Diatom chains are cohesive assemblies of unicellular microorganisms that are found in still and fresh waters. Some species are passively transported by ambient currents and settle due to the weight of their dense silica shells, while others have use various strategies to move or self-propel. One species in particular, called Bacillaria Paxillifer, forms colonies of stacked rectangular cells that slide along each other while remaining parallel. As observed in experiments, and reproduced by our numerical model, their intriguing coordinated motion, leads to beautiful and nontrivial trajectories at the scale of the colony. However, the effect of gravity and external flows on the dynamics of diatom chains must be investigated to understand the behavior of plankton and marine snow aggregates as they sink, and capture CO2, to the ocean depths...