Could you show your fit and the equation you used?

What are the enzyme and substrate?

the enzyme is Lysine monooxygenase

and the equation is substrate inhibition equation :

v= kcat[S]/(Km + [S] + [S2]/Kis) 

 The equation you use depends on the mechanism of substrate inhibition. By the figure you attached the equation you used could be right, but I suggest that you read more here http://onlinelibrary.wiley.com/doi/10.1002/bies.200900167/full and here: Plant Physiology and Biochemistry 41 (2003) 97–105. It may give you something to think about the biological function of substrate inhibution in your enzyme.

The fit of the data to the equation is very good. What is wrong with the numbers?

Maybe try dynafit (available for free) to test different models.

I used it recently and I nice data.

I agree the fit looks fine from the data you have presented. The only thing I would say is check that all other enzyme substrates are saturating and michealis-menten in nature (therefore satisfy steady state approximation). Also, nadph can react with oxygen in high concentrations to form ROS. So one thing to make sure of is that the inhibition isn't actually being caused by a drop in oxygen concentration or by the presence of peroxide or superoxide. Oxygen concentration can be measured by an electrode in a lysine free experiment or you can keep the nadph constant and use buffers containing different oxygen concentrations. catalase and superoxide disumtase can be added to make sure the ROS aren't playing a role.

Bastien is correct, DynaFit can be quite useful in fitting substrate inhibition data (and any other kind of enzyme kinetics or chemical kinetic data).   It is free for academic uses and you can download it from here:

   http://www.biokin.com/dynafit/

In DynaFit notation, one of the ways one could represent substrate inhibition is this:

[task]

   task = fit

   data = rates

   approximation = rapid-equilibrium

[mechanism]

   E + S E.S   :   Ks   dissociation

   E.S + S E.S.S  :   Ks2   dissociation

   E.S ---> E + P  :  kcat

This would apply under the "rapid equilibrium" approximation.  Here we assume that substrate inhibition comes about by the substrate binding twice, once "productively" and the second time "unproductively". 

For bi-substrate enzymes (A + B ---> P + Q) substrate inhibition very often happens when one of  the two substrates (say, B) is binding to a binary complex between the enzyme and the first product (say, P). This can only handled under the state approximation. 

For example, this is how an "Ordered Bi Bi" mechanism (with substrate inhibition) would look in DynaFit notation, under the steady-state approximation:

[task]

    task = fit

   data = rates

   approximation = king-altman

[mechanism]

    E + A EA : k1 k-1

    EA + B EAB : k2 k-2

    EAB EP + Q : k3 k-3

    E ---> E + P : k4 k-4

    EP + B EPB : k5 k-5 ; Substrate inhibition - B is an analog of Q

When DynaFit sees this input, it will derive the King-Altman rate equation for you, so you don't have to count "non-cyclic geometric patterns" and the like.  See also this BioKin Technical Note:

   http://www.biokin.com/publications/technotes/TN201503.html

This particular type of substrate inhibition ("B" being a structural analog of "Q") happens very often, for example in oxido-reductase enzymes (e.g., "B" = NAD+ being a structural analog of "Q" = NADH). It also happens with some frequency in protein kinases, where ADP is an structural analog of ATP.

The bottom line is that substrate inhibition in multi-substrate enzymes is very  common, almost to be expected.  It does not require us to imagine that there is anything "weird" going on.  As a side note, in the above example the maximum on the "B" saturation curve will be more prominent as substrate "A" approaches its own saturating concentration (whereas the saturation curve for "A" is a plain Michaelis-Menten hyperbola).

Now if there should be something truly unexpected about a substrate inhibition pattern, not explainable from theory of other available data, then my very first thought always goes to how the "initial" (presumably) reaction rates were actually determined.  Quite often the "initial" rates are not really what we think they are.  In extreme cases this can grossly distort the results of subsequent analyses.  You can go to my ResearchGate profile and look up a recent paper I posted there, to see what I mean.

• Kuzmic, P., Solowiej, J., and Murray, B. W., An algebraic model for the kinetics of covalent enzyme inhibition at low substrate concentrations, Anal. Biochem. 484 (2015) 82-90.

On a separate topic (since R2 was mentioned in the original post), please look at Figure 1 in that paper and make you own decision about what R2 is about -- and what it is not about.

Hope this helps...

P.S.: I just noticed that your enzyme is actually an oxido-reductase and that the substrate is NADPH.  I am guessing that the curve you just shows is obtained at a saturating concentration of the second substrate, correct?  If so, you could test if the substrate inhibition is "real" by gradually lowering the second substrate concentration to values below its own Km.  The saturating curve for NADH should resemble the classic hyperbola.  If it does, than you just discovered something new, namely, that your particular mutant is kinetically different from the wild-type enzyme.  If you need help with the global  fit of that type of substrate inhibition data (multiple saturation curves merged together, to get kcat, the two Km's and the Kii) please contact me and I'll show you how to do it in DynaFit.

 Thank you all for these helpful answers. 

Dr. Adam B Shapiro: 

the kinetic parameters using the fore mentioned equation is obtained using Kaleidagraph. I please look up the attached figure. 

Dr. Jason R Smith

So, I already know that my enzyme his higher oxidase activity than the wild type enzyme used to be in both absence and presence of the substrate. so, this gave me more to think about!!

Dr. Petr Kuzmic

Thank you for all this information. I will go through the paper. and check the Low concentration of the other substrate. in fact, the other substrate (L-lysine) is exhibiting substrate inhibition behavior but it is well fit to the equation I mention.

Also, I didn't mention that the wild type also exhibit substrate inhibition kinetics for both substrates, but the km is much higher in case of the mutant for L-lysine (~ 20-fold); that why I saturate the enzyme with L-lysine at higher concentration when NADPH is varied.

Dr. Florencio E. Podestá ·

Thank you. for the suggestion

Dr. Petr Kuzmic

I also have found some data when I am saturation the enzyme with 2 mM L-lysine when the km is ~7 mM and varying NADPH. the kinetics showing normal hyperbolic curve. but I think I will go higher than 2 mM. to be sure about this.

Heba, please be mindful that the equation you are using assumes that all other substrates are saturating and unchanging in their concentration relative to NADPH. As lysine is inhibitory as well, this is not physically possible unless the ki is >100-fold than the Km. All Km'e etc., are likely to be apparent constants, not actual constants.

Also, is mM correct or do you mean µM? mM concentrations is very far removed from biological concentrations, so I would also be mindful that the assay conditions are not guarenteed to be biologically relevent (that doesn't mean that they can't be though). I often see these very high Kms when using membrane associated proteins in a non-liposomal assay or when some other component is missing such as a reduction partner or cofactor.

I know that the rate is different when it is two-substrate dependent and also when there is inhibition. the ki for Lysine is ~ 20-fold higher than the km. but I can't even get this apparent constant for NADPH. 

and yes, the concentrations are expressed in mM (True); I have a km of ~ 350 uM (L-lysine) and 200 uM (NADPH) for the wild type. I think from the curve I had that I can get something close to km of NADPH (WT) but not for L-lysine. 

Am I correct about that!