Fractional Saturation of Hemoglobin

[catie1981]

Homework Statement

Calculate fractional saturation (YO2) for hemoglobin at venous O2 pressure (30 torr). Assume that p50 for hemoglobin is 26 torr, Hill constant is 3.

Homework Equations

YO2/1-YO2=(pO2/p50)^n

The Attempt at a Solution

(30/26)^3=1.54=(YO2/1-YO2)= 1.54 - 1.54YO2= YO2

This is pathetic. I am so mathematically retarded it hurts. How to solve for YO2...I can't seem to get it alone...why do they always play hard to get...grrr. Thanks for any help.

 

[catie1981]

OMG- I feel like a complete and utter idiot. I got it. *sheesh*

 

[Blueshift5]

I understand that it can be frustrating to struggle with mathematical equations. Let's break down the equation and see if we can make it easier to understand.

The equation you provided is known as the Hill equation, which describes the relationship between oxygen binding and oxygen pressure for hemoglobin. In this equation, YO2 represents the fractional saturation of hemoglobin, or the proportion of hemoglobin molecules that have oxygen bound to them.

First, we can rearrange the equation to solve for YO2 by multiplying both sides by (1-YO2):

YO2 = (pO2/p50)^n * (1-YO2)

Next, we can substitute in the given values for pO2 (30 torr), p50 (26 torr), and the Hill constant (3):

YO2 = (30/26)^3 * (1-YO2)

Now, we can simplify the equation:

YO2 = 1.54 * (1-YO2)

Multiplying out the parentheses, we get:

YO2 = 1.54 - 1.54*YO2

Finally, we can isolate YO2 by subtracting 1.54 from both sides:

YO2 - 1.54*YO2 = 1.54 - 1.54

Combining like terms, we get:

-0.54*YO2 = 0

Dividing both sides by -0.54, we get:

YO2 = 0

This means that at a venous oxygen pressure of 30 torr, the fractional saturation of hemoglobin is 0, indicating that very little oxygen is bound to hemoglobin molecules. This makes sense, as venous blood has already delivered oxygen to the tissues and is returning to the lungs to be re-oxygenated.

I hope this explanation helps to clarify the steps involved in solving this equation. Remember, practice makes perfect, and don't be too hard on yourself for struggling with math - it takes time and effort to build these skills. Keep at it and you will improve!