This thesis investigates the different levels of coupling in Archaea and Eukarya using a systems biology approach that integrates modelling, experiments, and theory. Specifically, chapter 2 summarizes the bidirectional coupling between cellular metabolism and the cell cycle machinery in budding yeast, which involves complex metabolic and biosynthetic reactions necessary for building new cells. Chapter 3 focuses on investigating the effect of the Cyclin B/Cdk1 complex on some yeast metabolic enzymes using in vitro phosphorylation assays, finding that Fba1 and Pgk may be phosphorylated by Cdk1. Additionally, this study examines the possible effect of Sic1 on the activities of three important metabolic enzymes, finding that Sic1 may have a slight negative effect on Hxk2 activity. The thesis also describes a minimal computer model of the cell cycle that predicts timely mitotic cyclin Clb2 expression and validates the model through chromatin immunoprecipitation experiments. The last two chapters focus on understanding the phenomenon of gear shifting in the hyperthermophilic archaeon Saccharolobus solfataricus. Chapter 5 describes gear shifting both at the substrate-level phosphorylation around glyceraldehyde-3 phosphate dehydrogenase, or at the membrane-linked oxidative phosphorylation with the involvement of alternative terminal oxidases. Specifically, with application of kinetic models, chapter 6 shows that the ATP/ADP ratio could well be the force driving the shifting of the organisms from the high-gear GAPDH plus PGK route to the low-gear GAPN. Overall, the study contributes to a better understanding of the coupling between metabolic and cell cycle machinery and the phenomenon of gear shifting in extremophilic organisms.