What do you think of the subject on which I wrote a book in French and entitled: Everything that happens in the "head" of cells and microorganisms. Do cells and microorganisms have a “brain”?
it depends upon your definition of "brain". Most definitions of a biological brain imply a nervous system, which microorganisms would not have. Also there is no "head" of a cell or a microorganism. So unless you are using the term in an unusual way, I probably would think not.
Indeed, cells and microorganisms do not have a brain or a head, but I used a metaphor in this title and that is why I put the words "brain" and "head" in quotation marks.
Notwithstanding the points already made, I think that rather a good bacterial 'head' metaphor might be the complex regulatory network which controls gene transcription, translation and activity of proteins in response to external (environmental) signals. The Che chemosensory system (describe for a variety of bacteria including Escherichia coli) might be the eyes which respond to nutrient signals (prey in the distance?) and this is linked to the flagella (the legs) enabling directed movement towards the nutrient source. You could challenge the head metaphor by asking whether it makes complex decisions (bacteria can) or has memory (... perhaps in the way proteins are modified to ramp up/down sensitivity in the Che system), or whether it can learn ...
Thank you for these excellent metaphors, for memories and decisions, I dedicated a part on the blob which is able to learn and make decisions but also to memorize and "teach" other blob.