# Handling standard deviations in enzyme kinetics? - Kcat/Km (Sep/10/2007 )

Not sure how to do this. Basically I have 2 values......

Km - 123.24 ± 14.01 (uM)

Kcat - 0.0654 ± 0.00191 (s -1)

I need to divide these two values to give me Kcat/Km

i.e. 0.0654 ± 0.00191 / 123.24 ± 14.01

but how on earth do I handle the degrees of freedom? That is my question. Hope someone can help please?

cheers

Km - 123.24 ± 14.01 (uM)

Kcat - 0.0654 ± 0.00191 (s -1)

I need to divide these two values to give me Kcat/Km

i.e. 0.0654 ± 0.00191 / 123.24 ± 14.01

but how on earth do I handle the degrees of freedom? That is my question. Hope someone can help please?

cheers

may be I miss the point but you only have to divide the units (1/s:µM = 1/sxµM)

Km - 123.24 ± 14.01 (uM)

Kcat - 0.0654 ± 0.00191 (s -1)

I need to divide these two values to give me Kcat/Km

i.e. 0.0654 ± 0.00191 / 123.24 ± 14.01

but how on earth do I handle the degrees of freedom? That is my question. Hope someone can help please?

cheers

K_cat/K_m = 5.31 x 10^-4

Uncertainty in measurement = sqrt( (0.00191/K_m)^2 + (14.01*[-K_cat/K_m^2])^2 ) = 6.0 x 10^-5

Final answer = (5.3 +/- 0.6) x 10^-4 (s^-1)/uM

Is this what you are looking for?

I'm not one hundred percent positive (sad, I'm in a stats course this semester) but I believe you have one degree of freedom here. You have here two independent observations (Km and Kcat) but when you use them to produce Kcat/Km you loose one degree of freedom. Essentially (this is how it was explained in class):

0.0654/123.24=0.0005 (I dropped the plus-minus values to make it easier)

Now, how many numbers can you change and keep the answer (0.0005) the same? One. If you change Kcat to say .045, in order to keep the answer at 0.0005 there is only one possible number for Km (90). You have no freedom in the value of Km. On the other side, if you change Km, say to 150, the only possible answer for Kcat is 0.075. See how you only have one degree of freedom? I know this doesn't cover more complex situations and somewhere out there a statistician is screaming but it works for the basics. I have a good pdf paper I can send you that explains degree of freedom in much more depth. Lemme know, it's good for getting to sleep.