McCulloch, W. S. & Pitts, W. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5, 115–133 (1943).
Google Scholar
Hopfield, J. J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl Acad. Sci. USA 79, 2554–2558 (1982).
Google Scholar
Qian, L., Winfree, E. & Bruck, J. Neural network computation with DNA strand displacement cascades. Nature 475, 368–372 (2011).
Google Scholar
Cherry, K. M. & Qian, L. Scaling up molecular pattern recognition with DNA-based winner-take-all neural networks. Nature 559, 370–376 (2018).
Google Scholar
Xiong, X. et al. Molecular convolutional neural networks with DNA regulatory circuits. Nat. Mach. Intell. 4, 625–635 (2022).
Google Scholar
Okumura, S. et al. Nonlinear decision-making with enzymatic neural networks. Nature 610, 496–501 (2022).
Google Scholar
Chen, Z. et al. A synthetic protein-level neural network in mammalian cells. Science 386, 1243–1250 (2024).
Google Scholar
Churchland, P. S. & Sejnowski, T. J. The Computational Brain (MIT Press, 2016).
Farmer, J. D., Packard, N. H. & Perelson, A. S. The immune system, adaptation, and machine learning. Physica D 22, 187–204 (1986).
Google Scholar
Vladimirov, N. & Sourjik, V. Chemotaxis: how bacteria use memory. Biol. Chem. 390, 1097–1104 (2009).
Google Scholar
Kieffer, C., Genot, A. J., Rondelez, Y. & Gines, G. Molecular computation for molecular classification. Adv. Biol. 7, 2200203 (2023).
Google Scholar
Nagipogu, R. T., Fu, D. & Reif, J. H. A survey on molecular-scale learning systems with relevance to DNA computing. Nanoscale 15, 7676–7694 (2023).
Google Scholar
Vasle, A. H. & Moškon, M. Synthetic biological neural networks: from current implementations to future perspectives. Biosystems 237, 105164 (2024).
Hjelmfelt, A., Weinberger, E. D. & Ross, J. Chemical implementation of neural networks and Turing machines. Proc. Natl Acad. Sci. USA 88, 10983–10987 (1991).
Google Scholar
Poole, W. et al. Chemical Boltzmann Machines. In 23rd International Conference on DNA Computing and Molecular Programming (DNA 23) (eds Brijder, R. & Qian, L.) 210–231 (Springer, 2017).
Vasić, M., Chalk, C., Luchsinger, A., Khurshid, S. & Soloveichik, D. Programming and training rate-independent chemical reaction networks. Proc. Natl Acad. Sci. USA 119, e2111552119 (2022).
Google Scholar
Buchler, N. E., Gerland, U. & Hwa, T. On schemes of combinatorial transcription logic. Proc. Natl Acad. Sci. USA 100, 5136–5141 (2003).
Google Scholar
Fernando, C. T. et al. Molecular circuits for associative learning in single-celled organisms. J. R. Soc. Interface 6, 463–469 (2009).
Google Scholar
Rizik, L., Danial, L., Habib, M., Weiss, R. & Daniel, R. Synthetic neuromorphic computing in living cells. Nat. Commun. 13, 5602 (2022).
Google Scholar
Bray, D. Protein molecules as computational elements in living cells. Nature 376, 307–312 (1995).
Google Scholar
Pandi, A. et al. Metabolic perceptrons for neural computing in biological systems. Nat. Commun. 10, 3880 (2019).
Google Scholar
Kim, J., Hopfield, J. & Winfree, E. Neural network computation by in vitro transcriptional circuits. Adv. Neural Inf. Process. Syst. 17, 681–688 (2004).
van der Linden, A. J. et al. DNA input classification by a riboregulator-based cell-free perceptron. ACS Synth. Biol. 11, 1510–1520 (2022).
Google Scholar
Genot, A. J., Fujii, T. & Rondelez, Y. Scaling down DNA circuits with competitive neural networks. J. R. Soc. Interface 10, 20130212 (2013).
Google Scholar
Lakin, M. R. & Stefanovic, D. Supervised learning in adaptive DNA strand displacement networks. ACS Synth. Biol. 5, 885–897 (2016).
Google Scholar
Evans, C. G., O’Brien, J., Winfree, E. & Murugan, A. Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly. Nature 625, 500–507 (2024).
Google Scholar
Pei, R., Matamoros, E., Liu, M., Stefanovic, D. & Stojanovic, M. N. Training a molecular automaton to play a game. Nat. Nanotechnol. 5, 773–777 (2010).
Google Scholar
Kim, J., Khetarpal, I., Sen, S. & Murray, R. M. Synthetic circuit for exact adaptation and fold-change detection. Nucleic Acids Res. 42, 6078–6089 (2014).
Google Scholar
Nakakuki, T. et al. DNA reaction system that acquires classical conditioning. ACS Synth. Biol. 13, 521–529 (2024).
Google Scholar
Rojas, R. Neural Networks: A Systematic Introduction (Springer, 2013).
MacQueen, J. Some methods for classification and analysis of multivariate observations. In Proc. Fifth Berkeley Symposium on Mathematical Statistics and Probability (eds Le Cam, L. M. & Neyman, J.) Vol. 1, 281–297 (University of California Press, 1967).
Yurke, B., Turberfield, A. J., Mills Jr, A. P., Simmel, F. C. & Neumann, J. L. A DNA-fuelled molecular machine made of DNA. Nature 406, 605–608 (2000).
Google Scholar
Soloveichik, D., Seelig, G. & Winfree, E. DNA as a universal substrate for chemical kinetics. Proc. Natl Acad. Sci. USA 107, 5393–5398 (2010).
Google Scholar
Chen, Y.-J. et al. Programmable chemical controllers made from DNA. Nat. Nanotechnol. 8, 755–762 (2013).
Google Scholar
Srinivas, N., Parkin, J., Seelig, G., Winfree, E. & Soloveichik, D. Enzyme-free nucleic acid dynamical systems. Science 358, eaal2052 (2017).
Google Scholar
Qian, L. & Winfree, E. A simple DNA gate motif for synthesizing large-scale circuits. J. R. Soc. Interface 8, 1281–1297 (2011).
Google Scholar
Qian, L. & Winfree, E. Scaling up digital circuit computation with DNA strand displacement cascades. Science 332, 1196–1201 (2011).
Google Scholar
Thubagere, A. J. et al. Compiler-aided systematic construction of large-scale DNA strand displacement circuits using unpurified components. Nat. Commun. 8, 14373 (2017).
Google Scholar
Johnson, H. A. & Condon, A. A coupled reconfiguration mechanism for single-stranded DNA strand displacement systems. In 28th International Conference on DNA Computing and Molecular Programming (DNA 28) (eds Ouldridge, T. E. & Wickham, S. F. J.) Vol. 238, 3:1–3:19 (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2022).
Yang, X., Tang, Y., Traynor, S. M. & Li, F. Regulation of DNA strand displacement using an allosteric DNA toehold. J. Am. Chem. Soc. 138, 14076–14082 (2016).
Google Scholar
Haley, N. E. et al. Design of hidden thermodynamic driving for non-equilibrium systems via mismatch elimination during DNA strand displacement. Nat. Commun. 11, 2562 (2020).
Google Scholar
Deng, L. The MNIST database of handwritten digit images for machine learning research [best of the web]. IEEE Signal Process. Mag. 29, 141–142 (2012).
Google Scholar
Seelig, G., Soloveichik, D., Zhang, D. Y. & Winfree, E. Enzyme-free nucleic acid logic circuits. Science 314, 1585–1588 (2006).
Google Scholar
Baldwin, J. M. A new factor in evolution. Am. Nat. 30, 441–451 (1896).
Google Scholar
Hinton, G. E. & Nowlan, S. J. How learning can guide evolution. Complex Syst. 1, 495–502 (1987).
Genot, A. J., Bath, J. & Turberfield, A. J. Reversible logic circuits made of DNA. J. Am. Chem. Soc. 133, 20080–20083 (2011).
Google Scholar
DelRosso, N. V., Hews, S., Spector, L. & Derr, N. D. A molecular circuit regenerator to implement iterative strand displacement operations. Angew. Chem. Int. Ed. 56, 4443–4446 (2017).
Google Scholar
Scalise, D., Dutta, N. & Schulman, R. DNA strand buffers. J. Am. Chem. Soc. 140, 12069–12076 (2018).
Google Scholar
Garg, S. et al. Renewable time-responsive DNA circuits. Small 14, 1801470 (2018).
Google Scholar
Hahn, J. & Shih, W. M. Thermal cycling of DNA devices via associative strand displacement. Nucleic Acids Res. 47, 10968–10975 (2019).
Google Scholar
Clamons, S., Qian, L. & Winfree, E. Programming and simulating chemical reaction networks on a surface. J. R. Soc. Interface 17, 20190790 (2020).
Google Scholar
Takinoue, M. DNA droplets for intelligent and dynamical artificial cells: from the viewpoint of computation and non-equilibrium systems. Interface Focus 13, 20230021 (2023).
Google Scholar
Wang, S. S. & Ellington, A. D. Pattern generation with nucleic acid chemical reaction networks. Chem. Rev. 119, 6370–6383 (2019).
Google Scholar
Mordvintsev, A., Randazzo, E., Niklasson, E. & Levin, M. Growing neural cellular automata. Distill 5, e23 (2020).
Google Scholar
Randazzo, E., Mordvintsev, A., Niklasson, E., Levin, M. & Greydanus, S. Self-classifying MNIST digits. Distill 5, e00027–002 (2020).
Google Scholar
Lopez, R., Wang, R. & Seelig, G. A molecular multi-gene classifier for disease diagnostics. Nat. Chem. 10, 746–754 (2018).
Google Scholar
Zhang, C. et al. Cancer diagnosis with DNA molecular computation. Nat. Nanotechnol. 15, 709–715 (2020).
Google Scholar
Cangialosi, A. et al. DNA sequence-directed shape change of photopatterned hydrogels via high-degree swelling. Science 357, 1126–1130 (2017).
Google Scholar
Fern, J. & Schulman, R. Modular DNA strand-displacement controllers for directing material expansion. Nat. Commun. 9, 3766 (2018).
Google Scholar
Stern, M. & Murugan, A. Learning without neurons in physical systems. Annu. Rev. Condensed Matter Phys. 14, 417–441 (2023).
Google Scholar
Sanger, T. D. Optimal unsupervised learning in a single-layer linear feedforward neural network. Neural Netw. 2, 459–473 (1989).
Google Scholar
Al-Harbi, S. H. & Rayward-Smith, V. J. Adapting k-means for supervised clustering. Appl. Intell. 24, 219–226 (2006).
Google Scholar
Dirks, R. M., Bois, J. S., Schaeffer, J. M., Winfree, E. & Pierce, N. A. Thermodynamic analysis of interacting nucleic acid strands. SIAM Rev. 49, 65–88 (2007).
Google Scholar
Fornace, M. E. et al. NUPACK: analysis and design of nucleic acid structures, devices, and systems. Preprint at https://doi.org/10.26434/chemrxiv-2022-xv98l (2022).
Cherry, K. M. & Qian, L. Supervised learning in DNA neural networks [Data set]. CaltechDATA https://doi.org/10.22002/5bvkt-r7y16 (2025).
