Interacting Particles on a Spherical Shell: A Group Theoretic Study
Many biological structures can be modeled as a system of interacting particles moving on a two-dimensional elastic membrane, for instance, protein clusters on cell-membranes and capsids of immature enveloped viruses. In this work, we present a model for such systems. We adopt the combination of the Helfrich model and the Lennard-Jones model as our energy representation of the particle-membrane system. The nonlinearity of the model gives rise to a complex competition of equilibrium states of the energy with symmetric features. We implement group-theoretic techniques to examine symmetric states and develop an automated computer program that systematically catalogs the symmetric equilibrium configurations for varying numbers of particles and model parameters.