A mixed inhibitor interacts with the enzyme alone and with the enzymesubstrate complex. The doublereciprocal equation for mixed inhibition is as follows:
1/V_{0} = α’/V_{max} + K_{m}•α/V_{max} • 1/[S] the reciprocal of V 0 equals alpha prime divided by V max plus K m times alpha divided by V max times the reciprocal of the substrate's concentration
where α = 1+[I]/k_{I} and α’ = 1+[I]/K’_{I} alpha equals one plus the inhibitor's concentration divided by K I and alpha prime equals one plus the inhibitor's concentration divided by K I
For mixed inhibition, the LineweaverBurk plots show both different slopes and different yintercepts 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}. K prime 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 divided by V max, therefore, multiplying this slope with V max already obtained gives K m.
Figure 1: a) LineweaverBurk plot showing the mixed inhibition. b) Shows the yintercepts of each linear regression plotted against the inhibitor concentration.
Noncompetitive inhibition
In the special case of mixed inhibition where α = α', i.e., K_{I} = K'_{I} alpha equals alpha prime, and so, K I equals K I prime , the type of inhibition is called noncompetitive inhibition. In this special case, the inhibitor interacts in a favorable manner with the enzymesubstrate complex as it does with the enzyme alone. When plotting kinetic data in a LineweaverBurk plot, a common xintercept shows that the competitor is noncompetitive.
The doublereciprocal equation for noncompetitive inhibition is thus as follows:
1/V_{0} = α/V_{max} + k_{m}•α/V_{max} • 1/[S] the reciprocal of V 0 equals alpha divided by V max plus K m times alpha divided by V max times the reciprocal of the substrate's concentration
where α = 1+[I]/K_{I} alpha equals one plus the inhibitor's concentration divided by 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 LineweaverBurk plot by dividing the slope with the yintercept [1]. To calculate V_{max} and K_{I}, the yintercepts of the different lines obtained from linear regression of LineweaverBurk 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 yintercept of this line, and K_{I} K m remains the same as the actual K m, and it can be calculated from a LineweaverBurk plot by dividing the slope with the yintercept. To calculate V max and K I, the yintercepts of the different lines obtained from linear regression of LineweaverBurk 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 yintercept of this line, and K I is calculated by dividing the yintercept with the slope.
Steps of calculating the kinetic parameters when using a noncompetitive inhibitor
 Prepare LineweaverBurk plots of the kinetic data and fit the data using linear regression (1 fit per inhibitor concentration).
 Calculate K_{m} by dividing the slope of any of these lines with the corresponding yintercept (K_{m} obtained should not depend on the line used). K m by dividing the slope of any of these lines with the corresponding yintercept. The K m obtained should not depend on the line used
 Plot the yintercepts of each of these fits as a function of the inhibitor concentration.
 To calculate V_{max}, V max take the reciprocal of the yintercept of this plot.
 To calculate K_{I}, K I divide the yintercept of this plot with the slope.
References

Lehninger, Albert L.; Nelson, David L.; Cox, Michael M. (2008). Principles of Biochemistry (5th ed.). New York, NY: W.H. Freeman and Company. ISBN 9780716771081.

Atkins, Peter W.; de Paula, Julio; Friedman, Ronald (2009). Quanta, Matter, and Change: A molecular approach to physical chemistry. Oxford University Press. ISBN 9780199206063.
Uncompetitive inhibition
Theory overview