The Ki is a constant and would not change under normal conditions. As Adam already alluded to, if inhibition is competitive, the Ki does not change, but the IC50 or apparent Ki does. However, if inhibition is uncompetitive or allosteric, it is possible that its Ki might differ between the substrate-bound and substrate-free states.

In general, No. The Ki is the equilibrium dissociation constant of the inhibitor. As long as the mode of inhibition is the same (and the buffer conditions and temperature), the Ki will be the same. The IC50 may change, however.

An exception could occur if there is a direct interaction between the inhibitor and the substrate.

The Ki is a constant and would not change under normal conditions. As Adam already alluded to, if inhibition is competitive, the Ki does not change, but the IC50 or apparent Ki does. However, if inhibition is uncompetitive or allosteric, it is possible that its Ki might differ between the substrate-bound and substrate-free states.

Agreed. In that case, there would be two different Kis, one for each state of the enzyme (substrate bound versus free).

I agree with the answers above, but I'd like to elaborate a bit on the concept.

If the inhibition you are observing is purely competitive, and excluding improbable phenomena such as a direct interaction (in solution, not on the enzyme) between substrate and inhibitor, there is no waythe observed Ki can vary depending on the substrate.

On the other hand, enzyme inhibition is often uncompetitive or mixed, which implies the possibility of binding simultaneously substrate and inhibitor to the enzyme. In these instances, it is totally possible (I would even say it is likely) that Ki changes depending on the substrate you are testing.

I agree with Stephen Boulton. I think that the Ki of an inhibitor change based on each type of inhibition.

I thing it is depend on inheritor concentration ,Vmax ,Km of that enzyme

Ki is the dissociation constant of the enzyme-inhibitor complex. So, it is not dependent on the enzyme concentration.

Ki measures the dissociation of inhibitor from the free enzyme E, and therefore will by definition not be influenced by substrates (the apparent Ki of course will change due to competition of S and I for E). However, in uncompetitive inhibition, I will interact only with ES, this is described by Kii which could very well change depending on substrate. In non-competitive inhibition, the inhibitor interacts with both E and ES, so both Ki and Kii are relevant.

In this case, probably water would be as an inhibitor as an expensive and custom-made inhibitor. Are we missing anything here?

Ki measures binding of an inhibitor to an enzyme. The binding is dependent on the structure of inhibitor.