Published: Feb. 1, 2013

Mathematical Model Of The Coupled Mechanisms Of Cell Adhesion, Contraction And Spreading

Franck Vernerey


Department of Civil, Environmental, and Architectural Engineering


Date and time: 

Friday, February 1, 2013 - 1:15pm


In recent years, research in cell biology has shown that mechanics is key to cell response, differentiation and disease. For instance, an increasing number of observations have shown that the ability of cells to contract, spread and differentiate is highly dependent on the stiffness and architecture of the surrounding matrix. While the origins of these intriguing behaviors are still poorly understood, it is now clear that cells fully make use of cross-talks between mechanics, chemistry and transport processes in order to organize their structure, generate forces and make appropriate decisions.

To better understand the underlying mechanisms of mechano-transduction, this presentation will introduce a mathematical model of cell spreading that couples the processes of adhesion, contraction and protrusion growth through actin polymerization at the cell edge. We will see that a single cell can be modeled as an active gel which can acquire a specific structure and exert contractile forces in response to its mechanical environment. When coupled with adhesion, these forces gives rise, in certain situations, to the growth of protrusion at the cell boundary, which promote cell spreading and potential differentiation. These biological concepts can be summarized by a coupled system of PDEs leading to a moving boundary problem whose solution can be derived using numerical methods such as finite elements and the levelset method. Numerical simulations show that the model is able to capture the dependency of cell spreading and contraction on substrate stiffness and chemistry. The very good agreement between model predictions and experimental observations not only confirms the strong role of mechanics in cell response but also pinpoint the fundamental processes at play.