Immune Response to a Variable Pathogen: A Stochastic Model with Two Interlocked Darwinian Entities

Figure 13

Computer result of the maturation process of T-lymphocytes. First a naïve T-lymphocyte (𝐿_Naive, green) in bone marrow or thymus undergoes T-cell receptor rearrangement (𝛽-selection). T-cells with high affinity to self-peptides MHC (𝐿_Self, black) are eliminated (negative selection), whereas T-cells with T cell receptors that are able to bind self-peptides MHC molecules with at least a weak affinity (𝐿_Mat->𝐼, blue and 𝐿_Mat->𝐴, red) survive (positive selection) and circulate in the peripheral lymphatic system. The matured T-lymphocyte, recognizing the antigen by high affinity to the antigen-loaded MHC (𝐿_Mat->𝐴, red), transforms into an effector cell and proliferates. Glimpses at generation at 𝑛=27 and 𝑛=83. Left: probabilities 𝑊^𝑆_𝑛(𝑁) of finding 𝑁 individuals of T lymphocytes (0≤𝑁≤𝑁_max). Upper right: extinction probability 𝑊(0) as a function of generations 𝑛. Lower right: average of T lymphocytes 𝐿 as a function of generations n. Parameter values and their change during the dynamics (a) 𝑛<50 (b) 50≤𝑛<100 (c) 100≤𝑛: maximal total number 𝑁_max=16; 𝛼_𝐿Naive=0.1, 𝛼_𝐿Self=0.1, 𝛼_{𝐿Mat->𝐼}=0.1, 𝛼_{𝐿Mat->𝐴}=0.1, 𝜌_𝐿Naive=2, 𝜌_𝐿Self=1, 𝜌_{𝐿Mat->𝐼}=1, 𝜌_𝐿Mat->A=1/4/1, 𝛽_𝐿Naive=0.95, 𝛽_𝐿Self=0.75, 𝛽_{𝐿Mat->𝐼}=0.99/0.75/0.75, 𝛽_{𝐿Mat->𝐴}=0.99/0.98/0.75, 𝜀_{𝐿Naive𝐿Self}=0.7, 𝜀_{𝐿Naive𝐿Mat->𝐼}=0.7, 𝜀_{𝐿Naive𝐿Mat->𝐴}=0.7.