Fitness of B cells in Germinal Center

The mutating B cell Receptor (BCR) binds to spikes of presented virus:

Fitness of the maturing B cells depends on receptor affinity ω, and spike density n, qualitatively as:

Mutations are assumed not to change the mean, but modify the variance (by μ)

Approximating the affinity distribution by a Gaussian of mean  and variance , Price's equation leads to

With these approximations, the equations are easily integrated to yield:

where         ,    and      .

In the above calculation, as in a more detailed agent based model, affinity is a non-monotonic function of target density:

Optimal affinity is achieved at target (spike) density of less than ~1 per area spanned by the BC:

too few targets at low density to be productive, too many targets at high density to be competitive.

In more detail, B cell attempts to pull in and digest the virus, with one or both hands:

Optimal affinity (and broadest variability) is achieved when target (spike) density is

a fraction of of area spanned by the B cell receptor.

Next (Optimal density) Outline Introduction Affinity Maturation Fitness & Evolution Optimal density Broadly neutralizing Abs EMF dynamics Summary