[hardy5086]

I'm having some trouble with a couple of things and haven't been able to work it out.
so 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.

the lab manual has asked "Using the approximated, simplified expressions for X (equation 2), Y (equation 3)
and B (equation 4), determine kcat, [E]0act and k2/K for each kinetic experiment.
From these values, determine KM and p."

I have calculated kcat, [E]0act and k2/k, but cant work out how to determine km.

equation 2 is simplified to x≈kcat.[E]0act   (if [ S] >>km)
equation 3 is simplified to y≈[E]0act      (if [ S] >>km and k2>>k3)
equation 4 is simplified to B≈k2[ S]/k     (if [ S]>>km and k2>>k3)

where kcat = k2k3/(k2+k3) ≈ k3   (if k2>>k3)
km = k3k/(k2+k3)

Hint: to determine KM, consider how k2/K can be derived from the expressions for
kcat and KM.

I'm getting lost at this bit.
any help would be appreciated.

Edit by Borek: corrected the formatting, [S] is a tag for strikeout which make the post unreadable.

[Babcock_Hall]

Your formatting is unclear and inconsistent.  Some things seem to have been left out entirely.  Can you remedy this?

[hardy5086]

attached is a picture of the page describing the equations they have provided, I'm just unsure how to determine km from this.
I have calculated the values of X, Y, and B so I know, Kcat, [E], and K2[ S ] / K.
I also know the value of [ S ] so have calculated a value of K2/k

[hardy5086]

sorry about the first post, didn't realize when I was trying to put S into brackets for substrate concentration that it would strike through the text instead.

[Babcock_Hall]

It would help if you used subscripts and were consistent about capitalizing K.  If you look a the definitions of K_M versus k_cat, they contain many common terms. 

[hardy5086]

Sorry again, I typed some and cut and pasted some from the manual so my capitalizing was inconsistent and didn't notice the subscript button above.
I see that they have common terms, but making use of that to solve for K_m is where I am getting lost.

[Babcock_Hall]

Try expressing the fraction k_cat/K_M and see if it helps.

[hardy5086]

Kcat/Km =(K2 K3/(K2+K3 ))/(K3 K/(K2+K3 ))

Ok, from that I can see K₂/K
But that is one intimidating equation. I don't even know where to begin trying to rearrange that to solve for K_m

[Babcock_Hall]

I may not have properly understood what you are doing.  Are you trying to find a value for K_M, or are you trying to express K_M in terms of rate constants?

[hardy5086]

Im trying to find a value of K_m.

[Babcock_Hall]

attached is a picture of the page describing the equations they have provided, I'm just unsure how to determine km from this.
I have calculated the values of X, Y, and B so I know, Kcat, [E], and K2[ S ] / K.
I also know the value of [ S ] so have calculated a value of K2/k

If you mean "calculated a value of k₂/K," then is that what you are looking for?

[hardy5086]

from equation 2, 3 and 4 I have calculated the value of K_cat, [E]_oact and knowing [ S] I rearranged equation 4 and calculated a value for K₂/K. I need to calculate K_m. the "hint" given in the manual is to determine K_m, consider how K₂/K can be derived from the expression for K_cat and K_m. im not sure how to do it.

[Babcock_Hall]

Chemists often use lowercase k's for rate constants and uppercase K's for equilibrium constants and the Michaelis constant. 

You have values for k_cat and k₂/K, correct?  You previously wrote an equation that can be rearranged to solve for K_M  in terms of k_cat, K, and k₂.  At first pass that seems like all that you need.

[Babcock_Hall]

Kcat/Km =(K2 K3/(K2+K3 ))/(K3 K/(K2+K3 ))

Ok, from that I can see K₂/K
But that is one intimidating equation. I don't even know where to begin trying to rearrange that to solve for K_m

When you have the same thing in the numerator and denominator, they cancel out.  That should simplify it considerably.

[hardy5086]

I haven't done much maths of this standard and am not exactly sure how to treat a fraction over a fraction when rearranging. you say like terms cancel out so does that mean I can simplify the equation from
K_cat/K_m =(K₂ K₃/(K₂+K₃ ))/(K₃ K/(K₂+K₃ )) to K_cat/K_m = K₂ K₃/(K₃ K) by cancelling out the term (K₂+K₃) from the top and bottom? and then cancel out the K₃ and be left with _cat/K_m = K₂/K ?