Cells of the immune system recognize antigens through cell-surface receptors, whose genes rearrange from segment libraries, creating a highly diverse repertoire of receptors capable of recognizing most proteins in the biological universe. This repertoire is further shaped by positive selection for functional receptors, deletion of receptors that recognize self proteins, mutations, and interaction with antigens. In studying immunological learning and memory, we face the challenge of modeling repertoire metadynamics, from stochastic generation of new clones, through competition between clones, to emergent cognitive properties. I will demonstrate this type of complex models using the example of lymphocyte gene rearrangement and clonal selection.

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1998-1999 Mathematics in Biology