Well, no it is not expected that Ki is different for the same inhibitor even if you have assayed in the presence of different substrates. Since Ki is the equilibrium constant of dissociation of the EI complex and is (should be) ignorant of what substrate that is present. However, and maybe this is where things get confused, the *inhibitory effect* that you observe in your activity assays will be different and dependent on the Km of the substrate(s). In a pure competitive inhibition Km(app)=Km(1+[I]/Ki).

cheers,

/micke

Hi Andrew

I'm not too surprised you're getting different Ki values against the two substrates as you are using two quite different assays - it may be worth determining Ki values against the same substrate under the two different sets of conditions (if that's possible) to see what variation you get there.

If the assay conditions were identical and there were no other interactions going on and the enzyme was following simple Michaelis-Menten kinetics then the Ki values should be the same regardless of the Km for each of the substrates (as you will be determining Ki from its effect on Km) - lose any one of those three conditions however and you may get changes in Ki depending on substrate.

On your last point, that one substrate is a competitive inhibitor of another, this is to be expected: both molecule must bind to the same site (as they are substrates), but only one can bind at any one time (so just like the definition of a competitive inhibitor). If you are measuring rate by looking at the depletion of one substrate only, or by looking at the production of the specific product of one of the substrates, you will only see the reaction of one of them - the other will appear to be a competitive inhibitor and its concentration will not decline sufficiently over the normal time-course of the assay to significantly alter its inhibitory effect.

This effect can be exploited to find unproductive binding orientations for substrates - follow the kinetics of the reaction using a radiolabelled substrate, but include some non-labelled substrate as well. The non-labelled substrate will appear to be a competitive inhibitor so you can measure its Ki - if the Ki=Km then binding is only in the productive orientation, if Ki

True Ki is independent on substrate whereas IC50 (inhibitor concentration at half of the enzyme activity in the absence of inhibitor) is dependent on assay conditions, i.e. substrate type and concentration.

You should determine if it is a true competitive process as most changes in Km are most likely not due to competitive inhibition.

The competitive inhibition equation requires a linear change in Km with increase in inhibitor concentration, if you do not see this then the change is more likely to be hyperbolic, like the curve you see for classical MM kinetics or receptor binding kinetics. This indicates that your inhibitor when binding changes the binding surface of the enzyme but does not stop the catalysis somewhat like you would see if you look at the kinetic properties for the same enzyme from different species. The hyperbolic shape of the curve shows the mass binding effect on your population of enzymes in your preparation as the population shifts from free enzyme to enzyme bound by the inhibitor.

The observation of 2 different Ki's for the two substrates is not surprising if you consider that they interact with the enzyme binding surface differently so will respond differently to any change that is produced by the binding of an inhibitor.

for more information see

Limitations of conventional inhibitor classifications.

Walsh R, Martin E, Darvesh S.

Integr Biol (Camb). 2011 Dec;3(12):1197-201.

or

Alternative Perspectives of Enzyme Kinetic Modeling

http://www.intechopen.com/books/medicinal-chemistry-and-drug-design/alternative-perspectives-of-enzyme-kinetic-modeling

Why are you using two different enzyme preps for the two different substrates? If at all possible you should try to assay both substrates with the same prep, preferably the purified protein.The 'apparent' Ki's you are getting are probably just too far from the true Ki. If not, the Ki value you get for the substrate assayed with the purified prep might be closer to the true value (although it all depends as well on what might be present in the purification buffer -e.g. detergents, if any were used..). Also, how are you fitting your data in order to get your Ki and how many data points are you analyzing? Maybe you need more data points (if at all possible)?

Comparing crude preps with highly purified enzymes is comparing apples and oranges. You also violated a basic principle: Change only one parameter: You changed substrate and prep. You microsomal prep was well dialized / purified over Sephadex G 20 (or similar matrixes) column to remove all possible small ligands which could interfere --although some protein protein interaction can theoretically also interfere.. That's very common. That the new substrate is competing for binding is naturally obvious otherwise it could not be a good substrate. Getting Kcat/Km is always a good parameter. Test you old substrate with the purified enzyme and then you can make real comparison and I assume most of your questions will disappear. Good luck, I hope you still have some of the purified prep..

If your experiments are performed correctly, and to calculate Ki you measured activity at variable [S] and fixed-variable [I], the Ki is independent of Km. If the Mechanism is truly competitive and your enzyme is under Rapid equilibrium conditions, you can compare the relative affinity of ligands using Ki and Km. (See Cleland WW (1967) Enzyme Kinetics. Annual Review of Biochemistry 36(1):77-112. for details on the meaning of variable and fixed-variable).

I seems that you could have a clearer picture if you determine the specific enzyme activity in your crude extract and then compare your results to the kinetics from your purified enzyme preparation.

Just another short comment: See Enzyme Kinetics by Irvin H.Segel. Some regard it as the "bibel" for enzyme kinetics.

Here my cautionary comment:

Two substrates do not necessarily have to be purely competitive, i.e., if they bind differently although at the same binding site. You can e.g., get mixed inhibition pattern. This happens when the two substrates bind partially at the same time in the catalytic center. See Segel, it is interesting reading.

Also: Definitely you should check carefully --as suggested several times by the other scientists!--- that you have done the correct derivation of your constants (e.g., if it is a two substrate reaction (A+B +Enz => => Enz-substrate complexes=> product(s => in these cases for instance, you can not just do simple one substrate variation and keeping the other saturated etc.) Also-- as several times pointed out above--, having assayed enough concentrations as well as having parallel or triple assays for each point. It is a common case that non MM kinetics are overlooked by too few points and ignoring smaller variations from the expected theoretical curve. Enzyme kinetics, as much fun as they are, can be sometimes tricky but very interesting. Don't waste you time with the math part if you have not done enough assay points. Have fun and good luck.

The whole designation of inhibitors as competitive, mixed non-competitive and non-competitive is most likely erroneous. Non-competitive inhibition when rearranged from

Vmax/(1+[I]/Ki)

to

Vmax-(Vmax [I]/([I]+Ki))

demonstrates that change in Vmax is a result of mass action binding of the inhibitor to the enzyme. This is the same curve observed with the Michaelis-Menten equation or receptor binding

when you try the same thing with the competitive inhibition equation you the Km being divided by 1-the mass action binding term which results in a need for the mix noncompetitive inhibition which has two binding constants for one binding event.

by replacing the competitive term with a term that does produce the same sort of mass binding term associated with the non-competitive equation you can produce an equation that only requires one binding constant to describe changes in Km and Vmax

The other problem with competitive, non-competitive and mixed noncompetitive inhibition is a failure to distinguish between binding constants and effect on the enzyme

taking the non-competitive inhibitor term above

Vmax-(Vmax [I]/([I]+Ki))

while this tern does recognize the mass binding of the inhibitior with

[I]/([I]+Ki)

it assumes that the inhibition is total with the inhibitor binding

"-Vmax"

while there can be all sorts of different levels of activity remaining when the inhibitor binds so this term should be replaces with a delta Vmax term

deriving kientic equations the way segel does in his book ignore the difference between binding constants and effect on the catalytic system.and should be considered carefully before you decide to use them.

Sincere thanks to everyone who has taken the trouble to post these very helpful and interesting replies. As an organic chemist, these comments are extremely useful to me. It's good to know that the Ki should be independent of substrate under identical conditions. I guess as our conditions were not identical, then some difference is to be expected.

The number of data points and quality of the data looks very good for classical competitive inhibition. In the light of your comments, I will need to discuss further with my postdoctoral co-worker, who has done a great job on the the recent kinetic studies with the purified enzyme. He has kept [I] constant and varied [S] whereas the previous inhibition studies with the crude prep were done by varying [I].

By the way, the enzyme is a racemase and many of the inhibitors we have used are probably also substrates. I was aware of the shortcomings of having used different preparations but this was a result of availability of inhibitors, enzyme and resources. The work with the microsomal prep was done some time ago by a collaborating group. There well may have been some interference as a result of using this crude preparation as suggested above. I agree that measuring the kinetics with the original substrate using the purified prep is very important for us to do.

Incidentally, I made mistake with my final point. The new substrate Ki was virtually the same as the first substrate Km (I was looking at Ki for the wrong enantiomer) so I assume this suggests only productive binding. Once again, many thanks and I may well be in touch individually subsequently. I will be away for a while so apologies if I don't respond immediately.