I am working on the effects of inhibitors, particularly of AlO and FeO on soil phosphatases. Currently, we want to test the effects of AlO and FeO on the activity of phosphatases. We only have one concentration of AlO and FeO per soil layer, the background concentration of those two found in the soil. In papers and books that I found, particularly Dick and Tabatabai 1987, it is necessary to get more than one concentration of inhibitor because alpha and beta are the effects of the Ki on how Vmax and Km changes. Ki is also the x-intercept of the linear regression of the inhibitor concentration and catalytic efficiency. We are currently using the Lineweaver-Burk plot for Michaelis-Menten Kinetics.
Is there anyway we derive Ki, alpha, and beta from only one concentration? Is there anyway to model it? Or we really need to know those values by experimentation (or by literature if ever). Thank you so much.
In principle, you can measure Ki with a single inhibitor concentration, but you would have no way to judge the precision of the measurement. Consider the rate equation for a single-substrate enzyme with a competitive inhibitor:
rate = Vmax[S]/{Km(1 + [I]/Ki) + [S]}
[I] is the inhibitor concentration, [S] is the substrate concentration.
If you already know the inhibitory mechanism (competitive in this case), and the values of Km, Vmax, [S] and [I] and you measure the rate (the initial rate, to be specific), you can solve for Ki. All assumptions related to Michaelis-Menten kinetics apply, and the inhibitor concentration should be substantially greater than the enzyme concentration.
I would not recommend this practice, but if you only have the one measurement, you can at least get an initial estimate of the Ki.
Paul John Joseph Cunanan Gubalan; I recommend keeping the amount of substrate constant, using different inhibitor concentrations, and drawing a dixon plot to find the constant of Ki.
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