### Abstract

Gene products (RNAs, proteins) often occur at low molecular counts inside individual cells, and hence are subject to considerable random fluctuations (noise) in copy number over time. Not surprisingly, cells encode diverse regulatory mechanisms to buffer noise. One such mechanism is the incoherent feedforward circuit. We analyze a simplistic version of this circuit, where an upstream regulator X affects both the production and degradation of a protein Y. Thus, any random increase in X's copy numbers would increase both production and degradation, keeping Y levels unchanged. To study its stochastic dynamics, we formulate this network into a mathematical model using the Chemical Master Equation formulation. We prove that if the functional dependence of Y's production and degradation on X is similar, then the steady-distribution of Y's copy numbers is independent of X. To investigate how fluctuations in Y propagate downstream, a protein Z whose production rate only depend on Y is introduced. Intriguingly, results show that the extent of noise in Z increases with noise in X, in spite of the fact that the magnitude of noise in Y is invariant of X. Such counter intuitive results arise because X enhances the time-scale of fluctuations in Y, which amplifies fluctuations in downstream processes. In summary, while feedforward systems can buffer a protein from noise in its upstream regulators, noise can propagate downstream due to changes in the time-scale of fluctuations.

Original language | English |
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Title of host publication | American Control Conference (ACC), 2016 |

Publisher | IEEE |

Pages | 406-411 |

ISBN (Print) | 978-1-4673-8682-1 |

DOIs | |

Publication status | Published - 1 Aug 2016 |

Event | American Control Conference 2016 - Boston, United States Duration: 6 Jul 2016 → 8 Jul 2016 |

### Conference

Conference | American Control Conference 2016 |
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Abbreviated title | ACC |

Country | United States |

City | Boston |

Period | 6/07/16 → 8/07/16 |

### Bibliographical note

The full text is currently unavailable on the repository.### Keywords

- Production
- Degradation
- Proteins
- Feedforward neural networks
- Correlation
- Regulators
- Mathematical model
- stochastic processes
- feedforward
- fluctuations
- genetics
- fluctuation time-scale
- stochastic analysis
- incoherent feedforward genetic motif
- gene product
- chemical master equation formulation

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## Cite this

Soltani, M., Platini, T., & Singh, A. (2016). Stochastic analysis of an incoherent feedforward genetic motif. In

*American Control Conference (ACC), 2016*(pp. 406-411). IEEE. https://doi.org/10.1109/ACC.2016.7524948