Measurement of enzyme reaction rates
Alkaline Phosphatase Kinetics
As was mentioned in the Intro., temperature control is all important. This protocol is designed to assure that this is achieved.
5 ml of reaction buffer [100mM imidazole: 50 mM acetate, pH 7, I = 0.05) was made up (no need to adjust pH) & placed in the 15 ml tube that is inserted in the thermostatic box as shown previously [PHOTOS]. Do this when first switching ON. This ensures that the buffer mixture is close to the correct temperature (25 deg C) when placed in the cells. Note that the exact temperature is less important than temperature stability.
The apparatus requires 10 min to come to thermal equilibrium from switch ON, prior to use.
Reaction buffer and substrate are placed in both cells, the top of the thermo box is put in place and the bridge balanced using the *10-turn pot.
* A simple 1-turn pot works fine for normal use.
Recording is started to ensure a flat baseline (i.e. that thermal equilibration is achieved) and then the enzyme (blood, urine or other aqueous sample) is quickly added (via the hole in the top of the box above the sample cell) in as small a volume as possible (I use 10 micro litres) and thoroughly stirred using the pipette tip.
Recording of the initial velocity or progress curve is commenced. The recorded rate is thus the rate of departure from the balanced condition. No rebalancing is required.
Calibration see CALIBRATION for much more detail
I have performed extensive experiments with NaCl & shown that the instrument response is precisely linear over a change in concentration of 0 – 10 mM [starting from a balanced condition with 0.1% NaCl in both cells & correcting for dilution].
However a more pragmatic calibration for enzyme measurements is to run a reaction to completion i.e. convert all the substrate to product & use the change in voltage before and after the reaction to calculate initial rates (vi) from the raw voltage data.
I did not concern myself with calculation of Vmax or Kcat for urease as the enzyme preparation I used was a crude extract of soya bean. The alkaline phosphatase was pure.
The values of Km determined agree well with previously reported values.
I used quite a strong buffer solution - the sensitivity will be increased at lower buffer concentrations.
The 'resistance' or more correctly impedance at 25Khz across the cells with 0.1% NaCl or the reaction buffer (described above) is ca. 650 ohms & therefore quite closely matches the resistances across the two halves of the 10-turn pot. The bridge is thus nearly symmetrical when balanced. This symmetrical condition gives the highest sensitivity & should be corrected for if you change the set-up as described below.
For initial velocity measurements [since very little prtoduct is produced] the buffer can be reduced to 10 mM or even 5 mM & this will lead to a 5-10-fold increase in sensitivity. NOTE, however that the 'resistance' or more correctly the impedance of the cells will increase & thus lead to an assymetric bridge configuration [2 x ca. 500 ohms from the pot & now 5-10 kohms across each of the cells]. This means that a 10 kohm pot should be used in place of the 1 kohm pot shown in the circuit under ELECTRONICS. When this is done - remember that the noise remains constant, so the S/N ratio will decrease.
It is NOT necessary to use a 10-turn pot, a simple 1-turn pot works fine; I used 10-turn pots during design & calibration to ensure the circuits function correctly but the starting balance position is not used for the analysis of results.
The polarisation of carbon electrodes is dependent on the current flow (see LOW COST ELECTRODES SECTION). This means that the unfortunate effects of polarisation can be reduced to a level that renders it unimportant if a low buffer concentration is used. This will usually be possible where a small change in concentration is being measured as the potential pH change will be small.
Thus for micromolar changes in concentration a 5 mM buffer should be fine & maybe even less will work well.
It is, of course, vital to ensure the initial desired pH is established before making a measurement.
Dialyse the enzyme solution against the reaction buffer solution if in doubt - this will ensure constant pH & salt concentration when the enzyme solution, in the smallest volume you can manage, is added to the reaction mixture.
Urease catalysed hydrolysis of Urea
(Time Scale in seconds)
Recording of whole reaction as a progress curve
This reaction (below) was recorded using 8-bit A-D conversion (the scope input on the Dr DAQ), in contrast to 12-bit (Ext input on Dr DAQ) for the previous results. There is notably more noise on the data. [S] = 10 mM.
Analysis of the progress Curve
The plot below uses initial velocities generated by determining the slope of the progress curve at many time points by using differentiation. This method can be unreliable if the reaction is inhibited by the product or if the enzyme inactivates during the run. Thus, initial velocities measured at different starting [S] values, are usually employed, as shown in the previous example. However it is clear in this example that at least the Km value is very similar in each case as shown here.
Initial Velocity (Michaelis-Menten) Analysis
of the urease-catalysed hydrolysis of Urea
IIt is very important, indeed vital, that the temperature of the two cells stays the same during an experiment. There is a big delay [10 min], [see Temperature Equilibration] if the cell temperatures differ, before they come back to thermal equilibrium.
Thus if any component is to be added to only one cell, it must either be matched with an equivalent addition to the other one [at the same temperature] OR the solution to be added must be brought to the correct temperature before addition. This is fairly easy to achieve if a small volume is added. I often use 0.01 ml [for the enzyme (blood etc.) addition to one cell]. It is best to try a few control experiments before commencing a series of assays.
The exactness of the temperature balance becomes more important as the sensitivity of the experiment increases. Thus measuring mM changes as initial rates requires less attention to temperature balance than does measurements of 10 micromolar changes.
Alkaline Phosphatase Kinetics
The sensitivity of these experiments is about 1/3 of the urease ones. This required more care in getting the balance condition accurately established. This situation resembles the measurement of most enzyme reactions - the urease system is unusally sensitive, since 3 charges are created on hydrolysis, rather than the one charge here.
The AMP stock solution was 100 mM in water. 0.01 ml 16 micromolar enzyme was used for each assay. 1 mM magnesium sulphate & 0.01% BSA was included in the buffer.
A progress curve recorded over 10,000 seconds (6000 used for the analysis below) using the same method as for the SS measurements (above), using 3 mM AMP & 0.32 micro-molar enzyme.
A very simple procedure was used to obtain initial velocities from the progress curve data. Firstly the data was subject to a 20 point moving average smooth (available in Excel) & then the rates were determined using a 10 point chord slope. These simple procedures can be conducted in a short time & seem to work well with good data. No doubt even better results could be obtained using the Savitsky-Golay method used for urease (above).
Note that although the data look quite noisy, the regression shows remarkably small errors, since so many points have been used.
The residuals of the [S]/vi vs [S] plot show a very even distribution, which not surprisingly increase in magnitude slightly at low substrate concentration.