Modeling the control of planar cell polarity

Perspectives on polarity - exploring biological asymmetry across scales

In this Perspective, Journal of Cell Science invited researchers working on cell and tissue polarity to share their thoughts on unique, emerging or open questions relating to their field. The goal of this article is to feature 'voices' from scientists around the world and at various career stages, to bring attention to innovative and thought-provoking topics of interest to the cell biology community. These voices discuss intriguing questions that consider polarity across scales, evolution, development and disease. What can yeast and protists tell us about the evolution of cell and tissue polarity in animals? How are cell fate and development influenced by emerging dynamics in cell polarity? What can we learn from atypical and extreme polarity systems? How can we arrive at a more unified biophysical understanding of polarity? Taken together, these pieces demonstrate the broad relevance of the fascinating phenomenon of cell polarization to diverse fundamental biological questions.

Molecular symmetry breaking in the Frizzled-dependent planar polarity pathway

The core planar polarity pathway consists of six proteins that form asymmetric intercellular complexes that segregate to opposite cell ends in developing tissues and specify polarized cell structures or behaviors. Within these complexes, the atypical cadherin Flamingo localizes on both sides of intercellular junctions, where it interacts homophilically in trans via its cadherin repeats, whereas the transmembrane proteins Frizzled and Strabismus localize to the opposite sides of apposing junctions. However, the molecular mechanisms underlying the formation of such asymmetric complexes are poorly understood. Using a novel tissue culture system, we determine the minimum requirements for asymmetric complex assembly in the absence of confounding feedback mechanisms. We show that complexes are intrinsically asymmetric and that an interaction of Frizzled and Flamingo in one cell with Flamingo in the neighboring cell is the key symmetry-breaking step. In contrast, Strabismus is unable to promote homophilic Flamingo trans binding and is only recruited into complexes once Frizzled has entered on the opposite side. This interaction with Strabismus requires intact intracellular loops of the seven-pass transmembrane domain of Flamingo. Once recruited, Strabismus stabilizes the intercellular complexes together with the three cytoplasmic core proteins. We propose a model whereby Flamingo exists in a closed conformation and binding of Frizzled in one cell results in a conformational change that allows its cadherin repeats to interact with a Flamingo molecule in the neighboring cell. Flamingo in the adjacent cell then undergoes a further change in the seven-pass transmembrane region that promotes the recruitment of Strabismus.

Prickle and Ror modulate Dishevelled-Vangl interaction to regulate non-canonical Wnt signaling during convergent extension

Convergent extension (CE) is a fundamental morphogenetic process where oriented cell behaviors lead to polarized extension of diverse tissues. In vertebrates, regulation of CE requires both non-canonical Wnt, its co-receptor Ror, and "core members" of the planar cell polarity (PCP) pathway. PCP was originally identified as a mechanism to coordinate the cellular polarity in the plane of static epithelium, where core proteins Frizzled (Fz)/ Dishevelled (Dvl) and Van Gogh-like (Vangl)/ Prickel (Pk) partition to opposing cell cortex. But how core PCP proteins interact with each other to mediate non-canonical Wnt/ Ror signaling during CE is not clear. We found previously that during CE, Vangl cell-autonomously recruits Dvl to the plasma membrane but simultaneously keeps Dvl inactive. In this study, we show that non-canonical Wnt induces Dvl to transition from Vangl to Fz. PK inhibits the transition, and functionally synergize with Vangl to suppress Dvl during CE. Conversely, Ror is required for the transition, and functionally antagonizes Vangl. Biochemically, Vangl interacts directly with both Ror and Dvl. Ror and Dvl do not bind directly, but can be cofractionated with Vangl. We propose that Pk assists Vangl to function as an unconventional adaptor that brings Dvl and Ror into a complex to serves two functions: 1) simultaneously preventing both Dvl and Ror from ectopically activating non-canonical Wnt signaling; and 2) relaying Dvl to Fz for signaling activation upon non-canonical Wnt induced dimerization of Fz and Ror.

Cell autonomous polarization by the planar cell polarity signaling pathway

Planar Cell Polarity (PCP) signaling polarizes epithelial cells in a plane orthogonal to their apical-basal axis. A core PCP signaling module both generates molecular asymmetry within cells and coordinates the direction of polarization between neighboring cells. Two subcomplexes of core proteins segregate to opposite sides of the cell, defining a polarity axis. Homodimers of the atypical cadherin Flamingo are thought to be the scaffold upon which these subcomplexes assemble and are required for intercellular polarity signaling. The central role for Flamingo homodimers in scaffolding and intercellular communication suggests that cells in which intercellular signaling via Flamingo is disabled should fail to polarize. We show that cells lacking Flamingo, or bearing a truncated Flamingo that cannot homodimerize do in fact polarize. Cell polarization requires both positive and negative feedback, and in a multicellular tissue, feedback might involve both intracellular and intercellular pathways. We identify positive and negative feedback pathways that operate cell autonomously to drive polarization.

BAC Recombineering and Transgenesis to Study Cell Polarity and Polarized Tissue Morphogenesis in Mice

Planar cell polarity (PCP) signaling plays a critical role in coordinating cell polarity during various organogenesis processes in mammals, and its disruption is causal to numerous congenital disorders in humans. To elucidate its actions in mammals, mouse genetics is an indispensable approach. Given that both gain- and loss-of-function of many PCP genes often cause similar defects, the standard mouse transgenic approach may not always be ideal for studying PCP genes in their wild-type and mutant forms. Here we describe using BAC (bacterial artificial chromosomes) transgenes as a versatile and effective alternative. Transgenes made from BACs, which are genomic clones 100-200 kb in size, can more faithful recapitulate endogenous gene expression levels and patterns. Bacterial based recombination system can be used to efficiently introduce mutations, fluorescent protein tags, and LoxP sites for conditional expressions. Cre can also be inserted into BACs to map the contribution of cells expressing any PCP gene of interest, and study PCP mediated tissue morphogenesis.

A theoretical framework for planar polarity establishment through interpretation of graded cues by molecular bridges

Planar polarity is a widespread phenomenon found in many tissues, allowing cells to coordinate morphogenetic movements and function. A common feature of animal planar polarity systems is the formation of molecular bridges between cells, which become polarised along a tissue axis. We propose that these bridges provide a general mechanism by which cells interpret different forms of tissue gradients to coordinate directional information. We illustrate this using a generalised and consistent modelling framework, providing a conceptual basis for understanding how different mechanisms of gradient function can generate planar polarity. We make testable predictions of how different gradient mechanisms can influence polarity direction.

Summary: This Hypothesis uses a theoretical framework to explore how molecular bridges provide a general mechanism to interpret different forms of tissue gradients to establish planar polarity.

Complexity: the organizing principle at the interface of biological (dis)order

The term complexity means several things to biologists.When qualifying morphological phenotype, on the one hand, it is used to signify the sheer complicatedness of living systems, especially as a result of the multicomponent aspect of biological form. On the other hand, it has been used to represent the intricate nature of the connections between constituents that make up form: a more process-based explanation. In the context of evolutionary arguments, complexity has been defined, in a quantifiable fashion, as the amount of information, an informatic template such as a sequence of nucleotides or amino acids stores about its environment. In this perspective, we begin with a brief review of the history of complexity theory. We then introduce a developmental and an evolutionary understanding of what it means for biological systems to be complex.We propose that the complexity of living systems can be understood through two interdependent structural properties: multiscalarity of interconstituent mechanisms and excitability of the biological materials. The answer to whether a system becomes more or less complex over time depends on the potential for its constituents to interact in novel ways and combinations to give rise to new structures and functions, as well as on the evolution of excitable properties that would facilitate the exploration of interconstituent organization in the context of their microenvironments and macroenvironments.

A synthetic planar cell polarity system reveals localized feedback on Fat4-Ds1 complexes

The atypical cadherins Fat and Dachsous (Ds) have been found to underlie planar cell polarity (PCP) in many tissues. Theoretical models suggest that polarity can arise from localized feedbacks on Fat-Ds complexes at the cell boundary. However, there is currently no direct evidence for the existence or mechanism of such feedbacks. To directly test the localized feedback model, we developed a synthetic biology platform based on mammalian cells expressing the human Fat4 and Ds1. We show that Fat4-Ds1 complexes accumulate on cell boundaries in a threshold-like manner and exhibit dramatically slower dynamics than unbound Fat4 and Ds1. This suggests a localized feedback mechanism based on enhanced stability of Fat4-Ds1 complexes. We also show that co-expression of Fat4 and Ds1 in the same cells is sufficient to induce polarization of Fat4-Ds1 complexes. Together, these results provide direct evidence that localized feedbacks on Fat4-Ds1 complexes can give rise to PCP.

Frizzled Receptors in Development and Disease

Frizzled proteins are the principal receptors for the Wnt family of ligands. They mediate canonical Wnt signaling together with Lrp5 and Lrp6 coreceptors. In conjunction with Celsr, Vangl, and a small number of additional membrane and membrane-associated proteins, they also play a central role in tissue polarity/planar cell polarity (PCP) signaling. Targeted mutations in 9 of the 10 mammalian Frizzled genes have revealed their roles in an extraordinarily diverse set of developmental and homeostatic processes, including morphogenetic movements responsible for palate, ventricular septum, ocular furrow, and neural tube closure; survival of thalamic neurons; bone formation; central nervous system (CNS) angiogenesis and blood-brain barrier formation and maintenance; and a wide variety of processes that orient subcellular, cellular, and multicellular structures relative to the body axes. The last group likely reflects the mammalian equivalent of tissue polarity/PCP signaling, as defined in Drosophila, and it includes CNS axon guidance, hair follicle and tongue papilla orientation, and inner ear sensory hair bundle orientation. Frizzled receptors are ubiquitous among multicellular animals and, with other signaling molecules, they very likely evolved to permit the development of the complex tissue architectures that provide multicellular animals with their enormous selective advantage.

Clustering and negative feedback by endocytosis in planar cell polarity signaling is modulated by ubiquitinylation of prickle

The core components of the planar cell polarity (PCP) signaling system, including both transmembrane and peripheral membrane associated proteins, form asymmetric complexes that bridge apical intercellular junctions. While these can assemble in either orientation, coordinated cell polarization requires the enrichment of complexes of a given orientation at specific junctions. This might occur by both positive and negative feedback between oppositely oriented complexes, and requires the peripheral membrane associated PCP components. However, the molecular mechanisms underlying feedback are not understood. We find that the E3 ubiquitin ligase complex Cullin1(Cul1)/SkpA/Supernumerary limbs(Slimb) regulates the stability of one of the peripheral membrane components, Prickle (Pk). Excess Pk disrupts PCP feedback and prevents asymmetry. We show that Pk participates in negative feedback by mediating internalization of PCP complexes containing the transmembrane components Van Gogh (Vang) and Flamingo (Fmi), and that internalization is activated by oppositely oriented complexes within clusters. Pk also participates in positive feedback through an unknown mechanism promoting clustering. Our results therefore identify a molecular mechanism underlying generation of asymmetry in PCP signaling.

Many epithelial cells display a level of organization in which cellular structures or appendages are positioned asymmetrically within the cell along an axis perpendicular to the apical-basal axis of the cell. When the direction of this polarization is coordinated within the plane of the epithelium, this phenomenon is referred to as planar cell polarity (PCP). PCP is organized, at least in part, by a group of molecules that interact across cell-cell junctions and segregate into two groups that localize on opposite sides of each cell. Their asymmetric localization is thought to both produce molecular asymmetry, and to mark polarized domains within the cell for subsequent morphological polarization. In segregating to produce molecular asymmetry, these proteins participate in both positive and negative feedback, much like ferromagnets, to align their localization within and between neighboring cells. In this work, we identify a mechanism for negative feedback that utilizes the protein Prickle, one of the PCP signaling components. Levels of Prickle are precisely regulated, in part by a ubiquitinylation mechanism that targets excess protein for degradation. Prickle mediates internalization and removal of one class of PCP proteins, thereby causing repulsion of opposite ‘poles.’ Excess Prickle disrupts this mechanism and interferes with establishing polarity.

A one-dimensional model of PCP signaling: polarized cell behavior in the notochord of the ascidian Ciona

Despite its importance in development and physiology the planar cell polarity (PCP) pathway remains one of the most enigmatic signaling mechanisms. The notochord of the ascidian Ciona provides a unique model for investigating the PCP pathway. Interestingly, the notochord appears to be the only embryonic structure in Ciona activating the PCP pathway. Moreover, the Ciona notochord as a single-file array of forty polarized cells is a uniquely tractable system for the study of polarization dynamics and the transmission of the PCP pathway. Here, we test models for propagation of a polarizing signal, interrogating temporal, spatial and signaling requirements. A simple cell-cell relay cascading through the entire length of the notochord is not supported; instead a more complex mechanism is revealed, with interactions influencing polarity between neighboring cells, but not distant ones. Mechanisms coordinating notochord-wide polarity remain elusive, but appear to entrain general (i.e., global) polarity even while local interactions remain important. However, this global polarizer does not appear to act as a localized, spatially-restricted determinant. Coordination of polarity along the long axis of the notochord requires the PCP pathway, a role we demonstrate is temporally distinct from this pathway's earlier role in convergent extension and intercalation. We also reveal polarity in the notochord to be dynamic: a cell's polarity state can be changed and then restored, underscoring the Ciona notochord's amenability for in vivo studies of PCP.

Mathematical modeling of sub-cellular asymmetry of fat-dachsous heterodimer for generation of planar cell polarity

Planar Cell Polarity (PCP) is an evolutionarily conserved characteristic of animal tissues marked by coordinated polarization of cells or structures in the plane of a tissue. In insect wing epithelium, for instance, PCP is characterized by en masse orientation of hairs orthogonal to its apical-basal axis and pointing along the proximal-distal axis of the organ. Directional cue for PCP has been proposed to be generated by complex sets of interactions amongst three proteins - Fat (Ft), Dachsous (Ds) and Four-jointed (Fj). Ft and Ds are two atypical cadherins, which are phosphorylated by Fj, a Golgi kinase. Ft and Ds from adjacent cells bind heterophilically via their tandem cadherin repeats, and their binding affinities are regulated by Fj. Further, in the wing epithelium, sub-cellular levels of Ft-Ds heterodimers are seen to be elevated at the distal edges of individual cells, prefiguring their PCP. Mechanisms generating this sub-cellular asymmetry of Ft-Ds heterodimer in proximal and distal edges of cells, however, have not been resolved yet. Using a mathematical modeling approach, here we provide a framework for generation of this sub-cellular asymmetry of Ft-Ds heterodimer. First, we explain how the known interactions within Ft-Ds-Fj system translate into sub-cellular asymmetry of Ft-Ds heterodimer. Second, we show that this asymmetric localization of Ft-Ds heterodimer is lost when tissue-level gradient of Fj is flattened, or when phosphorylation of Ft by Fj is abolished, but not when tissue-level gradient of Ds is flattened or when phosphorylation of Ds is abrogated. Finally, we show that distal enrichment of Ds also amplifies Ft-Ds asymmetry. These observations reveal that gradient of Fj expression, phosphorylation of Ft by Fj and sub-cellular distal accumulation of Ds are three critical elements required for generating sub-cellular asymmetry of Ft-Ds heterodimer. Our model integrates the known experimental data and presents testable predictions for future studies.

Methods for studying planar cell polarity

Planar cell polarity (PCP) is the polarity of epithelial cells in the plane orthogonal to the apical-basal axis, and is controlled by a partially defined signaling system. PCP related signaling also plays roles in cell migration, tissue re-organization and stem cell differentiation during embryonic development, and later, in regeneration and repair. Aberrant signaling has been linked to a broad range of pathophysiologies including cancer, developmental defects, and neurological disorders. The deepest mechanistic insights have come from studies of PCP in Drosophila. In this chapter we review tools and methods to study PCP signaling in Drosophila epithelia, where it was found to involve asymmetric protein localization that is coordinated between adjacent cells. Such signaling has been most extensively studied in wing, eye, and abdomen, but also in other tissues such as leg and notum. In the adult fly, PCP is manifested in the coordinated direction of hairs and bristles, as well as the organization of ommatidia in the eye. The polarity of these structures is preceded by asymmetric localization of PCP signaling proteins at the apical junctions of epithelial cells. Based on genetic and molecular criteria, the proteins that govern PCP can be divided into distinct modules, including the core module, the Fat/Dachsous/Four-jointed (Fat/Ds/Fj) module (often referred to as the 'global' module) as well as tissue specific effector modules. Different tissues and tissue regions differ in their sensitivity to disturbances in the various modules of the PCP signaling system, leading to controversies about the interactions among the modules, and emphasizing the value of studying PCP in multiple contexts. Here, we review methods including those generally applicable, as well as some that are selectively useful for analyses of PCP in eye (including eye discs), wing (including wing discs), pupal and adult abdomen, and the cuticle of larvae and embryos.

Damped propagation of cell polarization explains distinct PCP phenotypes of epithelial patterning

During epithelial patterning in metazoans cells are polarized in the plane of a tissue, a process referred to as planar cell polarity (PCP). Interactions between a few molecules produce distinct phenotypes in diverse tissues in animals from flies to humans and make PCP tightly associated with tissue and organ growth control. An interesting question is whether these phenotypes share common traits. Previous computational models revealed how PCP signalling determines cell polarization in some specific contexts. We have developed a computational model, examined PCP signalling in varied molecular contexts, and revealed how details of molecular interactions and differences in molecular contexts affect the direction, speed, and propagation of cell polarization. The main finding is that damped propagation of cell polarization can generate rich variances in phenotypes of domineering non-autonomy and error correction in different contexts. These results impressively demonstrate how simple molecular interactions cause distinct, yet inherently analogous, developmental patterning.

Wnt regulation of planar cell polarity (PCP)

Planar cell polarity (PCP), a process controlling coordinated, uniformly polarized cellular behaviors in a field of cells, has been identified to be critically required for many fundamental developmental processes. However, a global directional cue that establishes PCP in a three-dimensional tissue or organ with respect to the body axes remains elusive. In vertebrate, while Wnt-secreted signaling molecules have been implicated in regulating PCP in a β-catenin-independent manner, whether they function permissively or act as a global cue to convey directional information is not clearly defined. In addition, the underlying molecular mechanism by which Wnt signal is transduced to core PCP proteins is largely unknown. In this chapter, I review the roles of Wnt signaling in regulating PCP during vertebrate development and update our knowledge of its regulatory mechanism.

Multiscale modeling and analysis of planar cell polarity in the Drosophila wing

Modeling across multiple scales is a current challenge in Systems Biology, especially when applied to multicellular organisms. In this paper, we present an approach to model at different spatial scales, using the new concept of Hierarchically Colored Petri Nets (HCPN). We apply HCPN to model a tissue comprising multiple cells hexagonally packed in a honeycomb formation in order to describe the phenomenon of Planar Cell Polarity (PCP) signaling in Drosophila wing. We have constructed a family of related models, permitting different hypotheses to be explored regarding the mechanisms underlying PCP. In addition our models include the effect of well-studied genetic mutations. We have applied a set of analytical techniques including clustering and model checking over time series of primary and secondary data. Our models support the interpretation of biological observations reported in the literature.