  The immune response to an acute primary infection is a coupled process of
antigen proliferation, molecular recognition by naive B cells, and their
subsequent proliferation and antibody shedding. This process contains a
fundamental problem: the recognition of an exponentially time-dependent antigen
signal. Here we show that B cells can efficiently recognise new antigens by a
tuned kinetic proofreading mechanism, where the molecular recognition machinery
is adapted to the complexity of the immune repertoire. This process produces
potent, specific and fast recognition of antigens, maintaining a spectrum of
genetically distinct B cell lineages as input for affinity maturation. We show
that the proliferation-recognition dynamics of a primary infection is a
generalised Luria-Delbr\"uck process, akin to the dynamics of the classic
fluctuation experiment. This map establishes a link between signal recognition
dynamics and evolution. We derive the resulting statistics of the activated
immune repertoire: antigen binding affinity, expected size, and frequency of
active B cell clones are related by power laws. Their exponents define the
class of generalised Luria-Delbr\"uck processes; they depend on the antigen and
B cell proliferation rate, the number of proofreading steps, and the lineage
density of the naive repertoire. Empirical data of mouse immune repertoires are
found to be consistent with activation involving at least three proofreading
steps. Our model predicts key clinical characteristics of acute infections,
including the emergence of elite neutralisers and the effects of immune ageing.
More broadly, our results establish acute infections as a new probe into the
global architecture and functional principles of immune repertoires.

Populations and Evolution;Subcellular Processes