Calculating the maximum capacity of intracellular transport vesicles

In eukaryotic cells, vesicles transport protein cargo to various destinations in the cell. As part of an effort to count the number of cargo molecules in vesicles in cells, we asked a simple question: what is the maximum number of cargo molecules that can be packed into a vesicle? The answer to this question lies in the Tammes Problem, which seeks to determine the packing of circles on a spherical surface. The solution to this problem depends on the sizes of the vesicle and the cargo. We present here the computational results that determine the maximum theoretical capacity of a range of biologically relevant cargo in a variety of meaningful vesicle sizes. Our results could be generalized in order to describe an equation that allows the calculation of the approximate maximum capacity of any vesicle, whatever the size; provided that the size and geometry of the cargo is known.