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Computing mathematical functions with chemical reactions via stochastic logic.

Arnav Solanki1, Tonglin Chen1, Marc Riedel1

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This study introduces a novel method for computing mathematical functions using molecular reactions, inspired by digital design principles. The approach translates stochastic logic circuits into robust chemical reaction networks for applications in signal processing and machine learning.

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Area of Science:

  • Biochemistry
  • Computational Biology
  • Digital Logic Design

Background:

  • Stochastic logic utilizes random streams of binary values to represent probabilistic information.
  • Molecular systems represent variables through the concentration of molecular species.
  • Mathematical functions can be computed using logic gates in stochastic logic circuits.

Purpose of the Study:

  • To present a novel strategy for computing mathematical functions using molecular reactions.
  • To demonstrate the design of chemical reaction networks based on truth tables for analog functions.
  • To establish a link between stochastic logic and molecular systems for computation.

Main Methods:

  • Translating mathematical functions computed by stochastic logic circuits into chemical reaction networks.
  • Designing chemical reaction networks based on truth tables specifying analog functions.
  • Utilizing DNA strand displacement with DNA "concatemers" for experimental implementation.

Main Results:

  • Simulations confirm accurate and robust computation by the reaction networks, even with variations in reaction rates.
  • Reaction networks were developed to compute functions such as arctan, exponential, Bessel, and sinc.
  • The methodology provides a general and efficient approach for molecular computation.

Conclusions:

  • The proposed strategy offers a viable method for performing complex mathematical computations using molecular reactions.
  • The developed chemical reaction networks are accurate and robust, showing potential for practical applications.
  • DNA strand displacement presents a promising experimental platform for implementing these molecular computations.