“Parking-garage” structures in nuclear astrophysics and cellular biophysics

A striking shape was recently observed for the endoplasmic reticulum, a cellular organelle consisting of stacked sheets connected by helical ramps [Terasaki et al., Cell 154, 285 (2013)]. This shape is interesting both for its biological function, to synthesize proteins using an increased surface area for ribosome factories, and its geometric properties that may be insensitive to details of the microscopic interactions. In the present work, we find very similar shapes in our molecular dynamics simulations of the nuclear pasta phases of dense nuclear matter that are expected deep in the crust of neutron stars. There are dramatic differences between nuclear pasta and terrestrial cell biology. Nuclear pasta is 14 orders of magnitude denser than the aqueous environs of the cell nucleus and involves strong interactions between protons and neutrons, while cellular-scale biology is dominated by the entropy of water and complex assemblies of biomolecules. Nonetheless, the very similar geometry suggests both systems may have similar coarse-grained dynamics and that the shapes are indeed determined by geometrical considerations, independent of microscopic details. Many of our simulations self-assemble into flat sheets connected by helical ramps. These ramps may impact the thermal and electrical conductivities, viscosity, shear modulus, and breaking strain of neutron star crust. The interaction we use, with Coulomb frustration, may provide a simple model system that reproduces many biologically important shapes.

Figure 1

Self-assembly of a parking garage structure in a MD simulation with $40000$ nucleons that started from uniform random initial positions. Shown in panels (a)–(f) are the configuration after simulation times of $40000,400000,800000,1200000,1600000$, and $2000000$ fm/$c$ respectively. The color map at right is discussed in the text.

Figure 2

Three axis views, $X$ (left), $Y$(center), and $Z$ (right), of the final configuration of three MD simulations. Panels (a)–(c) at top are for the $40000$ nucleon simulation shown in Fig. 1. Panels (d)–(f) at center are for a simulation with $50000$ nucleons and panels (g)–(i) at bottom are for a simulation with $75000$ nucleons. The handedness of the helical holes in panels (a), (e), and (h) are indicated with L for left-handed and R for right-handed.

Figure 3

(a) Scanning electron micrograph of a thin slice of sheetlike ER from a mouse salivary gland. Serial sectioning allows three-dimensional reconstruction from large numbers of cross-sections (scale bar = 200 nm). (b) 3D reconstruction of a left-handed Terasaki ramp that appears in the black-outlined region in (a). (c) 3D reconstruction of a right-handed Terasaki ramp that appears in the white-outlined region in (a). (Figure adapted from Terasaki et al. [13].)