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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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Introduction to the mitotic shift. (A) The Drosophila wing imaginal disc. Neuroglian-GFP (green) marks the septate junctions. (B) The Drosophila wing disc epithelium. The rounded cell (center) is undergoing mitosis. (C) The mitotic shift in Drosophila (red) and Cucumis (green) [9,24]. The overall distribution of cellular shapes has a hexagonal mean (red and green). By contrast, the mitotic cell shape distribution (red and green) is shifted to have a heptagonal mean in both organisms. Hence, one distribution is approximately a shifted version of the other. Sample sizes for both organisms are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (D) Representative mitotic cells (as detected based on cell rounding) in the Drosophila wing imaginal disc. Mitotic cells show an enrichment in cell-cell contacts. Stars (black) mark neighboring cells; labeled cells’ polygonal topologies are designated in black. (E-F) An overview of mitotically induced topological transformations during epithelial proliferation. (E) An illustration of autonomous “side loss” during polygonal cell division. The octagonal cell (green) gives rise to two hexagonal daughters (grey). On average, a mitotic N-sided cell will give rise to daughters having (N + 4)/2 sides, making side loss a general trend except for rare polygonal cells in which N = 3 or N = 4. Note the creation of a set of new tri-cellular junctions (red), which are formed at either end of the cleavage plane (black), which is depicted as a dashed line. (F) Non-autonomous “side gaining” due to neighbor cell mitoses. In this example, a pentagonal cell (blue), gains one neighbor to become a hexagonal cell (grey). In general, during polygonal cell division, exactly two neighboring cells adjacent to the newly-formed tri-cellular junctions (red) will effectively gain one neighbor each.
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Figure 1: Introduction to the mitotic shift. (A) The Drosophila wing imaginal disc. Neuroglian-GFP (green) marks the septate junctions. (B) The Drosophila wing disc epithelium. The rounded cell (center) is undergoing mitosis. (C) The mitotic shift in Drosophila (red) and Cucumis (green) [9,24]. The overall distribution of cellular shapes has a hexagonal mean (red and green). By contrast, the mitotic cell shape distribution (red and green) is shifted to have a heptagonal mean in both organisms. Hence, one distribution is approximately a shifted version of the other. Sample sizes for both organisms are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (D) Representative mitotic cells (as detected based on cell rounding) in the Drosophila wing imaginal disc. Mitotic cells show an enrichment in cell-cell contacts. Stars (black) mark neighboring cells; labeled cells’ polygonal topologies are designated in black. (E-F) An overview of mitotically induced topological transformations during epithelial proliferation. (E) An illustration of autonomous “side loss” during polygonal cell division. The octagonal cell (green) gives rise to two hexagonal daughters (grey). On average, a mitotic N-sided cell will give rise to daughters having (N + 4)/2 sides, making side loss a general trend except for rare polygonal cells in which N = 3 or N = 4. Note the creation of a set of new tri-cellular junctions (red), which are formed at either end of the cleavage plane (black), which is depicted as a dashed line. (F) Non-autonomous “side gaining” due to neighbor cell mitoses. In this example, a pentagonal cell (blue), gains one neighbor to become a hexagonal cell (grey). In general, during polygonal cell division, exactly two neighboring cells adjacent to the newly-formed tri-cellular junctions (red) will effectively gain one neighbor each.

Mentions: Cellular structures are ubiquitous in natural systems, from the crack patterns of ceramic glazes and colloidal suspensions [1-4], to the bubble structures of a coarsening foam [5-8], to the complex tissues of living organisms [9-13] (Figures 1A-B). The subset of two-dimensional (planar) cellular structures constitutes an analytically tractable paradigm for uncovering the fundamental geometrical and mathematical constraints imposed by cell packing that govern cell shape in a contiguous tissue [5,14,15]. In a biological context, combined with physical forces [16-18], these constraints illuminate a non-genetic basis for biological form, and restrict the space of possible tissue architectures. Packing considerations impose powerful constraints on diverse features of cellular geometry, including area [9,14], topological neighbor correlations [15], distributions of the number of cellular neighbors [5,10,12,19], and the average polygonal shape of a given cell (which is hexagonal [20]), among others [21]. Beginning with D’Arcy Thompson and Frederic Lewis, it was appreciated in the early 20th century that such constraints might influence or correlate with important biological variables pertaining to the growth of tissues during development [9,22]. More recent work has suggested that packing constraints are likely to be involved in the coordination between proliferative growth and morphogenesis, as these processes are intrinsically linked in growing cell layers [12,17,23-27].


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)

Introduction to the mitotic shift. (A) The Drosophila wing imaginal disc. Neuroglian-GFP (green) marks the septate junctions. (B) The Drosophila wing disc epithelium. The rounded cell (center) is undergoing mitosis. (C) The mitotic shift in Drosophila (red) and Cucumis (green) [9,24]. The overall distribution of cellular shapes has a hexagonal mean (red and green). By contrast, the mitotic cell shape distribution (red and green) is shifted to have a heptagonal mean in both organisms. Hence, one distribution is approximately a shifted version of the other. Sample sizes for both organisms are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (D) Representative mitotic cells (as detected based on cell rounding) in the Drosophila wing imaginal disc. Mitotic cells show an enrichment in cell-cell contacts. Stars (black) mark neighboring cells; labeled cells’ polygonal topologies are designated in black. (E-F) An overview of mitotically induced topological transformations during epithelial proliferation. (E) An illustration of autonomous “side loss” during polygonal cell division. The octagonal cell (green) gives rise to two hexagonal daughters (grey). On average, a mitotic N-sided cell will give rise to daughters having (N + 4)/2 sides, making side loss a general trend except for rare polygonal cells in which N = 3 or N = 4. Note the creation of a set of new tri-cellular junctions (red), which are formed at either end of the cleavage plane (black), which is depicted as a dashed line. (F) Non-autonomous “side gaining” due to neighbor cell mitoses. In this example, a pentagonal cell (blue), gains one neighbor to become a hexagonal cell (grey). In general, during polygonal cell division, exactly two neighboring cells adjacent to the newly-formed tri-cellular junctions (red) will effectively gain one neighbor each.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Introduction to the mitotic shift. (A) The Drosophila wing imaginal disc. Neuroglian-GFP (green) marks the septate junctions. (B) The Drosophila wing disc epithelium. The rounded cell (center) is undergoing mitosis. (C) The mitotic shift in Drosophila (red) and Cucumis (green) [9,24]. The overall distribution of cellular shapes has a hexagonal mean (red and green). By contrast, the mitotic cell shape distribution (red and green) is shifted to have a heptagonal mean in both organisms. Hence, one distribution is approximately a shifted version of the other. Sample sizes for both organisms are given under the heading “Sample sizes for overall and mitotic cell shape distributions” in the Methods section. (D) Representative mitotic cells (as detected based on cell rounding) in the Drosophila wing imaginal disc. Mitotic cells show an enrichment in cell-cell contacts. Stars (black) mark neighboring cells; labeled cells’ polygonal topologies are designated in black. (E-F) An overview of mitotically induced topological transformations during epithelial proliferation. (E) An illustration of autonomous “side loss” during polygonal cell division. The octagonal cell (green) gives rise to two hexagonal daughters (grey). On average, a mitotic N-sided cell will give rise to daughters having (N + 4)/2 sides, making side loss a general trend except for rare polygonal cells in which N = 3 or N = 4. Note the creation of a set of new tri-cellular junctions (red), which are formed at either end of the cleavage plane (black), which is depicted as a dashed line. (F) Non-autonomous “side gaining” due to neighbor cell mitoses. In this example, a pentagonal cell (blue), gains one neighbor to become a hexagonal cell (grey). In general, during polygonal cell division, exactly two neighboring cells adjacent to the newly-formed tri-cellular junctions (red) will effectively gain one neighbor each.
Mentions: Cellular structures are ubiquitous in natural systems, from the crack patterns of ceramic glazes and colloidal suspensions [1-4], to the bubble structures of a coarsening foam [5-8], to the complex tissues of living organisms [9-13] (Figures 1A-B). The subset of two-dimensional (planar) cellular structures constitutes an analytically tractable paradigm for uncovering the fundamental geometrical and mathematical constraints imposed by cell packing that govern cell shape in a contiguous tissue [5,14,15]. In a biological context, combined with physical forces [16-18], these constraints illuminate a non-genetic basis for biological form, and restrict the space of possible tissue architectures. Packing considerations impose powerful constraints on diverse features of cellular geometry, including area [9,14], topological neighbor correlations [15], distributions of the number of cellular neighbors [5,10,12,19], and the average polygonal shape of a given cell (which is hexagonal [20]), among others [21]. Beginning with D’Arcy Thompson and Frederic Lewis, it was appreciated in the early 20th century that such constraints might influence or correlate with important biological variables pertaining to the growth of tissues during development [9,22]. More recent work has suggested that packing constraints are likely to be involved in the coordination between proliferative growth and morphogenesis, as these processes are intrinsically linked in growing cell layers [12,17,23-27].

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