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Tafintseva V.,Norwegian University of Life Sciences | Tafintseva V.,Center for Integrative Genetics at | Tondel K.,Kings College London | Tondel K.,Simula Research Laboratory | And 5 more authors.
Journal of Chemometrics | Year: 2014

The problem of structural ambiguity or "sloppiness" of a mathematical model is here studied by multivariate metamodeling techniques. If a given model is "sloppy", it means that a number of different parameter combinations-"a neutral parameter set"-can give more or less the same model behavior and thus equally good fit to data. This paper presents a way to characterize the structure of such sloppiness. The model used for illustration is a nonlinear dynamic model of reaction kinetics-a simple version of the S-system model. When fitted to time series data by various nonlinear curve fitting methods, an unexpected problem was discovered: For every time series, a large neutral parameter set was observed. Each of these sets was analyzed by principal component analysis and found to have clear, but nonlinear, subspace structure. The neutral parameter sets were found for many different time series data, and the global sloppiness structure of the model was characterized. This global sloppiness structure of the model allowed us to find strong correlations between parameters, and on this basis to simplify the original model. A method to reduce the ambiguity in kinetic model parameter estimates based on combining several time series is suggested. © 2014 John Wiley & Sons, Ltd. Source

Tafintseva V.,Norwegian University of Life Sciences | Tafintseva V.,Center for Integrative Genetics at | MacHina A.,University of Victoria | MacHina A.,Center for Integrative Genetics at | And 3 more authors.
Nonlinear Analysis: Real World Applications | Year: 2013

We describe generic sliding modes of piecewise-linear systems of differential equations arising in the theory of gene regulatory networks with Boolean interactions. We do not make any a priori assumptions on regulatory functions in the network and try to understand what mathematical consequences this may have in regard to the limit dynamics of the system. Further, we provide a complete classification of such systems in terms of polynomial representations for the cases where the discontinuity set of the right-hand side of the system has a codimension 1 in the phase space. In particular, we prove that the multilinear representation of the underlying Boolean structure of a continuous-time gene regulatory network is only generic in the absence of sliding trajectories. Our results also explain why the Boolean structure of interactions is too coarse and usually gives rise to several non-equivalent models with smooth interactions. © 2012 Elsevier Ltd. All rights reserved. Source

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