The first author of the study, Dr. Takefumi Negishi, commented "When I observed this structure dynamically moving and extending within the cell, I immediately thought this might be playing an essential role for cellular function." The structure was called an invagination.
The investigators used an advanced type of electron microscopy called Serial block-face (SBF) scanning electron microscopy (SEM) – SBF SEM. For a demonstration of how this technique works, check out the video below. An ultramicrotome slices thin sections off of a block of sample, then the freshly revelaed face is imaged. This is repeated many times to generate a 3D reconstruction of the sample.
One supervisor of the study, Professor Naoto Ueno of the National Institutes of Natural Sciences in Okazaki, Japan, said, "We hope our findings facilitates studies on similar membrane structures in other animals that might have diverse biological functions."
Sources: AAAS/Eurekalert! via National Institute for Basic Biology, eLife