The green alga Chlamydomonas reinhardtii can be grown phototrophically using light as an energy source or mixotrophically using reduced carbon in the form of acetate in addition to light. Acetate, despite increasing biomass, also inhibits photosynthesis as compared to cells grown phototrophically. A better understanding of acetate assimilation and how it regulates photosynthesis would enable a more efficient conversion of carbon into valuable products such as biofuels. In this thesis constraint-based modelling techniques are used in conjunction with a genome-scale model of the organism and experimental data to understand this phenomenon. Using flux balance analysis we show that the preferred route of acetate assimilation is likely to be via the enzyme acetyl-CoA synthase, and that exogenous acetate feeds into a modified tricarboxylic acid cycle, which bypasses the CO2 evolution steps. This is consistent with experimental data and explains increases in biomass with mixotrophic growth on acetate in comparison to phototrophic metabolism. Using a cycle decomposition algorithm with a mass-consistent adaptation of the model we were able to examine the role of cycles that further theoretically explain the down-regulation of photosynthesis observed when cells are grown in the presence of acetate. These results suggest that acetate modulates changes in the oxidative pentose phosphate pathway and increases mitochondrial respiration activity. Label-free proteomics was used to quantify 2951 polypeptides with various roles including the assimilatory route of acetate, photosynthesis, the Calvin-Benson cycle, central carbon metabolism and oxidative phosphorylation. We show how acetate assimilation induces a shift in central carbon metabolism to activate the oxidative pentose phosphate pathway. This results in the cycling of electrons around Photosystem I, which accounts for the down-regulation of photosynthesis.