Biological signaling networks transmit and process extra-cellular information, triggering complex transformations that lead to different cellular responses. The overall cellular behavior is well grasped by differential equations; the challenge is to produce mathematically affordable microscopic models leading to these equations. The usual modeling approach, based on chemical kinetics, is hampered by the large number of assumptions needed. As an alternative, we propose a spin-flip dynamics defined by asymmetric mean-field interactions. This dynamics yield density-profile processes whose trajectories converge almost surely to the solutions of dynamical systems with possibly complex behavior.