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Chapter 4 The AMPK–mTORC1 Switch and Autophagy
The cell’s recycling system
Autophagy (literally “self-eating”) is the process by which a cell wraps parts of itself (old proteins, damaged mitochondria) in a double-membrane structure, the autophagosome, and delivers them to the lysosome to be broken down and recycled. Yoshinori Ohsumi first described autophagy in yeast and then identified, through genetic screens, a set of genes it needs, laying the molecular foundations of the field; he was awarded the 2016 Nobel Prize in Physiology or Medicine (Takeshige et al. 1992; Tsukada and Ohsumi 1993).
Autophagy is tightly regulated by nutrition: it is suppressed when nutrients are plentiful and activated when they are scarce. At the core of this regulation are two protein kinases that sense nutrients and energy: mTORC1 and AMPK.
Two kinases, one switch
- mTORC1 senses amino acids and growth-factor signals (including insulin). When active it promotes protein synthesis and growth, and phosphorylates an inhibitory site on the autophagy-initiating kinase ULK1, shutting autophagy off.
- AMPK senses energy shortage (AMP and ADP rising relative to ATP). When active it phosphorylates activating sites on ULK1, starting autophagy directly, and inhibits mTORC1 by phosphorylating TSC2 and raptor (Inoki et al. 2003; Gwinn et al. 2008; Kim et al. 2011).
So AMPK inhibits mTORC1, and mTORC1 also dampens AMPK’s action to some extent. Two mutually inhibiting elements form a double-negative feedback, and in systems biology such a loop can, with suitable parameters, act as a bistable toggle switch: at the same input the system may sit in either of two stable states, “on” or “off”, depending on where it came from. Holczer and colleagues argued with mathematical modelling and cell experiments that the double-negative feedback between mTORC1 and AMPK is important for precise induction of autophagy (Holczer et al. 2019).
Note
A modelling assumption. The evidence that AMPK inhibits mTORC1 is strong; the reverse action of mTORC1 on AMPK is weaker and its mechanism still debated. The program below makes the mutual inhibition steep to display the properties of a bistable switch; this is an assumption, not an estimate of the actual parameters in cells.
Calculation
A minimal AMPK–mTORC1 toggle switch. The nutrient signal runs from 0 (fasted) to 1 (fed). Raise the nutrients slowly, then lower them slowly, and record the level of autophagy initiation.
# A minimal AMPK-mTORC1 toggle switch (a modelling assumption, illustrative parameters).
# Nutrient signal s in [0, 1]: s = 1 fed (insulin and amino acids high), s = 0 fasted (energy stress).
# dM/dt = 3 s / (1 + (A/0.5)^4) - M mTORC1 (M): driven by nutrients, inhibited by AMPK
# dA/dt = 3 (1 - s) / (1 + (M/0.5)^4) + 0.05 - A AMPK (A): driven by energy stress, inhibited by mTORC1
# AMPK inhibits mTORC1 (via TSC2 and raptor); the reverse arm, mTORC1 dampening AMPK, is weaker
# and debated, so the steep mutual inhibition here is an assumption. ULK1, the autophagy initiator,
# is switched on by AMPK and off by mTORC1: autophagy initiation = A/(A + 0.5) / (1 + (M/0.5)^2).
def settle(s, M, A, dt=0.01, T=60.0):
for _ in range(int(T / dt)):
dM = 3 * s / (1 + (A / 0.5) ** 4) - M
dA = 3 * (1 - s) / (1 + (M / 0.5) ** 4) + 0.05 - A
M += dM * dt; A += dA * dt
return M, A
def flux(M, A):
return A / (A + 0.5) / (1 + (M / 0.5) ** 2)
grid = [i / 10 for i in range(11)]
M, A = 0.0, 3.0 # start fully fasted
up = {}
for s in grid: # slowly feed
M, A = settle(s, M, A); up[s] = flux(M, A)
down = {}
for s in reversed(grid): # then slowly withdraw food
M, A = settle(s, M, A); down[s] = flux(M, A)
print("nutrient signal s | autophagy initiation, rising nutrients | falling nutrients")
for s in grid:
print(f"{s:17.1f} | {up[s]:38.2f} | {down[s]:17.2f}")
off = min(s for s in grid if up[s] < 0.2); on = max(s for s in grid if down[s] >= 0.2)
print(f"rising nutrients switch autophagy off at s = {off:.1f}; falling nutrients switch it back on only"
f" at s = {on:.1f} (hysteresis)")
# nutrient signal s | autophagy initiation, rising nutrients | falling nutrients
# 0.0 | 0.86 | 0.86
# 0.1 | 0.85 | 0.85
# 0.2 | 0.83 | 0.83
# 0.3 | 0.81 | 0.81
# 0.4 | 0.79 | 0.03
# 0.5 | 0.76 | 0.01
# 0.6 | 0.71 | 0.01
# 0.7 | 0.60 | 0.01
# 0.8 | 0.00 | 0.00
# 0.9 | 0.00 | 0.00
# 1.0 | 0.00 | 0.00
# rising nutrients switch autophagy off at s = 0.8; falling nutrients switch it back on only at s = 0.3 (hysteresis)
The most interesting property of this switch is hysteresis: as nutrients rise, autophagy stays on until passes 0.7; as they fall, it does not switch back on at the same point but only when has fallen to about 0.3. In this model, then, one meal can flip the switch to “off”, but flipping it back to “on” needs the nutrient signal to fall low enough for long enough. This offers a mechanistic possibility that how often one eats might matter more than how much at each meal, but only a possibility.
Meal schedules and the switch
Calculation
Several eating schedules fed into the same switch. Each meal pushes the nutrient signal up by 0.8; between meals it decays with time constant τ. The program labels time in hours, but no parameter is calibrated to human data, so only differences between schedules can be compared. The last line changes τ from 8 to 6 hours to test how fragile the conclusions are.
# Feeding schedules run through the toggle switch of the previous program. Each meal pushes the
# nutrient signal s up by 0.8 (capped at 1); between meals s decays with time constant tau (8 h).
# M and A relax with a 1-hour time constant. 'Hours on' counts hours per day with autophagy
# initiation above 0.5, averaged over days 3-7. The clock is labelled in hours, but NO parameter is
# calibrated to human data: compare schedules with each other, do not read off real hours.
import math
def simulate(meals_per_day, days=7, dt=0.02, fast_day=None, tau=8.0):
M, A, s, on = 0.5, 0.5, 0.5, 0.0
steps = int(24 / dt)
for d in range(days):
eaten = set()
for i in range(steps):
h = i * dt
for m in meals_per_day:
if (d != fast_day) and m not in eaten and h >= m:
s = min(1.0, s + 0.8); eaten.add(m)
s -= s / tau * dt
dM = 3 * s / (1 + (A / 0.5) ** 4) - M
dA = 3 * (1 - s) / (1 + (M / 0.5) ** 4) + 0.05 - A
M += dM * dt; A += dA * dt
if d >= 2 and A / (A + 0.5) / (1 + (M / 0.5) ** 2) > 0.5:
on += dt
return on / (days - 2)
SCHED = {"grazing: 6 small meals 07-22 h": (7, 10, 13, 16, 19, 22),
"three meals 07, 12, 19 h": (7, 12, 19),
"three meals + late snack 22 h": (7, 12, 19, 22),
"16:8, meals 12 and 20 h": (12, 20),
"16:8 early, meals 08 and 16 h": (8, 16)}
print("schedule | model hours per day with autophagy initiation 'on'")
for name, meals in SCHED.items():
print(f"{name:34s} | {simulate(meals):6.1f}")
print(f"{'three meals, one day a week fasted':34s} | {simulate((7, 12, 19), days=9, fast_day=4):6.1f}")
# How fragile is this? Let the nutrient signal fade faster (tau = 6 h instead of 8 h):
print("with tau = 6 h: three meals", f"{simulate((7, 12, 19), tau=6.0):.1f}", "h, 16:8", f"{simulate((12, 20), tau=6.0):.1f}",
"h, grazing", f"{simulate((7, 10, 13, 16, 19, 22), tau=6.0):.1f}", "h")
# schedule | model hours per day with autophagy initiation 'on'
# grazing: 6 small meals 07-22 h | 0.0
# three meals 07, 12, 19 h | 0.0
# three meals + late snack 22 h | 0.0
# 16:8, meals 12 and 20 h | 11.9
# 16:8 early, meals 08 and 16 h | 11.9
# three meals, one day a week fasted | 4.1
# with tau = 6 h: three meals 22.4 h, 16:8 24.0 h, grazing 0.0 hWith these parameters, grazing and three meals a day (with a late snack) keep the switch almost always “off”, a 16:8 schedule (two meals, a 16-hour overnight gap) keeps it “on” for about 12 model hours a day, and fasting one day a week raises the average to about 4 model hours. But the last line shows that if the nutrient signal fades a little faster, three meals a day also leave the switch “on” for most of the day. The conclusion depends entirely on uncalibrated parameters. This is just what the chapter means to show: the switch model tells us which quantities are worth measuring (how fast the nutrient signal fades, where the switch thresholds lie), but not how many hours a person must fast to “switch on autophagy”.
A mouse’s 24 hours are not a human’s 24 hours
The claim that “16 (or 24, or 48) hours of fasting switches on autophagy” is widespread. Its evidence comes mainly from mice.
Evidence
Mizushima and colleagues bred transgenic mice expressing fluorescently tagged LC3 (an autophagosome membrane protein) to observe autophagosomes in tissues. After 24 hours of starvation, autophagosomes increased clearly in many tissues, including skeletal muscle, heart and liver, with time courses that differed between organs (in skeletal muscle, for example, they rose further by 48 hours); in the brain almost no increase was seen (Mizushima et al. 2004).
Carrying these times over directly to people ignores one basic fact: mice run their metabolism much faster than we do.
Calculation
By Kleiber’s law, resting metabolic rate scales roughly with body mass to the 3/4 power, so the rate per kilogram scales with mass to the −1/4 power (Kleiber 1932). Compare a 25-gram mouse with a 70-kilogram human.
# Why a mouse's 24-hour fast is not a human's 24-hour fast. Kleiber's law: whole-body resting
# metabolic rate scales roughly as body mass^(3/4), so the rate PER KILOGRAM scales as mass^(-1/4).
# Masses: laboratory mouse 25 g, adult human 70 kg.
m_mouse, m_human = 0.025, 70.0
ratio = (m_human / m_mouse) ** 0.25
print(f"mass-specific metabolic rate, mouse / human: {ratio:.1f}x")
for h in (12, 24, 48):
print(f"a {h:2d}-hour fast in a mouse ~ {h * ratio / 24:4.1f} days of a human's metabolic time"
" (a naive scaling, see below)")
# Kleiber's formula itself: BMR (kcal/day) ~ 70 * M^0.75
for name, m in (("mouse", m_mouse), ("human", m_human)):
bmr = 70 * m ** 0.75
print(f"{name}: Kleiber estimate {bmr:7.1f} kcal/day = {bmr / m:5.0f} kcal per kg per day")
# Why the naive scaling is itself not a conversion table:
# * different processes scale differently: liver glycogen in a fasted mouse is largely gone within
# about 12-24 h, but autophagy in each tissue has its own kinetics (and the mouse brain showed
# little induction even at 48 h in GFP-LC3 mice);
# * mice are usually fasted during their active (dark) phase and are kept below thermoneutrality,
# which raises their energy use further;
# * in humans there is still no simple, non-invasive marker that times autophagic flux in tissues.
# mass-specific metabolic rate, mouse / human: 7.3x
# a 12-hour fast in a mouse ~ 3.6 days of a human's metabolic time (a naive scaling, see below)
# a 24-hour fast in a mouse ~ 7.3 days of a human's metabolic time (a naive scaling, see below)
# a 48-hour fast in a mouse ~ 14.5 days of a human's metabolic time (a naive scaling, see below)
# mouse: Kleiber estimate 4.4 kcal/day = 176 kcal per kg per day
# human: Kleiber estimate 1694.0 kcal/day = 24 kcal per kg per dayBy this scaling, the mass-specific metabolic rate of a mouse is about 7 times a human’s; in the crudest sense, a mouse fasting for 24 hours spends as much “metabolic time” as a human does in about a week. But even this is not a conversion table. Different physiological processes scale differently; laboratory mice are usually fasted during their active dark phase and housed below thermoneutrality, which raises their energy use further; and even in mice, autophagy runs on different time courses in different tissues. The conclusion of this book is therefore that autophagy timelines from animal experiments cannot be equated with any specific number of human hours, nor converted simply by Kleiber’s law.
Note
A marker is not the process. Measuring autophagy in humans is very hard. Autophagy is a flux: the rates of autophagosome formation, fusion with lysosomes and degradation of the contents together decide how much is recycled. More autophagosomes (or higher levels of proteins such as LC3) at one time point may mean more autophagy, or a block in degradation with autophagosomes piling up. International guidelines for autophagy research therefore stress that flux, not just markers, must be measured (Klionsky et al. 2021). In humans there is at present no simple, non-invasive marker that can time autophagy in each tissue. Some human studies have measured changes in the expression of autophagy-related genes in blood cells; Jamshed and colleagues, for example, found that early time-restricted eating raised LC3A expression in whole blood (Jamshed et al. 2019). But gene expression in blood cells is neither autophagic flux nor what happens in muscle, brain or liver.
Hypothesis · not established
The meal-frequency hypothesis (not yet established). If nutrient sensing really shows hysteresis, then with total energy and nutrient composition held constant, fewer meals (longer gaps between them) should affect nutrient-sensing pathways more than the same food eaten as many small meals. A testable implication: in human muscle biopsies, using a flux assay (for example comparing LC3-II accumulation in biopsy tissue with and without a lysosomal inhibitor), a two-meal schedule should show higher autophagic flux than a six-meal schedule. If the two schedules do not differ, or differ only in static markers and not in flux, the hypothesis is weakened.
Summary
The mutual inhibition of AMPK and mTORC1 can form a switch with hysteresis: one meal can shut autophagy off, and switching it back on needs the nutrient signal to fall far enough for long enough. But the switch model’s conclusions depend on uncalibrated parameters; autophagy timelines in mice cannot be converted into human hours; and humans lack a simple marker that can time autophagy. “How many hours of fasting switch on autophagy” is at present a question without an answer. The next chapter leaves mechanisms behind and asks what randomised trials in people have found.
References
Fan, Y. (2026). Ketone Metabolism, β-Hydroxybutyrate Signalling and the Bioenergetics of Intermittent Fasting: From the Randle Cycle and Epigenetic Inhibition to Autophagy Kinetics, Read Beside Classical Chinese Fasting Texts [酮体代谢、β-羟丁酸信号转导与间歇性禁食的生物能量学] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23753263 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).