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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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Cell-autonomous regulation: Robustness to perturbations.(A) Simulation output (time: 87 h) from a model as in Figure 3, yet with maximally ±25% noise added to cell cycle time (except first division ±10%, cf.Table S1 – Model 4; see also Figures S3A and S3C), which demonstrates that the symplast can act as a stabilizing framework that dissipates ‘noisy’ mechanical perturbations through its structure. Colouring is according to growth potential (defined in the Methods section) as a measure for ‘turgor pressure’. (B) Timer-based developmental transitions can amplify tissue distortion. Simulation output of timer mechanism with layer-specific cell cycle time (Model 5 at simulation time 90 h). Upon release from the ‘QC’ cells can divide 3 times. For the outer 6 cell files CCT = 900 min, the inner 6 CCT = 1080 min. Afterwards, cells undergo accelerated growth until 4440 min after ‘QC’-release. Therefore the inner cells lag behind if their release started more or less synchronous as is the case here (maximally ±10% noise). Synchronicity is an important factor determining stable patterning in itself. Counters are sensitive as they multiply and therefore consistently amplify differences in CCT. Cells in the centre are lagging behind in terms of growth. As simulation time passes the irregularities eventually result in severely distorted patterns. Colouring is according to growth potential (defined in the Methods section) as a measure for ‘turgor pressure’. (C) Simulation of Model 6 (Table S1) at simulation time 42 h, with a sizer-based cell cycle. One sizer, imposing division at a defined absolute cell size, is used despite differences in width of cells at similar positions along the main growth axis. Outer cell files have wider cells which reach the critical size before those of inner files. Therefore they undergo a much earlier exit from proliferation starting accelerated growth earlier, resulting in cell shape/tissue distortion. Cells in the centre are therefore lagging behind in terms of growth rate. Cell-autonomous regulatory systems appear inherently sensitive to this effect. Colouring is according to growth potential, GP or ‘turgor pressure’ (cf.Methods).
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pcbi-1003910-g004: Cell-autonomous regulation: Robustness to perturbations.(A) Simulation output (time: 87 h) from a model as in Figure 3, yet with maximally ±25% noise added to cell cycle time (except first division ±10%, cf.Table S1 – Model 4; see also Figures S3A and S3C), which demonstrates that the symplast can act as a stabilizing framework that dissipates ‘noisy’ mechanical perturbations through its structure. Colouring is according to growth potential (defined in the Methods section) as a measure for ‘turgor pressure’. (B) Timer-based developmental transitions can amplify tissue distortion. Simulation output of timer mechanism with layer-specific cell cycle time (Model 5 at simulation time 90 h). Upon release from the ‘QC’ cells can divide 3 times. For the outer 6 cell files CCT = 900 min, the inner 6 CCT = 1080 min. Afterwards, cells undergo accelerated growth until 4440 min after ‘QC’-release. Therefore the inner cells lag behind if their release started more or less synchronous as is the case here (maximally ±10% noise). Synchronicity is an important factor determining stable patterning in itself. Counters are sensitive as they multiply and therefore consistently amplify differences in CCT. Cells in the centre are lagging behind in terms of growth. As simulation time passes the irregularities eventually result in severely distorted patterns. Colouring is according to growth potential (defined in the Methods section) as a measure for ‘turgor pressure’. (C) Simulation of Model 6 (Table S1) at simulation time 42 h, with a sizer-based cell cycle. One sizer, imposing division at a defined absolute cell size, is used despite differences in width of cells at similar positions along the main growth axis. Outer cell files have wider cells which reach the critical size before those of inner files. Therefore they undergo a much earlier exit from proliferation starting accelerated growth earlier, resulting in cell shape/tissue distortion. Cells in the centre are therefore lagging behind in terms of growth rate. Cell-autonomous regulatory systems appear inherently sensitive to this effect. Colouring is according to growth potential, GP or ‘turgor pressure’ (cf.Methods).

Mentions: A consequence of the symplastic growth of the root is that at a given distance from the tip all cells have the same relative expansion rate [32]. As stated by Ivanov [33], any observed difference in cell lengths between tissues must therefore reflect differences in cell proliferation (see also [26]). Inversely, any form of growth regulation that results in different elongation rates for cells at the same distance from the tip would disrupt symplastic growth (Figure 1A). For instance, suppose all cells at the same (vertical) position in a downward growing root have the same absolute (areal) expansion rate, irrespective of their size (Model 1, Tables 1 and S1). With inner cell files narrower than outer cell files (similar to the real root) this fixed size increment results in consistently larger relative elongation rates for the inner tissue layers leading to tissue distortion and unbalanced distribution of mechanical stresses (Figure 1B and C). Note that the same situation would occur when adjacent files contain cells of similar width, but different lengths growing at the same absolute rates. Hence, non-uniform relative strain rates at some position along the principal growth axis eventually lead to malformations.


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)

Cell-autonomous regulation: Robustness to perturbations.(A) Simulation output (time: 87 h) from a model as in Figure 3, yet with maximally ±25% noise added to cell cycle time (except first division ±10%, cf.Table S1 – Model 4; see also Figures S3A and S3C), which demonstrates that the symplast can act as a stabilizing framework that dissipates ‘noisy’ mechanical perturbations through its structure. Colouring is according to growth potential (defined in the Methods section) as a measure for ‘turgor pressure’. (B) Timer-based developmental transitions can amplify tissue distortion. Simulation output of timer mechanism with layer-specific cell cycle time (Model 5 at simulation time 90 h). Upon release from the ‘QC’ cells can divide 3 times. For the outer 6 cell files CCT = 900 min, the inner 6 CCT = 1080 min. Afterwards, cells undergo accelerated growth until 4440 min after ‘QC’-release. Therefore the inner cells lag behind if their release started more or less synchronous as is the case here (maximally ±10% noise). Synchronicity is an important factor determining stable patterning in itself. Counters are sensitive as they multiply and therefore consistently amplify differences in CCT. Cells in the centre are lagging behind in terms of growth. As simulation time passes the irregularities eventually result in severely distorted patterns. Colouring is according to growth potential (defined in the Methods section) as a measure for ‘turgor pressure’. (C) Simulation of Model 6 (Table S1) at simulation time 42 h, with a sizer-based cell cycle. One sizer, imposing division at a defined absolute cell size, is used despite differences in width of cells at similar positions along the main growth axis. Outer cell files have wider cells which reach the critical size before those of inner files. Therefore they undergo a much earlier exit from proliferation starting accelerated growth earlier, resulting in cell shape/tissue distortion. Cells in the centre are therefore lagging behind in terms of growth rate. Cell-autonomous regulatory systems appear inherently sensitive to this effect. Colouring is according to growth potential, GP or ‘turgor pressure’ (cf.Methods).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4214622&req=5

pcbi-1003910-g004: Cell-autonomous regulation: Robustness to perturbations.(A) Simulation output (time: 87 h) from a model as in Figure 3, yet with maximally ±25% noise added to cell cycle time (except first division ±10%, cf.Table S1 – Model 4; see also Figures S3A and S3C), which demonstrates that the symplast can act as a stabilizing framework that dissipates ‘noisy’ mechanical perturbations through its structure. Colouring is according to growth potential (defined in the Methods section) as a measure for ‘turgor pressure’. (B) Timer-based developmental transitions can amplify tissue distortion. Simulation output of timer mechanism with layer-specific cell cycle time (Model 5 at simulation time 90 h). Upon release from the ‘QC’ cells can divide 3 times. For the outer 6 cell files CCT = 900 min, the inner 6 CCT = 1080 min. Afterwards, cells undergo accelerated growth until 4440 min after ‘QC’-release. Therefore the inner cells lag behind if their release started more or less synchronous as is the case here (maximally ±10% noise). Synchronicity is an important factor determining stable patterning in itself. Counters are sensitive as they multiply and therefore consistently amplify differences in CCT. Cells in the centre are lagging behind in terms of growth. As simulation time passes the irregularities eventually result in severely distorted patterns. Colouring is according to growth potential (defined in the Methods section) as a measure for ‘turgor pressure’. (C) Simulation of Model 6 (Table S1) at simulation time 42 h, with a sizer-based cell cycle. One sizer, imposing division at a defined absolute cell size, is used despite differences in width of cells at similar positions along the main growth axis. Outer cell files have wider cells which reach the critical size before those of inner files. Therefore they undergo a much earlier exit from proliferation starting accelerated growth earlier, resulting in cell shape/tissue distortion. Cells in the centre are therefore lagging behind in terms of growth rate. Cell-autonomous regulatory systems appear inherently sensitive to this effect. Colouring is according to growth potential, GP or ‘turgor pressure’ (cf.Methods).
Mentions: A consequence of the symplastic growth of the root is that at a given distance from the tip all cells have the same relative expansion rate [32]. As stated by Ivanov [33], any observed difference in cell lengths between tissues must therefore reflect differences in cell proliferation (see also [26]). Inversely, any form of growth regulation that results in different elongation rates for cells at the same distance from the tip would disrupt symplastic growth (Figure 1A). For instance, suppose all cells at the same (vertical) position in a downward growing root have the same absolute (areal) expansion rate, irrespective of their size (Model 1, Tables 1 and S1). With inner cell files narrower than outer cell files (similar to the real root) this fixed size increment results in consistently larger relative elongation rates for the inner tissue layers leading to tissue distortion and unbalanced distribution of mechanical stresses (Figure 1B and C). Note that the same situation would occur when adjacent files contain cells of similar width, but different lengths growing at the same absolute rates. Hence, non-uniform relative strain rates at some position along the principal growth axis eventually lead to malformations.

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