2013/05/25 by E Agliari, Elena Agliari, A Annibale +7 · 2 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Artificial Immune Systems Applications #Complex Network Analysis Techniques #Gene Regulatory Network Analysis #Graph #Human multitasking #Immune system #Phase transition #Replica #Signalling #Spurious relationship #Upper and lower bounds #cond-mat.dis-nn #physics.bio-ph #q-bio.CB
paper · pdf · doi:10.1088/1751-8113/46/41/415003
published as Journal of Physics A 46, 415003 (2013). (IOP Select: Highlights-2013)
arxiv created 2013/05/25 · openalex publication_date 2013/09/27 · arxiv updated 2015/04/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 N T T-lymphocytes can manage a number 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. © 2013 IOP Publishing Ltd.