Abstract
Understanding relationships between architectural properties of gene-regulatory networks (GRNs) has been one of the major goals in systems biology and bioinformatics, as it can provide insights into, e.g., disease dynamics and drug development. Such GRNs are characterized by their scale-free degree distributions and existence of network motifs – i.e., small-node subgraphs that occur more abundantly in GRNs than expected from chance alone. Because these transcriptional modules represent “building blocks” of complex networks and exhibit a wide range of functional and dynamical properties, they may contribute to the remarkable robustness and dynamical stability associated with the whole of GRNs. Here, we developed network-construction models to better understand this relationship, which produce randomized GRNs by using transcriptional motifs as the fundamental growth unit in contrast to other methods that construct similar networks on a node-by-node basis. Because this model produces networks with a prescribed lower bound on the number of choice transcriptional motifs (e.g., downlinks, feed-forward loops), its fidelity to the motif distributions observed in model organisms represents an improvement over existing methods, which we validated by contrasting their resultant motif and degree distributions against existing network-growth models and data from the model organism of the bacterium Escherichia coli. These models may therefore serve as novel testbeds for further elucidating relationships between the topology of transcriptional motifs and network-wide dynamical properties.
Highlights
The dynamics of complex networks are derived using graph theoretical measurements that are deduced from the topology of the network entities and their relationships
To further understand how transcriptional motifs “interact” via regulatory bonds, we have previously studied how the individual genes of E. coli are distributed through the feed-forward loops (FFLs) of its Gene regulatory networks (GRNs) (Mayo et al, 2012)
To conceptualize a downlink-based preferential attachment method, which is a collection of nodes, we must first identify a way to express a downlink motif from the substrate network into a single, effective “lumped” node. To achieve this we propose to apply a network transformation to the E. coli largest connected component (LCC), defined so that each node of the transformed network represents a downlink derived from the LCC; downlink “nodes” are connected to others with edges weighted by the number of nodes shared between the two downlink motifs
Summary
The dynamics of complex networks are derived using graph theoretical measurements that are deduced from the topology of the network entities and their relationships. Science collaboration networks are portrayed using nodes that represent scientists or authors, and links that connect pairs of nodes that coauthored an article (Albert and Barabási, 2002) Unlike engineered networks such as wireless sensor networks (Li et al, 2012) and airline transportation networks (Bensong et al, 2010), science collaboration networks fall under the “small world” category of Modified preferential attachment complex networks due to their smaller average over the ensemble of shortest connected paths through a network. Unlike engineered communication networks [as in Ghosh et al (2005)], GRNs exhibit a unique withstanding property – a phenomenon known as “Biological Robustness” (Kitano, 2004, 2007), which describes an ability of individual genes to adapt to and potentially resist disturbances to gene activity based, in part, on their connectivity to other genes of the network (Prill et al, 2005). Such a useful property could be potentially exploited to design engineered networks with similar communication properties (Ghosh et al, 2011; Kamapantula et al, 2012, 2014 and Kamapantula et al, under review)
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