Algebra, Geometry and Topology of ERK Kinetics
Lewis Marsha b c✉, Emilie Dufresned, Helen Mary Byrnec e, Heather A. Harringtonc
- aLudwig Institute for Cancer Research, University of Oxford, Oxford, UK. lewis.marsh@maths.ox.ac.uk
- bMathematical Institute, University of Oxford, Oxford, UK. lewis.marsh@maths.ox.ac.uk
- cMathematical Institute, University of Oxford, Oxford, UK
- dDepartment of Mathematics, The University of York, York, UK
- eLudwig Institute for Cancer Research, University of Oxford, Oxford, UK
- ✉Corresponding author
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Abstract
The MEK/ERK signalling pathway is involved in cell division, cell specialisation, survival and cell death (Shaul and Seger in Biochim Biophys Acta (BBA)-Mol Cell Res 1773(8):1213-1226, 2007). Here we study a polynomial dynamical system describing the dynamics of MEK/ERK proposed by Yeung et al. (Curr Biol 2019, https://doi.org/10.1016/j.cub.2019.12.052 ) with their experimental setup, data and known biological information. The experimental dataset is a time-course of ERK measurements in different phosphorylation states following activation of either wild-type MEK or MEK mutations associated with cancer or developmental defects. We demonstrate how methods from computational algebraic geometry, differential algebra, Bayesian statistics and computational algebraic topology can inform the model reduction, identification and parameter inference of MEK variants, respectively. Throughout, we show how this algebraic viewpoint offers a rigorous and systematic analysis of such models.
TL;DRA polynomial dynamical system describing the dynamics of MEK/ERK proposed by Yeung et al. is studied and it is demonstrated how methods from computational algebraic geometry, differential algebra, Bayesian statistics and computationalgebraic topology can inform the model reduction, identification and parameter inference ofMEK variants. (Semantic Scholar)