(173b) Derivation of Reduced Models for Signal Transduction Pathways Via Sensitivity and Observability Analysis

A significant amount of information has been presented in the literature on IL-6 signal transduction including the structure of the signal transduction pathway and qualitative information in the form of Western blots (Fasshauer et al., 2004; Heinrich et al., 2003; Lang et al., 2003). However, only a limited number of fundamental models (Huang et al., 2007; Schoeberl et al., 2002; Singh et al., 2006; Yamada et al., 2003) exist due to the limited amount of quantitative data which leads to these models containing a large number of uncertain parameters. One option to address this point is to perform sensitivity analysis of the parameters and only estimate the parameters that are determined to be important from data and set all other parameters to their nominal values. While this approach can result in models that provide a good fit for experimental data, it has the drawback that one has to deal with what is essentially an overparameterized model. Model reduction is another option to address this problem. A variety of different techniques exist for deriving a reduced-order model (Conzelmann et al, 2008; Dokoumetzidis and Aarons, 2009; Liebermeister et al, 2005; Sun and Hahn, 2006; ). Since the focus of this work is not to come up with a model that is faster to simulate but rather to derive a simplified model for IL-6 signal transduction that is easier to interpret, an approach that retains the physical meaning of some of the states and parameters of the model is used. The presented work uses sensitivity analysis where several important proteins for which measurement data is available are chosen as the outputs of the model. Model parameters are clustered based upon their sensitivity profile for each output. If several parameters are found in the same cluster, regardless of which protein was chosen as the output, then the mechanisms involving these signaling intermediates can be simplified. Representative state variables are then chosen for the reactions associated with each cluster of parameters via a measure involving observability analysis. This norm determines which proteins in the signaling pathway should be measured to maximize the information that can be extracted about the dynamics of proteins of the signal transduction pathway. The reduced model is then constructed based upon the selected state variables and the parameter clustering resulting from sensitivity analysis. Parameter estimation for the reduced model is performed using the nonlinear least squares optimization routine, lsqnonlin, from MATLAB.

Using this approach a simplified model of IL-6 signal transduction is derived where the number of parameters and states has been significantly reduced. The parameters of the reduced model are then re-estimated from the experimental data, resulting in a simple, yet accurate model describing IL-6 signaling.

References

Conzelmann, H., Fey, D., Gilles, E. D., (2008). Exact model reduction of combinatorial reaction networks. BMC Systems Biology, 2:78.

Dokoumetzidis, A., Aarons, L., (2009). Proper lumping in systems biology models. IET Syst. Biol., 3(1), 40 - 51.

Fasshauer, M., Kralisch, S., Klier, M., Lossner, U., Bluher, M., Klein, J., Paschke, R., (2004). Insulin resistance-inducing cytokines differentially regulate SOCS mRNA expression via growth factor- and JAK/Stat-signaling pathways in 3T3-L1 adipocytes. Journal of Endocrinology, 181, 129-138.

Heinrich, P. C., Behrmann, I., Haan, S., Hermanns, H. M., Muller-Newen, G., Schaper, F., (2003). Principles of interleukin (IL)-6-type cytokine signaling and its regulation. Biochemical Journal, 374, 1-20.

Huang, Z., Chu, Y., Senocak, F., Jayaraman, A., Hahn, J., (2007). Model update of signal transduction pathways in hepatocytes based upon sensitivity analysis. Proceedings Foundations of Systems Biology 2007, Stuttgart, Germany.

Liebermeister, W., Baur, U., and Klipp, E., (2005). Biochemical network models simplified by balanced truncation. FEBS Journal, 272, 4034-4043.

Schoeberl, B., Eichler-Jonsson, C., Gilles, E. D., Muller, G., (2002). Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nature Biotechnology, 20, 370-375.

Singh, A. K., Jayaraman, A., Hahn, J., (2006). Modeling regulatory mechanisms in IL-6 signal transduction in hepatocytes. Biotechnology & Bioengineering, 95(5), 850-862.

Sun, C., Hahn, J., (2006). Parameter reduction for stable dynamical systems based on Hankel singular. Chemical Engineering Science, 61, 5393 - 5403.

Yamada, S., Shionoa, S., Joob, A., Yoshimura, A., (2003). Control mechanism of JAK/STAT signal transduction pathway. Febs Letters, 534, 190-196.