Flow rate of transport network controls uniform metabolite supply to tissue

TL;DR

This study investigates how flow rate and network architecture in transport systems like plant xylem influence the uniform distribution of metabolites, identifying an optimal inflow rate for consistent supply.

Contribution

The paper introduces an analytical model and numerical simulations to determine the optimal flow rate and network adjustments for uniform metabolite supply in biological transport networks.

Findings

Optimal inflow rate achieves uniform metabolite distribution.

Network architecture can be optimized to compensate for sub-optimal flow rates.

Analytical results agree with numerical simulations.

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.