Skip to main content
Article thumbnail
Location of Repository

Bayesian inference of biochemical kinetic parameters using the linear noise approximation

By Michal Komorowski, Bärbel Finkenstädt, Claire V. Harper and D. A. (David A.) Rand


Background \ud Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data.\ud Results \ud We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo.\ud Conclusion \ud The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods

Topics: QH426
Publisher: BioMed Central Ltd.
OAI identifier:

Suggested articles


  1. (1992). A Rigorous Derivation of the Chemical Master Equation. Physica A doi
  2. (2004). A: Multivariate analysis of noise in genetic regulatory networks. doi
  3. (2002). Assigning numbers to the arrows: Parameterizing a gene regulation network by using accurate expression kinetics. doi
  4. (2008). Bayesian inference for a discretely observed stochastic kinetic model. Statistics and Computing doi
  5. (2007). Bayesian inference for dynamic transcriptional regulation; the Hes1 system as a case study. Bioinformatics doi
  6. (2005). DJ: Bayesian Inference for Stochastic Kinetic Models Using a Diffusion Approximation. Biometrics doi
  7. (1995). Does replication-induced transcription regulate synthesis of the myriad low copy number proteins of Escherichia coli? Bioessays doi
  8. (1977). Exact stochastic simulation of coupled chemical reactions. doi
  9. (2003). Fast Evaluation of Fluctuations in Biochemical Networks With the Linear Noise Approximation. Genome Res doi
  10. (2000). Floudas C: Global Optimization for the Parameter Estimation of Differential-Algebraic Systems. doi
  11. (2008). G: Single-Molecule Approach to Molecular Biology in Living Bacterial Cells. Annual Review of Biophysics doi
  12. (2007). H: A Hierarchy of Approximations of the Master Equation Scaled by a Size Parameter. doi
  13. (2002). Introduction to time series and forecasting doi
  14. (2003). JR: Parameter Estimation in Biochemical Pathways: A Comparison of Global Optimization Methods. Genome Res doi
  15. (2009). Kierzek A: Translational Repression Contributes Greater Noise to Gene Expression than Transcriptional Repression. Biophysical Journal doi
  16. (2001). Likelihood Inference for Discretely Observed Nonlinear Diffusions. Econometrica doi
  17. (2006). Lopes HF: Markov Chain Monte Carlo Stochastic Simulation for Bayesian Inference 2nd edition. Chapman & Hall/CRC; doi
  18. (1998). Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics doi
  19. (2005). O'Shea EK: Noise in Gene Expression: Origins, Consequences, and Control. Science doi
  20. (2007). Oudenaarden A: Stochastic gene expression out-of-steady-state in the cyanobacterial circadian clock. Nature doi
  21. (2007). Parameter estimation for differential equations: a generalized smoothing approach. doi
  22. (2006). Parameter estimation in stochastic biochemical reactions. Systems Biology, doi
  23. (2002). PS: Stochastic Gene Expression in a Single Cell. Science
  24. (2008). Reconstruction of transcriptional dynamics from gene reporter data using differential equations. Bioinformatics doi
  25. (2007). Simulated maximum likelihood method for estimating kinetic rates in gene expression. Bioinformatics doi
  26. (1987). Statistical Thermodynamics of Nonequilibrium Processes doi
  27. (1992). Stochastic differential equations: an introduction with applications 3rd edition. doi
  28. (1974). Stochastic differential equations: theory and applications WileyInterscience;
  29. (2009). Stochastic modelling for quantitative description of heterogeneous biological systems. Nature Reviews Genetics doi
  30. (2003). Systems Biology Is Taking Off. Genome Res
  31. (2005). TD: Counting Cytokinesis Proteins Globally and Locally in Fission Yeast. Science doi
  32. (1972). The Relationship between Stochastic and Deterministic Models for Chemical Reactions. doi
  33. (2001). van Oudenaarden A: Intrinsic noise in gene regulatory networks. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.