Inference Methods for Synthetic Gene Regulatory Networks

Abstract

This dissertation is concerned with inference methods for synthetic gene regulatory networks. In Chapters 2 and 3, we examine the input–output relation of recently developed synthetic multi–input promoters and describe two descriptive polynomial-Hill models for predicting their behavior. The first method uses only single–input induction data for parameter inference of the model, and predict the responses of multi–input system with n input. We demonstrate that this approach accurately predicts Boolean (on/off) responses of multi–input systems, consisting of novel chimeric transcription factors and hybrid promoters in Escherichia coli. The second method, on the other hand, uses only a small amount of multi–input data for parameter inference and accurately predicts analog multi–input system responses. We also develop a mechanistic model using the idea of the Boltzmann–Gibbs equilibrium distribution inspired by statistical mechanics, which predict the multi–input responses using a similar approach to that in the second method. Recent advances in experimental and imaging techniques have enabled unprecedented insights into the dynamical processes within individual cells. However, many feature of intracellular dynamics remain hidden, or can be measured only indirectly. This makes it challenging to reconstruct the regulatory networks that govern the biochemical processes underlying various cell functions. In Chapters 4 and 5, we demonstrate the Bayesian inference framework, based on replacing uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to rigorously obtain expressions for the likelihoods of model parameters. Consequently, this allows us to extend Markov Chain Monte Carlo (MCMC) methods to efficiently estimate reaction rates, and delay distribution parameters, from single–cell assays. We illustrate the advantages, and potential pitfalls, of the approach using a birth–death model with both synthetic and experimental data, and show that we can robustly infer model parameters using a relatively small number of measurements. We demonstrate how to do so even when only the relative molecule count within the cell is measured, as in the case of fluorescence microscopy.Mathematics, Department o