Rea Riccardo, Angelis Maria Grazia De, Baschetti Marco Giacinti
Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali (DICAM), Università di Bologna, Via Terracini 28, 40131 Bologna, Italy.
Membranes (Basel). 2019 Feb 2;9(2):26. doi: 10.3390/membranes9020026.
Facilitated transport membranes are particularly promising in different separations, as they are potentially able to overcome the trade-off behavior usually encountered in solution-diffusion membranes. The reaction activated transport is a process in which several mechanisms take place simultaneously, and requires a rigorous theoretical analysis, which unfortunately is often neglected in current studies more focused on material development. In this work, we selected and reviewed the main mathematical models introduced to describe mobile and fixed facilitated transport systems in steady state conditions, in order to provide the reader with an overview of the existing mathematical tools. An analytical solution to the mass transport problem cannot be achieved, even when considering simple reaction schemes such as that between oxygen (solute) and hemoglobin (carrier) (A+C⇄AC), that was thoroughly studied by the first works dealing with this type of biological facilitated transport. Therefore, modeling studies provided approximate analytical solutions and comparison against experimental observations and exact numerical calculations. The derivation, the main assumptions, and approximations of such modeling approaches is briefly presented to assess their applicability, precision, and flexibility in describing and understanding mobile and fixed site carriers facilitated transport membranes. The goal is to establish which mathematical tools are more suitable to support and guide the development and design of new facilitated transport systems and materials. Among the models presented, in particular, those from Teramoto and from Morales-Cabrera et al. seem the more flexible and general ones for the mobile carrier case, while the formalization made by Noble and coauthors appears the most complete in the case of fixed site carrier membranes.
促进传递膜在不同的分离过程中特别有前景，因为它们有可能克服溶液扩散膜中通常遇到的权衡行为。反应活化传递是一个多种机制同时发生的过程，需要进行严格的理论分析，遗憾的是，在目前更侧重于材料开发的研究中，这一点常常被忽视。在这项工作中，我们挑选并回顾了为描述稳态条件下的移动和固定促进传递系统而引入的主要数学模型，以便为读者提供现有数学工具的概述。即使考虑简单的反应方案，如氧气（溶质）和血红蛋白（载体）之间的反应（A + C⇄AC），质量传递问题的解析解也无法得到，这一反应已被处理此类生物促进传递的早期研究深入探讨过。因此，建模研究提供了近似解析解，并与实验观测结果和精确数值计算进行了比较。本文简要介绍了这些建模方法的推导、主要假设和近似，以评估它们在描述和理解移动和固定位点载体促进传递膜方面的适用性、精度和灵活性。目标是确定哪些数学工具更适合支持和指导新型促进传递系统和材料的开发与设计。在给出的模型中，特别是寺本的模型以及莫拉莱斯 - 卡布雷拉等人的模型，在移动载体情况下似乎更具灵活性和通用性，而诺布尔及其合作者的形式化表述在固定位点载体膜的情况下似乎最为完整。
