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Parameterizing Biological Networks

As biological systems are being increasingly investigated from the networks point of view, there is an escalated demand for computational models that quantitatively characterize those systems. As is the case with modeling any system, accurate and precise models that can both represent and predict their respective biological systems' behaviors are desired. An essential task in building such a model involves effective calibration of the parameters that define the model. With respect to a biological system, which is often modeled using differential equations derived from the chemical reactions that take place within it, the parameters can be regarded as reaction rates or initial conditions that specify its model. The task then is to determine the set of parameters that would enable the model to exhibit outputs that match experimental measurements. A major barrier to successful calibration is the limited amount of available experimental data, rising from the irreplaceable and unsteady nature of biological systems. This often leads to the existence of multiple possible sets of parameters that could potentially result in outputs that match the data. We explore robust optimization to develop computational methods that would allow us to select out the correct parameter set among many, with the eventual goal of being able to perform the task with limited qualitative system-specific information. Preliminary results obtained suggest that the addition of robustness constraints in optimizing for the parameters may help in selecting out the correct set, while indicating the need to carefully examine the choice of data that parameter estimation is performed with respect to. Furthermore, including the robustness constraints seems to make calibration based on noisy measured data more plausible. Research thus far has been conducted primarily in the context of signaling pathways, including the mitogen-activated protein kinase and Fas signaling pathways.