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 International Conference on Complex Systems (ICCS2007)

Time-Covariance Functions to Structurally Distinguish Gene Regulatory Networks

Vijayanarasimha Hindupur Pakka
University of Southampton

Srinandan Dasmahapatra
University of Southampton

Adam Prugel-Bennett
University of Southampton

     Full text: Not available
     Last modified: June 30, 2007

Looking at stochastic time-series of gene products such as mRNAs and proteins is vital for studying properties of Gene Regulatory Networks. The question that we ask is whether, each structurally different regulatory network exhibits individual statistical signatures which are noticeable in the time-series of proteins/mRNAs.

In this work, we use stochastic formulation for modelling simple 2-gene networks. We study the models by linearizing them using the well-known Fokker-Planck Equation. This gives the probability distribution of molecular species around the deterministic steady state solutions from which we further derive the time-covariance function between mRNAs. To study the differentiability between the networks, we propose to build a family of time-covariance plots for each network and comment on how ‘distinguishable’ these families are. One can then suggest to which network a given experimental time-series data belongs to. To build a family of covariance plots, we need to scan the immensely huge parameter space. We suggest procedures to reduce the dimension and size of this parameter space to manageable limits.

Current results reveal a clear distinguish-ability between the different 2-gene networks. Also, we show the dependence of models on each parameter using eigenvalue perturbation analysis, which can be used to reduce the parameter space and build the families of covariance plots.

Finally, we conclude by claiming that the structures of simple regulatory networks can be retrieved given the time-series data of the proteins/mRNAs. The second order time-dependent statistics are very effective as they can be obtained experimentally, studied analytically and also commented upon biologically.

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