Moebius soap films
DOI: 10.1063/PT.5.010057
For May’s issue of Physics Today I wrote a news story about a clever biophysical experiment by Aurélien Roux of the Curie Institute in Paris and his collaborators.
Roux wanted to find out how the protein dynamin forms a pouch of cell membrane that projects into the cell during a process called endocytosis. At the start of endocytosis, the pouch—termed a vesicle—is open to the cell’s exterior. In the final step, the neck of the vesicle, which is squeezed by a collar of polymerized dynamin, is pinched off, trapping the vesicle and its contents inside the cell.
Roux’s experiment popped back into my mind this morning when I encountered a paper in the Proceedings of the National Academy of Sciences entitled “Soap-Film Möbius Strip Changes Topology with a Twist Singularity.” Roux had told me that the mechanism by which the cell membrane changes its topology as the vesicle closes is unknown. Curious, I wondered if the new Möbius strip paper was relevant to endocytosis.
The paper was written by Raymond Goldstein, Keith Moffatt, and Adriana Pesci of the University of Cambridge and Renzo Ricca of the University of Milano-Bicocca. Here’s how it begins:
In an elegant article in 1940, the mathematician R. Courant laid out a number of fundamental questions about surfaces of minimal area that could be visualized with soap films spanning wire frames of various shapes. He noted that when the frame is a double loop it can support a film with a Möbius strip topology. Pulling apart and untwisting the loop leads to an instability whereby the film jumps with change of topology to a two-sided solution.
Goldstein and his coauthors point out that despite progress made on Courant’s questions, one stands out unanswered: What is the process that takes a one-sided film to a two-sided one?
In fact, if Goldstein’s paper is correct, that question is no longer unanswered. With a combination of high-speed videography and mathematical analysis, the Cambridge–Milan team demonstrates that the topological transition proceeds via a twist instability at the boundary wire. Clicking on the image of the Möbius soap film will take you to a video of the transition—filmed at 5600 frames a second!
I’m not sure whether the Cambridge–Milan team’s paper is directly relevant to Roux’s experiment. Still the team’s approach might be applicable to models of endocytosis. As a science writer, I found the possibiity of a link between the two papers intriguing enough to write what, I hope, is a not uninteresting blog post.
But if you’re a scientist, not a science writer, spotting possible links between diverse experiments and theories could be a source of inspiration and future projects. If you don’t already do so, read widely, attend seminars in topics outside your immediate field, and keep an open mind.
