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Learning and Inference in a Lattice Model of Multicomponent Condensates

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

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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 AsGet 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

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