Statistics of Cellular Evolution in Leukemia: Allelic Variations in Patient Trajectories Based on Immune Repertoire Sequencing

The evolution of a cancer system consisting of cancer clones and normal cells is a complex dynamic process with multiple interacting factors including clonal expansion, somatic mutation, and sequential selection. As a typical example, in patients with chronic lymphocytic leukemia (CLL), a monoclonal population of transformed B cells expands to dominate the B cell population in the peripheral blood and bone marrow. This expansion of transformed B cells suggests that they might evolve through processes distinct from those of normal B cells. Recent advances in next generation sequencing enable the high-throughput identification and tracking of individual B cell clones through sequencing of the V-D-J junction segments of the immunoglobulin heavy chain (IGH). Here we developed a statistical approach to modeling cellular evolution of the immune repertoire. Adapting the infinitely many alleles model from population genetics, we studied abnormalities occurring in the immune repertoire of patients as substantial deviations from the null model. The Ewens sampling test (EST) distinguished the immune repertoires of CLL patients with imminent relapse from healthy controls and patients in sustained remission. Extensive simulations based on sequencing data showed that EST is sensitive in detecting cancer-related derangements of the IGH repertoire. In addition, we suggest two potentially useful parameters: the rate at which donors B cell clones enter the circulation and the average time to regenerate a transplanted immune repertoire, both of which help to distinguish relapsing CLL patients from those in sustained remission and provide additional information about the dynamics of immune reconstitution in the latter patients. We anticipate that our models and statistics will be useful in diagnosis and prognosis of leukemia, and may be adapted for application to other diseases related to adaptive immunity.