Designing complex behaviors using transition-based allosteric self-assembly

Allosteric interactions occur when binding at one part of a complex affects the interactions at another part. Allostery offers a high degree of control in multi-species processes, and these interactions play a crucial role in many biological and synthetic contexts. Leveraging allosteric principles in synthetic systems holds great potential for designing materials and systems that can autonomously adapt, reconfigure, or replicate. In this work we establish a basic allosteric model and develop an intuitive design process, which we demonstrate by constructing systems to exhibit four different complex behaviors: controlled fiber growth, shape-shifting, sorting, and self-replication. In order to verify that the systems evolve according to the pathways we have developed, we also calculate and measure key length and time scales. Our findings demonstrate that with minimal interaction rules, allosteric systems can be engineered to achieve sophisticated emergent behaviors, opening new avenues for the design of responsive and adaptive materials.