An apparent paradox

The previous chapter found that, per molecule of oxygen, ketones yield less ATP than glucose. Yet in some experiments a heart supplied with ketones as well as glucose did more work without a matching rise in oxygen use. Richard Veech and colleagues explained this with mitochondrial thermodynamics (Sato et al. 1995; Veech et al. 2001; Veech 2004). This chapter computes the argument with the Nernst equation and then asks how much evidence there is for it in humans.

Where the energy comes from: the redox span

The mitochondrial respiratory chain passes electrons from NADH to oxygen, pumping protons across the inner membrane along the way, and the protons flowing back drive ATP synthesis. The “head” of energy depends on the redox potential difference between electron donor and acceptor. The potential of a couple is given by the Nernst equation:

$$E = E^{0\prime} – \frac{RT}{nF}\ln\frac{[\text{reduced}]}{[\text{oxidised}]}$$

where $n$ is the number of electrons transferred and $F$ the Faraday constant. The free energy released when an electron pair moves from NADH to coenzyme Q is:

$$\Delta G = -nF\,(E_{\text{Q}} – E_{\text{NAD}})$$

The free energy of ATP hydrolysis depends on the concentrations of ATP, ADP and inorganic phosphate:

$$\Delta G_{\text{ATP}} = \Delta G^{0\prime} + RT\ln\frac{[\text{ADP}][\text{P}_\text{i}]}{[\text{ATP}]}$$

Veech’s argument has two steps. First, ketone metabolism makes the free mitochondrial NAD couple more reduced (a higher NADH/NAD⁺ ratio) and the coenzyme Q couple more oxidised, widening the potential difference between them so that each electron pair can do more work. Second, in the perfused heart the measured free energy of ATP hydrolysis also became larger in magnitude (Sato et al. 1995; Veech 2004).

# Veech's thermodynamic argument, computed with the Nernst equation. Every concentration ratio below
# is ILLUSTRATIVE: chosen only to show the direction of change Veech and colleagues reported in the
# working perfused rat heart (Sato et al. 1995; Veech 2004), not their measured values.
#   E = E0' - (R T / n F) ln([reduced]/[oxidised])          (n = 2 electrons)
#   Delta G of the electron pair moved from NADH to coenzyme Q:  dG = -n F (E_Q - E_NAD)
#   Free energy of ATP hydrolysis:  dG_ATP = dG0' + R T ln([ADP][Pi]/[ATP])
import math
R, T, F = 8.314, 310.15, 96485.0
RT = R * T / 1000                       # kJ/mol
E0_NAD, E0_FUM = -0.320, 0.031          # volts at pH 7: NAD+/NADH and fumarate/succinate
# The Q couple is not measured directly in such experiments; it is commonly inferred from the
# fumarate/succinate ratio, on the assumption that succinate dehydrogenase (complex II) keeps the
# two couples close to equilibrium.
def E(E0, red_over_ox, n=2):
    return E0 - (R * T / (n * F)) * math.log(red_over_ox)

def dG_ATP(atp_mM, adp_uM, pi_mM, dG0=-30.5):
    return dG0 + RT * math.log((adp_uM * 1e-6) * (pi_mM * 1e-3) / (atp_mM * 1e-3))

states = {   # mitochondrial free [NADH]/[NAD+], [succinate]/[fumarate], cytosolic free ADP (uM), Pi (mM)
    "glucose only":         dict(nadh_nad=0.05, succ_fum=1.5, adp=60, pi=3.0),
    "glucose + ketones":    dict(nadh_nad=0.15, succ_fum=0.7, adp=40, pi=1.5),
}
print("state              E(NAD) mV  E(Q, via fumarate) mV  span mV  dG of span kJ/mol  dG_ATP kJ/mol")
for name, s in states.items():
    e_nad = E(E0_NAD, s["nadh_nad"]); e_q = E(E0_FUM, s["succ_fum"])
    span = e_q - e_nad
    dg_span = -2 * F * span / 1000
    g_atp = dG_ATP(8.0, s["adp"], s["pi"])
    print(f"{name:18s} {e_nad * 1000:9.0f} {e_q * 1000:21.0f} {span * 1000:8.0f} {dg_span:18.1f} {g_atp:14.1f}")
print(f"each 10-fold change in [NADH]/[NAD+] moves E(NAD) by {R * T / (2 * F) * math.log(10) * 1000:.1f} mV")
print(f"each 10-fold change in [ADP][Pi] moves dG_ATP by {RT * math.log(10):.1f} kJ/mol")
# state              E(NAD) mV  E(Q, via fumarate) mV  span mV  dG of span kJ/mol  dG_ATP kJ/mol
# glucose only            -280                    26      306              -59.0          -58.1
# glucose + ketones       -295                    36      330              -63.8          -60.9
# each 10-fold change in [NADH]/[NAD+] moves E(NAD) by 30.8 mV
# each 10-fold change in [ADP][Pi] moves dG_ATP by 5.9 kJ/mol

In these illustrative numbers, tripling NADH/NAD⁺ and halving succinate/fumarate widen the span between NAD and Q from 306 mV to 330 mV, raising the free energy per electron pair from −59.0 to −63.8 kJ/mol; at the same time, lower free ADP and inorganic phosphate change the free energy of ATP hydrolysis from −58.1 to −60.9 kJ/mol. The last two lines of the program give two useful rules of thumb: each tenfold change in NADH/NAD⁺ moves the potential by about 31 mV, and each tenfold change in the product of ADP and phosphate moves the free energy of ATP hydrolysis by about 5.9 kJ/mol.

The calculation shows the internal logic of Veech’s argument: any advantage of ketones lies not in more ATP per molecule of oxygen (they yield less), but in changing the redox state of the couples and the free energy of ATP hydrolysis. It also shows how sensitive the argument is to concentration ratios: changes of a few fold produce differences of tens of millivolts, and these ratios are hard to measure accurately in living tissue.

Where the evidence is, and where it ends

The present state of Veech’s hypothesis, then, is this: it has an experimental basis in the isolated heart and its internal logic is consistent; but it relies on concentration ratios that are hard to measure in vivo, and the evidence in the human brain and in exercise performance is inconsistent. “Ketones are a superfuel” goes far beyond the evidence.

Summary

Veech’s thermodynamic argument does not claim that ketones yield more ATP per molecule of oxygen; it claims that ketones change the redox state of mitochondrial couples and the free energy of ATP hydrolysis. The Nernst equation shows that the argument is logically sound but highly sensitive to concentration ratios. Evidence from the isolated heart supports it; evidence from the human heart points the same way but leaves the mechanism unsettled; evidence on exercise performance conflicts. The next chapter turns to another identity of ketones: as signalling molecules.