The Prion protein is the molecular hallmark of the incurable prion diseases affecting mammals, including humans. The protein-only hypothesis states that the misfolding, accumulation, and deposition of the Prion protein play a critical role in toxicity. The cellular Prion protein (PrPC) anchors to the extracellular leaflet of the plasma membrane and prefers cholesterol- and sphingomyelin-rich membrane domains. Conformational Prion protein conversion into the pathological isoform happens on the cell surface. In vitro and in vivo experiments indicate that Prion protein misfolding, aggregation, and toxicity are sensitive to the lipid composition of plasma membranes and vesicles. A picture of the underlying biophysical driving forces that explain the effect of Prion protein - lipid interactions in physiological conditions is needed to develop a structural model of Prion protein conformational conversion. To this end, we use molecular dynamics simulations that mimic the interactions between the globular domain of PrPC anchored to model membrane patches. In addition, we also simulate the Doppel protein anchored to such membrane patches. The Doppel protein is the closest in the phylogenetic tree to PrPC, localizes in an extracellular milieu similar to that of PrPC, and exhibits a similar topology to PrPC even if the amino acid sequence is only 25% identical. Our simulations show that specific protein-lipid interactions and conformational constraints imposed by GPI anchoring together favor specific binding sites in globular PrPC but not in Doppel. Interestingly, the binding sites we found in PrPC correspond to prion protein loops, which are critical in aggregation and prion disease transmission barrier (β2-α2 loop) and in initial spontaneous misfolding (α2-α3 loop). We also found that the membrane re-arranges locally to accommodate protein residues inserted in the membrane surface as a response to protein binding.