Nakamura, E.; Britto Bisso, F.; Gispert, I.; Moghimianavval, H.; Okuda, S.; Przybyszewska-Podstawka, A.; Chisholm, S.; Hemanth Kumar, V. S.; Perez Medina, V.; Wu, M.-R.; Cuba Samaniego, C.

Classification of high-dimensional information is a ubiquitous computing paradigm across diverse biological systems, including organs such as the brain, down to signaling between individual cells. Inspired by the success of artificial neural networks in machine learning, the idea of engineering genetic circuits that operate as neural networks emerges as a strategy to expand the classification capabilities of living systems. In this work, we design these biomolecular neural networks (BNNs) based on the molecular sequestration reaction, and experimentally characterize their behavior as linear classifiers for increasing levels of complexity. Initially, we demonstrate that a static, DNA-based system can effectively prototype a linear classifier, though we also identify its limitations to easily tune the slope of the decision boundary it generates. We then propose and experimentally validate a BNN at the protein level using a cell-free transcription-translation (TXTL) system, which overcomes the DNA-based system\'s limitation and behaves as a linear classifier even before it reaches its steady state (or, equivalently, out-of-equilibrium). Ultimately, we test a CRISPR-based design and its out-of-equilibrium behavior in a biological context by successfully constructing a linear classifier within mammalian cells. Overall, by leveraging mathematical modeling and experimental automation, we establish molecular sequestration as a universal scheme for implementing neural networks within living systems, paving the way for transformative advances in synthetic biology and programmable biocomputing systems.