First of all, the sugar "athelose" is hypothetical therefore it does not exist and only serves the purpose of illustration. This is similar to the lac operon in bacteria that utilizes lactose as its energy source (in the absence of glucose).
In the presence of glucose, the ath operon (operon for athelose) is repressed because the regulatory gene for synthesizing the enzyme that can metabolize athelose is off (so the operon is off), because of the presence of an active repressor (can be glucose or a metabolite of glucose; any marker that denotes the presence of high glucose concentrations).
In the absence of glucose, the ath operon is activated because since glucose is absent, the active repressor is also absent and will turn the operon on; and subsequently, the gene encoding for the enzyme that metabolizes operon is turned on, as this will function to make the bacterium capable in using athelose as an energy source.
