This application relates to methods, systems, and apparatus for replacing native heart valves with prosthetic heart valves and treating valvular insufficiency. In a representative embodiment, a support frame configured to be implanted in a heart valve comprises an annular main body formed by a plurality of angled struts, the main body including a plurality of peaks formed by the intersection of respective adjacent struts. The support frame further comprises one or more leaflet-engaging mechanisms configured to engage leaflets of the heart valve. The support frame can be radially expandable and collapsible.