What first principles for mathematical modeling in biology?

By analogy with theoretical physics, theoretical biology is not limited to mathematical modeling. Instead, theoretical biology should strive to find suitable first principles to ground the understanding of biological phenomena and ultimately frame biological experiments and mathematical models. First principles in physics are discussed in terms of symmetries and the associated conservation principles, on the one side, and optimization on the other side. In biology, we have argued instead that a strong notion of variation is fundamental. This notion encompasses new possibilities and is associated with the historicity of biological phenomena [3]. By contrast, the relative regularity of some aspects of biological organisms should be seen as the consequence of a mutual stabilization by the parts of organisms [2]. In this paper, we will focus on a last aspect which pertains to the way cellular behavior is framed theoretically: should cells of multicellular organisms be considered as spontaneously quiescent so that a stimulation would be required for them to move or proliferate, or should cells be considered as spontaneously moving and proliferating so that quiescence would be the result of constraints. We argue the latter and will show that this assumption can be used to build a model of epithelial morphogenesis in tissue culture.