I am working on a water purification system for pesticide and I want to find out the start to end procedure on how to calculate the catalytic/enzymatic activity.
As already mentioned the question is quite wide. To make short:
first find the substrate range for which you observe the saturation phenomenon of reaction rate (concentration of enzyme has to be constant and much less than any of the substrate concentrations, even for the lower considered). rate at saturation is Vmax. Rate for enzyme catalysed reaction is generally express as number of mole per min. If you know the amount of enzyme present in the assay sample then Vmax/mass of protein is the specfic activity (expressed as number of mole per min per mg of pure protein). And finally if you divide Vmax expressed as above by the number of moles of enzyme in the assay then you get kcat expressed as per min (which represents the turn over number of the enzyme with the given substrate, ie. the number of catalytic cycles performed by the enzyme in one minute).
Unfortunately, the answer will be dependent on the enzyme that you have, and also the nature of the inhibitor that you are (I guess?) using.
The usual approach would be to measure the activity of the enzyme at a range of substrate concentrations to determine the dependence of rate on substrate concentration. This often follows the Michaelis-Menten equation, but not always.
Studies on inhibitors will then depend on exactly what your question is, and what previous knowledge you have.
I would suggest firstly reading the relevant chapters in any good Biochemistry textbook (e.g. Voet, Voet & Pratt's "Biochemistry"). There are some very good more detailed texts available (e.g. Cook & Cleland's "Enzyme Kinetics and Mechanism" is excellent, but probably goes into far more detail than you want!).
If you gave some details of the enzyme that you are interested in, this might help with ideas on how to run the assay.
My enzyme is Organophosphate hydrolase. Since I am mechanical engg background, I have little knowledge about the technical aspects. Hence I am interested in a simple method for measuring the catalytic activity or turnover number with some explanations about which data and equation should I use and how to utilize my experimental data to get that number.
As already mentioned the question is quite wide. To make short:
first find the substrate range for which you observe the saturation phenomenon of reaction rate (concentration of enzyme has to be constant and much less than any of the substrate concentrations, even for the lower considered). rate at saturation is Vmax. Rate for enzyme catalysed reaction is generally express as number of mole per min. If you know the amount of enzyme present in the assay sample then Vmax/mass of protein is the specfic activity (expressed as number of mole per min per mg of pure protein). And finally if you divide Vmax expressed as above by the number of moles of enzyme in the assay then you get kcat expressed as per min (which represents the turn over number of the enzyme with the given substrate, ie. the number of catalytic cycles performed by the enzyme in one minute).
It rather depends on how much freedom you have over the substrate. It would be easiest if you can use a substrate with a 4-nitrophenol group (e.g. a paraoxon). The hydrolysis of this will release the 4-nitrophenol, which absorbs light at 405 nm (especially at high pH). This can be followed in real time to collect data using a plate reader or spectrophotometer to determine the initial rate (i.e. the rate during the hydrolysis of the first 10% of the substrate).
A normal experiment would then test the reactions at a range of substrate concentrations, aiming to find firstly a substrate concentration that gives half-maximal activity (the "Michaelis constant" or Km). Designing this sort of experiment is not something that can easily be broken down into a "one size fits all" protocol; and I would suggest that you need someone preferably local who can help you to design the details of the experiments, and interpret the results. Usually these things take a few iterations to get right. Once you have the data, they are fitted to the Michaelis-Menten equation (preferably using a statistical package, like SPSS/Graphpad/R).
Alas, the details of the experiment depend on the details of your enzyme, substrate, and equipment.
I sounds like your enzyme cleaves phosphate esters of organic compounds. There are two principal easy methods to measure such enymes, one is to use a chromogenic alternative substrate (such as X-P) that gets colored when the phosphate is cleaved off, but depends on the ability of enzyme to react with this compound. The other is to measure the appearance of free phosphate (e.g. via the malachite green method, which you can find by Google). If both don't work, you still can try to quantify your reaction product by HPLC and determine the reaction rate after stopping your reaction after certain time points.
For converting the activity data to specific activities or Michealis-Menten plots, consult the usual textbooks on biochemistry.