title: Modeling mammary organogenesis from biological first principles: Cells and their physical constraints.
abstract: In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As 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 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, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace.
authors.affiliation: Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France; Institut d'Histoire et de Philosophie des Sciences et des Techniques (IHPST) - UMR 8590, 13, rue du Four, 75006 Paris, France. Electronic address: mael.montevil@gmail.com.
authors.forename: Maël
authors.initials: M
authors.lastname: Montévil
authors.affiliation: Department of Integrative Physiology and Pathobiology, Tufts University School of Medicine, Boston, MA, USA. Electronic address: lucia.speroni@tufts.edu.
authors.forename: Lucia
authors.initials: L
authors.lastname: Speroni
authors.affiliation: Department of Integrative Physiology and Pathobiology, Tufts University School of Medicine, Boston, MA, USA; Centre Cavaillès, École Normale Supérieure, Paris, France; Institut d'Etudes Avancées de Nantes, France. Electronic address: carlos.sonnenschein@tufts.edu.
authors.forename: Carlos
authors.initials: C
authors.lastname: Sonnenschein
authors.affiliation: Department of Integrative Physiology and Pathobiology, Tufts University School of Medicine, Boston, MA, USA; Centre Cavaillès, République des Savoirs, CNRS USR3608, Collège de France et École Normale Supérieure, Paris, France. Electronic address: ana.soto@tufts.edu.
authors.forename: Ana M
authors.initials: AM
authors.lastname: Soto
mesh_terms: D000818:Animals; D055592:Biophysical Phenomena; D006801:Humans; D042361:Mammary Glands, Human / Q000166:cytology* / Q000254:growth & development; D008954:Models, Biological; D038081:Organogenesis
keywords: Acinar morphogenesis; Ductal morphogenesis; Mammary gland morphogenesis; Mathematical models; Organicism; Organizational closure