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

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

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

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

Percolation in a reduced equilibrium model of planar cell polarity

Planar cell polarity (PCP) is a biological phenomenon where a large number of cells get polarized and coordinatedly align in a plane. PCP is an example of self-organization through local and global interactions between cells. In this work, we have used a lattice-based spin model for PCP that mimics the alignment of cells through local interactions. We have investigated the equilibrium behavior of this model. In this model, alignment of cells leads to the formation of clusters of aligned cells, and such clustering exhibits percolation transition. Even though the alignment of a cell in this model depends upon its neighbors, finite-size scaling analysis shows that this model belongs to the universality class of simple two-dimensional random percolation.

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

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

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

A dynamically diluted alignment model reveals the impact of cell turnover on the plasticity of tissue polarity patterns

The polarization of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganization in response to an opposing instructive cue, which we here consider using the example of experimentally inducible body axis inversions in planarian flatworms. We define a dynamically diluted alignment model linking three processes: entrainment of cell polarity by a global signal, local cell-cell coupling aligning polarity among neighbours, and cell turnover replacing polarized cells by initially unpolarized cells. We show that a persistent global orienting signal determines the final mean polarity orientation in this stochastic model. Combining numerical and analytical approaches, we find that neighbour coupling retards polarity pattern reorganization, whereas cell turnover accelerates it. We derive a formula for an effective neighbour coupling strength integrating both effects and find that the time of polarity reorganization depends linearly on this effective parameter and no abrupt transitions are observed. This allows us to determine neighbour coupling strengths from experimental observations. Our model is related to a dynamic 8-Potts model with annealed site-dilution and makes testable predictions regarding the polarization of dynamic systems, such as the planarian epithelium.

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

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

Formation of polarity convergences underlying shoot outgrowths

The development of outgrowths from plant shoots depends on formation of epidermal sites of cell polarity convergence with high intracellular auxin at their centre. A parsimonious model for generation of convergence sites is that cell polarity for the auxin transporter PIN1 orients up auxin gradients, as this spontaneously generates convergent alignments. Here we test predictions of this and other models for the patterns of auxin biosynthesis and import. Live imaging of outgrowths from kanadi1 kanadi2 Arabidopsis mutant leaves shows that they arise by formation of PIN1 convergence sites within a proximodistal polarity field. PIN1 polarities are oriented away from regions of high auxin biosynthesis enzyme expression, and towards regions of high auxin importer expression. Both expression patterns are required for normal outgrowth emergence, and may form part of a common module underlying shoot outgrowths. These findings are more consistent with models that spontaneously generate tandem rather than convergent alignments.

DOI:http://dx.doi.org/10.7554/eLife.18165.001

Plants, unlike animals, are able to grow and develop throughout their lives. New leaves and flowers are made from outgrowths that constantly form at the tip of growing shoots. Groups of cells in the outer layer of the shoot tip arrange a protein called PIN1 so that it is more abundant on the cell surfaces that face towards the centre of the group. PIN1 transports a hormone called auxin out of plant cells and this “convergent” arrangement of PIN1 increases the levels of auxin in cells at the centre of the group, leading to the formation of a new outgrowth. However, it is not clear what causes these cells to position their PIN1 proteins in this way.

Several hypotheses have been proposed to explain how convergent patterns of PIN1 form. For example, according to the “up-the-gradient” hypothesis, PIN1 is allocated to the end of a cell that is next to a cell with a higher level of auxin. Abley et al. have now compared predictions from computer models with new experimental data from a plant called Arabidopsis to evaluate three hypotheses for how convergent PIN1 patterns form. A computer model based on the up-the-gradient hypothesis naturally creates convergent PIN1 patterns, even if each cell starts off with the same level of auxin. On the other hand, models based on two other hypotheses generate tandem alignments of PIN1 so that auxin is transported in the same direction along lines of cells.

Next, Abley et al. tested these models using mutant Arabidopsis plants that develop outgrowths from the lower surface of their leaves. These outgrowths form in a similar way to outgrowths at the growing shoot tip, but in a simpler context. The experiments show that the patterns of where auxin is produced in growing leaves were more compatible with the tandem alignment models than the up-the-gradient model. This suggests that plants use a tandem alignment mechanism to form convergences of PIN1 proteins that generate the local increases in auxin needed to make new outgrowths.

This study only examined a single layer of cells on the plant surface. Other cell layers also show highly organised patterns of PIN1 proteins, so a future challenge is to extend the approach to study the entire 3D structure of new shoot outgrowths.

DOI:http://dx.doi.org/10.7554/eLife.18165.002

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

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