Diffusion and flow across shape-perturbed plasmodesmata nanopores in plants

Anneline H Christensen,Kaare H Jensen,Howard A Stone

doi:10.1140/epjp/s13360-021-01727-y

Anneline H Christensen, Kaare H Jensen + Show 1 more

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https://doi.org/10.1140/epjp/s13360-021-01727-y

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Abstract

Plasmodesmata are slender nanochannels that link neighboring plant cells and enable the exchange of nutrients and signaling molecules. Recent experiments have demonstrated significant variability in the concentric pore shape. However, the impact of these geometric fluctuations on transport capacity is unknown. Here, we consider the effects on diffusion and advection of two ideal shape perturbations: a radial displacement of the entire central desmotubule and a harmonic variation in the cytoplasmic sleeve width along the length of the pore. We use Fick’s law and the lubrication approximation to determine the diffusive current and volumetric flow rate across the pore. Our results indicate that an off-center desmotubule always increases the pressure-driven flow rate. However, the diffusive current is only enhanced for particles comparable in size to the width of the channel. In contrast, harmonic variations in the cytoplasmic sleeve width along the length of the pore reduce both the diffusive current and the pressure-driven flow. The simple models presented here demonstrate that shape perturbations can significantly influence transport across plasmodesmata nanopores.

Highlights

Living organisms must confront the challenge of facilitating nutrient and signal exchange between proximal compartments [1]
Recalling that the displacement h0δ is limited by the initial gap height h0 (i.e., δ < 1), we observe that the flow rate can at most increase by 150% (Q = 5Q0/2), which occurs when δ = 1 and the desmotubule is in contact with the cell membrane
Current models assume that the annular pore geometry is perfectly concentric and static [7,26]

Summary

Introduction

Living organisms must confront the challenge of facilitating nutrient and signal exchange between proximal compartments [1]. Plants solve this problem, in part, using plasmodesmata (PD) nanopores [2]. PD are permanent channels that traverse the cell wall and directly link the cytoplasmic fluid of neighboring cells. Their shape is that of an approximately circular cylinder, and they are typically L ≈ 200−1000 nm long and 2a ≈ 25−50 nm in diameter [3,4].

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