242b

Yunfei Chu, Department of Chemical Engineering, Texas A& M University, College Station, TX 77843-3122 and **Juergen Hahn**, Department of Chemical Engineering, Texas A&M University, 3122 TAMU, College Station, TX 77843-3122.

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 systems^{9} 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 model^{2}:
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 **

1. Schoeberl B, Eichler-Jonsson C, Gilles ED, Muller G. Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nature Biotechnology. 2002; 20 (4): 370-375.

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

3. Yamada S, Shiono S, Joo A, Yoshimura A. Control mechanism of JAK/STAT signal transduction pathway. 2003; FEBS Letters 534 (1-3): 190-196.

4. Gadkar KG, Varner J, Doyle III FJ. Model identification of signal transduction networks from data using a state regulator problem. Systems Biology. 2005; 2 (1): 17-30.

5. Hu DW, Yuan JM. Time-dependent sensitivity analysis of biological networks: Coupled MAPK and PI3K signal transduction pathways. Journal of Physical Chemistry A. 2006; 110 (16): 5361-5370.

6. Liu G, Swihart MT, Neelamegham S. Sensitivity, principal component and flux analysis applied to signal transduction: the case of epidermal growth factor mediated signaling. Bioinformatics. 2005; 21 (7): 1194-1202.

7. Cho, KH, Shin, SY, Kolch, W, Wolkenhauer, O. Experimental design in systems biology, based on parameter sensitivity analysis using a Monte Carlo method: A case study for the TNF alpha-mediated NF-kappa B signal transduction pathway. Simulation-Transactions of the Society for Modeling and Simulation International. 2003; 79 (12): 726-739.

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.

9. Chu Y, Hahn J. Development of Parameter Sensitivity Analysis Techniques for Studying Interactions among Parameters and Application to Systems Biology. Dynamics of Continuous, Discrete and Impulsive Systems. 2007; In Press.

10. Silvey SD. Optimal design: an introduction to the theory for parameter estimation. London: Chapman and Hall, 1980.

11. Walter E, Pronzato L. Qualitative and quantitative experiment design for phenomenological models - A survey. Automatica. 1990; 26 (2): 195-213.

12. Heinrich PC, Behrmann I, Haan S, Hermanns HM, Muller-Newen G, Schaper F. Principles of interleukin (IL)-6-type cytokine signalling and its regulation. Biochemical Journal. 2003; 374: 1-20.

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