Mathematical model of physicochemical regulation of precipitation of bone hydroxyapatite

IF 1.3 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Frontiers in Applied Mathematics and Statistics Pub Date : 2023-12-19 DOI:10.3389/fams.2023.1294540
H. Poorhemati, Svetlana V. Komarova
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Abstract

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.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.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.
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骨羟基磷灰石沉淀的物理化学调控数学模型
骨骼、牙本质和珐琅质中羟基磷灰石的形成发生在特定细胞外基质蛋白的受限分子位点,并受多种矿化抑制剂的控制。然而,人们对理化因素(如所需离子的可用性和水环境的饱和状态)在生物矿化中的作用还不完全了解。我们模拟了骨间质(ISF)中发生的过程,骨间质被定义为含有七种化学成分(钙、磷酸盐、碳酸盐、钠、钾、镁和氯化物)并形成 30 种化学物质的水环境。我们模拟了这些化学物种之间的可逆平衡反应,并利用动力学理论计算了羟基磷灰石的过饱和度及其沉淀率。模拟的 ISF 离子强度正确,预测的平衡成分浓度与实验结果一致。生理 ISF 的过饱和度约为 15,这与之前的研究结果一致,即需要矿化抑制剂来防止矿物自发沉淀。只有总钙、总磷以及较小程度的总碳酸盐会影响离子可用性、溶液过饱和度和羟基磷灰石沉淀率。钙和磷酸盐的含量直接影响羟基磷灰石的沉淀,磷酸盐受 pH 值的影响,而 pH 值又影响羟基磷灰石的沉淀。通过数学模型捕捉调节骨矿化的物理化学和生物学因素,可以对佝偻病、低磷血症和慢性肾病等与 ISF 离子组成改变有关的复杂临床情况进行硅学研究。
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来源期刊
Frontiers in Applied Mathematics and Statistics
Frontiers in Applied Mathematics and Statistics Mathematics-Statistics and Probability
CiteScore
1.90
自引率
7.10%
发文量
117
审稿时长
14 weeks
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