Power-law distributions of T-cell clone abundances in a non-neutral birth-death-immigration model

T-cells can then die or proliferate to produce new T-cells carrying the same receptor. This process can be described by a stochastic multitype birth-death-immigration (BDI) process. However, predictions of a simple neutral BDI process, where cells of all receptor types have the same immigration, birth, and death rates, do not reproduce the experimentally measured power-law clone size distributions. However, it is known that T-cell proliferation depends on its specific affinity to self-ligands and T-cells of certain receptors are more likely to be produced in the thymus. Here, we study a non-neutral BDI model, in which each clone has a specific immigration rate and a specific peripheral proliferation rate arising from different ligand affinities. Realistic distributions of immigration rates are generated from measured DNA, while hypothetical distributions of proliferations rates are tested. We also include a carrying capacity through the death rate to model the competition of lymphocytes for cytokines and to ensure homeostasis of the system. The effects of sampling of T-cells from an organism are also calcuted. We show that a non-neutral model with sampling can describe the experimentally observed clone size distributions provided the appropriate T-cell heterogeneity is employed.