A tire assembly includes a tire having a pneumatic cavity, first and second sidewalls, a sidewall groove, an air passageway, and a pressure regulator mounted to an inner surface of the pneumatic tire cavity. The pressure regulator controls air pressure within the pneumatic tire cavity. The first and second sidewalls extend respectively from first and second tire bead regions to a tire tread region. The first sidewall has at least one bending region operatively bending when circumferentially within a rolling tire footprint. The sidewall groove defining groove sidewalls positioned within the bending region of the first tire sidewall. The groove and air passageway deform segment by segment between a non-deformed state and a deformed, constricted state in response to the bending of the first sidewall bending region circumferentially within the rolling tire footprint.