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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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Smooth developmental transitions through spatial signalling.Cells are instructed by spatial signals at a fixed distance from the growing root apex (cf.Table S1 – Model 8). They do not behave as clonal subpopulations and smooth developmental processes are a natural result. (A) Plot of root length versus simulation time shows a smooth transition to a steady linear organ growth (indicated by ‘*’). This is similar to experimental studies (cf.Figure 1 in [34]). (B) Plot of total cell number versus simulation time shows a roughly similar trend as in (A) (‘*’ indicating approximately steady increase). (C) Cell length along the principal growth axis (at simulation time 50 h) demonstrates that the exit of division and start of accelerated growth at a fixed position from the apex can lead to a smooth cell length profile as seen in experimental studies (compare Figure 2). Grey circles represent data points across all cell layers, whereas empty circles are data from the 2 outer (here called epidermal) cell layers only. The ‘epidermal’ data points lie roughly within the expected twofold range at each position along the longitudinal axis. The ‘polyloc’ method was used for curve fitting (cf.Methods). (D) Simulation output with areal strain rates (‘AS’ as defined in Methods) mapped on the cellular grid, showing the elongation zone with accelerated growth. This represents a snapshot at 45 h from a model similar to Model 8 (except a relative growth rate of 0.2 per simulation step of 30 min, occurring between 240–750 µm from the root apex and division at a size of 360 and 180 µm2 for outer and inner cell layers, respectively).
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pcbi-1003910-g005: Smooth developmental transitions through spatial signalling.Cells are instructed by spatial signals at a fixed distance from the growing root apex (cf.Table S1 – Model 8). They do not behave as clonal subpopulations and smooth developmental processes are a natural result. (A) Plot of root length versus simulation time shows a smooth transition to a steady linear organ growth (indicated by ‘*’). This is similar to experimental studies (cf.Figure 1 in [34]). (B) Plot of total cell number versus simulation time shows a roughly similar trend as in (A) (‘*’ indicating approximately steady increase). (C) Cell length along the principal growth axis (at simulation time 50 h) demonstrates that the exit of division and start of accelerated growth at a fixed position from the apex can lead to a smooth cell length profile as seen in experimental studies (compare Figure 2). Grey circles represent data points across all cell layers, whereas empty circles are data from the 2 outer (here called epidermal) cell layers only. The ‘epidermal’ data points lie roughly within the expected twofold range at each position along the longitudinal axis. The ‘polyloc’ method was used for curve fitting (cf.Methods). (D) Simulation output with areal strain rates (‘AS’ as defined in Methods) mapped on the cellular grid, showing the elongation zone with accelerated growth. This represents a snapshot at 45 h from a model similar to Model 8 (except a relative growth rate of 0.2 per simulation step of 30 min, occurring between 240–750 µm from the root apex and division at a size of 360 and 180 µm2 for outer and inner cell layers, respectively).

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)

Smooth developmental transitions through spatial signalling.Cells are instructed by spatial signals at a fixed distance from the growing root apex (cf.Table S1 – Model 8). They do not behave as clonal subpopulations and smooth developmental processes are a natural result. (A) Plot of root length versus simulation time shows a smooth transition to a steady linear organ growth (indicated by ‘*’). This is similar to experimental studies (cf.Figure 1 in [34]). (B) Plot of total cell number versus simulation time shows a roughly similar trend as in (A) (‘*’ indicating approximately steady increase). (C) Cell length along the principal growth axis (at simulation time 50 h) demonstrates that the exit of division and start of accelerated growth at a fixed position from the apex can lead to a smooth cell length profile as seen in experimental studies (compare Figure 2). Grey circles represent data points across all cell layers, whereas empty circles are data from the 2 outer (here called epidermal) cell layers only. The ‘epidermal’ data points lie roughly within the expected twofold range at each position along the longitudinal axis. The ‘polyloc’ method was used for curve fitting (cf.Methods). (D) Simulation output with areal strain rates (‘AS’ as defined in Methods) mapped on the cellular grid, showing the elongation zone with accelerated growth. This represents a snapshot at 45 h from a model similar to Model 8 (except a relative growth rate of 0.2 per simulation step of 30 min, occurring between 240–750 µm from the root apex and division at a size of 360 and 180 µm2 for outer and inner cell layers, respectively).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003910-g005: Smooth developmental transitions through spatial signalling.Cells are instructed by spatial signals at a fixed distance from the growing root apex (cf.Table S1 – Model 8). They do not behave as clonal subpopulations and smooth developmental processes are a natural result. (A) Plot of root length versus simulation time shows a smooth transition to a steady linear organ growth (indicated by ‘*’). This is similar to experimental studies (cf.Figure 1 in [34]). (B) Plot of total cell number versus simulation time shows a roughly similar trend as in (A) (‘*’ indicating approximately steady increase). (C) Cell length along the principal growth axis (at simulation time 50 h) demonstrates that the exit of division and start of accelerated growth at a fixed position from the apex can lead to a smooth cell length profile as seen in experimental studies (compare Figure 2). Grey circles represent data points across all cell layers, whereas empty circles are data from the 2 outer (here called epidermal) cell layers only. The ‘epidermal’ data points lie roughly within the expected twofold range at each position along the longitudinal axis. The ‘polyloc’ method was used for curve fitting (cf.Methods). (D) Simulation output with areal strain rates (‘AS’ as defined in Methods) mapped on the cellular grid, showing the elongation zone with accelerated growth. This represents a snapshot at 45 h from a model similar to Model 8 (except a relative growth rate of 0.2 per simulation step of 30 min, occurring between 240–750 µm from the root apex and division at a size of 360 and 180 µm2 for outer and inner cell layers, respectively).
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