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Simulating the Formation of Geometric Patterns By Tissue Cells

Mathematicians at Kyoto University have developed a model that simulates cell cooperation and movements during the formation of geometric patterns essential for the proper functioning of sensory endothelial tissue.

The final sensory epithelial geometric pattern achieved by olfactory cells (in orange) and supporting cells (in blue) in the presence of α-N-catenin KO (a cadherin-binding protein, essential for in cadherin-mediated cell-cell adhesion), as simulated by a mathematical model created by mathematicians at Kyoto University. Photo Credit: Kyoto University/Karel Svadlenka

If one uses a microscope to study sensory epithelial tissue, one may spot the consistent geometric patterns throughout the sample, resembling the patterns produced when light filters through a stained-glass window.

But why do sensory epithelial cells form such geometric patterns? Scientists hypothesise that their arrangements are key for certain properties like the detection of external stimuli and the ability to turn the stimuli into signals and transmit them to the brain.

Despite the knowledge that sensory epithelial cell patterns are essential for their functioning, the exact process by which they form such patterns synergistically remains largely unknown. However, it is known that the process involves frequent neighbour swaps, also known as topology changes, which are mediated by processes like cell intercalation, where the spatial positions of a group of cells are exchanged. During processes like these, a combination of adhesive changes as well as cytoskeletal changes provide the forces required for the desired cellular rearrangements to take place.

In a study conducted by Kobe University, it was further found that the adhesive changes are the result of the expression of different types of adhesion molecules by individual cells.

In light of this discovery, Kyoto University mathematicians have created a mathematical model that simulates the formation of cell patterns found in sensory epithelia, using a measure of the adhesive abilities of the adhesion molecules as inputs.

“This strongly supports the hypothesis that differential adhesion or interfacial tension is the main driving mechanism behind the formation of these patterns during organ development,” said Karel Svadlenka, the corresponding author of the study.

A novel mathematical approach was used to solve for the model solution, which allows for the retention of data regarding the volumes of individual cells as well as the connectivity between cells.

To test whether the model was a more accurate representation of the cell movement during the formation of the geometrical patterns, the entire process was imaged, and the concentration of adhesion molecules in between cells was sampled over certain intervals of time.

In addition to the above, yet another novel mathematical technique, inspired by the Esedoglu-Otto basic algorithm, was used to retain the cell volumes and to prevent the error of unnatural cell splitting from occurring in the model.

The use of these new mathematical techniques helped to predict the experimentally produced cell patterns in the target tissues with greater accuracy, solving the issue of the previously unaccounted for factors in the models which produced patterns that differed more greatly from the real patterns.

“It was surprising to be able to recover the experimentally observed pattern if we changed the parameters in our simulation,” added Svadlenka, “and this provided the clue that interfacial tension becomes a prevalent mechanism at later developmental stages of cellular patterns.”

The team believes that this discovery will lead to changes in the viewpoint of researchers in this field that the mechanism of cell rearrangements was significantly more complex.

Expressing excitement that his model, which spans both biology and mathematics, Svadlenka and his team hope that their research broadens the view of their peers in academia, to help them realise that the processes behind the rearrangement of cells was more complicated than previously thought. [APBN]

Source: Mohammad et al. (2022). A numerical algorithm for modeling cellular rearrangements in tissue morphogenesis. ;Communications Biology, ;5(1), 1-10.