[curiouscat]

I have the Km (μM)  Kcat (1/min) parameter values for a certain enzyme but they have been calculated at an enzyme conc. [E0] of 5 μM.

Would it be OK to use these same values at a higher [E0], say 20 μM?

Is there a way to extrapolate using the Michalis Menton enzyme kinetic parameters from one enzyme conc. to another?

[Babcock_Hall]

That is a more subtle question than it first appears to be.  If you look at the M-M equation, and use V_max = k_cat[enzyme], it is clearly linear in enzyme concentration.  However, every assay has to be validated to show that it is indeed linear with respect to enzyme concentration; it is one of the most important control experiments one can do.  I have written up some documents for my laboratory that tries to drive this important message home...

[curiouscat]

That is a more subtle question than it first appears to be.  If you look at the M-M equation, and use V_max = k_cat[enzyme], it is clearly linear in enzyme concentration.  However, every assay has to be validated to show that it is indeed linear with respect to enzyme concentration; it is one of the most important control experiments one can do.  I have written up some documents for my laboratory that tries to drive this important message home...

Would love to see those documents if you can share!

My problem here is one of estimation: I'm doing a literature driven assesment of a possible enzymatic process.

The activity parameters available were measured at a low [E0]. Why this was done I am not sure. For a viable process it would be nice if I could be using a much higher enzyme conc.

Of course, later this will be tested by experiments.

But my dilemma at this stage is how much of an [E0] could I reasonably assume to evaluate my process?

Is 5 micromoles a low / high / fair conc. as far as enzyme kinetics go?

[curiouscat]

Another way to put this is:

In your experience how good is the linearity assumption in Vmax = kcat[enzyme]?

Are there studies that have probed / tested this assumption over a range of enzyme concentrations?

[Babcock_Hall]

On the one hand, 5 µM is relatively high, as enzyme concentrations go.  On the other hand, if your enzyme has a low value of k_cat, then it will need more enzyme than otherwise, and 1 per minute is a relatively slow turnover number.  If someone has validated an assay under the same solution conditions up to a certain concentration of enzyme as you are using, then it should be fine.  If no one has, I would be very hesitant to make such an assumption.  Putting it another way, the assumption is probably best tested on a case-by-case basis, and for any change that I would make (even to a new pH), I would want to redo the linearity study.    The reasons why enzyme assays are not always linear with enzyme concentration are many, and so far the most thorough discussion I have found is in an old book (Enzymes) by Malcolm Dixon and Edwin Webb.  But one of the more common would be substrate depletion, which will happen more quickly at higher concentrations of enzyme.

[Babcock_Hall]

A related question concerns the linearity in time.  When I thought about this issue last summer, I came to the conclusion that there would be some overlap between the factors that will make the assay go nonlinear in time and when it will go nonlinear in [enzyme], but there are also factors that would affect one but not the other.  Feel free to comment about either document.

[curiouscat]

On the one hand, 5 µM is relatively high, as enzyme concentrations go.  On the other hand, if your enzyme has a low value of k_cat, then it will need more enzyme than otherwise, and 1 per minute is a relatively slow turnover number..

Sorry for confusing you. the (1/min) was merely my crude way of indicating the units.

The actual values are:

kcat    0.5 1/min
Km      0.6 microM
[E0]    5   micro M
[ S]     60  micro M  (max value tested)

[curiouscat]

Ideally I'd think the equation to use should be something like this

v= k x [E] / (kM1 + [E]) x [ S]/(kM2 + [ S])

This ought to take care of enzyme depletion as well as substrate depletion. That should scale across larger [E] ranges?

[Babcock_Hall]

You are missing the concentration of S in the numerator.  Also, I think we may be using the term "substrate depletion" differently.  I was only thinking about consumption of S to produce P during the course of the assay (one usually shoots for less than 5% or so during the period of measurement).  In the situation that you describe, the enzyme concentration is getting quite close to the substrate concentration, which is an atypical state of affairs.  It is often the case that the enzyme concentration is in the nano molar range, whereas substrate is in the micro molar or occasionally millimolar range.  Offhand I don't know of a good literature reference which deals with this kinetic situation.  Let me think on it.
EDT
I keep forgetting that if I enclose S or I in concentration brackets, that I get unwanted formatting.  I think I can put a space in between the first bracket and the letter:  [ S] or [ I]

[Yggdrasil]

Given that the concentration of enzyme is greater than the Km, at low substrate concentrations you will be looking at the pre-steady state kinetics (looking at single turnover events by the enzyme) rather than the steady state conditions (reflecting multiple turnover events) that the Michaelis Menten equation is meant to describe.

[Babcock_Hall]

curiouscat,

Is there any chance that the enzyme concentration is really in nano molar, not micro molar?

[curiouscat]

curiouscat,

Is there any chance that the enzyme concentration is really in nano molar, not micro molar?

Hmm...could be if the authors made an error.  Am I interpreting this snippet correctly?

Here's the relevant snippet:

[curiouscat]

Given that the concentration of enzyme is greater than the Km, at low substrate concentrations you will be looking at the pre-steady state kinetics (looking at single turnover events by the enzyme) rather than the steady state conditions (reflecting multiple turnover events) that the Michaelis Menten equation is meant to describe.

Ah! Great point.

So, that would imply it is just a bad measurement strategy employed by the study authors?

i.e. They ought to have taken measurements at way lower [ E0] or way higher [ S]?

Am I interpreting what you wrote correctly? In other words, is this kinetics data I got from the paper usable at all?

[Babcock_Hall]

They are implying steady-state, but my recollection is that being in steady state for an appreciable length of time requires that [ S] >> [ E].  One thing that is a bit odd; they give the concentration of "proteins" which implies that there is a mixture of proteins and that the concentration of any one enzyme might be less than that.  Just brainstorming here.

[curiouscat]

The mystery deepens! I got another set of kinetic constants for the same enzyme from the Uniprot database:

kcat is 0.34 sec(-1)

KM=1.4 µM

These seem quite different from the earlier constants. Unfortunately the [ E0] isn't mentioned here. (What good is kcat & kM is you don't mention a [ E0]? You can't use these constants quantitatively without an [ E0] value, right?)


http://www.uniprot.org/uniprot/E3W202