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Bayesian inference of biochemical kinetic parameters using the linear noise approximation

DOI: 10.1186/1471-2105-10-343

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Abstract:

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.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.The estimation of parameters in biokinetic models from experimental data is an important problem in Systems Biology. In general the aim is to calibrate the model so as to reproduce experimental results in the best possible way. The solution of this task plays a key role in interpreting experimental data in the context of dynamic mathematical models and hence in understanding the dynamics and control of complex intracellular chemical networks and the construction of synthetic regulatory circuits [1]. Among biochemical kinetic systems, the dynamics of gene expression and of gene regulatory networks are of particular interest. Recent developments of fluorescent microscopy allow us to quantify changes in protein concentration over time in single cells (e.g. [2,3]) even with single molecule precision (see [4] for review). Therefore an abundance of data is becoming available to estimate parameters of mathematical models in many important cellular systems.Single cell imaging techniques have revealed the stochastic nature of biochemical reactions (see [5] for review) t

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