Frizzled (Fz) signaling regulates the establishment of planar cell polarity (PCP). The PCP genes prickle and strabismus are thought to antagonize Fz signaling. They act in the same cell, R4, adjacent to that in which the Fz/PCP pathway is required in the Drosophila eye. Stbm and Pk interact physically; Stbm recruits Pk to the cell membrane. Through this interaction, Pk affects Stbm membrane localization and can cause clustering of Stbm. Pk is also known to interact with Dsh and is thought to antagonize Dsh by affecting its membrane localization. Thus the data suggest that the Stbm/Pk complex modulates Fz/Dsh activity, resulting in a symmetry-breaking step during polarity signaling (Jenny, 2003).

pk function is required in the R4 precursor, as opposed to fz PCP signaling in R3, for control of polarity establishment. Stbm, a transmembrane protein also required in R4, interacts genetically and physically with Pk. This interaction is important for the recruitment of Pk to the plasma membrane. In Xenopus animal-cap explants, Stbm and Pk relocalize each other to subdomains of the membrane. A model is proposed of how Pk/Stbm might regulate Fz/Dsh signaling activity (Jenny, 2003).

The in vitro molecular interaction between Pk and Stbm and their mutual relocalization in Xenopus animal caps suggest that they form multiprotein complexes. Several pieces of evidence indicate that the physical interaction is physiologically important: (1) correct membrane localization of Pk depends on stbm function because in stbm mutant tissue Pk staining is diffuse and absent (or strongly reduced) at the membrane; (2) Pk and Stbm interact genetically by mutually enhancing each other's GOF and LOF phenotypes in the eye; (3) pk is necessary for PCP signaling in the R4 precursor, the same cell in which stbm is required; (4) expression of the interacting domains of Pk or Stbm interferes with polarity establishment. In particular, a subfragment of 131 amino acids of the C-terminus of Pk, required for the molecular interaction, is sufficient to affect polarity (Jenny, 2003).

Both Pk and Stbm act as if they antagonize Fz signaling. (1) In zebrafish, Stbm overexpression can prevent Wnt11 from rescuing a wnt11 mutation. (2) In the Drosophila wing, overexpression of Pk leads to wing hairs pointing towards the source of the overexpressed protein, behaving like a fz LOF clone (whereas overexpression of Fz leads to hairs pointing away from the Fz source). stbm LOF clones show the opposite behavior to fz LOF clones: wing hairs point away from the mutant patch, consistent with the mutant tissue having a higher Fz-activity (Jenny, 2003).

In the Drosophila eye, evidence that pk acts antagonistically to fz comes from the fact that the Notch-signaling-responsive R4-specific reporter mdelta0.5-lacZ is expressed for a prolonged period in both R3/R4 precursors in a pk^sple1 mutant. This is explained if Fz activity in the R4 precursor is increased, resulting in higher levels of Dl there. This in turn leads to N activation and concomitant mdelta0.5-lacZ reporter expression in both cells of the R3/R4 pair. Conversely, in fz and dsh mutant eye discs (where Fz signaling is absent or reduced and thus Dl should not be upregulated) N-signaling activity and mdelta-lacZ expression is initially reduced in both cells. Fz activity is also antagonized by stbm in the eye. Mosaic analysis of stbm shows that it has the capability to instruct a cell to become R4 as long as the other cell of the R3/R4 pair is mutant for stbm. Therefore, in such an all-or-nothing situation, Stbm in the R3 precursor can override a positive signal of Fz, resulting in a cell fate switch to R4 fate (Jenny, 2003).

In a wild-type situation with all PCP components present in both cells, it is crucial that Stbm activity is higher in R4 than in R3 to ensure proper Fz-signaling regulation. Therefore it is an intriguing possibility that a Pk/Stbm complex in the R4 precursor ensures such higher Stbm activity, and the associated higher Fz repression there is important for a proper R3/R4 cell fate decision (Jenny, 2003).

How does the Stbm/Pk complex regulate Fz-signaling activity? During PCP establishment in the wing, Fz, Dsh, Dgo, Fmi and Pk are initially localized uniformly around the apical circumference of wing cells. During and after PCP signaling, these proteins relocalize and become differentially enriched: Pk concentrates on the proximal side of the cell, whereas Fz and Dsh become enriched distally. Fmi becomes enriched at both sides (Jenny, 2003).

In the eye, the situation is analogous. During PCP establishment, signaling components at the R3/R4 cell border are relocalized from a uniform to a more restricted pattern. Stbm-YFP is localized on the R4 but not on the R3 side, and Fz-GFP ends up on the R3 but not the R4 side. The analogy between the R4/R3 and proximal/distal cell borders is corroborated by the genetic requirements in R3 and R4: the distally localized factors Dsh and Fz are required in R3, while proximally localized Pk is required in R4. Fmi is localized on both poles of each wing cell and also required in both cells of the R3 and R4 pair. The function of fmi has been linked to both proposed complexes, the 'Fz/Dsh side' (fmi is required for apical localization of both Fz and Dsh) and the Stbm/Pk complex. In addition to the genetic interactions between fmi and stbm or pk, a reduced membrane staining of Pk in fmi^- clones in wing cells has been shown (Jenny, 2003).

How do these changes in localization occur? Localization studies in Drosophila and Xenopus suggest that Pk and Stbm influence each other's localization and form clusters in subdomains of the cell membrane. Interestingly, such Stbm/Pk complexes also affect Fz-dependent Dsh membrane localization. Thus it is an intriguing possibility that the patches observed in animal cap cells upon coinjection of Stbm with Pk represent the result of a similar, though unpolarized, symmetry-breaking step during PCP signaling (Jenny, 2003).

The PET/LIM domain of Pk can interact with the DEP-domain/C-terminus of Dsh. This interaction has been suggested to prevent Dsh membrane recruitment. Also, the C-terminus of Stbm can interact with Dsh as long as the PDZ domain is present. Since the data suggest that Pk regulates the activity and localization of Stbm, this regulation might promote or stabilize the interactions of Dsh with Stbm and/or Pk, thereby helping to pull Dsh away from a Fz-signaling complex. The Stbm/Pk complexes could then cause active release of Dsh from the membrane or target it for degradation, resulting in low levels of Dsh (and by inference Fz) at places where Pk and Stbm are enriched. Furthermore, in the R3 cell (or distally in the wing) an unknown factor might act to prevent either the formation of the Stbm/Pk complex or its effect on Dsh (Jenny, 2003).

Cell fate diversity is generated in part by the unequal segregation of cell-fate determinants during asymmetric cell division. In the Drosophila bristle lineage, the sensory organ precursor (pI) cell is polarized along the anteroposterior (AP) axis by Frizzled (Fz) receptor signaling. Fz localizes at the posterior apical cortex of the pI cell prior to mitosis, whereas Strabismus (Stbm) and Prickle (Pk), which are also required for AP polarization of the pI cell, co-localize at the anterior apical cortex. Thus, asymmetric localization of Fz, Stbm and Pk define two opposite cortical domains prior to mitosis of the pI cell. At mitosis, Stbm forms an anterior crescent that overlaps with the distribution of Partner of Inscuteable (Pins) and Discs-large (Dlg), two components of the anterior Dlg-Pins-Galphai complex that regulates the localization of cell-fate determinants. At prophase, Stbm promotes the anterior localization of Pins. By contrast, Dishevelled (Dsh) acts antagonistically to Stbm by excluding Pins from the posterior cortex. It is proposed that the Stbm-dependent recruitment of Pins at the anterior cortex of the pI cell is a novel read-out of planar cell polarity (Bellaïch, 2004).

Planar polarization of the pI cell occurs prior to division and is required, upon entry into mitosis, to direct the Dlg-Pins-Galphai and Baz-Par6-aPKC complexes at the anterior and posterior cortex, respectively. The localization of Pins at the anterior cortex is regulated positively by the Stbm-Pk complex and negatively by Dsh. (1) Loss of stbm activity results in a delay in the cortical localization of Pins during prophase; (2) concomitant expression of Stbm and Pk leads to a broadening of the cortical crescent of Pins at prophase; (3) loss of dsh PCP activity similarly results in an extended Pins crescent at prophase. Moreover, analysis of the defective partitioning of Pon::GFP suggests that the Stbm-Pk complex acts antagonistically to Dsh to localize at the anterior cortex a centrosome-attracting activity. It is proposed that the Stbm-Pk complex organizes the anterior cortex and recruits the Dlg-Pins-Galphai complex as well as molecules regulating spindle positioning (Bellaïch, 2004).

Cortical localization of Pins is a novel read-out of PCP signaling in the pI cell that is distinct from the ones previously identified in wing and eye cells. In wing epidermal cells, Fz promotes the formation of a polarized actin cytoskeleton via a pathway that possibly involves a direct interaction between Dsh and a Daam1-Rho complex and a Rho Kinase-dependent phosphorylation of cytoplasmic myosin. Whether Dsh also regulates microfilament assembly in pI cells remains to be studied. In photoreceptor cells, the read-out for PCP signaling is the transcriptional regulation of the Delta gene in R3. Thus, the conserved core of PCP signaling molecules have different, cell-type specific read-outs (Bellaïch, 2004).

How does Stbm direct the localization of Pins to the anterior cortex? One hypothesis is that Stbm directs the anterior localization of Pins via the regulated assembly of a Stbm-Dlg-Pins complex. The anterior accumulation of Pins depends on its interaction with Dlg. Evidence is provided that Stbm may bind Dlg. (1) In vitro binding studies indicate that Stbm interacts with Dlg. It is noted, however, that PDZ-containing proteins other than Dlg may also bind Stbm in this assay. (2) The localization of Stbm overlaps with the distribution of Pins and Dlg in dividing pI cells. (3) The PBM motif of Stbm appears to regulate the re-localization of Stbm in pI cells. The data are therefore consistent with a model in which, upon mitosis, the binding of Stbm to Dlg in turn promotes the binding of Pins to Dlg and, hence, localization of Pins at the anterior cortex where Stbm and Dlg accumulations overlap. This model predicts that the PBM of Stbm should be required for the anterior localization of Pins. It was found, however, that StbmDeltaPBM is fully functional and that Pins is properly recruited at the anterior cortex in stbm^6c mutant pI cells expressing StbmDeltaPBM. One interpretation of this result is that Stbm regulates the localization of Pins not only via the PBM-dependent assembly of the Dlg-Pins complex but also via a second PBM-independent mechanism. Since Dsh acts redundantly with Baz to localize Pins asymmetrically, it is suggested that this second mechanism may involve Dsh. Accordingly, in stbm^6c mutant pI cells, uniformly distributed Dsh activity would prevent Pins cortical localization. By contrast, since the PCP function of stbm does not depend on its PBM, the activity of Dsh should be restricted to the posterior cortex in stbm^6c mutant pI cells expressing StbmDeltaPBM. Dsh should therefore restrict Pins localization to the anterior cortex in this mutant background. Another interpretation of the correct localization of Pins in stbm^6c mutant pI cells expressing StbmDeltaPBM is that Stbm recruits Pins via a mechanism that does not involve an interaction with Dlg (or any other PDZ-containing proteins). Future studies will address how the Stbm-Pk complex regulates the localization of Pins in the pI cell (Bellaïch, 2004).

Different mechanisms appear to cooperate to maintain Pins asymmetric localization. baz is required for the asymmetric localization of Pins in the absence of dsh PCP activity. This indicates that Baz can regulate the maintenance of Pins asymmetric localization at prometaphase. The loss of asymmetric localization of Pins in dsh baz mutant pI cells suggests that Dsh may also contribute to maintain Pins asymmetric localization at prometaphase. Dsh does not merely act by excluding Stbm, a positive regulator of Pins localization in prophase, because Pins localizes asymmetrically in baz stbm double mutant pI cells. The mechanisms by which Baz and Dsh regulates Pins localization are not known. However, because Pins regulates its own localization via a Gß13F-dependent positive feedback loop, one hypothesis is that Baz and/or Dsh negatively regulates Gß13F signaling activity (Bellaïch, 2004).

One of the best examples of PCP in mammals is the stereotyped planar orientation of the stereociliary bundles that are located at the apical cortex of each mechanosensory hair cell within the cochlea. In these cells, the first sign of polarization is the stereotyped movement, at the luminal surface of the cell and along the neural-abneural axis, of the kinocilium, the single tubulin-based cilium, from the center towards the abneural pole of the cell. Recently, a mutation in a stbm homolog, Vangl2, has been shown to result in the defective orientation of the stereociliary bundles. This planar cell polarity defect appears to result from the randomly oriented center-to-periphery movement of the kinocilium. Because LGN, a mammalian homolog of Pins, is known to regulate microtubule stability, it is tempting to speculate that Vangl2 may regulate via LGN a microtubule-dependent process regulating kinocilium movement along the neural-abneural axis. Future studies will reveal whether the regulation of Pins/LGN cortical localization is a conserved read-out of PCP (Bellaïch, 2004).

The integument of the Drosophila adult abdomen bears oriented hairs and bristles that indicate the planar polarity of the epidermal cells. Four polarity genes, frizzled (fz), prickle (pk), Van gogh/strabismus (Vang/stbm) and starry night/flamingo (stan/fmi) were examined in this study, and what happens when these genes are either removed or overexpressed in clones of cells was examined. The edges of the clones are interfaces between cells that carry different amounts of gene products, interfaces that can cause reversals of planar polarity in the clone and wild-type cells outside them. To explain, a model is presented that builds on an earlier picture of a gradient of X, the vector of which specifies planar polarity and depends on two cadherin proteins, Dachsous and Fat. It is conjectured that the X gradient is read out, cell by cell, as a scalar value of Fz activity, and that Pk acts in this process, possibly to determine the sign of the Fz activity gradient (Lawrence, 2004).

Evidence is discussed that cells compare their scalar readout of the level of X with that of their neighbors and set their own readout toward an average of these. This averaging, when it occurs near the edges of clones, changes the scalar response of cells inside and outside the clones, leading to new vectors that change polarity. The results argue that Stan must be present in both cells being compared and acts as a conduit between them for the transfer of information, and that Vang assists in the receipt of this information. The comparison between neighbors is crucial, because it gives the vector that orients hairs: these hairs point toward the neighbor cell that has the lowest level of Fz activity (Lawrence, 2004).

Recently, it has been shown that, for a limited period shortly before hair outgrowth in the wing, the four proteins studied, as well as others, become asymmetrically localised in the cell membrane, and this process is thought to be instrumental in the acquisition of cell polarity. However, some results do not fit with this view -- it is suggested that these localisations may be more a consequence than a cause of planar polarity (Lawrence, 2004).

There are a number of simple systems in which isolated cells orient to a polarising signal. These include the localized outgrowth, or 'schmooing' of yeast in response to mating pheromone and directed migration of Dictyostelium cells up a gradient of cyclic AMP. Small differences (as little as 1%-5%) in receptor activation across single cells are sufficient to polarise them, a response that, in yeast and elsewhere probably depends on localised exocytosis. It is not known whether the polarisation of single, isolated cells is a model for planar polarity of cells in an epithelium, but it is likely that they share at least some of the mechanisms (Lawrence, 2004).

It has been proposed that, in the abdomen of Drosophila, morphogen gradients (Hh in the A compartment and Wg in the P compartment) organise a secondary gradient ('X'); the vector of X specifying the polarity of each cell. Although the composition of X is unknown, at least three proteins, Fj, Ds and Ft, are implicated. All three may be expressed, or be active, in bell-shaped distributions that peak near the A/P (Ds) or P/A (Fj, Ft) boundaries. Ds and Ft are transmembrane proteins in the cadherin superfamily; Fj probably acts in the Golgi. Ds and Ft are integrated into the membrane, suggesting that the X gradient itself may not be diffusible but instead might depend on information transfer from cell to cell (Lawrence, 2004).

How does Hh set up the X gradient? Although changing the real or perceived level of Hh does affect polarity, many clones (for example clones that lack Smo, an essential component of Hh reception) show there is no simple correlation between Hh concentration and polarity. For instance, large smo^- clones in the center of the A compartment are polarised normally, even though they are blind to Hh. Also, while smo^- clones in some regions of the A compartment do affect polarity, both mutant and wild-type cells are repolarised. Both these observations argue for some transfer of information about polarity between cells, a process that would be at least partly Hh independent. This paper explores this process and is concerned with four genes (stan, fz, Vang and pk) that probably act downstream of ds, ft and fj (Lawrence, 2004).

Perhaps normal cells could transfer information from one to another (this might be particularly important for nascent cells following mitosis) to help keep the readout of X as a smooth gradient? To do this they might make a comparison of their neighbors and modify this readout of X toward an average of those neighbors. X might be read by a receptor molecule and the results point to Fz being the most likely candidate. The results indicate that the comparison itself requires the cadherin Stan. Thus, a cell would need to read and compare (using Stan) the levels of X (recorded in the activity of Fz) in neighboring cells. Then, in a way analogous to how a Dictyostelium amoeba reads the vector of a cAMP gradient, a cell would determine its polarity from the vector of Fz activity. The results suggest that Vang also acts in this step, helping cells to sense the level of Fz activity in neighboring cells (Lawrence, 2004).

Some of the results are discussed in terms of the model (Lawrence, 2004). Clones that lack, or overexpress Fz cause local and consistent repolarisations of cells that extend from within the clone and affect normal wild-type cells outside it. Because simply removing the fz gene from all cells randomizes polarity in the ventral pleura, it is self-evident that these organised polarity reversals must result from an interaction between the clone and the surrounding cells. It has been argued that Stan and Fz act in this process, but how? Note that stan and fz are the only mutants that have randomised hairs in the pleura, and the results indicate that neither Stan nor Fz can function properly without the other. Averaging might depend on the capacity of Stan to form homophilic dimers as bridges between neighboring cells, with such Stan:Stan dimers serving as a conduit for information about the relative level of Fz activity in each cell. However, with respect to non-autonomy, the results with the two genes differ:

1. stan^- cells cannot be repolarised by, and cannot repolarise, neighboring cells. This shows that Stan is essential in both neighboring cells for the transfer of information between them. Without Stan, the cells cannot compare and cannot therefore determine any vector. However, a stan⁺ cell, even if it is adjacent to a stan^- cell, can be polarised normally; having Stan it should be able to read the levels of all neighboring cells except the stan^- one and, having Fz, it should be able to set its own level (Lawrence, 2004).
   
   
2. But, fz^- cells, unlike stan^- cells, can repolarise neighboring wild-type cells. Also, a fz^- cell, again unlike a stan^- cell, can itself be repolarised. The results also show that to be repolarised, or to polarise a neighbor, a fz^- cell must be adjacent to a stan⁺ fz⁺ cell. Such a fz^- cell will accumulate Stan in that membrane which abuts the stan⁺ neighbor so it should be able to read the level of the neighboring wild-type cell and be polarised accordingly. Consider a fz^- cell at the outer edge of a fz^- clone: lacking Fz, its activity level would be zero, but this level would be communicated by Stan to the neighboring cells. Wild-type cells outside would obviously have a higher level (than zero). The result would be that the two cells abutting the interface, the fz^- cell inside, and a fz⁺ cell outside, would both make hairs that point into the center of the clone. The nextmost interior cell would not be polarised, since all its neighbors would be cells with level zero. In contrast, the next most exterior cell would be repolarised, since its scalar level would be brought down by the averaging process (Lawrence, 2004).

How far does the non-autonomy spread into wild-type cells? This process can be stimulated. According to the model this range would depend on the value of a single adjustable parameter, a that relates to how much a cell's scalar is read from X. At one extreme for this parameter (a=0), when the scalar of a cell depends only on X, a wild-type cell just posterior to a clone of fz^- cells would reset its scalar as it was before; there could be no averaging and only that cell and its fz^- neighbor will be repolarised. Thus the non-autonomy would be limited to one cell. At the other extreme (a=1), any local disturbance produced by a clone would decay rapidly because of averaging, and the repolarisation will tend to be lost altogether. In between these extremes, the non-autonomy spreads more than one cell, but over diverse values for this parameter, the range is near the amount usually observed (2-4 cell diameters) (Lawrence, 2004).

It has been observed that fz^- clones have effects over longer range in backgrounds such as ds^- where the X gradient might be flatter than normal. Similarly, cells are normally polarised in large smo^- clones in the middle of the A compartment, where, because there can be no input from Hh, the X gradient could also be flat. Both these results are consistent with the model, because the range affected by averaging will increase (Lawrence, 2004).

Many of the proteins required for normal cell polarity, including Fz, Dsh, Dgo, Pk, Vang and Stan are found to be asymmetrically localised in the proximodistal axis of wing cells. This localisation is restricted to a brief period of just a few hours shortly before the wing hairs grow out, but, nevertheless it is assumed to be mechanistically important to planar polarity. For example, non-autonomy could be explained if localised proteins were components of one or more molecular complexes that propagate polarity from cell to cell. In support of this, note that loss of any of these proteins, including the removal of both Pk and Sple, prevents the asymmetric localisation of the others (Lawrence, 2004).

But the results do not seem to fit with such a mechanism, mainly because they provide evidence that polarity can propagate into cells that lack, or fail to localise all of these proteins. In particular, pk^- cells are normally polarised throughout the P compartment and can be repolarised in both compartments by sharp discontinuities in Fz activity even in the pleura (where polarity is randomized in fz^- and stan^- animals). At a minimum, these findings challenge the hypothesis that Pk itself is an essential component of a feedback amplification mechanism responsible for polarising cells. Furthermore, if it is assumed that the observed failure of Fz, Dsh, Vang and Stan to localize in pk^- wing cells reflects a general property, these results also challenge the idea that Fz, Dsh, Pk, Vang, Diego and Stan must be able to accumulate asymmetrically in order for cells to detect, and be polarised by, the X gradient, or by disparities in Fz activity. Indeed, Adler (2002) has already hinted that there is no convincing evidence that the asymmetric localisation of these proteins actually functions in planar polarity: 'the preferential accumulation [of proteins] along the...edges of wing cells is a process that intuitively seems likely to be part of a core system...but perhaps it is not and if not...this would leave rather little in the core' (Lawrence, 2004).

Are wing cells polarised only briefly just prior to the hair outgrowth? The reason for raising this possibility is that the proteins are apparently only asymmetrically localised at that time. If this localisation were not causal, as it is now suggested, it could be that the cells are polarised for all or most of development -- again arguing that the ephemeral localisation of the proteins is more a consequence than a cause of polarisation (Lawrence, 2004).

Planar cell polarity (PCP) signaling generates subcellular asymmetry along an axis orthogonal to the epithelial apical-basal axis. Through a poorly understood mechanism, cell clones that have mutations in some PCP signaling components, including some, but not all, alleles of the receptor frizzled, cause polarity disruptions of neighboring wild-type cells, a phenomenon referred to as domineering nonautonomy. A contact-dependent signaling hypothesis, derived from experimental results, is shown by reaction-diffusion, partial differential equation modeling and simulation to fully reproduce PCP phenotypes, including domineering nonautonomy, in the Drosophila wing. This work suggests that Fz does not require a Wnt ligand in PCP signaling but that its activity is regulated by interactions between neighboring cells and differential levels of the cytoplasmic mediators Pk and Dsh. The sufficiency of this model and the experimental validation of model predictions reveal how specific protein-protein interactions produce autonomy or domineering nonautonomy (Amonlirdviman, 2005).

As the understanding of cellular regulatory networks grows, system behaviors resulting from feedback effects have proven sufficiently complex so as to preclude intuitive understanding. The challenge now is to show that enough of a network is understood to explain such behaviors. Using mathematical modeling, the sufficiency of a proposed biological model is shown and its properties studied, to demonstrate that it can explain complex PCP phenotypes and provide insight into the system dynamics that govern them (Amonlirdviman, 2005).

Many epithelia are polarized along an axis orthogonal to the apical-basal axis. On the Drosophila adult cuticle, each hexagonally packed cell elaborates an actin-rich hair that develops from the distal vertex and points distally. Genetic analyses have identified a group of PCP proteins whose activities are required to correctly polarize these arrays. The domineering nonautonomy adjacent to cell clones mutant for some, but not other, PCP genes has not yet been adequately explained. For example, in the Drosophila wing, Van Gogh/strabismus (Vang; encoding a four-pass transmembrane protein) clones disrupt polarity proximal to the mutant tissue, whereas null frizzled (fz; encoding a seven-pass transmembrane protein) alleles disrupt polarity distal to the clone. Models to explain this phenomenon have often invoked diffusible factors, referred to as factor X or Z, because they have not yet been identified. It is proposed instead that the observed behaviors of known PCP proteins are sufficient to explain domineering nonautonomy (Amonlirdviman, 2005).

Fz and other PCP signaling components accumulate selectively on the distal or proximal side of wing cells. Evidence has been provided that these proteins function in a feedback loop that amplifies an asymmetry cue, which converts uniform distributions of PCP proteins into highly polarized distributions. The proposed feedback mechanism depends on several functional relationships. Fz recruits Dishevelled (Dsh; a cytoplasmic protein) to the cell membrane. In addition, Fz promotes the recruitment of Prickle-spinylegs (Pk; a LIM domain protein) and Vang to the cell membrane of the adjacent cell. Feedback is provided by the ability of Pk (and Vang) to cell-autonomously block Fz-dependent recruitment of Dsh. This feedback loop functions strictly locally, between adjacent cells. Global directionality is imposed through the agency of the novel transmembrane protein Four-jointed and the cadherins Dachsous and Fat (Ft). Widerborst, a regulatory subunit of protein phosphatase 2A, accumulates asymmetrically within each cell and is required to bias the feedback loop. Although the mechanism by which Ft biases the direction of the feedback loop is unknown, one possibility is that Ft may direct Widerborst distribution (Amonlirdviman, 2005).

However, it is not readily apparent that this biological model does not readily explain the complex patterns observed in fields of cells containing mutant clones, and it has been argued that it cannot account for some of the observed phenotypes. Indeed, progress in understanding PCP signaling has been hampered by an inability to deduce, given a particular signaling network hypothesis, definitive links between molecular genetic interventions and tissue patterning effects. For example, although it is apparent that removing Dsh or Fz would disrupt the feedback loop, it is not obvious how the feedback loop in adjacent wild-type cells responds, such that dsh mutant clones behave autonomously, whereas for most fz alleles, mutant clones behave nonautonomously. Interestingly, though, for some fz alleles, mutant clones produce an almost cell-autonomous phenotype. As another example, Pk overexpression promotes the asymmetric accumulation of Dsh and Fz, despite the role of Pk in the feedback loop as an inhibitor of Dsh membrane recruitment (Amonlirdviman, 2005).

A mathematical model has been developed based on the described feedback loop and an initial asymmetry input representing the global directional cue. Although mathematical modeling cannot prove the correctness of the underlying biological model, the ability of the mathematical model to capture the known behaviors of the system proves the feasibility of the biological model, provides testable hypotheses, and yields insight into the factors contributing to autonomy and nonautonomy (Amonlirdviman, 2005).

The features of the biological feedback loop model have been represented as a mathematical reaction-diffusion model that describes the concentrations of Dsh, Fz, Vang, and Pk throughout a network of cells. Although the mechanisms that underlie the local feedback loop are not fully understood, the essential logic of this feedback loop is preserved by representing these interactions as binding to form protein complexes (Amonlirdviman, 2005).

Inhibition of Dsh membrane recruitment by Pk and Vang is represented in the mathematical model as an increase in the backward reaction rate of reactions in which Dsh binds Fz (or Fz complexes) by a factor dependent on the local concentration of Pk and Vang. The specific mechanism for the introduction of the directional bias into the feedback loop network is not known. Two forms of a global biasing signal were therefore implemented, and the results using either of these models were similar. The resulting mathematical model consists of a system of 10 nonlinear partial differential equations. With a given set of model parameters, an array of cells could then be simulated, and the resulting hair pattern assigned on the basis of the final distribution of Dsh (Amonlirdviman, 2005).

The model parameters, including the initial protein concentrations, reaction rates, and diffusion constants, were not known, and so these parameters were identified by constraining them to result in specific qualitative features of the hair pattern phenotypes. A sensitivity analysis showed that the model results are not highly sensitive to the precise parameter values and suggests that the conclusions regarding the feasibility of the model are valid for considerable ranges of parameters (Amonlirdviman, 2005).

In simulated wild-type cells, Dsh and Fz localize to the distal membrane, and Vang and Pk localize to the proximal membrane, as is seen in vivo. Simulated clones of cells lacking fz function disrupt polarity in wild-type cells distal to the clones, whereas simulated clones lacking Vang function disrupt polarity on the proximal side of the clones. Simulated clones lacking dsh function result in the disruption of polarity within the mutant cells, but only show a mild effect outside of the clones. The nearly, though not fully cell autonomous, phenotype is similar to that which is observed experimentally. Clones lacking all pk function show only a subtle phenotype. Examination of protein distributions shows that the results are highly concordant with published observations. Similarly, simulated overexpression clones produce results closely mimicking observed experimental results. In simulations and in wings, relatively small clones lacking a global biasing signal show no phenotype, demonstrating that not all cells need to respond to the global directional signal for the feedback loop to cooperatively align all of the cells (Amonlirdviman, 2005).

Previously, it was found that Pk overexpression in the posterior wing domain enhances the accumulation of Fz and Dsh at cell boundaries, despite the observed ability of Pk and Vang to block Dsh recruitment. Consistent with these results, Dsh and Fz are seen in a simulation of this experiment to accumulate to higher levels in the region overexpressing pk than in the wild-type region, and they accumulate perpendicular to the wildtype orientation near the anterior-posterior boundary (Amonlirdviman, 2005).

The results suggested a mechanistic explanation for the difference between autonomous and nonautonomous fz alleles. Because the nearly autonomous fz alleles (fzJ22 and fzF31) have phenotypes similar to dsh clones, it is hypothesized that these alleles may be selectively deficient in complexing with Dsh, but normal in their ability to complex with Vang. Simulations of clones in which the interaction was disrupted between Dsh and Fz by reducing the corresponding forward reaction rates produced nearly cell autonomous polarity phenotypes (Amonlirdviman, 2005).

This hypothesis makes two easily testable predictions. (1) Fz autonomous proteins should be present in the membrane and should recruit Vang to the adjacent membrane, whereas Fz nonautonomous protein should not recruit Vang. It has previously been shown that GFP-tagged FzJ22, expressed in a wild-type background, is present at the apical cell cortex, but remains symmetrically distributed, a distribution in accordance with the simulation of this condition. Examining this further, it was found that in cells adjoining clones of the autonomous fzF31 allele, Vang is recruited to the boundary between wild-type and mutant cells, whereas substantially less Vang is recruited to those boundaries in cells adjoining clones of the nonautonomous fzR52 allele. Thus, Fz^autonomous proteins recruit Vang to the opposing cell surface, whereas nonautonomous alleles do not. (2) Autonomous Fz proteins should fail to recruit Dsh. Indeed, it was found that both are substantially impaired in Dsh recruitment, though somewhat less impaired than the very strong, nonautonomous fzR52 allele. Thus, strong fz alleles, many of which fail to accumulate Fz protein, display no or severely impaired interaction with Dsh and Vang, whereas autonomous alleles have impaired interaction with Dsh, but retain substantial ability to recruit Vang to the adjacent membrane. Notably, simulated overexpression of Fz with impaired Dsh interaction also produced the correct polarity disruption in cells proximal to the clones (Amonlirdviman, 2005).

The Dsh¹ protein produces nearly autonomous clones, and it carries a mutation in its DEP domain, which is required for membrane localization; autonomous fz alleles bear point mutations in the first cytoplasmic loop, suggesting these mutations may affect the same interaction. A low affinity interaction between the Dsh PDZ domain and a sequence in the cytoplasmic tail of Fz has been demonstrated. These data suggest that sequences in the Dsh DEP domain, and in the Fz first intracellular loop, are also important for Dsh membrane association. Thus, a regulated, bipartite, high affinity association of Dsh with Fz may be selectively disrupted in fz^autonomous alleles (Amonlirdviman, 2005).

The ability of the mathematical model to simultaneously reproduce all of the most characteristic PCP phenotypes demonstrates the feasibility of the underlying biological model as a PCP signaling mechanism. Further, the mathematical model demonstrates how the overall scheme of the model -- a local feedback loop between adjacent cells amplifying an initial asymmetry -- can explain the autonomous and nonautonomous behavior of PCP mutant clones. Alternative models invoking diffusible factors have not been supported by the identification of such factors, and the contact-dependent intercellular signaling model more readily accounts for the slight nonautonomy of dsh and fz^autonomous clones than do the diffusible factor models (Amonlirdviman, 2005).

The ability of the mathematical model to make predictions and provide a detailed picture of PCP signaling is limited by the lack of complete biological understanding. Although the validity of quantitative model predictions is subject to its assumptions and the set of features used in parameter identification, the model has allowed a direct connection of a biological model to the complex behaviors it is hypothesized to explain and to explore the implications of variations in the model (Amonlirdviman, 2005).