GripChain
When one O₂ binds hemoglobin, does it make all four subunits fill at once? No. Binding at one haem makes the others bind O₂ more readily — the effect travels through the subunit interfaces — but not all the way to all-or-none. That partial cooperativity is what gives hemoglobin its S-shaped oxygen curve. Set the cooperativity yourself and see. Everything runs locally; nothing about you is collected.
Toy model A simplified picture to show one idea. Not a measurement, and not a prediction. Of cooperative binding: the slider's curve is a simple model laid over the measured oxygen curve.
This is a common misreading — the idea that one binding event flips the whole protein completely, all or nothing. In this game you build the wrong extremes on purpose (independent sites, and an all-or-none switch) and find that the truth is the middle. The Hill coefficient n measures how cooperative the binding is — how steeply the curve rises — not how fast anything happens. The oxygen curve is drawn live from the Hill equation; no answer is stored. The science is written out below and works without JavaScript.
Press Start, then set the cooperativity to match what each round asks for.
Loading the game… If it does not start, the explanation below still works.
How to play. Press Start. Drag the cooperativity slider (or use the ←/→ arrow keys) until your blue curve matches what the round asks for, then press Enter or Lock in. The real curve is revealed and your fit is scored. Real hemoglobin sits near n = 2.8 — not at either edge.
Why this interface matters beyond the lungs
Fetal haemoglobin, built from gamma chains in place of beta chains, binds 2,3-BPG less tightly, so it holds oxygen more strongly than the mother's haemoglobin, which lets oxygen pass across the placenta to the fetus. Max Perutz and John Kendrew shared the 1962 Nobel Prize in Chemistry for the structures of haemoglobin and myoglobin; Perutz's later comparison of oxy- and deoxy-haemoglobin revealed the T and R states whose interface you just tuned.
Cooperative, but not all-or-none
Hemoglobin is a tetramer — two α and two β subunits (α₂β₂), each with a haem that binds one O₂. When an O₂ binds one haem, hemoglobin shifts between two quaternary states: T (tense, low affinity) and R (relaxed, high affinity). The structural change is a ~15° rotation of one αβ dimer relative to the other, which remodels the α1β2 (and α2β1) interface while the α1β1 / α2β2 dimers stay intact. The salt bridges and hydrogen bonds at that interface — MWC’s “quaternary constraints” — break and reform as the dimers rotate. This is how binding at one haem is felt at the others: through the interfaces where the subunits touch. Even in the Monod–Wyman–Changeux model, where all four subunits switch between T and R together, the switch is not tied to one particular O₂: T-state hemoglobin can hold some O₂ and R-state hemoglobin can be partly empty, so partly-filled molecules exist and n stays below 4. (The Koshland–Némethy–Filmer sequential model is the classical alternative.)
Three cooperativities, three curves
| Cooperativity | Hill n | Curve | What it means |
|---|---|---|---|
| Independent sites | n = 1 | Hyperbolic | Each haem binds O₂ on its own, unaffected by the others — like four separate myoglobins. With the same P50 it would give up less O₂ between the lungs (~100 mmHg) and the tissues (~40 mmHg) than real hemoglobin does. |
| Partly cooperative | n ≈ 2.8 | Sigmoidal (real) | Binding at one haem shifts hemoglobin toward the high-affinity R state through the α1β2 interface, so the next O₂ binds more readily — strongly but not completely. Partly-filled hemoglobins exist. Real hemoglobin. |
| All-or-none | n = 4 | Near-vertical switch | The common mistake: the idealized limit where the four haems fill together or not at all, so no partly-filled hemoglobin ever exists. Real hemoglobin never reaches it; its measured n stays below the number of sites. |
The Hill coefficient measures cooperativity; its theoretical maximum equals the number of sites (4 for hemoglobin). Real adult hemoglobin sits in the middle at n ≈ 2.8, with a P50 ≈ 26 mmHg (whole blood, pH 7.4, 37 °C). Myoglobin, a single non-cooperative subunit, is the n = 1 contrast — hyperbolic, with a much higher affinity (P50 ≈ 2 mmHg).
Why the middle matters
Because hemoglobin’s curve is sigmoidal, it loads O₂ in the lungs (pO₂ ≈ 100 mmHg, ~97% saturated) and unloads a large fraction in working tissues (pO₂ ≈ 40 mmHg, ~75% saturated). Four independent (n = 1) sites with the same P50 would give up less O₂ over the same range. Real hemoglobin cannot reach the all-or-none limit (n = 4), because partly-filled molecules always exist; n ≈ 2.8 is its measured cooperativity.
Methods & about
This is a teaching game and a simplification. The curve is the Hill equation Y = pO₂ⁿ / (P50ⁿ + pO₂ⁿ) — a phenomenological description; the exact four-site model is the Adair equation. The slider maps a cooperativity strength to the Hill coefficient n from 1 to 4 — n describes how steeply saturation rises with pO₂ (the degree of cooperativity), not a rate or a speed; your score is how near your n lands to each round’s answer. Nothing is fetched, no score history is kept, nothing is sent anywhere. A native version, when it ships, adds an interactive 3D T↔R hemoglobin.
Prefer a gentler protein puzzle? Try TwoIslands or the HingeHunt confidence games, or the Fold Commons apps. Everything we make is free and non-profit.