## Abstract

Chemical reaction networks (CRNs) provide a fundamental model in the study of molecular systems. Widely used as formalism for the analysis of chemical and biochemical systems, CRNs have received renewed attention as a model for molecular computation. This paper demonstrates that, with a new encoding, CRNs can compute any set of polynomial functions subject only to the limitation that these functions must map the unit interval to itself. These polynomials can be expressed as linear combinations of Bernstein basis polynomials with positive coefficients less than or equal to 1. In the proposed encoding approach, each variable is represented using two molecular types: a type-0 and a type-1. The value is the ratio of the concentration of type-1 molecules to the sum of the concentrations of type-0 and type-1 molecules. The proposed encoding naturally exploits the expansion of a power-form polynomial into a Bernstein polynomials. The method is illustrated first for generic CRNs; then the chemical reactions designed for two examples are mapped to DNA strand-displacement reactions.

Original language | English (US) |
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Title of host publication | 2016 IEEE Global Communications Conference, GLOBECOM 2016 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Electronic) | 9781509013289 |

DOIs | |

State | Published - 2016 |

Event | 59th IEEE Global Communications Conference, GLOBECOM 2016 - Washington, United States Duration: Dec 4 2016 → Dec 8 2016 |

### Publication series

Name | 2016 IEEE Global Communications Conference, GLOBECOM 2016 - Proceedings |
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### Other

Other | 59th IEEE Global Communications Conference, GLOBECOM 2016 |
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Country/Territory | United States |

City | Washington |

Period | 12/4/16 → 12/8/16 |

### Bibliographical note

Funding Information:This research is supported by the National Science Foundation grant CCF-14234707.