Spectral methods for prediction uncertainty quantification in Systems Biology

Uncertainty is ubiquitous in biological systems. These uncertainties can be the result of lack of knowledge or due to a lack of appropriate data. Additionally, the natural variability of biological systems caused by intrinsic noise, e.g. in stochastic gene expression, leads to uncertainties. With the help of numerical simulations the impact of these uncertainties on the model predictions can be assessed, i.e. the impact of the propagation of uncertainty in model parameters on the model response can be quantified. Taking this into account is crucial when the models are used for experimental design, optimisation, or decision-making, as model uncertainty can have a significant effect on the accuracy of model predictions. We focus here on spectral methods to quantify prediction uncertainty based on a probabilistic framework. Such methods have a basis in, e.g., computational mathematics, engineering, physics, and fluid dynamics, and, to a lesser extent, systems biology. In this chapter, we highlight the advantages these methods can have for modelling purposes in systems biology and do so by providing a novel and intuitive scheme. By applying the scheme to an array of examples we show its power, especially in challenging situations where slow converge due to high-dimensionality, bifurcations, and spatial discontinuities play a role.