PlanarCellPolarityInDrosophilaWing


Contributors


Brunel University, UK: Qian Gao, David Tree, Esther Bamigboye
University of Helsinki, Finland: Ville Rantanen
University of Milano Biccoca, Italy: Daniele Maccagnola


Background


Planar cell polarity (PCP) refers to the orientation of cells within the plane of the epithelium, orthogonal to the apical-basal polarity of the cells.

  • This polarisation is required for many developmental events in both vertebrates and non-vertebrates. Defects in PCP in vertebrates underlie developmental abnormalities in multiple tissues including the neural tube, the kidney and the inner ear (reviewed in [1]).
  • The adult Drosophila wing comprises about 30,000 hexagonal cells, each of which contains a single hair pointing in an invariant distal direction, see Fig. 1. This hair comprises actin bundles and is extruded from the membrane at the distal edge of the cell during pupal development at the conclusion of PCP signalling.
  • The signalling pathway involves key proteins Frizzled (Fz), Dishevelled (Dsh), Prickle (Pk) (reviewed in [2]),Flamingo (Fmi) and Van-Gogh (Vang). These proteins are thought to mediate the cell-cell communication that comprises PCP signalling and to establish the molecular asymmetry within and between cells which is subsequently transformed into the polarisation of the wing hairs (reviewed in [3]). The result is a polarisation of individual cells and local alignment of polarity between neighbouring cells.

Fig. 1

Modelling challenge


In this project we apply hierarchically coloured Petri nets (HCPN) to gain insight into mechanism of PCP. There is considerable controversy within the literature on PCP signalling in Drosophila over the nature of the polarising signal upstream of signalling by the PCP proteins that directs their polarised localisation.

The existence of feedback loops is widely accepted; they mediate the competition between the proximal and distal proteins. There are two other mechanisms which have been proposed in the literature (not mutually exclusive):

  • One theory postulates the existence of an unknown and as yet unidentified extra-cellular morphogen signal to which the PCP proteins respond. Despite the lack of positive data identifying such a morphogen signal [4] models based on this theory remain popular in the literature.
  • A second theory is that there is an intra-cellular mechanism within the wing epithelial cells, comprising biased microtubule transport of distal PCP proteins to the distal cell cortex.

Initially we wish to recapitulate the phenotypes of all known mutant conditions causing loss or gain of function. We hope to be able to address questions about the mechanisms underlying the polarising signal, the dynamics of signalling by the individual components and the signals downstream of the PCP proteins, which orchestrate the ultimate morphological manifestation of planar polarity.

Ultimately we expect that our model will make predictions about the mechanisms underlying the PCP signalling process, which will be testable in a biological laboratory.


Modelling


  • Each cell is divided into seven virtual compartments, see Fig. 2 (right). The three proximal and three distal membrane compartments are identical, respectively, and we use colouring to replicate the compartments across the cell. See Fig. 3 where the proximal and distal compartments have been folded using colouring.
  • A hexagonal grid of cells is used to model the wing tissue, see Fig. 2 (left), and the individual cell model is replicated over the grid using colouring. We use a two-level hierarchical structure over colours in order to describe the wing tissue and the compartmental structure within the cells.

Fig. 2

Fig. 3
  • The model can be wild-type, or modified to contain an Fz- mutant clone in a subset of the cells each of which have the concentration of Fz set to zero in order to model the knockout.
  • We obtain quantitative counterparts of our refined PCP model by assigning to each transition a rate function following mass-action kinetics. This quantitative model can be equally read as a stochastic or continuous model, with appropriate scaling of the kinetic constants.

Analysis


Preliminaries:

  • We confine ourselves to simulative methods to analyse our quantitative model in a stochastic and continuous setting.
  • To limit the computational expense, we use our generic HCPN model to generate an in-silico tissue based on a 15*15 honeycomb grid consisting of 112 cells in total. The underlying unfolded model comprises 8,624 species (places) and 9,184 reactions (transitions), and thus the ODEs system to be analysed consists of 8,624 equations. Some stochastic and continuous simulations results are given in Fig. 4.

Fig. 4
  • The runtime for unfolding and simulation for increasing size of an unbiased PCP model under development can be found in Table 1.

Table 1

Mutant experiment:

We have modelled the effect of a patch of cells lacking Fizzled in an otherwise wild-type field of cells by completely knocking out the concentration and transport of the corresponding places and transitions in our model. Using a particular function we produce a mutant clone of Fz- inside our in-silico tissue, comprising seven cells.

Cells in a Fz- clone have incorrect polarity and occasional multiple hairs. Wild-type cells distal, but not proximal adjacent to the clone have incorrect polarity, pointing proximally towards the clone (see Fig. 5, right). Our simulation result shows the same impact of a clone of Fz- mutated cells as observed in the biology laboratories (see Fig. 5, left).


Fig. 5

Conclusions


Our model has allowed us to generate behaviours as a first step to explain the complex behaviours observed in the biological system under study, and to explore the effects of mutations by introducing variations in patches of cells in our computational model.

Our analysis confirms that the behaviour of the model correctly demonstrates that the major accumulation of actin (from which the hairs are formed) occurs in the most distal part of wild-type cells, corresponding to the location of the prehair formation in wing cells of Drosophila.

Moreover our model confirms that the introduction of mutant clones disrupts the pattern of actin accumulation and hence hair orientation in wild-type cells on the distal side of the clone.


Materials


Computational materials and models

Student summer project report on imaging of PCP in Drosophila Melanogaster by Esther Bamighoye


Publications


  1. D Maccagnola, E Messina, Q Gao, D Gilbert:
    A Machine Learning Approach for Generating Temporal Logic Descriptions of Complex Model Behaviours;
    In Proc. Winter Simulation Conference 2012, accepted for publication. [ pdf ]
  2. Q Gao, F Liu, D Tree and D Gilbert:
    Multicell Modelling Using Coloured Petri Nets Applied to Planar Cell Polarity;
    In Proc. International Workshop on Biological Processes & Petri Nets (BioPPN 2011), satellite event of Petri Nets 2011, CEUR-WS.org, CEUR Workshop Proceedings, volume 724, pages 135–150, June 2011. [ pdf ]
  3. Q Gao, F Liu, D Gilbert, M Heiner and D Tree:
    A Multiscale Approach to Modelling Planar Cell Polarity in Drosophila Wing using Hierarchically Coloured Petri Nets;
    In Proc. 9th International Conference on Computational Methods in Systems Biology (CMSB 2011), Paris, ACM digital library, pages 209–218, September 2011. [ link ]
  4. Q Gao, F Liu, D Maccagnola, D Gilbert, M Heiner, D Tree:
    Multiscale Modelling and Analysis of Planar Cell Polarity in Drosophila Wing;
    Journal IEEE/ACM Transactions on Computational Biology and Bioinformatics, Vol 99, 2012. [ doi ].

References


  1. M. Simons and M. Mlodzik:
    Planar cell polarity signaling: From fly development to human disease;
    Annual Review of Genetics, 42: 517-540, 2008. [ pdf ]
  2. L. L. Wong and P. N. Adler:
    Tissue polarity genes of drosophila regulate the subcellular location for prehair initiation in pupal wing cells;
    Journal of Cell Biology, 123: 209-220, 1993. [ link ]
  3. D. I. Strutt:
    Asymmetric localization of frizzled and the establishment of cell polarity in the drosophila wing;
    Molecular Cell, 7: 367-375, 2002. [ link ]
  4. M. Povelones and R. Nusse:
    The role of the cysteine-rich domain of frizzled in wingless-armadillo signaling;
    EMBO Journal, 24:3493–3503, 2005. [ link ]
  5. J. Barrow:
    Wnt/PCP signaling: A veritable polar star in establishing patterns of polarity in embryonic tissues;
    Seminars in Cell and Developmental Biology, 17(2):185–193, 2006. [ link ]
  6. C. Yang, J. D. Axelrod and M. A. Simon:
    Regulation of frizzled by fat-like cadherins during planar polarity signaling in the drosophila compound eye;
    Cell, 108:675–688, 2002. [ link ]

latest update: November 25, 2012, at 11:34 AM