(533g) Sensitivity Analysis in Biological Modeling: an Application in the Model Development of Staphylococcal Enterotoxin B Pre-Apoptotic Pathways

Systems biology (re)emerges in the post-genomic era to ascertain the observed cellular behavior from the complex network of interactions among genes and proteins. One of the challenges in this system-level approach is the development of in silico models from experiments that can accurately capture the cellular behavior. The hurdles in this effort known as reverse engineering are multiple, including network size and complexity, and quantity and quality of measurements. Systems engineering approaches have been instrumental in decomposing this untenable problem into manageable tasks that are tractable for numerical simulations and analyses.

System analysis can help unraveling the complexity in cellular networks. One such method is sensitivity analysis, which shows the dependence of system behavior on model parameters. In cellular networks, high sensitivities point to the weakest links in the system which cellular behavior strongly depends on. By mapping these critical pathways back to the genotype, one can point to the set of genes and interactions that control the cellular behavior. This information can be used for guiding data-fitting and model refinement in the reverse-engineering effort. For the measurement aspect of modeling, information theoretic approach such as the Fisher information matrix (FIM) can provide a measure of the degree of information content in noisy measurement data for estimating the accuracy of parameter estimates. Also, the FIM-based sensitivity ranking consolidates the dynamical sensitivities into coefficients that can be easily compared. Using the FIM, the measurement selection algorithm that chooses the system variables (states) with the most information for parameter identification, allows a feedback from the modeling effort to the design of future experiments. These tools are included in a MATLAB-based graphical user interface (GUI) named BioSens [1], for ease-of-use by non-experts in systems theory.

The utility of sensitivity analysis and the Fisher information matrix is demonstrated in the model development of staphylococcal enterotoxin-B (SEB) response in kidney cells. SEB is a potential biological threat that is known to be a potent inducer of lethal toxic shock syndrome and cell apoptosis in kidney [2]. This effort represents a collaboration among 7 universities (U.C. Santa Barbara, U.C. Berkeley, UCLA, Thomas Jefferson U., Indiana U., Keck Graduate Institute, and NYU) and two research institutes (SRI and Walter-Reed). The initial experiments focused on RNA expressions in Pi3K and Ras signaling pathways as suggested by existing knowledge of the system and confirmed by clustering analysis. Sensitivity analysis coupled with a comparative study of the diagonal elements of the FIM, provided the information for iteratively refining the model. This model refinement involved incorporating more details in the subnetworks where the system is highly sensitive, using literature searches and database (such as GENEWAYS [3]). During this iterative process, the SEB model grew from 77 states and 179 parameters, to a more detailed system with 117 states and 356 parameters. The model sensitivity analysis led to the identification of two key signaling pathways in the SEB response; NF-KappaB and ERK. This result is also confirmed by promoter and clustering analysis [4, 5]. The next set of experiments then focuses on the ERK-activated transcription factors to obtain a more accurate representation of this subnetwork. By focusing on smaller subnetworks guided by sensitivity analysis, the model development is decomposed into numerically tractable steps.

[1] BioSens: Sensitivity Analysis Toolkit for Bio-SPICE. Available at http://www.chemengr.ucsb.edu/~ceweb/faculty/doyle/biosens/BioSens.htm

[2] Y. A. van Gessel, S. Mani, S. Bi, R. Hammamieh, J. W. Shupp, R. Das, G. D. Coleman, and M. Jett., Exp. Biol. Med. (2004) 229:1061-1071.

[3] A. Rzhetsky, I. Iossifov, T. Koike, M. Krauthammer, P. Kra, M. Morris, H. Yu, P.A. Duboue, W. Weng, W.J. Wilbur, V. Hatzivassiloglou., and C.J. Friedman, Biomed. Inform. (2004) 37:43-53.

[4] R. Vadigepalli, P. Chakravarthul, D.E. Zak, J.S. Schwaber, and G.E. Gonye, OMICS (2003) 7:235-52.

[5] L.M. Tran, M.P. Brynildsen, K.C. Kao, J.K. Suen, and J.C. Liao, Metab. Eng. (2005) 7:128-141.