Two major concepts of molecular biology are that (i) genes, the fundamental units of heredity, are encoded as sequences of chemical bases in DNA and (ii) a gene is expressed when its DNA sequence is transcribed into an RNA intermediate and , is translated into proteins. Proteins, in turn, perform regulatory, catalytic, mechanical, and electrical functions [1].

 

Gene expression is the process by which cells produce proteins from the information encoded in DNA. [1]. The information flow from DNA to proteins occur in following steps: Specialized proteins transcribe a region of DNA (gene) into Messenger RNA molecule, and RNA molecule is translated into a polypeptide chain, and polypeptides fold into three dimensional structure and modified with additional proteins to become biochemically active [1].

 

The process of gene expression allows for control at many levels. Changing the rate of transcription into RNA, stalling the process of it translation into protein, cleaving the final product protein into pieces can serve as mechanism for controlling the gene expression. Cells have evolved to use all of these mechanisms, however, regulation of the transcription is the most common. Transcription factors are the proteins that can bind to the DNA in order to regulate this process [1].

 

Genes, proteins, and metabolites can regulate one another in various ways. Regulatory proteins bind to DNA to affect the transcription of genes. Proteins can also combine to form multi-protein complexes that can take part in various functions in regulation, for example unzipping DNA or cleaving RNA. Metabolites can also attach proteins to alter their activity level. [1]. All these interactions form a complex network of regulatory control. Experimentally, it is quite hard to obtain the information on the levels of gene regulation. Major challenge in biology is to map out and model the topological and dynamical properties of these networks.

 

Recently, large amount of diverse types of genomic data are obtained to shed light on transcription regulation, e.g., DNA sequence data, micro-array gene expression data, and protein-DNA binding data. Advent of such diverse data motivated various researchers to develop computational methods to model transcription regulation.[2]. DNA-protein binding data is the direct information to understand the regulators involved in transcription. Time-series micro-array expression experiments are a complementary source of data which provides dynamic information about the expressions of thousands of genes that are activated or repressed in response to external stimuli [3].

 

An extensive studies on gene regulatory network modeling, using time-series data, have focused on continuous representation via differential equations.

 

In this model, the expression level of a gene is assumed to be the concentration of its transcript. The rate of change in the concentration of a particular transcript,  is given by a function,  of the concentrations of other RNA species;

 

,                                                                                                          (1)

 

where N is the number of transcripts in the network. In general, only a small subset of all RNA species regulates a particular transcript. In other words, the networks are sparse. [4]. Different forms for  can be adopted. A linear form for  can be represented as;

    ,                                                                                         (2)                                                                               is the relative concentration of transcript i. denotes time derivative [5] . Eqn (2) can be compactly represented in a discrete form for all data points,

 

 ,   where  ,       (3)

 

M is the number of data points. and   are  the relative expression levels of gene i, at time points  j and k respectively,  where ,  [5].

 

A significant problem in this model is the large number of parameters to be inferred. Protein-DNA binding data provides prior information for reducing the effective number of parameters of the model. In this regard, we introduce a Bayesian parameter estimation framework to integrate the time series and protein-DNA binding data in the context of linear ODE model. Binding data information is modified to indirect linkage between transcript abundance. Using the framework that was proposed by Sun et al, the network is decomposed into two components; a binary network ( ) representing the involvement of transcript j in the regulation transcript i. If , the relative binding intensity  is used to estimate the coefficient . Thus, . The observed binary binding data  is considered as the substitute of true binding, [2]. All parameters, , are treated as independent random variables. Using the Bayes rule, the posterior distribution over A matrix can be represented as;

 

,                                            (4)

 

where  is the prior, and   is the likelihood function. This framework is tested on artificial gene network and yeast data.

 

 

 

 

 

 

 

REFERENCES

 

[1] Driscoll, M. E., Gardner, T.S, Identification and control of gene networks in living organisms via supervised and unsupervised learning, Journal of Process Control 16 (2006) 303-311.

 

[2] Sun, N., Carroll, R.J, Zhao, H., Bayesian Error Analysis model for Reconstructing transcriptional regulatory networks, PNAS 103 (21) (2006), 7988-7993.

 

 

[3] Ernst, J., Vainass, O., Harbison, C. T., Simon, I., Bar-Joseph, Z., Reconstructing dynamic Regulatory maps.  Molecular Systems Biology  3 (74) (2007), 1-13.

 

[4] Gardner, T.S., Faith, J. J., Reverse-engineering transcription control networks.  Physics of Life Reviews  2  (2005), 65-88.

 

[5] Bansal, M., Giusy, D.G., Bernado, D., Inference of gene regulatory networks and compound mode of action from time course gene expression profiles. Bioinformatics 22 (2006), 815-822