Inventory, Not Recollection: Why a Second Infection Is Milder — Epoche B2
A common belief holds that once you have suffered an illness your body "recognises" the germ and destroys it on sight. The word recognise suggests a memory, as if the immune system stored a mental picture and consulted it. This essay argues the opposite: the faster, milder second response is a matter of inventory , not recollection. What changes between the first and second encounter is the size and quality of a cell population, and this difference can be stated quantitatively — indeed, it can be made to predict the number of days saved. Where the repertoire comes from Lymphocytes are the white blood cells of the adaptive immune system: B cells, which secrete antibodies, and T cells, which kill infected cells and license B cells to respond. Each carries on its surface a receptor of one particular shape, and it carries only that one. The system's problem is that the shapes must be ready before the pathogen arrives, because there is no time to design one afterwards. The solution is combinatorial, and the numbers can be multiplied out. The gene for an antibody's binding region is not inherited intact; it is assembled in each developing B cell by cutting and splicing from libraries of interchangeable segments — a process called V(D)J recombination. In the human heavy-chain locus there are roughly $40$ usable V segments, $25$ D segments and $6$ J segments, and one of each is chosen, giving about $$40 \times 25 \times 6 = 6{,}000$$ heavy chains. The light chain is built from V and J segments only — about $40 \times 5$ from one light-chain locus and $30 \times 4$ from the other, some $320$ in total. Since an antibody's binding site is formed by one heavy and one light chain together, and the two are chosen independently, the combinations multiply again: $$6{,}000 \times 320 \approx 1.9 \times 10^{6}.$$ On top of this, the enzyme that joins the segments adds and deletes nucleotides at the junctions at random, which multiplies the count by a further factor of at least a thousand and produces the most variable part of the binding surface. The theoretically available repertoire exceeds $10^{9}$. What a person actually carries is smaller, and limited by a different quantity: the number of cells. The body holds on the order of $10^{12}$ lymphocytes, and receptor sequencing puts the number of distinct specificities present at any moment at roughly $10^{7}$ to $10^{8}$. Dividing the cells among the specificities gives about $10^{4}$ to $10^{5}$ cells per clone, so the frequency of cells bearing any one specificity is $$f \sim \frac{10^{4}\text{ to }10^{5}}{10^{12}} = 10^{-8}\text{ to }10^{-7}.$$ One correction to the earlier version of this essay belongs here: its summary table quoted a starting frequency of $10^{-6}$, which is inconsistent with the figure just derived. The discrepancy is instructive rather than trivial, because it depends entirely on the denominator. Direct enumeration of naive T cells specific for a single defined target, using fluorescent complexes that bind only the matching receptor, has found on the order of tens to a few hundred such cells in a mouse — a frequency near $10^{-6}$ when measured against the relevant naive subset alone, and correspondingly smaller against all lymphocytes (Moon and colleagues, 2007). The table has been corrected below to state the denominator. The primary response: selection, not instruction Antigen — the molecular target on the pathogen — does not teach a cell what to make; it merely selects the few clones that already fit and drives their proliferation. This is Burnet's clonal selection theory, and it displaced a serious rival worth naming, because the contrast is exactly the one this essay is about. Pauling had proposed in 1940 that an antibody acquires its shape by folding around the antigen as around a template — an instructionist theory, in which the antigen genuinely does deposit information. Two observations killed it. Antibodies unfolded and allowed to refold in the absence of antigen recover their specificity, so no template is needed to maintain the shape. And the DNA rearrangement described above is completed in the bone marrow, irreversibly, before the cell has ever met anything. The specificity precedes the encounter. Selection is followed by multiplication. If a clone doubles every $\tau$ hours, then after time $t$ it has undergone $t/\tau$ doublings, each multiplying the number by two, so $$N(t) = N_0\,2^{t/\tau}.$$ A week is $168$ hours. With $\tau = 12$ h this is $14$ doublings and an expansion of $2^{14} \approx 1.6\times10^{4}$; with $\tau = 8$ h it is $21$ doublings and $2^{21} \approx 2\times10^{6}$. Measured expansions in vivo tend towards the lower figure, because not every daughter cell survives and the division rate slows as antigen is cleared; the upper figure is the ceiling that unrestrained division would reach. Affinity maturation: what a thousandfold means Meanwhile, in structures called germinal centres — temporary factories that form inside lymph nodes during an infection — B cells improve their receptors. The mechanism has two parts. In one zone the cells divide while an enzyme, activation-induced cytidine deaminase, deliberately damages the DNA of the receptor's variable region at a rate near $10^{-3}$ mutations per base pair per division. Since that region is roughly $360$ base pairs long, this is about $0.36$ mutations per cell per division — a mutation every third division or so — and it is about a million times the mutation rate of ordinary genomic DNA. The cell is running a targeted, quarantined mutagenesis. In the other zone the mutants compete. Antigen is displayed on the surface of specialised cells, and a B cell must capture some of it, digest it and present fragments to helper T cells in order to receive the survival signal. A cell whose mutated receptor grips more tightly captures more antigen, presents more fragments, and receives more help. Binding strength is thereby converted into survival probability