Abstract
The graphs of rational polynomial functions are of considerable importance in enzyme kinetics but a full analysis of the turning points and inflexions is only possible for 2 : 2 functions due to the complexity of the first and second derivatives for 3 : 3 and higher degree functions. This paper describes a simple method which can be applied to rational functions of any degree in order to discover the relationship between the coefficients necessary for the curve to have an initial sigmoid inflexion and a final inflexion (which implies a maximum in the graph). This technique is then applied to the current allosteric models. In addition, a full analysis of the 2 : 2 function with a maximum is given together with a method of separating this type of behaviour (partial substrate inhibition) from the 1 : 2 function (dead-end substrate inhibition).
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