Cellular processes operate on a wide range of time and length scales to produce complex and intricate dynamics. It is a great challenge to understand both how these dynamical patterns are produced, as well as why they are produced; that is, what functional or evolutionary role do they play? This is one of the most fruitful areas in which to apply the ideas of complex networks. Living cells have all the prerequisites for a useful representation as networks. First, cellular systems contain numerous non-identical active components—genes, proteins, RNA, etc. These are the nodes of the network. Second, there are many interactions between these components, which form the links between the nodes. Not every pair of components interacts, so the resulting network is not fully connected, nor is it a tree or other simple topology. Thus, cellular networks provide plenty of scope for analysing their structure and graph-theoretic properties, and numerous studies have taken advantage of this (see (1) for reviews and [2–9] for some examples).
Network representations of cellular systems can easily be augmented to address dynamical issues. Each node can be associated with a dynamical variable which could represent, for example, the concentration of that protein or the level of expression of that gene. Equations or rules governing the temporal dynamics of these variables can then be written, where the network structure determines which variables interact with each other. This usually requires encoding more information about the interactions into the network representation. For instance, apart from knowing that one node links to another, one needs to know the sign and strength of the interaction. However, in a network picture it is sometimes difficult to encode more detailed molecular information, such as whether the binding of a protein to DNA is accompanied by DNA looping, or whether a small molecule that binds to a protein can also bind equally well when that protein is bound to DNA.
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We thank our collaborators, with whom much of the work described here was done: J. Axelsen, I. Dodd, M. Micheelsen, S. Pigolotti, S. Semsey, G. Thon and G. Tiana. We acknowledge support from The Danish National Research Foundation and the Villum Kann Rasmussen Foundation.
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