Amended on 8 May 2018

Substrates of enzyme can not usually be easily dissoved into water. BAQ (biotinyl 6-aminoquinoline), an artificial substrate for biotinidase, which can dissolve at most at 144 μM, and V can not be directly measurable using this hydrophobic substrates.

Therefore, I have measured initial velosities at around Km values (Km for BAQ in biotinidase is usually 10 μM, and Lineweaver-Burk plot safely gives V value; please see file, J Chrom B rat BIN LIP Km). This HPLC method has given us the economized consumption of enzyme substrate BAQ (Sigma has abruptly stopped selling the BAQ, but we are able to study about kinetic studies by our stock as shown in attached file).

Further, HPLC-enzyme assay method is uniquely quantitative as shown in our file. Direct utilization of photometer without beforehand separation or purification is very dangerous due to violence against the Lambert-Beer's law. The c.a. 2-fold difference in determined values has recently been demonstrated in the fucoidan determination (please see Fig. 10 of the file; JCB Fucoidan transport).

Furthermore, thank you very much to Dr. Cydi Longering (EZBiolab, Carmel, CA, USA) for clearly indicating the important issue. Therefore, I have previously declared that the enzyme concentration less than 0.1 mg/mL and the substrate consumption less than 10% are both essential to obtain the true results.

Enzyme kinetics should be measured the initial velocity at a very dilute condition, and the sensitive, quantitative, and reliable HPLC method becomes to be the essential and indispensable tool for enzyme kinetics study.

Further, V is expressed as pmol of substrate changed/min per mg of enzyme and/or protein. Therefore, precise determination of enzyme and/or protein is also essential by using quantitative, sensitive and quick HPLC-photometric method (please see file; HPLC-Surf-SEC protein determination method). Thus, we have found that final enzyme and/or protein concentration should be less than 0.1 mg/mL of reaction-mixture solution.

Hi there,

The actual equation for substrate inhibition is v=Vm.S/(Km + S(1+S/Ki)). For such equation, mathematical function analysis tells you that v will be max when S=(Km*Ki)1/2.

The way to get Vmax from the Michaelis plot (V versus [S]) in this situation is to use nonlinear regression to fit the data to the rate equation to obtain estimates of the kinetic parameters Km, Ki, and Vmax. This method can also be used, of course, when there is not substrate inhibition and is preferable to reciprocal plots.

Kinetic curve looks like substrate inhibition can be caused by other factors, such as stability of the enzyme. If the enzyme slowly loses its activity during reaction by aggregation, degradation or sticking on the wall, it can looks like substrate inhibition. So you need to make sure it is substrate inhibition.

Cydi from EZBiolab

Back to your question: How do you measure the reaction progress? If using an optical method, such as fluorescence or absorbance, the concentration of substrate at any reaction time can be calculated by:

F=fs[S]+fp[P], where F is observed fluorescence (or any other signal) at a given time point, fs is fluorescence of substrate and fp is that of product. Because [S]+[P]=[initial concentration of S], you can easily calculate [P].

However, an assumption of M-M equation is that v is initial reaction rate and [S] remain unchanged. So if you reaction reached to the degree that product has been accumulated so much that [S] can not be considered as [S total], M-M equation is no longer valid any more.

Cydi from EZBiolab

You could try progress curve analysis, as described for example on pp. 54 of

@BOOK{Seg-75,

title = {Enzyme Kinetics},

author = {I.H. Segel},

publisher = {Wiley},

year = {1975, reprinted 1993},

address = {New York},

abstract = {ein bischen veraltet, aber mit seinen vielen Geschwindigkeitsgleichungen sehr zeitsparend.},

isbn = {978-0-4713-0309-1},

language = {engl},

}

Substrate inhibition is not one phenomenon, it may have different kinetic mechanisms depending on which substrate binds to which enzyme complex in a non-productive manner, and also on how the enzyme can come out of this complex, whether following its footsteps backwards (dead-end inhibition) of following some alternative route to the productive complex. The observed response also varies if the reaction rate is measured under Steady-state conditions or Rapid-equilibrium conditions. You will find the answer to your question in chapter SIX, part A. system A5 of the book by I.H. Segel Enzyme Kinetics, 1993 edition, Willey-Interscience, New York, 1993.

There you can find the general equation, the corresponding double reciprocal plots, and the algebraic expression for their minima (which correspond to the maxima you are asking for).

Best wishes

Rogelio