Roberts Paul A, Gaffney Eamonn A, Luthert Philip J, Foss Alexander J E, Byrne Helen M
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK.
Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK.
J Math Biol. 2016 Jul;73(1):1-38. doi: 10.1007/s00285-015-0931-y. Epub 2015 Sep 14.
The retina is the tissue layer at the back of the eye that is responsible for light detection. Whilst equipped with a rich supply of oxygen, it has one of the highest oxygen demands of any tissue in the body and, as such, supply and demand are finely balanced. It has been suggested that the protein neuroglobin (Ngb), which is found in high concentrations within the retina, may help to maintain an adequate supply of oxygen via the processes of transport and storage. We construct mathematical models, formulated as systems of reaction-diffusion equations in one-dimension, to test this hypothesis. Numerical simulations show that Ngb may play an important role in oxygen transport, but not in storage. Our models predict that the retina is most susceptible to hypoxia in the regions of the photoreceptor inner segment and inner plexiform layers, where Ngb has the potential to prevent hypoxia and increase oxygen uptake by 30-40 %. Analysis of a simplified model confirms the utility of Ngb in transport and shows that its oxygen affinity ([Formula: see text] value) is near optimal for this process. Lastly, asymptotic analysis enables us to identify conditions under which the piecewise linear and quadratic approximations to the retinal oxygen profile, used in the literature, are valid.
视网膜是眼球后部的组织层,负责光的检测。尽管视网膜有丰富的氧气供应,但它是体内对氧气需求最高的组织之一,因此,氧气的供需处于精细的平衡状态。有人提出,在视网膜中高浓度存在的蛋白质神经球蛋白(Ngb)可能通过运输和储存过程来帮助维持充足的氧气供应。我们构建了以一维反应扩散方程组形式表示的数学模型来检验这一假设。数值模拟表明,Ngb可能在氧气运输中起重要作用,但在储存方面并非如此。我们的模型预测,在光感受器内段和内网状层区域,视网膜最易受到缺氧影响,而在这些区域Ngb有潜力预防缺氧并使氧气摄取增加30% - 40%。对一个简化模型的分析证实了Ngb在运输中的作用,并表明其氧亲和力([公式:见原文]值)在此过程中接近最佳。最后,渐近分析使我们能够确定文献中用于视网膜氧分布的分段线性和二次近似有效的条件。