Mathematical model of physicochemical regulation of precipitation of bone hydroxyapatite

Introduction: Formation of hydroxyapatite in bone, dentin, and enamel occurs at restricted molecular sites of specific extracellular matrix proteins and is controlled by multiple mineralization inhibitors. However, the role of physicochemical factors, such as the availability of required ions and the saturation status of the aqueous environment in biological mineralization, is not fully understood. The goal of this study was to use mathematical modeling to describe the complex physicochemical environment permissive to the precipitation of biological hydroxyapatite. Methods: We simulated the processes occurring in the bone interstitial fluid (ISF) defined as an aqueous environment containing seven chemical components (calcium, phosphate, carbonate, sodium, potassium, magnesium, and chloride) that form 30 chemical species. We simulated reversible equilibrium reactions among these chemical species, and calculated supersaturation for hydroxyapatite and its precipitation rate using kinetic theory. Results and Discussion: The simulated ISF was of correct ionic strength and predicted the equilibrium component concentrations that were consistent with the experimental findings. Supersaturation of physiological ISF was ~15, which is consistent with prior findings that mineralization inhibitors are required to prevent spontaneous mineral precipitation. Only total calcium, total phosphate and to a lesser degree total carbonate affected ion availability, solution supersaturation and hydroxyapatite precipitation rate. Both calcium and phosphate levels directly affected hydroxyapatite precipitation, and phosphate was affected by pH, which additionally influenced hydroxyapatite precipitation. Integrating mathematical models capturing the physiochemical and biological factors regulating bone mineralization will allow in silico studies of complex clinical scenarios associated with alterations in ISF ion composition, such as rickets, hypophosphatemia, and chronic kidney disease.