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 the P50 (partial pressure at which the protein is 50% saturated) from the given data, you can use a Hill plot. The Hill equation is commonly used to describe the oxygen-binding curve for proteins like myoglobin.

The equation you provided is the Hill equation, which can be used to fit the data and estimate the value of P50. However, before using this equation, we need to transform the given data into a suitable form for the analysis.

First, we need to express the oxygen saturation (Theta, Θ) in terms of the oxygen pressure (P02, in mm Hg). We can accomplish this by plotting a graph of Theta versus P02.

Next, draw a line connecting the two data points closest to 50% saturation (0.5 and 1 mm Hg). Extend this line until it intersects the Theta = 0.5 value. The corresponding P02 value at this intersection will be our estimate of P50.

To estimate the fraction saturation of myoglobin at 30 mm Hg (partial pressure of O2 in venous blood), you can read the corresponding Theta value directly from the graph or calculate it using the estimated P50.

Here's a step-by-step guide to help you solve the problem:

1. Plot a graph with Theta (y-axis) versus P02 (x-axis) using the given data points.
2. Connect the two data points closest to 50% saturation (0.5 and 1 mm Hg) with a straight line.
3. Extend this line until it intersects the Theta = 0.5 value (or halfway between 0 and 1 on the y-axis).
4. Read the corresponding P02 value at the intersection point. This will be your estimated P50.
5. To find the fraction saturation at 30 mm Hg, locate the point on the graph representing 30 mm Hg on the x-axis and read the corresponding Theta value on the y-axis.

By following these steps, you can estimate both the P50 and the fraction saturation of myoglobin at 30 mm Hg.