Detection of malfunctioned reactions or molecules from clinical data is essential for disease treatments. Mathematical modeling approaches provide a thorough understanding of the behavior of systems, including biological networks. Therefore, mathematical models can be used to facilitate the inference of malfunctioned reactions that lead to human diseases from clinical data. For example, approaches based on the Boolean model have been utilized to determine the critical components whose dysfunction are most likely responsible for a significant impact on the output of signaling pathways 1-4. These approaches also have the potential to directly localize faulty genes. In a study of oxidative stress response5, Boolean modeling simulated gene sequences, and the faulty gene was detected according to the mismatch between the dysfunctional and normal sequences. Apart from model-based approaches, model-free approaches, or data-driven approaches, are commonly used for the detection of pathological states from “-omics” data based on pattern recognition techniques for patients with conditions like a gastrointestinal stromal tumor 6, 7 and various neurological diseases 8, 9. While these existing approaches yield preliminary avenues for fault detection in signaling pathways involved in human diseases, they either disregard the transient dynamics or have insufficient details of biological systems. In addition, methods based on the Boolean model are incapable of providing accurate and unique solutions for fault diagnosis, because the use of mathematical approximations (either 0 or 1) can cause a coincidence of identical calculation results to occur, although from different combinations of Boolean variables5.
In contrast, kinetic models, which can determine the time profiles of molecules in a signaling pathway, will provide a better platform for a more accurate and exhaustive detection of malfunctioned reactions. Significantly different from the Boolean model, a pure logical-based discrete model which considers a molecule either active or inactive and is unable to capture important intermediate states, an ordinary differential equation (ODE) model is a kinetic model which can generate continuous and quantitative profiles of molecule concentrations 10. Kinetic modeling is therefore a more practical method of investigating malfunction pathways in diseases because the severity of diseases varies from patient to patient. In a study about the EGFR-ERK signaling pathway, based on an ODE model, the reaction rate of c-Cbl and EGFR binding was reduced by a factor of 100 or 1000 to mimic the effects of the endocytosis impairment, and active ERK concentration at steady state was measured after treatment with different concentrations of regulator to reflect the functions of selected regulators 11. Besides, the influence of dysfunction also affects the oscillatory behavior as well 12-14. It is reported that a biological network can exhibit diverse dynamic behaviors caused by negative feedback loops, such as long-lasting oscillations 15.
This paper presents a kinetic model based approach we developed in order to infer malfunctioned reactions in signaling pathways by quantifying the similarity between the profiles shown in the clinical data and the output profiles predicted from the model in which certain reactions/molecules are malfunctioned. The developed approach was tested in two well-studied signaling pathways, i.e., Interleukin 6 (IL-6) signal transduction16, 17 and TNF-α/NFκB signaling pathway18, for four abnormal clinical conditions that include the up/down regulation of single reaction rate constants and up/down regulation of single molecules. Since limited quantitative clinical data were available for these two signaling pathways, the IL-6 model was used to generate artificial clinical data for the abnormal steady-state value shown in the two key molecules (i.e., nuclear STAT3 and SOCS3). Similarly, the TNF-α/NF-κB model was used to obtain the data in which abnormal oscillation dynamic was shown in the profile of NF-κB. Different levels of random noises were added into the simulation results to represent the noisy properties shown in real clinical data. The developed approach was used to identify the malfunctioned reactions/molecules from data. The results show that the developed approach was able to successfully identify the malfunctioned reactions/preexisting molecules from the clinical data. It was found that the developed approach was noise-robust and that it was able to reveal unique solution for the faulty components in a network.
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