Unfinished Business #3: evolving metabolic networks

Over the years, we’ve developed metabolic reconstructions for a number of different organisms. It’s a slow process, with each reaction the result of a human reading and interpreting a scientific paper. Reducing these networks to graphs (collections of nodes/metabolites, connected by edges/reactions) allows us to describe their structure using familiar graph-theoretic language like “scale-free” and “small-world” [1,2]. But the networks are more than graphs. Biochemical reactions can have multiple reactants and products, with varying stoichiometry. Rewriting the reaction

S₁ + S₂ ⟺ 2 P₁ + P₂

as a collection of edges

S₁ ⟺ P₁, S₁ ⟺ P₂, S₂ ⟺ P₁, S₂ ⟺ P₂

loses important information.

It would be incredibly useful to have an algorithm that generates a metabolic network structure for a given number of metabolites. The easy way to do this is to take a pan-organism super-network like Kegg or MetaCyc, and to extract a connected, functional sub-network of the right size. This method would ensure that the result has the correct structural properties, but would give us no insight as to how this network evolved.

A better, harder approach, is to “grow” the network, adding new metabolites and reactions according to certain rules that characterise the evolutionary pressures unto which the network is subjected. This approach has again been used with graphical representations [2,3], but not stoichiometric models.

What rules would we use to evolve these networks? Unlike graphs, these metabolic models must satisfy mass-balancing, which can be written as a matrix equation [4]. I anticipate that growing metabolic networks will require our choosing solutions from this equation, by applying probabilistic attachment ideas used to grow other (signalling, social) networks.

Can we synthesise a metabolic network that looks like Kegg?

References

1. H Jeong, B Tombor, Réka Albert, ZN Oltvai, and Albert-László Barabási (2000) “The large-scale organization of metabolic networks” Nature 407:651-654. doi:10.1038/35036627
2. Henry Dorrian, Kieran Smallbone, and Jon Borresen (2012) “Size dependent growth in metabolic networks” arXiv:1210.2550
3. Albert-László Barabási and Réka Albert (1999) “Emergence of scaling in random networks” Science 286: 509-512. doi:10.1126/science.286.5439.509
4. Albert Gevorgyan, Mark Poolman, and David Fell (2008) “Detection of stoichiometric inconsistencies in biomolecular models” Bioinformatics 24:2245-2251. doi:10.1093/bioinformatics/btn425

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