B cells hill-climb toward higher antigen affinity by repeating a cycle of mutation and selection: somatic hypermutation at roughly 10⁻³ per base pair per division, followed by competitive selection that keeps only the improved binders. Real antibody affinity constants rise from around 10⁵ M⁻&sup9; in germline antibodies to as high as 10⁵ M⁻&sup9; after maturation — a real, citable four-order-of-magnitude climb, corrected here from an earlier, overstated version of this same claim in this book's own index.
Inside a germinal center, B cells cycle between a dark zone, where they proliferate and undergo somatic hypermutation of their immunoglobulin genes at a rate on the order of 10⁻³ changes per base pair per cell division, and a light zone, where they compete for limited T-cell help and antigen displayed by follicular dendritic cells; only the clones whose mutated receptor binds antigen well enough survive and re-enter the cycle. Recent work (2025) additionally shows this hypermutation rate is not simply constant — B cells that have undergone many divisions actively suppress their own mutation rate, a regulatory mechanism that helps already-improved clones avoid picking up further, potentially deleterious mutations.
Germinal-center affinity maturation is naturally read as an iterated K→F cycle: each round, mutated receptors cross a selection threshold (K) if their affinity clears the competitive bar set by light-zone selection, and the surviving population folds (F) onto a higher-affinity attractor before the next round of mutation reopens the cycle. This is a real iterative improvement process, structurally similar to how this corpus's operator chain describes repeated compression-and-fold cycles elsewhere — and the honest limit of the analogy is that nothing in the measured affinity numbers above is claimed to converge specifically to this corpus's proved constants (ε₀=1/3, τ=2, or any n-bonacci value). The iterative structure is the genuine correspondence; the specific numbers are not being forced to match anything beyond themselves.
Victora, G.D., Nussenzweig, M.C. (2012). Germinal centers. Annu. Rev. Immunol. 30, 429–457.
Tas, J.M.J. et al. (2016). Visualizing antibody affinity maturation in germinal centers. Science 351, 1048–1054. — Source for per-clone fold-increase figures.
Regulated somatic hypermutation enhances antibody affinity maturation. Nature (2025). — Source for the mutation-rate self-suppression finding in §1.
See also: Ch 12 — VDJ Recombination · Book VI Index