Designing complex behaviours using allosteric self-assembly

Allosteric effects, where interactions at one part of a complex affect interactions at another part, result in a variety of complex structures and behaviours. These interactions play a crucial role in many natural biological contexts and have also been utilised in artificial nanotechnology systems. Leveraging allosteric principles in synthetic systems holds great potential for designing soft matter structures that can autonomously adapt, reconfigure and grow along pre-formulated pathways. In this work, using a simple allosteric model, we design systems to exhibit four different complex behaviours: shape-shifting, controlled fibre growth, sorting and self-replication. As well as showing the design of each behaviour, we also calculate and measure key length and time scales, to verify that the systems evolve according to the pathways we have prescribed. The allosteric signal-passing mechanism we use has been demonstrated experimentally in synthetic systems, meaning the behaviours we design here can feasibly be built. Our findings demonstrate that with minimal interaction rules, allosteric systems can be engineered to achieve sophisticated emergent behaviours, opening new avenues for the design of responsive and precisely controlled self-organising systems.