1. Modeling mammary organogenesis from biological first principles: The default state of cells and its physical constraints.

    The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts which originated from theoretical principles in physics and computer sciences. Instead, the authors propose to construct a mathematical model based on proper biological principles. Specifically, they use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cells and ii) the principle of organization. Cells display agency, move and proliferate unless constrained. They exert mechanical forces that i) act on collagen fibers and ii) on other cells. When fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of a closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research.

  2. What counterpart to the principle of inertia in Population Genetics ?

    In this paper, we will discuss the notion of inertia in Classical Mechanics and its possible counterparts in Theoretical Population Genetics. We will show that, in Population Genetics, changes take place in a mathematical space whose structure is not compatible with notions such as the conservation of momentum or of angular momentum. In spite of this difference, we will argue that there is a fundamental analogy holds between the two fields. The principle of inertia describes the behavior of a system when nothing acts upon it. In Mechanics, this behavior is described by the conservation of momentum. We will show that different situations may be analogous to inertia in evolution. In particular, Theoretical Population Genetics uses a similar line of reasoning in at least two cases: random genetic drift, and geometric growth. However, we will argue that genetic drift is mathematically very different from mechanical inertia as it is far richer in contingent events having lasting consequences.