Cortical Polarity of the RING Protein PAR-2 Is Maintained by Exchange Rate Kinetics at the Cortical-Cytoplasmic Boundary

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

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

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

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

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

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

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.

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

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

Design principles for selective polarization of PAR proteins by cortical flows

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

PP1 phosphatases control PAR-2 localization and polarity establishment in C. elegans embryos

Cell polarity relies on the asymmetric distribution of the conserved PAR proteins, which is regulated by phosphorylation/dephosphorylation reactions. While the kinases involved have been well studied, the role of phosphatases remains poorly understood. In Caenorhabditis elegans zygotes, phosphorylation of the posterior PAR-2 protein by the atypical protein kinase PKC-3 inhibits PAR-2 cortical localization. Polarity establishment depends on loading of PAR-2 at the posterior cortex. We show that the PP1 phosphatases GSP-1 and GSP-2 are required for polarity establishment in embryos. We find that codepletion of GSP-1 and GSP-2 abrogates the cortical localization of PAR-2 and that GSP-1 and GSP-2 interact with PAR-2 via a PP1 docking motif in PAR-2. Mutating this motif in vivo, to prevent binding of PAR-2 to PP1, abolishes cortical localization of PAR-2, while optimizing this motif extends PAR-2 cortical localization. Our data suggest a model in which GSP-1/-2 counteracts PKC-3 phosphorylation of PAR-2, allowing its cortical localization at the posterior and polarization of the one-cell embryo.

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.

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.

Going with the flow: insights from Caenorhabditis elegans zygote polarization

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

CDC-42 Interactions with Par Proteins Are Critical for Proper Patterning in Polarization

Many cells rearrange proteins and other components into spatially distinct domains in a process called polarization. This asymmetric patterning is required for a number of biological processes including asymmetric division, cell migration, and embryonic development. Proteins involved in polarization are highly conserved and include members of the Par and Rho protein families. Despite the importance of these proteins in polarization, it is not yet known how they interact and regulate each other to produce the protein localization patterns associated with polarization. In this study, we develop and analyse a biologically based mathematical model of polarization that incorporates interactions between Par and Rho proteins that are consistent with experimental observations of CDC-42. Using minimal network and eFAST sensitivity analyses, we demonstrate that CDC-42 is predicted to reinforce maintenance of anterior PAR protein polarity which in turn feedbacks to maintain CDC-42 polarization, as well as supporting posterior PAR protein polarization maintenance. The mechanisms for polarity maintenance identified by these methods are not sufficient for the generation of polarization in the absence of cortical flow. Additional inhibitory interactions mediated by the posterior Par proteins are predicted to play a role in the generation of Par protein polarity. More generally, these results provide new insights into the role of CDC-42 in polarization and the mutual regulation of key polarity determinants, in addition to providing a foundation for further investigations.

Switching states: dynamic remodelling of polarity complexes as a toolkit for cell polarization

Polarity is defined by the segregation of cellular components along a defined axis. To polarize robustly, cells must be able to break symmetry and subsequently amplify these nascent asymmetries. Finally, asymmetric localization of signaling molecules must be translated into functional regulation of downstream effector pathways. Central to these behaviors are a diverse set of cell polarity networks. Within these networks, molecules exhibit varied behaviors, dynamically switching among different complexes and states, active versus inactive, bound versus unbound, immobile versus diffusive. This ability to switch dynamically between states is intimately connected to the ability of molecules to generate asymmetric patterns within cells. Focusing primarily on polarity pathways governed by the conserved PAR proteins, we discuss strategies enabled by these dynamic behaviors that are used by cells to polarize. We highlight not only how switching between states is linked to the ability of polarity proteins to localize asymmetrically, but also how cells take advantage of 'state switching' to regulate polarity in time and space.

Guiding self-organized pattern formation in cell polarity establishment

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

Rapid diffusion-state switching underlies stable cytoplasmic gradients in the Caenorhabditis elegans zygote

Protein concentration gradients organize cells and tissues and commonly form through diffusion away from a local source of protein. Interestingly, during the asymmetric division of the Caenorhabditis elegans zygote, the RNA-binding proteins MEX-5 and PIE-1 form opposing concentration gradients in the absence of a local source. In this study, we use near-total internal reflection fluorescence (TIRF) imaging and single-particle tracking to characterize the reaction/diffusion dynamics that maintain the MEX-5 and PIE-1 gradients. Our findings suggest that both proteins interconvert between fast-diffusing and slow-diffusing states on timescales that are much shorter (seconds) than the timescale of gradient formation (minutes). The kinetics of diffusion-state switching are strongly polarized along the anterior/posterior (A/P) axis by the PAR polarity system such that fast-diffusing MEX-5 and PIE-1 particles are approximately symmetrically distributed, whereas slow-diffusing particles are highly enriched in the anterior and posterior cytoplasm, respectively. Using mathematical modeling, we show that local differences in the kinetics of diffusion-state switching can rapidly generate stable concentration gradients over a broad range of spatial and temporal scales.

Inferring a nonlinear biochemical network model from a heterogeneous single-cell time course data

Mathematical modeling and analysis of biochemical reaction networks are key routines in computational systems biology and biophysics; however, it remains difficult to choose the most valid model. Here, we propose a computational framework for data-driven and systematic inference of a nonlinear biochemical network model. The framework is based on the expectation-maximization algorithm combined with particle smoother and sparse regularization techniques. In this method, a “redundant” model consisting of an excessive number of nodes and regulatory paths is iteratively updated by eliminating unnecessary paths, resulting in an inference of the most likely model. Using artificial single-cell time-course data showing heterogeneous oscillatory behaviors, we demonstrated that this algorithm successfully inferred the true network without any prior knowledge of network topology or parameter values. Furthermore, we showed that both the regulatory paths among nodes and the optimal number of nodes in the network could be systematically determined. The method presented in this study provides a general framework for inferring a nonlinear biochemical network model from heterogeneous single-cell time-course data.

The PAR proteins: from molecular circuits to dynamic self-stabilizing cell polarity

PAR proteins constitute a highly conserved network of scaffolding proteins, adaptors and enzymes that form and stabilize cortical asymmetries in response to diverse inputs. They function throughout development and across the metazoa to regulate cell polarity. In recent years, traditional approaches to identifying and characterizing molecular players and interactions in the PAR network have begun to merge with biophysical, theoretical and computational efforts to understand the network as a pattern-forming biochemical circuit. Here, we summarize recent progress in the field, focusing on recent studies that have characterized the core molecular circuitry, circuit design and spatiotemporal dynamics. We also consider some of the ways in which the PAR network has evolved to polarize cells in different contexts and in response to different cues and functional constraints.

Single-molecule imaging and manipulation of biomolecular machines and systems

BACKGROUND

Biological molecular machines support various activities and behaviors of cells, such as energy production, signal transduction, growth, differentiation, and migration.

SCOPE OF REVIEW

We provide an overview of single-molecule imaging methods involving both small and large probes used to monitor the dynamic motions of molecular machines in vitro (purified proteins) and in living cells, and single-molecule manipulation methods used to measure the forces, mechanical properties and responses of biomolecules. We also introduce several examples of single-molecule analysis, focusing primarily on motor proteins and signal transduction systems.

MAJOR CONCLUSIONS

Single-molecule analysis is a powerful approach to unveil the operational mechanisms both of individual molecular machines and of systems consisting of many molecular machines.

GENERAL SIGNIFICANCE

Quantitative, high-resolution single-molecule analyses of biomolecular systems at the various hierarchies of life will help to answer our fundamental question: "What is life?" This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

Single-molecule fluorescence imaging of RalGDS on cell surfaces during signal transduction from Ras to Ral

RalGDS is one of the Ras effectors and functions as a guanine nucleotide exchange factor for the small G-protein, Ral, which regulates membrane trafficking and cytoskeletal remodeling. The translocation of RalGDS from the cytoplasm to the plasma membrane is required for Ral activation. In this study, to understand the mechanism of Ras–Ral signaling we performed a single-molecule fluorescence analysis of RalGDS and its functional domains (RBD and REMCDC) on the plasma membranes of living HeLa cells. Increased molecular density of RalGDS and RBD, but not REMCDC, was observed on the plasma membrane after EGF stimulation of the cells to induce Ras activation, suggesting that the translocation of RalGDS involves an interaction between the GTP-bound active form of Ras and the RBD of RalGDS. Whereas the RBD played an important role in increasing the association rate constant between RalGDS and the plasma membrane, the REMCDC domain affected the dissociation rate constant from the membrane, which decreased after Ras activation or the hyperexpression of Ral. The Y64 residue of Ras and clusters of RalGDS molecules were involved in this reduction. From these findings, we infer that Ras activation not merely increases the cell-surface density of RalGDS, but actively stimulates the RalGDS–Ral interaction through a structural change in RalGDS and/or the accumulation of Ral, as well as the GTP–Ras/RalGDS clusters, to induce the full activation of Ral.