A one-dimensional continuum model for ventral stress fibre formation #

Gordon R McNicol, Peter S Stewart, Matthew J Dalby

12:30 Monday in 3Q68.

Part of the Cell modelling session.

Abstract #

To function and survive, cells need to be able to sense and respond to their local environment in a process called mechanotransduction. Crucially, mechanical and biochemical perturbations to a cell can initiate signaling cascades which can induce, among other responses, cell growth, apoptosis, proliferation and differentiation.

At the heart of this process are focal adhesions, which serve as the anchor points which cells form to the surrounding extra-cellular matrix (ECM). From these adhesions, actin filaments can grow, interacting with myosin II to form contractile stress fibres, a key constituent of the cell cytoskeleton. In turn, these stress fibres exert forces on their attached adhesions, leading to the recruitment of mechanically sensitive proteins, promoting their maturation. As adhesions mature, certain signaling proteins are upregulated which increase actin polymerization and myosin activation, leading to the strengthening of stress fibres, closing a positive feedback loop. This process is pivotal in non-motile cells, where stress fibres are generally of ventral type, interconnecting focal adhesions and producing isometric tension.

We have formulated a one-dimensional continuum model to describe the coupled formation and maturation of stress fibres and focal adhesions. We use a set of reaction-diffusion-advection equations to describe three sets of biochemical events: the polymerisation of actin and bundling and activation of the resultant fibres; the formation and maturation of adhesions between the cell and substrate; and the upregulation of certain signaling proteins in response to focal adhesion and stress fibre formation. The evolution of these key proteins is then coupled to a Kelvin-Voigt viscoelastic description for the cell cytoplasm and for the ECM.

We employ this model to understand how cells respond to external and intracellular cues in vitro. We demonstrate that cells form weaker stress fibres and focal adhesions on compliant surfaces, myosin II inhibition leads to disruption of focal adhesions and cells preferentially form adhesions where ligands are most densely populated. Having replicated experimental observations, the model provides a platform for systematic investigation into how the cell biochemistry and mechanics influence the growth and development of the cell and facilitates prediction of internal cell measurements that are difficult to ascertain experimentally, such as stress distribution.