Retrieving Infinite Numbers of Patterns in a Spin-Glass Model of Immune Networks

TL;DR

This paper uses statistical mechanics to show how immune networks with finite connectivity can recall many defense strategies simultaneously, unlike neural networks, due to their specific network topology.

Contribution

It introduces a model of immune networks with finite connectivity and demonstrates how this topology enables extensive parallel immune responses.

Findings

Finite connectivity allows managing many immune clones simultaneously.

Weak ergodicity breaking supports multiple defense strategies.

The model explains immune system's parallel recall capabilities.

Abstract

The similarity between neural and immune networks has been known for decades, but so far we did not understand the mechanism that allows the immune system, unlike associative neural networks, to recall and execute a large number of memorized defense strategies {\em in parallel}. The explanation turns out to lie in the network topology. Neurons interact typically with a large number of other neurons, whereas interactions among lymphocytes in immune networks are very specific, and described by graphs with finite connectivity. In this paper we use replica techniques to solve a statistical mechanical immune network model with `coordinator branches' (T-cells) and `effector branches' (B-cells), and show how the finite connectivity enables the system to manage an extensive number of immune clones simultaneously, even above the percolation threshold. The system exhibits only weak ergodicity breaking, so that both multiple antigen defense and homeostasis can be accomplished.