we have determined mode of inhibition by plotting 1/V against 1/[s] in lineweaver-burk plot. Can we use the initial rate data to determine the order of the reaction with respect to inhibition and substrate?
If you are working with a single-substrate enzyme with a single active site, there are only 3 basic possibilities (noncompetitive, competitive, uncompetitive). The order of substrate and inhibitor binding is unequivocal. For a noncompetitive inhibitor, the substrate and inhibitor bind simultaneously, for a competitive inhibitor binding of substrate and inhibitor is mutually exclusive, and for an uncompetitive inhibitor the substrate must bind first.
If your enzyme reaction involves 2 or more substrates, the situation is potentially much more complicated. I advise you to read one of the textbooks on the subject, such as the one by I. Segel or the one by V. Leskovac:
Another interpretation of the word "order" in your question is the stoichiometry of substrate and inhibitor binding. This can also get complicated because if there are multiple binding sites there may be cooperativity between them. Cooperativity can be investigated by initial rate measurements, but does not necessarily measure the stoichiometry. Once again, I suggest that you refer to one of the advanced enzyme kinetics textbooks for a detailed description of methods and interpretation.
Although steady-state enzyme kinetics is a useful tool to investigate such matters, you should also consider using biophysical methods to measure binding stoichiometry, particularly for the inhibitor if it binds in the absence of the substrate. The interpretation is more straightforward. There are many methods available for this measurement, but the amount of protein required is much greater than for enzyme kinetics. Examples are equilibrium dialysis, ultrafiltration, isothermal titration calorimetry, and the Hummel and Dreyer (vacancy peak) gel filtration method.
Enzyme inhibitors are found in nature and are also designed and produced as part of pharmacology and biochemistry. Natural poisons are often enzyme inhibitors that have evolved to defend a plant or animal against predators. These natural toxins include some of the most poisonous compounds known. Artificial inhibitors are often used as drugs, but can also be insecticides such as malathion, herbicides such as glyphosate, or disinfectants such as triclosan. Other artificial enzyme inhibitors block acetylcholinesterase, an enzyme which breaks down acetylcholine, and are used as nerve agents in chemical warfare.
Adam 's answer is absolutely correct and probably supplies all the information you seek. If you are working with an enzyme that has more than substrate however, it is possible to determine the order in which the substates bind by determining the type of inhibition produced by products of the reaction. Standard texts in enzymology and publications by Cleland will provide all the details.
Gangutri Saikia, The order of the reaction in the sense of definition applies to reactions whose kinetic equation (rate law) has the form of a power monomial. Talking about the order of the enzymatic reaction described by the M-M equation, or various modifications of this equation, due to the type of inhibition, is a misunderstanding. In order to determine the type of inhibition, one should determine the kinetic curves cS vs t for various cI and differentiate them, and then use one of the graphical methods, e.g. L-B plot, H-W plot, E-H plot, CB-E plot and many others. One can also use nonlinear methods popularly known as nonlinear regression .