Brain energy: how the brain runs on about 20 watts

2023-07-09T00:00:00+00:00

I saved this so I would not have to look it up every time I need these numbers. The first version was a dump of hundreds of values without sources, and some were wrong. In this revision I kept only what I could check. Where a number is my own calculation, the calculation is shown.

The budget

In the average adult, the brain is about 2% of body weight and accounts for about 20% of the oxygen, and therefore the calories, the body consumes.^[1] Raichle and Gusnard point out something else: during most cognitive tasks, local changes in blood flow measured with PET are 5% or less. The lights are on all the time. The cost is baseline, not on demand.

That is where the 20 watts come from. By definition, 1 MET, the resting expenditure, is 3.5 mL of O2 per kg per minute.^[2] For 70 kg, that is about 245 mL/min for the whole body, and 20% of that is about 49 mL/min for the brain. Each litre of O2 burning glucose releases close to 21 kJ, so:

$$49\ \text{mL/min} \times 21\ \text{kJ/L} \approx 1.03\ \text{kJ/min} \approx 17\ \text{W}$$

About 20 watts, less than many light bulbs.

How much ATP that is per day

The old version said the brain produces about 7.8 kg of ATP a day, "close to 70% of the brain's own weight". The first number holds up. The second does not add up.

The calculation: 49 mL/min of O2 times 1,440 minutes is about 70 litres a day, or about 3.15 mol of O2. Fully oxidizing one glucose uses 6 O2 and yields between 30 and 32 ATP, with today's measured P/O ratios.^[3] That is about 5.3 ATP per O2:

$$3.15\ \text{mol} \times 5.3 \approx 16.7\ \text{mol ATP} \times 507\ \text{g/mol} \approx 8.5\ \text{kg}$$

About 8 kg of ATP recycled per day. With a brain of 1.3 to 1.4 kg, that is about six times its weight, not 70%. The molecule is remade all the time; the stock itself is small.

Where the energy goes

In 2001, Attwell and Laughlin built the first detailed signalling budget for rodent grey matter.^[4] In their estimate, action potentials took 47%, the postsynaptic effects of glutamate 34%, the resting potential 13% and glutamate recycling 3%.

In 2012, Howarth, Gleeson and Attwell redid the calculation after it turned out that action potentials in mammalian neurons are much more efficient than previously thought.^[5] In the cortex, most signalling energy, 50%, goes to postsynaptic glutamate receptors, 21% to action potentials, 20% to the resting potential, 5% to transmitter release and 4% to recycling.

What survives both versions: the synapse dominates. Keeping a neuron alive is relatively cheap; making it talk is what costs.

The thermodynamics behind it

Every reaction is governed by the Gibbs free energy:

$$\Delta G = \Delta H - T\Delta S$$

ATP hydrolysis releases −30.5 kJ/mol under standard conditions. Inside the cell, with the real concentrations of ATP, ADP and phosphate, the value is more negative. The old version of this post said −30.5 was the value under brain conditions, and it is not.

The membrane potential is an energy reservoir. The human brain has on average 86 billion neurons,^[6] each holding about −70 mV across a membrane about 7 nm thick. That gives a field of 10 million volts per metre:

$$\frac{0.070\ \text{V}}{7 \times 10^{-9}\ \text{m}} = 10^{7}\ \text{V/m}$$

The Nernst equation gives the equilibrium potential of each ion:

$$E_{\text{ion}} = \frac{RT}{zF} \ln\frac{[\text{ion}]{\text{out}}}{[\text{ion}]{\text{in}}}$$

with R = 8.314 J/(mol·K), T = 310 K, z the valence and F = 96,485 C/mol. For potassium, with 5 mM outside and 140 mM inside, RT/F is 26.7 mV and the logarithm is −3.33, so the equilibrium potential is about −89 mV. Keeping these gradients against diffusion is exactly what the sodium-potassium pump does, and that is why it sits at the top of every energy budget.

Processing information also costs. Landauer's principle says erasing one bit costs at least kT ln 2.^[7] At 310 K, that is about 3 × 10⁻²¹ J per bit. If the brain did 10¹⁶ bit operations per second, a number that is my guess and not a measurement, the theoretical minimum would be:

$$10^{16} \times 2.97 \times 10^{-21}\ \text{J} \approx 3 \times 10^{-5}\ \text{W}$$

Several orders of magnitude below the real 20 watts. The brain runs far from the physical limit; it pays for speed and reliability.

The respiratory chain, one line per part

Mammalian complex I has 45 subunits: 14 core ones, conserved from bacteria to humans, and 31 specific to mammals.^[8] It pumps 4 protons per NADH. Complex IV, cytochrome c oxidase, reduces O2 to water and pumps 4 protons per O2. Mammalian ATP synthase has a ring of 8 c subunits: each 360-degree turn makes 3 ATP and moves 8 protons, about 2.7 protons per ATP, and the shaft turns about 100 times per second.^[9]

When complex I fails, disease shows up. Schapira and colleagues compared the substantia nigra of nine people with Parkinson's disease and nine controls, and found a specific defect in complex I activity.^[10]

The fuels

Glucose is the main substrate. But not the only one. Owen and colleagues catheterized cerebral vessels in three people fasting for 5 to 6 weeks and saw β-hydroxybutyrate and acetoacetate replace glucose as the brain's predominant fuel.^[11]

There is also lactate. Pellerin and Magistretti showed in 1994 that glutamate taken up by astrocytes stimulates glycolysis and lactate production in them,^[12] and that gave rise to the astrocyte-neuron lactate shuttle hypothesis. The real size of that flux is still debated, as the same group acknowledges in the model it published in 2015.^[13]

Where the neurons are

Of the 86 billion neurons, only 19% are in the cerebral cortex, which is 82% of the brain's mass.^[6] Most of the rest is in the cerebellum. The old version said the cerebellum held 50% of the neurons; it holds a lot more than that.

Sleep as cleaning

Xie and colleagues measured in live mice that natural sleep, or anaesthesia, increases the brain's interstitial space by 60%, which speeds up the exchange between cerebrospinal fluid and interstitial fluid and the removal of β-amyloid.^[14] It is in mice, but it is one of the most concrete explanations of why we need to sleep.

What changes it

Ketogenic diet. In the randomized trial by Neal and colleagues, with 145 children with drug-resistant epilepsy, 38% of those on the diet had more than a 50% reduction in seizures, against 6% in the control group.^[15] β-hydroxybutyrate, besides being a fuel, inhibits class I histone deacetylases.^[16]

Exercise. In a trial with 120 older adults, one year of aerobic training increased hippocampal volume by 2%, reversing about 1 to 2 years of age-related loss, with better spatial memory.^[17]

Modelling metabolism

Recon3D is the most complete reconstruction of human metabolism: 3,288 genes, 13,543 reactions and 4,140 unique metabolites.^[18] The model by Jolivet and colleagues brings together neuron, astrocyte and vasculature, combining the Buxton-Wang vascular model, Hodgkin-Huxley membrane dynamics and the metabolic pathways.^[13]

The question that interests me most

If every thought is sustained by electrons crossing the respiratory chain and by ATP being broken down by the trillion, is there a metabolic signature of consciousness? I do not know, and I have not found anyone who does. But understanding how 20 watts do what a data centre cannot is, to me, the most beautiful computing question there is.

Raichle and Gusnard, Appraising the brain's energy budget, PNAS, 2002. ↩
Jetté, Sidney and Blümchen, Metabolic equivalents (METs) in exercise testing, exercise prescription, and evaluation of functional capacity, Clinical Cardiology, 1990. ↩
Hinkle, P/O ratios of mitochondrial oxidative phosphorylation, Biochimica et Biophysica Acta, 2005. ↩
Attwell and Laughlin, An energy budget for signaling in the grey matter of the brain, Journal of Cerebral Blood Flow and Metabolism, 2001. ↩
Howarth, Gleeson and Attwell, Updated energy budgets for neural computation in the neocortex and cerebellum, Journal of Cerebral Blood Flow and Metabolism, 2012. ↩
Azevedo and colleagues, Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain, Journal of Comparative Neurology, 2009. ↩ ↩2
Landauer, Irreversibility and heat generation in the computing process, IBM Journal of Research and Development, 1961. ↩
Zhu, Vinothkumar and Hirst, Structure of mammalian respiratory complex I, Nature, 2016. ↩
Watt and colleagues, Bioenergetic cost of making an adenosine triphosphate molecule in animal mitochondria, PNAS, 2010. ↩
Schapira and colleagues, Mitochondrial complex I deficiency in Parkinson's disease, Journal of Neurochemistry, 1990. ↩
Owen and colleagues, Brain metabolism during fasting, Journal of Clinical Investigation, 1967. ↩
Pellerin and Magistretti, Glutamate uptake into astrocytes stimulates aerobic glycolysis, PNAS, 1994. ↩
Jolivet and colleagues, Multi-timescale modeling of activity-dependent metabolic coupling in the neuron-glia-vasculature ensemble, PLOS Computational Biology, 2015. ↩ ↩2
Xie and colleagues, Sleep drives metabolite clearance from the adult brain, Science, 2013. ↩
Neal and colleagues, The ketogenic diet for the treatment of childhood epilepsy: a randomised controlled trial, Lancet Neurology, 2008. ↩
Shimazu and colleagues, Suppression of oxidative stress by β-hydroxybutyrate, an endogenous histone deacetylase inhibitor, Science, 2013. ↩
Erickson and colleagues, Exercise training increases size of hippocampus and improves memory, PNAS, 2011. ↩
Brunk and colleagues, Recon3D enables a three-dimensional view of gene variation in human metabolism, Nature Biotechnology, 2018. ↩

Brenner Cruvinel - cérebro