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

Elucidate growth control mechanisms using reconstructed spatiotemporal distributions of signaling events

A fundamental biological question is how diverse and complex signaling and patterning is controlled correctly to generate distinct tissues, organs, and body plans, but incorrectly in diseased cells and tissues. Signaling pathways important for growth control have been identified, but to identify the mechanisms their transient and context-dependent interactions encode is more difficult. Currently computational systems biology aims to infer the control mechanisms by investigating quantitative changes of gene expression and protein concentrations, but this inference is difficult in nature. We propose it is desirable to explicitly simulate events and orders of gene regulation and protein interactions, which better elucidate control mechanisms, and report a method and tool with three examples. The Drosophila wing model includes Wnt, PCP, and Hippo pathways and mechanical force, incorporates well-confirmed experimental findings, and generates novel results. The other two examples illustrate the building of three-dimensional and large-scale models. These examples support that reconstructed spatiotemporal distributions of key signaling events help elucidate growth control mechanisms. As biologists pay increasing attention to disordered signaling in diseased cells, to develop new modeling methods and tools for conducting new computational studies is important.

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.

Boundary propagation of planar cell polarity is robust against cell packing pattern

Planar cell polarity is an important property of epithelial tissue. The boundary propagation model was proposed as the mechanism of PCP induction, while it has been doubted whether it can induce PCP on wide tissue. Using simulation, a set of proteins can be shown to induce PCP, but it does not explain why and how the set can induce PCP. In this study, we made theoretical model and simulation model to explore when and how the boundary propagation induce PCP. We incorporated multipolar cell in our model. Intracellular interactions have been thought to amplify polarity of a cell, but we propose instead that they are to keep a cell-cell interface polarized, and bipolarity of cell is obtained as a result. We show that the boundary propagation can propagate polarity as long as average size of local cell group is constant and levels of PCP proteins are balanced in every cell. Therefore, this model provide an explanation for PCP induction on a tissue with multiple cell types.

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.