Abstract

Nearly all life forms require iron to survive and function. Microorganisms utilize a number of mechanisms to acquire iron including the production of siderophores, which are organic compounds that combine with ferric iron into forms that are easily absorbed by the microorganism. There has been significant experimental investigation into the role, distribution and function of siderophores in fungi but until now no predictive tools have been developed to qualify or quantify fungi-initiated siderophore–iron interactions. In this investigation, we construct the first mathematical models of siderophore function related to fungi. Initially, a set of partial differential equations are calibrated and integrated numerically to generate quantitative predictions on the spatio-temporal distributions of siderophores and related populations. This model is then reduced to a simpler set of equations that are solved algebraically giving rise to solutions that predict the distributions of siderophores and resultant compounds. These algebraic results require the calculation of zeros of cross products of Bessel functions and thus new algebraic expansions are derived for a variety of different cases that are in agreement with numerically computed values. The results of the modelling are consistent with experimental data while the analysis provides new quantitative predictions on the time scales involved between siderophore production and iron uptake along with how the total amount of iron acquired by the fungus depends on its environment. The implications to bio-technological applications are briefly discussed.

中文翻译：

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真菌引发的铁载体-铁相互作用的数学建模。

摘要

几乎所有的生命形式都需要铁才能生存和运作。微生物利用多种机制来获取铁，包括产生铁载体，这些有机化合物与三价铁结合形成易于被微生物吸收的形式。已经对真菌中铁载体的作用、分布和功能进行了重要的实验研究，但直到现在还没有开发出预测工具来限定或量化真菌引发的铁载体-铁相互作用。在这项调查中，我们构建了第一个与真菌相关的铁载体功能的数学模型。最初，对一组偏微分方程进行校准和数值积分，以对铁载体和相关种群的时空分布进行定量预测。然后将该模型简化为一组更简单的方程，这些方程通过代数求解，从而产生预测铁载体和合成化合物分布的解。这些代数结果需要计算贝塞尔函数的叉积的零点，因此可以为与数值计算值一致的各种不同情况导出新的代数展开式。建模结果与实验数据一致，而分析提供了新的定量预测，涉及铁载体产生和铁吸收之间的时间尺度，以及真菌获得的铁总量如何取决于其环境。简要讨论了对生物技术应用的影响。