Probabilistic inference in models of systems biology

Abstract

In Systems Biology, it is usual to use a set of ordinary differential equations to characterize biological function at a system level. The parameters in these equations generally reflect the reaction or decay rates of a molecular species, while states characterize the concentration values of species of interest, e.g. mRNA, proteins and metabolites. Often parameter values are estimated from in vitro experiments which may not be true reflections of the in vivo environments. With internal states, some may not be accessible for experimental measurement. Hence there is interest in estimating parameter values and states from noisy or incomplete observations taken at inputs/outputs of a system. This thesis explores several probabilistic inference approaches to do this.

The study starts from a thorough investigation of the effectivenesses of the most commonly used one-pass inference methods, from which the non-parametric particle filtering approach is shown to be the most powerful method in the sequential category. After this study, the family of Approximate Bayesian Computation (ABC) methods, also known as likelihood-free batch approach, is reviewed chronologically and its advantages and deficiencies are summarized via a statistical toy example and two biological models. Additionally, a novel ABC method coupled with the sensitivity analysis technique has been developed and demonstrated on three periodic and one transient biological models. This approach has the potential to solve problem in high dimension by selectively allocating computational budget. In order to assess the capability of the proposed method in real-world problems, we have modeled the polymer pathway and conducted quantitative analysis via the proposed inference approach.

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Identifiers

ORCID for Mahesan Niranjan: orcid.org/0000-0001-7021-140X

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