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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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Related in: MedlinePlus

Timers and counters can produce stable directional growth.Example simulations of counter and timer based models for root growth (Model 2 and Model 3 in Table S1). Upon release from the QC, cells can divide for a pre-programmed time duration (A–C) or number of times (D), followed by a fixed time duration of accelerated growth. (A) Total root length versus simulation time. It takes approximately 75 hours for the first cells to start accelerating growth (indicated by ‘*’). Subsequent sets of quasi synchronously dividing cells then grow exponentially for a fixed time, yielding a roughly linear area increase. (B) Total cell number versus simulation time. The cell number is built up exponentially till 12 (columns)×23 = 96 ‘clones’ are formed. These then undergo accelerated growth. One cell cycle later the next pool of 96 cells is ready to do the same and cell numbers increase by constant steps. (C) Detailed snapshots (at 99 hours, with diamond shaped markers, and 108 hours, with circular markers) of approximate cell length along the main growth axis. Subpopulations with narrow length distributions can be seen corresponding to dividing, accelerating and mature cells. The accelerating cell population occupies an increasing area until adding to the mature zone. The ‘polyloc method’ was used for curve fitting (cf.Methods). (D) Simulation output of Model 2 at 99 h (Table S1). The imposed growth and division rules have resulted in a highly regular grid with distinct zones of similar cell length (division zone (DZ) and elongation zone (EZ) are indicated). Areal strain rates (‘AS’ as defined in Methods) are mapped on the cellular grid, showing the elongation zone as a distinct region of relatively uniform accelerated growth.
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pcbi-1003910-g003: Timers and counters can produce stable directional growth.Example simulations of counter and timer based models for root growth (Model 2 and Model 3 in Table S1). Upon release from the QC, cells can divide for a pre-programmed time duration (A–C) or number of times (D), followed by a fixed time duration of accelerated growth. (A) Total root length versus simulation time. It takes approximately 75 hours for the first cells to start accelerating growth (indicated by ‘*’). Subsequent sets of quasi synchronously dividing cells then grow exponentially for a fixed time, yielding a roughly linear area increase. (B) Total cell number versus simulation time. The cell number is built up exponentially till 12 (columns)×23 = 96 ‘clones’ are formed. These then undergo accelerated growth. One cell cycle later the next pool of 96 cells is ready to do the same and cell numbers increase by constant steps. (C) Detailed snapshots (at 99 hours, with diamond shaped markers, and 108 hours, with circular markers) of approximate cell length along the main growth axis. Subpopulations with narrow length distributions can be seen corresponding to dividing, accelerating and mature cells. The accelerating cell population occupies an increasing area until adding to the mature zone. The ‘polyloc method’ was used for curve fitting (cf.Methods). (D) Simulation output of Model 2 at 99 h (Table S1). The imposed growth and division rules have resulted in a highly regular grid with distinct zones of similar cell length (division zone (DZ) and elongation zone (EZ) are indicated). Areal strain rates (‘AS’ as defined in Methods) are mapped on the cellular grid, showing the elongation zone as a distinct region of relatively uniform accelerated growth.

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)

Timers and counters can produce stable directional growth.Example simulations of counter and timer based models for root growth (Model 2 and Model 3 in Table S1). Upon release from the QC, cells can divide for a pre-programmed time duration (A–C) or number of times (D), followed by a fixed time duration of accelerated growth. (A) Total root length versus simulation time. It takes approximately 75 hours for the first cells to start accelerating growth (indicated by ‘*’). Subsequent sets of quasi synchronously dividing cells then grow exponentially for a fixed time, yielding a roughly linear area increase. (B) Total cell number versus simulation time. The cell number is built up exponentially till 12 (columns)×23 = 96 ‘clones’ are formed. These then undergo accelerated growth. One cell cycle later the next pool of 96 cells is ready to do the same and cell numbers increase by constant steps. (C) Detailed snapshots (at 99 hours, with diamond shaped markers, and 108 hours, with circular markers) of approximate cell length along the main growth axis. Subpopulations with narrow length distributions can be seen corresponding to dividing, accelerating and mature cells. The accelerating cell population occupies an increasing area until adding to the mature zone. The ‘polyloc method’ was used for curve fitting (cf.Methods). (D) Simulation output of Model 2 at 99 h (Table S1). The imposed growth and division rules have resulted in a highly regular grid with distinct zones of similar cell length (division zone (DZ) and elongation zone (EZ) are indicated). Areal strain rates (‘AS’ as defined in Methods) are mapped on the cellular grid, showing the elongation zone as a distinct region of relatively uniform accelerated growth.
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Related In: Results  -  Collection

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

pcbi-1003910-g003: Timers and counters can produce stable directional growth.Example simulations of counter and timer based models for root growth (Model 2 and Model 3 in Table S1). Upon release from the QC, cells can divide for a pre-programmed time duration (A–C) or number of times (D), followed by a fixed time duration of accelerated growth. (A) Total root length versus simulation time. It takes approximately 75 hours for the first cells to start accelerating growth (indicated by ‘*’). Subsequent sets of quasi synchronously dividing cells then grow exponentially for a fixed time, yielding a roughly linear area increase. (B) Total cell number versus simulation time. The cell number is built up exponentially till 12 (columns)×23 = 96 ‘clones’ are formed. These then undergo accelerated growth. One cell cycle later the next pool of 96 cells is ready to do the same and cell numbers increase by constant steps. (C) Detailed snapshots (at 99 hours, with diamond shaped markers, and 108 hours, with circular markers) of approximate cell length along the main growth axis. Subpopulations with narrow length distributions can be seen corresponding to dividing, accelerating and mature cells. The accelerating cell population occupies an increasing area until adding to the mature zone. The ‘polyloc method’ was used for curve fitting (cf.Methods). (D) Simulation output of Model 2 at 99 h (Table S1). The imposed growth and division rules have resulted in a highly regular grid with distinct zones of similar cell length (division zone (DZ) and elongation zone (EZ) are indicated). Areal strain rates (‘AS’ as defined in Methods) are mapped on the cellular grid, showing the elongation zone as a distinct region of relatively uniform accelerated growth.
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