Diversity of funnel plasmodesmata in angiosperms: the impact of geometry on plasmodesmal resistance
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Evaluation Summary:
The authors make an important contribution to our understanding of the universal mechanism of unloading of sugars from the phloem (the vascular tissue dedicated to long-distance sugar transport in plants) into root tip cells. Specifically, the authors investigate the pores (called plasmodesmata) present in the cell wall separating phloem cells from those cells into which sugars get unloaded in roots, which they found to have the same characteristic structure in all plant species investigated. The physical properties of these particular plasmodesmata suggest that they are especially suited for efficient and selective phloem unloading. The paper is relevant for audiences studying plant physiology and development. There are a few criticisms of the modelling work.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)
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Abstract
In most plant tissues, threads of cytoplasm, or plasmodesmata, connect the protoplasts via pores in the cell walls. This enables symplasmic transport, for instance in phloem loading, transport and unloading. Importantly, the geometry of the wall pore limits the size of the particles that may be transported, and also (co‐)defines plasmodesmal resistance to diffusion and convective flow. However, quantitative information on transport through plasmodesmata in non‐cylindrical cell wall pores is scarce. We have found conical, funnel‐shaped cell wall pores in the phloem‐unloading zone in growing root tips of five eudicot and two monocot species, specifically between protophloem sieve elements and phloem pole pericycle cells. 3D reconstructions by electron tomography suggested that funnel plasmodesmata possess a desmotubule but lack tethers to fix it in a central position. Model calculations showed that both diffusive and hydraulic resistance decrease drastically in conical and trumpet‐shaped cell wall pores compared with cylindrical channels, even at very small opening angles. Notably, the effect on hydraulic resistance was relatively larger. We conclude that funnel plasmodesmata generally are present in specific cell–cell interfaces in angiosperm roots, where they appear to facilitate symplasmic phloem unloading. Interestingly, cytosolic sleeves of most plasmodesmata reported in the literature do not resemble annuli of constant diameter but possess variously shaped widenings. Our evaluations suggest that widenings too small for unambiguous identification on electron micrographs may drastically reduce the hydraulic and diffusional resistance of these pores. Consequently, theoretical models assuming cylindrical symmetries will underestimate plasmodesmal conductivities.
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Evaluation Summary:
The authors make an important contribution to our understanding of the universal mechanism of unloading of sugars from the phloem (the vascular tissue dedicated to long-distance sugar transport in plants) into root tip cells. Specifically, the authors investigate the pores (called plasmodesmata) present in the cell wall separating phloem cells from those cells into which sugars get unloaded in roots, which they found to have the same characteristic structure in all plant species investigated. The physical properties of these particular plasmodesmata suggest that they are especially suited for efficient and selective phloem unloading. The paper is relevant for audiences studying plant physiology and development. There are a few criticisms of the modelling work.
(This preprint has been reviewed by eLife. We include the …
Evaluation Summary:
The authors make an important contribution to our understanding of the universal mechanism of unloading of sugars from the phloem (the vascular tissue dedicated to long-distance sugar transport in plants) into root tip cells. Specifically, the authors investigate the pores (called plasmodesmata) present in the cell wall separating phloem cells from those cells into which sugars get unloaded in roots, which they found to have the same characteristic structure in all plant species investigated. The physical properties of these particular plasmodesmata suggest that they are especially suited for efficient and selective phloem unloading. The paper is relevant for audiences studying plant physiology and development. There are a few criticisms of the modelling work.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)
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Reviewer #1 (Public Review):
In the manuscript "Diversity of funnel plasmodesmata in angiosperms: the impact of geometry on plasmodesmal resistance", the authors show using electron microscopy that the recently reported funnel shaped plasmodesmata (PDs) occur in the phloem unloading zone of a wide range of flowering plants. They also compute flow velocity profiles on detailed PD shapes extracted using electron tomography for four different species. To better understand the implications of the funnel geometry, the authors then apply a simple model. Together, these results illustrate how funnel PDs facilitate phloem unloading, an important aspect of plant growth, and provide insight into why this happens.
Funnel PDs were first reported a few years ago by Ross-Elliot et al (2017) in Arabidopsis thaliana. The authors have adapted sample …
Reviewer #1 (Public Review):
In the manuscript "Diversity of funnel plasmodesmata in angiosperms: the impact of geometry on plasmodesmal resistance", the authors show using electron microscopy that the recently reported funnel shaped plasmodesmata (PDs) occur in the phloem unloading zone of a wide range of flowering plants. They also compute flow velocity profiles on detailed PD shapes extracted using electron tomography for four different species. To better understand the implications of the funnel geometry, the authors then apply a simple model. Together, these results illustrate how funnel PDs facilitate phloem unloading, an important aspect of plant growth, and provide insight into why this happens.
Funnel PDs were first reported a few years ago by Ross-Elliot et al (2017) in Arabidopsis thaliana. The authors have adapted sample preparation protocols to become able to test how wide spread this specific PD geometry is. Based on their sample, it appears that funnel PDs occur in many if not all angiosperms. This implies that they are very relevant for the (growth) performance of most of our crop species. They have also extracted very detailed surfaces of funnel PDs in four different species using electron tomography and computed fluid flow velocities on these templates. These provide the community with a resource for assessing the worth of simple model geometries by computing the same profiles on those.
The manuscript, specifically including the modelling work, clearly adds to the growing awareness that the shape of plasmodesmata matters. This also implies that the details of plasmodesmata models matter, particularly when it comes to quantitative conclusions. This presents a challenge to the whole field: calculations on realistic PD shapes, as presented in figure 3, require a data quality that is often not feasible for sufficient numbers of PDs to capture the relevant variability among PDs within a single interface. Moreover, such complex models are not necessarily the most insightful. So, for an optimal connection with experiments, PD models should be as simple as possible, but no simpler.
In their modelling choices, however, I think the authors have made two simplifications that could have a large impact on their results. This holds even stronger for the manuscript in its current form, as the presentation of the results is mostly in terms of a few loose numbers, without any handles to assess how this depends on "hidden" model parameters like cell wall thickness. The results are described in a strongly quantitative way, whereas the numbers quoted are contingent on the parameters used and little effort is made to explore these dependencies or communicate them to the reader.
First, the authors opt for the simplest possible geometry (with desmotubule) that allows for gradual widening: they represent the outer lining of the channel as part of a cone. As the narrowest part of the channel most strongly reduces the flows through the channel, however, the details of the narrow region will have a strong impact on results and conclusions. One of the cited modelling papers, Deinum et al 2019, predicts based on their results with a multiple cylinder model, that the difference between immediate widening (as here) and widening after an initial straight ("neck") section could be substantial and have a significant impact on conclusions. For example, the O. sativa PD in figure 3B appears to have an approximately straight region of say 1/4 of its length, meaning that resistances could be reduced by at most 75% rather than the 98% and 94% mentioned in the discussion based on the geometry without neck. The flow velocity distributions calculated on the reconstructed PDs also seem to support this slightly more complex geometry.
Second, the models that are used for both diffusion and flow do not include the effects of particle size and particle behaviour in a narrow confinement. For the narrow end of PDs or the straight cylindrical geometries used as reference, this has severe impact (see Liesche and Schultz 2013, Deinum et al 2019 (both diffusive transport only) and Dolger et al 2014 (also including advection)). Including hindrance effects for diffusion and flow affects the scaling of the processes with local diameter, particularly for small diameters, and might make the quantitative results for diffusion and flow more similar, so without them, the suggestion that the model "supports the view that rapid phloem unloading in root tips proceeds mainly as bulk flow" is at best preliminary. On the other hand, including these hindrance effects, will make the "performance" of funnel PDs (or PD sections) relative to straight channels even more spectacular.
In summary, the model of funnel PDs presented here can best be viewed as a first investigation of the impact of the conical part of a funnel PD on the resistance of that specific part, rather than a definitive model of funnel PDs themselves. As such, the model is a valuable contribution to the field.
Even without improving the funnel PD model, the manuscript could become more insightful and have more impact if the current model with a few more calculations and some changes in presentation. I include only those could aid the reader in interpreting the results in the preprint.
When it comes to experimental determination of the model parameters, the focus on opening angle may be suboptimal. As actual funnel PDs are far from straight cone mantles, the precise determination of the opening angle will be terribly hard. What matters most for the model outcome, however, is the diameter of the narrow part and the length of the narrow part/how long it takes to widen to a (narrowest diameter dependent) critical diameter beyond which the resistance can be neglected relative to the narrow part. With that in mind, results could be interpreted more generally with respect to wall thickness by converting opening angle to inlet aperture/sleeve width. Computing such values, moreover, can make the same data "feel" different: For example, compare: (from preprint) "As a consequence, conical channels of 4 and 2 nm minimum sleeve width showed the same diffusive resistance as a cylindrical channel with an 8 nm sleeve at angles θ of only 1.5{degree sign} and 2.8{degree sign}, respectively" with (my calculation) {{[...] by increasing sleeve with from 4 to 14.5 nm or from 2 to 19.6 nm over the length of the PD}}. Importantly, the former statement depends on wall thickness, but the latter does not.
I find the strong focus on numerical values in the results and discussion sections misleading. It feels very exact, but in fact, these results are contingent on parameter choices (very importantly, wall thickness/PD length) and the simplified model used. Such numbers should never be quoted without the full context, but it is likely that that would happen anyway.
Finally, the modelling part is presented as an important aspect of the paper. It is, therefore, sad that the discussion of the model choices made is very minimal. There is no comparison of model choices between this model and other published PD models. While a relatively simple model compared to others could be justified as a starting point, the authors should at least try to estimate the impact of these difference on their results.
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Reviewer #2 (Public Review):
The phloem is the part of the plant vascular tissue which is dedicated to long-distance sugar transport. Sugars are produced during photosynthesis in green tissues. They then are distributed via the phloem and get unloaded in organs that cannot perform photosynthesis, such as roots.
Previously, the authors have investigated the mechanism of phloem unloading in roots of the model plant Arabidopsis thaliana. There, they found that a specific and novel plasmodesmata-type resides in the cell walls between phloem sieve tube cells and phloem pericycle cells - the latter are the cells into which phloem solutes get unloaded. Because of their specific shape, with a wider pore on the phloem side and a more narrow pore on the pericycle cell side, these plasmodesmata were named "funnel-plasmodesmata".
In the present …Reviewer #2 (Public Review):
The phloem is the part of the plant vascular tissue which is dedicated to long-distance sugar transport. Sugars are produced during photosynthesis in green tissues. They then are distributed via the phloem and get unloaded in organs that cannot perform photosynthesis, such as roots.
Previously, the authors have investigated the mechanism of phloem unloading in roots of the model plant Arabidopsis thaliana. There, they found that a specific and novel plasmodesmata-type resides in the cell walls between phloem sieve tube cells and phloem pericycle cells - the latter are the cells into which phloem solutes get unloaded. Because of their specific shape, with a wider pore on the phloem side and a more narrow pore on the pericycle cell side, these plasmodesmata were named "funnel-plasmodesmata".
In the present study, the authors intended to investigate the universality of their previous findings by extending their investigation to plant species other than Arabidopsis. Plasmodesmata can only be visualized with an electron microscope. Preparation of tissue for this kind of microscopy is a very laborious process, which, moreover, had to be adapted to each individual plant species. This was a very good reason for having restricted the analysis to a nevertheless very impressive total of 7 different plant species.Indeed, the authors found funnel plasmodesmata at the sieve tube - pericycle cell interface in all plants investigated. This finding makes it likely that the presence of funnel plasmodesmata at the sieve tube - pericycle cell interface is a general feature of the root unloading zone. Nevertheless, due to the limited number of species investigated, there may still be some exceptions to this "rule".
In a second part of the paper, the authors made use of the electron micrographs and measured the parameters of funnel plasmodesmata in the different plant species. Due to the small size of plasmodesmata and potential artefacts in the samples, measurements were not always exact, but it was always possible to obtain good estimates. Based on these, the authors calculated the general physical properties of funnel plasmodesmata. Finally, the authors came to the conclusion that the properties of funnel plasmodesmata are ideally suited for phloem unloading. They ensure a fast unloading while, at the same time, they probably still have a filtering function for bigger molecules.In addition, the authors rightly point out that their calculations demonstrate that the shape of plasmodesmata has a big impact on their function. This should be taken into consideration when estimating or calculating cell - cell diffusion or communication.
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Reviewer #3 (Public Review):
Ostermeyer et al. investigated the geometry of plasmodesmata in the vasculature of plant roots, and more specifically in the region where phloem is unloaded into the root tip. They developed a protocol based on transmission electron microscopy to image these plasmodesmata in 7 species of flowering plants, 2 monocots and 5 dicots. In all species, they found funnel-shaped plasmodesmata connecting sieve elements to neighbouring cells. They reconstructed typical 3D shapes of plasmodesmata (including the desmotubule) and quantified this geometry and its variations across species. Finally, they modelled diffusion and viscous flow in plasmodesmata with funnel-like geometries, showing that funnel-shaped plasmodesmata have a higher diffusive and viscous conductivity than cylindrical plasmodesmata with a radius equal …
Reviewer #3 (Public Review):
Ostermeyer et al. investigated the geometry of plasmodesmata in the vasculature of plant roots, and more specifically in the region where phloem is unloaded into the root tip. They developed a protocol based on transmission electron microscopy to image these plasmodesmata in 7 species of flowering plants, 2 monocots and 5 dicots. In all species, they found funnel-shaped plasmodesmata connecting sieve elements to neighbouring cells. They reconstructed typical 3D shapes of plasmodesmata (including the desmotubule) and quantified this geometry and its variations across species. Finally, they modelled diffusion and viscous flow in plasmodesmata with funnel-like geometries, showing that funnel-shaped plasmodesmata have a higher diffusive and viscous conductivity than cylindrical plasmodesmata with a radius equal to the minimal radius of the funnel. This increase in conductivity is much higher for viscous flow than for diffusion, suggesting that phloem unloading mostly occurs by bulk flow. Based on these results, the authors propose that the funnel shape enables plasmodesmata to simultaneously function as sieves and allow fast flow of small molecules.
Strengths. First, Ostermeyer et al. convincingly show the existence of funnel-shaped plasmodesmata in the phloem-unloading region of the root of several species. Second, they use mathematical models to assess the function of these plasmodesmata in movement of solutes between cells. Third, based on these models, they demonstrate that tapering of plasmodesmata is most effective in increasing bulk flow between cells.
Weaknesses. All conclusions on diffusion and bulk flow also apply to plasmodesmata with a central widening (with biconical shape), raising doubts about the function proposed for the funnel shape. This shape may well be the mere result of developmental constraints associated with differentiation of sieve elements. Finally, it is unclear wether the reference geometry in the model should be a cylinder with the minimal radius of the funnel, as assumed by the authors, a cylinder with the average radius of the funnel, or a cylinder with the same volume as the funnel.
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