Department of Information Engineering and Research Center E.Piaggio, University of Pisa, Pisa, Italy.
Sci Rep. 2017 Feb 7;7:42113. doi: 10.1038/srep42113.
About two decades ago, West and coworkers established a model which predicts that metabolic rate follows a three quarter power relationship with the mass of an organism, based on the premise that tissues are supplied nutrients through a fractal distribution network. Quarter power scaling is widely considered a universal law of biology and it is generally accepted that were in-vitro cultures to obey allometric metabolic scaling, they would have more predictive potential and could, for instance, provide a viable substitute for animals in research. This paper outlines a theoretical and computational framework for establishing quarter power scaling in three-dimensional spherical constructs in-vitro, starting where fractal distribution ends. Allometric scaling in non-vascular spherical tissue constructs was assessed using models of Michaelis Menten oxygen consumption and diffusion. The models demonstrate that physiological scaling is maintained when about 5 to 60% of the construct is exposed to oxygen concentrations less than the Michaelis Menten constant, with a significant concentration gradient in the sphere. The results have important implications for the design of downscaled in-vitro systems with physiological relevance.
大约二十年前，West 及其同事基于组织通过分形分布网络供应营养物质的前提，建立了一个模型，该模型预测代谢率与生物体的质量呈四分之三幂关系。四分之三幂律缩放被广泛认为是生物学的普遍规律，人们普遍认为，如果体外培养物遵守异速代谢缩放，它们将具有更大的预测潜力，例如，可以为研究中的动物提供可行的替代品。本文概述了一个理论和计算框架，用于在体外三维球形构建中建立四分之三的幂律缩放，从分形分布结束的地方开始。使用 Michaelis Menten 耗氧量和扩散模型评估了非血管球形组织构建物的异速缩放。这些模型表明，当构建物的约 5%至 60%暴露在低于 Michaelis Menten 常数的氧浓度下时，生理缩放得以维持，并且球体中存在显著的浓度梯度。这些结果对于设计具有生理相关性的缩小的体外系统具有重要意义。
