Network-of-queues approach to B-cell-receptor affinity discrimination

The immune system is one of the most complex signal processing machineries in biology. The adaptive immune system, consisting of B and T lymphocytes, is activated in response to a large spectrum of pathogen antigens. B cells recognize and bind the antigen through B-cell receptors (BCRs) and this is fundamental for B-cell activation. However, the system response is dependent on BCR-antigen affinity values that span several orders of magnitude. Moreover, the ability of the BCR to discriminate between affinities at the high end (e.g., 10^{9}M^{-1}-10^{10}M^{-1}) challenges the formulation of a mathematical model able to robustly separate these affinity-dependent responses. Queuing theory enables the analysis of many related processes, such as those resulting from the stochasticity of protein binding and unbinding events. Here we define a network of queues, consisting of BCR early signaling states and transition rates related to the propensity of molecular aggregates to form or disassemble. By considering the family of marginal distributions of BCRs in a given signaling state, we report a significant separation (measured as Jensen-Shannon divergence) that arises from a broad spectrum of antigen affinities.