The skewness value (4.89) confirms what is obvious by inspection - the distribution is far from symmetrical. Note that a few of the simulation data sets had best-fit values of Kprime greater than 100. In contrast, the distribution of Kprime is quite skewed. Accordingly, its skewness is close to zero. The distribution of Khalf is quite symmetrical and looks Gaussian. Using Prism's Monte Carlo analysis, I repeated the simulations 5000 times, fit each curve to both forms of the models, and tabulated the best-fit values of Kprime and Khalf, and computed the skewness of each. The X values matched those in the figure above, with triplicate Y values at each X. I simulated sigmoidal enzyme kinetics using Vmax=100, h=5, Kprime=25, and Gaussian scatter with a SD equal to 7.5. Simulations can determine parameter symmetry. Distribution of parameters are not always symmetrical The choice of model can determine the accuracy of the confidence intervals. If you think mechanistically, choose Kprime.īut the choice can be more than a matter of convenience and convention. For this example, if you prefer to think graphically, choose the Khalf. Another approach is to choose the form that fits the way you think. One way to choose between the two models is to match other text books and papers, so your results can easily be compared to others. But one model fits Khalf (the concentration needed to obtain a velocity half of maximal) and the other fits Kprime (a more abstract measure of substrate action). They both fit Vmax (the maximum activity extrapolated to very high concentrations of substrate) and h (Hill slope, describing the steepness of the curve). The fancy term is that they are parameterized differently. Even though the two equations express the same model, they are written differently. The two are equivalent, with Kprime equal to Khalf h, so the two fits will generate exactly the same curve, with the same sum-of-squares, the same R 2, and the same numbers of degrees of freedom. But there are two forms of that model that are commonly used: You want to fit the sigmoidal enzyme kinetics data to a standard model. Reparameterizing an equation does not change the best-fit curve
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