Is there a specific gene involved, perhaps? Would one be able to genetically engineer a bacterium to oxidize water and generate electrons quicker? I am speaking about this biological problem in terms of an application to solar cells. 

Edit: I am not inquiring to the existence of a gene responsible for photosynthesis, I am inquiring as to why some exoelectrogenic bacteria can produce electrons in electron transport more efficiently than others. Is there a reason for this that can be traced to a certain gene that makes certain exoelectrogens superior to others?