Design of a biochemical circuit motif for learning linear functions

Learning and adaptive behaviour are fundamental biological processes. A key goal in the field of bioengineering is to develop biochemical circuit architectures with the ability to adapt to dynamic chemical environments. Here, we present a novel design for a biomolecular circuit capable of supervised learning of linear functions, using a model based on chemical reactions catalysed by DNAzymes. To achieve this, we propose a novel mechanism of maintaining and modifying internal state in biochemical systems, thereby advancing the state of the art in biomolecular circuit architecture. We use simulations to demonstrate that the circuit is capable of learning behaviour and assess its asymptotic learning performance, scalability and robustness to noise. Such circuits show great potential for building autonomous in vivo nanomedical devices. While such a biochemical system can tell us a great deal about the fundamentals of learning in living systems and may have broad applications in biomedicine (e.g. autonomous and adaptive drugs), it also offers some intriguing challenges and surprising behaviours from a machine learning perspective.