Network Biology, 2014, 4(4): 155-169
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Network motif identification and structure detection with exponential random graph models

Munni Begum1, Jay Bagga1, Ann Blakey1, Sudipta Saha2
1Ball State University, Muncie, IN 47306, USA
2University of South Carolina, Columbia, SC, USA

Received 22 August 2014;Accepted 25 September 2014;Published online 1 December 2014

Local regulatory motifs are identified in the transcription regulatory network of the most studied model organism Escherichia coli (E. coli) through graphical models. Network motifs are small structures in a network that appear more frequently than expected by chance alone. We apply social network methodologies such as p* models, also known as Exponential Random Graph Models (ERGMs), to identify statistically significant network motifs. In particular, we generate directed graphical models that can be applied to study interaction networks in a broad range of databases. The Markov Chain Monte Carlo (MCMC) computational algorithms are implemented to obtain the estimates of model parameters to the corresponding network statistics. A variety of ERGMs are fitted to identify statistically significant network motifs in transcription regulatory networks of E. coli. A total of nine ERGMs are fitted to study the transcription factor - transcription factor interactions and eleven ERGMs are fitted for the transcription factor-operon interactions. For both of these interaction networks, arc (a directed edge in a directed network) and k-istar (or incoming star structures), for values of k between 2 and 10, are found to be statistically significant local structures or network motifs. The goodness of fit statistics are provided to determine the quality of these models.

Keywords biological networks;network motifs;transcriptional regulatory network;graphical models;exponential random graph models;Markov Chain Monte Carlo algorithms.

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