Atomistic simulation methods, namely molecular dynamics and well-tempered metadynamics, are used in this thesis to investigate apatite formation from different aspects. First, ions which are more abundant in SBFs under physiological conditions were identified and their interaction with the rutile surface was studied. Using free energy calculations, it was possible to identify ions with a favorable interaction with the rutile surface. Among the ionic species which were studied, potassium, sodium, calcium, carbonate and phosphate showed favorable adsorption on the surface. Consequently, these ions may either adsorb on the surface prior to apatite formation, and promote or inhibit it, or may be involved in the apatite formation. Further studies revealed that adsorption of phosphate either in the form of an ionic pair with a calcium ion, or either on a pre-adsorbed calcium on the surface is very favorable, indicating that the current apatite formation mechanism proposed experimentally is reasonable. Adsorption of several amino acids on the rutile surface was studied and the energetics of the adsorption events were quantified. Initially, the distance between the center of mass of the amino acid from the surface was chosen as the reaction coordinate, which is commonly used. However, the affinity of different amino acids for the surface based on different adsorption conformations could not be explained by this collective variable. The reweighting method was used to project the free energy profile to a two-dimensional phase space, in which energetics of different adsorption conformations, be via the side group, via the backbone, or via both, could be distinguished. It was observed that electrostatic forces between the surface charge point and the backbone group (amine group in specific) lead to the adsorption of amino acids on the surface via their backbone and irrespective of the nature of the side group. However, non-polar side groups did not lead to the adsorption of the amino acids while adsorption via the polar (Ser) and charged side groups (Arg, Lys and Asp) was favored, and the strongest when the charge of the side group was opposite to the charge of the surface. The effect of pre-adsorbed species on the adsorption of other species on the surface was studied. Results revealed that the Arg and Asp amino acids did not affect the adsorption of ions of interest on the surface, destructively. Calcium and phosphate were both able to compete with the pre-adsorbed amino acids for the charge point on the rutile surface and successfully adsorb in the vicinity of the charge point. Amino acids were also unable to disturb the pre-adsorbed calcium ions on the surface, suggesting that single amino acids do not significantly inhibit apatite formation. Finally, the adsorption of the TBP hexapeptide on the rutile surface was studied and different adsorption conformations were reported. Comparison with those previously reported in the literature, revealed that the adsorption conformations of TBP are mostly driven by the surface charge density and not the structure of the titanium oxide surface (its crystallinity or the crystallographic surface).