  The conformation and the phase diagram of a membrane protein are investigated
via grand canonical ensemble approach using a homopolymer model. We discuss the
nature and pathway of $\alpha$-helix integration into the membrane that results
depending upon membrane permeability and polymer adsorptivity. For a membrane
with the permeability larger than a critical value, the integration becomes the
second order transition that occurs at the same temperature as that of the
adsorption transition. For a nonadsorbing membrane, the integration is of the
first order due to the aggregation of $\alpha$-helices.
