Immune networks: multi-tasking capabilities near saturation

Alessia Annibale, Ton Coolen, Adriano Barra, Elena Agliari, Daniele Tantari

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)


Pattern-diluted associative networks were recently introduced as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T- and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with NT T-lymphocytes can manage a number $N_B={\mathcal {O}}(N_T^\delta )$ of B-lymphocytes simultaneously, with δ < 1. Here we study this model in the extensive load regime NB = αNT, with a high degree of pattern dilution, in agreement with immunological findings. We use graph theory and statistical mechanical analysis based on replica methods to show that in the finite-connectivity regime, where each T-lymphocyte interacts with a finite number of B-lymphocytes as NT → ∞, the T-lymphocytes can coordinate effective immune responses to an extensive number of distinct antigen invasions in parallel. As α increases, the system eventually undergoes a second order transition to a phase with clonal cross-talk interference, where the system's performance degrades gracefully. Mathematically, the model is equivalent to a spin system on a finitely connected graph with many short loops, so one would expect the available analytical methods, which all assume locally tree-like graphs, to fail. Yet it turns out to be solvable. Our results are supported by numerical simulations.
Original languageEnglish
Pages (from-to)415003
JournalJournal Of Physics A-Mathematical And Theoretical
Issue number41
Publication statusPublished - 27 Sept 2013


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