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I performed enzyme kinetics experiments on a three independent preparations of an enzyme and produced the following three datasets which I separately fit to the Michaelis-Menten equation:

$$ V= \frac{V_{max} \times S}{K_m + S} $$

I used R / nlme's nlsList function to do the fitting:

fit=nlsList(V~Vm*S/(Km+S)|prep,data=na.omit(kinetics),start=c(Vm=3.5,Km=50))

and I get some coefficient values that make sense and some reasonable predicted curves:

V versus S plot of 3 enzymes

how can I test for differences between the coefficients ($V_{max}$ and $K_m$) between the preparations? I think I can perform a t-test using the coefficient estimates and standard errors but I am not sure how.

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  • $\begingroup$ I'm pretty sure this has a duplicate somewhere. Ah, found it. Not quite an exact duplicate, but the approach here should work $\endgroup$ – Glen_b -Reinstate Monica Aug 20 '13 at 0:33
  • $\begingroup$ Ok, If I do that approach I can combine all my data into a single fit. I still don't know how to determine whether the coefficients are different. $\endgroup$ – Yashka Oreza Aug 20 '13 at 1:47
  • $\begingroup$ There's a couple of ways that should work. Oh, actually, rather than try to type it all in a comment, see for example, pages 16-17 here. There are other tests, but hopefully that will assist you enough. $\endgroup$ – Glen_b -Reinstate Monica Aug 20 '13 at 2:34
  • $\begingroup$ I am not sure what is on those pages that is relevant to what I'm trying to assess, but on page 13 and 14 there is an example using the puromycin dataset that is helpful. I can add one or two explicit difference variables to the model V~(Vm+deltaVm1.2*indicator2+deltaVm1.3*indicator3+S)*S/(Km+deltaKm1.2*indicator2+deltaKm1.3*indicator3S) and use dummy coding to determine the difference that going from prep 1 to prep 2 and prep 1 to prep 3 produces. But I'm still missing the comparison from prep 2 to prep 3. $\endgroup$ – Yashka Oreza Aug 20 '13 at 16:56
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    $\begingroup$ You can either (i) fit two models, one where prep2 and prep3 have the same dummies, and one where they have different dummies and compare them using an F test via the information I indicated, or (ii) reparameterize so that you have a single dummy representing the contrast (that difference in the two preparations) and test it via a t-test or F-test. (Well there are other ways but those should work okay). Failing that, if you post some data I could see if I could explain how to do it using your data as an example. $\endgroup$ – Glen_b -Reinstate Monica Aug 20 '13 at 21:18

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