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On the origins of the mitotic shift in proliferating cell layers.

Gibson WT, Rubinstein BY, Meyer EJ, Veldhuis JH, Brodland GW, Nagpal R, Gibson MC - Theor Biol Med Model (2014)

Bottom Line: Using both mathematical and experimental approaches, we show that the mitotic shift derives primarily from passive, non-autonomous effects of mitoses in neighboring cells on each cell's geometry over the course of the cell cycle.Taken together, our results strongly suggest that the mitotic shift reflects a time-dependent accumulation of shared cellular interfaces over the course of the cell cycle.These results uncover fundamental constraints on the relationship between cell shape and cell division that should be general in adherent, polarized cell layers.

View Article: PubMed Central - HTML - PubMed

Affiliation: Stowers Institute for Medical Research, 64110 Kansas City, MO, USA. mg2@stowers.org.

ABSTRACT

Background: During plant and animal development, monolayer cell sheets display a stereotyped distribution of polygonal cell shapes. In interphase cells these shapes range from quadrilaterals to decagons, with a robust average of six sides per cell. In contrast, the subset of cells in mitosis exhibits a distinct distribution with an average of seven sides. It remains unclear whether this 'mitotic shift' reflects a causal relationship between increased polygonal sidedness and increased division likelihood, or alternatively, a passive effect of local proliferation on cell shape.

Methods: We use a combination of probabilistic analysis and mathematical modeling to predict the geometry of mitotic polygonal cells in a proliferating cell layer. To test these predictions experimentally, we use Flp-Out stochastic labeling in the Drosophila wing disc to induce single cell clones, and confocal imaging to quantify the polygonal topologies of these clones as a function of cellular age. For a more generic test in an idealized cell layer, we model epithelial sheet proliferation in a finite element framework, which yields a computationally robust, emergent prediction of the mitotic cell shape distribution.

Results: Using both mathematical and experimental approaches, we show that the mitotic shift derives primarily from passive, non-autonomous effects of mitoses in neighboring cells on each cell's geometry over the course of the cell cycle. Computationally, we predict that interphase cells should passively gain sides over time, such that cells at more advanced stages of the cell cycle will tend to have a larger number of neighbors than those at earlier stages. Validating this prediction, experimental analysis of randomly labeled epithelial cells in the Drosophila wing disc demonstrates that labeled cells exhibit an age-dependent increase in polygonal sidedness. Reinforcing these data, finite element simulations of epithelial sheet proliferation demonstrate in a generic framework that passive side-gaining is sufficient to generate a mitotic shift.

Conclusions: Taken together, our results strongly suggest that the mitotic shift reflects a time-dependent accumulation of shared cellular interfaces over the course of the cell cycle. These results uncover fundamental constraints on the relationship between cell shape and cell division that should be general in adherent, polarized cell layers.

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A finite element model based on oldest cell divisions with noise can recapitulate most features of the mitotic shift. (A) Initial conditions and model output. Cells are chosen for division as a function of cellular age, with additive noise in the division ordering. The simulated tissue has toroidal boundary conditions, and undergoes at least 1050 mitoses. (B) The simulated distribution of cellular shapes. (C) The distribution of mitotic cells chosen for division. (D) Division likelihood as a function of polygon class, here displayed relative to the likelihood that a nonagon divides (which is taken to be 1). Panel (D), which is computed using Bayes rule, is well fit by an exponential function (the R2 coefficient is equal to 0.9989). (E) The simulated mitotic shift based on an oldest-cell division mechanism. (F) For comparison, the mitotic shift in Drosophila and in Cucumis. Sample sizes for the empirical overall and mitotic distributions are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section.
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Figure 5: A finite element model based on oldest cell divisions with noise can recapitulate most features of the mitotic shift. (A) Initial conditions and model output. Cells are chosen for division as a function of cellular age, with additive noise in the division ordering. The simulated tissue has toroidal boundary conditions, and undergoes at least 1050 mitoses. (B) The simulated distribution of cellular shapes. (C) The distribution of mitotic cells chosen for division. (D) Division likelihood as a function of polygon class, here displayed relative to the likelihood that a nonagon divides (which is taken to be 1). Panel (D), which is computed using Bayes rule, is well fit by an exponential function (the R2 coefficient is equal to 0.9989). (E) The simulated mitotic shift based on an oldest-cell division mechanism. (F) For comparison, the mitotic shift in Drosophila and in Cucumis. Sample sizes for the empirical overall and mitotic distributions are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section.

Mentions: Taken together, our mathematical and experimental results suggest that the mitotic shift is generated primarily due to the effects of side gaining over the course of the cell cycle, with non-autonomous induction of cell division playing a minimal role, if any. In order to test this hypothesis in a computational framework, we simulated epithelial proliferation (Figure 5A-C) using a finite element model of epithelial morphogenesis, which has been described previously [36]. Cells were chosen for division according to an oldest-cell division rule with additive noise, which simulates a roughly uniform but asynchronous cell cycle schedule. Divisions were implemented according to a longest-axis division rule, consistent with empirical measurements [24]. Consistent with our mathematical analysis from previous sections, this model produces a division likelihood function F(N) which is well-fit by an exponential function (R2 coefficient = 0.9989). Moreover, this approach exhibits a mitotic polygonal shape distribution that is shifted relative to the overall distribution (Figure 5E; compare with Figure 5F). We conclude that passive side-gaining over the course of the cell cycle is sufficient to account for most of the upward shift in polygonal sidedness observed empirically in Drosophila and in Cucumis.


On the origins of the mitotic shift in proliferating cell layers.

Gibson WT, Rubinstein BY, Meyer EJ, Veldhuis JH, Brodland GW, Nagpal R, Gibson MC - Theor Biol Med Model (2014)

A finite element model based on oldest cell divisions with noise can recapitulate most features of the mitotic shift. (A) Initial conditions and model output. Cells are chosen for division as a function of cellular age, with additive noise in the division ordering. The simulated tissue has toroidal boundary conditions, and undergoes at least 1050 mitoses. (B) The simulated distribution of cellular shapes. (C) The distribution of mitotic cells chosen for division. (D) Division likelihood as a function of polygon class, here displayed relative to the likelihood that a nonagon divides (which is taken to be 1). Panel (D), which is computed using Bayes rule, is well fit by an exponential function (the R2 coefficient is equal to 0.9989). (E) The simulated mitotic shift based on an oldest-cell division mechanism. (F) For comparison, the mitotic shift in Drosophila and in Cucumis. Sample sizes for the empirical overall and mitotic distributions are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4048254&req=5

Figure 5: A finite element model based on oldest cell divisions with noise can recapitulate most features of the mitotic shift. (A) Initial conditions and model output. Cells are chosen for division as a function of cellular age, with additive noise in the division ordering. The simulated tissue has toroidal boundary conditions, and undergoes at least 1050 mitoses. (B) The simulated distribution of cellular shapes. (C) The distribution of mitotic cells chosen for division. (D) Division likelihood as a function of polygon class, here displayed relative to the likelihood that a nonagon divides (which is taken to be 1). Panel (D), which is computed using Bayes rule, is well fit by an exponential function (the R2 coefficient is equal to 0.9989). (E) The simulated mitotic shift based on an oldest-cell division mechanism. (F) For comparison, the mitotic shift in Drosophila and in Cucumis. Sample sizes for the empirical overall and mitotic distributions are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section.
Mentions: Taken together, our mathematical and experimental results suggest that the mitotic shift is generated primarily due to the effects of side gaining over the course of the cell cycle, with non-autonomous induction of cell division playing a minimal role, if any. In order to test this hypothesis in a computational framework, we simulated epithelial proliferation (Figure 5A-C) using a finite element model of epithelial morphogenesis, which has been described previously [36]. Cells were chosen for division according to an oldest-cell division rule with additive noise, which simulates a roughly uniform but asynchronous cell cycle schedule. Divisions were implemented according to a longest-axis division rule, consistent with empirical measurements [24]. Consistent with our mathematical analysis from previous sections, this model produces a division likelihood function F(N) which is well-fit by an exponential function (R2 coefficient = 0.9989). Moreover, this approach exhibits a mitotic polygonal shape distribution that is shifted relative to the overall distribution (Figure 5E; compare with Figure 5F). We conclude that passive side-gaining over the course of the cell cycle is sufficient to account for most of the upward shift in polygonal sidedness observed empirically in Drosophila and in Cucumis.

Bottom Line: Using both mathematical and experimental approaches, we show that the mitotic shift derives primarily from passive, non-autonomous effects of mitoses in neighboring cells on each cell's geometry over the course of the cell cycle.Taken together, our results strongly suggest that the mitotic shift reflects a time-dependent accumulation of shared cellular interfaces over the course of the cell cycle.These results uncover fundamental constraints on the relationship between cell shape and cell division that should be general in adherent, polarized cell layers.

View Article: PubMed Central - HTML - PubMed

Affiliation: Stowers Institute for Medical Research, 64110 Kansas City, MO, USA. mg2@stowers.org.

ABSTRACT

Background: During plant and animal development, monolayer cell sheets display a stereotyped distribution of polygonal cell shapes. In interphase cells these shapes range from quadrilaterals to decagons, with a robust average of six sides per cell. In contrast, the subset of cells in mitosis exhibits a distinct distribution with an average of seven sides. It remains unclear whether this 'mitotic shift' reflects a causal relationship between increased polygonal sidedness and increased division likelihood, or alternatively, a passive effect of local proliferation on cell shape.

Methods: We use a combination of probabilistic analysis and mathematical modeling to predict the geometry of mitotic polygonal cells in a proliferating cell layer. To test these predictions experimentally, we use Flp-Out stochastic labeling in the Drosophila wing disc to induce single cell clones, and confocal imaging to quantify the polygonal topologies of these clones as a function of cellular age. For a more generic test in an idealized cell layer, we model epithelial sheet proliferation in a finite element framework, which yields a computationally robust, emergent prediction of the mitotic cell shape distribution.

Results: Using both mathematical and experimental approaches, we show that the mitotic shift derives primarily from passive, non-autonomous effects of mitoses in neighboring cells on each cell's geometry over the course of the cell cycle. Computationally, we predict that interphase cells should passively gain sides over time, such that cells at more advanced stages of the cell cycle will tend to have a larger number of neighbors than those at earlier stages. Validating this prediction, experimental analysis of randomly labeled epithelial cells in the Drosophila wing disc demonstrates that labeled cells exhibit an age-dependent increase in polygonal sidedness. Reinforcing these data, finite element simulations of epithelial sheet proliferation demonstrate in a generic framework that passive side-gaining is sufficient to generate a mitotic shift.

Conclusions: Taken together, our results strongly suggest that the mitotic shift reflects a time-dependent accumulation of shared cellular interfaces over the course of the cell cycle. These results uncover fundamental constraints on the relationship between cell shape and cell division that should be general in adherent, polarized cell layers.

Show MeSH
Related in: MedlinePlus