A transcatheter prosthesis with radially compressed and expanded configurations. An elongate member encircling at least a portion of the prosthesis, and configured to provide a seal between the prosthesis and a native anatomy when the prosthesis is deployed in the radially expanded configuration. The elongate member may be a resilient elongate member having a radially contracted state, when in tension, to hold at least the portion of the prosthesis in the radially compressed configuration, and having a radially expanded state, when relaxed, to provide the seal between at least the portion of the prosthesis and a native anatomy when the prosthesis is deployed. A system for delivering the transcatheter prosthesis may include a delivery catheter having an elongate cinching member encircling at least a second portion of the prosthesis, wherein the elongate cinching member is configured to hold the second portion of the prosthesis in the radially compressed configuration.