TimeCovariance Functions to Structurally Distinguish Gene Regulatory Networks
Vijayanarasimha Hindupur Pakka
University of Southampton
Srinandan Dasmahapatra
University of Southampton Adam PrugelBennett
University of Southampton Full text:
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Last modified: June 30, 2007
Abstract
Looking at stochastic timeseries 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 timeseries of proteins/mRNAs.
In this work, we use stochastic formulation for modelling simple 2gene networks. We study the models by linearizing them using the wellknown FokkerPlanck Equation. This gives the probability distribution of molecular species around the deterministic steady state solutions from which we further derive the timecovariance function between mRNAs. To study the differentiability between the networks, we propose to build a family of timecovariance plots for each network and comment on how ‘distinguishable’ these families are. One can then suggest to which network a given experimental timeseries 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 distinguishability between the different 2gene 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 timeseries data of the proteins/mRNAs. The second order timedependent statistics are very effective as they can be obtained experimentally, studied analytically and also commented upon biologically.
