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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 binary tree representation of the side-gaining process. (A) The function G(m,n,V) represents the probability that an m-sided cell gains n sides after V of its immediate neighbors have divided. Side-gaining is a binary event which occurs when a neighboring cell’s cleavage plane impinges on a common interface. For each neighboring division, either one or zero sides is gained. Q(m) is the probability that an m-sided cell gains a side due to a single neighboring division. On the binary tree, horizontal paths represent a failure to gain a side, which occurs with probability 1-Q(m). Elevated paths represent side-gaining events. Note that to compute G(m,n,V), multiple paths representing different stochastic trajectories must be summed. (B) A more concrete representation of the side-gaining process, which here depicts the different cell shape trajectories for a hexagon, and its potential transitions to a heptagonal or octagonal state due to side-gaining.
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Figure 2: A binary tree representation of the side-gaining process. (A) The function G(m,n,V) represents the probability that an m-sided cell gains n sides after V of its immediate neighbors have divided. Side-gaining is a binary event which occurs when a neighboring cell’s cleavage plane impinges on a common interface. For each neighboring division, either one or zero sides is gained. Q(m) is the probability that an m-sided cell gains a side due to a single neighboring division. On the binary tree, horizontal paths represent a failure to gain a side, which occurs with probability 1-Q(m). Elevated paths represent side-gaining events. Note that to compute G(m,n,V), multiple paths representing different stochastic trajectories must be summed. (B) A more concrete representation of the side-gaining process, which here depicts the different cell shape trajectories for a hexagon, and its potential transitions to a heptagonal or octagonal state due to side-gaining.

Mentions: In order to approximately compute the subset of neighbors that divide in the orientation of the cell in question, we consider the probability Q(m) that an m-sided cell gains a new edge due to the mitosis of a neighboring cell. Q(m) negatively correlates with the polygon class, m [24]. In terms of Q(m), we can compute the probability G(m,k,V) that an m-sided cell gains k sides after V of its neighbor cells have divided (see Figures 2A-B). For example, the probability G(m,0,V) that the m-sided cell gains zero sides after V divisions is the following:


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 binary tree representation of the side-gaining process. (A) The function G(m,n,V) represents the probability that an m-sided cell gains n sides after V of its immediate neighbors have divided. Side-gaining is a binary event which occurs when a neighboring cell’s cleavage plane impinges on a common interface. For each neighboring division, either one or zero sides is gained. Q(m) is the probability that an m-sided cell gains a side due to a single neighboring division. On the binary tree, horizontal paths represent a failure to gain a side, which occurs with probability 1-Q(m). Elevated paths represent side-gaining events. Note that to compute G(m,n,V), multiple paths representing different stochastic trajectories must be summed. (B) A more concrete representation of the side-gaining process, which here depicts the different cell shape trajectories for a hexagon, and its potential transitions to a heptagonal or octagonal state due to side-gaining.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: A binary tree representation of the side-gaining process. (A) The function G(m,n,V) represents the probability that an m-sided cell gains n sides after V of its immediate neighbors have divided. Side-gaining is a binary event which occurs when a neighboring cell’s cleavage plane impinges on a common interface. For each neighboring division, either one or zero sides is gained. Q(m) is the probability that an m-sided cell gains a side due to a single neighboring division. On the binary tree, horizontal paths represent a failure to gain a side, which occurs with probability 1-Q(m). Elevated paths represent side-gaining events. Note that to compute G(m,n,V), multiple paths representing different stochastic trajectories must be summed. (B) A more concrete representation of the side-gaining process, which here depicts the different cell shape trajectories for a hexagon, and its potential transitions to a heptagonal or octagonal state due to side-gaining.
Mentions: In order to approximately compute the subset of neighbors that divide in the orientation of the cell in question, we consider the probability Q(m) that an m-sided cell gains a new edge due to the mitosis of a neighboring cell. Q(m) negatively correlates with the polygon class, m [24]. In terms of Q(m), we can compute the probability G(m,k,V) that an m-sided cell gains k sides after V of its neighbor cells have divided (see Figures 2A-B). For example, the probability G(m,0,V) that the m-sided cell gains zero sides after V divisions is the following:

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