The claim

Richard Veech, a biochemist at the US National Institutes of Health who had trained with Hans Krebs, spent much of his career arguing that ketone bodies are not merely an emergency fuel but a better one. His most quoted evidence came from the working rat heart.

In popular writing this became “ketones produce more energy per unit of oxygen than glucose”, sometimes “a super-fuel”. This chapter checks the stoichiometry first and then looks at what Veech actually argued.

ATP per molecule of oxygen

When a fuel is oxidised in the mitochondria, its electrons are carried by NADH and FADH₂ to the respiratory chain, which uses their energy to pump protons; the proton gradient drives the synthesis of ATP. Current measurements put the yield at about 2.5 ATP for each pair of electrons from NADH and 1.5 for each pair from FADH₂ (Hinkle 2005). With those numbers, the ATP made per molecule of oxygen consumed can be counted for each fuel.

P_O_NADH, P_O_FADH2 = 2.5, 1.5            # ATP per pair of electrons to oxygen (Hinkle 2005)

def atp(nadh, fadh2, direct):
    return nadh * P_O_NADH + fadh2 * P_O_FADH2 + direct

fuels = {   # (ATP made, O2 used per molecule)
    # glycolysis + pyruvate dehydrogenase + 2 turns of the citric acid cycle
    "glucose":                (atp(10, 2, 4), 6.0),
    # BHB -> acetoacetate (1 NADH), then 2 acetyl-CoA; activation costs 1 GTP
    "beta-hydroxybutyrate":   (atp(1 + 2 * 3, 2 * 1, 2 * 1) - 1, 4.5),
    # 7 rounds of beta-oxidation, then 8 acetyl-CoA; activation costs 2 ATP
    "palmitate (fatty acid)": (atp(7 + 8 * 3, 7 + 8 * 1, 8) - 2, 23.0),
}
print(f"{'fuel':24s} {'ATP':>6s} {'O2':>5s} {'ATP per O2':>11s}")
for name, (a, o2) in fuels.items():
    print(f"{name:24s} {a:6.1f} {o2:5.1f} {a / o2:11.2f}")
# fuel                        ATP    O2  ATP per O2
# glucose                    32.0   6.0        5.33
# beta-hydroxybutyrate       21.5   4.5        4.78
# palmitate (fatty acid)    106.0  23.0        4.61

Per molecule of oxygen, glucose gives the most ATP, β-hydroxybutyrate about 10 per cent less, and fatty acids a little less again. This is a well-known pattern: the more reduced a fuel, the more oxygen it needs per ATP, because a larger share of its electrons enters the chain through FADH₂ or bypasses the first proton pump. On stoichiometry alone, the claim that ketones give more ATP per unit of oxygen than glucose is wrong.

What Veech actually argued: the free energy of ATP

Veech’s argument was not about counting ATP. It was about how much work each ATP can do.

The energy released when ATP is split into ADP and phosphate is not a fixed number. It depends on how far the reaction is from equilibrium inside the cell, that is, on the concentrations of ATP, ADP and inorganic phosphate (Pi):

$$\Delta G_{\text{ATP}} = \Delta G^{\circ\prime} + RT \ln \frac{[\text{ADP}][\text{P}_\text{i}]}{[\text{ATP}]} .$$

With $\Delta G^{\circ\prime} \approx -30.5$ kJ/mol and the concentrations found in cells, the actual value is around −55 to −65 kJ/mol, about twice the textbook figure.

from math import log

R, T = 8.314e-3, 310.0           # kJ/(mol K), K
dG0 = -30.5                      # standard free energy of ATP hydrolysis, kJ/mol (pH 7)

def dG_atp(atp_mM, adp_mM, pi_mM):
    return dG0 + R * T * log((adp_mM / 1000) * (pi_mM / 1000) / (atp_mM / 1000))

for label, atp_, adp, pi in (("resting cell (illustrative)", 8.0, 0.05, 2.0),
                             ("same ATP, a little more ADP", 8.0, 0.10, 2.0),
                             ("same ATP, less ADP and Pi", 8.0, 0.03, 1.0)):
    dG = dG_atp(atp_, adp, pi)
    print(f"{label:30s} ATP {atp_:4.1f}  ADP {adp:5.2f}  Pi {pi:3.1f} mM  ->  dG = {dG:6.1f} kJ/mol")
# resting cell (illustrative)    ATP  8.0  ADP  0.05  Pi 2.0 mM  ->  dG =  -59.6 kJ/mol
# same ATP, a little more ADP    ATP  8.0  ADP  0.10  Pi 2.0 mM  ->  dG =  -57.8 kJ/mol
# same ATP, less ADP and Pi      ATP  8.0  ADP  0.03  Pi 1.0 mM  ->  dG =  -62.7 kJ/mol

A shift of a few kilojoules per mole sounds small, but every ion pump and every contracting muscle fibre is paid in this currency. If each ATP releases more free energy, the same work needs fewer ATP, and fewer ATP need less oxygen. That is the sense in which a heart can become “more efficient” without any change in the ATP yield per oxygen.

Where the extra free energy comes from

Veech’s explanation ran through the redox states of the respiratory chain. Oxidising β-hydroxybutyrate produces NADH directly inside the mitochondrion, making the mitochondrial NAD couple more reduced; at the same time, in his measurements, the coenzyme Q couple became more oxidised. The energy available to the first proton pump depends on the difference in redox potential between these two couples. Widening it raises the proton-motive force the chain can maintain, and with it the phosphorylation potential, the ratio of ATP to ADP and Pi, which is what sets $\Delta G_{\text{ATP}}$ (Veech 2004). Chapter 5 puts numbers on the NAD side of this argument.

The human result is a useful correction. Ketones clearly change how the heart works, and the clinical interest in them for heart failure is real. But the specific claim of greater efficiency, which in the rat heart came with high ketone and insulin conditions, has not so far been reproduced in the human heart.

What this means for fasting and the brain

Three conclusions follow. First, ketones do not give more ATP per unit of oxygen than glucose; anyone who says they do has made an arithmetic mistake. Second, the more interesting argument concerns the free energy of ATP and the redox state of the mitochondria, and it was made in isolated rat organs perfused with several millimolar ketones, levels that people reach only after days of fasting or on strict ketogenic diets. Third, in a 16:8 schedule, where blood ketones at the end of the fast are a few tenths of a millimolar and supply perhaps a tenth of the brain’s fuel (Chapter 3), the thermodynamic effects described here are unlikely to be large. That is a prediction, not a measurement, and Chapter 9’s trial includes the measurements that could test its consequences.