A graph model for the evolution of specificity in humoral immunity

The immune system protects the body against health-threatening entities, known as antigens, through very complex interactions involving the antigens and the system's own entities. One remarkable feature resulting from such interactions is the immune system's ability to improve its capability to fight antigens commonly found in the individual's environment. This adaptation process is called the evolution of specificity. In this paper, we introduce a new mathematical model for the evolution of specificity in humoral immunity, based on Jerne's functional, or idiotypic, network. The evolution of specificity is modeled as the dynamic updating of connection weights in a dynamic graph whose nodes are related to the network's idiotypes. At the core of this weight-updating mechanism are the increase in specificity caused by clonal selection and the decrease in specificity due to the insertion of uncorrelated idiotypes by the bone marrow. As we demonstrate through numerous computer experiments, for appropriate choices of parameters the new model correctly reproduces, in qualitative terms, several immune functions.