## Abstract

Markov chains are commonly used in numerous signal processing and statistical modeling applications. This paper describes an approach to implement any first-order Markov chain using molecular reactions in general and DNA in particular. Markov chain consists of two parts: a set of states, and state transition probabilities. Each state is modeled by a unique molecular type, referred as a data molecule. Each state transition is modeled by a unique molecular type, referred as a control molecule, and a unique molecular reaction. Each reaction consumes data molecules of one state and produces data molecules of another state. The concentrations of control molecules are initialized according to the probabilities of corresponding state transitions in the chain. The steady-state probability of Markov chain is computed by equilibrium concentration of data molecules. We demonstrate our method for the Gambler's Ruin problem as an instance of the Markov chain process. Both stochastic chemical kinetics and mass-action kinetics validate the computed probabilities using the proposed model. The molecular reactions are then mapped to DNA strand displacement reactions. The error in the probability of ruin computed by the proposed model is shown to be less than 1% for DNA strand displacement reactions.

Original language | English |
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Title of host publication | 2015 IEEE International Conference on Digital Signal Processing, DSP 2015 |

Pages | 689-693 |

Number of pages | 5 |

ISBN (Electronic) | 9781479980581, 9781479980581 |

DOIs | |

State | Published - Sep 9 2015 |

Event | IEEE International Conference on Digital Signal Processing, DSP 2015 - Singapore, Singapore Duration: Jul 21 2015 → Jul 24 2015 |

### Publication series

Name | International Conference on Digital Signal Processing, DSP |
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Volume | 2015-September |

### Conference

Conference | IEEE International Conference on Digital Signal Processing, DSP 2015 |
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Country/Territory | Singapore |

City | Singapore |

Period | 7/21/15 → 7/24/15 |

### Bibliographical note

Publisher Copyright:© 2015 IEEE.

Copyright:

Copyright 2016 Elsevier B.V., All rights reserved.

## Keywords

- DNA strand-displacement
- Gambler's ruin problem
- Markov chain
- Molecular computation
- molecular reaction

## ASJC Scopus subject areas

- Signal Processing