(573f) Structural Analysis of Biological Regulatory Networks

Systems biology is an emerging field of biological research devoted to developing a systems-level understanding of genetic or metabolic pathways by investigating the inter-relationships and interactions of RNA transcripts, proteins and metabolites [1]. Mathematical systems biology is the application of systems and control theory to this end. Structural properties of biological systems are of particular interest to systems biologists. These include the network of gene interactions and biochemical pathways, as well as the mechanisms by which such interactions modulate the physical properties of intracellular and multicellular structures [2]. Progress in experimental techniques like genome sequencing and high throughput measurements have made it possible to collect large amounts of data that can be used in the systems level analysis of biological systems.

High dimensional data sets generated by high-throughput techniques like DNA microarray are the outputs of complex networked systems which are driven by transcription factors/regulatory signals. Determining which regulatory signals are active (and their strengths, if possible) is an important problem in the analysis of Gene Regulatory Networks (GRN). Typical quantitative approaches include PCA [3], SVD[4], ICA [5]. However, there are two main problems with these approaches. The first is that these assumptions are difficult to justify or interpret from a biological standpoint. The second is that these do not incorporate available structural or connectivity information which can be obtained using bioinformatics tools such as PAINT [6]. A recently published quantitative technique, (NCA [7]) has been shown to respect the available connectivity structure, for a certain class of networks. However, it cannot be applied when the connectivity structure does not belong to the specified class.

In many situations, it is often the case that it is possible to fix certain parametric entries that capture the system information at zero, while the other entries may be known with less precision. In other words, the system is structurally constrained, as in the the above situation. This has led to the study of certain structural properties of the system. A system possesses a structural property if "almost every" system with the same structure has this property. Structural analysis has found several applications in control, fault diagnosis, sensor placement etc.

In this contribution, we formally define certain structural properties that are useful in the analysis of GRN, viz., structural observability and distinguishability. We then describe an algorithmic approach to determine which regulatory signals are active, based on the available microarray data and structural connectivity information.

The proposed method can be applied to any network, for which the connectivity structure is known. The method is demonstrated on synthetic networks and yeast cycle network using publicly available microarray data from cell cycle experiments. Comparison with known cell cycle indicate that a significant proportion (50-60%) of the dynamics predicted from measured microarray data can be explained by structural and connectivity analysis. This approach can be complemented with a quantitative method, if applicable. This approach is particularly useful when the the reliability and precision of quantitative data is questionable.

References:

[1] O. Wolkenhauer. Mathematical modelling in the post-genome era: understanding genome expression and regulation- a system theoretic approach. BioSystems, 65: 1.18, 2002.

[2] H. Kitano. Systems biology: A brief overview. Science, 295:1662.1665, 2002.

[3] S. Raychaudhuri, J.M. Stuart, and R.B. Altman. Principal components analysis to summarize microarray experiments: application to sporulation time series. In Pacific Symposium on Biocomputing 2000, 2000.

[4] W. Liebermeister. Linear modes of gene expression determined by independent component analysis. Bioinformatics, 18:51.60, 2002.

[5] M.K.S. Yeung, J. Tegnxer, and J.J. Collins. Reverse engineering gene networks using singular value decomposition and robust regression. PNAS, 99:6163.6168, 2002.

[6] R. Vadigepalli, P. Chakravarthula, D.E. Zak., J.S. Schwaber, and G.E. Gonye. PAINT: A promoter analysis and interaction network generation tool for genetic regulatory network identification. OMICS: A Journal of Integrative Biology, 7:235.252, 2003.

[7] J. Liao, R. Boscolo, Y-L. Yang, L.M. Tran, C. Sabatti, and V.P. Roychowdhury. Network component analysis: Reconstruction of regulatory signals in biological systems. PNAS, 100:15522.15527, 2003.