All plant cells are encased by walls, which provide structural support and control their morphology. How plant cells regulate the deposition of the wall to generate complex shapes is a topic of ongoing research. Scientists have identified several model systems, the epidermal pavement cells of cotyledons and leaves being an ideal platform to study the formation of complex cell shapes. These cells indeed grow alternating protrusions and indentations resulting in jigsaw puzzle cell shapes. How and why these cells adopt such shapes has shown to be a challenging problem to solve, notably because it involves the integration of molecular and mechanical regulation together with cytoskeletal dynamics and cell wall modifications. In this review, we highlight some recent progress focusing on how these processes may be integrated at the cellular level along with recent quantitative morphometric approaches.

The current prognostic parameters, including tumor volume, biochemistry, or immunohistochemistry, are not sufficient to reflect the properties of cancer cells that distinguish them from normal cells. Our focus is to evaluate the effects of a combination of microtubule-polymerizing Taxol® and -depolymerizing colchicine on IAR20 PC1 liver cells by measuring the surface fractal dimension as a descriptor of two-dimensional vascular geometrical complexity. The fractal dimension offers a rapid means of assessing cell shape. Furthermore, we show correlations of fractal dimensions of cell contours with the latent factors from our previously employed cell shape analysis.

In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –, distinguished by specific interaction potentials and, eventually, also by the use of modified interaction criteria. For example, membrane sub-particles may interact only on a two-dimensional surface embedded on three-dimensional space, described via a restricted Delaunay triangulation. The model can be used not only to study cell shape and movement, but also has the potential to investigate the coupling between internal space-resolved movement of molecules and determined cell behaviors.