Modeling and analysis of intracellular signaling networks is an important area in systems biology. Signaling pathways are the cellular information routes by which cells sense their surroundings and adjust to environmental changes or hormonal stimuli. A great number of mathematical models have been developed and analysis of these models can contribute to a better understanding of the biological mechanism (for some specific example see references 1-3). However, analysis of such complex systems is often non-trivial as these models can include tens or even hundreds of parameters and variables. Local sensitivity analysis^4-6 is often performed to identify the key components due to its simplicity. However, strong interactions among components in a signaling pathway may exist resulting in linear methods not returning adequate information. Global sensitivity analysis techniques^7,8 can deal with some of the shortcomings of local methods as they allow to perturb many parameters simultaneously which results in information about the interactions among the parameters. However, global sensitivity analysis techniques can be computationally expensive and usually return only an averaged value of the sensitivities over a region in parameter space.

In this work, a recently developed technique for parameter sensitivity analysis of nonlinear systems⁹ is extended to also include aspects of experimental design. Incorporating experimental design procedures into parameter sensitivity analysis methods is important as experimental design and sensitivity analysis influence one another. Additionally, since conducting experiments for elucidating mechanisms involved in signal transduction can be time consuming and expensive, it is desired to gain as much information about the system as possible before undertaking experimental investigations. A systematic approach for experimental design is to maximize some optimality criterion^10,11 of the Fisher information matrix. Due to the interactions among parameters the Fisher information matrix is dependent on the parameter values. However, the exact values of the parameters are not known prior to estimation. Differential analysis and a sampling-based approach are simultaneously used to deal with interactions resulting from the effect that uncertainty in the parameter values has on parameter sensitivity analysis. The presented procedure determines the key factors influencing the accuracy of the estimation as well as the likelihood of a parameter set to be the optimal selection for different nominal values of the parameters and for different values of the inputs to the system.

The presented method is used to investigate a signal transduction pathway model²: the IL (interleukin)-6-type cytokines are an important family of mediators involved in the regulation of the acute-phase response to injury and infection.¹² The IL-6 model contains two signaling mechanisms: Janus-associated kinases (JAK) & signal transducers and transcription factors 3 (STAT3) are activated in one pathway while the other pathway involves the activation of mitogen-activated protein kinases (MAPK). The model is described by 68 nonlinear ordinary differential equations and includes 118 parameters. The presented procedure performs a sensitivity analysis on the results computed from local sensitivity in order to determine how the sensitivity results change with variations in the parameter values and experimental conditions. It is shown that the local sensitivity values change drastically with variations of the nominal value of the parameters due to nonlinearity of the signal transduction model. It is also shown that the amount of stimulation of the signal transduction pathway has a strong influence on the results, e.g., a high concentration of the cytokine IL-6 actually has a negative effect on parameter estimability. The reason for this finding is that a very high dose of IL-6 leads to saturation of the receptor complexes with IL-6 resulting in reduced sensitivity of the signal transduction pathway to changes in the IL-6 concentration.  

Literature Cited

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8.      Zi ZK, Cho KH, Sung MH, Xia XF, Zheng JS, Sun ZR. In silico identification of the key components and steps in IFN-gamma induced JAK-STAT signaling pathway. FEBS Letters. 2005; 579 (5): 1101-1108.

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