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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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Computational predictions of the mitotic shift based on a stochastic model of the side-gaining process. (A) Prediction of the mitotic cell shape distribution for the Drosophila wing disc epithelium (empirical values shown in grey). In the absence of cleavage plane bias (blue), the computational prediction is not quite as accurate as when the bias is included (red). Sample sizes for the empirical Drosophila mitotic polygonal distribution are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (A’) Prediction of the mitotic cell shape distribution in the epidermis of Cucumis. Here, cleavage plane bias similarly improves the accuracy of the prediction. Sample sizes for the empirical Cucumis mitotic polygonal distribution are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (B) For the Drosophila prediction, a plot of the (l2-norm)2 deviation from the empirical mitotic cell shape distribution as a function of the relationship between division likelihood and polygon class. Here, division likelihood is assumed to increase exponentially as a function of polygon class. The ordinate (exponential constant) gives the precise form of the exponential. Note that positive values strongly outperform negative values. Hence, a model in which division likelihood increases with polygon class is more consistent with the data than a model in which it decreases or remains the same. (B’) For Cucumis, the results are nearly identical to those of Drosophila.
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Figure 3: Computational predictions of the mitotic shift based on a stochastic model of the side-gaining process. (A) Prediction of the mitotic cell shape distribution for the Drosophila wing disc epithelium (empirical values shown in grey). In the absence of cleavage plane bias (blue), the computational prediction is not quite as accurate as when the bias is included (red). Sample sizes for the empirical Drosophila mitotic polygonal distribution are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (A’) Prediction of the mitotic cell shape distribution in the epidermis of Cucumis. Here, cleavage plane bias similarly improves the accuracy of the prediction. Sample sizes for the empirical Cucumis mitotic polygonal distribution are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (B) For the Drosophila prediction, a plot of the (l2-norm)2 deviation from the empirical mitotic cell shape distribution as a function of the relationship between division likelihood and polygon class. Here, division likelihood is assumed to increase exponentially as a function of polygon class. The ordinate (exponential constant) gives the precise form of the exponential. Note that positive values strongly outperform negative values. Hence, a model in which division likelihood increases with polygon class is more consistent with the data than a model in which it decreases or remains the same. (B’) For Cucumis, the results are nearly identical to those of Drosophila.

Mentions: The predicted form of the mitotic distribution P(N/D) depends on the choice of the function F (see equation 15). Consistent with the analyses of the first two sections, past studies of Drosophila and Cucumis monolayer cell sheets demonstrate that the function F is monotone increasing [9,19,24]. Specifically, F is well fit by an exponential function (based on Mathematica’s FindFit function; see references [19,24]). To test whether our modeling framework is able to predict the form of the mitotic cell shape distribution in a proliferating polygonal network, we compared our computational results with empirical data from Drosophila and Cucumis. In each case, we assumed an exponential form for the function F, and searched the parameter space of increasing, decreasing, and flat F functions. To measure the distance between the empirical and the predicted form of the mitotic cell shape distribution, we used the square of the l2-norm, (l2-norm)2. Strikingly, for increasing F functions, the predicted mitotic distribution P(N/D) closely matches the empirical distribution of mitotic cells (Figures 3B-B’; Additional file 2: Figure S2). By contrast, and consistent with the mathematical analysis of the previous sections, flat or decreasing F functions failed to match the data closely (Figures 3B-B’; Additional file 2: Figure S2). We find that including cleavage plane bias, Q(m), improves our estimate (compare blue and red bars, Figures 3A-B). These results, which are consistent with more exhaustive modeling approaches, suggest that our analysis is accurate for the case of Drosophila and Cucumis. Hence, in principle, a simple model of side gaining can account for the mitotic shift in these organisms.


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)

Computational predictions of the mitotic shift based on a stochastic model of the side-gaining process. (A) Prediction of the mitotic cell shape distribution for the Drosophila wing disc epithelium (empirical values shown in grey). In the absence of cleavage plane bias (blue), the computational prediction is not quite as accurate as when the bias is included (red). Sample sizes for the empirical Drosophila mitotic polygonal distribution are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (A’) Prediction of the mitotic cell shape distribution in the epidermis of Cucumis. Here, cleavage plane bias similarly improves the accuracy of the prediction. Sample sizes for the empirical Cucumis mitotic polygonal distribution are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (B) For the Drosophila prediction, a plot of the (l2-norm)2 deviation from the empirical mitotic cell shape distribution as a function of the relationship between division likelihood and polygon class. Here, division likelihood is assumed to increase exponentially as a function of polygon class. The ordinate (exponential constant) gives the precise form of the exponential. Note that positive values strongly outperform negative values. Hence, a model in which division likelihood increases with polygon class is more consistent with the data than a model in which it decreases or remains the same. (B’) For Cucumis, the results are nearly identical to those of Drosophila.
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Figure 3: Computational predictions of the mitotic shift based on a stochastic model of the side-gaining process. (A) Prediction of the mitotic cell shape distribution for the Drosophila wing disc epithelium (empirical values shown in grey). In the absence of cleavage plane bias (blue), the computational prediction is not quite as accurate as when the bias is included (red). Sample sizes for the empirical Drosophila mitotic polygonal distribution are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (A’) Prediction of the mitotic cell shape distribution in the epidermis of Cucumis. Here, cleavage plane bias similarly improves the accuracy of the prediction. Sample sizes for the empirical Cucumis mitotic polygonal distribution are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (B) For the Drosophila prediction, a plot of the (l2-norm)2 deviation from the empirical mitotic cell shape distribution as a function of the relationship between division likelihood and polygon class. Here, division likelihood is assumed to increase exponentially as a function of polygon class. The ordinate (exponential constant) gives the precise form of the exponential. Note that positive values strongly outperform negative values. Hence, a model in which division likelihood increases with polygon class is more consistent with the data than a model in which it decreases or remains the same. (B’) For Cucumis, the results are nearly identical to those of Drosophila.
Mentions: The predicted form of the mitotic distribution P(N/D) depends on the choice of the function F (see equation 15). Consistent with the analyses of the first two sections, past studies of Drosophila and Cucumis monolayer cell sheets demonstrate that the function F is monotone increasing [9,19,24]. Specifically, F is well fit by an exponential function (based on Mathematica’s FindFit function; see references [19,24]). To test whether our modeling framework is able to predict the form of the mitotic cell shape distribution in a proliferating polygonal network, we compared our computational results with empirical data from Drosophila and Cucumis. In each case, we assumed an exponential form for the function F, and searched the parameter space of increasing, decreasing, and flat F functions. To measure the distance between the empirical and the predicted form of the mitotic cell shape distribution, we used the square of the l2-norm, (l2-norm)2. Strikingly, for increasing F functions, the predicted mitotic distribution P(N/D) closely matches the empirical distribution of mitotic cells (Figures 3B-B’; Additional file 2: Figure S2). By contrast, and consistent with the mathematical analysis of the previous sections, flat or decreasing F functions failed to match the data closely (Figures 3B-B’; Additional file 2: Figure S2). We find that including cleavage plane bias, Q(m), improves our estimate (compare blue and red bars, Figures 3A-B). These results, which are consistent with more exhaustive modeling approaches, suggest that our analysis is accurate for the case of Drosophila and Cucumis. Hence, in principle, a simple model of side gaining can account for the mitotic shift in these organisms.

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