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For nij <1, the Hill rate law represents Michaelis-Menten kinetics.
Figure 1 shows a training data set created from artificial system A with the Hill rate law (Eq. 1).
Clearly, the Hill rate law has more parameters and hence is more likely to fit complex curves.
The best-known examples are probably Michaelis-Menten and Hill rate laws, which are ultimately explicit, but in truth approximate a multivariate system of underlying chemical processes.
Since the ANN rate law (Eq. 2) has fewer parameters than the Hill rate law (Eq. 1), and hence a smaller degree of freedom, it is harder for the ANN models to fit data obtained from Hill systems.
The second phase of DFE addresses the mathematical formulation of each process in the biological system by attempting to convert these numerical plots into mathematical representations, such as a Michaelis-Menten or Hill rate law or a power-law description.
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Odefy [ 13] converts discrete Boolean networks into quantitative differential equation systems by applying Hill-type rate laws [ 14] to each transition.
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