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Chapter 3 Hormesis and Mitochondrial Low-Dose Stress
The “opposite direction” at low doses
The traditional picture in toxicology is monotonic: the larger the dose, the stronger the effect, with no observable effect below some threshold. Hormesis describes a different shape: at low doses the response departs from the control in the direction opposite to that seen at high doses, giving a biphasic curve. A substance that inhibits cell growth at high doses might, for example, raise growth slightly above control at low doses.
Evidence
Calabrese and Baldwin (2002) gave a widely cited definition (Calabrese and Baldwin 2002). Hormesis is an adaptive response characterised by biphasic dose–response relationships whose stimulatory part has broadly similar quantitative features of amplitude and range, and which is either directly induced or the result of compensatory processes following an initial disruption of homeostasis. The data they collected show that the maximum stimulation is usually only 30–60 % above control and generally no more than twofold; in about 90 % of 2,609 examples the stimulatory range spanned 5- to 100-fold in dose, immediately below the toxicity threshold. They stressed two points: because the stimulation is modest, judging causality requires stronger designs and replication; and whether an effect is beneficial or harmful should not be part of the definition, but left to an evaluation of the specific biological and ecological context.
The last point is often overlooked. “A little poison is good for you” turns a description of a curve’s shape into a value judgement: a measure that rises at low doses may be good news (more antioxidant enzymes) or bad news (faster tumour-cell proliferation).
Calculation
An illustrative biphasic curve, with the response relative to control
and , , (dose in arbitrary units). The program first finds the maximum stimulation, the dose at which the response returns to control (the zero equivalent point, ZEP) and the width of the stimulatory zone. It then simulates a typical experiment: a control group and 4 low-dose groups of samples each, a coefficient of variation of 35 %, and a one-sided -test of each low-dose group against control, compared with a threshold curve that has no low-dose stimulation at all.
Calculation
# Biphasic response r(d) = (1 + S d/(d + K)) / (1 + (d/T)^4), arbitrary dose units.
# Part 2: control + 4 low doses, n per group, CV 35 %, one-sided t-tests (fixed seed).
import math, random
S, K, T = 0.4, 0.05, 3.0
r = lambda d: (1 + S * d / (d + K)) / (1 + (d / T) ** 4)
grid = [i / 10000 for i in range(1, 60001)]
d_max = max(grid, key=r)
zep = next(d for d in grid if d > d_max and r(d) < 1) # zero equivalent point
half = next(d for d in grid if r(d) - 1 >= (r(d_max) - 1) / 2)
print(f"maximum stimulation {r(d_max) - 1:+.0%} at dose {d_max:.2f}; back to control (ZEP) at"
f" {zep:.2f}")
print(f"half-maximal stimulation at dose {half:.3f}: stimulatory zone spans {zep / half:.0f}-fold")
DOSES = (0.01, 0.03, 0.1, 0.3, 1, 2, 3, 4)
print("dose: " + " ".join(f"{d:6.2f}" for d in DOSES))
print("response: " + " ".join(f"{r(d):6.2f}" for d in DOSES))
T05 = {8: 1.860, 18: 1.734, 38: 1.686, 78: 1.665} # one-sided 0.05 t quantiles
def experiment(curve, n, rng, doses=(0.01, 0.03, 0.1, 0.3)):
def group(mean):
g = [rng.gauss(mean, 0.35) for _ in range(n)]; m = sum(g) / n
return m, sum((x - m) ** 2 for x in g) / (n - 1)
mc, vc = group(1.0)
return [(m - mc) / math.sqrt((vc + v) / n) > T05[2 * n - 2]
for m, v in (group(curve(d)) for d in doses)]
rng = random.Random(30)
flat = lambda d: 1 / (1 + (d / T) ** 4) # threshold curve, no hormesis
print(" n/group | P(lowest dose significant) | P(any of 4 significant) | same, flat curve (false)")
for n in (5, 10, 20, 40):
runs = [experiment(r, n, rng) for _ in range(2000)]
low = sum(h[0] for h in runs) / 2000; anyh = sum(any(h) for h in runs) / 2000
false = sum(any(experiment(flat, n, rng)) for _ in range(2000)) / 2000
print(f" {n:3d} | {low:5.1%} | {anyh:5.1%} |"
f" {false:5.1%}")
# maximum stimulation +37% at dose 0.76; back to control (ZEP) at 2.37
# half-maximal stimulation at dose 0.043: stimulatory zone spans 55-fold
# dose: 0.01 0.03 0.10 0.30 1.00 2.00 3.00 4.00
# response: 1.07 1.15 1.27 1.34 1.36 1.16 0.70 0.34
# n/group | P(lowest dose significant) | P(any of 4 significant) | same, flat curve (false)
# 5 | 8.9% | 54.4% | 14.8%
# 10 | 10.5% | 77.2% | 13.9%
# 20 | 14.8% | 95.3% | 14.5%
# 40 | 21.1% | 99.7% | 14.2%The curve’s maximum stimulation is 37 %, at a dose of 0.76; at a dose of 2.37 it returns to control, and above that it turns into inhibition. Half-maximal stimulation is reached at a dose of 0.043, so the stimulatory zone spans about 55-fold in dose, in line with the typical range Calabrese and colleagues describe.
The second part of the program shows why low-dose effects are hard to confirm. The lowest dose (0.01) is only 7 % above control: even with 40 samples per group, the chance of detecting it is about 21 %, and with 5 per group about 9 %. Conversely, if all 4 low-dose groups are tested and “hormesis” is declared whenever any one of them is significant, about 14–15 % of experiments come out “positive” even when the true curve has no low-dose stimulation at all, almost three times the nominal 5 %. Small samples, multiple comparisons and selective reporting together can both miss real small effects and manufacture spurious ones.
Evidence
A critique of extending the concept. Kendig, Le and Belcher (2010) reviewed the history of the hormesis concept (Kendig et al. 2010). They acknowledged that such responses can be found in both pharmacological and toxicological studies, but argued that acceptance of the concept has been limited by poor conceptual understanding, inappropriate use and the lack of a defined mechanism; that looking back at existing studies is problematic; and that, for want of a shared vocabulary, the concept has been applied to many unrelated dose–response relationships. They recommended unbiased, descriptive criteria for examining low-dose effects and a clear, concise definition.
Mitochondrial low-dose stress
A leading application of hormesis to the biology of ageing is the hypothesis of mitochondrial hormesis (mitohormesis).
Evidence
Ristow and Zarse (2010) proposed the concept (Ristow and Zarse 2010): reactive oxygen species (ROS) produced when mitochondrial respiration rises are not merely damaging by-products but also signals; moderately raised ROS can induce antioxidant defences and stress resistance, ultimately increasing tolerance of later stress, and in some model organisms extending lifespan. An important basis for the hypothesis is the worm experiment of Schulz and colleagues (2007): restricting glucose increased mitochondrial respiration and ROS in C. elegans and extended lifespan, while treatment with antioxidants abolished the extension (Schulz et al. 2007).
Note
Limits on extrapolating from animals to humans. A worm lives a few weeks, and its metabolism, stress pathways and tissues differ greatly from ours. Interventions that extend lifespan in worms often fail to do the same in mice, and in humans there are no lifespan data at all. “Mitohormesis extends life” is therefore an untested extrapolation in humans. Human studies can measure only intermediate steps, such as insulin sensitivity after exercise, maximal oxygen uptake or the expression of certain muscle proteins, and these are markers, not lifespan or healthspan.
Antioxidants and exercise: a result not consistently replicated
If part of the benefit of exercise comes from ROS signalling, then taking large amounts of antioxidants during training might in principle blunt the adaptation. This consequence can be tested in people.
Evidence
The original result. Ristow and colleagues reported a 4-week exercise intervention in the Proceedings of the National Academy of Sciences in 2009, with 19 previously untrained and 20 pretrained healthy young men, who took a combination of vitamins C and E or no supplement (Ristow et al. 2009). Insulin sensitivity, measured with the hyperinsulinaemic–euglycaemic clamp, improved with exercise only in those who did not take the antioxidants.
Evidence
Later trials. Two reports by Yfanti and colleagues studied 21 moderately trained young men, randomised double-blind to antioxidants or placebo during 12 weeks of strenuous supervised endurance training five times a week. The 2010 report found that maximal oxygen uptake, maximal power output, power at the lactate threshold, muscle glycogen and muscle oxidative enzyme activities all rose markedly in both groups, with no difference between them (Yfanti et al. 2010); the 2011 report found that clamp-measured insulin-stimulated glucose uptake rose by about 17 % with antioxidants and about 19 % with placebo, a similar amount (Yfanti et al. 2011). In a randomised double-blind trial by Paulsen and colleagues (2014), 54 young men and women trained for endurance for 11 weeks: maximal oxygen uptake rose by about 8 % in both groups, with no difference in the improvement of running performance, but the mitochondrial protein COX4 and cytosolic PGC-1α rose in muscle in the placebo group and not in the supplement group, a significant difference between groups (Paulsen et al. 2014).
Taken together, these studies allow the following statement: large doses of antioxidants may blunt changes in some cellular markers induced by training, but in these trials they did not consistently blunt improvements in maximal oxygen uptake, performance or insulin sensitivity. The studies differed in participants, training, duration, supplement composition and dose, so inconsistent results are not surprising. “Antioxidants block the benefits of exercise” cannot be written as an established conclusion.
Note
This book gives no doses and neither recommends nor advises against any supplement. The studies above used particular vitamin combinations and doses, which the book deliberately does not repeat. Their question was the mechanism of exercise adaptation, not what people should eat, and they say nothing about whether low doses or antioxidants from food have any similar effect.
Acute pulses and recovery
Another common claim about hormesis is that stress must come as an acute pulse with enough recovery time for adaptation to appear, while chronic, continuous stress causes damage. This can be written as the simplest possible systems model.
Calculation
Each session (one every gap days) delivers a stress
pulse of size
.
It raises acute strain
by
,
where
is adaptive capacity, and the strain recovers with a time constant of
1.5 days; it also produces a signal that raises
towards a ceiling of 3, while
falls back to 1 with a time constant of 12 days. The model’s key
assumption is that training before the strain has recovered discounts
the adaptive signal, which is
;
is the fraction of the signal that is “quenched”, a parameter standing
for anything that blunts the signal, not the dose of any product. The
outcome, “net resilience”, is the mean of
minus the mean strain
over the last four weeks.
Calculation
# Pulse + recovery toy model: a pulse s every `gap` days adds strain s/C (recovers, tau 1.5 d) and
# a signal s (1 - beta) max(0, 1 - D/2) that raises capacity C towards 3 (decays to 1, tau 12 d).
# beta = quenched share of the signal, not a dose of anything. Net = mean C - mean D, last 4 weeks.
def run(gap, s=1.0, beta=0.0, days=140, dt=0.01, gamma=0.25, cmax=3.0):
C, D, sumC, sumD, n = 1.0, 0.0, 0.0, 0.0, 0
spd = round(1 / dt)
for i in range(days * spd):
if i % (gap * spd) == 0: # a session starts
d_before = D
D += s / C
C += gamma * s * (1 - beta) * max(0.0, 1 - d_before / 2) * (cmax - C) / (cmax - 1)
D -= D / 1.5 * dt
C -= (C - 1) / 12 * dt
if i >= (days - 28) * spd:
sumC += C; sumD += D; n += 1
return sumC / n, sumD / n
GAPS = (1, 2, 4, 7)
print("net resilience (capacity C - mean strain D); rows = pulse size s, columns = gap in days")
print(" pulse s | " + " | ".join(f"every {g} d" for g in GAPS))
for s in (0.5, 1, 2, 3, 4):
cells = []
for g in GAPS:
c, d = run(g, s=s)
cells.append(f" {c - d:+5.2f} ")
print((f" {s:3.1f} | " + " | ".join(cells)).rstrip())
c0, d0 = run(2, s=2); c1, d1 = run(2, s=2, beta=0.5)
print(f"every 2 d, s = 2: C = {c0:.2f}, strain {d0:.2f}; with half the signal quenched:"
f" C = {c1:.2f}, strain {d1:.2f}")
c3, d3 = run(1, s=3)
print(f"every day, s = 3: C = {c3:.2f}, mean strain {d3:.2f} (no recovery, adaptation stalls)")
# net resilience (capacity C - mean strain D); rows = pulse size s, columns = gap in days
# pulse s | every 1 d | every 2 d | every 4 d | every 7 d
# 0.5 | +1.37 | +1.28 | +1.17 | +1.11
# 1.0 | +1.34 | +1.41 | +1.31 | +1.20
# 2.0 | +0.90 | +1.44 | +1.47 | +1.36
# 3.0 | -3.47 | +1.32 | +1.54 | +1.48
# 4.0 | -4.96 | +1.14 | +1.56 | +1.56
# every 2 d, s = 2: C = 2.16, strain 0.72; with half the signal quenched: C = 1.77, strain 0.87
# every day, s = 3: C = 1.00, mean strain 4.47 (no recovery, adaptation stalls)
The model shows three things. First, at a fixed frequency, net resilience is an inverted U in pulse size: with one session a day, a pulse of 0.5 is best (+1.37), rising to 2 lowers it to +0.90, and at 3 it falls to −3.47, because strain cannot recover, the adaptive signal is completely suppressed, stays at 1 and mean strain reaches 4.47. Second, the longer the recovery, the larger the best pulse: with a session every 2 days the best is near (+1.44), while with one every 4 days the value is still rising at (+1.56). Third, when half the signal is quenched, the same training (every 2 days, ) lowers adaptive capacity from 2.16 to 1.77, while mean strain rises from 0.72 to 0.87.
These numbers have no units and no calibration to human data; the model only shows that dose, frequency and recovery must be considered together, the origin of Chapter 6’s training models and of Chapter 8’s “stress pulses against sleep recovery”.
Hypothesis · not established
Insufficient recovery blunts adaptation to low-dose stress (not established). If the “acute pulse + recovery” structure matters for human adaptation, then for the same total training, placing hard sessions on consecutive days with less sleep recovery in between should bring smaller improvements in maximal oxygen uptake and heart-rate recovery than spacing them at least 48 hours apart. This could be tested in a randomised crossover or parallel design; if the two arrangements produce the same adaptation, the hypothesis is weakened.
Chapter summary
Hormesis is a biphasic dose–response shape whose definition leaves out “beneficial”; low-dose stimulation is usually only 30–60 %, easy both to miss and to invent. Mitohormesis is supported in worms, with no lifespan evidence in humans. “Antioxidants block the benefits of exercise” has not replicated consistently: some muscle markers were blunted, while gains in maximal oxygen uptake, performance and insulin sensitivity were not. Dose, frequency and recovery must be considered together. The next chapter turns to proteostasis and its critical point.
References
Fan, Y. (2026). Ageing Kinetics, the mTOR-AMPK Autophagy Switch and Hormesis: From the Gompertz Mortality Law and Mitohormesis to Cardiorespiratory Fitness Epidemiology, Read Beside Classical Chinese Longevity Philosophy [衰老动力学、mTOR-AMPK自噬开关与毒物兴奋效应的生物数学模型] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23770092 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).