From nine hallmarks to twelve

The step from “nine hallmarks to twelve” in the author’s framework is correct. Two points need adding. First, most of the “experiments” behind the criteria are animal experiments; for most hallmarks there is not yet human evidence that improving it extends healthy human life. Second, listing autophagy as a hallmark of its own shows that its standing in the framework has risen, but it does not mean that “promoting autophagy” is anti-ageing; Chapter 2 of Book 5 pointed out that both too little and too much autophagy can do harm.

This chapter examines the quantitative structure of one hallmark: proteostasis.

The proteostasis network

Proteins in a cell are continually synthesised, folded, used and degraded. Misfolded proteins that are not repaired or removed in time stick together into aggregates. The system that maintains this balance is called the proteostasis network.

These two points suggest that the decline of proteostasis may not be slow and even but may have a critical point, and that the sequestration of chaperones by aggregates forms a positive feedback. A mass-balance model can test this inference.

A mass-balance model

# dM/dt = p - V H M/(1 + M) - kd M - ka M^2, dA/dt = ka M^2 - c A, H = 1/(1 + A^2) (illustrative).
# Part 1: lower c slowly, then raise it again. Part 2: V and c decline with model age.
P, KD, KA = 1.0, 0.1, 0.2

def settle(M, A, V, c, T=400.0, dt=0.02):
    for _ in range(int(T / dt)):
        H = 1 / (1 + A * A)
        M, A = (M + (P - V * H * M / (1 + M) - KD * M - KA * M * M) * dt,
                A + (KA * M * M - c * A) * dt)
    return M, A

down = [0.40, 0.30, 0.25, 0.22, 0.20, 0.18, 0.16, 0.14, 0.12]
M, A, res = 0.4, 0.1, {}
for c in down + down[::-1]:
    M, A = settle(M, A, 3.0, c); res.setdefault(c, []).append(A)
print("clearance c:        " + " ".join(f"{c:5.2f}" for c in down))
print("aggregates, falling:" + " ".join(f"{res[c][0]:5.2f}" for c in down))
print("aggregates, rising: " + " ".join(f"{res[c][-1]:5.2f}" for c in down))

def collapse_age(v_loss, c_loss, V0=3.0, c0=0.40):
    M, A = settle(0.4, 0.1, V0, c0)
    for year in range(20, 121):
        V, c = V0 * (1 - v_loss) ** (year - 20), c0 * (1 - c_loss) ** (year - 20)
        M, A = settle(M, A, V, c, T=20.0)
        if A > 2.0:
            return f"collapse (A > 2) at age {year}, V = {V:.2f}, c = {c:.3f}"
    return "no collapse by age 120"
for v_loss, c_loss in ((0.01, 0.01), (0.01, 0.005), (0.005, 0.01), (0.0, 0.01), (0.01, 0.0)):
    print(f"chaperone loss {v_loss:.1%}/y, clearance loss {c_loss:.1%}/y: "
          + collapse_age(v_loss, c_loss))
# clearance c:         0.40  0.30  0.25  0.22  0.20  0.18  0.16  0.14  0.12
# aggregates, falling: 0.10  0.14  0.17  0.19  0.22  0.25  0.30  0.39  6.31
# aggregates, rising:  0.10  0.14  0.17  2.74  3.27  3.83  4.48  5.28  6.31
# chaperone loss 1.0%/y, clearance loss 1.0%/y: collapse (A > 2) at age 60, V = 2.01, c = 0.268
# chaperone loss 1.0%/y, clearance loss 0.5%/y: collapse (A > 2) at age 76, V = 1.71, c = 0.302
# chaperone loss 0.5%/y, clearance loss 1.0%/y: collapse (A > 2) at age 77, V = 2.25, c = 0.226
# chaperone loss 0.0%/y, clearance loss 1.0%/y: no collapse by age 120
# chaperone loss 1.0%/y, clearance loss 0.0%/y: no collapse by age 120

As the clearance rate falls from 0.40 to 0.14, aggregates rise only slowly, from 0.10 to 0.39; at 0.12 they jump to 6.31, about a 16-fold increase. This is a typical critical transition: before the collapse, the level of aggregates gives almost no hint that a collapse is near.

The return journey matters even more. Raising the clearance rate step by step after the collapse, the system does not retrace its path: with clearance back at 0.22, aggregates are still 2.74; only at 0.25 does the system return to the low-aggregate state (0.17). Between 0.14 and 0.22 the same clearance rate corresponds to two quite different steady states, and which one the system occupies depends on where it came from. This hysteresis arises from the positive feedback of aggregates sequestering chaperones; Book 13 of this series discussed the general properties of bistability and hysteresis.

The second part shows two declines interacting. With chaperone capacity and clearance each falling by 1 % a year, the model collapses at age 60; letting only one of them fall while the other stays constant, there is no collapse even by 120; if either falls half as fast (0.5 % a year), the collapse is postponed to 76–77. In this model, then, two declines that are each tolerable can together cross the critical point, and slowing either of them pushes the critical point back by more than a decade.

Heat-shock proteins and inducible chaperone capacity

Chaperone capacity is not fixed. When cells meet heat, oxidative or proteotoxic stress, the heat-shock transcription factor HSF-1 is activated and heat-shock proteins are rapidly made in greater amounts. This heat-shock response is an example, at the level of proteostasis, of the hormesis of Chapter 3: a moderate proteotoxic stress induces a higher chaperone capacity. In the model it corresponds to a temporary rise in $V$.

If the inducibility of chaperone capacity declines with age (Ben-Zvi and colleagues saw exactly an early decline of the inducible heat-shock response in worms (Ben-Zvi et al. 2009)), the same stress that acts as “training” in youth might push the system over the critical point in old age. This is an inference, not evidence.

Chapter summary

The hallmarks of ageing grew from nine in 2013 to twelve in 2023, adding disabled macroautophagy, chronic inflammation and dysbiosis; the criteria for a hallmark rest mostly on animal experiments. The proteostasis network consists of synthesis, chaperone-assisted folding and degradation, and the sequestration of chaperones by aggregates forms a positive feedback. A mass-balance model shows a critical clearance rate: crossing it makes aggregates jump, and recovery needs more clearance capacity than before the collapse (hysteresis); two declines that are each tolerable can together cross the critical point. These are structural conclusions of a model, and the corresponding rates have not been measured in humans. The next chapter leaves the cell and returns to populations: the epidemiology of cardiorespiratory fitness and mortality.