Construction principles and control over transport systems organization in biological tissues

Abstract

The main common principles of the long-range transport systems construction in animal and plant tissues are summarized. The results of measurement of conducting system geometry in Cotinus obovatus leaf are analyzed. It is shown that the principles of design of the conducting systems in animals and higher plants are the same and correspond to the model of optimal pipeline. The mathematical model of fluid motion in the conducting system of the leaf as a mo tion in a branching pipeline with permeable walls is investigated. The cost of a bifurcation of the vessels is analyzed. The hypothesis of the control principle of optimal transport system formation in the growing leaf is discussed. As an example the self-similar conducting system with loops is investigated and compared with some venation systems in plant leaves.

Long-distance liquid transport in plants

“…Relationship (12) has also been obtained in the detailed measurements on the fluid and gas transport systems in fish and insects, the trophic fluid transport systems of a variety of suspension-feeding marine invertebrates (molluscs, brachiopods, lophophorates, sponges) [44], the conducting systems of plant [96] leaves [29,30,53], tree branchings [105], and even in the bifurcations of axons [5]. In contrast to the arterial systems, the physiological mechanisms that can provide development of the optimal tree-like transportation networks in all the mentioned systems are not clear.…”

“…9a), which provides liquid delivery at minimum total energy cost, was proposed in [4] and generalized to the m-branching pipeline (Fig. 9b) in [30]. Each tube of the pipeline is divided into m tubes with equal lengths and diameters, so the number of the tubes in the generation j = 1...n is m j−1 , the total volume and resistivity of the pipeline are [30]:…”

“…9b) in [30]. Each tube of the pipeline is divided into m tubes with equal lengths and diameters, so the number of the tubes in the generation j = 1...n is m j−1 , the total volume and resistivity of the pipeline are [30]:…”

“…9b), χ = 1 for the Darcy flow, and χ = 2 for the Poiseuille flow. The solution of the optimization problemẆ → min for the branching pipeline is [30]:…”

Experimental research on leaf vein geometric characteristics of multibranch horizontal well for coalbed methane recovery

“…Moisture, inorganic salts, and organic matter in the leaves are all transported in an efficient manner . Kizilova et al discovered that branches are the most basic plant structure, reaching 5‐9 levels in plant transport systems and connecting to each other to form a network. Huve et al used microscopy to observe the flow velocity of leaf veins at all levels, and the results showed that thinner veins had slower internal water flows.…”