Gaz is the daughter of Professor Membrane, as well as his youngest child. It has been said, however, that Dib was created by the Professor in his lab and it was unknown for Gaz, and are therefore making Dib his non-biological child and Gaz unconfirmed. Nevertheless, Membrane still treats them as such... when he's around. Usually, the Professor is busy in his lab, and communicates with his children via recorded messages.
However, based on their live interactions, it is clear that the Professor and Gaz have a lot in common: Both of them have little patience for Dib's antics, for their own reasons (the Professor considers Dib insane, while Gaz just thinks he's annoying).
Professor MembraneProfessor Membrane often neglects both of his children, maintaining contact with them mostly through floating screens that are oftentimes pre-recorded. However, he shows affection towards them in limited occasions; in "Gaz, Taster of Pork", when the Professor can't invent a cure for his daughter's "disease", he becomes rather desperate. He "protects" Gaz by putting her in a special insulating suit and confining her to quarantine, then he builds an entire speciality area to try to find the cure. They then go out to have dinner at Bloaty's after she is cured. In "Game Slave 2", he insists in her being escorted by Dib to the midnight Game Slave 2 video game console sale, because it could be too "dangerous" to go by herself, showing genuine worry. However, he does show willingness to let his very young children wander the streets at night, which leaves up to debate how much he really cares about their safety. It can be argued that Gaz is Professor Membrane's favorite of the two, considering that her brother often makes a fool of himself with his paranormal preoccupation. He even goes so far as to state that Gaz should find Dib and "Make sure he doesn't do anything embarrassing." He shows a tendency of picking her up a lot, often to carry her on his shoulder. He has stated on occasion that "You're my funny child!" Compared to Dib, who would likely be his "insane child."
In several issues of the comic series, Membrane is shown taking the time to play games with Gaz, showing a somewhat increased dedication towards spending time with her physically.