# How to Calculate the p50 and Hill Coefficient for Myoglobin and Hemoglobin

Here is the formula that is used to calculate the p50 of hemoglobin and myoglobin: Note: n=1 for myoglobin calculations since it only contains one heme group.

Suppose you are given the following problems:

1. Calculate the fraction of oxygen sites bound to myoglobin when the pO2 is 5 torr
2. Calculate the partial pressure of oxygen needed to reach 80% saturation in myoglobin
3. Calculate the partial pressure of oxygen needed to reach 99% saturation in myoglobin.
4. Calculate the fraction of oxygen sites bound in hemoglobin when the pO2 is only 5 torr
5. Calculate the fraction of oxygen needed to reach 80% saturation in hemoglobin.

Before we begin, let’s define a few things:

p50 of myoglobin = 2.8 torr

p50 of hemoglobin = 26 torr

What is p50? p50 refers to the pressure at which myoglobin or hemoglobin is 50% bound to oxygen.

Using the formula above, we plug in the given pO2 value (5 torr) into the numerator and denominator and the given p50 above, as follows: Simplifying the equation we get: yO2 = 0.641

To get a percentage, multiple the answer by 100:

0.641 * 100 = 64%

This question is similar to #1, however, we are simply given the % of oxygen saturation and now simply have to solve for (pO2)

We setup the equation like this: Solving for X (check out mathway.com for an explanation) we get 11.2 torr

The solution is similar to #2, except the percentage is different (0.99)

The answer comes out to be 277.2 torr.

Note: You must convert the given percentage into decimal form (divide by 100)

Using the initial Hill formula, we follow the same steps as we did for answer #1.

However, since we’re dealing with hemoglobin and hemoglobin has 4 heme groups, the n coefficient refers to how many heme groups we’re dealing with.

The setup of the equation goes like this: There’s a bit more algebra involved here but the final answer comes out to be 0.0071 or 0.71% 