Flow rate of transport network controls uniform metabolite supply to tissue.

Felix J Meigel,Karen Alim

doi:10.1098/rsif.2018.0075

Abstract

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.

Highlights

Transport processes organized in network structures are ubiquitous in our life, from road traffic [1] and power networks [2] to river estuaries [3] and vascular systems of extended organisms [4,5]
We investigated what is needed to achieve a uniform supply rate of metabolites to tissue via a tubular transport network
Optimizing for uniform supply rate across a transport network is a novel perspective regarding the theoretical investigation of optimal transport networks, where the P1⁄4

Summary

Introduction

Transport processes organized in network structures are ubiquitous in our life, from road traffic [1] and power networks [2] to river estuaries [3] and vascular systems of extended organisms [4,5]. Krogh assumes that metabolites are provided by the vasculature at a constant rate at all vessel walls [16]. This strong simplification neglects that vascular network architecture and resulting asymmetries in flow-based transport give rise to large variations in metabolite availability within the network. Instead research has focused on network flow and not transport properties identifying scaling relationships regarding the network’s fluid dynamics [20 –27]. Another branch of theoretical models for vascular systems

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