GripChain
When one part of a protein changes shape, does the news reach the rest instantly? Hemoglobin says no. Its four O₂-binding subunits talk to each other — but only through the parts that touch, and it takes time. That through-contact conversation is what gives hemoglobin its famous S-shaped oxygen curve. Set the coupling yourself and see. Everything runs locally; nothing about you is collected.
This is misconception M13 — the idea that an allosteric signal teleports across a protein. In this game you build the wrong extremes on purpose (no link, and instant teleport) and find that the truth is the middle. The oxygen curve is drawn live from the Hill equation; no answer is stored. The science is written out below and works without JavaScript.
Loading the game… If it does not start, the explanation below still works.
How to play. Press Start. Drag the coupling 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.
The signal does not teleport
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. The signal travels through the parts that touch: a real mechanical change over a finite time, not action at a distance. (Model: Monod–Wyman–Changeux concerted T⇌R; the Koshland–Némethy–Filmer sequential model is the classical alternative.)
Three couplings, three curves
| Coupling | Hill n | Curve | What it means |
|---|---|---|---|
| No link | n = 1 | Hyperbolic | Subunits never feel each other — four independent sites, like four separate myoglobins. Grips O₂ in the lungs but barely lets go in the tissues. |
| Through contact | n ≈ 2.8 | Sigmoidal (real) | The reshape spreads through the parts that touch — the α1β2 salt-bridge interface — and takes a finite time. Real hemoglobin. Loads in the lungs, unloads a big share in the tissues. |
| Instant teleport | n → 4 | Near-vertical switch | The M13 mistake: one O₂ instantly flips all four at once, as if the signal jumped across the protein with no physical path. Steeper than the real curve — allostery is not a wire. |
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 far less O₂ over the same range. An instant “teleport” switch (n → 4) would be too brittle. The through-contact middle is the efficient, real answer.
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 coupling strength to the Hill coefficient n from 1 to 4; 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.