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METHODS article
Front. Syst. Biol.
Sec. Data and Model Integration
Volume 4 - 2024 |
doi: 10.3389/fsysb.2024.1419809
Spectral expansion methods for prediction uncertainty quantification in Systems Biology
Provisionally accepted- 1 Wageningen University and Research, Wageningen, Netherlands
- 2 Freiburg Center for Data Analysis and Modeling, University of Freiburg, Freiburg, Germany
Uncertainty is ubiquitous in biological systems. For example, since gene expression is intrinsically governed by noise, nature shows a fascinating degree of variability. If we want to use a model to predict the behaviour of such an intrinsically stochastic system, we have to cope with the fact that the model parameters are never exactly known, but vary according to some distribution. A key question is then to determine how the uncertainties in the parameters affect the model outcome. Knowing the latter uncertainties is crucial when a model is used for, e.g., experimental design, optimisation, or decision-making. To establish how parameter and model prediction uncertainties are related, Monte Carlo approaches could be used. Then, the model is evaluated for a huge number of parameters sets, drawn from the multivariate parameter distribution. However, when model solutions are computationally expensive this approach is intractable. To overcome this problem, so-called spectral expansion (SE) methods have been developed to quantify prediction uncertainty within a probabilistic framework. Such SE methods have a basis in, e.g., computational mathematics, engineering, physics, and fluid dynamics, and, to a lesser extent, systems biology. The computational costs of SE schemes mainly stem from the calculation of the expansion coefficients. Furthermore, SE effectively leads to a surrogate model which captures the dependence of the model on the uncertainty parameters, but is much simpler to execute compared to the original model. In this paper, we present an innovative scheme for the calculation of the expansion coefficients. It guarantees that the model has to be evaluated only a restricted number of times. Especially for models of high complexity this may be a huge computational advantage. By applying the scheme to a variety of examples we show its power, especially in challenging situations where solutions slowly converge due to high computational costs, bifurcations, and discontinuities.
Keywords: Systems Biology, Computational systems biology, mathematical modelling, spectral expansion, surrogate models
Received: 18 Apr 2024; Accepted: 27 Aug 2024.
Copyright: © 2024 Deneer, Molenaar and Fleck. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Christian Fleck, Freiburg Center for Data Analysis and Modeling, University of Freiburg, Freiburg, 79104, Germany
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