A Dynamic Graph Model of Endochondral Ossification can assess the Importance of Biological Actors in Differentiation

Cell-based tissue engineering constructs are a promising avenue for the treatment of long bone defects since they provide the primordial ingredients for bone regeneration. The construct provides the appropriate micro-environment through the carrier, cells to form tissue and chemical cues to kick start the natural bone forming process. Clearly this approach will benefit from a more comprehensive appreciation of how cell populations and the microenvironment provided by the carrier can impact on bone formation in all its complexities. A cornucopia of studies of developmental biology have revealed many biological actors that together form a central network that orchestrates cell behaviour during this process and assures its robustness. This knowledge can be brought to bear specifically in the form of a mathematical model of endochondral ossification, the dominant type of ossification. This model can facilitate the understanding of how growth factors and transcription factors influence cell fate decisions and consequently answer the question whether they can boost bone healing. The model formalism accommodates the qualitative information that is typically available in developmental studies. The network comprises 46 nodes and 161 interactions, shown to be important in endochondral ossification. To simulate network dynamics in discrete time the normalized value of each gene is determined by additive functions where all interactions are assumed to be equally powerful. Furthermore, each species is represented by a fast variable (activity level, as determined by post translation modifications) which is assumed to be in equilibrium with a slow variable (mRNA) at all times. Through a Monte Carlo approach the importance of each node in the stability of chondrocytic phenotypes (proliferating, hypertrophic) is assessed. The hypertrophic state, driven by Runx2, is more stable than the proliferating chondrocyte. This higher stability seems to be conferred by faster reactions that favor the hypertrophic phenotype. In addition, the results point out that some transcription factors are necessary for the induction of a certain phenotype, whereas other transcription factors are required to maintain the phenotype, but are not necessary capable of inducing it. Overall, the model allows the importance of several important factors in the fate decision of mesenchymal cells to be quantitatively assessed based mainly on topological information.status: publishe