In reality, many enzymes have more than one substrate (A, B) and more than one product (P, Q). For example, the enzyme alcohol dehydrogenase catalyzes the oxidation of ethanol with NAD (a biological oxidizing agent) to form acetaldehyde and NADH. How do you do enzymes kinetics on these more complicated systems? The answer is fairly straightforward. You keep one of the substrates (B, for example) fixed, and vary the other substrate (A) and obtain a series of hyperbolic plots of \(v_o\) vs. \(A\) at different fixed \(B\) concentrations. This would give a series of linear 1/v vs 1/A double-reciprocal plots (Lineweaver-Burk plots) as well. The pattern of Lineweaver-Burk plots depends on how the reactants and products interact with the enzyme.
In this mechanism, both substrates must bind to the enzyme before any products are made and released. The substrates might bind to the enzyme in a random fashion (A first then B or vice-versa) or in an ordered fashion (A first followed by B). An abbreviated notation scheme developed by W.W. Cleland is shown below for the sequential random and sequential ordered mechanisms. For both mechanisms, Lineweaver-Burk plots at varying A and different fixed values of B give a series of intersecting lines. Derivative curves can be solved to obtain appropriate kinetic constants.