  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...
