ATP Hydrolysis: The Gibbs Free Energy That Runs Your Body

Hydrolysing ATP to ADP and phosphate has a standard free-energy change (ΔG°′) of about −30.5 kJ/mol (−7.3 kcal/mol). Inside a living cell the reactants aren't at standard 1 M concentrations, and the cell keeps ATP high relative to its products, which pushes the real ΔG to roughly −50 kJ/mol. Cells use that release to drive reactions that couldn't run on their own, by coupling them to ATP hydrolysis.

The number that runs your body

You don't keep much ATP on hand. You remake it constantly. A rough but well-grounded estimate is that a person turns over about their own body weight in ATP each day, on the order of 60 kg (BioNumbers, BNID 105606).

The arithmetic behind that comes from oxygen. Buono and Kolkhorst worked out that each litre of oxygen you consume corresponds to about 0.136 kg of ATP resynthesized, and an average college student uses 400 to 500 litres of oxygen a day (cited in BNID 105606). That is 54 to 68 kg of ATP a day. Their memorable example was a marathon world-record holder who, by the same reasoning, resynthesized about 60 kg of ATP in just over two hours.

Convert that to molecules. ATP's molar mass is about 507 g/mol (Wikipedia), so:

60,000 g ÷ 507 g/mol ≈ 118 mol per day

118 mol × 6.02 × 10²³ ÷ 86,400 s ≈ 8 × 10²⁰ molecules per second

Roughly 10²¹ ATP molecules hydrolysed and remade every second, mostly while you are doing nothing in particular. (The site's companion piece, ATP: Why Your Body Makes 40 Kg of It Per Day, tells the turnover story from the physiology side.)

Standard versus cellular ΔG: why cells get more

The −30.5 kJ/mol figure is ΔG°′: the free-energy change when ATP, ADP and phosphate are all at 1 mol/L, at pH 7 (Wikipedia). Even that standard value isn't a single number. It depends on magnesium, because Mg²⁺ ions bind and stabilize ATP. Measured standard values run from about −28 to −34 kJ/mol depending on the Mg²⁺ concentration (Milo & Phillips, Cell Biology by the Numbers; BNID 101989).

But no cell holds anything at 1 M. What matters is the actual Gibbs free energy change, which depends on concentrations:

ΔG = ΔG°′ + RT ln([ADP][Pi] / [ATP])

Cells keep that ratio tiny. Living cells hold the ATP/ADP ratio about ten orders of magnitude from equilibrium, with ATP around five times more concentrated than ADP (Wikipedia). Because the ratio inside the logarithm is far below one, the log term is strongly negative and ΔG becomes more negative than ΔG°′.

To see how much, take some illustrative round numbers: ATP at 5 mM, ADP at 1 mM (fivefold lower) and phosphate at 5 mM, at body temperature (310 K).

[ADP][Pi] / [ATP] = (0.001 × 0.005) ÷ 0.005 = 0.001

RT ln(0.001) = 0.008314 × 310 × (−6.91) ≈ −17.8 kJ/mol

ΔG ≈ −30.5 − 17.8 ≈ −48 kJ/mol

That lands inside the range textbooks quote. Alberts and colleagues give 46 to 54 kJ/mol of usable energy per ATP inside a cell, "because the ratio of ATP to the products ADP and phosphate is kept so high" (Essential Cell Biology, ch. 3). Measured values spread further: about −47 kJ/mol in E. coli growing on glucose, and up to about −70 kJ/mol in the muscle of athletes recovering after exertion (Milo & Phillips).

The gap between −30.5 and −50 isn't a correction. It is the point. A cell's power comes from how far it holds ATP from equilibrium.

Why ATP? Stable on the shelf, unstable on demand

A useful currency has to keep until you spend it. ATP is stable in water between pH 6.8 and 7.4 when there are no catalysts around, even though hydrolysis is strongly favoured (Wikipedia). It is thermodynamically unstable but kinetically stable: the same split between "favoured" and "happening" that keeps diamonds from turning into graphite. Enzymes decide when the reaction actually runs, and what it runs into.

One common phrase is worth correcting. ATP's phosphate links are often called "high-energy bonds". The energy isn't sitting in a bond waiting to be snapped. Breaking any bond costs energy. What hydrolysis releases is the difference in free energy between ATP plus water and the more stable products.

Why ATP rather than its chemical cousins? Nobody knows. GTP is chemically similar and does a different set of jobs, and Alberts and colleagues say plainly that why evolution chose ATP as the main carrier "remains a mystery" (Essential Cell Biology, ch. 3).

Coupling: how ATP pays for uphill reactions

Cells constantly need reactions with positive ΔG. They pay for them by coupling.

The standard example is glutamine. Making it from glutamic acid and ammonia has ΔG°′ ≈ +14.2 kJ/mol, so it won't go on its own. The enzyme glutamine synthetase first uses ATP to phosphorylate glutamic acid, making a high-energy intermediate, which then reacts with ammonia. Both steps happen on the surface of the same enzyme (Alberts et al., ch. 3). Add the free energies:

+14.2 + (−30.5) = −16.3 kJ/mol

The overall reaction is downhill, and it runs. This is the essential trick of metabolism: an unfavourable reaction gets dragged along by a favourable one through a shared intermediate. Simply having ATP nearby does nothing. The enzyme has to physically link the two.

How cells make it: ATP synthase and the proton gradient

In mitochondria, ATP is made by ATP synthase, a molecular machine in the inner membrane of mitochondria (and in the thylakoid membranes of chloroplasts). It sits across the membrane and lets protons flow from high concentration to low, using the energy of that flow to join ADP and phosphate. Its F₀ part rotates and drives the F₁ part, which makes the ATP (Wikipedia).

The proton gradient is set up by the electron transport chain as food molecules are oxidized. So the chain of payments runs from food, to a proton gradient, to ATP, to work. Mitochondria themselves have an evolutionary history worth knowing, and the site tells it in Mitochondria: The Ancient Bacteria Inside Every Cell.

Where it goes

Some of the biggest customers:

• Motors. A molecular motor pushing with about 5 pN over a 10 nm step does work of order 50 pN·nm, a little over 10 k_BT, which is well within what one ATP delivers in a cell (Milo & Phillips).
• Pumps. Moving ions against their gradients stores energy across membranes, and the cell spends ATP to keep those gradients charged. That stored energy is the subject of Membrane Potential: Ion Gradients as Thermodynamic Batteries.
• Biosynthesis. Building proteins, nucleic acids and lipids, with reactions like the glutamine example above.

Muscle keeps a backup. Phosphocreatine is "a rapidly mobilizable reserve of high-energy phosphates" in skeletal muscle, heart and brain. Creatine kinase transfers its phosphate to ADP to remake ATP, and the reaction runs in reverse when ATP is plentiful (Wikipedia). It is a buffer, not a store: it holds ATP levels steady through the first moments of a hard effort.

Information costs ATP too. Copying DNA accurately and building proteins without errors take energy. Charles Bennett estimated that the enzymes of DNA replication, transcription and translation dissipate 20 to 100 kT per step, far above the theoretical floor for erasing a bit (Bennett, 1982). That floor is the subject of Landauer's Limit.

The distance from equilibrium

ATP's textbook value describes a condition no cell is ever in. Living things spend most of their food holding ATP far from equilibrium, and the extra 20 kJ/mol or so they gain from that is what does their work.

The pebble: you don't run on ATP; you run on how far you keep it from equilibrium.

FAQ

How much energy does ATP hydrolysis release?

Under standard conditions (1 M concentrations, pH 7), ΔG°′ ≈ −30.5 kJ/mol (−7.3 kcal/mol), varying from about −28 to −34 kJ/mol with magnesium. Inside cells, the usable energy is about 46 to 54 kJ/mol, and measured values range from about −47 to −70 kJ/mol.

Why is ΔG in the cell different from ΔG°′?

Because ΔG depends on concentrations: ΔG = ΔG°′ + RT ln([ADP][Pi]/[ATP]). Cells hold ATP high and ADP and phosphate low, so the log term is large and negative and hydrolysis releases more free energy than the standard value.

How does ATP make unfavourable reactions happen?

By coupling. An enzyme transfers a phosphate from ATP to a reactant, making a reactive intermediate, so the overall reaction combines both free-energy changes. Glutamine synthesis (+14.2 kJ/mol) plus ATP hydrolysis (−30.5 kJ/mol) gives −16.3 kJ/mol.

How much ATP does the body use in a day?

About one body weight's worth, roughly 60 kg for an adult, based on oxygen consumption. That is about 118 moles, or close to 10²¹ molecules hydrolysed and remade every second.

Is ATP the only energy currency?

No. GTP is chemically similar and powers a different set of cellular jobs, and other activated carriers move electrons or chemical groups. ATP is the most widely used, and why evolution settled on it is still an open question.

Further Reading

• Alberts, B. et al. Essential Cell Biology, 6th ed. W. W. Norton. Chapter 3, section "Activated Carriers and Biosynthesis." https://nerd.wwnorton.com/ebooks/epub/ecb6/EPUB/content/3.3-chapter03.xhtml
• Milo, R. & Phillips, R. Cell Biology by the Numbers. "How much energy is released in ATP hydrolysis?" https://book.bionumbers.org/how-much-energy-is-released-in-atp-hydrolysis/
• BioNumbers BNID 101989, standard free energy of ATP hydrolysis (Rosing & Slater, 1972). https://bionumbers.hms.harvard.edu/bionumber.aspx?id=101989
• BioNumbers BNID 105606, daily turnover of ATP in humans (Buono & Kolkhorst, 2001, Advances in Physiology Education 25, 70-71). https://bionumbers.hms.harvard.edu/bionumber.aspx?id=105606
• Bennett, C. H. (1982). "The thermodynamics of computation: a review." International Journal of Theoretical Physics 21, 905-940. https://doi.org/10.1007/BF02084158
• "Adenosine triphosphate." Wikipedia: https://en.wikipedia.org/wiki/Adenosine_triphosphate
• "ATP synthase." Wikipedia: https://en.wikipedia.org/wiki/ATP_synthase
• "Phosphocreatine." Wikipedia: https://en.wikipedia.org/wiki/Phosphocreatine

This is Part 6 of the Gibbs Free Energy series. Next: Protein Folding: Free Energy's Masterpiece