Observation of the self-assembly of clusters of cells in three dimensions has raised questions about the forces that drive changes in the shape of the cell clusters. Cells that self-assemble into a toroidal cluster about the base of a conical pillar have been observed in the laboratory to spontaneously climb the conical pillar. Assuming that cell cluster reorganization is due solely to surface diffusion, a mathematical model based on the thermodynamics of an isothermal dissipative system is presented. The model shows that the cluster can reduce its surface area by climbing the conical pillar, however, this is at the expense of increasing its gravitational potential energy. As a result, the kinetics of the climb are affected by parameters that influence this energy competition, such as the slope of the conical pillar and a parameter of the model κ that represents the influence of the surface energy of the cluster relative to its gravitational potential energy.
A theoretical and simulation study of the self-assembly of a binary blend of diblock copolymers