Mitochondria play a central role in cellular function and dysfunction, participating in the regulation of cell cycle, metabolism, signalling, cell growth and cell death. In the model system of budding yeast S. cerevisiae, the division of mitochondria is regulated by dynamic interactions between the Fis1p, Mdv1p/Caf4p and Dnm1p GTPase, which are assembled into fission complexes on the outer mitochondrial membrane. The recruitment of Fis1p and Mdv1p in the complex is of vital importance not only for the scission of mitochondria, but also for the retention of functional mitochondrial structures in the cell. However, the exact roles of Fis1p and Mdv1p in the mitochondrial network remodelling remain elusive and their dynamic participation in the assembly of the fission machinery is still poorly characterised in yeast, mostly due to challenges in the sensitive and accurate quantification of low-abundant proteins. The aim of this thesis is to capture the dynamics of Fis1p and Mdv1p mitochondrial proteins by generating a set of quantitative parameters for protein concentrations and kinetic rates in absolute numbers of copies per cell. To achieve this, the non-invasive fluorescence spectroscopy techniques, FCS and FCCS, were optimised in live yeast cells of different strain backgrounds. A library of twenty-two GFP and mCherry protein fusion strains of S. cerevisiae and S. uvarum, as well as four additions sets of S. cerevisiae x S. uvarum hybrid strains were constructed in order to allow the quantification of Fis1p and Mdv1p dynamics under varying environmental conditions, cell-cycle stages, and genetic perturbations. Fis1p was observed to diffuse, localising both in the cytoplasm and mitochondria whereas Mdv1p was observed exclusively at mitochondrial structures. New data were generated regarding the absolute number of protein copies in different nutritional media, the physical state of the proteins (bound and unbound forms), the heterogeneity in protein abundance within the cell population, the effect of the allelic dosage, the expression of the protein in mitotically-dividing and G0-synchronised cells, and finally the differential behaviour of the proteins in response to fermentation and respiration. A compensatory mechanism which controls Fis1p abundance upon deletion of one allele was observed in Fis1p but not in Mdv1p, suggesting differential regulation of Fis1p and Mdv1p protein expression. Moreover, the proportion of Mdv1p mitochondrial-associated subunits increased significantly under respiratory growth. This could indicate that a higher amount of Mdv1p is required to regulate mitochondrial fission in conditions where mitochondrial function is essential. Collectively, the FCCS data provided by this study support a differential role of Fis1p and Mdv1p in the assembly of the fission complex. The identified levels of Mdv1p copies and portion of bound-molecules suggest a steady state of the protein during the fission process which is further linked to the recruitment of Mdv1p to mitochondria. In contrast, Fis1p requirement was not related to any environmental changes or cell-cycle stages. These data provide valuable information regarding the regulation and role of Fis1p and Mdv1p in the yeast mitochondrion.