Is the immune network a complex network?

TL;DR

This paper investigates whether the immune network modeled by cellular automata exhibits properties of complex networks, revealing different behaviors in chaotic, ordered, and transition regimes that relate to immune system dynamics.

Contribution

It classifies the immune network model's regimes as complex networks, highlighting how different phases exhibit distinct topological properties and dynamic behaviors.

Findings

Chaotic regime shows random network characteristics.

Ordered phase exhibits exponential degree distribution and power law clustering.

Transition region displays mixed behavior, not scale-free as in other biological networks.

Abstract

Some years ago a cellular automata model was proposed to describe the evolution of the immune repertoire of B cells and antibodies based on Jerne's immune network theory and shape-space formalism. Here we investigate if the networks generated by this model in the different regimes can be classified as complex networks. We have found that in the chaotic regime the network has random characteristics with large, constant values of clustering coefficients, while in the ordered phase, the degree distribution of the network is exponential and the clustering coefficient exhibits power law behavior. In the transition region we observed a mixed behavior (random-like and exponential) of the degree distribution as opposed to the scale-free behavior reported for other biological networks. Randomness and low connectivity in the active sites allow for rapid changes in the connectivity distribution of the immune network in order to include and/or discard information and generate a dynamic memory. However it is the availability of the low concentration nodes to change rapidly without driving the system to pathological states that allow the generation of dynamic memory and consequently a reproduction of immune system behavior in mice. Although the overall behavior of degree correlation is positive, there is an interplay between assortative and disassortative mixing in the stable and transition regions regulated by a threshold value of the node degree, which achieves a maximum value on the transition region and becomes totally assortative in the chaotic regime.