(390c) SHREDing a Biochemical Network Into Hierarchical Modules

Hierarchical modularity has emerged as an
organizational principle of biochemical networks, providing insights into the
coordinated regulation of reactions within and across pathways. In principle, the
modularity of a biochemical network should allow the system to be partitioned into
minimally interdependent parts, which in turn can facilitate detailed analysis
of each part in the context of the overall system. In practice, modularity
analysis has often relied on ad hoc
decisions to mainly corroborate existing knowledge. While there is general
agreement that a module should consist of a biologically meaningful group of
connected components in the network, there is little consensus on the metric
needed to quantitatively evaluate the quality of a partition. The goal of this
study is to investigate a novel metric that can be used to systematically partition a biochemical network into functionally
relevant groups of reactions. The metric, termed the Shortest Retroactive
Distance (ShReD),
characterizes the retroactive connectivity between any two reactions in a
network arising from potential feedback interactions, thereby grouping togther
network components which mutually influence each other. We evaluate the metric
using two test networks: epidermal growth factor receptor (EGFR) signaling and liver
drug transformation.    

Each test network was abstracted as a
reaction-centric directed. An edge was drawn between
two reaction nodes existed if one reaction produced either a reactant or
allosteric effector of the other reaction. The ShReD
between two reactions was calculated as the path-length of the shortest cycle that
involves both reaction nodes. Using ShReD as the measure of connectivity, we
adapted Newman's algorithm¹ to obtain a set of hierarchical partitions.
Briefly, Newman's original algorithm divides
an undirected network such that the
resulting partition maximizes the number of connections within each sub-network relative
to the number of expected connections between two randomly chosen nodes in
the network. In this study, the partitions were performed based on the ShReD metric, rather than the undirected connectivity used
in Newman's work.

For the EGFR network, the
partitions obtained using Newman's original algorithm and ShReD
were largely similar (not shown). Importantly, the ShReD
partition generated reaction modules with larger numbers of cyclical
interactions. For the metabolic network, which included cofactors, the ShReD partition again generated hierarchical modules whose
compositions compared favorably with canonical associations based on textbook
biochemistry (Fig. 1). The Newman partition was unable to generate any
hierarchy. Interestingly, the ShReD partition
revealed a 'redox' module involving reactions of xenobiotic transformation,
glucose metabolism, pyruvate metabolism, and lipid metabolism interacting
through shared production and consumption of NADPH.

Fig. 1. ShReD-based hierarchical partition of a hepatocyte metabolic network.
The pie charts represent modules of reactions. Each pie represents the fraction
of  

In
conclusion, our novel metric ShReD, combined with Newman's algorithm, is to our
knowledge the first modularity analysis technique that partitions a biochemical
network to preserve cylical interactions between reactions.

1. Newman, ME (2006). Proc Natl Acad Sci
U S A. 103(23): 8577-82.