# Associative Pattern Recognition Through Macro-molecular Self-Assembly

- 247 Downloads

## Abstract

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.

### Keywords

Self-assembly Pattern recognition Associative memory Neural networks Attractors## Notes

### Acknowledgements

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.

### References

- 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.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.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.Purvis, J.E., Lahav, G.: Encoding and decoding cellular information through signaling dynamics. Cell
**152**(5), 945–956 (2013)CrossRefGoogle Scholar - 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.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.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.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.Hertz, J., Krogh, A., Palmer, R.: Introduction to the Theory of Neural Computation. Basic Books, New York (1991)Google Scholar
- 10.Amit, D.J., Gutfreund, H., Sompolinsky, H.: Spin-glass models of neural networks. Phys. Rev. A
**32**(2), 1007 (1985)ADSMathSciNetCrossRefGoogle Scholar - 11.MacKay, D.J.C.: Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge (2003)MATHGoogle Scholar
- 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.Chaudhuri, R., Fiete, I.: Computational principles of memory. Nat. Neurosci.
**19**(3), 394–403 (2016)CrossRefGoogle Scholar - 14.Seung, H.S.: Learning continuous attractors in recurrent networks. NIPS
**97**, 654–660 (1997)Google Scholar - 15.Wu, S., Hamaguchi, K., Amari, S.I.: Dynamics and computation of continuous attractors. Neural Comput.
**20**(4), 994–1025 (2008)MathSciNetCrossRefMATHGoogle Scholar - 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.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.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.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.Hopfield, J.J.: Neurodynamics of mental exploration. Proc. Natl. Acad. Sci. USA
**107**(4), 1648–1653 (2010)ADSCrossRefGoogle Scholar - 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.Fink, T., Ball, R.: How many conformations can a protein remember? Phys. Rev. Lett.
**87**(19), 198103 (2001)ADSCrossRefGoogle Scholar - 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.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.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.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.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.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.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.Wei, B., Dai, M., Yin, P.: Complex shapes self-assembled from single-stranded DNA tiles. Nature
**485**(7400), 623–626 (2012)ADSCrossRefGoogle Scholar - 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.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.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.Kubie, J.L., Muller, R.U.: Multiple representations in the hippocampus. Hippocampus
**1**(3), 240–242 (1991)CrossRefGoogle Scholar - 35.Curto, C., Itskov, V.: Cell groups reveal structure of stimulus space. PLoS Comput. Biol.
**4**(10), e1000205 (2008)ADSMathSciNetCrossRefGoogle Scholar - 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.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.Wu, S., Amari, S.-I.: Computing with continuous attractors: stability and online aspects. Neural Comput.
**17**(10), 2215–2239 (2005)MathSciNetCrossRefMATHGoogle Scholar - 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.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.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.Jacobs, W.M., Frenkel, D.: Predicting phase behavior in multicomponent mixtures. J. Chem. Phys.
**139**, 024108 (2013)ADSCrossRefGoogle Scholar - 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.Haxton, T.K., Whitelam, S.: Do hierarchical structures assemble best via hierarchical pathways? Soft Matter
**9**(29), 6851–6861 (2013)ADSCrossRefGoogle Scholar - 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.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.Koyama, S.: Storage capacity of two-dimensional neural networks. Phys. Rev. E
**65**(1), 016124 (2001)ADSCrossRefGoogle Scholar - 48.Derrida, B., Gardner, E., Zippelius, A.: An exactly solvable asymmetric neural network model. EPL
**4**(2), 167 (1987)ADSCrossRefGoogle Scholar - 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.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