Reaction diffusion model of the enzymatic erosion of insoluble fibrillar matrices
Reaction diffusion model of the enzymatic erosion of insoluble fibrillar matrices
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DOI：
10.1016/s0006-3495(02)75208-9
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发表时间：
2002-08-01
影响因子：
3.4
通讯作者：
Parnas, H
中科院分区：
文献类型：
--
作者：
Tzafriri, AR;Bercovier, M;Parnas, H
预测体内生物降解的时间过程是设计越来越多的生物医学应用（如缝合线、组织类似物和药物输送装置）的关键问题。这种生物可降解装置的设计受到缺乏固体蛋白质基质的酶促侵蚀的定量模型的阻碍。在这项工作中，我们推导并模拟了一个反应扩散模型的纤维状凝胶的酶侵蚀，成功地再现了这个过程的主要定性特征。所提出的模型的一个关键方面是将空间位阻纳入酶动力学的标准Michaelis-Menten计划。在瞬时扩散的限制下，模型方程类似于溶液中酶降解的标准方程。通过这种类比，总的准稳态近似用于推导近似的解析解，这些解对于广泛的体外条件是有效的。使用这些解析近似，实验理论方法推导出明确估计所有的动力学模型参数。此外，解析近似正确地描述了特征的双曲线依赖的酶浓度和细纤维的零级侵蚀率的侵蚀。为了明确，发表的纤维胶原蛋白的酶降解的实验结果的分析表明，在这些实验中的扩散的作用进行了阐述。
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.