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Haldane effect curve (blood CO2 dissociation)

What equation determines the shape of the blood $\ce{CO2}$ dissociation curve? I know that since it factors all possible forms of $\ce{CO2}$ carriage, there are a bunch of factors (e.g. Henry's law, formation of bicarbonates and carbaminohaemoglobin, how these are affected by protonation and oxygenation of haemoglobin, etc.) but these don't really seem to explain the non-linear shape. Whereas for oxygen it's fairly straightforward (saturation can be derived using equilibrium kinetics).

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