A mixed inhibitor interacts with the enzyme alone and with the enzyme-substrate complex. The double-reciprocal equation for mixed inhibition is as follows:
1/V_{0} = α’/V_{max} + k_{m}•α/V_{max} • 1/[S]
where α = 1+[I]/k_{I} and α’ = 1+[I]/k’_{I}
For mixed inhibition, the Lineweaver-Burk plots show both different slopes and different y-intercepts at different inhibitor concentrations. To calculate the parameters, in this case, 2 new plots must be prepared: first, plot the intercepts against the inhibitor concentrations; this makes it possible to obtain K’_{I} and V_{max}, as described under uncompetitive inhibition. Second, plot the slopes against the inhibitor concentrations; from this, K_{I} can be found. The slope of this plot is k_{m} / V_{max}, therefore multiplying this slope with V_{max} already obtained gives K_{m}.
Figure 1: a) Lineweaver-Burk plot showing the mixed inhibition. b) Shows the y-intercepts of each linear regression plotted against the inhibitor concentration.
In the special case of mixed inhibition where α = α', i.e., K_{I} = K'_{I}, the type of inhibition is called noncompetitive inhibition. In this special case, the inhibitor interacts in a favorable manner with the enzyme-substrate complex as it does with the enzyme alone. When plotting kinetic data in a Lineweaver-Burk plot, a common x-intercept shows that the competitor is noncompetitive [1,2].
The double-reciprocal equation for noncompetitive inhibition is thus as follows:
1/V_{0} = α/V_{max} + k_{m}•α/V_{max} • 1/[S]
where α = 1+[I]/k_{I}
When plotting kinetic data using a noncompetitive inhibitor, the apparent K_{m} remains the same as the actual K_{m}, and it can be calculated from a Lineweaver-Burk plot by dividing the slope with the y-intercept [1]. To calculate V_{max} and K_{I}, the y-intercepts of the different lines obtained from linear regression of Lineweaver-Burk plots at different inhibitor, concentrations must be plotted against the inhibitor concentration. When fitted using linear regression, V_{max} and K_{I} can be calculated from this plot in the same manner as that in the case of uncompetitive inhibition: V_{max} is calculated by taking the reciprocal to the y-intercept of this line, and K_{I} is calculated by dividing the y-intercept with the slope.
Lehninger, Albert L.; Nelson, David L.; Cox, Michael M. (2008). Principles of Biochemistry (5th ed.). New York, NY: W.H. Freeman and Company. ISBN 978-0-7167-7108-1.
Atkins, Peter W.; de Paula, Julio; Friedman, Ronald (2009). Quanta, Matter, and Change: A molecular approach to physical chemistry. Oxford University Press. ISBN 978-0-19-920606-3.