Affinity Maturation

Antibody maturation takes place in Germinal Centers formed in lymph nodes:

Computational Model:

 

The processes of (hyper)mutation/competition/selection lead to rapid Population Evolution:

Trait  ω   confers a fitness   f(ω)   to   N(ω)    individuals in a mixed population

Fitness  f(ω)  then governs reproduction rates according to                 

Population averages  can be defined by                                              

Mean fitness evolves (in the absence of mutations) as                            

green bullet Roland Fisher's Fundamental Theorem of Natural Selection

Including the possibility of mutations, the mean value of a trait, such as the affinity ω, evolves as

green bullet George Price's Equation:                                              

Approximating the affinity distribution by a Gaussian of mean    and variance  ,

Price's equation (assuming neutral mutations) leads to evolution of the mean as

while the variance evolves (assuming dominance of hyper-mutations) as

Within these approximations mean affinity increases along with fitness proportionately to the time-varying variance, as

To use the  equations in Affinity Maturation, we need to describe the dependence of fitness on affinity,

and process of mutations.