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Putting theory to the test: which regulatory mechanisms can drive realistic growth of a root?

De Vos D, Vissenberg K, Broeckhove J, Beemster GT - PLoS Comput. Biol. (2014)

Bottom Line: Whereas simple cell-autonomous regulatory rules based on counters and timers can produce stable growth, it was found that steady developmental zones and smooth transitions in cell lengths are not feasible.Alternatively, a model representing the known cross-talk between auxin, as the cell proliferation promoting factor, and cytokinin, as the cell differentiation promoting factor, predicts the effect of hormone-perturbations on meristem size.By down-regulating PIN-mediated transport through the transcription factor SHY2, cytokinin effectively flattens the lateral auxin gradient, at the basal boundary of the division zone, (thereby imposing the ULSR) to signal the exit of proliferation and start of elongation.

View Article: PubMed Central - PubMed

Affiliation: Molecular Plant Physiology and Biotechnology, Department of Biology, University of Antwerp, Antwerp, Belgium.

ABSTRACT
In recent years there has been a strong development of computational approaches to mechanistically understand organ growth regulation in plants. In this study, simulation methods were used to explore which regulatory mechanisms can lead to realistic output at the cell and whole organ scale and which other possibilities must be discarded as they result in cellular patterns and kinematic characteristics that are not consistent with experimental observations for the Arabidopsis thaliana primary root. To aid in this analysis, a 'Uniform Longitudinal Strain Rule' (ULSR) was formulated as a necessary condition for stable, unidirectional, symplastic growth. Our simulations indicate that symplastic structures are robust to differences in longitudinal strain rates along the growth axis only if these differences are small and short-lived. Whereas simple cell-autonomous regulatory rules based on counters and timers can produce stable growth, it was found that steady developmental zones and smooth transitions in cell lengths are not feasible. By introducing spatial cues into growth regulation, those inadequacies could be avoided and experimental data could be faithfully reproduced. Nevertheless, a root growth model based on previous polar auxin-transport mechanisms violates the proposed ULSR due to the presence of lateral gradients. Models with layer-specific regulation or layer-driven growth offer potential solutions. Alternatively, a model representing the known cross-talk between auxin, as the cell proliferation promoting factor, and cytokinin, as the cell differentiation promoting factor, predicts the effect of hormone-perturbations on meristem size. By down-regulating PIN-mediated transport through the transcription factor SHY2, cytokinin effectively flattens the lateral auxin gradient, at the basal boundary of the division zone, (thereby imposing the ULSR) to signal the exit of proliferation and start of elongation. This model exploration underlines the value of generating virtual root growth kinematics to dissect and understand the mechanisms controlling this biological system.

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Importance of radially uniform (longitudinal) strain rates.(A) Schematic representation of the ‘ULSR’. Growth of the root apex is simplified as occurring strictly vertically. Arrows indicate that local strain rates are the same at each position along the vertical axis. In our modelling framework one horizontal axis can intersect cells with various average positions, sizes and strain rates thereby inevitably challenging the ULSR. (B–C) Simulation output of Model 1 (Table S1) with growth defined as a constant increment to a cell's target area. Cells in inner files are narrower and therefore longitudinal strain will be higher. This leads to growth irregularity with faster growth for central files creating an imbalance in the observed strain rates and distortion of the originally horizontal cell walls across the diverse layers. (B) Starting state of cell grid. (C) Cell grid depicted at simulation time 108 h.
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pcbi-1003910-g001: Importance of radially uniform (longitudinal) strain rates.(A) Schematic representation of the ‘ULSR’. Growth of the root apex is simplified as occurring strictly vertically. Arrows indicate that local strain rates are the same at each position along the vertical axis. In our modelling framework one horizontal axis can intersect cells with various average positions, sizes and strain rates thereby inevitably challenging the ULSR. (B–C) Simulation output of Model 1 (Table S1) with growth defined as a constant increment to a cell's target area. Cells in inner files are narrower and therefore longitudinal strain will be higher. This leads to growth irregularity with faster growth for central files creating an imbalance in the observed strain rates and distortion of the originally horizontal cell walls across the diverse layers. (B) Starting state of cell grid. (C) Cell grid depicted at simulation time 108 h.

Mentions: Kinematic growth analyses aim to infer properties of cell growth and division from microscopic time series of the growing root, yielding detailed profiles of cell expansion (extension) and cell division (partitioning) along the principal axis of growth [3]. Among others Green [26] developed and advocated this method. Interestingly, Green also derived how proposed elemental growth models would be manifested in a kinematic framework. Based on our current concepts of growth regulation we have extended this analysis that relates changes in cell size along the root axis to relative rates of cell division and expansion. To this end we used the vertex-based plant modelling software VirtualLeaf [25] to directly simulate a selection of distinct growth models (see Methods). These models evolve a two-dimensional cellular grid that represents an axial bisection of the growing root apex (Figure 1A and 1B). Cells are defined as polygons and cell wall segments correspond to the edges acting as linear springs. Cells and cell walls are endowed with biochemical properties represented by reaction and transport equations and logical rules. Specifying regulatory mechanisms ( = input) amounts to specifying rules that minimally determine (i) cellular growth rates (via changing target areas), (ii) cell division rates and orientation (here strictly horizontal), (iii) the transition at the border of the QC and the proximal meristem, (iv) the transition between division and elongation zone (DZ and EZ, respectively), and (v) the transition to mature (differentiated) cells. By modifying those rules and analysing the resulting virtual phenotypes in terms of microscopic and kinematic characteristics we then delineate the requirements for cell growth and division needed to produce a realistic and stably growing root. We have opted here to look at proposed elementary mechanisms and gradually increase the degree of realism compared to real data.


Putting theory to the test: which regulatory mechanisms can drive realistic growth of a root?

De Vos D, Vissenberg K, Broeckhove J, Beemster GT - PLoS Comput. Biol. (2014)

Importance of radially uniform (longitudinal) strain rates.(A) Schematic representation of the ‘ULSR’. Growth of the root apex is simplified as occurring strictly vertically. Arrows indicate that local strain rates are the same at each position along the vertical axis. In our modelling framework one horizontal axis can intersect cells with various average positions, sizes and strain rates thereby inevitably challenging the ULSR. (B–C) Simulation output of Model 1 (Table S1) with growth defined as a constant increment to a cell's target area. Cells in inner files are narrower and therefore longitudinal strain will be higher. This leads to growth irregularity with faster growth for central files creating an imbalance in the observed strain rates and distortion of the originally horizontal cell walls across the diverse layers. (B) Starting state of cell grid. (C) Cell grid depicted at simulation time 108 h.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4214622&req=5

pcbi-1003910-g001: Importance of radially uniform (longitudinal) strain rates.(A) Schematic representation of the ‘ULSR’. Growth of the root apex is simplified as occurring strictly vertically. Arrows indicate that local strain rates are the same at each position along the vertical axis. In our modelling framework one horizontal axis can intersect cells with various average positions, sizes and strain rates thereby inevitably challenging the ULSR. (B–C) Simulation output of Model 1 (Table S1) with growth defined as a constant increment to a cell's target area. Cells in inner files are narrower and therefore longitudinal strain will be higher. This leads to growth irregularity with faster growth for central files creating an imbalance in the observed strain rates and distortion of the originally horizontal cell walls across the diverse layers. (B) Starting state of cell grid. (C) Cell grid depicted at simulation time 108 h.
Mentions: Kinematic growth analyses aim to infer properties of cell growth and division from microscopic time series of the growing root, yielding detailed profiles of cell expansion (extension) and cell division (partitioning) along the principal axis of growth [3]. Among others Green [26] developed and advocated this method. Interestingly, Green also derived how proposed elemental growth models would be manifested in a kinematic framework. Based on our current concepts of growth regulation we have extended this analysis that relates changes in cell size along the root axis to relative rates of cell division and expansion. To this end we used the vertex-based plant modelling software VirtualLeaf [25] to directly simulate a selection of distinct growth models (see Methods). These models evolve a two-dimensional cellular grid that represents an axial bisection of the growing root apex (Figure 1A and 1B). Cells are defined as polygons and cell wall segments correspond to the edges acting as linear springs. Cells and cell walls are endowed with biochemical properties represented by reaction and transport equations and logical rules. Specifying regulatory mechanisms ( = input) amounts to specifying rules that minimally determine (i) cellular growth rates (via changing target areas), (ii) cell division rates and orientation (here strictly horizontal), (iii) the transition at the border of the QC and the proximal meristem, (iv) the transition between division and elongation zone (DZ and EZ, respectively), and (v) the transition to mature (differentiated) cells. By modifying those rules and analysing the resulting virtual phenotypes in terms of microscopic and kinematic characteristics we then delineate the requirements for cell growth and division needed to produce a realistic and stably growing root. We have opted here to look at proposed elementary mechanisms and gradually increase the degree of realism compared to real data.

Bottom Line: Whereas simple cell-autonomous regulatory rules based on counters and timers can produce stable growth, it was found that steady developmental zones and smooth transitions in cell lengths are not feasible.Alternatively, a model representing the known cross-talk between auxin, as the cell proliferation promoting factor, and cytokinin, as the cell differentiation promoting factor, predicts the effect of hormone-perturbations on meristem size.By down-regulating PIN-mediated transport through the transcription factor SHY2, cytokinin effectively flattens the lateral auxin gradient, at the basal boundary of the division zone, (thereby imposing the ULSR) to signal the exit of proliferation and start of elongation.

View Article: PubMed Central - PubMed

Affiliation: Molecular Plant Physiology and Biotechnology, Department of Biology, University of Antwerp, Antwerp, Belgium.

ABSTRACT
In recent years there has been a strong development of computational approaches to mechanistically understand organ growth regulation in plants. In this study, simulation methods were used to explore which regulatory mechanisms can lead to realistic output at the cell and whole organ scale and which other possibilities must be discarded as they result in cellular patterns and kinematic characteristics that are not consistent with experimental observations for the Arabidopsis thaliana primary root. To aid in this analysis, a 'Uniform Longitudinal Strain Rule' (ULSR) was formulated as a necessary condition for stable, unidirectional, symplastic growth. Our simulations indicate that symplastic structures are robust to differences in longitudinal strain rates along the growth axis only if these differences are small and short-lived. Whereas simple cell-autonomous regulatory rules based on counters and timers can produce stable growth, it was found that steady developmental zones and smooth transitions in cell lengths are not feasible. By introducing spatial cues into growth regulation, those inadequacies could be avoided and experimental data could be faithfully reproduced. Nevertheless, a root growth model based on previous polar auxin-transport mechanisms violates the proposed ULSR due to the presence of lateral gradients. Models with layer-specific regulation or layer-driven growth offer potential solutions. Alternatively, a model representing the known cross-talk between auxin, as the cell proliferation promoting factor, and cytokinin, as the cell differentiation promoting factor, predicts the effect of hormone-perturbations on meristem size. By down-regulating PIN-mediated transport through the transcription factor SHY2, cytokinin effectively flattens the lateral auxin gradient, at the basal boundary of the division zone, (thereby imposing the ULSR) to signal the exit of proliferation and start of elongation. This model exploration underlines the value of generating virtual root growth kinematics to dissect and understand the mechanisms controlling this biological system.

Show MeSH
Related in: MedlinePlus