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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.
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