Dynamic stability in random and scale-free B-lymphocyte networks

One of the most intriguing features of the immune system is regulation: a limited response when perturbed repeatedly. We propose a minimal network model for immune regulation in a lymphocyte network containing two types of elements: B lymphocytes and ligands that bind to their receptors. Effective interactions between B cells, mediated by other components of the immune system can be excitatory or inhibitory. In our model, B cell clones and ligand species are represented by nodes, and interactions by links. We expect that, as in many complex systems, the connectivity distribution is broad, motivating study of the model on a scale-free network; for comparison we study the same dynamics on a random graph. We characterize the dynamics of the model and its response to perturbations. Our model reproduces several key features of immune system dynamics: regulation (saturation of response), and more rapid response upon repeated perturbation with the same agents. Our results suggest that a scale-free network of interactions contributes to the regulation and dynamics of the immune system.