The mathematics of the connections between cells to form tissues and organs

Researchers have discovered a mathematical principle that explains how cells connect with each other to form tissues and organs.

An international team led by researchers from the Higher Council for Scientific Research (CSIC) in Spain has discovered a new mathematical principle that explains how cells connect with each other to form tissues. The finding is an important step forward in understanding how organs are formed during embryonic development and the pathologies associated with this process. Specialists from the Institute of Integrative Systems Biology (I2SysBio), a mixed center of the CSIC and the University of Valencia (UV), and the Institute of Biomedicine of Seville (IBiS), of the CSIC, the Virgen del Rocío University Hospital, have worked on the research. and the University of Seville, all these entities in Spain.

The research has been carried out using the fruit fly as a model, and may have future implications for the creation of artificial tissues and organs in the laboratory, a great challenge for biology and biomedicine.

This scientific team published in the journal Nature Communications, in 2018, a study that had a great scientific and media impact, in which it was shown that epithelial cells can adopt a geometric shape during the formation of organs that had not been described until then. moment: the scutoid.

“That the cells adopt this geometric shape is due to the energy savings that it entails when packing to form tissues when there is a certain level of curvature, for example, when a fold is formed in a tissue,” explains one of the leading authors this work, Luisma Escudero, IBiS researcher. “Our research represented an important paradigm shift, because until then epithelia had always been studied using mathematical concepts to describe their organization in two dimensions, something that is related to the connection between cells and how they communicate with each other to form these organs. correctly”.

“However, as we showed then, epithelial cells can have complex shapes in three dimensions, such as scutoids, and cells and organs are also three-dimensional. Therefore, in this study we consider whether there are mathematical and/or biophysical principles in 3D and, by combining experiments with fly tissues and computational models of tubular tissues, we have been able to develop a biophysical model that relates for the first time the geometry of the tissue and the physical properties of the cells with how they are connected to each other”, says Escudero.

Tissue where epithelial cells form a tube. Microscope image (top) and computer processing (bottom) to quantify tissue properties. (Images: I2SysBio / IBiS)

The key, the ‘social relationships’ of cells

Javier Buceta, I2SysBio researcher and co-leader of the study, establishes a simile to explain this new scientific advance, resorting to anthropology. “The anthropologist Robin Dunbar determined that human beings have an average of five close friends that are given by different social and personal factors. At the cellular level, our article has revealed that there is an equivalent principle, concluding that the number of close neighbors of a cell, that is, its close friends, is determined in this case by the geometry of the tissue and its energetic relationships”.

“Thus, taking into account a series of energetic, biological and geometric considerations, we have discovered that, for example, the more connections an epithelial cell has with others, the more energy it needs to establish new connections with other cells, while if it is little connected to other neighbors, the cell needs less energy to establish that link”, highlights Buceta.

In this research, the scientists altered tissue, reducing adhesion between cells to put their model to the test. “This causes the organization to change, as it is easier, less costly energetically speaking, for cells to contact new cells,” says Buceta. The results of the experiments confirmed the quantitative principle proposed by the researchers.

The researchers point out that, analyzing the behavior of tissues from the point of view of materials, other previous works have observed that their rigidity depends on cellular connectivity. “In this way, tissues can behave in a more or less viscous way, that is, more fluid or more solid. Our results quantitatively show how the geometry of the scutoids determines cellular connectivity and, therefore, how they can be a biological instrument to regulate the properties, as a material, of tissues and organs”, they conclude.

In addition to the Institute of Integrative Systems Biology and the Institute of Biomedicine of Seville, researchers from the University of Seville, Johns Hopkins University in the United States and the University of the Basque Country, among other institutions, have also participated in this work.

The study is titled “A quantitative biophysical principle to explain the 3D cellular connectivity in curved epithelia”. And it has been published in the academic journal Cell Systems. (Source: CSIC)