Chang Joshua C, Miura Robert M
Clinical Center, National Institutes of Health, Bethesda, Maryland 20892, USA and Mathematical Biosciences Institute, The Ohio State University, Columbus, Ohio 43210, USA.
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
J Chem Phys. 2016 Apr 21;144(15):154906. doi: 10.1063/1.4946002.
In vertebrates, insufficient availability of calcium and inorganic phosphate ions in extracellular fluids leads to loss of bone density and neuronal hyper-excitability. To counteract this problem, calcium ions are usually present at high concentrations throughout bodily fluids-at concentrations exceeding the saturation point. This condition leads to the opposite situation where unwanted mineral sedimentation may occur. Remarkably, ectopic or out-of-place sedimentation into soft tissues is rare, in spite of the thermodynamic driving factors. This fortunate fact is due to the presence of auto-regulatory proteins that are found in abundance in bodily fluids. Yet, many important inflammatory disorders such as atherosclerosis and osteoarthritis are associated with this undesired calcification. Hence, it is important to gain an understanding of the regulatory process and the conditions under which it can go awry. In this manuscript, we extend mean-field continuum classical nucleationtheory of the growth of clusters to encompass surface shielding. We use this formulation to study the regulation of sedimentation of calcium phosphate salts in biological tissues through the mechanism of post-nuclear shielding of nascent mineral particles by binding proteins. We develop a mathematical description of this phenomenon using a countable system of hyperbolic partial differential equations. A critical concentration of regulatory protein is identified as a function of the physical parameters that describe the system.
在脊椎动物中,细胞外液中钙和无机磷酸根离子供应不足会导致骨密度降低和神经元过度兴奋。为了应对这个问题,钙离子通常以高浓度存在于全身体液中——浓度超过饱和点。这种情况会导致相反的情况,即可能发生不必要的矿物质沉淀。值得注意的是,尽管存在热力学驱动因素,但异位或沉积到软组织中的情况很少见。这一幸运的事实归因于体液中大量存在的自调节蛋白。然而,许多重要的炎症性疾病,如动脉粥样硬化和骨关节炎,都与这种不期望的钙化有关。因此,了解调节过程以及它可能出错的条件非常重要。在本手稿中,我们将团簇生长的平均场连续介质经典成核理论扩展到包括表面屏蔽。我们使用这种公式来研究通过结合蛋白对新生矿物质颗粒进行核后屏蔽的机制,从而调节生物组织中磷酸钙盐的沉淀。我们使用双曲型偏微分方程的可数系统对这一现象进行了数学描述。确定了调节蛋白的临界浓度作为描述系统的物理参数的函数。