Derivation of the Hyperbolic Oxygen Binding Curve of Myoglobin

The binding equilibrium is described by the following equation

Mb + O 2 <=> MbO 2

where Mb is nonoxygenated myoglobin and MbO 2 is oxygenated myoglobin. As a result,

where the equilibrium constant K is called an association constant or affinity constant. The quantities in brackets denote molar concentrations of oxygenated myoglobin [MbO 2], nonoxygenated myoglobin [Mb], and free oxygen [O 2]. The fraction of myoglobin sites occupied is defined as follows:

Each myoglobin molecule has only one site, so the total number of available sites is proportional to the total concentration of myoglobin, [MbO 2] + [Mb]. Therefore,

where we have used [MbO 2] = K[Mb][O 2] from equation (7.1) to obtain the expression on the right. The concentration of unliganded myoglobin, [Mb], can be factored out of the numerator and denominator to give

or

where we have made use of the fact that 1/K = [O 2]1/2, the oxygen concentration when half of the myoglobin molecules have oxygen bound to them. It is easy to check this relationship by setting = 1/2 in equation (7.4). Because oxygen concentration is proportional to oxygen partial pressure, equation (7.5) can equally well be written as

where P 50 is the oxygen partial pressure for half-saturation. Equation 7.6 describes the hyperbolic oxygen binding curve of myoglobin in Figure 7.6.

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