Department of Applied Mathematics, NUI Galway, Galway, Ireland; Department of Mathematics, Thu Dau Mot University, Binh Duong, Vietnam.
MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland.
Math Biosci. 2018 Sep;303:126-138. doi: 10.1016/j.mbs.2018.07.002. Epub 2018 Jul 11.
Hyaluronic acid (Hyaluronan) is a linear, high molecular weight polysaccharide that forms an important component of the extracellular matrix. It is an excellent biomaterial, and it is increasingly being used in biotechnology, biomedical applications, and drug delivery. Polymer chains of hyaluronan occur in many different lengths in nature, and can be as large as multiples of ten thousand. Since the biological function of a hyaluronan chain often depends on its molecular weight, it is of value for applications to develop reliable quantitative descriptions of the degradation processes of hyaluronan. In particular, the development of such models should assist with the rational design of production processes to create polymer chains in a given molecular weight category for a specific application. In this paper, we propose a new mathematical model for the degradation of hyaluronan by the enzyme streptococcus pneumoniae hyaluronate lyase. The model is based on a processive kinetic mechanism and consists of a coupled system of nonlinear ordinary differential equations for the species of interest. The model parameters are estimated using published experimental data, and good agreement between theory and experiment is found. Numerical experimentation and a Sobol global sensitivity analysis reveal that the key model parameters are the initial enzyme concentration and the rate constants for enzyme adsorption and catalysis.
透明质酸（Hyaluronan）是一种线性高分子量多糖，是细胞外基质的重要组成部分。它是一种极好的生物材料，越来越多地被用于生物技术、生物医学应用和药物输送。透明质酸的聚合物链在自然界中存在许多不同的长度，最大可达数千倍。由于透明质酸链的生物学功能通常取决于其分子量，因此开发可靠的定量描述透明质酸降解过程的方法对于应用具有重要价值。特别是，此类模型的开发应该有助于合理设计生产工艺，以便在特定应用中为给定分子量类别创建聚合物链。在本文中，我们提出了一种新的数学模型，用于描述肺炎链球菌透明质酸酶对透明质酸的降解作用。该模型基于连续动力学机制，由感兴趣的物种的耦合非线性常微分方程组组成。模型参数是使用已发表的实验数据进行估计的，理论与实验之间存在良好的一致性。数值实验和 Sobol 全局敏感性分析表明，关键的模型参数是初始酶浓度和酶吸附和催化的速率常数。
