  Teams of cooperating sperm have been found across several vertebrate and
invertebrate species, ranging from sperm pairs to massive aggregates containing
hundreds of cells. Although the biochemical mechanisms involved in the
aggregation process are still unclear, it was found that aggregation can
enhance the mobility of the cells, thus offering an advantage during
fertilization. Here, we report a thorough computational investigation on the
role of cellular geometry in the performance of sperm aggregates. The sperm
head is modelled as a persistent random walker characterized by a non-trivial
three-dimensional shape and equipped with an adhesive region, where cell-cell
binding occurs. By considering both a simple parametric head shape and a
computer reconstruction of a real head shape based on morphometric data, we
demonstrate that the geometry of the head and the structure of the adhesive
region crucially affects both the stability and mobility of the aggregates. Our
analysis further suggests that the apical hook commonly found in the sperm of
muroid rodents, might serve to shield portions of the adhesive region and
promote efficient alignment of the velocities of the interacting cells.
