Hello,
I am trying to measure the kinetic parameters of an enzyme and inhibition kinetics for inhibition reactions, studied through HPLC. Can anyone help me with the path to take for the determination of these parameters. Like for Km and Vmax calculation, I can use different [S] at different time points. How do I do it for Ki calculation?
Thanks
Regards
Surbhi
I will assume we are talking about Michaelis-Menten kinetics and a non-covalent inhibitor that is in rapid equilibrium with the enzyme. If these conditions are not met, ignore what follows.
There are rate equations for the various modes of inhibition that include the parameter Ki. The simplest ones are for single-substrate enzymes with competitive, noncompetitive and uncompetitive inhibitors. These equations, which are extensions of the Michaelis-Menten equation, can be found in all the introductory biochemistry textbooks or on-line. For the more complex rate equations describing inhibition of enzymes with multiple substrates, you need to consult an advanced enzymology textbook, such as Segel's or Leskovac's.
https://www.amazon.com/Enzyme-Kinetics-Behavior-Equilibrium-Steady-State/dp/0471303097/ref=asc_df_0471303097/?tag=hyprod-20&linkCode=df0&hvadid=317002210742&hvpos=&hvnetw=g&hvrand=11671922287620580938&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9002079&hvtargid=pla-490282203998&psc=1
https://www.amazon.com/Comprehensive-Enzyme-Kinetics-Vladimir-Leskovac/dp/0306467127
The most thorough experiment and analysis to measure Ki involves varying the substrate(s) and the inhibitor concentration in a matrix, measuring the initial rate at each condition, then fitting all the data to the rate equation by a global nonlinear regression using a suitable computer program. It is a lot of work to do this when you have only an HPLC assay to measure the reaction rates, especially if the enzyme uses 2 or 3 substrates. You have to make sure that you always measure the initial rate, which means taking multiple time points for each condition.
An older method of analyzing this type of data is to use reciprocal plots and replots. These plots are very thoroughly described in Segel's book.
A shortcut can be employed if you already know the mode of inhibition of the inhibitor and can therefore write the rate equation. You also need to have already measured the substrate(s) Km(s) (and Kis, for some mechanisms) Then you can run the reaction at a single substrate concentration (or a single set of substrate concentrations for enzymes that use more than one substrate) and just vary the inhibitor concentration. You can then measure the IC50, the concentration of inhibitor that inhibits the initial reaction rate by 50%. From the IC50, you can compute the Ki using the rate equation, the substrate concentration(s) and Km(s) (and Kis if applicable), and the relevant Cheng-Prusoff equation.
The Cheng-Prusoff equation is derived from the rate equation. It relates the IC50 to the Ki of the inhibitor and incorporates the substrate concentrations and Kms (and Kis, if applicable). Cheng and Prusoff published a paper on this a while ago, but you can also easily derive it for your specific case with a bit of simple algebra.
https://www.sciencedirect.com/science/article/abs/pii/0006295273901962?via%3Dihub
Please look at the following below links which may help you in your analysis:
https://pubs.rsc.org/en/content/articlepdf/2020/an/d0an00721h
https://core.ac.uk/download/pdf/81206719.pdf
https://www.hindawi.com/journals/jchem/2018/2387926/
Thanks
Hello all,
I am doing this experiment first for Km and Vmax calculations. The problem I am facing is, the product formed after the reaction is being calculated in terms of AUC, which is in units of mV/AU, from the HPLC data. Do I need to have a standard to convert this to concentrations or just with the AUCs at different concentrations, the kinetic parameters can be analyzed.Please suggest.
Assuming that the peak area is directly proportional to the product concentration, you can use the peak areas to measure the Km, because it is in terms of substrate concentration. The Km will be the substrate concentration that gives half the maximal rate (peak area, in this case). It would be advisable to prepare a standard curve of product concentration versus peak are to make sure that there is a direct proportionality.
For Vmax, it is important to convert peak are to product concentration because Vmax is in terms of product amount (e.g. micromoles/minute). You also need to do this is order to calculate kcat from Vmax.
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