Elsevier

Journal of Biomechanics

Volume 49, Issue 3, 8 February 2016, Pages 401-407
Journal of Biomechanics

Oriented cell division affects the global stress and cell packing geometry of a monolayer under stretch

https://doi.org/10.1016/j.jbiomech.2015.12.046Get rights and content

Abstract

Cell division plays a vital role in tissue morphogenesis and homeostasis, and the division plane is crucial for cell fate. For isolated cells, extensive studies show that the orientation of divisions is sensitive to cell shape and the direction of extrinsic mechanical forces. However, it is poorly understood that how the cell divides within a cell monolayer and how the local stress change, due to the division, affects the global stress of epithelial monolayers. Here, we use the vertex dynamics models to investigate the effects of division orientation on the configurations and mechanics of a cell monolayer under stretch. We examine three scenarios of the divisions: dividing along the stretch axis, dividing along the geometric long axis of cells, and dividing at a random angle. It is found that the division along the long cell axis can induce the minimal energy difference, and the global stress of the monolayer after stretch releases more rapidly in this case. Moreover, the long-axis division can result in more random cell orientations and more isotropic cell shapes within the monolayer, comparing with other two cases. This study helps understand the division orientation of cells within a monolayer under mechanical stimuli, and may shed light on linking individual cell׳s behaviors to the global mechanics and patterns of tissues.

Introduction

The formation and development of animal tissues requires the coordinated movements of their constituent cells, including cell growth, cell intercalation, and cell division (Lecuit and Lenne, 2007, Heisenberg and Bellaïche, 2013, Guillot and Lecuit, 2013). Among these cellular processes, cell division can dictate the topological disorder in epithelia (Gibson et al., 2006), control the homeostatic cell packing geometry (Ragkousi and Gibson, 2014), and drive the morphogenesis of tissues (Kondo and Hayashi, 2013). Furthermore, the cell division axis determines the future positions of daughter cells, and is crucial for the cell fate (Théry et al., 2005).

In recognition of its significance in biological functions, much effort has been directed toward investigating the orientation of cell division under different microenvironments (Théry et al., 2005, Fink et al., 2011, Gibson et al., 2011, LeGoff et al., 2013). At the cellular level, cell shape is thought to dictate the orientation of the division plane that mitotic cells tend to divide orthogonal to their geometric long axis (Hofmeister, 1863, Gray et al., 2004, Strauss et al., 2006). Recently, Fink et al. (2011) experimentally showed that the external force can bias dynamic subcortical actin structures, resulting in the alignment of daughter cells with the external force field. Moreover, the effect of geometric constraints from microenvironments (e.g., extracellular matrix) on the cell division orientation has been examined (Théry et al., 2005, Minc et al., 2011). In these studies, attentions have been mainly paid to the unicellular systems. To date, however, little is known about the orientation of cell division within a cell monolayer, where the cell geometry does not exist in isolation. Harris et al., 2012, Harris et al., 2013 developed a testing device to characterize the mechanical properties of freely suspended epithelial monolayers. Interestingly, using this device, Wyatt et al. (2015) found that when the epithelia was subjected to a stretch, the cell divided aligning with its geometric long axis, rather than with the stretching axis. In spite of these studies, the mechanisms governing the orientation of cell division in different microenvironments remain unclear, and understanding how the local changes at cellular level affects the tissue-scale mechanical properties is still a challenge.

Various theoretical and computational techniques, such as Cellular Potts models (Graner and Glazier, 1992, Käfer et al., 2007), Flocking models (Basan et al., 2013, Sepúlveda et al., 2013) and phase field methods (Camley et al., 2014), have been developed to study the spatial and temporal evolution of cells within epithelial monolayers. Among them, vertex dynamics models have proven to be a powerful tool to study the epithelial morphogenesis and cellular biological processes within epithelia (Farhadifar et al., 2007, Rauzi et al., 2008, Marinari et al., 2012, Fletcher et al., 2014, Xu et al., 2015). By using this approach, Marinari et al. (2012) showed that the cell delamination could relieve the overcrowding-induced anisotropy of a tissue. Rauzi et al. (2008) used this method to study the role of the tension anisotropy in driving tissue elongation, and compared their predictions with experimental observations. This approach also verified the experimental results that the apoptotic cells could drive the folding of epithelia (Monier et al., 2015) and the rosette formation during the apical-contraction phase (Kuipers et al., 2014).

In this paper, we employ the vertex dynamics models to investigate the orientation of cell division within an epithelial monolayer under stretch, and show how the local topology change of dividing cells influences the global stress and cell packing of the monolayer. It is found that the cell division aligns with the long axis of cell shapes, rather than with the stretching direction or at a random orientation. Furthermore, the global stress of cell monolayers releases more rapidly when the cell divides along its long axis. Finally, the geometric long-axis division can result in a more random cell packing orientations and more isotropic cell shapes, comparing with other two division options.

Section snippets

Model of the cell monolayer

Consider a large number of cells forming a confluent monolayer sheet, in which the cell shape is affected by its adjacent cells. In vertex dynamics models, each cell in the monolayer is modeled as a polygon with vertices and edges shared between adjacent cells (see Fig. 1(a)). The locations of the vertices and edges provide complete information about the configuration of cell sheet. Based on this framework, the vertex dynamics models describe the movement of cell position and the change in cell

Results and discussions

We normalize the system by the length scale A0, the time scale η/(KeA0), and the force scale KeA03/2. Farhadifar et al. (2007) used the vertex dynamics model to study the physical basis of epithelial cell packing geometry and compared the predictions with their experimental observations. They showed the parameter region to obtain the stable cell network systems that can support the stretch. Our previous work (Xu et al., 2015) also showed the parameters to capture the essential mechanical

Conclusions

In summary, we have studied the effects of the orientation of cell division on the stress and cell packing geometry of a monolayer, when the monolayer is largely stretched. We investigate three cases of orientated cell division: (I) dividing along the stretch axis, (II) dividing along the long cell axis, and (III) dividing at a random orientation. It is found that the division along the long cell axis has a minimal energy difference. The division of the cell induces a sudden decrease in the

Conflict of interest statement

The authors declare that there are no conflicts of interest associated with the present study.

Acknowledgments

Financial supports from the National Natural Science Foundation of China (No. 11402193) and the Fundamental Research Funds for the Central Universities of China are acknowledged.

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