Cell migration requires a precise temporal and spatial coordination of several processes which allow the cell to efficiently move. The extension and retraction of membrane protrusion, as well as adhesion are controlled by the Rho-family small GTPases. Tight coordination of the activity of Rho-family GTPases has been known to be essential for cell migration and it has been shown that two members of the family, RhoA and Rac1 mutually inhibit each other. The consequence of this double-negative feedback loop is a strict spatiotemporal separation of their activities. Using an integrated systems biology approach that combines predictive mathematical modelling and extensive wet-lab experimentation, we construct a data-validated mathematical model of the Rac1/PAK/RhoA network. In silico analyses allowed us to untangle the network complexity and identify the key conditions that characterize the network input-output responses. Importantly, model predictions helped to formulate hypotheses and design appropriate experiments to test them. Using the highly motile MDA-MB-231 breast cancer cell line as the experimental model, we predicted and validated the presence of bistability at various levels via manipulation of PAK using a small inhibitor, IPA-3. We then experimentally demonstrated bistability in the activities of Rac1 and RhoA, as well as bistable responses of actin dynamics, cell migration and the switching of cell morphology from elongated, mesenchymal to a rounded, amoeboid-like shape in 3-dimensional matrices. These findings provide a tractable dynamic and mechanistic description of a biological phenomenon that is well described but still poorly understood. Moreover, breaking the Rac1/RhoA feedback by inhibiting PAK could switches the Rac/RhoA balance from a high Rac1-GTP to a high RhoA-GTP and which in turn could arrests actin polymerisation and migration in breast cancer cells, opening a new therapeutic avenue to treat invasive breast cancer.