I'm working with a tri-substrate system and want to gain insight into the the enzyme's mechanism and the relationship on substrate concentration and rate. I plan to use a microplate assay where I keep two substrates at the same concentration but vary the concentration of the third. Is this a sensible plan and if it works what do I do with this data?
Regards
Harry
The easy way is to do 3 separate sets of measurements. In each set, one of the substrate concentrations is varied and the other two are held constant at a saturating concentration. Then analyze these 3 data sets in the usual way for a single-substrate reaction to measure the Km for each substrate. Once you have measured each of the Kms, you can tell whether the concentrations you chose as saturating were really saturating. If not, the measured Kms will not be the true Kms and you will have to redo the experiment at a higher concentration of that substrate. This approach might be OK for your situation, if (a) all you want to know are the Kms for the substrates and (b) there is no substrate inhibition.
The thorough approach requires varying the concentrations of all 3 substrates in a matrix, covering a range of concentrations above and below the Kms. I find that a 2-fold geometric dilution series works well, with about 8 concentration of each substrate, including a zero concentration blank. Once you have measured the initial rate for every point in the matrix, preferably in triplicate, you will have a complete data set for the next stage, which is fitting the results to all the reasonable kinetic rate equations using a nonlinear regression computer program. If you see any substrate inhibition, you will have to incorporate it into the rate equations. For all the rate equations, and how to incorporate substrate inhibition, you can consult Segel's or Leskovac's books on steady-state enzyme kinetics. Each of the rate equations describes the results for one of the possible steady-state kinetic mechanisms. The chi-squared value for each of the fits will show which of the equations fits the data best, resulting in a short list of most likely kinetic mechanisms. Fitting will also supply the true Kms and some other kinetic constants.
Since you are using a microplate assay, you can collect a lot of data pretty quickly, so this complicated experiment becomes practical. If you have a continuous assay method for your enzyme reaction, it is vastly easier than using an endpoint assay because you only need one well to measure an initial rate and be sure it was an initial rate. If you can do a continuous assay in 384-well plates and have suitable pipetting equipment, the whole 8x8x8 matrix in triplicate can be done in 4 plates. If you use an endpoint assay and take multiple time points, you may need 2 dozen 384-well plates.
Hi Adam. Thanks very much for another perfect answer! I'll try the thorough method and let you know how I get on.
Best wishes
Harry
It is not necessary to use the whole 8x8x8 matrix. Using Taguchi's sparse matrix approach, you need only 2k+1 experiments (with k the number of factors), or the next higher number dividable by n (the number of different values per factor). In your case k = 3 and n = 8, so only 8 experiments are required (2*3+1 is 7, the next higher number dividable by 8 is 8). I have described the procedure in chapter 34 of Buxbaum 2011.
Actually, in enzyme kinetics one should work with at least 12 different, equally spaced concentrations to minimise experimental error. Thus 12 experiments would be required if a balanced matrix design is used.
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