Solve Km with Alpha-ChymotrypsinHydrolysis & 4-Nitrophenyl Trimethylacetate

[hard0174]

I did a practical and am now trying to do the data analysis of it. the prac was the alpha-chymotrypsin catalyzed hydrolysis of 4-nitrophenyl trimethylacetate.
I have values for X, Y and B and the lab manual has asked "Using the approximated, simplified expressions for X (equation 2), Y (equation 3) and B (equation 4), determine K_cat, [E]_0act and K₂/K for each kinetic experiment.
From these values, determine K_m and p."

I have calculated K_cat, [E]_0act and K₂/K, but can't work out how to determine K_m.
the simplified equations are -
equation 2 is simplified to x ≈ K_cat.[E]_0act (if [ S] >>k_m)
equation 3 is simplified to y ≈ [E]_0act (if [ S] >>K_m and K₂>>K₃)
equation 4 is simplified to B ≈ K₂[ S]/K (if [ S]>>K_m and K₂>>K₃)

where K_cat = K₂K₃/(K₂+K₃) ≈ K₃ (if K₂>>K₃)
K_m = K₃K/(K₂+K₃)
the lab manual suggests "to determine K_m, consider how K₂/K can be derived from the expressions for
K_cat and K_m."
I'm lost and not sure how to solve for K_m. I have spent hours on it and just don't understand what it is I'm supposed to do.

 

[epenguin]

I did a practical and am now trying to do the data analysis of it. the prac was the alpha-chymotrypsin catalyzed hydrolysis of 4-nitrophenyl trimethylacetate.
I have values for X, Y and B and the lab manual has asked "Using the approximated, simplified expressions for X (equation 2), Y (equation 3) and B (equation 4), determine K_cat, [E]_0act and K₂/K for each kinetic experiment.
From these values, determine K_m and p."

I have calculated K_cat, [E]_0act and K₂/K, but can't work out how to determine K_m.
the simplified equations are -
equation 2 is simplified to x ≈ K_cat.[E]_0act (if [ S] >>k_m)
equation 3 is simplified to y ≈ [E]_0act (if [ S] >>K_m and K₂>>K₃)
equation 4 is simplified to B ≈ K₂[ S]/K (if [ S]>>K_m and K₂>>K₃)

where K_cat = K₂K₃/(K₂+K₃) ≈ K₃ (if K₂>>K₃)
K_m = K₃K/(K₂+K₃)
the lab manual suggests "to determine K_m, consider how K₂/K can be derived from the expressions for
K_cat and K_m."
I'm lost and not sure how to solve for K_m. I have spent hours on it and just don't understand what it is I'm supposed to do.

It is too hard work to guess some essentials of this question. I do not know what X, Y, B and p are. You give what equations 1, 2, 3 simplify to when [ S] >> K_m , but not what these equations are. Maybe these simplified equations are meant to be used together with some others. Anyway, realize that you cannot get any information about K_m from data where [ S] >> K_m.

Really there are a great number of books or online sources that explain how to determine K_m if that is the problem. Usually that involves expressing the Michaelis equation In terms of modified variables such as 1/v, 1/[ S] or others, and fitting to the best straight line.

If you need to reproduce here some of the lab manual photographically from an iPad or the like please use DocScan HD or similar app to clean it up, because we get some horrible unreadable dirty yellow pages often.

 

[hard0174]

yes, I agree that there are easier ways to express K_m but the lab isn't asking for that determination sadly. however, the problem has been resolved. K_m can be determined by combining equations
K_cat = K₂K₃/(K₂+K₃) ≈ K₃ (if K₂>>K₃)
K_m = K₃K/(K₂+K₃)