TY - JOUR

T1 - Immune networks: multi-tasking capabilities near saturation

AU - Annibale, Alessia

AU - Coolen, Ton

AU - Barra, Adriano

AU - Agliari, Elena

AU - Tantari, Daniele

PY - 2013/9/27

Y1 - 2013/9/27

N2 - 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.

AB - 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.

U2 - 10.1088/1751-8113/46/41/415003

DO - 10.1088/1751-8113/46/41/415003

M3 - Article

SN - 1751-8113

VL - 46

SP - 415003

JO - Journal Of Physics A-Mathematical And Theoretical

JF - Journal Of Physics A-Mathematical And Theoretical

IS - 41

ER -