# Modelling cells and tissues

## Theoretical Problem

Cells are elementary objects in biology. Their behavior is not simple and it is usually insufficient to consider them as a physical object. For example, a cell subjected to a mechanical stress can react actively depending on the cell type and the underlying evolutionary history.

## First attempts

Arnaud Pocheville and I have analyzed cells inside organisms by using ecological concepts. The viewpoint that we have developed is inspired by the notion of default state proposed by Soto and Sonnenschein, see below.

## Theoretical principle

In two papers, we build on the notion of a default state for cells. The idea is to propose that a behavior (the default state) does not need causes, signals, or stimuli to happen. The notion of default state is then similar to the principle of inertia which describes what an object does when no forces applies to it. Then, causes are by definition elements that lead to a departure of the default state. We defend the idea that the default state is proliferation with variation and motility and we call constraints the causes that lead to a departure from it. These two papers develop several aspects of this default state.

## Mammary gland morphogenesis

During my stay in the experimental lab of A. Soto and C. Sonnenschein, I focused on mammary gland development in vivo and in vitro. In particular, we are looking into the role of the extracellular matrix, hormones and the effect of endocrine disruptors. I also used this biological object in several later work.

#### Experimental

I contributed to the real time study of early morphogenis by epithelial cells in 3D gels in vitro.

We also developed a software for the automatic mormophetric analysis of epithelial strucutres in these gels.

#### Models

Using the default state — proliferation with variation and motility — as a principle, we modeled the behavior of cells in 3D gels of collagen. We also show that the notion of default state clarifies the diversity of assumptions in the mathematical modeling literature.

Videos showing simulations of the model.

We also wrote an informal introduction to our modelling strategy, including a discussion of its biological background.

## Modelling methodology

I wrote a chapter for *Methods in Molecular Biology* which describes the key ingredients of mathematical modeling in biology. The aim is mainly to make the hypotheses of mathematical modeling explicit and I expand in particular on the case of cell proliferation.