Systems and methods for replacing a heart valve. An expansible helical anchor is formed as multiple coils to support a valve prosthesis. At least one of the coils is expandable to a second, larger diameter upon application force from within the anchor. A gap is defined between adjacent coils sufficient to prevent engagement by at least one of the adjacent coils with the native heart valve. An expansible heart valve prosthesis is provided and is configured to be delivered into the anchor and expanded inside the coils into engagement. This moves the coil from the first diameter to the second diameter while securing the anchor and prosthesis together. The system further includes a seal on the expansible heart valve prosthesis configured to engage the helical anchor and prevent blood leakage past the heart valve prosthesis after implantation of the heart valve prosthesis in the helical anchor.