Optimal Experimental Design Applied to Models of Microbial Gene Regulation
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Microbial gene expression is a comparatively well understood process, but regulatory interactions between genes can give rise to complicated behaviours. Regulatory networks can exhibit strong context dependence, time-varying interactions and multiple equilibrium. The qualitative diagrammatic models often used in biology are not well suited to reasoning about such intricate dynamics. Fortunately, mathematics offers a natural language to model gene regulation because it can quantify the various system inter-dependencies with much greater clarity and precision. This added clarity makes models of microbial gene regulation a valuable tool for studying both natural and synthetic gene regulatory systems. However models are only as good as the knowledge and assumptions they are built on. Specifically, all models depend on unknown parameters -- constant that quantify specific rates and interaction strengths within the regulatory system. In systems biology parameters are generally fit, rather than measured directly, because their values are contextually dependent on state of the microbial host. This fitting requires collecting observations of the modeled system. Exactly what is measured, how many times and under what experimental conditions defines an experimental design. The experimental design is intimately linked to the accuracy of any resulting parameter estimates for a model, but determining what experimental design will be useful for fitting can be difficult. Optimal experimental design (OED) provides a set of statistical techniques that can be used make design choices that improve parameter estimation accuracy. In this thesis I examine the use of OED methods applied to models of microbial gene regulation. I have specifically focused on optimal design methods that combine asymptotic parametric accuracy objectives, based on the Fisher information matrix, with relaxed formulations of the design optimization problem. I have applied these OED methods to three biological case studies. (1) I have used these methods to implement a multiple-shooting optimal control algorithm for optimal design of dynamic experiments. This algorithm was applied to a novel model of transcriptional regulation that accounts for the microbial host's physiological context. Optimal experiments were derived for estimating sequence-specific regulatory parameters and host-specific physiological parameters. (2) I have used OED methods to formulate an optimal sample scheduling algorithm for dynamic induction experiments. This algorithm was applied to a model of an optogenetic induction system -- an important tool for dynamic gene expression studies. The value of sampling schedules within dynamic experiments was examined by comparing optimal and naive schedules. (3) I derived an optimal experimental procedure for fitting a steady-state model of single-cell observations from a bistable regulatory motif. This system included a stochastic model of gene expression and the OED methods made use of the linear noise approximation to derive a tractable design algorithm. In addition to these case-studies, I also introduce the NLOED software package. The package can perform optimal design and a number of other fitting and diagnostic procedures on both static and dynamic multi-input multi-output models. The package makes use automatic differentiation for efficient computation, offers a flexible modeling interface, and will make OED more accessible to the wider biological community. Overall, the main contributions of this thesis include: developing novel OED methods for a variety of gene regulatory scenarios, studying optimal experimental design properties for these scenarios, and implementing open-source numerical software for a variety of OED problems in systems biology.
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Nathan Braniff (2020). Optimal Experimental Design Applied to Models of Microbial Gene Regulation. UWSpace. http://hdl.handle.net/10012/16600