Inducing chondrogenesis in MSC/chondrocyte co-cultures using exogenous TGF-β: a mathematical model

The differentiation of mesenchymal stem cells (MSCs) into chondrocytes (native cartilage cells), or chondrogenesis, is a key step in the tissue engineering of articular cartilage, where the motility and high proliferation rate of MSCs used as seed cells are exploited. Chondrogenesis is regulated by transforming growth factor-beta (TGF-β), a short-lived cytokine whose effect is prolonged by storage in the extracellular matrix. Tissue engineering applications require the complete differentiation of an initial population of MSCs, and two common strategies used to achieve this in vitro are (1) co-culture the MSCs with chondrocytes, which constitutively produce TGF-β; or (2) add exogenous TGF-β. To investigate these strategies we develop an ordinary differential equation model of the interactions between TGF-β, MSCs and chondrocyte. Here the dynamics of TGF-β are much faster than those of the cell processes; this difference in time-scales is exploited to simplify subsequent model analysis. Using our model we demonstrate that under strategy 1 complete chondrogenesis will be induced if the initial proportion of chondrocytes exceeds a critical value. Similarly, under strategy 2 we find that there is a critical concentration of exogenous TGF-β above which all MSCs will ultimately differentiate. Finally, we use the model to demonstrate the potential advantages of adopting a hybrid strategy where exogenous TGF-β is added to a co-culture of MSCs and chondrocytes, as compared to using either strategy 1 or 2 in isolation.