Cells of the green alga Chlamydomonas reinhardtii cultured in the presence of acetate perform mixotrophic growth, involving both photosynthesis and organic carbon assimilation. Under such conditions, cells exhibit a reduced capacity for photosynthesis but a higher growth rate, compared to phototrophic cultures. Better understanding of the down regulation of photosynthesis would enable more efficient conversion of carbon into valuable products like biofuels. In this study, Flux Balance Analysis (FBA) and Flux Variability Analysis (FVA) have been used with a genome scale model of C. reinhardtii to examine changes in intracellular flux distribution in order to explain their changing physiology. Additionally, a reaction essentiality analysis was performed to identify which reaction subsets are essential for a given growth condition. Our results suggest that exogenous acetate feeds into a modified tricarboxylic acid (TCA) cycle, which bypasses the CO2 evolution steps, explaining increases in biomass, consistent with experimental data. In addition, reactions of the oxidative pentose phosphate and glycolysis pathways, inactive under phototrophic conditions, show substantial flux under mixotrophic conditions. Importantly, acetate addition leads to an increased flux through cyclic electron flow (CEF), but results in a repression of CO2 fixation via Rubisco, explaining the down regulation of photosynthesis. However, although CEF enhances growth on acetate, it is not essential-impairment of CEF results in alternative metabolic pathways being increased. We have demonstrated how the reactions of photosynthesis interconnect with carbon metabolism on a global scale, and how systems approaches play a viable tool in understanding complex relationships at the scale of the organism.