Understanding the mechanism of fast transitions between conformed states of large biomolecules is central to reconciling the dichotomy between the relatively high speed of metabolic processes and slow (random-walk based) estimates on the speed of biomolecular processes. Here we use the dynamical systems approach to suggest that the reduced time of transition between different conformations is due to features of the dynamics of molecules that are a consequence of their structural features. Long-range and local effects both play a role. Long-range molecular forces account for the robustness of final states and nonlinear processes that channel localized, bounded disturbances into collective, modal motions. Local interconnections provide fast transition dynamics. These properties are shared by a class of networked systems with strong local interconnections and long-range nonlinear forces that thus exhibit flexibility and robustness at the same time.