In view of the importance of the hydroxyapatite/collagen composite of both natural bone tissue and synthetic biomaterials for hard tissue replacement, we have employed a combination of electronic structure calculations based on the Density Functional Theory and molecular dynamics simulations to investigate the adsorption of three major collagen I amino acids, as well as a complete peptide strand, at two hydroxyapatite surfaces, both in vacuo and in a liquid water environment. The free amino acids as well as the peptide form multiple interactions with the surfaces and bind more strongly to the (01.0) surface than the (0001) surface, in agreement with experiment, which has found that in natural bone the (01.0) surface grows preferentially from a collagen matrix.