Modelling and analysis of planar cell polarity

Epithelial polarization by the planar cell polarity complex is exclusively non-cell autonomous

For cells to polarize collectively along a tissue plane, asymmetrically localized planar cell polarity (PCP) complexes must form intercellular contacts between neighboring cells. Yet, it is unknown whether asymmetric segregation of PCP complexes requires cell-cell contact, or if cell autonomous, antagonistic interactions are sufficient for polarization. To test this, we generated mouse chimeras consisting of dual PCP-reporter cells mixed with unlabeled cells that cannot form PCP bridges. In the absence of intercellular interactions, PCP proteins failed to polarize cell autonomously. Rather, PCP-mediated contacts along single cell-cell interfaces were sufficient to sort PCP components to opposite sides of the junction, independent of junction orientation. Thus, intercellular binding of PCP complexes is the critical step that initiates sorting of opposing PCP complexes to generate asymmetry.

Cluster Assembly Dynamics Drive Fidelity of Planar Cell Polarity Polarization

In planar cell polarity (PCP) signaling, distinct molecular subcomplexes segregate to opposite sides of each cell, where they interact across intercellular junctions to form asymmetric clusters. Although proximal-distal asymmetry within PCP clusters is the defining feature of PCP signaling, the mechanism by which this asymmetry develops remains unclear. Here, we developed a method to count the number of monomers of core PCP proteins within individual clusters in live animals and used it to infer the underlying molecular dynamics of cluster assembly and polarization. Measurements over time and space in wild type and in strategically chosen mutants demonstrate that cluster assembly is required for polarization, and together with mathematical modeling provide evidence that clusters become increasingly asymmetric and correctly oriented as they increase in size. We propose that cluster assembly dynamics amplify weak and noisy inputs into a robust cellular output, in this case cell and tissue-level polarization.

Emergence of planar cell polarity from the interplay of local interactions and global gradients

Planar cell polarity (PCP) - tissue-scale alignment of the direction of asymmetric localization of proteins at the cell-cell interface - is essential for embryonic development and physiological functions. Abnormalities in PCP can result in developmental imperfections, including neural tube closure defects and misaligned hair follicles. Decoding the mechanisms responsible for PCP establishment and maintenance remains a fundamental open question. While the roles of various molecules - broadly classified into 'global' and 'local' modules - have been well-studied, their necessity and sufficiency in explaining PCP and connecting their perturbations to experimentally observed patterns have not been examined. Here, we develop a minimal model that captures the proposed features of PCP establishment - a global tissue-level gradient and local asymmetric distribution of protein complexes. The proposed model suggests that while polarity can emerge without a gradient, the gradient not only acts as a global cue but also increases the robustness of PCP against stochastic perturbations. We also recapitulated and quantified the experimentally observed features of swirling patterns and domineering non-autonomy, using only three free model parameters - rate of protein binding to membrane, the concentration of PCP proteins, and the gradient steepness. We explain how self-stabilizing asymmetric protein localizations in the presence of tissue-level gradient can lead to robust PCP patterns and reveal minimal design principles for a polarized system.

Planar cell polarity: intracellular asymmetry and supracellular gradients of Dachsous

The slope of a supracellular molecular gradient has long been thought to orient and coordinate planar cell polarity (PCP). Here we demonstrate and measure that gradient. Dachsous (Ds) is a conserved and elemental molecule of PCP; Ds forms intercellular bridges with another cadherin molecule, Fat (Ft), an interaction modulated by the Golgi protein Four-jointed (Fj). Using genetic mosaics and tagged Ds, we measure Ds in vivo in membranes of individual cells over a whole metamere of the Drosophila abdomen. We find as follows. (i) A supracellular gradient rises from head to tail in the anterior compartment (A) and then falls in the posterior compartment (P). (ii) There is more Ds in the front than the rear membranes of all cells in the A compartment, except that compartment's most anterior and most posterior cells. There is more Ds in the rear than in the front membranes of all cells of the P compartment. (iii) The loss of Fj removes intracellular asymmetry anteriorly in the segment and reduces it elsewhere. Additional experiments show that Fj makes PCP more robust. Using Dachs (D) as a molecular indicator of polarity, we confirm that opposing gradients of PCP meet slightly out of register with compartment boundaries.

Distinct mechanisms of planar polarization by the core and Fat-Dachsous planar polarity pathways in the Drosophila wing

Planar polarity describes the coordinated polarization of cells within a tissue plane, and in animals can be determined by the “core” or Fat-Dachsous pathways. Current models for planar polarity establishment involve two components: tissue-level “global” cues that determine the overall axis of polarity and cell-level feedback-mediated cellular polarity amplification. Here, we investigate the contributions of global cues versus cellular feedback amplification in the core and Fat-Dachsous pathways during Drosophila pupal wing development. We present evidence that these pathways generate planar polarity via distinct mechanisms. Core pathway function is consistent with strong feedback capable of self-organizing cell polarity, which can then be aligned with the tissue axis via weak or transient global cues. Conversely, generation of cell polarity by the Ft-Ds pathway depends on strong global cues in the form of graded patterns of gene expression, which can then be amplified by weak feedback mechanisms.

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The core and Fat-Dachsous planar polarity pathways function via distinct mechanisms

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The core can self-organize planar polarity and be oriented by weak upstream cues

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Fat-Dachsous are oriented by strong gradient cues but show poor self-organization

Cell fate determination is influenced by Notch heterogeneity

Notch signaling (NS) determines the fate of adjacent cells during metazoans development. This intercellular signaling mechanism regulates diverse development processes like cell differentiation, proliferation, survival and is considered responsible for maintaining cellular homeostasis. In this study, we elucidate the role of Notch heterogeneity (NH) in cell fate determination. We studied the role of NH at intercellular, intracellular and the coexistence of Notch variation simultaneously at the intracellular and intercellular level in direct cell-cell signaling on an irregular cell mosaic. In addition, the effect of intracellular Notch receptor diffusion on an irregular cell lattice is also taken into account during Delta-Notch lateral inhibition (LI) process. Through mathematical and computational models, we discovered that the classical checkerboard pattern formation can be reproduced with an accuracy of 70-81% by accounting for NH in a realistic epithelial layer of multicellular organisms.

Molecular mechanisms mediating asymmetric subcellular localisation of the core planar polarity pathway proteins

Planar polarity refers to cellular polarity in an orthogonal plane to apicobasal polarity, and is seen across scales from molecular distributions of proteins to tissue patterning. In many contexts it is regulated by the evolutionarily conserved ‘core' planar polarity pathway that is essential for normal organismal development. Core planar polarity pathway components form asymmetric intercellular complexes that communicate polarity between neighbouring cells and direct polarised cell behaviours and the formation of polarised structures. The core planar polarity pathway consists of six structurally different proteins. In the fruitfly Drosophila melanogaster, where the pathway is best characterised, an intercellular homodimer of the seven-pass transmembrane protein Flamingo interacts on one side of the cell junction with the seven-pass transmembrane protein Frizzled, and on the other side with the four-pass transmembrane protein Strabismus. The cytoplasmic proteins Diego and Dishevelled are co-localised with Frizzled, and Prickle co-localises with Strabismus. Between these six components there are myriad possible molecular interactions, which could stabilise or destabilise the intercellular complexes and lead to their sorting into polarised distributions within cells. Post-translational modifications are key regulators of molecular interactions between proteins. Several post-translational modifications of core proteins have been reported to be of functional significance, in particular phosphorylation and ubiquitination. In this review, we discuss the molecular control of planar polarity and the molecular ecology of the core planar polarity intercellular complexes. Furthermore, we highlight the importance of understanding the spatial control of post-translational modifications in the establishment of planar polarity.

How do the Fat-Dachsous and core planar polarity pathways act together and independently to coordinate polarized cell behaviours?

Planar polarity describes the coordinated polarization of cells within the plane of a tissue. This is controlled by two main pathways in Drosophila: the Frizzled-dependent core planar polarity pathway and the Fat–Dachsous pathway. Components of both of these pathways become asymmetrically localized within cells in response to long-range upstream cues, and form intercellular complexes that link polarity between neighbouring cells. This review examines if and when the two pathways are coupled, focusing on the Drosophila wing, eye and abdomen. There is strong evidence that the pathways are molecularly coupled in tissues that express a specific isoform of the core protein Prickle, namely Spiny-legs. However, in other contexts, the linkages between the pathways are indirect. We discuss how the two pathways act together and independently to mediate a diverse range of effects on polarization of cell structures and behaviours.

DAnkrd49 and Bdbt act via Casein kinase Iε to regulate planar polarity in Drosophila

The core planar polarity proteins are essential mediators of tissue morphogenesis, controlling both the polarised production of cellular structures and polarised tissue movements. During development the core proteins promote planar polarisation by becoming asymmetrically localised to opposite cell edges within epithelial tissues, forming intercellular protein complexes that coordinate polarity between adjacent cells. Here we describe a novel protein complex that regulates the asymmetric localisation of the core proteins in the Drosophila pupal wing. DAnkrd49 (an ankyrin repeat protein) and Bride of Doubletime (Bdbt, a non-canonical FK506 binding protein family member) physically interact, and regulate each other’s levels in vivo. Loss of either protein results in a reduction in core protein asymmetry and disruption of the placement of trichomes at the distal edge of pupal wing cells. Post-translational modifications are thought to be important for the regulation of core protein behaviour and their sorting to opposite cell edges. Consistent with this, we find that loss of DAnkrd49 or Bdbt leads to reduced phosphorylation of the core protein Dishevelled and to decreased Dishevelled levels both at cell junctions and in the cytoplasm. Bdbt has previously been shown to regulate activity of the kinase Discs Overgrown (Dco, also known as Doubletime or Casein Kinase Iε), and Dco itself has been implicated in regulating planar polarity by phosphorylating Dsh as well as the core protein Strabismus. We demonstrate that DAnkrd49 and Bdbt act as dominant suppressors of Dco activity. These findings support a model whereby Bdbt and DAnkrd49 act together to modulate the activity of Dco during planar polarity establishment.

In many animal tissues, sheets of cells are polarised in the plane of the tissue, which is evident by the production of polarised structures, such as hairs on the fly wing that point in the same direction or cilia that beat in the same direction. One group of proteins controlling this coordinated polarity are the core planar polarity proteins, which localise asymmetrically within cells such that some core proteins localise to one cell end and others to the opposite cell end. It is thought that modifications such as phosphorylation may locally regulate core protein stability, and this promotes sorting of proteins to different cell ends. We identify two proteins, DAnkrd49 and Bdbt, that form a complex and regulate core protein asymmetry. Loss of either protein causes a reduction in overall levels of the core protein Dishevelled (Dsh), and a reduction in its phosphorylation. We provide evidence that the effect on core protein asymmetry is mediated via regulation of the kinase activity of Discs overgrown (Dco, also known as Doubletime/Casein Kinase Iε) by DAnkrd49 and Bdbt. We propose that modulation of Dco activity by DAnkrd49 and Bdbt is a key step in the sorting of core proteins to opposite cell ends.

The role of intracellular interactions in the collective polarization of tissues and its interplay with cellular geometry

Planar cell polarity (PCP), the long-range in-plane polarization of epithelial tissues, provides directional information that guides a multitude of developmental processes at cellular and tissue levels. While it is manifest that cells utilize both intracellular and intercellular interactions, the coupling between the two modules, essential to the coordination of collective polarization, remains an active area of investigation. We propose a generalized reaction-diffusion model to study the role of intracellular interactions in the emergence of long-range polarization, and show that the nonlocality of cytoplasmic interactions, i.e. coupling of membrane proteins localized on different cell-cell junctions, is of vital importance to the faithful detection of weak directional signals, and becomes increasingly more crucial to the stability of polarization against the deleterious effects of large geometric irregularities. We demonstrate that nonlocal interactions are necessary for geometric information to become accessible to the PCP components. The prediction of the model regarding polarization in elongated tissues, is shown to be in agreement with experimental observations, where the polarity emerges perpendicular to the axis of elongation. Core PCP is adopted as a model pathway, in term of which we interpret the model parameters. To this end, we introduce three distinct classes of mutations, (I) in membrane proteins, (II) in cytoplasmic proteins, and (III) local enhancement of geometric disorder. Comparing the in silico and in vivo phenotypes, we show that our model successfully recapitulates the salient phenotypic features of these mutations. Exploring the parameter space helps us shed light on the role of cytoplasmic proteins in cell-cell communications, and make falsifiable predictions regarding the cooperation of cytoplasmic and membrane proteins in the establishment of long-range polarization.

Planar cell polarity (PCP) is an indispensable and conserved pathway in morphogenesis. In spite of the advances in understanding the different modules of PCP, a comprehensive picture of the intracellular protein-protein interactions necessary for the emergence of long-range tissue polarity is still lacking. In order to address this question, we devised a generalized reaction-diffusion model, through which we investigated the role of cytoplasmic interactions in PCP pathways. The length scale of intracellular interactions is demonstrated to be crucial to the stability of the cytoplasmic segregation of membrane proteins in disordered tissues, as well as the capacity of polarization field for detecting the gradient and geometrical cues. Finally, three classes of mutants are investigated within the context of our model. Comparison with the in vivo observations allows us to infer the major contributions of cytoplasmic proteins to the emergence of tissue polarity, and make testable predictions regarding the cooperation of cytoplasmic and membrane proteins in the coordination of collective polarization.

Experimental and Theoretical Evidence for Bidirectional Signaling via Core Planar Polarity Protein Complexes in Drosophila

In developing tissues, sheets of cells become planar polarized, enabling coordination of cell behaviors. It has been suggested that "signaling" of polarity information between cells may occur either bidirectionally or monodirectionally between the molecules Frizzled (Fz) and Van Gogh (Vang). Using computational modeling we find that both bidirectional and monodirectional signaling models reproduce known non-autonomous phenotypes derived from patches of mutant tissue of key molecules but predict different phenotypes from double mutant tissue, which have previously given conflicting experimental results. Furthermore, we re-examine experimental phenotypes in the Drosophila wing, concluding that signaling is most likely bidirectional. Our modeling suggests that bidirectional signaling can be mediated either indirectly via bidirectional feedbacks between asymmetric intercellular protein complexes or directly via different affinities for protein binding in intercellular complexes, suggesting future avenues for investigation. Our findings offer insight into mechanisms of juxtacrine cell signaling and how tissue-scale properties emerge from individual cell behaviors.

Reciprocal action of Casein Kinase Iε on core planar polarity proteins regulates clustering and asymmetric localisation

The conserved core planar polarity pathway is essential for coordinating polarised cell behaviours and the formation of polarised structures such as cilia and hairs. Core planar polarity proteins localise asymmetrically to opposite cell ends and form intercellular complexes that link the polarity of neighbouring cells. This asymmetric segregation is regulated by phosphorylation through poorly understood mechanisms. We show that loss of phosphorylation of the core protein Strabismus in the Drosophila pupal wing increases its stability and promotes its clustering at intercellular junctions, and that Prickle negatively regulates Strabismus phosphorylation. Additionally, loss of phosphorylation of Dishevelled - which normally localises to opposite cell edges to Strabismus - reduces its stability at junctions. Moreover, both phosphorylation events are independently mediated by Casein Kinase Iε. We conclude that Casein Kinase Iε phosphorylation acts as a switch, promoting Strabismus mobility and Dishevelled immobility, thus enhancing sorting of these proteins to opposite cell edges.

Mouse ICM Organoids Reveal Three-Dimensional Cell Fate Clustering

During mammalian preimplantation, cells of the inner cell mass (ICM) adopt either an embryonic or an extraembryonic fate. This process is tightly regulated in space and time and has been studied previously in mouse embryos and embryonic stem cell models. Current research suggests that cell fates are arranged in a salt-and-pepper pattern of random cell positioning or a spatially alternating pattern. However, the details of the three-dimensional patterns of cell fate specification have not been investigated in the embryo nor in in vitro systems. We developed ICM organoids as a, to our knowledge, novel three-dimensional in vitro stem cell system to model mechanisms of fate decisions that occur in the ICM. ICM organoids show similarities to the in vivo system that arise regardless of the differences in geometry and total cell number. Inspecting ICM organoids and mouse embryos, we describe a so far unknown local clustering of cells with identical fates in both systems. These findings are based on the three-dimensional quantitative analysis of spatiotemporal patterns of NANOG and GATA6 expression in combination with computational rule-based modeling. The pattern identified by our analysis is distinct from the current view of a salt-and-pepper pattern. Our investigation of the spatial distributions both in vivo and in vitro dissects the contributions of the different parts of the embryo to cell fate specifications. In perspective, our combination of quantitative in vivo and in vitro analyses can be extended to other mammalian organisms and thus creates a powerful approach to study embryogenesis.

Enhanced Delta-Notch Lateral Inhibition Model Incorporating Intracellular Notch Heterogeneity and Tension-Dependent Rate of Delta-Notch Binding that Reproduces Sprouting Angiogenesis Patterns

Endothelial cells adopt unique cell fates during sprouting angiogenesis, differentiating into tip or stalk cells. The fate selection process is directed by Delta-Notch lateral inhibition pathway. Classical Delta-Notch models produce a spatial pattern of tip cells separated by a single stalk cell, or the salt-and-pepper pattern. However, classical models cannot explain alternative tip-stalk patterning, such as tip cells that are separated by two or more stalk cells. We show that lateral inhibition models involving only Delta and Notch proteins can also recapitulate experimental tip-stalk patterns by invoking two mechanisms, specifically, intracellular Notch heterogeneity and tension-dependent rate of Delta-Notch binding. We introduce our computational model and analysis where we establish that our enhanced Delta-Notch lateral inhibition model can recapitulate a greater variety of tip-stalk patterning which is previously not possible using classical lateral inhibition models. In our enhanced Delta-Notch lateral inhibition model, we observe the existence of a hybrid cell type displaying intermediate tip and stalk cells’ characteristics. We validate the existence of such hybrid cells by immuno-staining of endothelial cells with tip cell markers, Delta and CD34, which substantiates our enhanced model.

Robust Asymmetric Localization of Planar Polarity Proteins Is Associated with Organization into Signalosome-like Domains of Variable Stoichiometry

In developing epithelia, the core planar polarity proteins physically interact with each other and localize asymmetrically at opposite cell ends, forming intercellular complexes that link the polarity of neighboring cells. Using quantitative imaging to examine the composition of the core protein complex in vivo, we find that complex composition is unexpectedly plastic. The transmembrane proteins Frizzled and Flamingo form a stoichiometric nucleus in the complex, while the relative levels of the other four core proteins can vary independently. Exploring the functional consequences of this, we show that robust cell polarization is achieved over a range of complex stoichiometries but is dependent on maintaining appropriate levels of the components Frizzled and Strabismus. We propose that the core proteins assemble into signalosome-like structures, where stable association is not dependent on one-to-one interactions with binding partners, and signaling functions can act over a wide range of complex compositions.

A Dual Function for Prickle in Regulating Frizzled Stability during Feedback-Dependent Amplification of Planar Polarity

The core planar polarity pathway coordinates epithelial cell polarity during animal development, and loss of its activity gives rise to a range of defects, from aberrant morphogenetic cell movements to failure to correctly orient structures, such as hairs and cilia. The core pathway functions via a mechanism involving segregation of its protein components to opposite cells ends, where they form asymmetric intracellular complexes that couple cell-cell polarity. This segregation is a self-organizing process driven by feedback interactions between the core proteins themselves. Despite intense efforts, the molecular pathways underlying feedback have proven difficult to elucidate using conventional genetic approaches. Here we investigate core protein function during planar polarization of the Drosophila wing by combining quantitative measurements of protein dynamics with loss-of-function genetics, mosaic analysis, and temporal control of gene expression. Focusing on the key core protein Frizzled, we show that its stable junctional localization is promoted by the core proteins Strabismus, Dishevelled, Prickle, and Diego. In particular, we show that the stabilizing function of Prickle on Frizzled requires Prickle activity in neighboring cells. Conversely, Prickle in the same cell has a destabilizing effect on Frizzled. This destabilizing activity is dependent on the presence of Dishevelled and blocked in the absence of Dynamin and Rab5 activity, suggesting an endocytic mechanism. Overall, our approach reveals for the first time essential in vivo stabilizing and destabilizing interactions of the core proteins required for self-organization of planar polarity.

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.

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.

Collective polarization model for gradient sensing via Dachsous-Fat intercellular signaling

Dachsous-Fat signaling via the Hippo pathway influences proliferation during Drosophila development, and some of its mammalian homologs are tumor suppressors, highlighting its role as a universal growth regulator. The Fat/Hippo pathway responds to morphogen gradients and influences the in-plane polarization of cells and orientation of divisions, linking growth with tissue patterning. Remarkably, the Fat pathway transduces a growth signal through the polarization of transmembrane complexes that responds to both morphogen level and gradient. Dissection of these complex phenotypes requires a quantitative model that provides a systematic characterization of the pathway. In the absence of detailed knowledge of molecular interactions, we take a phenomenological approach that considers a broad class of simple models, which are sufficiently constrained by observations to enable insight into possible mechanisms. We predict two modes of local/cooperative interactions among Fat-Dachsous complexes, which are necessary for the collective polarization of tissues and enhanced sensitivity to weak gradients. Collective polarization convolves level and gradient of input signals, reproducing known phenotypes while generating falsifiable predictions. Our construction of a simplified signal transduction map allows a generalization of the positional value model and emphasizes the important role intercellular interactions play in growth and patterning of tissues.

Functional modelling of planar cell polarity: an approach for identifying molecular function

BACKGROUND

Cells in some tissues acquire a polarisation in the plane of the tissue in addition to apical-basal polarity. This polarisation is commonly known as planar cell polarity and has been found to be important in developmental processes, as planar polarity is required to define the in-plane tissue coordinate system at the cellular level.

RESULTS

We have built an in-silico functional model of cellular polarisation that includes cellular asymmetry, cell-cell signalling and a response to a global cue. The model has been validated and parameterised against domineering non-autonomous wing hair phenotypes in Drosophila.

CONCLUSIONS

We have carried out a systematic comparison of in-silico polarity phenotypes with patterns observed in vivo under different genetic manipulations in the wing. This has allowed us to classify the specific functional roles of proteins involved in generating cell polarity, providing new hypotheses about their specific functions, in particular for Pk and Dsh. The predictions from the model allow direct assignment of functional roles of genes from genetic mosaic analysis of Drosophila wings.

Is a persistent global bias necessary for the establishment of planar cell polarity?

Planar cell polarity (PCP)--the coordinated polarisation of a whole field of cells within the plane of a tissue-relies on the interaction of three modules: a global module that couples individual cellular polarity to the tissue axis, a local module that aligns the axis of polarisation of neighbouring cells, and a readout module that directs the correct outgrowth of PCP-regulated structures such as hairs and bristles. While much is known about the molecular components that are required for PCP, the functional details of--and interactions between--the modules remain unclear. In this work, we perform a mathematical and computational analysis of two previously proposed computational models of the local module (Amonlirdviman et al., Science, 307, 2005; Le Garrec et al., Dev. Dyn., 235, 2006). Both models can reproduce wild-type and mutant phenotypes of PCP observed in the Drosophila wing under the assumption that a tissue-wide polarity cue from the global module persists throughout the development of PCP. We demonstrate that both models can also generate tissue-level PCP when provided with only a transient initial polarity cue. However, in these models such transient cues are not sufficient to ensure robustness of the resulting cellular polarisation.

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.

Asymmetric protein localization in planar cell polarity: mechanisms, puzzles, and challenges

The polarization of epithelial cells along an axis orthogonal to their apical-basal axis is increasingly recognized for roles in a variety of developmental events and physiological functions. While now studied in many model organisms, mechanistic understanding is rooted in intensive investigations of planar cell polarity (PCP) in Drosophila. Consensus has emerged that two molecular modules, referred to here as the global and core modules, operate upstream of effector proteins to produce morphological PCP. Proteins of the core module develop subcellular asymmetry, accumulating in two groups on opposite sides of cells, consistent with proposed functions in producing cell polarity and in communicating that polarity between neighboring cells. Less clear are the molecular and cell biological mechanisms underlying core module function in the generation and communication of subcellular asymmetry and the relationship between the global and the core modules. In this review, we discuss these two unresolved questions, highlighting important studies and potentially enlightening avenues for further investigation. It is likely that results from Drosophila will continue to inform our views of the growing list of examples of PCP in vertebrate systems.

The frizzled/stan pathway and planar cell polarity in the Drosophila wing

Drosophila has been the key model system for studies on planar cell polarity (PCP). The rich morphology of the insect exoskeleton contains many structures that display PCP. Among these are the trichomes (cuticular hairs) that cover much of the exoskeleton, sensory bristles, and ommatidia. Many genes have been identified that must function for the development of normal PCP. Among these are the genes that comprise the frizzled/starry night (fz/stan) and dachsous/fat pathways. The mechanisms that underlie the function of the fz/stan pathway are best understood. All of the protein products of these genes accumulate asymmetrically in wing cells and there is good evidence that this involves local intercellular signaling between protein complexes on the distal edge of one cell and the juxtaposed proximal edge of its neighbor. It is thought that a feedback system, directed transport, and stabilizing protein-protein interactions mediate the formation of distal and proximal protein complexes. These complexes appear to recruit downstream proteins that function to spatially restrict the activation of the cytoskeleton in wing cells. This leads to the formation of the array of distally pointing hairs found on wings.

Pointing in the right direction: new developments in the field of planar cell polarity

Planar cell polarity (PCP) is observed in an array of developmental processes that involve collective cell movement and tissue organization, and its disruption can lead to severe developmental defects. Recent studies in flies and vertebrates have identified new functions for PCP as well as new signalling components, and have proposed new mechanistic models. However, despite this progress, the search to simplify principles of understanding continues and important mechanistic uncertainties still pose formidable challenges.

Modeling the control of planar cell polarity

A growing list of medically important developmental defects and disease mechanisms can be traced to disruption of the planar cell polarity (PCP) pathway. The PCP system polarizes cells in epithelial sheets along an axis orthogonal to their apical-basal axis. Studies in the fruitfly, Drosophila, have suggested that components of the PCP signaling system function in distinct modules, and that these modules and the effector systems with which they interact function together to produce emergent patterns. Experimental methods allow the manipulation of individual PCP signaling molecules in specified groups of cells; these interventions not only perturb the polarization of the targeted cells at a subcellular level, but also perturb patterns of polarity at the multicellular level, often affecting nearby cells in characteristic ways. These kinds of experiments should, in principle, allow one to infer the architecture of the PCP signaling system, but the relationships between molecular interactions and tissue-level pattern are sufficiently complex that they defy intuitive understanding. Mathematical modeling has been an important tool to address these problems. This article explores the emergence of a local signaling hypothesis, and describes how a local intercellular signal, coupled with a directional cue, can give rise to global pattern. We will discuss the critical role mathematical modeling has played in guiding and interpreting experimental results, and speculate about future roles for mathematical modeling of PCP. Mathematical models at varying levels of inhibition have and are expected to continue contributing in distinct ways to understanding the regulation of PCP signaling.