Geometric restrictions to the agglomeration of spherical particles

Within the scope of the European Horizon 2020 project ACDC – Artificial Cells with Distributed Cores to Decipher Protein Function, we aim at the development of a chemical compiler governing the three-dimensional arrangement of droplets, which are filled with various chemicals. Neighboring droplets form bilayers containing pores through which chemicals can move from one droplet to its neighbors. When achieving a desired three-dimensional configuration of droplets, we can thus enable gradual biochemical reaction schemes for various purposes, e.g., for the production of some desired macromolecules for pharmaceutical purposes. In this paper, we focus on geometric restrictions to possible arrangements of droplets. We present analytic results for the buttercup problem and a heuristic optimization method for the kissing number problem, which we then apply to find (quasi) optimum values for a bidisperse kissing number problem, in which the center sphere exhibits a larger radius.