Apparently these creatures can have fairly complex behavior – they can hunt, avoid obstacles, flee from danger, and (possibly) learn. Yet they don’t have a brain or neurons to direct behavior or store information. How do they do it? What’s causing them to react to their environment?
It’s chemically based and it’s very different to the chain of events that leads to superficially similar behaviour in organisms with brains.
In simple terms there are proteins in the cells surface that change shape when they are exposed to certain molecules. That changes the chemistry inside the cell in such that the organism moves away form or towards the source of the chemical.
Imagine that a cell is plastic bag filled with water, and that there are chemical detectors dotted all around the outside of the bag that send a simple switch signals through to the inside. When the switch is closed the cell tends to move towards whatever part of the bag the switch is located at. As a result whichever area of the cell wall has more open switches will be the direction of travel. That’s highly simplified but accurate enough for basic understanding.
In the case of hunting the direction from which the chemical signal is strongest is moved towards. IOW it’s simply following a scent trail.
In the case of avoidance of obstacles and danger either the physical pressure from contact with the obstacle causes changes in protein shape, or the chemicals released from the object are detected.