... some might tell you that for rolex its the bracelet president, the dial within the dial for Lange, or the royal oak bezel of AP, etc...
If we are talking DNA, its a good question, not that obvious for Patek. I guess it would be the simple dial of the calatrava. But for me, its the nautilus line, but its personal, as it was the 1st patek that i saw decades ago, and in my mind, i associate Patek to the nautilus, like i associate AP to the royal oak. Then again, its hard to tell you what in the nautilus i assicate with Patek .
Very good question 
It would have been easier to speak about which model we associate with each brand
JLC : reverso
Lange : LAnge 1
Rolex : daydate
AP : Royal oak
Patek : ... Calatrava