Bootstrapping least-squares estimates in biochemical reaction networks

Daniel F. Linder, Grzegorz A. Rempała

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageEnglish (US)
Pages (from-to)125-146
Number of pages22
JournalJournal of biological dynamics
Issue number1
StatePublished - 2015
Externally publishedYes


  • 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


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