cycle. A popular implementation of this scheme uses repressor genes in bacteria, creating the synthetic genetic oscillator known as the Repressilator. We consider the main collective modes produced when two identical Repressilators are mean-field-coupled via the quorum-sensing mechanism. In-phase and anti-phase oscillations of the coupled oscillators emerge from two Andronov-Hopf bifurcations of the homogeneous steady state. Using the rate of the repressor's production and the value of coupling strength as the bifurcation parameters, we performed one-parameter continuations of limit cycles and two-parameter continuations of their bifurcations to show how bifurcations of the in-phase and anti-phase oscillations influence the dynamical behaviors for this system. Pitchfork bifurcation of the unstable in-phase cycle leads to the creation of novel inhomogeneous limit cycles with very different amplitudes, in contrast to the well-known asymmetrical limit cycles arising from oscillation death. The Neimark-Sacker bifurcation of the anti-phase cycle determines the border of an island in two-parameter space containing almost all the interesting regimes including the set of resonant limit cycles, the area with stable inhomogeneous cycle, and very large areas with chaotic regimes resulting from torus destruction and period doubling of resonant cycles and inhomogeneous cycles. We discuss the structure of the chaos skeleton to show the role of inhomogeneous cycles in its formation. Many regions of multistability and transitions between regimes are presented. These results provide new insights into the coupling-dependent mechanisms of multistability and collective regime symmetry breaking in populations of identical multidimensional oscillators.

Spontaneous divergence of disease status in an economic epidemiological game

We introduce a game inspired by the challenges of disease management in livestock farming and the transmission of endemic disease through a trade network. Success in this game comes from balancing the cost of buying new stock with the risk that it will be carrying some disease. When players follow a simple memory-based strategy we observe a spontaneous separation into two groups corresponding to players with relatively high, or low, levels of infection. By modelling the dynamics of both the disease and the formation and breaking of trade relationships, we derive the conditions for which this separation occurs as a function of the transmission rate and the threshold level of acceptable disease for each player. When interactions in the game are restricted to players that neighbour each other in a small-world network, players tend to have similar levels of infection as their neighbours. We conclude that success in economic-epidemiological systems can originate from misfortune and geographical circumstances as well as by innate differences in personal attitudes towards risk.

Engineering Light-Responsive Contractile Actomyosin Networks with DNA Nanotechnology

External control and precise manipulation is key for the bottom-up engineering of complex synthetic cells. Minimal actomyosin networks have been reconstituted into synthetic cells; however, their light-triggered symmetry breaking contraction has not yet been demonstrated. Here, light-activated directional contractility of a minimal synthetic actomyosin network inside microfluidic cell-sized compartments is engineered. Actin filaments, heavy-meromyosin-coated beads, and caged ATP are co-encapsulated into water-in-oil droplets. ATP is released upon illumination, leading to a myosin-generated force which results in a motion of the beads along the filaments and hence a contraction of the network. Symmetry breaking is achieved using DNA nanotechnology to establish a link between the network and the compartment periphery. It is demonstrated that the DNA-linked actin filaments contract to one side of the compartment forming actin asters and quantify the dynamics of this process. This work exemplifies that an engineering approach to bottom-up synthetic biology, combining biological and artificial elements, can circumvent challenges related to active multi-component systems and thereby greatly enrich the complexity of synthetic cellular systems.

Effects of Microstripe Geometry on Guided Cell Migration

Cell migration on material surfaces is a fundament issue in the fields of biomaterials, cell biology, tissue engineering, regenerative medicine, etc. Herein, we aim to guide cell migration by flat microstripes with significant contrast of cell adhesion and varied geometric features of the adhesive stripes. To this end, we designed and fabricated cell-adhesive arginine-glycine-aspartate (RGD) microstripes on the nonfouling poly(ethylene glycol) (PEG) background and examined the microstripe-guided adhesion and migration of a few cell types. The migration of cell clusters adhering on the RGD regions was found to be significantly affected by the widths and arc radiuses of the guided microstripes. The cells migrated fastest on the straight microstripes with width of about 20 μm, which we defined as single file confined migration (SFCM). We also checked the possible left-right asymmetric bias of cell migration guided by combinatory microstripes with alternative wavy and quasi-straight stripes under a given width, and found that the velocity of CCW (counter clockwise) migration was higher than that of CW (clockwise) migration for primary rat mesenchymal stem cells (rMSCs), whereas no left-right asymmetric bias was observed for NIH3T3 (mouse embryonic fibroblast cell line) and Hela (human cervix epithelial carcinoma cell line) cells. Comparison of migration of cells on the nanotopological stripe and smooth surfaces further confirmed the importance of cell orientation coherence for guided cell migration and strengthened the superiority of SFCM.

Protein-protein interaction network controlling establishment and maintenance of switchable cell polarity

Cell polarity underlies key processes in all cells, including growth, differentiation and division. In the bacterium Myxococcus xanthus, front-rear polarity is crucial for motility. Notably, this polarity can be inverted, independent of the cell-cycle, by chemotactic signaling. However, a precise understanding of the protein network that establishes polarity and allows for its inversion has remained elusive. Here, we use a combination of quantitative experiments and data-driven theory to unravel the complex interplay between the three key components of the M. xanthus polarity module. By studying each of these components in isolation and their effects as we systematically reconstruct the system, we deduce the network of effective interactions between the polarity proteins. RomR lies at the root of this network, promoting polar localization of the other components, while polarity arises from interconnected negative and positive feedbacks mediated by the small GTPase MglA and its cognate GAP MglB, respectively. We rationalize this network topology as operating as a spatial toggle switch, providing stable polarity for persistent cell movement whilst remaining responsive to chemotactic signaling and thus capable of polarity inversions. Our results have implications not only for the understanding of polarity and motility in M. xanthus but also, more broadly, for dynamic cell polarity.

The asymmetric localization of cellular components (polarity) is at the core of many important cellular functions including growth, division, differentiation and motility. However, important questions still remain regarding the design principles underlying polarity networks and how their activity can be controlled in space and time. We use the rod-shaped bacterium Myxococcus xanthus as a model to study polarity and its regulation. Like many bacteria, in M. xanthus a well-defined front-rear polarity axis enables efficient translocation. This polarity axis is defined by asymmetric polar localization of a switch-like GTPase and its cognate regulators, and can be reversed in response to signaling cues. Here we use a combination of quantitative experiments and data-driven theory to deduce the network of interactions among the M. xanthus polarity proteins and to show how the combination of positive- and negative-feedback interactions give rise to asymmetric polar protein localization. We rationalize this network topology as operating as a spatial toggle switch, providing stable polarity for persistent cell movement whilst remaining responsive to chemotactic signaling and capable of polarity inversions. Our results have broader implications for our understanding of dynamic cell polarity and GTPase regulation in both bacteria and eukaryotic cells.

The steering gaits of sperm

Sperm are highly specialized cells, which have been subject to substantial evolutionary pressure. Whereas some sperm features are highly conserved, others have undergone major modifications. Some of these variations are driven by adaptation to mating behaviours or fitness at the organismic level. Others represent alternative solutions to the same task. Sperm must find the egg for fertilization. During this task, sperm rely on long slender appendages termed flagella that serve as sensory antennas, propellers and steering rudders. The beat of the flagellum is periodic. The resulting travelling wave generates the necessary thrust for propulsion in the fluid. Recent studies reveal that, for steering, different species rely on different fundamental features of the beat wave. Here, we discuss some examples of unity and diversity across sperm from different species with a particular emphasis on the steering mechanisms. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.

Formation of Polarized, Functional Artificial Cells from Compartmentalized Droplet Networks and Nanomaterials, Using One-Step, Dual-Material 3D-Printed Microfluidics

The bottom-up construction of synthetic cells with user-defined chemical organization holds considerable promise in the creation of bioinspired materials. Complex emulsions, droplet networks, and nested vesicles all represent platforms for the engineering of segregated chemistries with controlled communication, analogous to biological cells. Microfluidic manufacture of such droplet-based materials typically results in radial or axisymmetric structures. In contrast, biological cells frequently display chemical polarity or gradients, which enable the determination of directionality, and inform higher-order interactions. Here, a dual-material, 3D-printing methodology to produce microfluidic architectures that enable the construction of functional, asymmetric, hierarchical, emulsion-based artificial cellular chassis is developed. These materials incorporate droplet networks, lipid membranes, and nanoparticle components. Microfluidic 3D-channel arrangements enable symmetry-breaking and the spatial patterning of droplet hierarchies. This approach can produce internal gradients and hemispherically patterned, multilayered shells alongside chemical compartmentalization. Such organization enables incorporation of organic and inorganic components, including lipid bilayers, within the same entity. In this way, functional polarization, that imparts individual and collective directionality on the resulting artificial cells, is demonstrated. This approach enables exploitation of polarity and asymmetry, in conjunction with compartmentalized and networked chemistry, in single and higher-order organized structures, thereby increasing the palette of functionality in artificial cellular materials.

A Polarizing Issue: Diversity in the Mechanisms Underlying Apico-Basolateral Polarization In Vivo

Polarization along an apico-basolateral axis is a hallmark of epithelial cells and is essential for their selective barrier and transporter functions, as well as for their ability to provide mechanical resiliency to organs. Loss of polarity along this axis perturbs development and is associated with a wide number of diseases. We describe three steps involved in polarization: symmetry breaking, polarity establishment, and polarity maintenance. While the proteins involved in these processes are highly conserved among epithelial tissues and species, the execution of these steps varies widely and is context dependent. We review both theoretical principles underlying these steps and recent work demonstrating how apico-basolateral polarity is established in vivo in different tissues, highlighting how developmental and physiological contexts play major roles in the execution of the epithelial polarity program.

Non-equilibrium landscape and flux reveal how the central amygdala circuit gates passive and active defensive responses

Uncovering the underlying physical principles of biology is important for understanding the biological function yet challenging. Take an example, the animals' defensive systems are very effective to threats. However, the underlying physical mechanisms are still unclear. We developed a non-equilibrium physics framework in terms of landscape and flux to study a central lateral amygdala (CeL) neural circuit based on experimental findings. We show that the distinct active and passive defensive responses of the animals upon threats are a result of non-equilibrium phase transitions. Such non-equilibrium phase transitions result from thermodynamic symmetry breaking, which is induced dynamically by the non-equilibrium flux. This gives rise to the emergence and selection of passive and active fear defensive responses, which can be quantified by the changes on the topography of the underlying non-equilibrium landscape. We have found the strengthened synaptic transmissions to both the SOM+ and SOM- CeL neurons are necessary for the acquisition and expression of active fear responses. This suggests a way to induce active responses and facilitates the design of new therapeutic strategies for cognitive dysfunction. We have also found that sufficient energy supply is crucial for the ability of selecting the appropriate defensive responses through stabilizing functional states against fluctuations.

Symmetry breaking and functional incompleteness in biological systems

Symmetry-based explanations using symmetry breaking (SB) as the key explanatory tool have complemented and replaced traditional causal explanations in various domains of physics. The process of spontaneous SB is now a mainstay of contemporary explanatory accounts of large chunks of condensed-matter physics, quantum field theory, nonlinear dynamics, cosmology, and other disciplines. A wide range of empirical research into various phenomena related to symmetries and SB across biological scales has accumulated as well. Led by these results, we identify and explain some common features of the emergence, propagation, and cascading of SB-induced layers across the biosphere. These features are predicated on the thermodynamic openness and intrinsic functional incompleteness of the systems at stake and have not been systematically analyzed from a general philosophical and methodological perspective. We also consider possible continuity of SB across the physical and biological world and discuss the connection between Darwinism and SB-based analysis of the biosphere and its history.

Theoretical tool bridging cell polarities with development of robust morphologies

Despite continual renewal and damages, a multicellular organism is able to maintain its complex morphology. How is this stability compatible with the complexity and diversity of living forms? Looking for answers at protein level may be limiting as diverging protein sequences can result in similar morphologies. Inspired by the progressive role of apical-basal and planar cell polarity in development, we propose that stability, complexity, and diversity are emergent properties in populations of proliferating polarized cells. We support our hypothesis by a theoretical approach, developed to effectively capture both types of polar cell adhesions. When applied to specific cases of development – gastrulation and the origins of folds and tubes – our theoretical tool suggests experimentally testable predictions pointing to the strength of polar adhesion, restricted directions of cell polarities, and the rate of cell proliferation to be major determinants of morphological diversity and stability.

Cells have the power to organise themselves to form complex and stable structures, whether it is to create a fully shaped baby from a single egg, or to allow adult salamanders to grow a new limb after losing a leg. This ability has been scrutinised at many different levels. For example, researchers have looked at the chemical messages exchanged by cells, or they have recorded the different shapes an embryo goes through during development. However, it is still difficult to reconcile the information from these approaches into a description that makes sense at multiple scales.

When an embryo develops, sheets of cells fold and unfold to create complex 3D shapes, like the tubes that make our lungs. Moulding sheets into tubes relies on interactions between cells that are not the same in all directions. In fact, two types of asymmetry (or polarity) guide these interactions. Apical-basal polarity runs across a sheet of cells, which means that the top surface of the sheet differs from the bottom. Planar cell polarity runs along the sheet and distinguishes one end from the other. For instance, apical-basal polarity marks the inner and outer surfaces of our skin, while planar cell polarity controls the direction in which our hair grows.

Nissen et al. set out to investigate how these polarities help cells in an embryo organise themselves to form complicated folds and tubes. To do this, simple mathematical representations of both apical-basal and planar cell polarities were designed. The representations were then combined to create computer simulations of groups of cells as these divide and interact with each other.

Simulations of ‘cells’ with only apical-basal polarity were able to generate different shapes in the ‘tissues’ produced, including many found in living organisms. External conditions, such as how cells were arranged to start with, determined the resulting shape. With both apical-basal and planar cell polarities, the simulations reproduced an important change that occurs during early development. They also replicated how the tubes that transport nutrients and oxygen form.

These results show that simple properties of individual cells, such as polarities, can produce different shapes in developing tissues and organs, without the need for a complicated overarching program. Abnormal changes in cell polarity are also associated with diseases such as cancer. The mathematical model developed by Nissen et al. could therefore be a useful tool to study these events.

Polarity of CD4+ T cells towards the antigen presenting cell is regulated by the Lck adapter TSAd

Polarization of T cells towards the antigen presenting cell (APC) is critically important for appropriate activation and differentiation of the naïve T cell. Here we used imaging flow cytometry (IFC) and show that the activation induced Lck and Itk adapter T cell specific adapter protein (TSAd), encoded by SH2D2A, modulates polarization of T cells towards the APC. Upon exposure to APC presenting the cognate antigen Id, Sh2d2a−/− CD4+ T cells expressing Id-specific transgenic T cell receptor (TCR), displayed impaired polarization of F-actin and TCR to the immunological synapse (IS). Sh2d2a−/− T-cells that did polarize F-actin and TCR still displayed impaired polarization of PKCξ, PAR3 and the microtubule-organizing center (MTOC). In vitro differentiation of activated Sh2d2a−/− T cells was skewed towards an effector memory (Tem) rather than a central memory (Tcm) phenotype. A similar trend was observed for Id-specific TCR Sh2d2a−/− T cells stimulated with APC and cognate antigen. Taken together our data suggest that TSAd modulates differentiation of experienced T cells possibly through polarization of CD4+ T cells towards the APC.

Mapping the Assembly of Metal-Organic Cages into Complex Coordination Networks

Structural transformations of supramolecular assemblies play an important role in the synthesis of complex metal-organic materials. Nonetheless, often little is known of the assembly pathways that lead to the final product. This work describes the conversion of cubic metal-organic polyhedra to connected-cage networks of varying topologies. The neutral cubic cage assembly of formula {Pd₃ [PO(NiPr)₃ ]}₈ (PZDC)₁₂ has been synthesized from {Pd₃ [(NiPr)₃ PO](OAc)₂ (OH)}₂ ⋅2 (CH₃ )₂ SO and 2,5-pyrazenedicarboxilic acid (PZDC-2H). This 42-component self-assembly is the largest known among the neutral cages with Pd^II ions. The cage contains twenty-four vacant carboxylate O-sites at the PZDC ligands that are available for further coordination. Post-assembly reactions of the cubic cage with Fe^II and Zn^II ions produced cage-connected networks of dia and qtz topologies, respectively. During these reactions, the discrete cubic cage transforms into a network of tetrahedral cages that are bridged by the 3D metal ions. The robustness of the [Pd₃ {[PO(NiPr)₃ }]³⁺ molecular building units made it possible to map the post-assembly reactions in detail, which revealed a variety of intermediate 1D and 2D cage networks. Such step-by-step mapping of the transformation of discrete cages to cage-connected frameworks is unprecedented in the chemistry of coordination driven assemblies.

Symmetry and symmetry breaking in cancer: a foundational approach to the cancer problem

Symmetry and symmetry breaking concepts from physics and biology are applied to the problem of cancer. Three categories of symmetry breaking in cancer are examined: combinatorial, geometric, and functional. Within these categories, symmetry breaking is examined for relevant cancer features, including epithelial-mesenchymal transition (EMT); tumor heterogeneity; tensegrity; fractal geometric and information structure; functional interaction networks; and network stabilizability and attack tolerance. The new cancer symmetry concepts are relevant to homeostasis loss in cancer and to its origin, spread, treatment and resistance. Symmetry and symmetry breaking could provide a new way of thinking and a pathway to a solution of the cancer problem.

Trans-generational transmission of altered phenotype resulting from flubendiamide-induced changes in apoptosis in larval imaginal discs of Drosophila melanogaster

The eye and wing morphology of Drosophila melanogaster maintain unique, stable pattern of genesis from larval eye and wing imaginal discs. Increased apoptosis in cells of eye and wing discs was found to be associated with flubendiamide (fluoride containing insecticide) exposure (at the range 0.25-10μg/mL) in D. melanogaster larvae. The chemical fed larvae on attaining adulthood revealed alterations in morphology and symmetry of their compound eyes and wings through scanning electron microscopy. Nearly 40% and 30% of flies (P generation) demonstrated alterations in eyes and wings respectively. Transmission electron microscopic study (at the range 1-20μg/mL) also established variation in the rhabdomere and pigment cell orientation as well as in the shape of the ommatidium. Subsequent SEM study with F₁ and F₂ generation flies also revealed structural variation in eye and wing. Decrease in percentage of altered eye and wing phenotype was noted in subsequent generations (P> F₁>F₂). Thus, the diamide insecticide, flubendiamide, expected to be environmentally safe at sub-lethal concentrations was found to increase apoptosis in larvae and thereby cause morphological alteration in the adult D. melanogaster. This study further demonstrated trans-generational transmission of altered phenotype in three subsequent generations of a non-target insect model, D. melanogaster.

Many roads to symmetry breaking: molecular mechanisms and theoretical models of yeast cell polarity

Mathematical modeling has been instrumental in identifying common principles of cell polarity across diverse systems. These principles include positive feedback loops that are required to destabilize a spatially uniform state of the cell. The conserved small G-protein Cdc42 is a master regulator of eukaryotic cellular polarization. Here we discuss recent developments in studies of Cdc42 polarization in budding and fission yeasts and demonstrate that models describing symmetry-breaking polarization can be classified into six minimal classes based on the structure of positive feedback loops that activate and localize Cdc42. Owing to their generic system-independent nature, these model classes are also likely to be relevant for the G-protein–based symmetry-breaking systems of higher eukaryotes. We review experimental evidence pro et contra different theoretically plausible models and conclude that several parallel and non–mutually exclusive mechanisms are likely involved in cellular polarization of yeasts. This potential redundancy needs to be taken into consideration when interpreting the results of recent cell-rewiring studies.

Evolutionary dynamics in the fungal polarization network, a mechanistic perspective

Polarity establishment underlies proper cell cycle completion across virtually all organisms. Much progress has been made in generating an understanding of the structural and functional components of this process, especially in model species. Here we focus on the evolutionary dynamics of the fungal polarization protein network in order to determine general components and mechanistic principles, species- or lineage-specific adaptations and the evolvability of the network. The currently available genomic and proteomic screens in a variety of fungal species have shown three main characteristics: (1) certain proteins, processes and functions are conserved throughout the fungal clade; (2) orthologous functions can never be assumed, as various cases have been observed of homologous loci with dissimilar functions; (3) species have, typically, various species- or lineage-specific proteins incorporated in their polarization network. Further large-scale comparative and experimental studies, including those on non-model species representing the great fungal diversity, are needed to gain a better understanding of the evolutionary dynamics and generalities of the polarization network in fungi.

Spontaneous symmetry breaking due to the trade-off between attractive and repulsive couplings

Spontaneous symmetry breaking is an important phenomenon observed in various fields including physics and biology. In this connection, we here show that the trade-off between attractive and repulsive couplings can induce spontaneous symmetry breaking in a homogeneous system of coupled oscillators. With a simple model of a system of two coupled Stuart-Landau oscillators, we demonstrate how the tendency of attractive coupling in inducing in-phase synchronized (IPS) oscillations and the tendency of repulsive coupling in inducing out-of-phase synchronized oscillations compete with each other and give rise to symmetry breaking oscillatory states and interesting multistabilities. Further, we provide explicit expressions for synchronized and antisynchronized oscillatory states as well as the so called oscillation death (OD) state and study their stability. If the Hopf bifurcation parameter (λ) is greater than the natural frequency (ω) of the system, the attractive coupling favors the emergence of an antisymmetric OD state via a Hopf bifurcation whereas the repulsive coupling favors the emergence of a similar state through a saddle-node bifurcation. We show that an increase in the repulsive coupling not only destabilizes the IPS state but also facilitates the reentrance of the IPS state.

Where to Go: Breaking the Symmetry in Cell Motility

Cell migration in the “correct” direction is pivotal for many biological processes. Although most work is devoted to its molecular mechanisms, the cell’s preference for one direction over others, thus overcoming intrinsic random motility, epitomizes a profound principle that underlies all complex systems: the choice of one axis, in structure or motion, from a uniform or symmetric set of options. Explaining directional motility by an external chemo-attractant gradient does not solve but only shifts the problem of causation: whence the gradient? A new study in PLOS Biology shows cell migration in a self-generated gradient, offering an opportunity to take a broader look at the old dualism of extrinsic instruction versus intrinsic symmetry-breaking in cell biology.

Directional cell motility is enabled by chemoattractant gradient and symmetry-breaking. This Primer argues that the recent observation of cells generating a gradient in a uniformly distributed nutrient reveals the multilayered nature of symmetry-breaking in cell locomotion.

Spatial landmarks regulate a Cdc42-dependent MAPK pathway to control differentiation and the response to positional compromise

A fundamental problem in cell biology is to understand how spatial information is recognized and integrated into morphogenetic responses. Budding yeast undergoes differentiation to filamentous growth, which involves changes in cell polarity through mechanisms that remain obscure. Here we define a regulatory input where spatial landmarks (bud-site-selection proteins) regulate the MAPK pathway that controls filamentous growth (fMAPK pathway). The bud-site GTPase Rsr1p regulated the fMAPK pathway through Cdc24p, the guanine nucleotide exchange factor for the polarity establishment GTPase Cdc42p. Positional landmarks that direct Rsr1p to bud sites conditionally regulated the fMAPK pathway, corresponding to their roles in regulating bud-site selection. Therefore, cell differentiation is achieved in part by the reorganization of polarity at bud sites. In line with this conclusion, dynamic changes in budding pattern during filamentous growth induced corresponding changes in fMAPK activity. Intrinsic compromise of bud-site selection also impacted fMAPK activity. Therefore, a surveillance mechanism monitors spatial position in response to extrinsic and intrinsic stress and modulates the response through a differentiation MAPK pathway.

Dynamic Opposition of Clustered Proteins Stabilizes Cortical Polarity in the C. elegans Zygote

Dynamic maintenance of cell polarity is essential for development and physiology. Here we combine experiments and modeling to elucidate mechanisms that maintain cortical polarity in the C. elegans zygote. We show that polarity is dynamically stabilized by two coupled cross-inhibitory feedback loops: one involves the oligomeric scaffold PAR-3 and the kinase PAR-1, and the other involves CDC-42 and its putative GAP CHIN-1. PAR-3 and CDC-42 are both required locally to recruit PAR-6/PKC-3, which inhibits PAR-1 (shown previously) and inhibits local growth/accumulation of CHIN-1 clusters. Conversely, PAR-1 inhibits local accumulation of PAR-3 oligomers, while CHIN-1 inhibits CDC-42 (shown previously), such that either PAR-1 or CHIN-1 can prevent recruitment of PAR-6/PKC-3, but loss of both causes complete loss of polarity. Ultrasensitive dependence of CHIN-1 cluster growth on PAR-6/PKC-3 endows this core circuit with bistable dynamics, while transport of CHIN-1 clusters by cortical flow can stabilize the AP boundary against diffusive spread of PAR-6/PKC-3.

Studying Cell Division Plane Positioning in Early-Stage Embryos

Unraveling the mechanisms that govern division plane orientation is a major challenge to understand plant development. In this respect, the Arabidopsis early embryo is a model system of choice since embryogenesis is relatively simple and cell division planes orientation is highly predictable. Here, we present an integrated set of protocols to study 3D cell division patterns in early-stage Arabidopsis embryos that combine both cellular and sub-cellular localization of selected protein markers with spatial organization of cells, cytoskeleton, and nuclei.