Numerical algebraic geometry for model selection and its application to the life sciences

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to non-linearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data is available. Here, we consider polynomial models (e.g., mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometric structures relating models and data, and we demonstrate its utility on examples from cell signaling, synthetic biology, and epidemiology.Comment: References added, additional clarification

Inhibition of vascular endothelial growth factor with a sequence-specific hypoxia response element antagonist

Vascular endothelial growth factor (VEGF) and its receptors have been implicated as key factors in tumor angiogenesis that are up-regulated by hypoxia. We evaluated the effects of DNA-binding small molecules on hypoxia-inducible transcription of VEGF. A synthetic pyrrole-imidazole polyamide designed to bind the hypoxia response element (HRE) was found to disrupt hypoxia-inducible factor (HIF) binding to HIRE. In cultured HeLa cells, this resulted in a reduction of VEGF mRNA and secreted protein levels. The observed effects were polyamide-specific and dose-dependent. Analysis of genome-wide effects of the HIRE-specific polyamide revealed that a number of hypoxia-inducible genes were down-regulated. Pathway-based regulation of hypoxia-inducible gene expression with DNA-binding small molecules may represent a new approach for targeting angiogenesis