The most principal methods of studying hydroxyapatite (HAP) nanostructures and proton transfer peculiarities, its polarization properties are presented in this paper. HAP is one of the most widely used materials in medicine and biotechnology. The interaction between HAP biomaterials and living cells is improved, if the HAP surface is charged. The charge is inducible on HAP ceramics by the proton transport along the OH chains in columnar channels. These chains are formed by OH ions along c-axis and are surrounded by calcium triangles. The paper presents ab initio quantum-chemical calculations (with Gaussian98 code, HF, 6-31G(d)), which clarify the double-well asymmetric potential energy profile and were held to investigate the energy barriers for proton transport along the columnar channel. The calculated values of barriers can explain long storage of polarization charge, which is observed in experiments. The value of applied electric field could switch asymmetry of double-wall potential and made the proton transfer possible is of the order of $10^9$ V/m, but proton tunneling is possible at $10^6$ V/m. The estimated value of HAP surface polarization $\sim0.1$C/m$^2$ influences movement of living cells and leads to their adhesion on the charged HAP surface.