An intracellular partitioning-based framework for tissue cell polarity in plants and animals

Many plant and animal tissues exhibit coordinated cell polarities over extended domains. For example, the hairs on a Drosophila wing or the distribution of auxin transporters in a developing leaf show highly coordinated orientations (Fig. 1A,B). To understand the mechanisms underlying tissue cell polarity, it helps to define two basic types of coordination: lateral and longitudinal. These types of coordination can be illustrated for a single file of cells, in which polarities are aligned head to tail (longitudinal coordination, Fig. 1C) or aligned lateral to the direction of polarity (lateral coordination, Fig. 1D). Both types of coordination can occur together within a sheet of cells, as the polarity of each cell in the plane may be aligned with both its flanking cells (lateral coordination) and with those ahead or behind it (longitudinal coordination) (Fig. 1E). Similar considerations apply to a three-dimensional (3D) block of cells, except that lateral coordination can be extended to a further dimension (Fig. 1F). A key problem is understanding how such patterns of lateral and longitudinal coordination may be established over extended domains.

One type of model assumes that neighbouring cells have the ability to compare concentrations of specific molecules and align their polarities accordingly. For example, a model for planar polarity coordination in Drosophila proposes that the level of Frizzled protein activity in neighbouring cells is compared so that the polarity of each cell becomes oriented towards the neighbour with the lowest Frizzled activity (Simon, 2004; Lawrence et al., 2007). Similarly, it has been proposed that plant cells orient their polarity according to the concentration of auxin in neighbours (Bayer et al., 2009; Jönsson et al., 2006; Smith et al., 2006). Another type of model proposes that polarities are established through differential molecular interactions at cell interfaces, which may be modulated by graded signals. For example, it has been proposed that planar polarity in Drosophila depends on establishing different molecular complexes on either side of cell-cell interfaces, with a bias provided by signals that vary across and/or between cells (Amonlirdviman et al., 2005; Le Garrec et al., 2006; Burak and Shraiman, 2009). Yet other types of model propose that polarity depends on measuring molecular fluxes across membranes, concentration gradients across extracellular spaces or gradients in stresses across cells (Mitchison, 1980; Sachs, 1981; Rolland-Lagan and Prusinkiewicz, 2005; Bayer et al., 2009; Heisler et al., 2010; Wabnik et al., 2010). In all of the above models, polarisation of individual cells depends on asymmetric cues or polarisable neighbours.

By contrast, we propose a framework that is based on cells having the ability to polarise in the absence of asymmetric cues or polarisable neighbours, a possibility also suggested by Meinhardt (Meinhardt, 2007). We call this process intracellular partitioning. Tissue cell polarity emerges by coordination of polarities established by intracellular partitioning, through coupling between neighbouring cells (cell-cell coupling) and operation of tissue polarity organisers. To illustrate how the intracellular partitioning-based framework may generate tissue cell polarity patterns, we present a series of simplified theoretical cases and explore their consequences through computer simulations, which are run until a stable state is reached (details of how computer simulations are implemented and the range of parameters explored can be found in supplementary material Appendix S1). For simplicity, we restrict our analysis of tissue cell polarity to one-dimensional (1D) cell files or two-dimensional (2D) cell sheets. The utility of the framework is then illustrated by applying it to canonical examples of tissue cell polarity in plants and animals.

Key features of this framework are as follows. (1) It is applicable to both plant and animal tissue cell polarity. Previous models of tissue cell polarity have considered plant and animal systems separately. We show how both systems may be viewed as involving cell-cell coupling, which may be direct (animals) or indirect (plants). (2) It leads to a new model for polarity coordination in plants. In contrast to previously proposed plant models, the model we propose does not invoke measurement of fluxes, comparison of concentrations between cells, response to physical stresses or measurement of gradients across the thickness of cell walls. (3) It allows different cell polarity systems to be placed in an evolutionary context.

To illustrate how intracellular partitioning may operate, we consider a simple system with two types of molecular component, A and B, the active forms of which will eventually define opposite ends of the cell. In reality, each component may comprise multiple molecular entities; for the sake of simplicity, here we treat each component as a single entity. The components can be in two states: an inactive cytosolic form, A or B, or an active membrane-bound form, A^* or B^* (Fig. 2A,B). The inactive forms diffuse more rapidly than the active membrane-bound forms. The active forms are autocatalytic (i.e. A^* promotes the activation of A to generate more A^*) and cross-inhibitory (i.e. A^* promotes deactivation of B^*, and vice versa). We refer to A, A^*, B and B^* as polarity components.

Starting from a uniform concentration of polarity components in a cell and small random fluctuations (noise) in the concentrations of A^* and B^* in the membrane, such a system may lead to a polarised distribution, with a high concentration of A^* at one end and B^* at the other end of the cell (Fig. 2C). This system is similar to other reaction-diffusion systems that generate polarity within individual cells (Meinhardt, 2007). With an initially uniform distribution of A^* and B^* across a tissue, and noise within cells (Fig. 3A), intracellular partitioning leads to polarities that are oriented randomly from one cell to the next (Fig. 3B,C; polarity is shown as pointing from the B^* to A^* cell ends in this figure and in all subsequent figures). Non-polarised cells arise if intracellular partitioning components are absent or fail to interact effectively.

We build on the notion of intracellular partitioning to generate a more coordinated polarity pattern by incorporating interactions at interfaces of neighbouring cells. This process of cell-cell coupling may lead to local alignment of polarities. Cell-cell coupling may involve direct molecular contacts between juxtaposed cells or indirect interactions mediated by diffusible molecules.

Assume that A^* in a given cell can physically interact with B^* in the juxtaposed membrane of its neighbour, forming an intercellular A^*-B^* bridging complex. We can modify the intracellular partitioning mechanism described above such that auto-activation and/or cross-inhibition are influenced by the A^*-B^* complex; for example, suppose the A^*-B^* complex inhibits A^* on the B^* side of the complex (Fig. 4A). Computer simulations of this system show that an initially uniform (but noisy) distribution of A^* and B^* in a single file of cells (Fig. 4C) can eventually give rise to regions of aligned polarity (Fig. 4D).

We can extend the role of the A^*-B^* complex such that all of the auto-activation and cross-inhibition interactions are dependent on it (Fig. 4B). In this case, uncomplexed A^* and B^* have no role other than allowing formation of A^*-B^* complexes, while the diffusible A and B forms still play a role in intracellular partitioning. This system also gives rise to regions of locally aligned polarity (Fig. 4E). With this model, an isolated cell (i.e. a cell with no neighbours) no longer becomes polarised because it is unable to form A^*-B^*complexes. Nevertheless, an individual cell within a group of cells that are incapable of polarising can become polarised through its own intracellular partitioning system (Fig. 4F,G). We use the latter model for all further simulations involving direct cell-cell coupling. A further step towards dependency on neighbours is illustrated by a model for tissue polarity proposed for Drosophila in which a diffusible component (C^*) creates an effective repulsion between the two orientations of the membrane-spanning complexes (A^*-B^* and B^*-A^*) (Burak and Shraiman, 2009). In this model, the B^* end of the complex promotes production of C^* within the same cell, which then inhibits the complexes in which A^* is located within that cell. Considering a cell in isolation this would lead to all complexes being oriented with B^* pointing into that cell, because inward-pointing B^* can inhibit inward-pointing A^* but not vice versa. In the presence of neighbouring cells, inhibition becomes mutual because inward-pointing A^* can now inhibit inward-pointing B^* by influencing the production of C^* in the neighbouring cell (via the B^* end of the complex, which points into the neighbour). Consequently, in such a model, polarisation of a cell depends on its neighbours also having an intact polarisation system. All above models can give rise to direct cell-cell coupling but can be distinguished experimentally by defining the cellular contexts under which individual cells can become polarised.

When applied to a 2D array of cells, direct cell-cell coupling models lead to locally coordinated groups of cells or swirled patterns of orientations (e.g. Fig. 4H) (Burak and Shraiman, 2009). In these cases, coordination is both longitudinal and lateral.

Consider again the direct cell-cell coupling model in which the only role of the A^*-B^* membrane-spanning complex is inhibition of A^* at the B^* end of the complex (Fig. 4A). With this system, A^* in one cell effectively inhibits formation of A^* in the juxtaposed membrane of its neighbour. In Fig. 5A, we show a parsimonious way of achieving an equivalent process without direct cell-cell contacts. In this case, A^* in one cell promotes export of a small mediator molecule, M (green dot), which can diffuse through the extracellular space. This extracellular M triggers a membrane receptor that then locally inhibits A^* in the membrane (i.e. M favours B^* over A^*). This system could allow A^* in the cell exporting M to inhibit A^* in its neighbour. However, an apparent problem is that extracellular M also causes inhibition of A^* in the exporting cell. This is because M affects both cells equally (Fig. 5A, dotted arrows). Thus, intuitively it seems unlikely that such a system would generate cell-cell coupling.

However, computer simulations show that this indirect system can generate longitudinal coordination of cell polarities in a single file of cells, despite extracellular M acting equally on both membranes at each cell-cell interface (Fig. 5B). In these simulations, we assume that both intracellular and extracellular M diffuse rapidly compared with A^* and B^*, and that M is produced and degraded at uniform rates in all cells. We also assume that M can move across the cell membrane independently of polarity components, with a higher permeability for cell entry than exit. A cell that has been polarised through intracellular partitioning thus exports M at the A^*-rich end and has a net passive import of M at other locations, giving a flow of M along its polarity. Because M flows in the same direction as the cell polarity, it tends to accumulate within cells at the end of the cell file to which the polarity points (right end in Fig. 5B). Thus, cells end up pointing towards a region with high intracellular M concentration.

To understand how polarity coordination arises with this system, consider a scenario in which all cells have their polarity aligned except for one cell, labelled R in Fig. 5C, which has opposite polarity compared with the others. In this situation, extracellular space at the A^* end of the R cell (left end) has high concentrations of extracellular M, because it is flanked on both sides by A^*-rich membranes (and A^* promotes export of M). These high levels of extracellular M diminish A^* at this end of the R cell (as M inhibits A^*), as well as along the adjacent membrane of its left neighbour. The other end of the R cell (right end) has low levels of extracellular M because M is transported away from the extracellular space on both sides. Low levels of M favour A^*, both along the right membrane of cell R, as well as along the adjacent membrane of its right neighbour. Although cell R is in an unfavourable situation along both membranes, its flanking neighbours are only so along one of their membranes. Taken together, these processes would therefore be expected to reverse the polarity of the R cell alone, and thus align it with the other cells of the file.

An attractive feature of indirect cell-cell coupling is that it does not require reading of gradients in M across the thickness of the extracellular space or gradients of M in the cytoplasm along the length of the cell. Indeed, in our implementation of indirect cell-cell coupling, we assume that the level of M is uniform both within the cytoplasm of a cell and across the thickness of the extracellular space, although the system also works if gradients of M are allowed to form within cells. The mechanism of indirect cell-cell coupling we present requires intracellular partitioning: if A^* and B^* do not auto-activate and cross-inhibit then cells have no polarity (Fig. 5D).

The same indirect cell-cell coupling model applied to a 2D array of cells leads to locally coordinated groups of cells, or swirled patterns of orientations, which are both laterally and longitudinally coordinated (Fig. 5E). Thus, the outcomes of indirect and direct cell coupling are comparable (compare Fig 4H with Fig. 5E).

The model of indirect cell-cell coupling arises naturally from the intracellular partitioning-based framework presented here and may be of particular relevance to plants. This is because the plant cell wall is a major barrier to direct interactions between proteins in the plasma membranes of adjacent cells. (There are channels through plant cell walls, called plasmodesmata, but it is currently unclear whether they play a role in control of tissue cell polarity.) Thus, cell-cell coupling in both plant and animal systems can be viewed as different elaborations of a common underlying system. By contrast, it is unclear how previous models, which do not incorporate intracellular partitioning (e.g. Burak and Shraiman, 2009), could be extended to both systems.

In many cases, cell polarity is coordinated across a large domain of tissue, such as a wing or leaf. Moreover, this polarity is related to the overall morphology of the structure, such as its proximodistal axis. Such organisation suggests that there are reference regions in the tissue that actively influence polarity and from where polarity information propagates. We refer to these reference regions as ‘tissue polarity organisers’ (Green et al., 2010). The term organiser has been used in several developmental contexts (e.g. Spemann and Mangold, 1924; Sabatini et al., 1999) but here we use it specifically in relation to the coordination of tissue cell polarity. Because cell polarity can be influenced to point away from or towards organisers, it is convenient to refer to two types of tissue cell polarity organiser, plus (+) or minus (-) respectively, according to their resultant effect on polarity. Although regions of organiser activity are often expected to be associated with sites of polarity divergence (+) or convergence (-), such polarity patterns are not sufficient to infer the presence of an organiser because they may also arise through polarity propagation from organisers located elsewhere. There are various mechanisms by which tissue cell polarity organisers may influence cell polarity over an extended domain. These mechanisms need not be mutually exclusive. We first consider direct modulations of polarity components, then tissue gradients and finally modulation of mediator levels for systems with indirect cell-cell coupling.

Cell-cell coupling together with intracellular partitioning generates swirls of polarity in a 2D array of cells (Fig 4H, Fig. 5E). To produce polarity that is coordinated with respect to the tissue, polarity components of this system can be modulated at tissue boundaries. With direct cell-cell coupling, for example, expression of only A and A^* in a column of cells at the left boundary of the tissue and only B and B^* in a column at the right boundary, results in a pattern in which polarity points from left to right across the tissue (Fig. 6A). The presence of only A^* in leftmost cells causes B^* to be elevated in the juxtaposed membrane of their right neighbours, through cell-cell coupling, giving the neighbours a rightwardly oriented polarity (cell polarity points from the B^*-rich to the A^*-rich end). The same effect then propagates through cell-cell coupling to the cells further along to the right. Similar considerations apply to the right boundary expressing only B^*. One limitation of using direct modulation of polarity components as organisers of tissue polarity is the restricted range over which polarity is coordinated (Burak and Shraiman, 2009).

We may simulate the effect of introducing mutant patches into this model, as these predict patterns that can be evaluated experimentally through creation of clones (Lawrence et al., 2007). When mutant patches are introduced, polarity reversals are generated in the surrounding tissue. For example, a mutant patch that lacks A^* (and thus only expresses B^*) exhibits polarity reversal towards the right end of the patch (Fig. 6B). The patch is effectively acting as a minus organiser. The outer cell border within the mutant patch exhibits inwardly oriented polarities with respect to B^* concentrations (polarity points away from the B^*-rich end). This is because the A^* in the wild-type neighbours draws B^* in mutant border cells towards them through cell-cell coupling. The resulting inwardly oriented polarity of mutant cells is restricted to cells on the border of the patch, as cells further in do not have neighbours with A^*.

For indirect cell-cell coupling, polarity coordination may arise in a similar manner (Fig. 6C). In this case, coordination arises because cells at the left boundary, which express only A^*, export M at all locations around their membranes (A^* promotes M export), whereas cells at the right boundary only import M (because they lack A^*). This creates a high level of extracellular M at the left boundary of the tissue and a low level at the right boundary. This situation favours A^* at the right end of the cells near the boundaries (extracellular M inhibits A^*), biasing the orientation of polarity to point rightwards. The level of intracellular M becomes high in the minus organiser at the right boundary, because cells continually pump M towards it.

Another way of coordinating tissue cell polarity is through concentration gradients. Suppose we have a concentration gradient along a single file of cells for a signalling molecule S (Fig. 7A). In principle, the distribution of S carries two types of information. One is the gradient along the length of each cell, as each cell has a higher concentration of extracellular S at its left compared with its right end (Fig. 7B). We refer to this as a cellular gradient. The other type of information is the gradient between cells: the average concentration of S surrounding a cell is higher than that for its right neighbour and lower than that for its left neighbour (Fig. 7C). We refer to this as an intercellular gradient. We next consider how the cellular and intercellular aspects of the S gradient may lead to coordinated polarity for 2D cell arrays.

We begin with an array of cells with an intracellular partitioning system but no cell-cell coupling. S is produced at a high rate by the leftmost cells, degraded at a high rate by the rightmost cells, and diffuses in the extracellular space producing a left-to-right graded decline in S concentration. Assume that the concentration of S at each location in the extracellular space can be sensed through a membrane-bound receptor for which S is a ligand, and that triggering of the receptor promotes local conversion of A to A^*. According to this system, each cell within the array will tend to have more A^* in the membrane at its left end, relative to its right end, because of the gradient in S across the cell. This will bias the intracellular partitioning process such that the A^*-rich end will form at the left of all cells. Because the gradient in S across the cell has the same orientation for all cells, cell polarities are oriented leftwards throughout the tissue, pointing up the S gradient (Fig. 8A). In this case, the left boundary cells producing S at a high rate serve as the minus organiser, whereas the right boundary where S is degraded at a high rate acts as a plus organiser.

With this system, coordination of polarity depends on the extent to which concentration gradients of S are aligned between cells. Polarity components are not directly involved in tissue coordination and thus act cell-autonomously. A patch that lacks A^*, for example, does not influence the polarity of the surrounding wild-type cells and the cells within the patch have no polarity (Fig. 8B). By contrast, a mutant patch with a high degradation rate of S will influence the polarity of the tissue surrounding it by influencing neighbouring cellular concentration gradients (Fig. 8C). The gradient across cells near the right end of the patch will be reversed because they are adjacent to a region with low S concentration. As this mechanism depends on cellular gradients in S, it may become less effective for larger tissues as the gradient becomes shallow.

The above analysis assumes that cellular gradients in S act on a system with intracellular partitioning but no cell-cell coupling. If the system incorporates cell-cell coupling, similar results are obtained, except that a mutant patch lacking A^* shows polarity reversal (at its left end, Fig. 8D). In addition, incorporation of cell-cell coupling allows coordinated polarity to extend further into the regions where the gradient in S is shallow (data not shown).

Consider a case in which extracellular S is graded across the tissue and that it promotes production of a factor, F, within each cell, in proportion to the total level of S in the cell surroundings. In this case, the gradient in extracellular S leads to a stepped response, corresponding to the level of F in each cell. F is uniform within each cell but is graded across the tissue so that each cell has a higher level of F than its right neighbour, forming an intercellular gradient (Fig. 9A). Suppose that F within a cell increases production of the A polarity component above a basal rate of F-independent production. For example, F might be a transcription factor involved in generating A. In this situation, a higher level of F in the cell leads to raised levels of both A and A^* (the concentration of A^* is dependent on A). Thus, each cell has a neighbour to its left with a slightly higher overall concentration of both A and A^* (except for cells at the left boundary, which have no left neighbours). If we assume this promotion of A levels operates in a system with direct cell-cell coupling, the slight excess of A^* in the left neighbour will tend to bias B^* towards the left of the cell. Polarity will therefore be coordinated to point left to right (from B^*-rich to A^*-rich ends) across the tissue (lateral and longitudinal coordination). Thus, even in the absence of intracellular gradients in F, an organised pattern of tissue cell polarity emerges (Fig. 9A). In contrast to the cellular gradient mechanism, in this case a high level of S (and thus F) corresponds to a plus organiser whereas a low level corresponds to a minus organiser, even though in both cases S is enhancing A^* (compare polarity orientations in Fig. 8A and Fig. 9A). A mutant patch that lacks A^* causes polarity reversal at its right end (Fig. 9B). The outer cell border within the mutant patch exhibits inwardly oriented polarities with respect to B^* concentrations, as described earlier (Fig. 6B and Fig. 8D). Similar results have been obtained with other direct cell-cell coupling models (Le Garrec et al., 2006; Burak and Shraiman, 2009).

For systems based on indirect cell-cell coupling, tissue cell polarity organisers may also act by influencing mediator (M) production or degradation. If M is produced at a higher rate in the column of cells at the left boundary and degraded at a higher rate in the column at the right, then polarity can become organised across the tissue, pointing from left to right (lateral and longitudinal coordination, Fig. 10A). This coordination partly arises because the gradient in extracellular M across the cells, generated by non-directed transport, inhibits A^* at the left end of each cell, biasing polarity. However, in the absence of indirect cell-cell coupling this would only coordinate polarity of cells near the boundaries, as shown in simulations in which A^* does not affect export of M (Fig. 10B). Incorporation of indirect cell-cell coupling then allows this coordination to propagate through the tissue (Fig. 10A). In this situation, the leftmost column of cells is acting as a plus organiser while the rightmost column acts as a minus organiser.

According to this model, the plus organiser corresponds to a region that produces M at a high rate while the minus organiser corresponds to a region that degrades M. The steady-state intracellular level of M is high in plus organiser regions and low in minus organiser regions. If the degradation rate of M in the right file is not sufficiently high, then M can accumulate in the rightmost column of cells through transport. This accumulation in turn leads to high levels of extracellular M at the right boundary, which may lead to polarity disruption as the cells at the right boundary switch from being sinks to sources of M (Fig. 10C). This effect may be counteracted if cells in the rightmost column are unable to export M (e.g. the lack A^*, Fig. 10D). In this situation, the cells on the right can accumulate intracellular M through transport towards them, while their extracellular M is kept low because of the higher permeability of cells to M entry than M exit. Thus, the plus organiser at the left boundary now has low levels of intracellular M as it has a high net rate of M influx, whereas the minus organiser at the right boundary has high levels of intracellular M as it imports M at a high rate. A similar result is obtained if cells at the right boundary import M at a higher than basal rate, instead of exporting M at a reduced rate.

In all cases, M flows along the direction of polarity, but it can appear to flow either to a region with high intracellular M concentration (Fig 5B; Fig. 10D) or low intracellular M concentration (Fig. 10A), depending on whether organisers influence production and degradation of M and/or export and import of M.

Our simulations for single cell files show that cell-cell coupling provides an effective mechanism for longitudinal coordination of polarity (Fig. 4D,E; Fig. 5B). However, analysis of 2D arrays shows that cell-cell coupling also generates a degree of lateral coordination, illustrated by swirled patterns of polarity (Fig. 4H; Fig. 5E). Lateral coordination may arise because cells are not organised in distinct files in the 2D arrays, but are interlaced. To test this idea, we applied cell-cell coupling to a 2D array comprising a grid of square cells. With this cellular configuration, broad swirls of polarity are no longer observed (Fig. 11A,B). Instead, polarity can be coordinated longitudinally along single cell files, with lateral neighbours often showing opposite polarities as this pattern maximises contact between A^* and B^* in neighbours. However, in contrast to coordination systems based on cell-cell coupling, those involving intracellular partitioning combined with cellular gradients (Fig. 8A-C) are relatively insensitive to cell geometry (Fig. 11C). This is because cell polarity orientation is determined by cell-autonomous reading of the gradient in S and is thus independent of cell neighbours.

These simulations illustrate the effect of cell shape and configurations on cell-cell coupling mechanisms in regular arrays. However, in many biological situations, cells do not have completely regular geometries and sizes. Irregularities are inevitable during periods of cell proliferation if cells divide asynchronously and do not rearrange rapidly. If we apply cell-cell coupling systems to a grid of cells with irregular shapes, both lateral and longitudinal coordination still occur, as evidenced by swirled patterns, but are less effective than with hexagonal cells using the same parameters (Fig. 11D,E, compare with Fig. 4H; Fig. 5E). Similar effects of lattice disorder on polarity coordination have been described for other models that invoke cell interface interactions (Ma et al., 2008). With irregular cell geometries, organisers of tissue polarity lead to polarity coordination, although this is less effective than for hexagonal cells (Fig. 11F-I, compare with Fig. 6A,C; Fig. 9A and Fig. 10A).

The examples described above show how the intracellular partitioning-based framework provides a possible explanation for the generation of tissue cell polarity in plants and animals. Intracellular partitioning alone provides a mechanism for generating individual cell polarity in the absence of asymmetric cues. This establishes a ground state of randomly oriented polarities. This process may be modified by incorporating cell-cell coupling, which leads to local alignment of polarities. We show that cell-cell coupling can operate both directly, through membrane-spanning complexes, or indirectly, through mediator molecules. Incorporation of cell-cell coupling can lead to coordination of polarity across a tissue by selective expression of polarity components in boundary domains. Tissue coordination may be further enhanced through tissue gradients, which may operate at the cellular and/or intercellular level. Several of these mechanisms may act synergistically to establish and maintain polarity over extended domains. These systems can coordinate polarity for tissues with irregular cell geometries generated by cell division and growth, although coordination is less consistent than for regular hexagonal arrays.

To illustrate how the framework outlined above can be used in different contexts, we apply it to some well-studied examples in animals and plants.

One of the best-studied tissue cell polarity systems in animals involves polarised orientation of hairs or bristles in Drosophila (Goodrich and Strutt, 2011). The Drosophila wing, for example, comprises two juxtaposed sheets of cells, with each cell producing a distally pointing hair near its distal vertex. Several mutants, such as frizzled (fz) and Van Gogh (Vang, also known as strabismus) have been identified that disrupt this coordinated pattern. Evidence that these genes play a role in polarity coordination comes from analysis of clonal patches of mutant tissue. Such patches exhibit reversal of polarity for a few rows of wild-type cells at one end of the clone. In some cases, such as fz^- clones, polarity is reversed at the distal end of the clone; in other cases, such as Vang^- clones, polarity is reversed at the proximal end of the clone. Fz is a seven-pass transmembrane protein and is localised to the distal end of developing wing cells, whereas Vang is a four-pass transmembrane protein and is localised at the proximal end. These proteins interact with cytosolic proteins that also show polarised distributions: Dishevelled (Dsh) and Diego (Dgo) are localised at the distal end; and Prickle (Pk) is localised at the proximal end. In addition to these components, a seven-pass transmembrane cadherin protein Flamingo [Fmi, also known as Starry Night (Stan)] is present at both proximal and distal ends. Fmi most likely acts as a bridge between complexes on membranes of neighbouring cells (Usui et al., 1999; Lawrence et al., 2004; Strutt and Strutt, 2007). These six proteins (Fz, Vang, Dsh, Dgo, Pk and Fmi) have been placed in the same pathway: the core PCP pathway (Strutt and Strutt, 2009).

The observation of polarity reversals in the tissue surrounding mutant patches suggests that the core PCP genes are involved in one or more aspects of polarity coordination. In principle, they could encode components of a cell-cell coupling system (Fig. 9B), or be involved in enhancing degradation or production of a signalling molecule S (Fig. 8C). Two findings support their participation in cell-cell coupling. First, pathway components have polarised cellular locations. Such a localisation is expected if they are polarity components but not if they are involved in production or degradation of S. Second, reorientation of polarity occurs within fz^- mutant tissue in a single cell layer that abuts Fz-expressing tissue (Lawrence et al., 2004), as expected for cell-cell coupling models, in which mutant regions contain a single layer of polarised cells (Fig. 6B; Fig. 8D; Fig. 9B). By contrast, there is no expectation that polarity would extend for only a single cell if Fz influenced the level of S, as a change in the gradient of S could, in principle, extend over several cells.

Several models based on direct cell-cell coupling have been proposed for how the core PCP pathway operates. These models have been designed to account for the observed polarity patterns in mutants, clonal patches, protein localisation and protein interactions. However, the formal relationships between the models have been unclear because each model has been presented as an individual solution. We next view these models through the framework described here so as to highlight their essential features (i.e. whether they involve intracellular partitioning, cell-cell coupling, cellular or intercellular gradients) and clarify experiments that might distinguish between them.

One model invokes interface interactions combined with intracellular bias (Amonlirdviman et al., 2005). Complexes are formed at each end of the cell, corresponding to the A^* and B^* components in the framework presented here. The A^* complex involves Fz and Dsh, whereas the B^* complex involves Vang and Pk. There is a bias in each cell such that higher levels of the A^* complex are promoted at the distal end. Formation of the A^* complex in one membrane promotes formation of the B^* complex in the juxtaposed membrane of the neighbouring cell via interactions between Fz and Vang. Antagonism between A^* and B^* is mediated by B components Pk and Vang, which inhibit the formation of A^* (Dsh binding to Fz). This system is equivalent to having direct cell-cell coupling combined with cellular gradients.

A second model involves cell interface interactions combined with a ligand that is high at the proximal end of the wing and declines distally (Le Garrec et al., 2006). The ligand is graded both along the length of each cell and between cells, and is needed to activate Fz, which then interacts with other components (Dsh, Dgo and Fmi) to generate A^*. A^* in the membrane of one cell can form a complex with B^* (Vang, Pk, Fmi) in the juxtaposed membrane of the neighbouring cell via Fmi bridges. All polarity components can diffuse, except for the bridged A^*-B^* complex. Inhibition between A^* and B^* is mediated by A components (Dsh and Fz) that inhibit formation of fully active B^* (Vang, Pk, Fmi). With the parameters used in the model, the intercellular gradient in the ligand leads to a Fz-containing complex being localised distally within each cell. This system is equivalent to direct cell-cell coupling combined with intercellular gradients.

A third model for PCP in Drosophila involves membrane-spanning complexes, with one orientation of the complex across the membrane (A^*-B^*) inhibiting formation of complexes with the opposite orientation (B^*-A^*) (Burak and Shraiman, 2009). There is an inhibitory messenger molecule (C^*) that diffuses within each cell, creating an effective repulsion between the two possible orientations of the complex when cells have neighbours, thus ensuring that they become localised to the opposite ends of a cell. Tissue coordination is generated most effectively by an intercellular gradient. This model is also equivalent to direct cell-cell coupling combined with intercellular gradients.

The first two models assume that polarity is generated in the context of gradients across or between cells (Amonlirdviman et al., 2005; Le Garrec et al., 2006). Cells would therefore be expected to be unpolarised with respect to the PCP proteins in the absence of asymmetric cues, such as ligand or expression gradients. Thus, individual cell polarity is fully dependent on global gradients across the tissue. This dependency does not apply in the case of the third model, because this mechanism generates swirls of polarity in the absence of a global orienting signal (Burak and Shraiman, 2009). However, with this model there is still a strong dependency on neighbours, as a cell cannot become polarised unless its neighbours are polarisable. Thus, it should not be possible, experimentally, to produce a single polarised cell. A further step towards independence from neighbours is given by the models described here. These systems have the potential to produce single polarised cells through intracellular partitioning, even when neighbours lack the ability to polarise (Fig. 4G). Each of these models could operate for Drosophila PCP, but they can be distinguished experimentally by testing the extent to which polarisation of individual cells depends on neighbours and global gradients.

All of the above models involve direct cell-cell coupling, but a seemingly different type of model has been proposed based on cell-cell comparisons (Adler et al., 1997; Lawrence et al., 2004). According to this model, cells compare levels of Fz activity with their neighbours, via Fmi bridges, and orient polarity so as to point to the neighbour with lowest Fz activity. However, this model does not provide an explicit mechanism for how cells are able to compare Fz concentrations with their neighbours, or how individual cell polarity is established and becomes aligned with the Fz activity gradient. As shown in our theoretical analysis and by others (Le Garrec et al., 2006; Burak and Shraiman, 2009), the combination of direct cell-cell coupling and intercellular tissue gradients can lead to cells orienting polarities according to differences in the level of polarity components (i.e. the level of A^*, Fig. 9). The system behaves as if cells are comparing levels with neighbours and orienting their polarity accordingly. However, this behaviour is not an explicit input to the model but an outcome of molecular interactions. Thus, cell-cell comparison models can be seen as a different level of description rather than being contradictory to direct cell-cell coupling models.

A further complication with evaluating models is that the core PCP genes do not provide the only polarity components. If they did, then mutants in these genes would be expected to produce cells that lack polarity. This result is observed with respect to the position in the cell where the hair initiates: complete loss of core PCP proteins leads to hairs initiating in the cell centre instead of distally (Wong and Adler, 1993). However, with regard to hair orientation, individual cell polarity is still evident in the mutants, as each cell hair does not point vertically out of the tissue plane but in a direction along the plane. Moreover, this individual cell polarity is still coordinated to some extent between neighbours, giving swirls or broad domains of alignment (Wong and Adler, 1993). These observations suggest that the polarity system has redundancy and does not only depend on the core PCP pathway. In tissues such as the abdomen, some of this redundancy reflects the operation of a second pathway, involving the Fat (Ft) and Dachsous (Ds) cadherin proteins (Lawrence et al., 2007). However, even double mutants that lack activity in both the core PCP and Ft/Ds pathways have hairs pointing along the plane of the tissue; they even show swirled organisation in some areas (Casal et al., 2006), indicating that further levels of redundancy are involved. In support of this conclusion, a fz-independent system based on septate junction proteins Gliotactin (Gli) and Coracle (Cora) has been described that is also involved in alignment of hair polarity (Venema et al., 2004).

A further question is how do organisers act to coordinate polarity over the tissue? For example, hairs point distally with respect to the Drosophila wing. This suggests that organisers are most likely to be located at the hinge region at the proximal edge of the wing and/or at the distal tip of the wing, which is defined by the intersection of the anteroposterior and dorsoventral compartment boundaries (see Goodrich and Strutt, 2011). Tissue boundaries are thus expected to be locations where polarity components are modulated, and/or sources or sinks of underlying tissue gradients. Wing cells exhibit irregular shapes at early stages when cells are still dividing (Classen et al., 2005). At these stages, PCP proteins, such as Vang, already show preferential orientations towards the wing margin (Aigouy et al., 2010). Thus, coordinated polarity of core PCP proteins occurs in the context of irregular cell geometries. Such coordination may arise through organisers that are based on the modulation of polarity components and/or tissue gradients (Fig. 11F,H).

Evidence for tissue gradients playing a role comes from analysis of planar polarity in the Drosophila eye. Cells in the eye become polarised through preferential distribution of the cadherin Ds (A^*) to one cell end and its binding partner the cadherin Ft (B^*) to the opposite cell end (Ambegaonkar et al., 2012; Brittle et al., 2012). Planar polarity patterns are specified by opposite gradients in expression of Ds and the Golgi-associated protein Four-jointed (Fj) (Simon, 2004). Fj expression is highest at the equator whereas Ds expression is highest at the pole. As these transcriptional gradients operate through the nucleus, they act at the intercellular level. As shown in Fig. 9, an intercellular gradient in A^* levels is expected to orient polarity such that the B^*-rich end of the cell is oriented towards regions with higher A^* expression. This is consistent with the observation that Ft-rich (B^*-rich) ends are oriented towards regions with higher Ds (A^*) expression at the pole. Fj has been proposed to modify Ft or Ds so that the ability of Ft (B^*) to form intercellular bridges is enhanced relative to Ds (A^*) (Brittle et al., 2010; Simon et al., 2010). Thus, the expression gradient in Fj is equivalent to an intercellular gradient in B^* levels, and should orient the A^*-rich end of the cell towards regions with higher B^* (Fj) expression. Consistent with this expectation, Ds-rich ends are oriented towards regions with high Fj expression at the equator. The tissue gradients in Ds and Fj expression depend on graded distributions of morphogens, such as Wingless, that emanate from tissue and compartment boundaries. Thus, in terms of our framework, graded Wingless levels take the place of S, regulating the expression of Ds and of Fj.

The most intensively studied tissue cell polarity system in plants involves localisation of the PIN auxin efflux carriers (Krecek et al., 2009). Several PIN proteins, such as PIN1, PIN2, PIN3, PIN4 and PIN7, can exhibit coordinated polarised distributions within cells of particular tissues. For example, PIN1 in the root is located at the basal (rootward) end of vascular cells, whereas PIN2 is at the apical (shootward) end of epidermal cells (Blilou et al., 2005). PIN tissue cell polarity is also related to sites of high auxin concentration. Auxin maxima, for example, are observed at regions around which PIN polarities are orientated, such as the quiescent centre of the root tip and the centre of initiating leaf primordia (Blilou et al., 2005; Heisler et al., 2005). The PIN polarity pattern can also be influenced by application of auxin, suggesting that auxin may feed back to influence the polarity of the cells that transport it (Jönsson et al., 2006; Smith et al., 2006).

Several models have been proposed to account for how tissue cell polarity of PIN proteins is established. In one type of model, cells become polarised if they sense that their neighbours have different auxin concentrations. PIN proteins then become localised to the cell end with the highest auxin level in its neighbour (Bayer et al., 2009; Jönsson et al., 2006; Smith et al., 2006; Sahlin et al., 2009). This leads to auxin flowing up intercellular auxin gradients. Such up-the-gradient cell-cell comparison models can account for observed PIN1 and auxin distributions, and spacing patterns between organ primordia (phyllotaxy). However, these models raise the question how do cells sense auxin levels in their neighbours or align their polarity accordingly? One possibility is that disparities in auxin concentrations between adjacent ends of neighbouring cells generate differential physical stresses in the cell wall between them. If the cell preferentially allocates PINs to its membranes next to walls under the highest stress (corresponding to those interfaces that have the highest auxin increase from the cell to its neighbour), PIN polarity would arise (Heisler et al., 2010).

In another type of model, cells become polarised if there is a flux of auxin across them. Cells detect the level of net auxin flux at cell-cell interfaces and localise PIN molecules to the membranes with maximum flux out of a cell (Rolland-Lagan and Prusinkiewicz, 2005; Stoma et al., 2008; Bayer et al., 2009). This leads to polarity being aligned with the direction of auxin flow. An advantage of these with-the-flux models is that they can account for observed venation patterns, as these arise through formation of channels of high auxin flux (canalisation). However, mechanisms for flux sensing remain to be identified.

An alternative model for aligning polarity with the direction of auxin flow is that cells detect auxin gradients across the thickness of cell walls through a diffusible auxin receptor, with a diffusion constant that is decreased by auxin binding (Wabnik et al., 2010). PINs are then preferentially localised to the membrane with the higher auxin signal. This model can also recapitulate observed patterns of PIN polarisation during formation of vasculature. However, it is unclear whether the candidate auxin receptor protein [ABP1 (Sauer and Kleine-Vehn, 2011)] has the required auxin-dependent mobility within a cell wall, and whether auxin gradients across the thickness of a cell wall would be sufficiently large, given the thinness of the wall and the high diffusion rate of auxin.

The intracellular partitioning-based framework presented here represents a further type of model for tissue cell polarity of PIN proteins. Unlike the above models, which assume that a cell does not become polarised in the absence of auxin gradients or flux across it, we propose that cells can become polarised even in the absence of asymmetries in auxin, through intracellular partitioning. Auxin then acts as a mediator, M, that coordinates polarities through indirect cell-cell coupling. As shown in the theoretical examples, if the A^* component leads to enhanced PIN activity (M export) and extracellular auxin (M) inhibits A^*, polarities become co-aligned with directions of auxin flow, similar to the outcome of with-the-flux models. According to the intracellular partitioning-based model, polarity points away from regions with high extracellular auxin (plus organisers) and towards regions with low extracellular auxin (minus organisers). However, the level of intracellular auxin need not correlate with these extracellular levels. Intracellular auxin can be high at a plus organiser because of high auxin production rates (Fig. 10A) or it may be high at a minus organiser because auxin may accumulate there through transport (provided that extracellular auxin is kept low; Fig. 6C, Fig. 10D). The latter outcome is consistent with polarities pointing towards regions with high expression of auxin-inducible gene markers, such as DR5 (Heisler et al., 2005). Thus, the intracellular partitioning-based model is equally compatible with observed PIN polarity patterns associated with up-the-gradient or with-the-flux models. There have been other approaches to reconciling these patterns using a unified mechanism (Bayer et al., 2009; Stoma et al., 2008; Merks et al., 2007). However, unlike these models, our model does not invoke cell-cell comparisons or measurements of flux. Our model also does not involve detection of stresses or detection of gradients across cell walls. Instead, alignments arise through the interplay between intracellular partitioning and auxin transport processes.

A distinctive feature of the model proposed here is that there is a separable mechanism for intracellular partitioning. Candidate components for intracellular partitioning are the Rho-GTPases, a family of small G-proteins that may be either membrane bound or cytosolic (Yang, 2008). The inactive form is released from the membrane and becomes cytosolic through interaction with guanine nucleotide dissociation inhibitor proteins (GDIs). In animals, polarity of migrating cells is associated with segregation of different members of the Rho-GTPase family, typically with high levels of active Rac and Cdc42 (equivalent to A^*) at the front region of the cells and high levels of active Rho (e.g. B^*) at the back region. Computational modelling has shown that this asymmetry can be accounted for through mutual inhibition of the A^* and B^* forms, together with faster diffusion of the cytosolic GDI-linked A and B forms (Marée et al., 2006; Jilkine et al., 2007). A similar model might underlie polarity of pavement cells in plants. Here, different members of Rho-like GTPases from plants, called ROPs, are thought to antagonise each other such that ROP2 (equivalent to A^*) becomes localised to regions that form protrusions (lobes), while ROP6 (e.g. B^*) becomes localised to indentation (Fu et al., 2005; Xu et al., 2010). As with the model for animal cells, the inactive cytosolic forms, which are associated with GDIs, play a key role in allowing the pattern to form.

If intracellular partitioning through ROPs is linked to tissue polarity with auxin acting as mediator, ROPs would be expected to influence auxin transport, while auxin levels should influence ROPs. Localisation of PIN1 is correlated with that of ROP2 and its effectors in pavement cell lobes, consistent with ROP2 enhancing local PIN1 levels and thus auxin export (Xu et al., 2010). Auxin has also been shown to activate ROPs within minutes through a local membrane-bound auxin receptor (ABP1), consistent with auxin feeding back to influence intracellular partitioning (Xu et al., 2010). Based on these findings, it is feasible that an indirect cell-cell coupling model could coordinate polarity between neighbouring pavement cells, where active ROP2 (A^*) increases auxin efflux, through promoting functional PIN1 localisation. In this instance, indirect cell-cell coupling would apply to interdigitation between adjacent cells, but the principles are very similar to those described here for indirect cell-cell coupling as applied to tissue cell polarity.

Many aspects of our intracellular partitioning-based framework for plant tissue cell polarity remain to be explored and tested further. For example, the framework predicts that cells should be able to polarise in the absence of asymmetric cues. It has been shown that separation of plant cells by cell wall digestion and protoplast formation leads to a loss of asymmetric PIN1 localisation (Boutté et al., 2006), which could be taken as evidence against intracellular partitioning. However, it is unclear whether such treatments affect activity of polarity components and also whether polarity has indeed been fully lost, as PIN1 is not a determinant of intracellular partitioning but only a target that enables cell-cell coupling. Thus, further polarity markers and ways of generating cells in uniform environments are needed.

Another prediction is that polarity should point away from regions with high extracellular auxin. At first sight, this prediction seems inconsistent with experiments in which microdroplets containing auxin are applied to apical meristems (Bayer et al., 2009). PIN polarity is seen to converge towards the site of auxin application, suggesting that polarity is being oriented up the extracellular auxin gradient. However, these experiments do not lead to the generation of polarity convergence points in new locations, but at positions at which primordia are about to emerge (I2 positions). It is therefore possible that auxin application is simply accelerating formation of a pattern that is nascent in the meristem, rather than specifying a new convergence point.

A further prediction concerns the effect of cell ablation. PIN polarity has been shown to be oriented away from sites of ablation in nearby cells (Heisler et al., 2010). The local effect of ablation is not disrupted by the auxin transport inhibitor NPA or by uniform application of external auxin; observations that have been taken to suggest that mechanical signals rather than auxin transport are responsible for coordinating PIN polarity (Heisler et al., 2010). An alternative explanation is that cell ablation causes an increase in extracellular auxin, which orients polarity according to the model described here. We show that, even in the absence of active efflux (i.e. when A^* does not promote M export), coordination of polarity can extend over a few cells because of the gradient in extracellular auxin across the cells, generated by non-directed transport (left cells of Fig. 10B). Uniform application of external auxin need not disrupt polarity coordination as local gradients may still arise and be propagated through indirect cell-cell coupling.

A further test would be to determine whether polarity organisers act in the manner predicted. According to the intracellular partitioning-based framework, organisers correspond to regions where intracellular partitioning components or mediator (auxin) levels are modulated. This modulation could involve ROP/GDI activity, auxin biosynthesis (Zhao, 2010), auxin export (Křeček et al., 2009), auxin conjugation (Ludwig-Müller, 2011) or auxin import (Yang et al., 2006). These processes would therefore be targets of genes expressed in candidate regions of organiser activity, such as the root tip, base and tip of organ primordia, or base and tip of leaf serrations. Genes expressed in such boundary domains have been described and include LATERAL SUPPRESSOR, members of the NAC and LBD families and PLETHORA (Greb et al., 2003; Aida et al., 2004; Aida and Tasaka, 2006; Majer and Hochholdinger, 2011). It should be possible to test whether these genes influence polarity components and auxin distributions in a manner predicted by the intracellular partitioning-based framework.

In the framework for plant tissue polarity presented here, we make several simplifying assumptions. For example, we assume that all cells have the same level of PIN and that there is no feedback of intracellular auxin levels on PIN expression or auxin import. More elaborate models that incorporate modulation of PIN levels may allow the framework to be extended and account for patterns such as phyllotaxy, venation or reflux loops.

We show how tissue cell polarity may be established through an intracellular partitioning-based framework. Intracellular partitioning components can be modulated by incorporating interface interactions to produce cell-cell coupling that generates local alignment. Alignment across a tissue is established through tissue polarity organisers that are typically located at boundary regions. These organisers can act by modulating polarity components directly and/or through tissue gradients. We have shown how this framework can be applied to both animal and plant systems. A distinctive feature of animal cells is that molecules may bridge from one cell to another, allowing direct cell-cell coupling. Plant cells, however, are separated by cell walls, and polarities may be coupled more indirectly through transport of small mediator molecules such as auxin.

The intracellular partitioning-based framework allows different cell polarity systems to be placed in an evolutionary context. Cell polarity can be exhibited by individual cells in the absence of external molecular asymmetries (Wedlich-Soldner and Li, 2003). This is evident both for unicellular organisms, such as yeast (Johnson et al., 2011; Mogilner et al., 2012), and for individual cells from multicellular organisms, such as fish epidermal keratocytes (Verkhovsky et al., 1999; Marée et al., 2012) and isolated plant xylem cells (Oda and Fukuda, 2012). Thus, systems for generating intracellular partitioning are widespread and evolutionarily ancient, suggesting that they may provide a basic building block for establishing tissue polarity (Meinhardt, 2007). The tissue polarity mechanisms observed in plants and animals would then reflect the distinct constraints of each system during the evolution of multicellularity from unicellular ancestors, which already possessed intracellular partitioning systems. In animals, systems may have evolved in which individual cell polarities have become completely dependent on cell-cell interactions, so that intracellular partitioning no longer operates for a cell in isolation. These may represent evolutionary derived states, much as the mitochondria and chloroplasts may be viewed as derived states in which a prokaryote becomes completely dependent on its cellular host and no longer operates in isolation.

Many of the components and predictions of the intracellular partitioning-based framework remain to be tested. The framework thus provides a unifying and testable working hypothesis for tissue polarity that serves to guide further experimental and theoretical studies.

We thank Emily Abrash, Paul Adler, Desmond Bradley, Jordi Chan, Florent Patin, Jean-François LeGarrec, Xana Rebocho, Anne-Gaelle Rolland Lagan, Susana Sauret-Güeto and Georg Walther for helpful discussions and comments on the manuscript. We also thank Erika Kuchen for providing the image used in Fig. 1B.