We are looking into several biological networks to gain new insights on their structure, organization and function.  Our research benefits from a rigorous application of both traditional and spectral graph theoretic methods.

Some of our contributions are are described below.

Transcription Regulatory networks contain canonical motifs, including the Feed Forward
Loop (FFL), Single Input Module (SIM), and Multiple Input Module (MIM). A challenge
for network analysis is to identify and enumerate the motifs, required to illuminate their biological
significance.  Although there is consensus about the definition of the FFL, published definitions of the SIM
and MIM are unclear and often used inconsistently. We provided, for the first time, a complete
and consistent definition of SIM and MIM, and algorithms for enumerating SIMs and MIMs in any
network. From the algorithmic point of view, enumeration of SIMs and MIMs is substantially harder
than enumerating FFLs.

Further, the inference that these types of motifs have been selected for function rests on the
idea that their occurrences are significantly more frequent than random. Our analysis of several large
biological networks suggests, in contrast, that the frequencies of appearance of common subgraphs is
similar in natural and corresponding random networks. Indeed, certain topological features of
biological networks give rise naturally to the common appearance of the motifs. This led us to question
whether there is a good reason to believe that the structures of motifs have been selected for their
functional contribution to the operation of networks.

References:
A. S. Konagurthu and A. M. Lesk, Single and Multiple input module in regulatory networks, Proteins, (2008, in press)
A. S. Konagurthu and A. M. Lesk, On the origin of distribution patterns of motifs in biological networks. BMC systems biology (2008, in press)