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

Type
Article

Authors
Gross, Elizabeth
Davis, Brent
Ho, Kenneth L.
Bates, Daniel J.
Harrington, Heather A.

KAUST Grant Number
KUK-C1-013-04

Online Publication Date
2016-10-12

Print Publication Date
2016-10

Date
2016-10-12

Abstract
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 nonlinearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data are 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 geometrical structures relating models and data, and we demonstrate its utility on examples from cell signalling, synthetic biology and epidemiology.

Citation
Gross E, Davis B, Ho KL, Bates DJ, Harrington HA (2016) Numerical algebraic geometry for model selection and its application to the life sciences. Journal of The Royal Society Interface 13: 20160256. Available: http://dx.doi.org/10.1098/rsif.2016.0256.

Acknowledgements
E.G., K.L.H., D.J.B. and H.A.H. acknowledge funding from the American Institute of Mathematics (AIM). E.G. was supported by the US National Science Foundation grant DMS-1304167. B.D. was partially supported by NSF DMS-1115668. K.L.H. acknowledges support from NSF DMS-1203554. D.J.B. gratefully acknowledges partial support from NSF DMS-1115668, NSF ACI-1440467, and the Mathematical Biosciences Institute (MBI). H.A.H. gratefully acknowledges funding from AMS Simons Travel Grant, EPSRC Fellowship EP/K041096/1, King Abdullah University of Science and Technology (KAUST) KUK-C1-013-04 and MPH Stumpf Leverhulme Trust Grant.

Publisher
The Royal Society

Journal
Journal of The Royal Society Interface

DOI
10.1098/rsif.2016.0256

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