Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany.
Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
J R Soc Interface. 2018 May;15(142). doi: 10.1098/rsif.2018.0075.
Life and functioning of higher organisms depends on the continuous supply of metabolites to tissues and organs. What are the requirements on the transport network pervading a tissue to provide a uniform supply of nutrients, minerals or hormones? To theoretically answer this question, we present an analytical scaling argument and numerical simulations on how flow dynamics and network architecture control active spread and uniform supply of metabolites by studying the example of xylem vessels in plants. We identify the fluid inflow rate as the key factor for uniform supply. While at low inflow rates metabolites are already exhausted close to flow inlets, too high inflow flushes metabolites through the network and deprives tissue close to inlets of supply. In between these two regimes, there exists an optimal inflow rate that yields a uniform supply of metabolites. We determine this optimal inflow analytically in quantitative agreement with numerical results. Optimizing network architecture by reducing the supply variance over all network tubes, we identify patterns of tube dilation or contraction that compensate sub-optimal supply for the case of too low or too high inflow rate.
高等生物的生命和功能依赖于代谢物持续不断地输送到组织和器官中。遍布组织的运输网络需要具备哪些条件，才能为营养物质、矿物质或激素提供均匀的供应？为了从理论上回答这个问题，我们提出了一个分析性的扩展论点，并通过研究植物木质部导管的例子进行了数值模拟，以了解流动动力学和网络结构如何控制代谢物的主动扩散和均匀供应。我们将流体流入率确定为均匀供应的关键因素。在低流入率下，代谢物在靠近入口处就已经耗尽，而过高的流入率会使代谢物在网络中迅速流过，导致靠近入口处的组织供应不足。在这两种情况之间，存在一个使代谢物均匀供应的最佳流入率。我们以与数值结果定量一致的方式对该最佳流入率进行了分析。通过减少所有网络管道的供应方差来优化网络结构，我们确定了在流入率过低或过高的情况下，补偿供应不足的管道扩张或收缩模式。
