Clark A, Clark P A
Biophys J. 1985 Dec;48(6):931-8. doi: 10.1016/S0006-3495(85)83856-X.
The oxygen concentration in tissue can vary on several length scales. The basic scale of variation is determined by capillary spacing. It is this scale that is manifest in the simplest Krogh cylinder model. A second, smaller scale of variation is associated with the consumption of oxygen by mitochondria. This paper gives a theoretical analysis of these smaller-scale oxygen variations near an isolated mitochondrion. To illustrate the effects of shape, we have carried out the calculations for prolate spheroids as well as for spheres. The principal result is that the local drop in oxygen pressure around a consuming mitochondrion is of the order of (gamma/3K) (3V/4 pi)2/3, where gamma is the oxygen consumption rate per unit mitochondrial volume, K is the Krogh oxygen diffusivity of the surrounding tissue, and V is the mitochondrial volume. The theory is applied to skeletal muscle in vivo and to hepatocytes in cell suspension experiments. In both cases, we find that local oxygen variations produced by oxygen consumption are much smaller than the cell-wide variations produced by the collective effect of all the mitochondria. For example, in maximally consuming skeletal muscle, the drop in oxygen pressure around a consuming mitochondrion is only of the order of 0.03 Torr.
组织中的氧浓度会在几个长度尺度上发生变化。变化的基本尺度由毛细血管间距决定。正是这个尺度在最简单的克勒勃屈利圆柱体模型中得以体现。第二个较小的变化尺度与线粒体对氧的消耗有关。本文对孤立线粒体附近这些较小尺度的氧变化进行了理论分析。为了说明形状的影响，我们对长椭球体以及球体进行了计算。主要结果是，消耗氧的线粒体周围局部氧分压的下降约为(γ/3K)(3V/4π)^(2/3)，其中γ是单位线粒体体积的氧消耗率，K是周围组织的克勒勃屈利氧扩散率，V是线粒体体积。该理论应用于体内骨骼肌以及细胞悬浮实验中的肝细胞。在这两种情况下，我们发现由氧消耗产生的局部氧变化远小于所有线粒体的集体效应所产生的全细胞范围的变化。例如，在最大程度消耗氧的骨骼肌中，消耗氧的线粒体周围氧分压的下降仅约为0.03托。
