Unfortunately, there is not a simple answer to this question, because it depends on the circumstances, particularly the kinetic mechanism of the enzyme and the mode of inhibition of the inhibitor.
I recommend the following textbook to introduce this topic:
Evaluation of Enzyme Inhibitors in Drug Discovery: A Guide for Medicinal Chemists and Pharmacologists, by Robert A. Copeland.
Thanks Adam for your reply. I read the theory regarding enzyme kinetic mechanism and types of enzyme inhibitor( reversible, irreversible...) but when i tried to do it practically , i faced problems to calculate ki. Suppose, i want to find out ki of caspase-8 inhibitor, which parameters i need to check and how will i calculate it, i can not decide.
It is important to know that Caspase-8 is a protease, a single-substrate enzyme.
The next important point is the nature of the inhibition. Is it a rapid equilibrium inhibitor (not time dependent, i.e. the IC50 is the same at any time of measurement, as long as the rate of reaction is equal to the initial rate), or is its inhibition time-dependent?
If the inhibitor is in rapid equilibrium with the enzyme, is the IC50 close to the enzyme concentration (tight binding) or far above it?
If it is a time-dependent inhibitor, is it reversible or irreversible?
These questions must be answered in order to know how to analyze the data.
For an inhibitor in rapid equilibrium, standard introductory biochemistry textbook Michaelis-Menten kinetics apply, as long as the inhibition was not measured under tight-binding conditions ([I]>>[E]). In such a case, you have to determine whether the inhibitor is competitive, non-competitive, or uncompetitive. The Ki is a parameter in the M-M equation for each of these types of inhibitor. You can measure it by the old double-reciprocal plot methods (Lineweaver-Burk plot and Dixon plot, for example), or you can use more modern nonlinear regression.
For a tight-binding inhibitor in rapid equilibrium, you should use the tight-binding equation of Morrison to measure the Kd of the inhibitor.
For time-dependent inhibition, you must use a completely different analysis, which is covered in the book I suggested before. In some cases, it may not be technically possible to measure the Ki, only the parameter kinact/KI.
To start, it would be very useful to have a set of reaction progress curves (product concentration versus time) measured at a single enzyme concentration, a single substrate concentration, but a range of inhibitor concentrations. Plot these on the same set of axes. This will help you to decide which analysis needs to be done by showing whether inhibition is time-dependent or not.
Thank you once again Adam for your valuable suggestion. Actually, my inhibitor follows time dependent inhibition and it is reversible competitive inhibitor. I made two graphs : One is different substrate concentrations against different time points and another one is different inhibitor concentrations vs different times whereas substrate concentration is fixed. Is it the right way to determine Ki? If it is, what should i do next to calculate Ki value?
The usual method of analyzing time-dependent inhibition requires progress curves measured at a fixed substrate concentration with different inhibitor concentrations. Using nonlinear regression, each progress curve is fit to the equation describing the shape of this curve, which is
[P]=vst+(vi -vs) [1-exp(-kobst)]/kobs
vi is the initial rate and vs is the steady-state rate. t is time. [P] is product concentration, although it could also just be the raw measurement. You will need a program for doing the nonlinear regression. The only numbers you have to supply the program are a column for time and a column for [P] for each inhibitor concentration. The output will be values of vi, vs and kobs. You could also enter measured values of vi and vs if you are confident of them.
One then makes of plot of kobs versus inhibitor concentration. This plot could be linear or it could be curved.
The explanation gets more complicated after this point, so I recommend you read about it in Chapter 6 of the Copeland textbook. It's too long to write about here.
You will also need to know the Km of the substrate, which you will have measured from varying the substrate concentration, using Michaelis-Menten kinetic analysis..
https://www.youtube.com/watch?v=GEXimPr6YNY for (uncompetitive)
https://www.youtube.com/watch?v=pORApV-wZsM&list=PLLE3R1rwJOY5yB8r59xjB8F4x0-nlifDG&index=11(for competitve )
https://www.youtube.com/watch?v=kpDGUFCyt3o&list=PLLE3R1rwJOY5yB8r59xjB8F4x0-nlifDG&index=13( for mixed inhibtion)
these videos will be more helpful for you
every type of inhibtion has an equation to calculate ki.
Thank you Marwa Zayed for your suggestions. I have solved the issues.
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