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Structure versus function: a topological perspective on immune networks

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Abstract

Many recent advances have been made in understanding the functional implications of the global topological properties of biological networks through the application of complex network theory, particularly in the area of small-world and scale-free topologies. Computational studies which attempt to understand the structure–function relationship usually proceed by defining a representation of cells and an affinity measure to describe their interactions. We show that this necessarily restricts the topology of the networks that can arise—furthermore, we show that although simple topologies can be produced via representation and affinity measures common in the literature, it is unclear how to select measures which result in complex topologies, for example, exhibiting scale-free functionality. In this paper, we introduce the concept of the potential network as a method in which abstract network topologies can be directly studied, bypassing any definition of shape-space and affinity function. We illustrate the benefit of the approach by studying the evolution of idiotypic networks on a selection of scale-free and regular topologies, finding that a key immunological property—tolerance—is promoted by bi-partite and heterogeneous topologies. The approach, however, is applicable to the study of any network and thus has implications for both immunology and artificial immune systems.

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Notes

  1. Note that the structure of this network is rarely given any thought when choosing a combination of shape-space and affinity function in the AIS literature.

  2. Though strictly speaking it is only the distributions that are scale-free, scales can be present in other network properties.

  3. Theoretical studies in both disciplines tend to study low-dimensional models; although this is clearly in contrast to realistic engineering problems which are characterized by high-dimensionality, it still allows some insights to be gained.

  4. However, this has recently begun to be addressed by (McEwan and Hart 2008) using an approach which attempts to ground machine-learning more thoroughly in an immunological context with proposed benefits in terms of scaling and avoiding the ’curse of dimensionality’.

  5. Except for cells at the edges as described in 5.1.1.

  6. The same also holds at very large values of r when the stimulation circles overlap.

  7. Despite known regularity in the underlying networks.

  8. The effect is even more pronounced when sampling biological data: (Stumpf et al. 2005) show that yeast interactome maps for example generated by yeast two-hybrid (Y2H) assay data cover only approximately 3–9% of the complete interactome (Han et al. 2005).

  9. This could be easily modified and does not weaken the results.

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Authors and Affiliations

  1. Edinburgh Napier University, Edinburgh, Scotland, UK

    Emma Hart

  2. IRIDIA, Universite de Bruxelles, Bruxelles, Belgium

    Hugues Bersini & Francisco Santos

Authors
  1. Emma Hart
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  2. Hugues Bersini
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  3. Francisco Santos
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Correspondence to Emma Hart.

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Hart, E., Bersini, H. & Santos, F. Structure versus function: a topological perspective on immune networks. Nat Comput 9, 603–624 (2010). https://doi.org/10.1007/s11047-009-9138-8

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