Statistical mechanics of clonal expansion in lymphocyte networks modelled with slow and fast variables

TL;DR

This paper applies statistical mechanics to model the adaptive immune system, analyzing how B and T cell populations evolve on different timescales and predicting clone size distributions using a theoretical framework that aligns with experimental data.

Contribution

It introduces a novel statistical mechanics approach to model lymphocyte interactions with different timescales, deriving clone size distributions independently of network topology.

Findings

Derived stationary distributions for B and T cell populations.

Predicted B clone size distributions consistent with experimental observations.

Developed a Bethe-Peierls based framework for random network topologies.

Abstract

We study the Langevin dynamics of the adaptive immune system, modelled by a lymphocyte network in which the B cells are interacting with the T cells and antigen. We assume that B clones and T clones are evolving in different thermal noise environments and on different timescales. We derive stationary distributions and use statistical mechanics to study clonal expansion of B clones in this model when the B and T clone sizes are assumed to be the slow and fast variables respectively and vice versa. We derive distributions of B clone sizes and use general properties of ferromagnetic systems to predict characteristics of these distributions, such as the average B cell concentration, in some regimes where T cells can be modelled as binary variables. This analysis is independent of network topologies and its results are qualitatively consistent with experimental observations. In order to obtain full distributions we assume that the network topologies are random and locally equivalent to trees. The latter allows us to employ the Bethe-Peierls approach and to develop a theoretical framework which can be used to predict the distributions of B clone sizes. As an example we use this theory to compute distributions for the models of immune system defined on random regular networks.