AIC – Akaike Information Criterion and Enzyme Inhibition

  This program allows the calculation of parameters of the Akaike Information Criterion (Akaike, 2003) for the statistical discrimination between nonlinear models.


1 Equation:

\[ AIC = n \cdot \ln!\left(\frac{SSE}{n}\right) + 2k + \left[\frac{2k(k+1)}{n-k-1}\right] \]

Where:

  • k = p + 1 (with p being the number of model parameters);
  • SSE = sum of squared residuals from the fit.

\[ probab.B = \frac{e^{-0.5 \cdot \Delta AIC}}{1 + e^{-0.5 \cdot \Delta AIC}} \]

Where:

  • probab. B = probability that model B is better than model A (range 0–1);
  • \(\Delta\)AIC = difference AIC\(_B\) − AIC\(_A\).

2 Files

  1. AIC program
  2. Source code

3 Usage:

  To run the program, the following data must be entered sequentially into the stack:


# Data input

1. After selecting "AIC", the program requests the following values (INPUT):
   n, kA, kB, ssA, ssB
2. After ENTER, the program computes:
   "AIC_A, AIC_B, delta, prob.B"

4 Example

  The table and figures below refer, respectively, to enzyme inhibition data reported by Bezerra et al. (2013), and to the data input and output obtained for a pair of competing models.


Table 1 – Experimental enzyme inhibition data (n = 105). Source: Bezerra et al., 2013.

Type Control Competitive Pure non-competitive Mixed non-competitive Uncompetitive
SSE 1540.1 613.1 1122.7 613.2 1436.4
p 2 3 3 4 3
(a) Input of values for comparison between control and competitive models.
(b) Comparison results obtained.
Figure 1: Execution of the program for comparison between control and competitive models of enzyme inhibition.
  By running the AIC program, the following comparison results were obtained for selected pairs of models:

Table 2 — Results of model comparison using the AIC criterion.

Model A / B AIC\(_A\) AIC\(_B\) \(\Delta\) Probab. B
Control / Competitive 288.2 193.7 -94.6 1.0
Control / Mixed NComp. 288.2 195.9 -92.3 1.0
Competitive / Mixed NComp. 193.7 195.9 2.2 0.25
  Based on these results, the probability associated with model B supports the selection of the competitive enzyme inhibition model, with a 75% likelihood over the mixed non-competitive model, in agreement with the conclusions reported by the authors.

References

  1. Akaike, Hirotugu. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723, 2003.

  2. Bezerra, Rui M. F., Irene Fraga, and Albino A. Dias. Utilization of integrated Michaelis–Menten equations for enzyme inhibition diagnosis and determination of kinetic constants using the Solver supplement of Microsoft Office Excel. Computer Methods and Programs in Biomedicine, 109(1), 26–31, 2013.

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