A computer simulation of geometrical configurations during cell division

Honda, Hiroaki; Yamanaka, Hachiro I.; Dan-Sohkawa, Marina

doi:10.1016/0022-5193(84)90039-0

Cited by 40 publications

(30 citation statements)

References 11 publications

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“…Honda et al account for the cellular pattern formation mechanisms of various monolayered cell sheets in terms of interactions between adjacent cells, on the basis of cell shapes observed in the apical surface of the cell sheet (7,8,9,10,11). Thus, observation of all cell shapes (that is, all cell boundaries) in the apical suface of the epidermis could provide useful information for analysing the formation mechanisms of the cellular pattern in the wing epidermis.…”

Section: Introductionmentioning

confidence: 98%

Scale Arrangement Pattern in a Lepidopteran Wing. 1. Periodic Cellular Pattern in the Pupal Wing of Pieris rapae

Yoshida

Aoki

1989

Dev Growth Differ

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In most species of lepidopteran insects, anteroposterior rows formed by scales are arranged at regular intervals in the adult wing; within each row two kinds of scales are alternately arranged. To investigate the cellular basis for the scale arrangement pattern, we examined cell arrangement in the epidermal monolayer of the pupal wing of a small white cabbage butterfly, Pieris rapae, by scanning electron microscopy and light microscopy. The arrangement of scale precursor cells, closely resembling that of scales in the adult wing, was observed in the wing epidermis of the early pupa. Scale precursor cells are proximodistally elongated and form anteroposterior rows. Within a row two kinds of scale precursor cells are nearly alternately arranged, which is not so precise as the alternation of scales in the adult wing. Individual rows of scale precursor cells are separated by rows of single or double undifferentiated general epidermal cells. Occasionally, arrangement abnormalities occur both in the adult and the pupal wing. The cellular basis for the regular spacing of scale rows is discussed.

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Section: Introductionmentioning

confidence: 98%

Scale Arrangement Pattern in a Lepidopteran Wing. 1. Periodic Cellular Pattern in the Pupal Wing of Pieris rapae

Yoshida

Aoki

1989

Dev Growth Differ

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“…Although vertex models (proposed by Honda in the 1980s [14,31,32]) clearly ignore many features of real cell shape, they are thought to capture the essential physics when cells are close to polygonal, and they have been applied successfully to study many features of epithelial morphogenesis [7,10,33,34]. Moreover, they have the advantage of being both simple and straightforwardly extensible to include effects ranging from the dynamics of proteins localized at the edges to buckling into the third dimension [19,34,35].…”

Section: Introductionmentioning

confidence: 99%

Vertex stability and topological transitions in vertex models of foams and epithelia

2017

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In computer simulations of dry foams and of epithelial tissues, vertex models are often used to describe the shape and motion of individual cells. Although these models have been widely adopted, relatively little is known about their basic theoretical properties. For example, while fourfold vertices in real foams are always unstable, it remains unclear whether a simplified vertex model description has the same behavior. Here, we study vertex stability and the dynamics of T1 topological transitions in vertex models. We show that, when all edges have the same tension, stationary fourfold vertices in these models do indeed always break up. In contrast, when tensions are allowed to depend on edge orientation, fourfold vertices can become stable, as is observed in some biological systems. More generally, our formulation of vertex stability leads to an improved treatment of T1 transitions in simulations and paves the way for studies of more biologically realistic models that couple topological transitions to the dynamics of regulatory proteins.

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“…Similarly, A T ,j is the cell's natural (or target) area, and C T ,j = 2(pA T ,j ) 1/2 its natural perimeter. Finally l and b are positive constants, and g S is a positive constant whose value depends on whether edge m is on an external boundary or not (Honda et al 1984;Nagai & Honda 2001).…”

Section: (Iii) Cell-vertex Modelmentioning

confidence: 99%

A hybrid approach to multi-scale modelling of cancer

Osborne

Walter²,

Kershaw

et al. 2010

Phil. Trans. R. Soc. A.

115

170

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In this paper, we review multi-scale models of solid tumour growth and discuss a middleout framework that tracks individual cells. By focusing on the cellular dynamics of a healthy colorectal crypt and its invasion by mutant, cancerous cells, we compare a cellcentre, a cell-vertex and a continuum model of cell proliferation and movement. All models reproduce the basic features of a healthy crypt: cells proliferate near the crypt base, they migrate upwards and are sloughed off near the top. The models are used to establish conditions under which mutant cells are able to colonize the crypt either by top-down or by bottom-up invasion. While the continuum model is quicker and easier to implement, it can be difficult to relate system parameters to measurable biophysical quantities. Conversely, the greater detail inherent in the multi-scale models means that experimentally derived parameters can be incorporated and, therefore, these models offer greater scope for understanding normal and diseased crypts, for testing and identifying new therapeutic targets and for predicting their impacts. This journal is

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A computer simulation of geometrical configurations during cell division

Cited by 40 publications

References 11 publications

Scale Arrangement Pattern in a Lepidopteran Wing. 1. Periodic Cellular Pattern in the Pupal Wing of Pieris rapae

Scale Arrangement Pattern in a Lepidopteran Wing. 1. Periodic Cellular Pattern in the Pupal Wing of Pieris rapae

Vertex stability and topological transitions in vertex models of foams and epithelia

A hybrid approach to multi-scale modelling of cancer

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