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Differentiable Programming of Indexed Chemical Reaction Networks and Reaction-Diffusion Systems

Authors Inhoo Lee , Salvador Buse , Erik Winfree

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ACM Subject Classification
  • Computer systems organization → Molecular computing
Keywords
  • Differentiable Programming
  • Chemical Reaction Networks
  • Reaction-Diffusion Systems

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Abstract

Many molecular systems are best understood in terms of prototypical species and reactions. The central dogma and related biochemistry are rife with examples: gene i is transcribed into RNA i, which is translated into protein i; kinase n phosphorylates substrate m; protein p dimerizes with protein q. Engineered nucleic acid systems also often have this form: oligonucleotide i hybridizes to complementary oligonucleotide j; signal strand n displaces the output of seesaw gate m; hairpin p triggers the opening of target q. When there are many variants of a small number of prototypes, it can be conceptually cleaner and computationally more efficient to represent the full system in terms of indexed species (e.g. for dimerization, M_p, D_pq) and indexed reactions (M_p + M_q → D_pq). Here, we formalize the Indexed Chemical Reaction Network (ICRN) model and describe a Python software package designed to simulate such systems in the well-mixed and reaction-diffusion settings, using a differentiable programming framework originally developed for large-scale neural network models, taking advantage of GPU acceleration when available. Notably, this framework makes it straightforward to train the models’ initial conditions and rate constants to optimize a target behavior, such as matching experimental data, performing a computation, or exhibiting spatial pattern formation. The natural map of indexed chemical reaction networks onto neural network formalisms provides a tangible yet general perspective for translating concepts and techniques from the theory and practice of neural computation into the design of biomolecular systems.

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Inhoo Lee, Salvador Buse, and Erik Winfree. Differentiable Programming of Indexed Chemical Reaction Networks and Reaction-Diffusion Systems. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DNA.31.4

Author Details

Inhoo Lee
  • California Institute of Technology, Pasadena, CA, USA
Salvador Buse
  • California Institute of Technology, Pasadena, CA, USA
Erik Winfree
  • California Institute of Technology, Pasadena, CA, USA

Funding

  • Lee, Inhoo: Schmidt Academy for Software Engineering, NSF CCF/FET Award 2212546.
  • Buse, Salvador: Open Philanthropy Good Ventures Foundation, NSF CCF/FET Award 2212546.
  • Winfree, Erik: NSF CCF/FET Award 2212546.

Acknowledgements

Many thanks to inspirational and technical discussions with Alex Mordvintsev, Andrew Stuart, Lulu Qian, Kevin Cherry and members of the Winfree, Qian, and Rothemund groups. Inhoo Lee and Salvador Buse are co-first authors.

Supplementary Materials

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