Mathematical modelling of growth control in Drosophila development

Have you ever wondered why your hands are the size they are? Or why some people have bigger hands, but they are almost identical in shape and proportion to your hands? The control of organ growth is highly complex, but highly important, as when the control system fails, we get overgrowth, and frequently cancer. How does the organ know when to stop growing? How does it control its shape? If we can understand this, perhaps we will be able to understand what happens when tissues over grow, and treat the problem (e.g. cancer) at its source. Many biologists have successfully used the Drosophila wing as a model to study growth control, revealing many parallels to human growth control. I hope to put all these data, the pieces of a puzzle, together, into a mathematical/computer model and eventually make a virtual wing. I‘ll be able to compare the relative importance of the different control mechanisms, something that‘s quite hard to do via experiments. I may find that internal control is key, and the environment plays little role, or vice versa. I can also model different cancerous conditions, and quickly test treatments before deciding whether they are worth trying experimentally/clinically.

How tissue size is controlled is a fundamental biological question that remains remarkably ill-understood. The development of organs of appropriate size and shape depends both on the extent and orientation of growth. This project aims to understand how tissue growth is sensed and restricted in vivo. I propose to use a combination of mathematical modelling and experimental approaches, using Drosophila development as a model system.

The imaginal discs are the precursors to the Drosophila adult appendages. Since they are flat epithelial sheets during much of development, imaginal discs are highly suitable for mathematical modelling. In addition, imaginal discs can readily be manipulated genetically to study the loss- or gain-of-function for any gene. Together with live imaging of cultured imaginal discs, I will be able to monitor the dynamics of cells in wild type and various mutant imaginal discs.

In Drosophila wing imaginal discs, the orientation of cell elongation and cell division predominantly along the proximo-distal (PD) axis determines the elongated shape of the wing. Recent evidence suggests that proteins controlling planar cell polarity such as Fat (Ft), Dachsous (Ds), and Dachs are able to co-ordinately regulate both growth rates and growth orientation. Of particular interest, Dachs protein is asymmetrically localised along the PD axis, with higher levels on the distal side. Since Dachs is an atypical myosin, does it restrict membrane growth by contracting the membrane where it is localised, thereby promoting cell elongation and therefore cell division along the PD axis? To answer this question, I will build a model of a 2D field of cells that grow and divide according to experimentally derived rules and parameters for wild type tissue. I can compare virtual clonal experiments with live developing clones. Through experimentation, I will measure the necessary parameters, such as tensile strength of Dachs, amounts of Dachs, and rates of membrane elongation (live movies). I can also easily expand my model to include more factors, and study how gradients of various morphogens in the wing can affect the localisation of Dachs and growth orientation.

This interdisciplinary research should allow us to study more accurately the dynamics of growth orientation and to formulate and test less intuitive hypotheses to reveal new insights into the mechanisms of growth control. Given the fact that tissue overgrowth is the cause of human cancer, I hope that this project will have an impact on cancer as well as developmental biology.