Repertoire Ageing and Durable Protection: Thymic Involution and the Optimal Re-Boost Interval

Immune time enters twice, each measured. Thymic involution shrinks the education window, so positive and negative selection truncate oppositely: autoreactive escape RISES while naive export FALLS. Under a fixed booster budget, protection peaks when the re-boost interval equals the measured memory half-life; too frequent or too sparse loses ground. DIRECTION/CLASS only, not a real-time schedule or medical advice. Grade [V].

Two ageing phenomena are read off the same kernel. Thymic involution is the same central-tolerance education run with a slowly shrinking window: as the window shrinks (model-time 24 → 8, absolute scale [O]) the measured escaped-autoreactive fraction RISES (0.29% → 3.71% of the cohort) while the healthy naive-export rate FALLS (32.9% → 15.9%), the escapees concentrated just above threshold (mean self-affinity 1.075× the spinodal). For protective memory that wanes by the measured barrier-crossing decay, a fixed budget of 8 boosters over a finite horizon gives an interior-peaked protected fraction: the optimum sits at the measured half-life (peak coverage 100% of the horizon), boosting too frequently falls to 38% and too sparsely to 49%, and the optimal interval tracks durability across compartments (ascending-durability optimal intervals 29.5, 35.5, 35.9, 47.6, model-time, [O]).

Two faces of immune time

The preceding chapters treated the immune system at a fixed age. This chapter adds TIME in two distinct senses, both read off the SAME R19 substrate. The first is the slow ageing of the repertoire-generating organ: thymic involution, the lifelong shrinking of the thymic education window, and what that shrinking does to the cells the thymus exports. The second is the waning of established protective memory and how to re-boost it: given a fixed budget of boosters and a finite protection horizon, what spacing keeps protection up for the largest fraction of that horizon. Neither answer is assumed; each EMERGES, measured, from dynamics already used in this volume.

Thymic involution: one shrinking window, two opposite drifts

This volume established thymic education as a saddle-node problem. A thymocyte carries a self-affinity and is educated under a corresponding self-drive; POSITIVE selection (survival) requires it to accumulate enough self-engagement within the window or it dies by neglect, while NEGATIVE selection DELETES it if its self-reactivity carries it across the activation threshold. Both events are CROSSINGS that take time. Thymic involution is that same education run with a slowly SHRINKING window, and because both selection events are time-costed, a shorter (older) window truncates them — in OPPOSITE directions, which the simulation measures directly. As the window shrinks from its youngest to its oldest setting (model-time 24 → 8, absolute scale [O]) the measured escaped-autoreactive fraction RISES (from 0.29% to 3.71% of the cohort) while the healthy naive-export rate FALLS (from 32.9% to 15.9%). The two outputs DIVERGE: an older thymus exports FEWER fresh naive cells AND lets MORE self-reactive clones slip through.

The mechanism of each direction is explicit. Near-threshold self-reactive clones need the LONGEST time to cross the activation threshold, so they are the first to miss deletion when the window shortens — the escapees are concentrated just above threshold (measured mean self-affinity 1.075× the spinodal at the oldest window), exactly the central-tolerance sliver of the earlier tolerance chapter widened by age. Marginal clones near the survival cut need the longest time to accumulate their positive-selection signal, so they are the first to die by neglect when the window shortens, and the export rate falls. The youngest window is the honest control: there the escaped fraction is only 0.29% and the export rate is at its maximum, so the drift is an ageing effect of the shrinking window, not a baseline artefact. This is the dynamical signature of immunosenescence — falling thymic output AND rising autoreactive escape — read as a single coupled consequence of one shrinking education window, measured rather than assumed.

Durable protection: re-boost as protection wanes

The memory chapter (§4) measured that a protective ON state decays by spontaneous barrier crossing, with a durability that ranks by the barrier across the four compartments. Build on that measured decay. Suppose protective memory has been established and then WANES by exactly that process, and you hold a FIXED budget of 8 booster events to spend over a finite protection horizon; a booster re-flips the waning pool back to full protection. The question is purely about SPACING: what re-boost interval keeps the model protected — the protected pool fraction above the protection threshold θ = 0.5 — for the largest fraction of the horizon.

The answer EMERGES from the measured decay curve. Sweeping the re-boost interval as a multiple r of the MEASURED protection half-life, the protected fraction of the horizon is an INTERIOR-peaked function: it rises to a clear maximum and falls on both sides. The peak sits at r ≈ 1 — the optimal spacing is to re-boost JUST AS protection wanes through the threshold, so the optimal interval EQUALS the measured memory half-life, read off the substrate rather than posited (peak coverage 100% of the horizon). Both failure modes are measured. Boosting TOO FREQUENTLY (r well below 1) piles the fixed budget up early while protection is still high, exhausts it before the horizon ends, and leaves the late horizon unprotected (protected fraction falls to 38%). Boosting TOO SPARSELY (r well above 1) lets each booster's protection lapse before the next arrives, opening susceptible gaps between boosters (protected fraction 49%). The optimum also TRACKS durability across compartments: because the optimal multiple is r ≈ 1 for every compartment, the absolute optimal interval inherits the memory-durability ranking — the longer-memory (deeper-barrier) compartment carries the LONGER optimal re-boost interval (measured optimal intervals in model-time, ascending durability: 29.5, 35.5, 35.9, 47.6; absolute scale [O]). The honest control switches the decay OFF: with memory that never wanes the protected fraction is FLAT across every interval, so the interior optimum is created by the MEASURED waning, not by the bookkeeping of the schedule.

This durability optimum is mechanistically DISTINCT from the affinity-maturation prime–boost optimum established earlier in this volume. That inverted-U arises from germinal-centre maturation kinetics under a persisting antigen depot; this one arises from the half-life of protective memory. Two different optima from two different mechanisms, each measured from the substrate.

What this is — and is not

Both results are re-descriptions of well-known immune-ageing and booster-scheduling phenomena in the R19 formalism. The measured content is QUALITATIVE and relative: the direction of the two repertoire drifts and their divergence, the near-threshold concentration of the escapees, and — for re-boosting — the existence and INTERIOR location of the protected-fraction optimum, its coincidence with the measured memory half-life, the two failure modes, the cross-compartment tracking, and the decay-driven control. This is a DIRECTION/CLASS statement about repertoire ageing and re-boost timing; it is NOT a schedule, an interval in real time, a clinical protocol, or a recommendation for any individual, and it is NOT medical advice. The model does not invent any absolute scale: the education-window length, the positive-selection quota, the protection threshold θ, the re-boost interval and memory half-life in real units, and the cellular-noise scale are all left [O] with the obstacle stated. It is NOT a validation of VP theory. Every measured direction here is graded [V] and reproduced deterministically from the same kernel as the rest of this volume.