The Rapoports themselves are a long distinguished rabbinic family that traces its roots back to Central Europe and Northern Italy in the 15th century.
However, in a dispute with Rabbi Moshe Khaim Ephraim, the Baal Shem Tov's grandson, around the year 1800, the non-Chasidic and the Chasidic communities separated into two groups.
The Bick family were responsible for the official religious "business" of the community, such as relations with the Russian authorities and kashrut rulings.
Other members of the family included R. Isaac Bick who was the head of the Beit Din in Medzhybizh until 1902 when he left for Rhode Island by way of Hester St. in NY City.
Chapin, David A. and Weinstock, Ben, The Road from Letichev: The history and culture of a forgotten Jewish community in Eastern Europe, Volume 1.