My laboratory is engaged in studying the mechanisms that underlie the formation of cubic membranes- a 3D nano-periodic membrane structure that occurs in a wide variety of living systems. Cubic membranes represent highly curved surfaces (Fig. 1) that correspond to the mathematical anology of triply periodic minimal surfaces used in describing both crystalline and liquid crystalline materials at a variety of length scales. Today, three types of cubic membranes, namely gyroid (G), double-diamond (D), and primitive (P) with respect to the surfaces describing them, have been recognized. Cubic membranes, thus, provide us an attractive model to study 3D global cell topology and various cellular (mal)functions at nanometer scale, which might have a major impact on our understanding of the physiology and patho-physiology of living cells.
Figure 1:
The
bilayer constellation of a 3D mathematical model of cubic membrane. Three
parallel periodic cubic surfaces can be used to describe a biological membrane (bilayer),
in which case the centered surface is the ‘imaginary’ midbilayer surface and
the two parallel surfaces are the two apolar/polar surfaces.