The following data describe the binding of oxygen to human myoglobin at 37oC.

P02 (mm Hg) = 0.5 1 2 3 4
Theta = .161 .277 .434 .535 .605

P02 (mm Hg) = 6 8 12 20
Theta = .697 .754 .821 .885

From these data, estimate:

a). P50
b) the fraction saturation of myoglobin at 30 mm, the partial pressure of O2 in venous blood.

I don’t know how to start and go about solving this problem.

Should I use this formula to calculate P50? Y=[S]^n / [S]^n + [S50]^n

Some please help.

To estimate P50 and the fraction saturation of myoglobin at 30 mm, we can use a plotting method called the Hill plot. This involves plotting the values of Theta (fraction saturation) against the corresponding values of P02 (partial pressure of oxygen), and then analyzing the resulting graph.

Here's how to approach it:

Step 1: Plotting the Data
Using the data provided, create a graph with P02 (mm Hg) on the x-axis and Theta on the y-axis. Plot the points for both sets of data given.

Step 2: Analyzing the Graph
Look at the shape of the graph. For myoglobin, we expect the curve to be sigmoidal (S-shaped). This kind of curve indicates cooperative binding, where the binding of one oxygen molecule makes it easier for subsequent oxygen molecules to bind.

Step 3: Estimating P50
P50 is the partial pressure of oxygen at which myoglobin is 50% saturated. In other words, it represents the P02 value at the midpoint of the sigmoidal curve. To estimate P50, locate the midpoint on the x-axis (where Theta is 0.5), and read off the corresponding P02 value. This is your estimate for P50.

Step 4: Estimating Fraction Saturation at 30 mm
To estimate the fraction saturation (Theta) at 30 mm P02, locate the point on the x-axis where P02 is 30 mm. Read off the corresponding Theta value from the graph. This will give you an estimate of the fraction saturation of myoglobin at 30 mm P02.

It is not necessary to use the formula you mentioned in your question. The Hill plot method is commonly used to estimate P50 and other binding parameters.

I hope this explanation helps you understand how to approach this problem.