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Topic Name: Researchers Create Mathematical Model of Fruit Fly Eyes to show how Cells Pack Together

Category: Biodesign

Research persons: Sascha Hilgenfeldt, Richard W. Carthew

Location: Northwestern University, United States

Details

Many researchers have tried to create a mathematical model of how cells pack together to form tissue, but most models have many different complicated factors and no model is universal.

Researchers at Northwestern University have now created a functional equation – using only two parameters – to show how cells pack together to create the eyes of Drosophila, better known as the fruit fly. They hope that the pared-down equation can be applied to different kinds of tissues, leading to advances in regenerative medicine.

Sascha Hilgenfeldt, associate professor of engineering sciences and applied mathematics and mechanical engineering, teamed up with Richard W. Carthew, professor of biochemistry, molecular biology, and cell biology in the Weinberg College of Arts and Science, and Sinem Erisken, a McCormick undergraduate studying biomedical engineering, to create the model.

The interdisciplinary effort among geneticists, engineers and mathematicians began 18 months ago, when Hilgenfeldt, who specializes in foam, soft matter and fluid mechanics, teamed with Carthew, who has studied the biological features of fruit fly eyes.

Hilgenfeldt knew that when it comes to creating a model that shows what determines the shape of functional cells in tissues, the myriad factors – including the bulk of the cell, what’s going on inside of the cell, and how the cell forms – make it very difficult to quantify.

“That’s a nightmare for quantitative scientists,” he said. “It’s extremely complicated.”

But the cells in a fruit fly’s eye act more like foam in that the structure of the cells depends only on the energy of their interfaces, or the surface where the cells touch. That energy is divided into two parts – the energy from the stretching of the cells’ membranes and the energy of the “glue” (the adhesion molecules) that holds the neighboring cell membranes together. Hilgenfeldt took those two factors and created a quantitative model of cell geometries in the fruit fly retina. So instead of needing to know all the different cell factors to create the model, he just needed the two energy components to create the model.

“It’s one of the most quantitative models I’ve seen for a biological system,” Hilgenfeldt said. “For this system, mainly all you need to know is the interfacial energies and everything falls into place.”

Such a model helps researchers understand how the presence of the glue energy changes the shape of the eye and will help them study how those adhesion molecules develop and function during embryo development.

Further down the road, having these kinds of models could help scientists learn how to grow regenerative tissues. Hilgenfeldt also hopes to see how far he can take this model – testing whether it will work in tissues that have much more variation in their cell patterns.

“It is very promising for quantitative science to be able to do something about these complex biological systems,” he said.

Though the undergraduate student who worked on the research has graduated, Hilgenfeldt said another undergraduate student will help continue the research through the Research Training Group (RTG) program in applied mathematics. The program emphasizes interdisciplinary research with teams composed of applied mathematicians, scientists and engineers. It is funded by a $2.1 million National Science Foundation grant.

“This is precisely what the grant is supposed to do,” Hilgenfeldt said. “Interdisciplinary work across all the stages of academic life – from undergrad to faculty.”

About Drosophila
Drosophila is a genus of small flies, belonging to the family Drosophilidae, whose members are often called "fruit flies" or more appropriately vinegar flies, wine flies, pomace flies, grape flies, and picked fruit-flies, a reference to the characteristic of many species to linger around overripe or rotting fruit. A second, related fly family, the Tephritidae, are also called fruit flies; these feed primarily on unripe or ripe fruit, with many species being regarded as destructive agricultural pests, especially the Mediterranean fruit fly. One species of Drosophila in particular, D. melanogaster, has been heavily used in research in genetics and is a common model organism in developmental biology. Indeed, the terms "fruit fly" and "Drosophila" are often used synonymously with D. melanogaster in modern biological literature. The entire genus, however, contains about 1,500 species and is very diverse in appearance, behavior, and breeding habitat. Scientists who research Drosophila are often called Drosophilists.
Drosophila are small flies, typically pale yellow to reddish brown to black, with red eyes. Many species, including the noted Hawaiian picture-wings, have distinct black patterns on the wings. The plumose (feathery) arista, bristling of the head and thorax, and wing venation are characters used to diagnose the family. Most are small, about 2–4 millimetres long, but some, especially many of the Hawaiian species, are larger than a house fly.

Note for Cell Adhesion Molecules
Cell Adhesion Molecules (CAMs) are proteins located on the cell surface involved with the binding with other cells or with the extracellular matrix (ECM) in the process called cell adhesion.
Most of the CAMs belong to 4 protein families: Ig (immunoglobulin) superfamily (IgSF CAMs), the integrins, the cadherins and the selectins.
Functions
Embryonic development 
Formation of Nervous System 
Holding tissues together in adults 
Inflammation and wound healing 
Metastasis of tumors
Transmits signal into and out of the cell

These proteins are typically transmembrane receptors and are composed of three domains: an intracellular domain that interacts with the cytoskeleton, a transmembrane domain and an extracellular domain that interacts either with other CAMs of the same kind (homophilic binding) or with other CAMs or the extracellular matrix (heterophilic binding).

In figure 4, Cells in the fruit fly retina form very geometric patterns