Scaling, crumpled wires, and genome packing in virions

The packing of a genome in virions is a topic of intense current interest in biology and biological physics. The area is dominated by allometric scaling relations that connect, e.g., the length of the encapsulated genome and the size of the corresponding virion capsid. Here we report scaling laws obtained from extensive experiments of packing of a macroscopic wire within rigid three-dimensional spherical and nonspherical cavities that can shed light on the details of the genome packing in virions. We show that these results obtained with crumpled wires are comparable to those from a large compilation of biological data from several classes of virions.

Figure 1

(a) Typical PVC cavity used in our experiments. (b) Typical syringe cavity also used in our experiments showing the plunger and the pin used to immobilize it. In the interior of the cavity there is a partially ordered configuration of wire. See the text for details.

Figure 2

(a) Sample in a POC with the central hole filled by a nonordered structure. (b) Sample in a NOC. See the text for details.

Figure 3

Figure-$\mathsf{8}$-like pattern cut from a NOC of wire. See the text for details.

Figure 4

Packing fraction of the wire versus the aspect ratio of the cavity for a NOC (black circles) and a POC (red squares). The lines are the medium packing fraction of genetic material in virions: The dashed blue line is for the almost spherical viral capsids while the solid black line refers to nonspherical capsids. See the text for details.

Figure 5

Volume of the cylindrical cavities plotted versus the length of the wire injected. The dashed line of the best fit has slope $A=1.32\pm 0.03$.