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The Use of Chemostats in Microbial Systems Biology
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Least squares estimation in stochastic biochemical networks.

Grzegorz A Rempala1

  • 1Department of Biostatistics, Georgia Health Sciences University, Augusta, USA. grempala@georgiahealth.edu

Bulletin of Mathematical Biology
|July 4, 2012
PubMed
Summary

This study analyzes the asymptotic properties of least-squares estimates (LSEs) for reaction constants in biochemical networks. The findings show LSEs are consistent and asymptotically normal, converging with network size to deterministic models.

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Area of Science:

  • Biochemical network modeling
  • Stochastic dynamical systems
  • Systems biology

Background:

  • Biochemical reaction networks are often modeled as stochastic processes due to inherent randomness.
  • Parameter estimation in these models is crucial for understanding biological mechanisms.
  • Longitudinal data from partially observed systems present unique estimation challenges.

Purpose of the Study:

  • To investigate the asymptotic properties of least-squares estimates (LSEs) for reaction constants in mass-action, stochastic biochemical network models.
  • To establish the consistency and asymptotic normality of LSEs under specific conditions.
  • To provide a framework for parameter estimation in large-scale biochemical systems.

Main Methods:

  • Modeling biochemical networks as continuous-time, pure jump Markov processes.
  • Utilizing longitudinal data from partially observed system trajectories.
  • Applying statistical analysis to determine asymptotic properties of LSEs.
  • Deriving asymptotic covariance structure using systems of ordinary differential equations (ODEs).

Main Results:

  • The vector of least-squares estimates (LSEs) is shown to be jointly consistent and asymptotically normal.
  • The asymptotic covariance structure of LSEs is determined by a system of ODEs.
  • These asymptotic properties are valid as the biochemical network size increases, leading to convergence to deterministic ODE models.

Conclusions:

  • Least-squares estimation provides reliable parameter estimates for stochastic biochemical networks, especially in large systems.
  • The convergence of stochastic models to deterministic ODEs simplifies asymptotic analysis.
  • The findings offer a robust statistical foundation for analyzing complex biological systems using experimental data.