Active hunting in a single cell - function and evolution of nematocysts and ocelliods in dinoflagellates

How does the most complex single-celled eukaryotes, a group of marine dinoflagellates, function?  Each single-celled organism can apparently hunt down prey by swimming around, using the eyes to watch out for prey, which is then harpooned and eaten.
The eyes are structurally similar to vertebrate eyes with analogues to a retina, lens and cornea; and the “harpoons” are complex ballistic organelles. How do these single-celled organisms function without a coordinating brain? What is the function of the eye? What triggers the harpooning? Which food do they prey upon and how do they take-up food?
Advances in single-celled molecular analyses combined with experiments exposing cells to different preys and conditions will hopefully answer some of these questions. If successful, it will open for complex studies on the physiological functioning of single-celled organisms and potentially allow inferences on development of complex organs like the camera eye.