Computational models evaluating the impact of sieve plates and radial water exchange on phloem pressure gradients

Abstract

The sugar conducting phloem in angiosperms is a high resistance pathway made up of sieve elements bounded by sieve plates. The high resistance generated by sieve plates may be a trade-off for promoting quick sealing in the event of injury. However, previous modeling efforts have demonstrated a wide variation in the contribution of sieve plates towards total sieve tube resistance. In the current study, we generated high resolution scanning electron microscope images of sieve plates from balsam poplar and integrated them into a mathematical model using Comsol Multiphysics software. We found that sieve plates contribute upwards of 85% towards total sieve tube resistance. Utilizing the Navier-Stokes equations, we found that oblong pores may create over 50% more resistance in comparison with round pores of the same area. Although radial water flows in phloem sieve tubes have been previously considered, their impact on alleviating pressure gradients has not been fully studied. Our novel simulations find that radial water flow can reduce pressure requirements by half in comparison with modeled sieve tubes with no radial permeability. We discuss the implication that sieve tubes may alleviate pressure requirements to overcome high resistances by regulating their membrane permeability along the entire transport pathway.

Modelling the physiological relevance of sucrose export repression by an Flowering Time homolog in the long‐distance phloem of potato

“…The model reproduced experimentally measured sap sucrose concentrations and velocities well. Interestingly, our model indicated that high viscosity in the phloem was the major resistance factor in potato, in contrast to sieve‐tube geometry reported in earlier work on larger plants (Stanfield, Schulte, Randolph, & Hacke, 2019; Thompson & Holbrook, 2003). This result is consistent with the higher sucrose concentration (Jensen et al, 2013), shorter stem‐length, and higher flow velocity (Comtet et al, 2017; Windt et al, 2006) reported for herbaceous species, suggesting it might be a general property of small herbaceous crop species.…”

Aquaporins Respond to Chilling in the Phloem by Altering Protein and mRNA Expression

“…One way the membrane can counteract this loss of conductivity may be from upregulating aquaporin abundance in the plasma membrane. More aquaporin abundance means greater rates of radial water flows into the sieve tubes [12], which have the effect of decreasing viscosity and lowering pressure gradients. In effect, this upregulation of aquaporins in the membrane may be a way to counteract some aquaporin gating via a temporary pressure surge.…”

“…However, the intervening transport phloem which connects source and sink is often neglected due to the difficulty of accessing this deeply embedded tissue. The importance of the transport phloem for influencing long-distance translocation cannot be understated, as it may act as an exchange point for water and nutrients [11], which has been modeled to significantly influence pressure profiles [12].…”

Loading regulation prevents phloem failure during drought and widens the range of phloem and stomatal traits

“…This is surprising as increased phloem structural resistance should make the plant more vulnerable to run-away viscosity, especially during drought. Structural aspects of the phloem that contribute to resistance may be in the form of its cell diameter and the porosity of their end walls (sieve plates) (e.g., Mullendore et al 2010, Stanfield et al 2019). In addition, the scaling of the conduits from source-sink may also play a role to minimize resistance and maintain adequate pressure gradients in both leaves and stems (Carvalho et al 2017, Savage et al 2017; this scaling increases in magnitude as pathway resistance per unit length lowers in taller trees to maintain flow at great heights (Clerx et al 2020).…”