The role of theorem proving in systems biology.

Theorems offer a rarity in biology, a guarantee that something will always be true if certain conditions are met. We show that modeling and theorem proving are distinct while playing mutually supporting roles in understanding cellular phenomena. Using two recently proven theorems from systems biology as examples, we demonstrate that theorems are not an alternative to mechanistic models. Rather, theorem proving, in conjunction with conventional mathematical (mechanistic) modeling, is an essential tool for a deeper understanding in systems biology.

A stem cell niche dominance theorem.

BACKGROUND: Multilevelness is a defining characteristic of complex systems. For example, in the intestinal tissue the epithelial lining is organized into crypts that are maintained by a niche of stem cells. The behavior of the system 'as a whole' is considered to emerge from the functioning and interactions of its parts. What we are seeking here is a conceptual framework to demonstrate how the "fate" of intestinal crypts is an emergent property that inherently arises from the complex yet robust underlying biology of stem cells. RESULTS: We establish a conceptual framework in which to formalize cross-level principles in the context of tissue organization. To this end we provide a definition for stemness, which is the propensity of a cell lineage to contribute to a tissue fate. We do not consider stemness a property of a cell but link it to the process in which a cell lineage contributes towards tissue (mal)function. We furthermore show that the only logically feasible relationship between the stemness of cell lineages and the emergent fate of their tissue, which satisfies the given criteria, is one of dominance from a particular lineage. CONCLUSIONS: The dominance theorem, conceived and proven in this paper, provides support for the concepts of niche succession and monoclonal conversion in intestinal crypts as bottom-up relations, while crypt fission is postulated to be a top-down principle.