From soap bubbles to Drosophila eyes

The most general theme that runs through my research till date is that the structure of systems at very small length scales (called microstructure since these changes can only be observed in a microscope, and not with naked eyes) evolve, and this evolution can be understood using the principle of minimization of free energy. So, typically, we first write down a free energy; then, we write an evolution equation for the microstructure using the principle that the time evolution of the system should be such that the free energy continuously keeps decreasing; we typically solve the evolution equations numerically, and look at the resulting microstructures at various times. All this may sound pretty complicated, though they really aren’t.

Even though we are interested only in microstructures, it is important to note that same things happen even at larger length scales. An example that everybody can identify with is the soap bubbles or beer head; in these systems, at the beginning, there are many bubbles; so, for each bubble, the walls of the liquid film cost energy; thus, in an effort to reduce this energy (known as interfacial energy), the bubbles coalesce. This process is known as coarsening.

There are several programs written to study the evolution of soap bubbles and such systems using the principle of minimization of energy (interfacial, in this case). In fact, you can also make the study more complicated and interesting by introducing constraints; for example, it can be shown that two rings held on top of each other at a distance, when dipped in a soap solution will make a catenoid. A very good free program that can do not only such minimization, but can also show the results graphically rather nicely is known as the Surface Evolver.

Till now, I have only seen Surface Evolver being used in the materials and metallurgical literature. Now, via this Science Blog post, I understand that some researchers from Northwestern University, have used Surface Evolver to successfully model the evolution of epithelial cells. The paper, published in PNAS, is authored by Hilgenfeldt, Erisken and Carthew and is titled Physical modeling of cell geometric order in an epithelial tissue:

In multicellular organisms, cells pack together to form tissues of intricate and well defined morphology. How such cell-packing geometries arise is an important open question in biology, because the functionality of many differentiated tissues depends on their reliable formation. We show that combining adhesive forces due to E- and N-cadherin with a quantitative description of cell membrane elasticity in an interfacial energy model explains not only the qualitative neighbor relations, but also the detailed geometry of a tissue. The characteristic cellular geometries in the eyes of both wild-type Drosophila and genetic mutants are accurately reproduced by using a fixed set of few, physically motivated parameters. The model predicts adhesion strengths in the eye epithelium, quantifies their role relative to membrane elasticity, and reveals how simple minimization of interfacial energy can give rise to complex geometric patterns of important biological functionality.

A nice paper. Take a look!

Tags: cellular structure, epithelial cell, interfacial energy, microstructural evolution, Surface Evolver