- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Evolutionary chemical learning in dimerization networks

Alexei V. Tkachenko1,*, Bortolo Matteo Mognetti2, and Sergei Maslov3,4,5,†

  • *Contact author: oleksiyt@bnl.gov
  • †Contact author: maslov@illinois.edu
PDF

Phys. Rev. E 114, 035404 – Published 2 September, 2026

DOI: https://doi.org/10.1103/bszq-gftl

Abstract

We present a framework for chemical learning based on competitive dimerization networks (CDNs)—systems in which multiple molecular species, e.g., proteins or DNA-RNA oligomers, reversibly bind to form dimers. We show numerically that these networks can, in principle, be trained in vitro through directed evolution, enabling the implementation of complex learning tasks such as multiclass classification without digital hardware or prior knowledge of all microscopic association constants. Each molecular species functions analogously to a neuron, with binding affinities acting as tunable synaptic weights. A training protocol involving mutation, selection, and amplification of DNA-based components allows CDNs to robustly discriminate among noisy input patterns. The resulting classifiers exhibit strong output contrast and high mutual information between input and output, especially when guided by a contrast-enhancing loss function. Comparative analysis with in silico gradient descent training reveals closely correlated performance. These results establish CDNs as a promising platform for analog physical computation, bridging synthetic biology and machine learning, and advancing the development of adaptive, energy-efficient molecular computing systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (37)

  1. A. Krizhevsky, I. Sutskever, and G. E. Hinton, ImageNet classification with deep convolutional neural networks, Commun. ACM 60, 84 (2017).
  2. I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT Press, Cambridge, MA, 2016).
  3. X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, All-optical machine learning using diffractive deep neural networks, Science 361, 1004 (2018).
  4. B. J. Shastri, A. N. Tait, T. Ferreira de Lima, W. H. P. Pernice, H. Bhaskaran, C. D. Wright, and P. R. Prucnal, Photonics for artificial intelligence and neuromorphic computing, Nat. Photon. 15, 102 (2021).
  5. C. Li, D. Belkin, Y. Li, P. Yan, M. Hu, N. Ge, H. Jiang, E. Montgomery, P. Lin, Z. Wang, et al., Efficient and self-adaptive in-situ learning in multilayer memristor neural networks, Nat. Commun. 9, 2385 (2018).
  6. M. Stern, D. Hexner, J. W. Rocks, and A. J. Liu, Supervised learning in physical networks: From machine learning to learning machines, Phys. Rev. X 11, 021045 (2021).
  7. M. Sitti, Physical intelligence as a new paradigm, Extreme Mech. Lett. 46, 101340 (2021).
  8. A. Murugan, Z. Zeravcic, M. P. Brenner, and S. Leibler, Multifarious assembly mixtures: Systems allowing retrieval of diverse stored structures, Proc. Natl. Acad. Sci. USA 112, 54 (2015).
  9. 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).
  10. A. Momeni, B. Rahmani, M. Malléjac, P. del Hougne, and R. Fleury, Backpropagation-free training of deep physical neural networks, Science 382, 1297 (2023).
  11. M. Stern and A. Murugan, Learning without neurons in physical systems, Annu. Rev. Condens. Matter Phys. 14, 417 (2023).
  12. D. Bray, Protein molecules as computational elements in living cells, Nature (London) 376, 307 (1995).
  13. U. S. Bhalla and R. Iyengar, Emergent properties of networks of biological signaling pathways, Science 283, 381 (1999).
  14. B. A. Kramer, J. Sarabia Del Castillo, and L. Pelkmans, Multimodal perception links cellular state to decision-making in single cells, Science 377, 642 (2022).
  15. W. Poole, A. Ortiz-Muñoz, A. Behera, N. S. Jones, T. E. Ouldridge, E. Winfree, and M. Gopalkrishnan, Chemical Boltzmann machines, in DNA Computing and Molecular Programming, edited by R. Brijder and L. Qian (Springer International Publishing, Cham, Switzerland, 2017), pp. 210–231.
  16. C. Floyd, A. R. Dinner, A. Murugan, and S. Vaikuntanathan, Limits on the computational expressivity of non-equilibrium biophysical processes, Nat. Commun. 16, 7184 (2025).
  17. S. Maslov and I. Ispolatov, Propagation of large concentration changes in reversible protein-binding networks, Proc. Natl. Acad. Sci. USA 104, 13655 (2007).
  18. S. Maslov, K. Sneppen, and I. Ispolatov, Spreading out of perturbations in reversible reaction networks, New J. Phys. 9, 273 (2007).
  19. M. P. Nikitin, Non-complementary strand commutation as a fundamental alternative for information processing by DNA and gene regulation, Nat. Chem. 15, 70 (2023).
  20. J. Parres-Gold, M. Levine, B. Emert, A. Stuart, and M. B. Elowitz, Contextual computation by competitive protein dimerization networks, Cell 188, 1984 (2025).
  21. S. Brannetti, S. Gentile, E. D. Grosso, S. Otto, and F. Ricci, Covalent dynamic DNA networks to translate multiple inputs into programmable outputs, J. Am. Chem. Soc. 147, 5755 (2025).
  22. J. SantaLucia, A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics, Proc. Natl. Acad. Sci. USA 95, 1460 (1998).
  23. L. M. Adleman, Molecular computation of solutions to combinatorial problems, Science 266, 1021 (1994).
  24. G. Seelig, D. Soloveichik, D. Y. Zhang, and E. Winfree, Enzyme-free nucleic acid logic circuits, Science 314, 1585 (2006).
  25. D. Soloveichik, G. Seelig, and E. Winfree, DNA as a universal substrate for chemical kinetics, Proc. Natl. Acad. Sci. USA 107, 5393 (2010).
  26. N. Srinivas, J. Parkin, G. Seelig, E. Winfree, and D. Soloveichik, Enzyme-free nucleic acid dynamical systems, Science 358, eaal2052 (2017).
  27. H. E. Klumpe, J. Garcia-Ojalvo, M. B. Elowitz, and Y. E. Antebi, The computational capabilities of many-to-many protein interaction networks, Cell Syst. 14, 430 (2023).
  28. K. O. Stanley, J. Clune, J. Lehman, and R. Miikkulainen, Designing neural networks through neuroevolution, Nat. Mach. Intell. 1, 24 (2019).
  29. Y. Wang, P. Xue, M. Cao, T. Yu, S. T. Lane, and H. Zhao, Directed evolution: Methodologies and applications, Chem. Rev. 121, 12384 (2021).
  30. J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
  31. J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Natl. Acad. Sci. USA 81, 3088 (1984).
  32. K. K. Yan, D. Walker, and S. Maslov, Fluctuations in mass-action equilibrium of protein binding networks, Phys. Rev. Lett. 101, 268102 (2008).
  33. P. Varilly, S. Angioletti-Uberti, B. M. Mognetti, and D. Frenkel, A general theory of DNA-mediated and other valence-limited colloidal interactions, J. Chem. Phys. 137, 094108 (2012).
  34. Figure interactive version available at https://atkachen00.github.io/ChemClassifierWeb.
  35. K. Trifonova, M. J. Falk, M. Rouches, S. Vaikuntanathan, M. B. Elowitz, and A. Murugan, Trainable computation in molecular networks, bioRxiv (2026).
  36. A. Tkachenko, Chemclassifierweb: Data and code repository, 2025, https://github.com/atkachen00/ChemClassifierWeb.
  37. D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, in The 3rd International Conference on Learning Representations (ICLR, San Diego, 2015), arXiv:1412.6980.

Outline

Information

Phys. Rev. E 114, 035404– Published 2 September, 2026
  • Received 4 November 2025
  • Accepted 30 July 2026
Article part of CHORUS
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation