A statistical framework to optimize experimental design for inference problems in systems biology based on normalized data

Abstract

Inference problems in Systems Biology are primarily based on the theoretical assumption that a measured dataset comprises noisy realizations following some underlying stochastic distribution, having well-defined statistical properties. This uncertainty in the input quantities propagates through the inference process, influences the uncertainty of the estimated model parameters and subsequently affects the quality and reliability of model predictions. Understanding the mechanisms of noise propagation over an inference problem will therefore be instrumental in designing an optimal and robust experimental protocol to reduce the uncertainty of the estimated quantities of interest. This thesis investigates the underlying mechanisms of noise propagation from measured experimental data to estimated parameters by developing a statistical framework to characterize and analyse non-linear transformations of stochastic distributions. Among such non-linear transformations, data normalization, a required step for some common experimental techniques, requires specific attention, representing an additional modification of noise properties. Mathematically, the normalization step translates into ratios of two distributions. We consider standard assumptions on the distributions associated with biological raw data. In this thesis we explore three specific classes of inference problems relevant for Systems Biology applications. At first we consider the problem of statistical inference of different parametrized error models for normalized data. Subsequently, we investigate the effect of such error models when coupled with different normalization strategies on results of parameter estimation for dynamic models of biochemical reaction networks. We conclude this thesis by analysing the effects of noise propagation on Modular Response Analysis based network reconstruction. From our simulation results, we observe that non-linear noise transformations may lead to very uncertain and/or erroneous inference results. Additionally, based on the quantification of statistical measures for accuracy and precision of the inference results, we derive practical advice for an optimized and robust experimental design in order to reduce the uncertainty of the estimated quantities.