We analyse an Ising-like Hamiltonian describing the free energy of cell adhesion on a substrate as a lattice of 3-state mechanosensing sites involving focal adhesion kinase (FAK). We use Monte Carlo stochastic algorithm to find equilibrium configurations of these mechanosensors in two representative geometries: on a 1D ring representing the rim of a cell on flat surface, and a 2D bounded surface representing the whole area of cell contact with flat surface. The level of FAK activation depend on the pulling force applied to the individual FAK-integrin via actin-myosin contractile networks, and the details of the coupling between individual sensors in a cluster. Strong coupling is shown to make the FAK sensors experience a sharp on-off behaviour in their activation, while at low coupling the activation/autoinhibition transition occurs over a broad range of pulling force. We find that the activation/autoinhibition transition of FAK in the 2D system with strong coupling occurs with a hysteresis, the width of which depends on the rate of change of force. The effect of introducing a mediating protein (such as Src) in limited quantity to control FAK activation is explored, and visualisations of clustering in both topologies are presented. In particular the results on the bounded 2D surface indicate that clustering of active FAK occurs preferentially at the boundary, in agreement with experimental observations of focal adhesions in cells.
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