- Perspective
- Open Access
Could Living Cells Use Phase Transitions to Process Information?
Phys. Rev. X 16, 020501 – Published 12 May, 2026
DOI: https://doi.org/10.1103/j16b-xnms
Abstract
To maintain homeostasis, living cells process information with networks of interacting molecules. Traditional models for cellular information processing have focused on networks of chemical reactions between molecules. Here, we describe how networks of physical interactions could contribute to the processing of information inside cells. In particular, we focus on the impact of biomolecular condensation, a structural phase transition found in cells. Biomolecular condensation has recently been implicated in diverse cellular processes. Some of these are essentially computational, including classification and control tasks. We place these findings in the broader context of embodied computation, an emerging framework for describing how the native dynamics of nonlinear physical systems can be leveraged to perform complex computations. The synthesis of these ideas raises questions about expressivity (the range of problems that cellular phase transitions might be able to solve) and learning (how these systems could adapt and evolve to solve different problems). This emerging area of research presents diverse opportunities across molecular biophysics, soft matter, and embodied computation.
Physics Subject Headings (PhySH)
Article Text
References (132)
- B. Desvergne, L. Michalik, and W. Wahli, Transcriptional regulation of metabolism, Physiol. Rev. 86, 465 (2006).
- V. W. Wu, N. Thieme, L. B. Huberman, A. Dietschmann, D. J. Kowbel, J. Lee, S. Calhoun, V. R. Singan, A. Lipzen, Y. Xiong et al., The regulatory and transcriptional landscape associated with carbon utilization in a filamentous fungus, Proc. Natl. Acad. Sci. U.S.A. 117, 6003 (2020).
- R. R. Alfieri and P. G. Petronini, Hyperosmotic stress response: comparison with other cellular stresses, Pflügers Arch.-Eur. J. Physiol. 454, 173 (2007).
- J. M. Raser and E. K. O’Shea, Noise in gene expression: origins, consequences, and control, Science 309, 2010 (2005).
- B. R. Parry, I. V. Surovtsev, M. T. Cabeen, C. S. O’Hern, E. R. Dufresne, and C. Jacobs-Wagner, The bacterial cytoplasm has glass-like properties and is fluidized by metabolic activity, Cell 156, 183 (2014).
- T. J. Böddeker, K. A. Rosowski, D. Berchtold, L. Emmanouilidis, Y. Han, F. H. Allain, R. W. Style, L. Pelkmans, and E. R. Dufresne, Non-specific adhesive forces between filaments and membraneless organelles, Nat. Phys. 18, 571 (2022).
- O. D. Weiner, Regulation of cell polarity during eukaryotic chemotaxis: The chemotactic compass, Curr. Opin. Cell Biol. 14, 196 (2002).
- H. H. Mattingly, K. Kamino, B. B. Machta, and T. Emonet, Escherichia coli chemotaxis is information limited, Nat. Phys. 17, 1426 (2021).
- A. Dongre and R. A. Weinberg, New insights into the mechanisms of epithelial–mesenchymal transition and implications for cancer, Nat. Rev. Mol. Cell Biol. 20, 69 (2019).
- B. L. Bohnsack and K. K. Hirschi, Nutrient regulation of cell cycle progression, Annu. Rev. Nutr. 24, 433 (2004).
- D. T. Scadden, The stem-cell niche as an entity of action, Nature (London) 441, 1075 (2006).
- A. J. Engler, S. Sen, H. L. Sweeney, and D. E. Discher, Matrix elasticity directs stem cell lineage specification, Cell 126, 677 (2006).
- A. H. Lang, H. Li, J. J. Collins, and P. Mehta, Epigenetic landscapes explain partially reprogrammed cells and identify key reprogramming genes, PLoS Comput. Biol. 10, e1003734 (2014).
- M. Smart and A. Zilman, Emergent properties of collective gene-expression patterns in multicellular systems, Cell Rep. Phys. Sci. 4, 101247 (2023).
- Y. E. Antebi, J. M. Linton, H. Klumpe, B. Bintu, M. Gong, C. Su, R. McCardell, and M. B. Elowitz, Combinatorial signal perception in the BMP pathway, Cell 170, 1184 (2017).
- C. J. Su, A. Murugan, J. M. Linton, A. Yeluri, J. Bois, H. Klumpe, M. A. Langley, Y. E. Antebi, and M. B. Elowitz, Ligand-receptor promiscuity enables cellular addressing, Cell Syst. 13, 408 (2022).
- A. S. Hansen and E. K. O’Shea, Limits on information transduction through amplitude and frequency regulation of transcription factor activity, eLife 4, e06559 (2015).
- J. E. Purvis and G. Lahav, Encoding and decoding cellular information through signaling dynamics, Cell 152, 945 (2013).
- J. A. Papin, T. Hunter, B. O. Palsson, and S. Subramaniam, Reconstruction of cellular signalling networks and analysis of their properties, Nat. Rev. Mol. Cell Biol. 6, 99 (2005).
- T. I. Lee, N. J. Rinaldi, F. Robert, D. T. Odom, Z. Bar-Joseph, G. K. Gerber, N. M. Hannett, C. T. Harbison, C. M. Thompson, I. Simon et al., Transcriptional regulatory networks in Saccharomyces cerevisiae, Science 298, 799 (2002).
- M. M. Babu, N. M. Luscombe, L. Aravind, M. Gerstein, and S. A. Teichmann, Structure and evolution of transcriptional regulatory networks, Curr. Opin. Struct. Biol. 14, 283 (2004).
- J. Huelsken and J. Behrens, The Wnt signalling pathway, J. Cell Sci. 115, 3977 (2002).
- D. E. Clapham, Calcium signaling, Cell 131, 1047 (2007).
- J.-Y. Youn, B. J. Dyakov, J. Zhang, J. D. Knight, R. M. Vernon, J. D. Forman-Kay, and A.-C. Gingras, Properties of stress granule and P-body proteomes, Mol. Cell 76, 286 (2019).
- A. S. Holehouse and B. B. Kragelund, The molecular basis for cellular function of intrinsically disordered protein regions, Nat. Rev. Mol. Cell Biol. 25, 187 (2024)..
- J.-M. Choi, A. S. Holehouse, and R. V. Pappu, Physical principles underlying the complex biology of intracellular phase transitions, Annu. Rev. Biophys. 49, 107 (2020).
- N. Rostam, S. Ghosh, C. F. W. Chow, A. Hadarovich, C. Landerer, R. Ghosh, H. Moon, L. Hersemann, D. M. Mitrea, I. A. Klein, A. A. Hyman, and A. Toth-Petroczy, CD-CODE: Crowdsourcing condensate database and encyclopedia, Nat. Methods 20, 673 (2023).
- S. F. Banani, H. O. Lee, A. A. Hyman, and M. K. Rosen, Biomolecular condensates: Organizers of cellular biochemistry, Nat. Rev. Mol. Cell Biol. 18, 285 (2017).
- S. Ambadi Thody, H. D. Clements, H. Baniasadi, A. S. Lyon, M. S. Sigman, and M. K. Rosen, Small-molecule properties define partitioning into biomolecular condensates, Nat. Chem. 16, 1794 (2024).
- A. E. Posey, A. Bremer, N. A. Erkamp, A. Pant, T. P. Knowles, Y. Dai, T. Mittag, and R. V. Pappu, Biomolecular condensates are characterized by interphase electric potentials, J. Am. Chem. Soc. 146, 28268 (2024).
- M. Farag, S. R. Cohen, W. M. Borcherds, A. Bremer, T. Mittag, and R. V. Pappu, Condensates formed by prion-like low-complexity domains have small-world network structures and interfaces defined by expanded conformations, Nat. Commun. 13, 7722 (2022).
- N. Galvanetto, M. T. Ivanović, A. Chowdhury, A. Sottini, M. F. Nüesch, D. Nettels, R. B. Best, and B. Schuler, Extreme dynamics in a biomolecular condensate, Nature (London) 619, 876 (2023).
- L. Emmanouilidis, L. Esteban-Hofer, F. F. Damberger, T. de Vries, C. K. X. Nguyen, L. F. Ibáñez, S. Mergenthal, E. Klotzsch, M. Yulikov, G. Jeschke, and F. H.-T. Allain, NMR and EPR reveal a compaction of the RNA-binding protein FUS upon droplet formation, Nat. Chem. Biol. 17, 608 (2021).
- C. P. Brangwynne, T. J. Mitchison, and A. A. Hyman, Active liquid-like behavior of nucleoli determines their size and shape in Xenopus laevis oocytes, Proc. Natl. Acad. Sci. U.S.A. 108, 4334 (2011).
- L. Jawerth, E. Fischer-Friedrich, S. Saha, J. Wang, T. Franzmann, X. Zhang, J. Sachweh, M. Ruer, M. Ijavi, S. Saha, J. Mahamid, A. A. Hyman, and F. Jülicher, Protein condensates as aging Maxwell fluids, Science 370, 1317 (2020).
- M. Ijavi, R. W. Style, L. Emmanouilidis, A. Kumar, S. M. Meier, A. L. Torzynski, F. H. Allain, Y. Barral, M. O. Steinmetz, and E. R. Dufresne, Surface tensiometry of phase separated protein and polymer droplets by the sessile drop method, Soft Matter 17, 1655 (2021).
- I. Alshareedah, M. M. Moosa, M. Pham, D. A. Potoyan, and P. R. Banerjee, Programmable viscoelasticity in protein-RNA condensates with disordered sticker-spacer polypeptides, Nat. Commun. 12, 6620 (2021).
- Y. Dai, Z. Zhou, W. Yu, Y. Ma, K. Kim, N. Rivera, J. Mohammed, E. Lantelme, H. Hsu-Kim, A. Chilkoti, and L. You, Biomolecular condensates regulate cellular electrochemical equilibria, Cell 187, 5951 (2024).
- M. Zeng, Y. Shang, Y. Araki, T. Guo, R. L. Huganir, and M. Zhang, Phase transition in postsynaptic densities underlies formation of synaptic complexes and synaptic plasticity, Cell 166, 1163 (2016).
- S. A. Shelby, I. Castello-Serrano, K. C. Wisser, I. Levental, and S. L. Veatch, Membrane phase separation drives responsive assembly of receptor signaling domains, Nat. Chem. Biol. 19, 750 (2023).
- Y. LeCun, Y. Bengio, and G. Hinton, Deep learning, Nature (London) 521, 436 (2015).
- A. Zentner, E. V. Halingstad, C. Chalk, M. P. Brenner, A. Murugan, E. Winfree, and K. Shrinivas, Information processing driven by multicomponent surface condensates, arXiv:2509.08100.
- R. Braz Teixeira, G. Carugno, I. Neri, and P. Sartori, Liquid Hopfield model: Retrieval and localization in multicomponent liquid mixtures, Proc. Natl. Acad. Sci. U.S.A. 121, e2320504121 (2024).
- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers (Princeton University Press, Princeton, NJ, 2021).
- A. Klosin, F. Oltsch, T. Harmon, A. Honigmann, F. Jülicher, A. A. Hyman, and C. Zechner, Phase separation provides a mechanism to reduce noise in cells, Science 367, 464 (2020).
- D. Deviri and S. A. Safran, Physical theory of biological noise buffering by multicomponent phase separation, Proc. Natl. Acad. Sci. U.S.A. 118, e2100099118 (2021).
- B. R. Sabari et al., Coactivator condensation at super-enhancers links phase separation and gene control, Science 361, eaar3958 (2018).
- A. Boija, I. A. Klein, B. R. Sabari, A. Dall’Agnese, E. L. Coffey, A. V. Zamudio, C. H. Li, K. Shrinivas, J. C. Manteiga, N. M. Hannett, B. J. Abraham, L. K. Afeyan, Y. E. Guo, J. K. Rimel, C. B. Fant, J. Schuijers, T. I. Lee, D. J. Taatjes, and R. A. Young, Transcription factors activate genes through the phase-separation capacity of their activation domains, Cell 175, 1842 (2018).
- X. Su, J. A. Ditlev, E. Hui, W. Xing, S. Banjade, J. Okrut, D. S. King, J. Taunton, M. K. Rosen, and R. D. Vale, Phase separation of signaling molecules promotes T cell receptor signal transduction, Science 352, 595 (2016).
- S. F. Shimobayashi, P. Ronceray, D. W. Sanders, M. P. Haataja, and C. P. Brangwynne, Nucleation landscape of biomolecular condensates, Nature (London) 599, 503 (2021).
- H. Yoo, C. Triandafillou, and D. A. Drummond, Cellular sensing by phase separation: Using the process, not just the products, J. Biol. Chem. 294, 7151 (2019).
- D. S. Protter and R. Parker, Principles and properties of stress granules, Trends Cell Biol. 26, 668 (2016).
- H. Glauninger, J. A. Bard, C. J. W. Hickernell, E. M. Airoldi, W. Li, R. H. Singer, S. Paul, J. Fei, T. R. Sosnick, E. W. Wallace, and D. A. Drummond, Transcriptome-wide mRNA condensation precedes stress granule formation and excludes stress-induced transcripts, bioRxiv (2024).
- A. Ali, R. Garde, O. C. Schaffer, J. A. M. Bard, K. Husain, S. K. Kik, K. A. Davis, S. Luengo-Woods, M. G. Igarashi, D. A. Drummond, A. H. Squires, and D. Pincus, Adaptive preservation of orphan ribosomal proteins in chaperone-dispersed condensates, Nat. Cell Biol. 25, 1691 (2023).
- C. Hetz, K. Zhang, and R. J. Kaufman, Mechanisms, regulation and functions of the unfolded protein response, Nat. Rev. Mol. Cell Biol. 21, 421 (2020).
- E. W. Dijkstra, Selected Writings on Computing: A Personal Perspective (Springer, New York, 1982), pp. 60–66.
- L. H. Hartwell, J. J. Hopfield, S. Leibler, and A. W. Murray, From molecular to modular cell biology, Nature (London) 402, C47 (1999).
- D. Endy, Foundations for engineering biology, Nature (London) 438, 449 (2005).
- R. A. Brooks, Intelligence without representation, Artif. Intell. 47, 139 (1991).
- B. Ulmann, Analog Computing (Oldenbourg Wissenschaftsverlag Verlag, Berlin/Boston, 2013).
- V. Braitenberg, Vehicles: Experiments in Synthetic Psychology (MIT Press, Cambridge, MA, 1986).
- M. S. Bull, L. A. Kroo, and M. Prakash, Excitable mechanics embodied in a walking cilium, arXiv:2107.02930.
- J. Laydevant, L. G. Wright, T. Wang, and P. L. McMahon, The hardware is the software, Neuron 112, 180 (2023).
- M. Levin, Technological approach to mind everywhere: An experimentally-grounded framework for understanding diverse bodies and minds, Front. Syst. Neurosci. 16, 768201 (2022).
- R. Pfeifer and G. Gómez, in Creating Brain-Like Intelligence, Lecture Notes in Computer Science (Springer, Berlin, 2009), pp. 66–83.
- H. Hauser, A. J. Ijspeert, R. M. Füchslin, R. Pfeifer, and W. Maass, Towards a theoretical foundation for morphological computation with compliant bodies, Biol. Cybern. 105, 355 (2011).
- D. Bray, Protein molecules as computational elements in living cells, Nature (London) 376, 307 (1995).
- S. Erbas-Cakmak, S. Kolemen, A. C. Sedgwick, T. Gunnlaugsson, T. D. James, J. Yoon, and E. U. Akkaya, Molecular logic gates: The past, present and future, Chem. Soc. Rev. 47, 2228 (2018).
- N. Nandagopal and M. B. Elowitz, Synthetic biology: Integrated gene circuits, Science 333, 1244 (2011).
- L. Qian, E. Winfree, and J. Bruck, Neural network computation with DNA strand displacement cascades, Nature (London) 475, 368 (2011).
- N. E. Buchler, U. Gerland, and T. Hwa, On schemes of combinatorial transcription logic, Proc. Natl. Acad. Sci. U.S.A. 100, 5136 (2003).
- H. Zhang, J. Wu, D. Fang, and Y. Zhang, Hierarchical mechanical metamaterials built with scalable tristable elements for ternary logic operation and amplitude modulation, Sci. Adv. 7, eabf1966 (2021).
- T. Dubček, D. Moreno-Garcia, T. Haag, P. Omidvar, H. R. Thomsen, T. S. Becker, L. Gebraad, C. Bärlocher, F. Andersson, S. D. Huber et al., In-sensor passive speech classification with phononic metamaterials, Adv. Funct. Mater. 34, 2311877 (2024).
- P. L. McMahon, The physics of optical computing, Nat. Rev. Phys. 5, 717 (2023).
- L. G. Wright, T. Onodera, M. M. Stein, T. Wang, D. T. Schachter, Z. Hu, and P. L. McMahon, Deep physical neural networks trained with backpropagation, Nature (London) 601, 549 (2022).
- M. Stern, C. Arinze, L. Perez, S. E. Palmer, and A. Murugan, Supervised learning through physical changes in a mechanical system, Proc. Natl. Acad. Sci. U.S.A. 117, 14843 (2020).
- D. Woods, D. Doty, C. Myhrvold, J. Hui, F. Zhou, P. Yin, and E. Winfree, Diverse and robust molecular algorithms using reprogrammable DNA self-assembly, Nature (London) 567, 366 (2019).
- E. Winfree, Algorithmic self-assembly of DNA, Ph.D. thesis, California Institute of Technology, Pasadena, CA, 1998.
- C. G. Evans, J. O’Brien, E. Winfree, and A. Murugan, Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly, Nature (London) 625, 500 (2024).
- R. Pfeifer, M. Lungarella, and F. Iida, Self-organization, embodiment, and biologically inspired robotics, Science 318, 1088 (2007).
- S. Collins, A. Ruina, R. Tedrake, and M. Wisse, Efficient bipedal robots based on passive-dynamic walkers, Science 307, 1082 (2005).
- T. Wang, C. Pierce, V. Kojouharov, B. Chong, K. Diaz, H. Lu, and D. I. Goldman, Mechanical intelligence simplifies control in terrestrial limbless locomotion, Sci. Robot. 8, eadi2243 (2023).
- J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. U.S.A. 79, 2554 (1982).
- D. Krotov and J. J. Hopfield, Large associative memory problem in neurobiology and machine learning, arXiv:2008.06996.
- J. A. Hertz, A. S. Krogh, and R. G. Palmer, Introduction to the Theory of Neural Computation (Basic Books, Boca Raton, FL, 1991), Vol. 1.
- A. Murugan, Z. Zeravcic, M. P. Brenner, and S. Leibler, Multifarious assembly mixtures: Systems allowing retrieval of diverse stored structures, Proc. Natl. Acad. Sci. U.S.A. 112, 54 (2015).
- Thomas M. A. Fink and R. C. Ball, How many conformations can a protein remember?, Phys. Rev. Lett. 87, 198103 (2001).
- W. M. Jacobs, Self-assembly of biomolecular condensates with shared components, Phys. Rev. Lett. 126, 258101 (2021).
- K. Hornik, M. Stinchcombe, and H. White, Multilayer feedforward networks are universal approximators, Neural Netw. 2, 359 (1989).
- M. Raghu, B. Poole, J. Kleinberg, S. Ganguli, and J. Sohl-Dickstein, Survey of expressivity in deep neural networks, arXiv:1611.08083.
- M. J. Kearns and U. Vazirani, An Introduction to Computational Learning Theory (MIT Press, London, 2019).
- J. Parres-Gold, M. Levine, B. Emert, A. Stuart, and M. B. Elowitz, bioRxiv, 2023.10.30.564854 (2023).
- C. Chalk, S. Buse, K. Shrinivas, A. Murugan, and E. Winfree, Learning and inference in a lattice model of multicomponent condensates, in 30th International Conference on DNA Computing and Molecular Programming (DNA 30), Leibniz International Proceedings in Informatics (LIPIcs) Vol. 314, edited by S. Seki and J. M. Stewart (Schloss Dagstuhl—Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2024), pp. 5:1–5:24.
- J. Gunawardena, Learning outside the brain: Integrating cognitive science and systems biology, Proc. IEEE 110, 590 (2022).
- G. Montufar, Restricted Boltzmann machines: Introduction and review, arXiv:1806.07066.
- W. Zhong, D. J. Schwab, and A. Murugan, Associative pattern recognition through macro-molecular self-assembly, J. Stat. Phys. 167, 806 (2017).
- M. S. Heltberg, A. Lucchetti, F.-S. Hsieh, D. P. Minh Nguyen, S. hong Chen, and M. H. Jensen, Enhanced DNA repair through droplet formation and p53 oscillations, Cell 185, 4394 (2022).
- C. Girard, D. Zwicker, and R. Mercier, The regulation of meiotic crossover distribution: a coarse solution to a century-old mystery?, Biochem. Soc. Trans. 51, 1179 (2023).
- D. B. McAffee, M. K. O’Dair, J. J. Lin, S. T. Low-Nam, K. B. Wilhelm, S. Kim, S. Morita, and J. T. Groves, Discrete LAT condensates encode antigen information from single pMHC: TCR binding events, Nat. Commun. 13, 7446 (2022).
- W. Y. C. Huang, S. Alvarez, Y. Kondo, Y. K. Lee, J. K. Chung, H. Y. M. Lam, K. H. Biswas, J. Kuriyan, and J. T. Groves, A molecular assembly phase transition and kinetic proofreading modulate Ras activation by SOS, Science 363, 1098 (2019).
- W. L. White, H. K. Yirdaw, A. J. Ben-Sasson, J. T. Groves, D. Baker, and H. Y. Kueh, Proofreading and single-molecule sensitivity in T cell receptor signaling by condensate nucleation, Proc. Natl. Acad. Sci. U.S.A. 122, e2422787122 (2025).
- R. Rossetto, G. Wellecke, and D. Zwicker, Binding and dimerization control phase separation in a compartment, Phys. Rev. Res. 7, 023145 (2025).
- A. J. Genot, T. Fujii, and Y. Rondelez, Computing with competition in biochemical networks, Phys. Rev. Lett. 109, 208102 (2012).
- C. Kieffer, A. J. Genot, Y. Rondelez, and G. Gines, Molecular computation for molecular classification, Adv. Biol. 7, e2200203 (2023).
- D. Zwicker, The intertwined physics of active chemical reactions and phase separation, Curr. Opin. Colloid Interface Sci. 61, 101606 (2022).
- N. Ziethen, J. Kirschbaum, and D. Zwicker, Nucleation of chemically active droplets, Phys. Rev. Lett. 130, 248201 (2023).
- E. Jambon-Puillet, A. Testa, C. M. Lorenz, R. W. Style, A. Rebane, and E. R. Dufresne, Phase-separated droplets swim to their dissolution, bioRxiv (2023).
- J. D. Wurtz and C. F. Lee, Stress granule formation via ATP depletion-triggered phase separation, New J. Phys. 20, 045008 (2018).
- D. Zwicker, A. A. Hyman, and F. Jülicher, Suppression of Ostwald ripening in active emulsions, Phys. Rev. E 92, 012317 (2015).
- J. Soeding, D. Zwicker, S. Sohrabi-Jahromi, M. Boehning, and J. Kirschbaum, Mechanisms for active regulation of biomolecular condensates, Trends Cell Biol. 30, 4 (2020).
- J. Kirschbaum and D. Zwicker, Controlling biomolecular condensates via chemical reactions, J. R. Soc. Interface 18, 20210255 (2021).
- D. Zwicker, R. Seyboldt, C. A. Weber, A. A. Hyman, and F. Jülicher, Growth and division of active droplets provides a model for protocells, Nat. Phys. 13, 408 (2017).
- D. Carati and R. Lefever, Chemical freezing of phase separation in immiscible binary mixtures, Phys. Rev. E 56, 3127 (1997).
- T. Aslyamov, F. Avanzini, E. Fodor, and M. Esposito, Nonideal reaction-diffusion systems: Multiple routes to instability, Phys. Rev. Lett. 131, 138301 (2023).
- L. Demarchi, A. Goychuk, I. Maryshev, and E. Frey, Enzyme-enriched condensates show self-propulsion, positioning, and coexistence, Phys. Rev. Lett. 130, 128401 (2023).
- L. Menou, C. Luo, and D. Zwicker, Physical interactions in non-ideal fluids promote Turing patterns, J. R. Soc. Interface 20, 20230244 (2023).
- V. Galstyan, K. Husain, F. Xiao, A. Murugan, and R. Phillips, Proofreading through spatial gradients, eLife 9, e60415 (2020).
- J. J. Hopfield, Kinetic proofreading: A new mechanism for reducing errors in biosynthetic processes requiring high specificity, Proc. Natl. Acad. Sci. U.S.A. 71, 4135 (1974).
- M. Stern and A. Murugan, Learning without neurons in physical systems, Annu. Rev. Condens. Matter Phys. 14, 417 (2023).
- M. Hofweber and D. Dormann, Friend or foe—Post-translational modifications as regulators of phase separation and RNP granule dynamics, J. Biol. Chem. 294, 7137 (2019).
- J. Wang, J.-M. Choi, A. S. Holehouse, H. O. Lee, X. Zhang, M. Jahnel, S. Maharana, R. Lemaitre, A. Pozniakovsky, D. Drechsel, I. Poser, R. V. Pappu, S. Alberti, and A. A. Hyman, A molecular grammar governing the driving forces for phase separation of prion-like RNA binding proteins, Cell 174, 688 (2018).
- R. Zhu, J. M. Del Rio-Salgado, J. Garcia-Ojalvo, and M. B. Elowitz, Synthetic multistability in mammalian cells, Science 375, eabg9765 (2022).
- K. Trifonova, M. J. Falk, M. Rouches, S. Vaikuntanathan, M. Elowitz, and A. Murugan, Trainable computation in molecular networks, bioRxivorg (2025), 10.64898/2025.12.28.696421.
- J. A. Owen, D. Osmanović, and L. Mirny, Design principles of 3D epigenetic memory systems, Science 382, eadg3053 (2023).
- T. E. Schaus, S. Woo, F. Xuan, X. Chen, and P. Yin, A DNA nanoscope via auto-cycling proximity recording, Nat. Commun. 8, 696 (2017).
- K. M. Cherry and L. Qian, Scaling up molecular pattern recognition with DNA-based winner-take-all neural networks, Nature (London) 559, 370 (2018).
- S. Alberti, A. Gladfelter, and T. Mittag, Considerations and challenges in studying liquid-liquid phase separation and biomolecular condensates, Cell 176, 419 (2019).
- V. A. Baulin et al., Intelligent soft matter: Towards embodied intelligence, Soft Matter 21, 4129 (2025).
- J. Gong, N. Tsumura, Y. Sato, and M. Takinoue, Computational DNA droplets recognizing miRNA sequence inputs based on liquid–liquid phase separation, Adv. Funct. Mater. 32, 2202322 (2022).
- M. Takinoue, DNA droplets for intelligent and dynamical artificial cells: From the viewpoint of computation and non-equilibrium systems, Interface Focus 13, 20230021 (2023).
- H. Udono, J. Gong, Y. Sato, and M. Takinoue, DNA droplets: Intelligent, dynamic fluid, Adv. Biol. 7, e2200180 (2023).
- G. Fabrini, S. P. Nuccio, J. M. Stewart, S. Li, A. Tang, P. W. K. Rothemund, E. Franco, M. Di Antonio, and L. Di Michele, bioRxiv 2023.10.06.561174 (2023).