Designing bistable nanostructures for target behavior

Many biological machines function through controlled conformational transitions, yet designing synthetic nanostructures with prescribed dynamical behavior remains a major challenge. Here, we develop a modular inverse-design framework for bistable nanostructures whose function is controlled by an energy profile along a geometric reaction coordinate. Inspired by proteins with rigid domains connected by flexible hinges, we introduce a hinge-arm paradigm in which a small bistable hinge controls the energetics of a conformational transition, while rigid arms map this transition onto the separation between external binding sites. Specifically, we ask which features of a target energy profile can be programmed under different design constraints. We find that the energy barriers and the binding-site separations in the two metastable states can be readily designed, while controlling the location of the transition state or the full shape of the energy profile requires additional design freedom. Using a differentiable design framework, we find that some optimized solutions are numerically inexact but still display the functional behavior for which the target profile was selected, emphasizing the importance of function-based evaluation criteria. These results establish a practical hierarchy of designability for bistable nanostructures and provide a route toward synthetic nanomachines that couple conformational transitions to target behavior.