Document Open Access Logo

Learning and Inference in a Lattice Model of Multicomponent Condensates

Authors Cameron Chalk, Salvador Buse, Krishna Shrinivas, Arvind Murugan, Erik Winfree

PDF
Thumbnail PDF

File

LIPIcs.DNA.30.5.pdf
  • Filesize: 8.46 MB
  • 24 pages

Document Identifiers

Author Details

Cameron Chalk
  • California Institute of Technology, USA
Salvador Buse
  • California Institute of Technology, USA
Krishna Shrinivas
  • Northwestern University, USA
Arvind Murugan
  • The University of Chicago, USA
Erik Winfree
  • California Institute of Technology, USA

Funding

  • Chalk, Cameron: National Science Foundation grants 2008589 and 2212546
  • Buse, Salvador: Open Philanthropy Project graduate fellowship, National Science Foundation 2008589 and 2212546
  • Murugan, Arvind: National Science Foundation grants 2239801 and 2317138
  • Winfree, Erik: National Science Foundation grants 2008589 and 2212546

Acknowledgements

The authors thank Paul Rothemund, Lulu Qian, Yancheng Du, Emre Alca, Aman Bhargava, Andrej Košmrlj, Inhoo Lee, Mohini Misra, and others for valuable discussion.

Cite As Get BibTex

Cameron Chalk, Salvador Buse, Krishna Shrinivas, Arvind Murugan, and Erik 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), Volume 314, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DNA.30.5

Abstract

Life is chemical intelligence. What is the source of intelligent behavior in molecular systems? Here we illustrate how, in contrast to the common belief that energy use in non-equilibrium reactions is essential, the detailed balance equilibrium properties of multicomponent liquid interactions are sufficient for sophisticated information processing. Our approach derives from the classical Boltzmann machine model for probabilistic neural networks, inheriting key principles such as representing probability distributions via quadratic energy functions, clamping input variables to infer conditional probability distributions, accommodating omnidirectional computation, and learning energy parameters via a wake phase / sleep phase algorithm that performs gradient descent on the relative entropy with respect to the target distribution. While the cubic lattice model of multicomponent liquids is standard, the behaviors exhibited by the trained molecules capture both previously-observed phenomena such as core-shell condensate architectures as well as novel phenomena such as an analog of Hopfield associative memories that perform recall by contact with a patterned surface. Our final example demonstrates equilibrium classification of MNIST digits. Experimental implementation using DNA nanostar liquids is conceptually straightforward.

Subject Classification

ACM Subject Classification
  • Hardware → Biology-related information processing
  • Theory of computation → Probabilistic computation
  • Applied computing → Systems biology
Keywords
  • multicomponent liquid
  • Boltzmann machine
  • phase separation

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. David H Ackley, Geoffrey E Hinton, and Terrence J Sejnowski. A learning algorithm for Boltzmann machines. Cognitive Science, 9(1):147-169, 1985. Google Scholar
  2. Daniel J Amit, Hanoch Gutfreund, and Haim Sompolinsky. Storing infinite numbers of patterns in a spin-glass model of neural networks. Physical Review Letters, 55(14):1530, 1985. Google Scholar
  3. Silvia Biffi, Roberto Cerbino, Francesca Bomboi, Elvezia Maria Paraboschi, Rosanna Asselta, Francesco Sciortino, and Tommaso Bellini. Phase behavior and critical activated dynamics of limited-valence DNA nanostars. Proceedings of the National Academy of Sciences, 110(39):15633-15637, 2013. Google Scholar
  4. Robert Brijder. Computing with chemical reaction networks: a tutorial. Natural Computing, 18:119-137, 2019. Google Scholar
  5. Jehoshua Bruck. On the convergence properties of the Hopfield model. Proceedings of the IEEE, 78(10):1579-1585, 1990. Google Scholar
  6. Jeong-Mo Choi, Alex S Holehouse, and Rohit V Pappu. Physical principles underlying the complex biology of intracellular phase transitions. Annual Review of Biophysics, 49(1):107-133, 2020. Google Scholar
  7. Matthew Cook, David Soloveichik, Erik Winfree, and Jehoshua Bruck. Programmability of chemical reaction networks. In Algorithmic Bioprocesses, pages 543-584. Springer, 2009. Google Scholar
  8. David Doty. Theory of algorithmic self-assembly. Communications of the ACM, 55(12):78-88, 2012. Google Scholar
  9. John Duchi, Elad Hazan, and Yoram Singer. Adaptive subgradient methods for online learning and stochastic optimization. Journal of Machine Learning Research, 12(7), 2011. Google Scholar
  10. Constantine G Evans and Erik Winfree. Physical principles for DNA tile self-assembly. Chemical Society Reviews, 46(12):3808-3829, 2017. Google Scholar
  11. Constantine Glen Evans, Jackson O’Brien, Erik Winfree, and Arvind Murugan. Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly. Nature, 625(7995):500-507, 2024. Google Scholar
  12. Marina Feric, Nilesh Vaidya, Tyler S Harmon, Diana M Mitrea, Lian Zhu, Tiffany M Richardson, Richard W Kriwacki, Rohit V Pappu, and Clifford P Brangwynne. Coexisting liquid phases underlie nucleolar subcompartments. Cell, 165(7):1686-1697, 2016. Google Scholar
  13. Archa H Fox, Shinichi Nakagawa, Tetsuro Hirose, and Charles S Bond. Paraspeckles: where long noncoding RNA meets phase separation. Trends in Biochemical Sciences, 43(2):124-135, 2018. Google Scholar
  14. Geoffrey E Hinton and Terrence J Sejnowski. Analyzing cooperative computation. In Proceedings of the Fifth Annual Conference of the Cognitive Science Society, pages 2554-2558, 1983. Google Scholar
  15. John J Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences, 79(8):2554-2558, 1982. Google Scholar
  16. John J Hopfield, David I Feinstein, and Richard G Palmer. Unlearning has a stabilizing effect in collective memories. Nature, 304(5922):158-159, 1983. Google Scholar
  17. William M Jacobs and Daan Frenkel. Predicting phase behavior in multicomponent mixtures. The Journal of Chemical Physics, 139(2), 2013. Google Scholar
  18. William M Jacobs and Daan Frenkel. Phase transitions in biological systems with many components. Biophysical Journal, 112(4):683-691, 2017. Google Scholar
  19. Byoung-jin Jeon, Dan T Nguyen, and Omar A Saleh. Sequence-controlled adhesion and microemulsification in a two-phase system of DNA liquid droplets. The Journal of Physical Chemistry B, 124(40):8888-8895, 2020. Google Scholar
  20. Nancy Kedersha and Paul Anderson. Mammalian stress granules and processing bodies. Methods in Enzymology, 431:61-81, 2007. Google Scholar
  21. Tsung-Dao Lee and Chen-Ning Yang. Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model. Physical Review, 87(3):410, 1952. Google Scholar
  22. Andrew S Lyon, William B Peeples, and Michael K Rosen. A framework for understanding the functions of biomolecular condensates across scales. Nature Reviews Molecular Cell Biology, 22(3):215-235, 2021. Google Scholar
  23. Sheng Mao, Milena S Chakraverti-Wuerthwein, Hunter Gaudio, and Andrej Košmrlj. Designing the morphology of separated phases in multicomponent liquid mixtures. Physical Review Letters, 125(21):218003, 2020. Google Scholar
  24. Sheng Mao, Derek Kuldinow, Mikko P Haataja, and Andrej Košmrlj. Phase behavior and morphology of multicomponent liquid mixtures. Soft Matter, 15(6):1297-1311, 2019. Google Scholar
  25. Jose A Morin, Sina Wittmann, Sandeep Choubey, Adam Klosin, Stefan Golfier, Anthony A Hyman, Frank Jülicher, and Stephan W Grill. Sequence-dependent surface condensation of a pioneer transcription factor on DNA. Nature Physics, 18(3):271-276, 2022. Google Scholar
  26. Satoshi Murata. Molecular Robotics: An Introduction. Springer Nature, 2022. Google Scholar
  27. Arvind Murugan, Zorana Zeravcic, Michael P Brenner, and Stanislas Leibler. Multifarious assembly mixtures: Systems allowing retrieval of diverse stored structures. Proceedings of the National Academy of Sciences, 112(1):54-59, 2015. Google Scholar
  28. Matthew J Patitz. An introduction to tile-based self-assembly and a survey of recent results. Natural Computing, 13:195-224, 2014. Google Scholar
  29. William Poole, Andrés Ortiz-Munoz, Abhishek Behera, Nick S Jones, Thomas E Ouldridge, Erik Winfree, and Manoj Gopalkrishnan. Chemical Boltzmann machines. In DNA Computing and Molecular Programming (DNA23), pages 210-231. Springer, 2017. Google Scholar
  30. William Poole, Thomas Ouldridge, Manoj Gopalkrishnan, and Erik Winfree. Detailed balanced chemical reaction networks as generalized Boltzmann machines. arXiv preprint arXiv:2205.06313, 2022. Google Scholar
  31. Arpan Kumar Rai, Jia-Xuan Chen, Matthias Selbach, and Lucas Pelkmans. Kinase-controlled phase transition of membraneless organelles in mitosis. Nature, 559(7713):211-216, 2018. Google Scholar
  32. Benjamin R Sabari, Alessandra Dall’Agnese, Ann Boija, Isaac A Klein, Eliot L Coffey, Krishna Shrinivas, Brian J Abraham, Nancy M Hannett, Alicia V Zamudio, John C Manteiga, et al. Coactivator condensation at super-enhancers links phase separation and gene control. Science, 361(6400):eaar3958, 2018. Google Scholar
  33. Ruslan Salakhutdinov and Geoffrey Hinton. Deep Boltzmann machines. In Artificial Intelligence and Statistics, pages 448-455. PMLR, 2009. Google Scholar
  34. Andrej Šali, Eugene Shakhnovich, and Martin Karplus. Kinetics of protein folding: A lattice model study of the requirements for folding to the native state. Journal of Molecular Biology, 235(5):1614-1636, 1994. Google Scholar
  35. Yusuke Sato, Tetsuro Sakamoto, and Masahiro Takinoue. Sequence-based engineering of dynamic functions of micrometer-sized DNA droplets. Science Advances, 6(23):eaba3471, 2020. Google Scholar
  36. John E Savage. Models of Computation: Exploring the Power of Computing. Addison-Wesley Reading, 1998. Google Scholar
  37. Benjamin Scellier and Yoshua Bengio. Equilibrium propagation: Bridging the gap between energy-based models and backpropagation. Frontiers in Computational Neuroscience, 11:24, 2017. Google Scholar
  38. Ludovica Serricchio, Dario Bocchi, Claudio Chilin, Raffaele Marino, Matteo Negri, Chiara Cammarota, and Federico Ricci-Tersenghi. Daydreaming Hopfield networks and their surprising effectiveness on correlated data. arXiv preprint arXiv:2405.08777, 2024. Google Scholar
  39. Krishna Shrinivas and Michael P Brenner. Phase separation in fluids with many interacting components. Proceedings of the National Academy of Sciences, 118(45):e2108551118, 2021. Google Scholar
  40. Krishna Shrinivas and Michael P Brenner. Multiphase coexistence capacity in complex fluids. bioRxiv, pages 2022-10, 2022. Google Scholar
  41. Krishna Shrinivas, Benjamin R Sabari, Eliot L Coffey, Isaac A Klein, Ann Boija, Alicia V Zamudio, Jurian Schuijers, Nancy M Hannett, Phillip A Sharp, Richard A Young, et al. Enhancer features that drive formation of transcriptional condensates. Molecular Cell, 75(3):549-561, 2019. Google Scholar
  42. Wilton T Snead and Amy S Gladfelter. The control centers of biomolecular phase separation: how membrane surfaces, PTMs, and active processes regulate condensation. Molecular Cell, 76(2):295-305, 2019. Google Scholar
  43. Héctor J Sussmann. Learning algorithms for Boltzmann machines. In Proceedings of the 27th IEEE Conference on Decision and Control, pages 786-791. IEEE, 1988. Google Scholar
  44. Masahiro Takinoue. DNA droplets for intelligent and dynamical artificial cells: from the viewpoint of computation and non-equilibrium systems. Interface Focus, 13(5):20230021, 2023. Google Scholar
  45. Rodrigo Braz Teixeira, Giorgio Carugno, Izaak Neri, and Pablo Sartori. Liquid Hopfield model: retrieval and localization in heterogeneous liquid mixtures. arXiv preprint arXiv:2310.18853, 2023. Google Scholar
  46. Hirotake Udono, Jing Gong, Yusuke Sato, and Masahiro Takinoue. DNA droplets: intelligent, dynamic fluid. Advanced Biology, 7(3):2200180, 2023. Google Scholar
  47. Laurent Younes. Synchronous Boltzmann machines can be universal approximators. Applied Mathematics Letters, 9(3):109-113, 1996. Google Scholar
  48. Weishun Zhong, David J Schwab, and Arvind Murugan. Associative pattern recognition through macro-molecular self-assembly. Journal of Statistical Physics, 167:806-826, 2017. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact