While there is no mention of purple buttons in the book, pearl or white buttons play an important part throughout.
At the end of chapter four, Dupin works out that if Edmund locked the door, his sister must have been forced from Edmund's room through a window, and by a person in the opposite apartment. After breaking into the apartment, Edmund finds a pearl button on the floor that belongs to his sister. He explains that his sister is both a lover of shoes and the fairytale Hansel and Gretel, concluding that she must have taken the pearl button off her shoe in order to leave behind a trail.
Dupin finds a second button, a white button, on page 145 in the cemetery behind Mrs. Whitman's house. As Dupin says at the time, "It suggests but one thing: until very recently your sister was alive."