Tzafriri Abraham R, Bercovier Michel, Parnas Hanna
School of Computer Science and Engineering, Department of Neurobiology, The Hebrew University, Jerusalem 91904, Israel.
Biophys J. 2002 Aug;83(2):776-93. doi: 10.1016/S0006-3495(02)75208-9.
Predicting the time course of in vivo biodegradation is a key issue in the design of an increasing number of biomedical applications such as sutures, tissue analogs and drug-delivery devices. The design of such biodegradable devices is hampered by the absence of quantitative models for the enzymatic erosion of solid protein matrices. In this work, we derive and simulate a reaction diffusion model for the enzymatic erosion of fibrillar gels that successfully reproduces the main qualitative features of this process. A key aspect of the proposed model is the incorporation of steric hindrance into the standard Michaelis-Menten scheme for enzyme kinetics. In the limit of instantaneous diffusion, the model equations are analogous to the standard equations for enzymatic degradation in solution. Invoking this analogy, the total quasi-steady-state approximation is used to derive approximate analytical solutions that are valid for a wide range of in vitro conditions. Using these analytical approximations, an experimental-theoretical method is derived to unambiguously estimate all the kinetic model parameters. Moreover, the analytical approximations correctly describe the characteristic hyperbolic dependence of the erosion rate on enzyme concentration and the zero-order erosion of thin fibers. For definiteness, the analysis of published experimental results of enzymatic degradation of fibrillar collagen is demonstrated, and the role of diffusion in these experiments is elucidated.
预测体内生物降解的时间进程是越来越多生物医学应用（如缝线、组织类似物和药物递送装置）设计中的关键问题。由于缺乏固体蛋白质基质酶促侵蚀的定量模型，此类可生物降解装置的设计受到阻碍。在这项工作中，我们推导并模拟了一个用于纤维状凝胶酶促侵蚀的反应扩散模型，该模型成功再现了这一过程的主要定性特征。所提出模型的一个关键方面是将空间位阻纳入酶动力学的标准米氏方程。在瞬时扩散的极限情况下，模型方程类似于溶液中酶促降解的标准方程。利用这种类比，采用总准稳态近似来推导适用于广泛体外条件的近似解析解。利用这些解析近似，推导了一种实验 - 理论方法来明确估计所有动力学模型参数。此外，解析近似正确地描述了侵蚀速率对酶浓度的特征双曲线依赖性以及细纤维的零级侵蚀。为明确起见，展示了对已发表的纤维状胶原蛋白酶促降解实验结果的分析，并阐明了扩散在这些实验中的作用。
