Cubic membranes represent highly curved, three-dimensional nanoperiodic structures that correspond to mathematically well defined triply periodic minimal surfaces. Although they have been observed in numerous cell types and under different conditions, particularly in stressed, diseased, or virally infected cells, knowledge about the formation and function of nonlamellar, cubic structures in biological systems is scarce, and research so far is restricted to the descriptive level. We show that the “organized smooth endoplasmic reticulum” (OSER; Snapp, E.L., R.S. Hegde, M. Francolini, F. Lombardo, S. Colombo, E. Pedrazzini, N. Borgese, and J. Lippincott-Schwartz. 2003. J. Cell Biol. 163:257–269), which is formed in response to elevated levels of specific membrane-resident proteins, is actually the two-dimensional representation of two subtypes of cubic membrane morphology. Controlled OSER induction may thus provide, for the first time, a valuable tool to study cubic membrane formation and function at the molecular level.

Summary. Through computer simulation of images produced by the transmission electron microscope (TEM), we have identified threedimensional periodic cubic membrane structures in giant amoebae (Chaos carolinensis) mitochondria. The cubic membranes are based on the highly curved three-dimensional periodic cubic surfaces, sharing the same geometry of mathematically defined periodic minimal surfaces. The double-membrane structures identified here divide space into three separate and convoluted subspaces. Specimen preparation, specifically the tendency to cut oblique sections, of this membrane crystal has added to the complexity of the resulting TEM projections and until now prevented researchers from recognizing them. It is the added complexity of the oblique sections, though, that allows us to match the TEM projection to a computer simulation of the same with confidence. In this study, formation of cubic membrane structures in amoeba mitochondria was found to be dependent on diet. The cubic structures only occurred in the absence of food, and disappeared in the presence of food, suggesting a structural adaptation and possible advantages for amoebs survival in nature. The verification of mathematically well-defined structures in unfed amoeba mitochondria is also important to the understanding of the mitochondrial bioenergetics in relation to the topology of the inner membrane, where major cellular energy production as well as free-radical generation are taking place. This understanding may carry great impact upon human health as far as aging and age-related degenerative diseases are concerued, especially as mitochondrial disorders have been implicated in these processes.

Biological membranes are among the most fascinating assemblies of biomolecules: a bilayer less than 10 nm thick, composed of rather small lipid molecules that are held together simply by noncovalent forces, defines the cell and discriminates between "inside" and "outside", survival, and death. Intracellular compartmentalization-governed by biomembranes as well-is a characteristic feature of eukaryotic cells, which allows them to fulfill multiple and highly specialized anabolic and catabolic functions in strictly controlled environments. Although cellular membranes are generally visualized as flat sheets or closely folded isolated objects, multiple observations also demonstrate that membranes may fold into "unusual", highly organized structures with 2D or 3D periodicity. The obvious correlation of highly convoluted membrane organizations with pathological cellular states, for example, as a consequence of viral infection, deserves close consideration. However, knowledge about formation and function of these highly organized 3D periodic membrane structures is scarce, primarily due to the lack of appropriate techniques for their analysis in vivo. Currently, the only direct way to characterize cellular membrane architecture is by transmission electron microscopy (TEM). However, deciphering the spatial architecture solely based on two-dimensionally projected TEM images is a challenging task and prone to artifacts. In this review, we will provide an update on the current progress in identifying and analyzing 3D membrane architectures in biological systems, with a special focus on membranes with cubic symmetry, and their potential role in physiological and pathophysiological conditions. Proteomics and lipidomics approaches in defined experimental cell systems may prove instrumental to understand formation and function of 3D membrane morphologies.

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