Advancing Elementary Flux Mode Analysis for Large-Scale Metabolic Flux Networks Under Steady State

Abstract

Cellular metabolism is a dynamic process regulating the production and consumption of metabolites. These reaction rates, or metabolic fluxes, are regulated at multiple cellular levels by genes, transcripts, proteins, and metabolites. Advancements in technological and computational methods are leading to increasingly comprehensive estimates of steady state fluxes. In this thesis, I focus on advancing methods to analyse steady state flux data using minimal, steady state pathways known as elementary flux modes (EFMs). Since an arbitrary set of steady state fluxes can be reconstructed by a positive, linear combination of EFMs, these pathways can be viewed as functional units of steady state flow within and through a metabolic flux network. Working with EFMs present two challenges, however; the non-uniqueness of flux decomposition in terms of EFMs, and scaling of EFM analysis in large networks. Here, I address both computational problems and show how EFM analysis can be used to characterize the flow of metabolites and their atomic constituents in large-scale metabolic networks. In the first part of this thesis, I develop a biophysically-motivated method enforcing a Markovian constraint to uniquely decompose fluxes onto EFMs in strictly-unimolecular reaction networks. I refer to this method as the cycle-history Markov chain (CHMC) and prove its correctness with both discrete- and continuous-time Markov chains. Using the CHMC, I address biophysical questions regarding the distribution of pathway fluxes in a unimolecular, sphingolipid kinetic model of healthy and Alzheimer's disease patients. My statistical analyses of EFM weights support a dominant pathway flux hypothesis, whereby the majority of network fluxes are explained by a small subset of highly active EFMs. In my final aim, I generalize my Markov chain method to any type of metabolic network, including those with multispecies reactions. I do this through my proposal of atomic elementary flux modes (AEFMs) which explain the minimal, steady state flow of indivisible atoms in a metabolic network. By constraining atomic movements with atom mapping predictions, I show that AEFMs, unlike EFMs, can be enumerated in five large-scale metabolic networks by means of an atomic cycle-history Markov chain (ACHMC). In a subsequent analysis of a single set of inferred fluxes in a human liver cancer cell line (HepG2), I further show that glutamine-derived carbon AEFMs exhibit pathway flux dominance, with the most active AEFMs corresponding to well-known metabolic subsystems and the recently discovered non-canonical tricarboxylic acid (TCA) cycle. Altogether, my (atomic) cycle-history Markov chain ((A)CHMC) methods address fundamental challenges in EFM analysis and showcase the potential of both EFMs and AEFMs to further our understanding of cellular metabolism.