P50 (pressure)

In

The concept of p₅₀ is derived from considering the fractional saturation of a protein by a gas. Imagine myoglobin, a protein which is able to bind a single molecule of oxygen, as per the reversible reaction below, whose equilibrium constant K (which is also a dissociation constant, since it describes a reversible association-dissociation event) is equal to the product of the concentrations (at equilibrium) of free myoglobin and free oxygen, divided by the concentration of myoglobin-oxygen complex.

${\displaystyle {\ce {Mb+O_{2}<=>Mb\cdot O_{2}}}}$

${\displaystyle {\ce {\it {{K}={\rm {\frac {[Mb][O_{2}]}{[Mb\cdot O_{2}]}}}}}}}$

The fractional saturation Y_O2 of the myoglobin is what proportion of the total myoglobin concentration is made up of oxygen-bound myoglobin, which can be rearranged as the concentration of free oxygen over the sum of that concentration and the dissociation constant K. Since diatomic oxygen is a gas, its concentration in solution can be thought of as a partial pressure.

${\displaystyle Y_{O_{2}}={\rm {{\frac {[Mb\cdot O_{2}]}{[Mb]+[Mb\cdot O_{2}]}}\Rightarrow {\rm {{\frac {[O_{2}]}{\it {{K}\,{\rm {+\,[O_{2}]}}}}}\Rightarrow {\rm {\frac {\it {p{\rm {O_{2}}}}}{\it {{K}\,{\rm {+\,{\it {p{\rm {O_{2}}}}}}}}}}}}}}}}$

From defining the p₅₀ as the partial pressure at which the fractional saturation is 50%, we can deduce that it is in fact equal to the dissociation constant K.

${\displaystyle {\frac {p_{50}}{K+p_{50}}}=0.5\Rightarrow p_{50}=K}$

For example, myoglobin's p₅₀ for

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