Journal of Statistical Physics

, Volume 167, Issue 3–4, pp 806–826 | Cite as

Associative Pattern Recognition Through Macro-molecular Self-Assembly

  • Weishun Zhong
  • David J. Schwab
  • Arvind Murugan


We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of N distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical attractors to recognize and reconstruct partially corrupted patterns. Traditional parameters of pattern recognition theory, such as sparsity, fidelity, and capacity are related to physical parameters, such as nucleation barriers, interaction range, and non-equilibrium assembly forces. Notably, we find that self-assembly bears greater similarity to continuous attractor neural networks, such as place cell networks that store spatial memories, rather than discrete memory networks. This relationship suggests that features and trade-offs seen here are not tied to details of self-assembly or neural network models but are instead intrinsic to associative pattern recognition carried out through short-ranged interactions.


Self-assembly Pattern recognition Associative memory Neural networks Attractors 



We thank Michael Brenner, Nicolas Brunel, John Hopfield, David Huse, Stanislas Leibler, Pankaj Mehta, Remi Monasson, Sidney Nagel, Sophie Rosay, Zorana Zeravcic and James Zou for discussions. DJS was partially supported by NIH Grant No. K25 GM098875-02.


  1. 1.
    Graves, A., Mohamed, A.R., Hinton, G.: Speech recognition with deep recurrent neural networks. In: 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 6645–6649 (2013)Google Scholar
  2. 2.
    Krizhevsky, A., Sutskever, I., Hinton, G.E.: ImageNet classification with deep convolutional neural networks. In: Pereira, F., Burges, C.J.C., Bottou, L., Weinberger, K.O. (eds.) Advances in Neural Information Processing Systems 25, pp. 1097–1105. Curran Associates, Inc., Red Hook (2012)Google Scholar
  3. 3.
    Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. In: Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2009. 1 Jan 1982Google Scholar
  4. 4.
    Purvis, J.E., Lahav, G.: Encoding and decoding cellular information through signaling dynamics. Cell 152(5), 945–956 (2013)CrossRefGoogle Scholar
  5. 5.
    Levine, J.H., Lin, Y., Elowitz, M.B.: Functional roles of pulsing in genetic circuits. Science 342(6163), 1193–1200 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    Brubaker, S.W., Bonham, K.S., Zanoni, I., Kagan, J.C.: Innate immune pattern recognition: a cell biological perspective. Annu. Rev. Immunol. 33, 257–290 (2015)CrossRefGoogle Scholar
  7. 7.
    Murugan, A., Zeravcic, Z., Brenner, M.P., Leibler, S.: Multifarious assembly mixtures: systems allowing retrieval of diverse stored structures. Proc. Natl. Acad. Sci. USA 112(1), 54–59 (2015)ADSCrossRefGoogle Scholar
  8. 8.
    Amit, D., Gutfreund, H., Sompolinsky, H.: Storing infinite numbers of patterns in a spin-glass model of neural networks. Phys. Rev. Lett. 55(14), 1530–1533 (1985)ADSCrossRefGoogle Scholar
  9. 9.
    Hertz, J., Krogh, A., Palmer, R.: Introduction to the Theory of Neural Computation. Basic Books, New York (1991)Google Scholar
  10. 10.
    Amit, D.J., Gutfreund, H., Sompolinsky, H.: Spin-glass models of neural networks. Phys. Rev. A 32(2), 1007 (1985)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    MacKay, D.J.C.: Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  12. 12.
    Burak, Y., Fiete, I.R.: Fundamental limits on persistent activity in networks of noisy neurons. Proc. Natl. Acad. Sci. USA 109(43), 17645–17650 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    Chaudhuri, R., Fiete, I.: Computational principles of memory. Nat. Neurosci. 19(3), 394–403 (2016)CrossRefGoogle Scholar
  14. 14.
    Seung, H.S.: Learning continuous attractors in recurrent networks. NIPS 97, 654–660 (1997)Google Scholar
  15. 15.
    Wu, S., Hamaguchi, K., Amari, S.I.: Dynamics and computation of continuous attractors. Neural Comput. 20(4), 994–1025 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Monasson, R., Rosay, S.: Crosstalk and transitions between multiple spatial maps in an attractor neural network model of the hippocampus: phase diagram. Phys. Rev. E 87(6), 062813 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    Monasson, R., Rosay, S.: Crosstalk and transitions between multiple spatial maps in an attractor neural network model of the hippocampus: collective motion of the activity. Phys. Rev. E 89(3), 1 (2014)CrossRefGoogle Scholar
  18. 18.
    Battaglia, F., Treves, A.: Attractor neural networks storing multiple space representations: a model for hippocampal place fields. Phys. Rev. E 58(6), 7738–7753 (1998)ADSCrossRefGoogle Scholar
  19. 19.
    Seung, H.S., Lee, D.D., Reis, B.Y., Tank, D.W.: Stability of the memory of eye position in a recurrent network of conductance-based model neurons. Neuron 26(1), 259–271 (2000)CrossRefGoogle Scholar
  20. 20.
    Hopfield, J.J.: Neurodynamics of mental exploration. Proc. Natl. Acad. Sci. USA 107(4), 1648–1653 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    Hopfield, J.J.: Understanding emergent dynamics: using a collective activity coordinate of a neural network to recognize time-varying patterns. Neural Comput. 27(10), 2011–2038 (2015)CrossRefGoogle Scholar
  22. 22.
    Fink, T., Ball, R.: How many conformations can a protein remember? Phys. Rev. Lett. 87(19), 198103 (2001)ADSCrossRefGoogle Scholar
  23. 23.
    Barish, R.D., Schulman, R., Rothemund, P.W.K., Winfree, E.: An information-bearing seed for nucleating algorithmic self-assembly. Proc. Natl. Acad. Sci. USA 106(15), 6054–6059 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    Friedrichs, M.S., Wolynes, P.G.: Toward protein tertiary structure recognition by means of associative memory hamiltonians. Science 246(4928), 371 (1989)ADSCrossRefGoogle Scholar
  25. 25.
    Sasai, M., Wolynes, P.G.: Molecular theory of associative memory hamiltonian models of protein folding. Phys. Rev. Lett. 65(21), 2740 (1990)ADSCrossRefGoogle Scholar
  26. 26.
    Sasai, M., Wolynes, P.G.: Unified theory of collapse, folding, and glass transitions in associative-memory hamiltonian models of proteins. Phys. Rev. A 46(12), 7979 (1992)ADSCrossRefGoogle Scholar
  27. 27.
    Bohr, H.G., Wolynes, P.G.: Initial events of protein folding from an information-processing viewpoint. Phys. Rev. A 46(8), 5242 (1992)ADSCrossRefGoogle Scholar
  28. 28.
    Schafer, N.P., Kim, B.L., Zheng, W., Wolynes, P.G.: Learning to fold proteins using energy landscape theory. Isr. J. Chem. 54(8–9), 1311–1337 (2014)CrossRefGoogle Scholar
  29. 29.
    Ke, Y., Ong, L.L., Shih, W.M., Yin, P.: Three-dimensional structures self-assembled from DNA bricks. Science 338(6111), 1177–1183 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    Wei, B., Dai, M., Yin, P.: Complex shapes self-assembled from single-stranded DNA tiles. Nature 485(7400), 623–626 (2012)ADSCrossRefGoogle Scholar
  31. 31.
    Colgin, L.L., Leutgeb, S., Jezek, K., Leutgeb, J.K., Moser, E.I., McNaughton, B.L., Moser, M.-B.: Attractor-map versus autoassociation based attractor dynamics in the hippocampal network. J. Neurophysiol. 104(1), 35–50 (2010)CrossRefGoogle Scholar
  32. 32.
    Jezek, K., Henriksen, E.J., Treves, A., Moser, E.I., Moser, M.-B.: Theta-paced flickering between place-cell maps in the hippocampus. Nature 478(7368), 246–249 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    Wills, T.J., Lever, C., Cacucci, F., Burgess, N., O’Keefe, J.: Attractor dynamics in the hippocampal representation of the local environment. Science 308(5723), 873–876 (2005)ADSCrossRefGoogle Scholar
  34. 34.
    Kubie, J.L., Muller, R.U.: Multiple representations in the hippocampus. Hippocampus 1(3), 240–242 (1991)CrossRefGoogle Scholar
  35. 35.
    Curto, C., Itskov, V.: Cell groups reveal structure of stimulus space. PLoS Comput. Biol. 4(10), e1000205 (2008)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    Pfeiffer, B.E., Foster, D.J.: Hippocampal place-cell sequences depict future paths to remembered goals. Nature 497(7447), 74–79 (2013)ADSCrossRefGoogle Scholar
  37. 37.
    Ponulak, F., Hopfield, J.J.: Rapid, parallel path planning by propagating wavefronts of spiking neural activity. Front. Comput. Neurosci. 7, 98 (2013)CrossRefGoogle Scholar
  38. 38.
    Wu, S., Amari, S.-I.: Computing with continuous attractors: stability and online aspects. Neural Comput. 17(10), 2215–2239 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Jezek, K., Henriksen, E.J., Treves, A., Moser, E.I., Moser, M.-B.: Theta-paced flickering between place-cell maps in the hippocampus. Nature 478(7368), 246–249 (2011)ADSCrossRefGoogle Scholar
  40. 40.
    Hedges, L.O., Mannige, R.V., Whitelam, S.: Growth of equilibrium structures built from a large number of distinct component types. Soft Matter 10(34), 6404–6416 (2014)ADSCrossRefGoogle Scholar
  41. 41.
    Murugan, A., Zou, J., Brenner, M.P.: Undesired usage and the robust self-assembly of heterogeneous structures. Nat. Commun. 6, 6203 (2015)ADSCrossRefGoogle Scholar
  42. 42.
    Jacobs, W.M., Frenkel, D.: Predicting phase behavior in multicomponent mixtures. J. Chem. Phys. 139, 024108 (2013)ADSCrossRefGoogle Scholar
  43. 43.
    Jacobs, W.M., Reinhardt, A., Frenkel, D.: Communication: theoretical prediction of free-energy landscapes for complex self-assembly. J. Chem. Phys. 142(2), 021101 (2015)ADSCrossRefGoogle Scholar
  44. 44.
    Haxton, T.K., Whitelam, S.: Do hierarchical structures assemble best via hierarchical pathways? Soft Matter 9(29), 6851–6861 (2013)ADSCrossRefGoogle Scholar
  45. 45.
    Whitelam, S., Schulman, R., Hedges, L.: Self-assembly of multicomponent structures in and out of equilibrium. Phys. Rev. Lett. 109(26), 265506 (2012)ADSCrossRefGoogle Scholar
  46. 46.
    Levy, E.D., Pereira-Leal, J.B., Chothia, C., Teichmann, S.A.: 3D complex: a structural classification of protein complexes. PLoS Comput. Biol. 2(11), e155 (2006)ADSCrossRefGoogle Scholar
  47. 47.
    Koyama, S.: Storage capacity of two-dimensional neural networks. Phys. Rev. E 65(1), 016124 (2001)ADSCrossRefGoogle Scholar
  48. 48.
    Derrida, B., Gardner, E., Zippelius, A.: An exactly solvable asymmetric neural network model. EPL 4(2), 167 (1987)ADSCrossRefGoogle Scholar
  49. 49.
    Nishimori, H., Whyte, W., Sherrington, D.: Finite-dimensional neural networks storing structured patterns. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 51(4), 3628–3642 (1995)MathSciNetGoogle Scholar
  50. 50.
    Lang, A.H., Li, H., Collins, J.J., Mehta, P.: Epigenetic landscapes explain partially reprogrammed cells and identify key reprogramming genes. PLoS Comput. Biol. 10(8), e1003734 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Weishun Zhong
    • 1
  • David J. Schwab
    • 2
  • Arvind Murugan
    • 1
  1. 1.Department of Physics and the James Franck InstituteUniversity of ChicagoChicagoUSA
  2. 2.Department of PhysicsNorthwesternEvanstonUSA

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