Hydroxyapatite is an inorganic component of bone and teeth. Stoichiometric hydroxyapatite is an ionic crystal with Ca²⁺, PO₄^3-, and OH^- as the main components, and the crystal system is hexagonal. In this study, we considered the application of the PC software “PyMOL” to hydroxyapatite. Although this software requires the three- dimensional coordinates of each molecule, we could use the data which were obtained in our previous study. Using this software, we can freely view the stereo structure of any molecules from any direction simply by operating a PC mouse. In addition to the CG of hydroxyapatite, we could show the CG of fluoridated hydroxyapatite with the partial substitution of OH^- by F^-, and Mg^- containing hydroxyapatite with that of Ca²⁺ by Mg²⁺.

Bone and teeth are composed of an inorganic hydroxyapatite and organic collagen. Tooth enamel contains more than 95% of highly crystallized hydroxyapatite, while bone and tooth dentine contain 60-70% of poorly crystallized hydroxyapatite [1,2]. Strictly speaking, they are carbonate-containing hydroxyapatites, so-called “carbonate apatites” (CO3Ap), which contain several % of CO32- ions [3].

Stoichiometric hydroxyapatite (HAp: Ca₁₀ (PO₄)₆(OH)₂) is an ionic crystal with Ca²⁺, PO₄^3-, and OH^- as the main components, and the crystal system is hexagonal (a = b = 9.432 Å, c = 6.881 Å, α = β = 90º, γ = 120º) [4,5]. It has been reported that almost all elements in the periodic table can adopt the positions of the main components above-mentioned [6]. Therefore, “apatites” has the meaning of thieves because they are very complicated substances from the Greek language. Thus, real apatites contain many trace elements.

The analysis of hydroxyapatite was delayed until 1964 [5], although the crystal structure of fluorapatite (FAp: Ca₁₀ (PO₄)₆F₂) was initially analyzed in 1930 by Náray-Szabó [7]. Because OH^- ions in hydroxyapatite shift just 0.3 Å from the stable position, it was difficult to determine the accurate crystal structure solely by X-ray diffraction analysis. Finally, it was determined by combining with neutron diffraction analysis [8]. Hydroxyapatite is sudo-hexagonal (rhombohedral), while FAp is a typical hexagonal crystal. Due to the development of computer science, Okazaki and Sato [9] could successfully construct a crystal model of HAp with a personal computer and the program “PROTGRA” [10]. In their paper, the computer graphics (CG) of HAp and FAP were shown accurately according to the radii of Ca²⁺ (0.99 Å), P⁵⁺ (0.33 Å), O^2- (1.40 Å), H⁺ (negligible), and F^- (1.36 Å) based on the data of Pauling [11]. OH^- ions in hydroxyapatite shift just 0.3 Å from the stable position, while F^- ions in fluorapatite are present at levels of just 1/4 and 3/4 of the height of the crystal unit cell. Lattice dimensions of a = 9.37 Å and c = 6.88 Å were adopted from the data reported by Náray-Szabó [7]. Compared with the structure of hydroxyapatite, that of fluorapatite can readily be seen to be crystallographically more stable. The computer graphics display demonstrated that fluoride ions serve to stabilize the hydroxyapatite crystals and prevent dental caries.

Recently, the PC software “PyMOL”, which can draw polymer CG on Windows, is often used worldwide. We considered the application of “PyMOL” to hydroxyapatite. At present, “PyMOL” is licensedby Schrödinger. We have already succeeded in the CG drawing of tetrafluoroethylene (PTFE) [12]. Using this software, we can freely view the stereo structure of any molecules. However, this software requires the three- dimensional coordinates of each molecule. Fortunately, we could use the data shown in Table 1, which were obtained in our previous study [9].

The atomic radius of each element is set as the Von der Waals radius by default, and a ball and stick (BS) model is initially drawn. Therefore, each radius was changed into an ionic radius based on Pauling data [11], and then modified slightly to be able to visualize it clearly as follows: Ca²⁺ (0.99 Å), P⁵⁺ (0.33 Å → 0.70 Å), O^2- (1.40 Å → 1.20 Å), H⁺ (negligible → 0.40 Å), F^- (1.36 Å → 1.20 Å), and Mg²⁺ (0.65 Å)

Computer Graphics
Figure 1 shows the original BS model of the hydroxyapatite with the Van der Waals radius displayed from directions perpendicular (Figure 1A) and parallel (Figure 1B) to the c-axis. Figure 2 is an ionic model observed from the same direction as Figure 1. Figure 3 shows the posterior view. We can view the structure freely from any direction simply by operating a PC mouse.

Furthermore, as mentioned above, almost all of the elements in the periodic table can replace for the main components of Ca²⁺, PO₄^3-, and OH^- [4]. Figure 4, as an example, shows the CG of fluoridated hydroxyapatite with the partial substitution of OH^- by F^- (Figure 4A), and Mg-containing hydroxyapatite with that of Ca²⁺ by Mg²⁺ (Figure 4B). Interestingly, some of the crystallographic properties of partially substituted fluoridated hydroxyapatites still remain unknown, although many studies have been conducted [13-16].

Future Trends
Bological apatites such as bone and teeth are carbonate-containing hydroxyapatite (CO₃Ap). A number of crystallographic studies on CO₃Ap have been reported [3,15, 17-20]. Enamel apatite contains 1~3 wt% of CO₃^2- ions, and bone and dentine contain more CO₃^2- ions, 5~6 wt% [2]. It is known that CO₃^2- ions of biological apatites, which are created in aqueous solution, adopt mainly PO₄^3- positions, contrary to CO₃Ap synthesized under dry conditions at a high temperature, in which CO₃^2- ions adopt OH^- positions. Interestingly, since the molecular weight of hydroxyapatite is 1,000 and that of CO₃^2- ions is 60 (6 wt%), in the case of bone apatite, approximately one CO₃^2- ion can replace six PO₄^3- ions in a unit cell of hydroxyapatite.

We can also draw the CG of CO₃Ap. However, the accurate direction of CO₃^2- is still unknown, because the content of CO₃^2- ions in CO₃Ap is small, and the crystallinity of CO₃Ap decreases with an increase in the CO₃^2- ion content. At present, we consider the possibility of CO₃^2- existing parallel to the c-axis being strong from the viewpoint of the shortening of the a-axis observed on X-ray diffraction analysis.