Cubic membranes: a legend beyond the Flatland* of cell membrane organization

Abstract

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.

Figure 1.

Computer simulation of cubic membrane architecture. (a) A pair of 3D periodic cubic surfaces illustrates the structure and symmetry of the cubic regions of OSER membranes. Each surface shown represents the center of a membrane bilayer, indicating the close proximity of two bilayer membranes in that model. (b) Examples of computer-simulated 2D projections for the respective G- and D-type cubic surfaces, at different viewing angles. These simulated 2D projection maps form a library that is used to match the membrane patterns of interest, as observed by TEM.

Figure 2.

Identification of cubic membrane morphologies in TEM micrographs. Two examples of the DTC method, applied to TEM images of OSER (adopted from Snapp et al., 2003). (a) The original TEM micrograph (Snapp et al., 2003 Fig. 2 c) matches perfectly to the theoretical superimposed projections of balanced (2-parallel surfaces) gyroid cubic membranes, as depicted in b. Asterisks indicate one of the multicontinuous, yet distinct, subvolumes of cubic membrane architecture. A double diamond projection (c) matches the TEM micrograph (d) adopted from Fig. 7 b of Snapp et al., (2003). The arrows in a and d indicate the continuity of one cubic membrane subvolume (between closely arranged bilayers) and the cytoplasm (Cy). Signature patterns of the theoretical projection are indistinguishable to the electron density pattern of the TEM micrographs. The simulated projections are generated from sections with a thickness of 1/4 of a unit cell, viewed along the direction [36, 30, 17] for gyroid (b) and [28, 16, 5] for double diamond-type (c). The unit cell is the smallest structural unit that possesses the symmetry and properties of cubic membranes. Bars: (a) 100 nm; (d) 160 nm.