### Abstract

The paper proposes new computational methods of computing confidence bounds for the least-squares estimates (LSEs) of rate constants in mass action biochemical reaction network and stochastic epidemic models. Such LSEs are obtained by fitting the set of deterministic ordinary differential equations (ODEs), corresponding to the large-volume limit of a reaction network, to network's partially observed trajectory treated as a continuous-time, pure jump Markov process. In the large-volume limit the LSEs are asymptotically Gaussian, but their limiting covariance structure is complicated since it is described by a set of nonlinear ODEs which are often ill-conditioned and numerically unstable. The current paper considers two bootstrap Monte-Carlo procedures, based on the diffusion and linear noise approximations for pure jump processes, which allow one to avoid solving the limiting covariance ODEs. The results are illustrated with both in-silico and real data examples from the LINE 1 gene retrotranscription model and compared with those obtained using other methods.

Original language | English (US) |
---|---|

Pages (from-to) | 125-146 |

Number of pages | 22 |

Journal | Journal of biological dynamics |

Volume | 9 |

DOIs | |

State | Published - Jan 1 2015 |

Externally published | Yes |

### Fingerprint

### Keywords

- 60J28
- 62F
- 92C40
- 92C45
- bootstrap monte-carlomethod
- density-dependent Markov jump process
- diffusion approximation
- least-squares estimation
- network reverse engineering
- reaction network

### ASJC Scopus subject areas

- Ecology, Evolution, Behavior and Systematics
- Ecology

### Cite this

*Journal of biological dynamics*,

*9*, 125-146. https://doi.org/10.1080/17513758.2015.1033022

**Bootstrapping least-squares estimates in biochemical reaction networks.** / Linder, Daniel F; Rempała, Grzegorz A.

Research output: Contribution to journal › Article

*Journal of biological dynamics*, vol. 9, pp. 125-146. https://doi.org/10.1080/17513758.2015.1033022

}

TY - JOUR

T1 - Bootstrapping least-squares estimates in biochemical reaction networks

AU - Linder, Daniel F

AU - Rempała, Grzegorz A.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The paper proposes new computational methods of computing confidence bounds for the least-squares estimates (LSEs) of rate constants in mass action biochemical reaction network and stochastic epidemic models. Such LSEs are obtained by fitting the set of deterministic ordinary differential equations (ODEs), corresponding to the large-volume limit of a reaction network, to network's partially observed trajectory treated as a continuous-time, pure jump Markov process. In the large-volume limit the LSEs are asymptotically Gaussian, but their limiting covariance structure is complicated since it is described by a set of nonlinear ODEs which are often ill-conditioned and numerically unstable. The current paper considers two bootstrap Monte-Carlo procedures, based on the diffusion and linear noise approximations for pure jump processes, which allow one to avoid solving the limiting covariance ODEs. The results are illustrated with both in-silico and real data examples from the LINE 1 gene retrotranscription model and compared with those obtained using other methods.

AB - The paper proposes new computational methods of computing confidence bounds for the least-squares estimates (LSEs) of rate constants in mass action biochemical reaction network and stochastic epidemic models. Such LSEs are obtained by fitting the set of deterministic ordinary differential equations (ODEs), corresponding to the large-volume limit of a reaction network, to network's partially observed trajectory treated as a continuous-time, pure jump Markov process. In the large-volume limit the LSEs are asymptotically Gaussian, but their limiting covariance structure is complicated since it is described by a set of nonlinear ODEs which are often ill-conditioned and numerically unstable. The current paper considers two bootstrap Monte-Carlo procedures, based on the diffusion and linear noise approximations for pure jump processes, which allow one to avoid solving the limiting covariance ODEs. The results are illustrated with both in-silico and real data examples from the LINE 1 gene retrotranscription model and compared with those obtained using other methods.

KW - 60J28

KW - 62F

KW - 92C40

KW - 92C45

KW - bootstrap monte-carlomethod

KW - density-dependent Markov jump process

KW - diffusion approximation

KW - least-squares estimation

KW - network reverse engineering

KW - reaction network

UR - http://www.scopus.com/inward/record.url?scp=84988822551&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988822551&partnerID=8YFLogxK

U2 - 10.1080/17513758.2015.1033022

DO - 10.1080/17513758.2015.1033022

M3 - Article

C2 - 25898769

AN - SCOPUS:84988822551

VL - 9

SP - 125

EP - 146

JO - Journal of Biological Dynamics

JF - Journal of Biological Dynamics

SN - 1751-3758

ER -