Question

Calculate the p₅₀ value for hemoglobin if Yo₂ = 0.82 when pO₂ = 25 torr.

Short answer

The p₅₀ value for hemoglobin if Yo₂ = 0.82 when pO₂ = 25 torr is 17.11 torr.

Step-by-step solution

Equation for the p50 value

To determine the p₅₀ of hemoglobin, Hill equation is used, which is as follows:

$Y_{O_2}=\frac{{\left(p{O}_2\right)}^n}{{\left(p_{50}\right)}^n+{\left(p{O}_2\right)}^n}$

Here,is the fractional saturation= 0.82; p₅₀ is the oxygen pressure where hemoglobin is half saturated, which is to be determined; pO₂ is the partial pressure of oxygen = 25 torr; n is the Hill constant of hemoglobin = 4.

Derivation of the Hill equation

From the above equation, we could be able to construct an equation for p₅₀.

$\begin{array}{rcl}{Y}_{O_2}& =& \frac{{\left(p{O}_2\right)}^n}{{\left(p_{50}\right)}^n+{\left(p{O}_2\right)}^n}\\ Y_{O_2}*{\left(p_{50}\right)}^n+Y_{O_2}*{\left(p{O}_2\right)}^n& =& {\left(p{O}_2\right)}^n\\ Y_{O_2}*{\left(p_{50}\right)}^n& =& {\left(p{O}_2\right)}^n-Y_{O_2}*{\left(p{O}_2\right)}^n\\ {\left(p_{50}\right)}^n& =& \frac{{\left(p{O}_2\right)}^n-Y_{O_2}*{\left(p{O}_2\right)}^n}{Y_{O_2}}\\ {\left(p_{50}\right)}^n& =& \frac{{\left(p{O}_2\right)}^n-\left(1-Y_{O_2}\right)}{Y_{O_2}}\end{array}$

Determination of p50 value

Putting all the values in the above equation, we get,

$\begin{array}{rcl}{\left(p_{50}\right)}^4& =& \frac{{\left(25\right)}^4\left(1-0.82\right)}{0.82}\\ {\left(p_{50}\right)}^4& =& \frac{390625*0.18}{0.82}\\ {\left(p_{50}\right)}^4& =& 85747\\ p_{50}& =& {\left(85747\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\\ p_{50}& =& 17.11torr\end{array}$

Hence, the value of p₅₀ is 17.11 torr