Abstract
Tailored graph ensembles are a developing bridge between statistical mechanics and biologicalnetworks. In this thesis, this concept is used to generate a suite of rigorous mathematical tools
to quantify and compare the topology of cellular signalling networks.
Earlier published results to quantify the entropy of constrained random graph ensembles are
extended by looking at constraints relating to directed graphs, bipartite graphs, neighbourhood
compositions and generalised degrees. To incorporate constraints relating to the average number
of short loops, a number of innovative techniques are reviewed and extended, moving the
analysis beyond the usual tree-like assumption. The generation of unbiased sample networks
under some of these new constraints is studied.
A series of illustrations of how these concepts may be applied to systems biology are developed.
Topological observables are obtained from real biological networks and the entropy of the associated random graph ensemble is calculated. Certain studies on over-represented motifs are
replicated and the influence of the choice of null model is considered. The correlation between
the topological role of each protein and its lethality is studied in yeast.
Throughout, this document aims to promote looking at a network as a realisation satisfying
certain constraints rather than just as a list of nodes and edges. This may initially seem to be
an abstract approach, but it is in fact a more natural viewpoint within which to consider many
fundamental questions regarding the origin, function and design of observed real networks.
| Date of Award | 2014 |
|---|---|
| Original language | English |
| Awarding Institution |
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| Supervisor | Ton Coolen (Supervisor) & Franca Fraternali (Supervisor) |