Fig. 5: Internal network control and external input control for cancer reversion.

a Defining control strategies in a cellular system. A cellular system is represented by \({{{\dot{\boldsymbol x}}}} = f({{{\boldsymbol{x}}}},{{{\boldsymbol{u}}}})\), where x is the n-dimensional state vector of genes and f(x, u) is a vector field that describes the dynamics of the system related to the input signal u, which is an m-dimensional control vector of genes. Near an equilibrium point in the nonlinear system, the vector field f can be approximated by Ax + Bu, where A is an adjacency matrix and B is an appropriate dimensional matrix of constant coefficients of input weights. The system output can be described as a simple weighted combination of the state variables, y = Cx. b An internal network control (IC) mediates alterations in a signaling pathway to restore the attractor landscape of normal cells. c External input control (EC) that effectively modifies the epigenetic landscape to make the normal state more stable. An example of EC is a growth factor receptor inhibitor that prevents cells from maintaining a cancer state by completely blocking a specific trajectory related to uncontrolled proliferation.