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College of Engineering and Computing

Biomedical Engineering

Globally Deterministic Methods for Nonconvex Numerical Optimization

The past few years have witnessed an enormous increase in the availability and quality of high-throughput data characterizing the status of cells at the genomic, proteomic, metabolic and physiological levels. In most cases, these data were interpreted as simple snapshots or in a comparative setting with the goal of differentiating between normal and perturbed or diseased cells. It is now feasible to use the same methods to record the status of cells over time. The resulting time series data contain enormous amounts of information on the dynamics of functioning cells. Several groups of scientists around the world have begun to develop methods for inferring from these profiles the underlying functional networks at the genomic or metabolic level. In principle, this task is a straightforward matter of defining a suitable model and estimating its structure, but numerous conceptual and computational difficulties have made the implementation of this inverse problem challenging.  Metabolic systems may be formulated as Generalized Mass Action (GMA) models. The estimation problem can be posed as a global optimization task, for which novel techniques can be developed to determine the best set of parameter values given the measured responses of the biological system. The challenge is that this task is nonconvex. Nonetheless, deterministic optimization techniques can be used to find a global solution that best reconciles the model parameters and measurements. Specifically, branch-and-bound principles may be used to identify the best set of model parameters from observed time course data and illustrates this method with an existing model of the fermentation pathway in Saccharomyces cerevisiae.  This is a relatively simple yet representative system with five dependent states and a total of 19 unknown parameters of which the values are to be determined.


 • P. K. Polisetty, E. P. Gatzke , and E. O. Voit. "Yield Optimization of Regulated Metabolic Systems Using Deterministic Branch-and-Reduce Methods." Bioengineering and Biotechnology, 2008, 99(5), 1154-1169.

• P. K. Polisetty, E. O. Voit, and E. P. Gatzke.  "Identification of Metabolic System Parameters Using Global Optimization Methods."  Theoretical Biology and Medical Modeling, January 2006, 3(4) 1-15.

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