From “is there autophagy?” to “who flips the switch?”

The history of autophagy, Yoshinori Ohsumi’s yeast experiments and the 2016 Nobel Prize (The Nobel Assembly at Karolinska Institutet 2016), together with three conclusions this book takes over (the autophagy timeline of fasted mice cannot be converted into human hours; a marker is not flux; humans have no simple marker that times autophagy in tissues (Klionsky et al. 2021)), are covered in Chapter 2 of Book 5 and Chapter 4 of Book 17; Book 17 also showed the hysteresis of an AMPK–mTORC1 toggle switch with a program.

This chapter asks two new questions: how do the signals “plenty of nutrients” and “too little energy” converge on one autophagy-initiating kinase, and when does “eating around the clock locks the system in an anabolic state, so damaged proteins pile up linearly” actually hold?

mTORC1: the master scheduler of growth

The phosphorylation logic of ULK1

At the heart of autophagy initiation is the kinase ULK1 (Atg1 in yeast), the point where the mTORC1 and AMPK signals meet.

The two pictures lead to very different conclusions about “energy troughs switching on autophagy”. The program below writes them as versions of one small model.

# mTORC1 (M) and AMPK (A) with steep mutual inhibition; inputs n (nutrients), e (energy stress).
# ULK1: model A = A/(A + 3M + 0.1) (Kim et al. 2011); B = A without cross-inhibition;
# C = 0.3/(0.3 + 3M + 0.1 + A), AMPK restraining ULK1 (after Park et al. 2023). Illustrative.
def steady(n, e, cross, h=4, dt=0.01, T=40.0):
    M = A = 0.2
    for _ in range(int(T / dt)):
        im = 1 / (1 + (A / 0.4) ** h) if cross else 1.0
        ia = 1 / (1 + (M / 0.4) ** h) if cross else 1.0
        M, A = M + (n * im - M) * dt, A + (e * ia + 0.02 - A) * dt
    return M, A

def ulk1(n, e, cross, variant=False):
    M, A = steady(n, e, cross)
    return 0.3 / (0.3 + 3 * M + 0.1 + A) if variant else A / (A + 3 * M + 0.1)

E = (0.0, 0.25, 0.5, 0.75, 1.0)
print("ULK1 activity; columns: energy stress e = " + "  ".join(f"{e:4.2f}" for e in E))
for title, cross, var in (("A mutual inhibition", True, False), ("B no cross-inhibition",
                          False, False), ("C AMPK restrains ULK1", True, True)):
    for n in (1.0, 0.5, 0.0):
        print(f"  {title:22s} n = {n:3.1f}:  " + "  ".join(f"{ulk1(n, e, cross, var):4.2f}"
                                                    for e in E))
# ULK1 activity; columns: energy stress e = 0.00  0.25  0.50  0.75  1.00
#   A mutual inhibition    n = 1.0:  0.01  0.01  0.01  0.01  0.86
#   A mutual inhibition    n = 0.5:  0.01  0.06  0.51  0.79  0.88
#   A mutual inhibition    n = 0.0:  0.17  0.73  0.84  0.89  0.91
#   B no cross-inhibition  n = 1.0:  0.01  0.08  0.14  0.20  0.25
#   B no cross-inhibition  n = 0.5:  0.01  0.14  0.25  0.32  0.39
#   B no cross-inhibition  n = 0.0:  0.17  0.73  0.84  0.89  0.91
#   C AMPK restrains ULK1  n = 1.0:  0.09  0.09  0.09  0.09  0.20
#   C AMPK restrains ULK1  n = 0.5:  0.16  0.15  0.23  0.24  0.21
#   C AMPK restrains ULK1  n = 0.0:  0.71  0.45  0.33  0.26  0.21

Model A (mutual inhibition) gives a very steep switch. With the nutrient signal at 1, ULK1 activity stays at about 0.01 as energy stress rises from 0 to 0.75 and jumps to 0.86 only at 1.00; once the nutrient signal falls to 0.5, moderate energy stress (0.5) is enough to switch it on (0.51). Model B (no mutual inhibition) is gradual: at the same nutrient signal of 1 and energy stress of 1, ULK1 reaches only 0.25. Mutual inhibition turns a graded input into an almost all-or-none output, which is the origin of the bistable switch described in Book 17.

Model C reaches the opposite conclusion. With plenty of nutrients and maximal energy stress, ULK1 is only 0.20; with nutrients withdrawn and no energy stress it reaches 0.71, the highest value in the table; and adding energy stress on top of nutrient withdrawal lowers ULK1 to about 0.2. If Park and colleagues’ results hold in tissues too, then the main signal that opens autophagy is the withdrawal of amino acids and insulin (mTORC1 switching off), not the energy trough itself.

“Locked in the anabolic state”: an inference with conditions

The other part of the author’s framework says that eating around the clock keeps mTORC1 active and autophagy off, so that damaged proteins pile up linearly, while periodic energy troughs regularly switch the clean-up on. This is a claim about a mass balance, and it can be written as an equation and checked.

# dD/dt = p - (b + c u(t)) D; u switches on with hours since the last meal, H50 = 12 h assumed
# (not a measured human value). Longest overnight fast 16 h. Illustrative, uncalibrated.
import math

SCHEDULES = {"grazing: 6 meals in 15 h (9 h fast)": (7, 10, 13, 16, 19, 22),
             "3 meals in 12 h (12 h fast)": (7, 13, 19),
             "2 meals in 10 h (14 h fast)": (9, 19),
             "2 meals in 8 h (16 h fast)": (11, 19)}

def u_of(h_of_day, meals, h50):
    since = min((h_of_day - m) % 24 for m in meals)      # hours since the last meal
    return 1 / (1 + math.exp(-(since - h50) / 1.5))

def mean_damage(meals, b, c, h50=12.0, days=60, dt=0.02):
    D, last = 0.0, []                                    # p = 1 per hour
    for i in range(int(days * 24 / dt)):
        D += (1.0 - (b + c * u_of((i * dt) % 24, meals, h50)) * D) * dt
        if i * dt >= (days - 7) * 24: last.append(D)
    return sum(last) / len(last)

print("mean damage in the last week, relative to no inducible clearance (D = p / b)")
print(" schedule                              | c/b = 0.5 | c/b = 2 | c/b = 5 | c/b = 2, H50 14 h")
B = 0.01
for name, meals in SCHEDULES.items():
    row = [mean_damage(meals, B, k * B) * B for k in (0.5, 2, 5)]
    alt = mean_damage(meals, B, 2 * B, h50=14.0) * B
    print(f" {name:37s} |   {row[0]:5.2f}   |  {row[1]:5.2f}  |  {row[2]:5.2f}  |   {alt:5.2f}")
# Linear piling-up needs zero basal clearance:
for b in (0.0, 0.001, 0.01):
    d30 = mean_damage((7, 13, 19), b, 0.0, days=30); d60 = mean_damage((7, 13, 19), b, 0.0)
    print(f"b = {b:5.3f}, no inducible clearance: mean D, days 24-30 = {d30:6.1f};"
          f" days 54-60 = {d60:6.1f}")
# mean damage in the last week, relative to no inducible clearance (D = p / b)
#  schedule                              | c/b = 0.5 | c/b = 2 | c/b = 5 | c/b = 2, H50 14 h
#  grazing: 6 meals in 15 h (9 h fast)   |    1.00   |   0.98  |   0.96  |    1.00
#  3 meals in 12 h (12 h fast)           |    0.98   |   0.92  |   0.82  |    0.97
#  2 meals in 10 h (14 h fast)           |    0.95   |   0.82  |   0.64  |    0.91
#  2 meals in 8 h (16 h fast)            |    0.92   |   0.74  |   0.53  |    0.84
# b = 0.000, no inducible clearance: mean D, days 24-30 =  636.0; days 54-60 = 1356.0
# b = 0.001, no inducible clearance: mean D, days 24-30 =  470.0; days 54-60 =  742.0
# b = 0.010, no inducible clearance: mean D, days 24-30 =   99.8; days 54-60 =  100.0

The program leads to three conclusions. First, linear piling-up requires the basal clearance to be exactly zero. As long as $b > 0$, damage tends to a plateau $p/b$ even without any inducible clearance: with $b = 0.01$ per hour, mean damage is about 100 in both days 24–30 and days 54–60. Only with $b = 0$ does damage rise linearly, from 636 to 1,356. With a very small $b$ (0.001), damage is still rising after two months, but it is slowly approaching a high plateau, not piling up without limit.

Second, the fasting window changes the height of the plateau. With a ratio of inducible to basal clearance $c/b$ of 2, the 16-hour fast lowers mean damage to about 74 % of the grazing schedule; with $c/b = 0.5$, only to 92 %; with $c/b = 5$, to 53 %. How much damage intermittent eating clears therefore depends entirely on a ratio that we do not know in humans.

Third, the conclusion is sensitive to the assumed timing of the switch. Moving $H_{50}$ from 12 to 14 hours, at the same $c/b = 2$, weakens the effect of the 16-hour fast from 0.74 to 0.84, and the 12-hour fast has almost no effect (0.97).

Chapter summary

mTORC1 integrates nutrient and growth signals, promoting synthesis and inhibiting autophagy; rapamycin extends lifespan in mice, but this is neither human evidence nor a reason to take the drug. ULK1 is where the mTORC1 and AMPK signals converge: in the classical picture AMPK activates and mTORC1 inhibits ULK1, and mutual inhibition makes the switch almost all-or-none, while cell studies from 2023 suggest that AMPK may restrain ULK1 under energy stress, in which case the main signal opening autophagy is nutrient withdrawal. “Eating around the clock makes damaged protein pile up linearly” holds only when basal clearance is zero; in general damage tends to a plateau, and the fasting window changes the plateau’s height by an amount that depends on parameters not yet measured in humans. The next chapter turns to another kind of “benefit of a low dose”: hormesis.