Introduction

Hydroxyapatite (HAp), Ca10(PO4)6(OH)2, is the most stable phase of calcium phosphate under physiological conditions, and it is a major constituent of bone and teeth. Therefore, HAp is of great interest as an implantable and biocompatible material [1,2,3,4]. Several methods have been developed for the synthesis of biocompatible HAp [5,6,7,8].

Tetracalcium phosphate (Ca4(PO4)2O: TeCP) was used as a fertilizer because of the higher solubility relative to apatite minerals. TeCP is a component in several calcium phosphate cements for biomaterials. TeCP has been reported [9,10,11] to react with acid dicalcium phosphate anhydrous (CaHPO4 2H2O: DCPD) at a Ca/P molar ratio of 1.67 to form HAp, as expressed in Eq. (1):

$$ {2\mathrm{Ca}\mathrm{HPO}}_4\ {2\mathrm{H}}_2\mathrm{O}+{2\mathrm{Ca}}_4{\left({\mathrm{PO}}_4\right)}_2\mathrm{O}\to {\mathrm{Ca}}_{10}{\left({\mathrm{PO}}_4\right)}_6{\left(\mathrm{OH}\right)}_2+3\ {\mathrm{H}}_2\mathrm{O}. $$
(1)

Brown and Chow [9] developed a self-setting apatite cement (SSAC) system. The dense paste of the cement sets within 15 min in vivo and isothermally converts to microporous HAp [12]. The transformed HAp contains 1 to 2% carbonate, and its crystallinity and solubility greatly depend on the concomitant carbonate contents [13].

It is known that the geometrical structures of seashells, which are formed by the deposition of precise arrays [14] of inorganic crystals in many proteins, involve controlled nucleation at interfaces. The peptides and proteins involved in mineralization are also involved in the calcification of hard tissues in the human body [15]. The adsorptions of amino acids and proteins on the HAp surface are reported to have a specific effect on the crystalline growth rate of HAp [16,17,18]. Hence, the surface interaction between HAp and amino acids is a very important factor of biophysics in the human body.

Attenuated total reflection (ATR)-infrared (IR) spectroscopy, which is a direct molecular interaction analysis method, is applied to the HAp cement formation process to evaluate rapid crystal growth kinetics [19]. A bending vibration of the phosphate acid group in HAp was observed at 1000 to 1200 cm−1 as a key band of HAp formation. High-time-resolution IR spectroscopic analysis of the phosphate acid group was found to be a useful method to evaluate HAp crystal growth kinetics.

The surface adsorption of amino acids on HAp [20] could be evaluated kinetically by the ATR-IR method because amino acids are electrostatically adsorbed on HAp, and the adsorption depends on the electrochemical conditions of the amino acids and HAp structure. In this study, the influence of amino acids on HAp crystal growth was investigated by combining ATR-IR spectroscopy and the multivariate analysis method. The simulation of the HAp surface was performed using the molecular dynamic model to understand the amino acid interaction.

Materials and methods

Materials

TeCP and DCPD powders were obtained from Taihei Chemical Industrial Co. (Osaka, Japan) and Wako Pure Chemical Industries (Osaka, Japan), respectively. Apatite cement samples were prepared according to the procedure described by Brown and Chow [9]. The raw material powders of the HAp cement were prepared by mixing TeCP (0.0618 g) and DCPD (0.0291 g) powders, in which the Ca/P ratios were 1.67. All other chemicals were of analytical regent grade and were obtained from Wako Pure Chemical Industries.

Methods

Infrared spectra were measured with an FT-IR spectrometer (FT/IR-6500, JASCO Co., Tokyo, Japan) equipped with an ATR accessory, which was inserted directly into the light beam. Five milligrams of mixed TeCP-DCPD powder was kneaded with 10.0 μL of 0.1 w/v% of l-alanine (Ala), l-asparagine (Asn), l-serine (Ser) or o-phospho-l-serine (Pser), or 0.2 M of pH 6.8 phosphoric buffer (PB). Each paste sample was put on the germanium glass of the ATR accessory. The sample was covered with a Parafilm sheet at room temperature. The IR spectra of the paste samples were measured in the range of 1300 to 800 cm−1 at a resolution of 4 cm−1. The IR spectrum data of 64 scans were averaged and corrected. The room air spectrum was subtracted from the averaged data as a background.

MCR-ALS

Multivariate curve resolution alternative least squares (MCR-ALS) is one of the multivariate analysis methods developed by Tauler [21, 22]. MCR-ALS is easily adapted to analysis in a variety of contexts for many different data metrics. As reported in other works [23,24,25], the MCR algorithm can decompose the spectra of mixtures to the n contributions of the components involved in the vibrational spectra. The datasets of IR spectrum metrics are arranged in the matrix D, with the vibrational spectra as the r rows and the c columns. Both rows and columns are the measured IR absorbance values at each wavelength.

The MCR decomposition of IR spectrum matrix D is carried out, according to the following equation:

$$ D=C\ {S}^T+E $$
(2)

where matrix C is called the “concentration profiles.” The matrix ST is the spectral contribution of n components in the c columns of the decomposed spectra. Here, E is a residual, which contains the IR spectrum dataset variance that cannot be explained by the product CST.

Molecular dynamics calculation of HAp crystal surface

Simulation models of the HAp surface were performed using BIOVIA Materials studio 2018 modeling software [26]. The constructed HAp (221) face and (110) face surfaces with vacuum layers were modeled. The model calculation used condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) [27]. The details of COMPASS were described elsewhere [28,29,30]. The total energy and the parameters of the constructed layer cell were evaluated for surface dynamic conditions.

Software

The chemometrics were performed by the UNSCRAMBLER software v.10.4, 64 bit (Camo Software AS, Oslo, Norway). The molecular dynamics calculation was performed by BIOVIA Materials studio 2018 (Dassault Systèmes, Vélizy-Villacoublay, France).

Results and discussion

Effect of solute on HAp crystal growth with ATR-IR spectra

Figure 1a–e shows the changes in the ATR-IR spectra of the TeCP-DCPD mixtures after they were kneaded with PB or 0.1 w/v% solutions of Ala, Asn, Ser, or Pser. The broad IR absorption in the range of 900 to 800 cm−1 is due to free water in aqueous phase. The characteristic peak shifts in the range of 900 to 1200 cm−1 are attributable to the phosphate ions of calcium phosphates.

Fig. 1
figure 1

Infrared spectra of the supersaturated samples with several solutions. a pH 6.8 phosphate buffer, b asparagine solution, c alanine solution, d serine solution, and eo-phospho-l-serine solution. Color line legends show time (min)

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For the latter range, the absorption bands of HAp-related materials are respectively assigned as follows [15, 19]: the bands at 962 and from 976 to 1190 cm−1 are assigned to the ν1 and ν3 vibrational modes of PO43− ions, respectively. The characteristic peak of 1024 cm−1 is due to the ν3 phosphate vibration of HAp [8]. The characteristic peaks at 1024 cm−1 due to the PO43− symmetric vibration of HAp increased with time after the samples were kneaded with PB, Ala, or Asn. In contrast, the spectrum of a supersaturated sample showed no remarkable change in IR absorbance after it was kneaded with Pser. This result suggests that Pser inhibits the crystal growth of HAp.

In a previous study [31], polymorphic transformation of carbamazepine in supersaturated suspensions was analyzed by the MCR-ALS method based on IR spectra. The results clarified the effects of hydroxypropyl cellulose on the crystal growth mechanism. In the present study, the IR spectra of the sample suspensions were calculated by MCR-ALS to evaluate the inhibition mechanism of various kinds of amino acid on the HAp transformation process in supersaturated samples with amino acids.

Crystal growth quantification in supersaturated calcium phosphate sample by MCR-ALS based on IR spectra

Figure 2a and b shows the principal sources of transformation of the calcium phosphate samples estimated by MCR-ALS. The blue, red, and green curves in Fig. 2a respectively represent the spectra of the principal sources 1 (S1), 2 (S2), and 3 (S3) obtained by MCR-ALS analysis. The blue, red, and green lines in Fig. 2b show the IR spectra of the DCPD, HAp, and TeCP powders as reference samples. The results suggest that S1, S2, and S3 can be respectively assigned to DCPD, HAp, and the background based on comparison with the characteristic IR peaks of standard samples. Background absorbance change was also reported in the phase transformation [32] and polymorphic transform [33] in previous studies. In the present study, the results suggest that phase transformation of the SSAC system caused sample density changes.

Fig. 2
figure 2

Decomposed sources based on IR spectra with MCR-ALS calculation (a) and IR spectra of reference bulk materials (b)

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Figure 3 shows the source 2 score profile (HAp crystal concentration) of the SSAC in the presence of various amino acids. The scores of the SSAC in the presence of Asn, Ala, PB, Ser, and Pser samples at 54 min were, respectively, 0.1965, 0.01636, 0.01495, 0.00401, and 0.00048. TeCP and DCPD in the SSACs were transformed into HAp depending on environmental temperature [34]. It was reported that HAp was also stable under neutral to alkaline conditions (pH 7 to 9) [35]. It was also reported that HAp crystal growth was inhibited by amino acid adsorption on the seed crystal surface with electrostatic interactions [36, 37]. The previous score profiles presented in Fig. 3 show that HAp crystal growth was inhibited by Ser and Pser. The induction period of crystal growth was 20 min in the Ser solution sample. The results suggest that HAp crystal growth was completely inhibited in the Pser sample. The inhibitory effects of amino acids on HAp crystal growth indicate that it is possible to control crystal growth speed.

Fig. 3
figure 3

Time profiles of HAp concentration in supersaturated samples based on source 2 values

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Kinetic analysis of phase transformation of hydroxyapatite

To verify the crystal growth mechanism, the phase transformation of calcium phosphate samples was analyzed based on several solid-state kinetic model equations. Table 1 shows the solid-state crystal growth mechanism according to kinetic analysis [38]. The first-order mechanism (FO), one-half-order mechanism (OH), two-thirds-order mechanism (TT), one-dimensional diffusion (1DD), two-dimensional diffusion (2DD), Jander three-dimensional diffusion (3DD), two-dimensional growth of nuclei (2DA), and three-dimensional growth of nuclei (3DA) were fitted for kinetic analysis of HAp crystal growth.

Table 1 Kinetic equations for general crystal growth mechanisms
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Figure 4a–h shows the plots based on the respective solid-state kinetic models. The linearities of the plots were evaluated by the least-squares method, and the correlation coefficients are summarized in Table 2. The coefficient values of the HAp transformation process indicate that the transformations with Asn, Als, PB, Lser, and Pser can be assigned to the 2DA, 3DD, FO, OH, and FO mechanisms, respectively.

Fig. 4
figure 4

Kinetic plots of HAp crystal growth based on source 2 values: a first-order mechanism, b one-half-order mechanism, c two-thirds-order mechanism, d one-dimensional diffusion (1DD), e two-dimensional diffusion (2DD), f Jander three-dimensional diffusion (3DD), g two-dimensional growth of nuclei (2DA), and h three-dimensional growth of nuclei (3DA)

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Table 2 Decision coefficient of fitted time profiles of HAp crystal growth for several kinetic equations
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In general, there are three rate-determining steps of crystal growth in a saturated solution [39]. The first is diffusion of a reactant, second is reaction on the surface, and third is diffusion of reaction heat. In a previous study [19], polymorphic transformation of carbamazepine was controlled by changing the mother liquid viscosity. Since the viscosity of the mother liquid of HAp was not increased by the addition of Ser and Pser, inhibition of HAp crystal growth by both amino acids did not affect the diffusion process. The second possibility is the decrease in surface free energy due to the adsorption of amino acids. Controlling the surface free energy of HAp through the chemisorption of poly-phosphonates on the surface of HAp can improve its properties as a biomaterial [40]. HAp crystal growth and its mechanical strength as an implant have been improved by the adsorption of collagen [41]. Bisphosphonate chemical adsorption on HAp in bone suppressed the activation of osteoclasts [42]. Tanaka et al. [20] reported that anionic species were concomitantly liberated from the surface of HAp to maintain the electroneutrality of the seed crystal or cluster surface. Calcium, phosphate, hydrogen, and carbonate ions in a supersaturated solution contacting amino acids are taken up on the HAp surface. The pKa of Ala, Asn, Ser, and Pser were reported to be 2.3/9.9, 2.0/8.8, 2.2/9.2, and 1.2/9.4 [43]. The surface interaction between HAp seed crystals and their inhibition by amino acids depending on their electrostatic interaction has been reported [20, 26]. It was suggested that Ser and Pser are selectively adsorbed onto a specific plane of the HAp surface with electrostatic force, and decreased HAp surface free energy results in the inhibition of HAp crystal growth.

Molecular dynamics calculation of HAp crystal surface

The existence of the HAp crystal depends on the nucleation and crystal growth process and the thermodynamic stability of samples. The molecular dynamics of the HAp surface with amino acids were calculated to investigate the effect of amino acids on the HAp crystal growth phase. Figure 5 illustrates a 3D view of the constructed HAp (221) face (a) and (110) face (b) surface models and the amino acid inserted model with a vacuum layer. It is known that the largest face of biocompetitive apatite crystal is the (221) face. Fei et al. reported [44] fibronectin adsorbs on nano-HAp (110) face. The vacuum layer was inserted as 50 Å in the C-axis direction to eliminate the effect of other periodic layers. The total cell volumes of the HAp (221) face model and (110) face model were 65,181 Å3 and 39,297 Å3, respectively. All HAp crystals were regarded as constraints of the molecular model for calculations. The lattice parameters of the model HAp layers are listed in Table 3. The molecular model of Ala, Asn, Ser, and Pser was inserted in the center of both model layers. The geometrical optimizations of the inserted amino acid models were calculated by COMPASS [28] with medium quality and the force field assigned mode. The electrostatic and van der Waals simulations were selected in the Ewald simulation.

Fig. 5
figure 5

Constructed HAp surface models of HAp (221) face (a) and (110) face (b)

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Table 3 Surface model parameter of HAp (221) face and HAp (110) face
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Table 4 shows the geometrical optimized total energy and the factors of the HAp (211) face and (110) face with amino acids. The total energy was the sum of the valence energy of the diagram and cross terms and the nonbond energy. The total energies of the HAp (221) and (110) face models were determined as Pser < Asn < Ser < Ala. The most significant contribution to total energy was electrostatic energy. The electrostatic energies of Ala, Asn, Ser, and Pser were, respectively, − 1597, − 2661, − 1933, and − 3178 kcal/mol for the HAp (221) surface model. The results suggested that all amino acids were molecularly adsorbed on both HAp crystal surfaces. The simulation results suggested that the electrostatic energies of the nonbond energy were primal factors of adsorption. In other adsorption simulation research [45], the molecular dynamics simulation of nucleation of HAp with a collagen model was reported. The calculation models show that collagen peptide binds to the HA(01\( \overline{1} \)0) face in the aqueous phase. The inhibitory activity of HAp crystal growth with Pser was reported in HAp experiments of amino acid adsorption with the Langmuir model [46]. The investigation of the thermodynamic stability of HAp was also demonstrated. The order of the stability value differed from the experimental value because of the vacuum model, and pure HAp was suggested. Further investigation of simulation experiments of the hydroxyapatite surface in the aqueous model is underway for other amino acid models.

Table 4 Surface model total energy and their contribution on HAp (221) face and HAp (110) face
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Conclusion

The effect of Ala, Asn, Ser, and Pser adsorption on calcium phosphate phase transformation was investigated by ATR-IR spectroscopy with high-time-resolution measurement. HAp crystal growth kinetics were evaluated based on IR spectra by MCR-ALS decomposition. The crystal growth rate constants of supersaturated calcium phosphate samples were found to be significantly dependent on the amino acids. The supersaturated samples containing Ala and Asn were rapidly transformed into HAp; however, the phase transformation of HAp containing Pser and Ser was significantly inhibited. The kinetic analysis suggested that Pser and Ser are selectively adsorbed on a specific plane of the HAp surface with electrostatic force and decrease the surface free energy of HAp seed crystals. The molecular dynamics were applied to calculate the adsorption energy of amino acids on the HAp crystal surface. The pure HAp surface was modeled in the simulation method, and the simulations were successfully calculated. The adsorbed total energy of the amino acid model on the crystal surface was investigated. It was found that the most significant contribution to the adsorption factor was electrostatic energy of the nonbond energy in the models.