Hypergraph Models of Metabolism

In this paper, we employ a directed hypergraph model
to investigate the extent to which environmental variability influences
the set of available biochemical reactions within a living cell.
Such an approach avoids the limitations of the usual complex
network formalism by allowing for the multilateral relationships (i.e.
connections involving more than two nodes) that naturally occur
within many biological processes. More specifically, we extend the
concept of network reciprocity to complex hyper-networks, thus
enabling us to characterise a network in terms of the existence
of mutual hyper-connections, which may be considered a proxy
for metabolic network complexity. To demonstrate these ideas, we
study 115 metabolic hyper-networks of bacteria, each of which
can be classified into one of 6 increasingly varied habitats.
In particular, we found that reciprocity increases significantly
with increased environmental variability, supporting the view that
organism adaptability leads to increased complexities in the resultant
biochemical networks.

• Nicole Pearcy
• Jonathan J. Crofts
• Nadia Chuzhanova

• Complexity
• hypergraphs
• reciprocity
• metabolism.

[1] M. Buchanan, G. Caldarelli, P. De Los Rios, F. Rao, M. Vendruscolo
(Eds), Networks in Cell Biology, Cambridge University Press, 2010.
[2] S. Klamt, U. Haus, F. Theis, Hypergraphs and cellular networks, PLoS
Computational Biology, 5(5) e1000385 (2009).
[3] P. Holme, Model validation of simple-graph representations of
metabolism, Journal of the Royal Society Interface, 6(40) pp. 1027–1034
(2009).
[4] P. Holme, M. Huss, Substance graphs are optimal simple-graph
representations of metabolism, Chinese Science Bulletin, 55(27–28)
pp. 3161–3168 (2010).
[5] R. Monta˜ez, M.A. Medina, R.V. Sol´e, C. Rodr´ıguez, When metabolism
meets topology: Reconciling metabolite and reaction networks, Bioessays,
32(3) pp. 246–256 (2010).
[6] Mark J. Newman, Networks: An Introduction, Oxford University Press,
2010.
[7] Ernesto Estrada, The Structure of Complex Networks, Oxford University
Press, 2011.
[8] E. Estrada, J.A. Rodriguez-Velazquez, Subgraph centrality and clustering
in complex hyper-networks, Physica A 364 pp. 581–594 (2006).
[9] W. Zhou, L. Nakhleh, Properties of metabolic graphs: biological
organization or representation artifacts?, BMC Bioinformatics, 12(132)
(2011).
[10] J. Guillaume, M. Latapy, Bipartite structure of all complex networks,
Information Processing Letters, 90 pp. 215–221 (2004).
[11] A. Ducournau, A. Bretto, Random walks in directed hypergraphs and
application to semi-supervised image segmentation, Computer Vision and
Image Understanding, 120 pp. 91–102 (2014).
[12] A. Bellaachia, M. Al-Dhelaan, Random walks in hypergraph,
in Proceedings of the 2013 International Conference on Applied
Mathematics and Computational Methods, Venice Italy, pp. 187–194
(2013).
[13] A. Vazquez, Finding hypergraph communities: a Bayesian approach
and variational solution, Journal of Statistical Mechanics: Theory and
Experiment, (2009) P07006.
[14] T. Michoel, B. Nachtergaele, Alignment and integration of complex
networks by hypergraph-based spectral clustering, Physical Review E
86(056111) (2012).
[15] S. Wasserman, K. Faust, Social Network Analysis. Methods and
Applications, Cambridge University Press, 1994.
[16] D. Garlaschelli, M.I. Loffredo, Patterns of link reciprocity in directed
networks, Physical Review Letters, 93(268701) (2004).
[17] G. Gallo, G. Longo, S. Pallottino, S. Nguyen, Directed hypergraphs and
applications, Discrete applied mathematics, 42(2) (1993).
[18] J.A. Rodr´ıguez, On the Laplacian spectrum and walk-regular
hypergraphs, Linear and Multilinear Algebra, 51(3) (2003).
[19] M. Kanehisa, The KEGG database, Silico Simulation of Biological
Processes, 247(91) (2002).
[20] A. Samal, A. Wagner, O.C.Martin, Environmental versatility promotes
modularity in genome-scale metabolic networks, BMC Systems Biology,
5(1) (2011).
[21] A. Samal, O.C. Martin, Randomizing genome-scale metabolic networks,
PloS One, 6(7) (2011).
[22] M. Parter, N. Kashtan, U. Alon, Environmental variability and
modularity of bacterial metabolic networks, BMC Evolutionary Biology,
7(1) (2007).
[23] A. Kreimer, E. Borenstein, U. Gophna, E. Ruppin, The evolution of
modularity in bacterial metabolic networks, Proceedings of the National
Academy of Sciences, 105(19) (2008).
[24] S.C. Janga, M.M. Babu, Network-based approaches for linking
metabolism with environment, Genome Biology, 9(11), (2009).
[25] J.J. Crofts, E. Estrada, A statistical mechanics description of
environmental variability in metabolic networks, Journal of Mathematical
Chemistry, 52(2) (2014).