Figure 2
Diagram illustrating the dynamics of Eqs (1) and (2). Here, the symbol for the empty set, \(\varnothing \), represents everything that is outside of the system we are considering. There exists a constant influx of B cells at position x from a pool of naive cells given by H(x)—see Eq. (8)—occurring at rate σN. Base proliferation occurs at a rate \(\tilde{r}\), while an additional term representing birth-limited selection is given by a proliferation weighted by the affinity Q(x) at rate σM. Cells at position x can further produce offspring at a different position x′ due to mutations represented by a diffusion coefficient D. Natural death of B cells occurs at a rate gB, and a further decay is the result competition for limited resources in the GC, whose carrying capacity is given by K. Proliferation and diffusion terms are further modulated by the function G(t), representing GC activity and given by Eq. (7). A fraction δ of B cells at position x produce antibodies at position x at rate \(\tilde{k}\), weighted by their affinity Q(x), which subsequently decay at a rate gAb.
