Mathematical model capturing physicochemical and biological regulation of bone mineralization.

Bone mineralization is a complex process tightly regulated by both biological factors such as collagen maturation as well as physicochemical factors such as pH. A previous model of biological mineralization captured the biological regulation of bone mineralization dynamics, but not the impact of bone microenvironment such as ion availabilities which may be altered in hypo or hyperphosphatemia. To build an integrated model of bone mineralization, we utilized two previously developed models which addressed a distinct aspect of bone mineralization. The first model described the processes of the extracellular matrix formation and maturation, inhibitor and nucleator formation and removal and their combined action in regulating bone mineralization. The second model simulated the bone interstitial fluid (BIF) permissive to precipitation of hydroxyapatite and described the physicochemical process of hydroxyapatite precipitation. The resulting bone mineralization model accounts for biological and physicochemical aspects of the process. The integrated model was analyzed for the impact of physicochemical factors (pH, levels of calcium and phosphate) on the mineralization dynamics. Model predictions were compared to experimental findings using two outcomes characterizing mineralization dynamics: mineralization delay that corresponds to histomorphometry measures of osteoid volume or thickness, and mineralization degree that corresponds to bone mineral density distribution. We identified the limitation of the previously developed model in predicting the mineralization delay observed in the situations of hypophosphatemia and hypocalcemia and proposed a model adaptation that predicts these outcomes. The resulting mathematical model can be used for in silico testing of hypotheses regarding the role of different physicochemical, molecular, or cellular factors in causing a specific disruption in mineralization dynamics.