A coupled mechano-biochemical model for cell polarity guided anisotropic root growth
Curation statements for this article:-
Curated by eLife
Evaluation Summary:
The paper describes the development of a mechano-chemical model for plant root development. As such, it presents a significant advance relative to other root models that have focussed predominantly on either the mechanical or auxin patterning aspects of root development, as evidenced by the potential of the model to reproduce a series of hormonal and mechanical perturbation experiments. The current conclusion that a set of minimal principles for self-organized root tip patterning is revealed must be moderated, as patterning inputs are essential to produce the reported observations.
(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 #3 agreed to share their name with the authors.)
This article has been Reviewed by the following groups
Listed in
- Evaluated articles (eLife)
Abstract
Plants develop new organs to adjust their bodies to dynamic changes in the environment. How independent organs achieve anisotropic shapes and polarities is poorly understood. To address this question, we constructed a mechano-biochemical model for Arabidopsis root meristem growth that integrates biologically plausible principles. Computer model simulations demonstrate how differential growth of neighboring tissues results in the initial symmetry-breaking leading to anisotropic root growth. Furthermore, the root growth feeds back on a polar transport network of the growth regulator auxin. Model, predictions are in close agreement with in vivo patterns of anisotropic growth, auxin distribution, and cell polarity, as well as several root phenotypes caused by chemical, mechanical, or genetic perturbations. Our study demonstrates that the combination of tissue mechanics and polar auxin transport organizes anisotropic root growth and cell polarities during organ outgrowth. Therefore, a mobile auxin signal transported through immobile cells drives polarity and growth mechanics to coordinate complex organ development.
Article activity feed
-
-
Author Response:
Reviewer #1:
The paper describes the development of a mechano-chemical model for plant root development that incorporates mechanical aspects of cell growth and division, chemical aspects of (amongst other auxin processes) polar auxin transport and auxin patterning, and the feedbacks between these processes. As such it presents a significant advance relative to other root models that have focussed predominantly on either the mechanical or auxin patterning aspects of root development, as evidenced by the potential of the model to reproduce a series of hormonal and mechanical perturbation experiments. Additionally, the efficient flexible manner in which mechanics are incorporated make the model potentially suitable for studying e.g. conditions in which aberrant division planes lead to additional cell file formation, or …
Author Response:
Reviewer #1:
The paper describes the development of a mechano-chemical model for plant root development that incorporates mechanical aspects of cell growth and division, chemical aspects of (amongst other auxin processes) polar auxin transport and auxin patterning, and the feedbacks between these processes. As such it presents a significant advance relative to other root models that have focussed predominantly on either the mechanical or auxin patterning aspects of root development, as evidenced by the potential of the model to reproduce a series of hormonal and mechanical perturbation experiments. Additionally, the efficient flexible manner in which mechanics are incorporated make the model potentially suitable for studying e.g. conditions in which aberrant division planes lead to additional cell file formation, or for studying tissue shape regeneration after root tip excision.
Still, the claim that this study reveals a set of minimal principles for self-organized root tip patterning in which interplays between mechanics, growth and auxin patterning are essential is less strongly substantiated. By superimposing an auxin source in the middle vasculature cells and an auxin sink in the topmost outer cells the authors effectively impose the polar auxin transport directions of the tissue outside the simulated domain, which likely causes the simulated domain to align with this rather than displaying truly self-organized patterning.
We thank Reviewer for recognition of our work and suggestions that helped to improve this manuscript.
Most plant organ models include some sort of boundary conditions to mimic connection to the rest of the organisms (i.e. Mahonen et al., 2014; Grieneisen et al., 2007, Band et al., 2012). In fact, root is connected to hypocotyl and auxin must flow in and flow out to reflect this natural phenomena. We add clarification on that issue in the revised manuscript and supplemental section (Lines: 215-222 and 497-503). Therefore, we believe this assumption is biologically sound and necessary to retain continuity of the model. Furthermore, cell polarity is not established by source or sinks but local mechanisms that act at the level of each individual cell that interpret incoming signals (flux or concentration). Without that local interpretation cells are blind as these cells do not sense global gradients everything is local. Again, as suggested by Reviewer we had weakened the claim of entirely self-organizing phenomena in the manuscript.
Also, in the model mechanics has been made to impact PIN polarity, but it has not been demonstrated if in absence of PIN polarity dependence on mechanics PIN patterning would be different, i.e. if the mechanical feedback on PIN patterning is necessary or rather that the source and sink prepattern dominate.
Both components are necessary. Mechanics constrains where PINs can be deposited whereas auxin defines which side is preferred (either flux or regulator-based) and controls the rate of cell growth. When we remove mechanics feedback growth on PIN polarity is less robust (as auxin only defines growth rates and final PIN polarity) , see Fig. 2 - supplement 7). Results of severely perturbed mechanics are presented in Fig. 5E. We added clarification on that matter in the revised manuscript (Lines: 267-274).
Similarly, the feedback of auxin on mechanics is I believe limited to cellular auxin levels determining cellular growth rates and does not appear to control cellular growth anisotropy (i.e. predominant longitudinal growth of cells), which arose from the initial symmetry breaking of differential growth rates. As such the actual coupling between mechanics and auxin patterning and the extent of self-organization is less than suggested.
Indeed, we thank reviewer for spotting this potential confusion. We revised text to explain that particular matter better (Lines: 226-230). However, it is important to mention that auxin effect on cell growth speed (although non-polar) will have consequences for overall organ shape and thus its mechanical properties. In other words, there is always coupling between mechanical and biochemical layers in our model.
Some matters are rather unclear in the manuscript in its current form. It is for example unclear how exactly does auxin translate into cellular growth rate and how does this result in stable, coordinated growth across cell files. In a previous study it was shown that since auxin levels differ significantly across cell files (e.g. much higher in vasculature than in neighboring cell files), problems in coordinated cell growth may occur (https://pubmed.ncbi.nlm.nih.gov/25358093/). It is unclear how such problems are avoided here.
We thank reviewer for raising this matter. Now, we have explained what relation between auxin levels and growth rates is (Lines: 226-230). As for suggested study it seems to have a different inner working (for instance cells tend to slide against each other) and therefore it is difficult to compare with our approach. In our model cells share the common wall with their neighbors (as in real plant tissues) and therefore cell sliding is impossible. Moreover, cells are considered as almost incompressible objects (as they are filled with water). This is mimicked in our model by the internal meshing of the cell with provide resistance to compression and shearing due to the action of the distance constraint. This model feature is described in bullet point 1 of the supplemental section: Position-based dynamics implementation. To conclude, we have never seen that problem in our simulations as biomechanics layer always compensates for overgrowing cells.
Similarly, in the discussion authors mention possible uses of the model such as studying tropisms. However the latter requires incorporating an elongation zone in which cells undergo rapid and extreme cell elongation. It seems that the current model only incorporates slow cytoplasmic cell growth and division occurring in the meristem, and it is unclear whether the used model formalism would be capable of stably simulating these far more anisotropic growth processes in a numerically stable and efficient manner.
Although outside of scope of this study, we are exploring those possibilities in current framework. The current implementation of the model will require the addition of new features in order to allow the modelling of the elongation zone. Most notably, it would be necessary to dynamically remeshing the elongating cells in order to avoid the appearance of extremely thin and long triangles, which would definitely cause some numerical instabilities to the system solutions. Therefore, the extension of the current model to incorporate alternative biological processes such as rapid cell elongation are feasible but it requires the implementation of new computational procedures and thus it is a matter of ongoing research efforts.
Summarizing the authors have generated a highly valuable combined mechano-chemical modeling framework for root tip development that can be used to various applications, but that was somewhat oversold.
Reviewer #3:
Marconi, M et al. developed a new mechano-biochemical computational framework to study plant morphogenesis. A positional information is self-organized by a diffusing substance that regulates acquiring cell polarity and modulates cell growth by changing the cell's biomechanical properties. The model for the root meristem functioning in Arabidopsis thaliana is composed of a minimal set of experimentally derived principles for self-organization of organ patterning. This study is an excellent methodological achievement that also brought some new biological results. Although all the results are there, the manuscript requires major revision to present the framework better to avoid miscommunication.
We thank Reviewer for positive assessment of our work and for valuable comments of how to improve this manuscript.
Framework:
Good: The framework looks very promising to study tissue morphogenesis (not necessarily in plants). So it has the sense to make it available for the scientific community. Now the code can be downloaded from the google disc using a password; I encourage the authors to add a permanent link and the tutorial to the framework in the final version of the paper.
Not good: The manuscript structure does not allow us to see all the advantages of the framework; the information about it is spread throughout the text. The main text misses essential details, while the materials and methods section contains a lot of discussions. E.g., CTM are mentioned several times in the results section without explaining how you modeled them. Another example is on the line 188 where the reference about "put together growth biomechanics" leads us the Figure 1 without any details about that. I would suggest adding a first section of the Results and the main figure about the framework, its basics, advantages, and limitations. Also, to add a bit more about PBD technology.
We very much value suggestions from Reviewer, however, our intention was to build up the story staring from initial symmetry breaking through pure mechanics and later add the polar transport to complete the framework. We believe revealing all aspects of the model at once would overwhelm reader and we would very much avoid it. Otherwise, as suggested we revised manuscript to clarify assumptions and model elements.
Root model:
Good:
• The application of the model delivered some new and important results for plant biologists. E.g., the authors confirmed the hypothesis that the start of anisotropic root growth (elongation) results from the differential expansion of neighboring tissues.
• They also showed self-organization of a complex auxin distribution (PIN polarization) map, which reproduces tiny properties like the switch in PIN polarity from rootward to shootward in the cortex.
• The authors also showed that auxin reflux in the meristem is not that important for auxin maximum maintenance under normal conditions but gives an advantage in shoot-independent growth.
• The fact that the authors were able to "grow" a "whole root" from the embryonic-like structure under a limited number of predefined rules is inspiring and promising.
Can be better:
- I am not sure that I understand the visualization of PINs on the figures. The authors do not distinguish between PIN levels and PIN polarities. It is clear that they managed to model PIN polarities correctly, but I am not sure about PIN levels. If PIN levels are shown by red rectangular, then columella does not have any PINs (which is incorrect). Is it so?
Figures in pdf may have been lower quality due to conversion. Now, we provide high resolution figures with revised version of the manuscript. Columella PINs although weakly expressed (low auxin) are clearly visible in magnification as thin rectangular elements.
- It sounds great that you simulated an oscillating behavior in the root growth, but actually, you did not. Simulating periodic application of auxin treatment to simulate oscillation is a trivial solution, that only sounds great, but disappoints when you look into detail. Instead, I would suggest simulation of restoration of root growth after it is inhibited by auxin application.
We apologize for the misunderstanding. Experiments by Fendrych et al, 2018 use external auxin applications to modulate growth inhibition in the periodic fashion. We intended to replicate these particular experiments using our framework. We clarify this description in the revised manuscript (also pointed by Reviewer 2) (Lines: 327-333).
- Looking at the resulting solution, it looks like that auxin maximum in QC emerges because one QC cell adopts auxin from two vascular cells. Or maybe because columella does not have PINs. If it is so, it has to be stated; otherwise, there is an impression that auxin maximum self-organizes due to flux pattern only.
In fact, auxin does come from the vascular, columella does have PINs, it is emerging property of auxin transport in our model.
- It also looks like that QC does not grow during calculation, if it so, it has to be stated, because then it is one of the factors that "eventually reproducing the non-trivial shape of the root" (line 214). The rules to get "the non-trivial shape" should be explicitly stated. E.g., how did you get that only columella stem cells have divided and not other columella cells that are bigger in size?
Indeed, we now specify that the QC does not grow nor divide, so are columella cells, which do not divide anymore as they are differentiated. All these assumptions are supported experimentally as pointed in the revised text (Lines: 236-237).
- I noticed the formation of left-to-write asymmetry in auxin distribution in the root meristem that was self-organized. It will be great if you elaborate on that more. Especially considering that you simulated pin2 mutant where this asymmetry got lost.
We check that left-right asymmetry is not a prevalent pattern it may change in WT-like simulations.
- I was also quite excited looking on the bending root (Figure 2 - supplement 8) correlated with this left-to-write auxin distribution asymmetry. It will be great if you elaborate on the root bending more in the manuscript.
The root bending is just a spurious event, roots in the model tend to bend after a while (currently there is no gravity response integrated in the model, so roots are not forced to grow straight).
Not good:
- There is a mess with anatomical terminology usage in the manuscript. The authors name the basal part of the embryo as the root or radicle, which is incorrect. There is no root or hypocotyl at the heart stage and even at the torpedo or bending-cotyledon stages. Consider starting growing the root from the mature embryo stage and not from the heart one. Otherwise, you study the formation of "apical-basal polarity" in embryo development and not root development.
We thank Reviewer for this suggestion and modified text accordingly. We refer to the organ as the basal part of the embryo (BPE) (Line: 131).
- Another problem with the terminology is that the definitions are sometimes given later than they were used, and there is a lot of introduction in the results and material and methods section, which disturb the comprehension of the text. E.g., QC is introduced in the last results chapter (line 324).
We have inspected that issue and found that the QC is introduced at Line: 236, together with its full name.
- The only experimental data given in the manuscript is an analysis of hypocotyl and root growth in the seedling soon after germination. Using this data to confirm the results on "growing the root" from the heart-stage embryo is confusing. The results of the experimental data analysis are also quite obvious and did not require an experiment :). Having Eva Benkova among the co-authors, the manuscript should be supplemented with better experimental data that confirm or demonstrate the modeling results' appropriateness. The authors refer to confirmations from the published data in the rest of the text instead of explicitly comparing computational and experimental results. The manuscript will certainly win from such a direct comparison.
Actually, it would not be bad if the authors did not use the experimental data at all, because all the facts discussed are well known; the authors can give just references. It just looks strange why only one (and not very relevant) experiment is shown from a vast collection of Prof. Eva Benkova.
As indicated by Reviewer, majority of the work is computational tested against experimental observations and additional experiment was done to support model predictions regarding the symmetry breaking part which was not published before and strengthen the manuscript in our opinion.
-
Evaluation Summary:
The paper describes the development of a mechano-chemical model for plant root development. As such, it presents a significant advance relative to other root models that have focussed predominantly on either the mechanical or auxin patterning aspects of root development, as evidenced by the potential of the model to reproduce a series of hormonal and mechanical perturbation experiments. The current conclusion that a set of minimal principles for self-organized root tip patterning is revealed must be moderated, as patterning inputs are essential to produce the reported observations.
(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 #3 agreed to share their name with the authors.)
-
Reviewer #1 (Public Review):
The paper describes the development of a mechano-chemical model for plant root development that incorporates mechanical aspects of cell growth and division, chemical aspects of (amongst other auxin processes) polar auxin transport and auxin patterning, and the feedbacks between these processes. As such it presents a significant advance relative to other root models that have focussed predominantly on either the mechanical or auxin patterning aspects of root development, as evidenced by the potential of the model to reproduce a series of hormonal and mechanical perturbation experiments. Additionally, the efficient flexible manner in which mechanics are incorporated make the model potentially suitable for studying e.g. conditions in which aberrant division planes lead to additional cell file formation, or for …
Reviewer #1 (Public Review):
The paper describes the development of a mechano-chemical model for plant root development that incorporates mechanical aspects of cell growth and division, chemical aspects of (amongst other auxin processes) polar auxin transport and auxin patterning, and the feedbacks between these processes. As such it presents a significant advance relative to other root models that have focussed predominantly on either the mechanical or auxin patterning aspects of root development, as evidenced by the potential of the model to reproduce a series of hormonal and mechanical perturbation experiments. Additionally, the efficient flexible manner in which mechanics are incorporated make the model potentially suitable for studying e.g. conditions in which aberrant division planes lead to additional cell file formation, or for studying tissue shape regeneration after root tip excision.
Still, the claim that this study reveals a set of minimal principles for self-organized root tip patterning in which interplays between mechanics, growth and auxin patterning are essential is less strongly substantiated. By superimposing an auxin source in the middle vasculature cells and an auxin sink in the topmost outer cells the authors effectively impose the polar auxin transport directions of the tissue outside the simulated domain, which likely causes the simulated domain to align with this rather than displaying truly self-organized patterning. Also, in the model mechanics has been made to impact PIN polarity, but it has not been demonstrated if in absence of PIN polarity dependence on mechanics PIN patterning would be different, i.e. if the mechanical feedback on PIN patterning is necessary or rather that the source and sink prepattern dominate. Similarly, the feedback of auxin on mechanics is I believe limited to cellular auxin levels determining cellular growth rates and does not appear to control cellular growth anisotropy (i.e. predominant longitudinal growth of cells), which arose from the initial symmetry breaking of differential growth rates. As such the actual coupling between mechanics and auxin patterning and the extent of self-organization is less than suggested.
Some matters are rather unclear in the manuscript in its current form. It is for example unclear how exactly does auxin translate into cellular growth rate and how does this result in stable, coordinated growth across cell files. In a previous study it was shown that since auxin levels differ significantly across cell files (e.g. much higher in vasculature than in neighboring cell files), problems in coordinated cell growth may occur (https://pubmed.ncbi.nlm.nih.gov/25358093/). It is unclear how such problems are avoided here. Similarly, in the discussion authors mention possible uses of the model such as studying tropisms. However the latter requires incorporating an elongation zone in which cells undergo rapid and extreme cell elongation. It seems that the current model only incorporates slow cytoplasmic cell growth and division occurring in the meristem, and it is unclear whether the used model formalism would be capable of stably simulating these far more anisotropic growth processes in a numerically stable and efficient manner.
Summarizing the authors have generated a highly valuable combined mechano-chemical modeling framework for root tip development that can be used to various applications, but that was somewhat oversold.
-
Reviewer #2 (Public Review):
The work by Marconi et al. echoes previous work conducted at the shoot apical meristem where PIN transport has been modeled in realistic templates, and with mechanics, for iterative morphogenesis (phyllotaxis). The two most appealing parts of this study to me are:
(i) The initial symmetry breaking event where differential growth can promote anisotropic root growth (a trichome-like model for the radicle)
(ii) The link between growth and reflux loop, including the tests in mutants and decapitation/regeneration. In particular "auxin influx from the LRC and subsequent 'bipolar' PINs localization in the cortex tissues may be important elements of the sustained auxin-dependent root growth" is key.Somehow, the underlined molecular hypothesis (phosphatase model) is a bit secondary - this is rather an algorithmic …
Reviewer #2 (Public Review):
The work by Marconi et al. echoes previous work conducted at the shoot apical meristem where PIN transport has been modeled in realistic templates, and with mechanics, for iterative morphogenesis (phyllotaxis). The two most appealing parts of this study to me are:
(i) The initial symmetry breaking event where differential growth can promote anisotropic root growth (a trichome-like model for the radicle)
(ii) The link between growth and reflux loop, including the tests in mutants and decapitation/regeneration. In particular "auxin influx from the LRC and subsequent 'bipolar' PINs localization in the cortex tissues may be important elements of the sustained auxin-dependent root growth" is key.Somehow, the underlined molecular hypothesis (phosphatase model) is a bit secondary - this is rather an algorithmic way to generate emerging properties; other molecular mechanisms might provide the same outcome. Overall, this represents a major advance in the field. However, some points would require attention: 1/ PIN polarity rather depends on actin filaments, thus the relation between cytoplasmic microtubules, cortical microtubules, and mechanical stress is a bit confusing, 2/ the paper describes two systems (the radicle from the embryo and the growing primary root) with no clear link between both, 3/ Although I understand that this paper only describes a model (based on existing wet data), the wording is sometimes misleading and suggests that digital data are also real data.
-
Reviewer #3 (Public Review):
Marconi, M et al. developed a new mechano-biochemical computational framework to study plant morphogenesis. A positional information is self-organized by a diffusing substance that regulates acquiring cell polarity and modulates cell growth by changing the cell's biomechanical properties. The model for the root meristem functioning in Arabidopsis thaliana is composed of a minimal set of experimentally derived principles for self-organization of organ patterning. This study is an excellent methodological achievement that also brought some new biological results. Although all the results are there, the manuscript requires major revision to present the framework better to avoid miscommunication.
Framework:
Good: The framework looks very promising to study tissue morphogenesis (not necessarily in plants). So it …
Reviewer #3 (Public Review):
Marconi, M et al. developed a new mechano-biochemical computational framework to study plant morphogenesis. A positional information is self-organized by a diffusing substance that regulates acquiring cell polarity and modulates cell growth by changing the cell's biomechanical properties. The model for the root meristem functioning in Arabidopsis thaliana is composed of a minimal set of experimentally derived principles for self-organization of organ patterning. This study is an excellent methodological achievement that also brought some new biological results. Although all the results are there, the manuscript requires major revision to present the framework better to avoid miscommunication.
Framework:
Good: The framework looks very promising to study tissue morphogenesis (not necessarily in plants). So it has the sense to make it available for the scientific community. Now the code can be downloaded from the google disc using a password; I encourage the authors to add a permanent link and the tutorial to the framework in the final version of the paper.
Not good: The manuscript structure does not allow us to see all the advantages of the framework; the information about it is spread throughout the text. The main text misses essential details, while the materials and methods section contains a lot of discussions. E.g., CTM are mentioned several times in the results section without explaining how you modeled them. Another example is on the line 188 where the reference about "put together growth biomechanics" leads us the Figure 1 without any details about that. I would suggest adding a first section of the Results and the main figure about the framework, its basics, advantages, and limitations. Also, to add a bit more about PBD technology.
Root model:
Good:
• The application of the model delivered some new and important results for plant biologists. E.g., the authors confirmed the hypothesis that the start of anisotropic root growth (elongation) results from the differential expansion of neighboring tissues.
• They also showed self-organization of a complex auxin distribution (PIN polarization) map, which reproduces tiny properties like the switch in PIN polarity from rootward to shootward in the cortex.
• The authors also showed that auxin reflux in the meristem is not that important for auxin maximum maintenance under normal conditions but gives an advantage in shoot-independent growth.
• The fact that the authors were able to "grow" a "whole root" from the embryonic-like structure under a limited number of predefined rules is inspiring and promising.
Can be better:
I am not sure that I understand the visualization of PINs on the figures. The authors do not distinguish between PIN levels and PIN polarities. It is clear that they managed to model PIN polarities correctly, but I am not sure about PIN levels. If PIN levels are shown by red rectangular, then columella does not have any PINs (which is incorrect). Is it so?
It sounds great that you simulated an oscillating behavior in the root growth, but actually, you did not. Simulating periodic application of auxin treatment to simulate oscillation is a trivial solution, that only sounds great, but disappoints when you look into detail. Instead, I would suggest simulation of restoration of root growth after it is inhibited by auxin application.
Looking at the resulting solution, it looks like that auxin maximum in QC emerges because one QC cell adopts auxin from two vascular cells. Or maybe because columella does not have PINs. If it is so, it has to be stated; otherwise, there is an impression that auxin maximum self-organizes due to flux pattern only. =
It also looks like that QC does not grow during calculation, if it so, it has to be stated, because then it is one of the factors that "eventually reproducing the non-trivial shape of the root" (line 214). The rules to get "the non-trivial shape" should be explicitly stated. E.g., how did you get that only columella stem cells have divided and not other columella cells that are bigger in size?
I noticed the formation of left-to-write asymmetry in auxin distribution in the root meristem that was self-organized. It will be great if you elaborate on that more. Especially considering that you simulated pin2 mutant where this asymmetry got lost.
I was also quite excited looking on the bending root (Figure 2 - supplement 8) correlated with this left-to-write auxin distribution asymmetry. It will be great if you elaborate on the root bending more in the manuscript.
Not good:
There is a mess with anatomical terminology usage in the manuscript. The authors name the basal part of the embryo as the root or radicle, which is incorrect. There is no root or hypocotyl at the heart stage and even at the torpedo or bending-cotyledon stages. Consider starting growing the root from the mature embryo stage and not from the heart one. Otherwise, you study the formation of "apical-basal polarity" in embryo development and not root development.
Another problem with the terminology is that the definitions are sometimes given later than they were used, and there is a lot of introduction in the results and material and methods section, which disturb the comprehension of the text. E.g., QC is introduced in the last results chapter (line 324).
The only experimental data given in the manuscript is an analysis of hypocotyl and root growth in the seedling soon after germination. Using this data to confirm the results on "growing the root" from the heart-stage embryo is confusing. The results of the experimental data analysis are also quite obvious and did not require an experiment :). Having Eva Benkova among the co-authors, the manuscript should be supplemented with better experimental data that confirm or demonstrate the modeling results' appropriateness. The authors refer to confirmations from the published data in the rest of the text instead of explicitly comparing computational and experimental results. The manuscript will certainly win from such a direct comparison.
Actually, it would not be bad if the authors did not use the experimental data at all, because all the facts discussed are well known; the authors can give just references. It just looks strange why only one (and not very relevant) experiment is shown from a vast collection of Prof. Eva Benkova.
-
-