Exploring the elastic features of spherically shaped biological assemblies and soft matter systems

Using a numerical simulation, we study the elastic features of biological assemblies (e.g. viruses and bacteria) and soft matter systems (e.g. colloidosomes and nanoparticle covered droplets) that possess a spherical shape in which the proteins (particles) on the colloidosomes or virus shells are mechanically linked to form a stress-bearing spherical structure that may dramatically enhance the surface rigidity. The dependence of the rigidity enhancement upon the density of the cross-linked proteins situated on the surface of the virus is explored. We determine the percolation threshold P(ce) by considering bond percolation on the spherical elastic networks involving nearest neighbor forces. The percolation threshold of such networks is very different from that of a two-dimensional triangular lattice due to the topological effect. We find that the threshold probability for the spherical elastic network is considerably smaller than for an unwrapped network, which reveals that the spherical topology induces more rigidity to the network.