Increasing recombinant protein production yields from bacterial cultures remains an important challenge in biotechnology. Acetate accumulation due to high dissolved carbon dioxide ($pCO_2$) concentrations in the medium has been identified as a factor that negatively affects such yields. Under appropriate culture conditions, acetate could be re-assimilated by bacterial cells to maintain heterologous proteins production. In this work, we developed a simplified metabolic network aiming to establish a reaction rate analysis for a recombinant Escherichia coli when producing green fluorescent protein (GFP) under controlled $pCO_2$ concentrations. Because E. coli is able to consume both glucose and acetate, the analysis was performed in two stages. Our results indicated that GFP synthesis is an independent process of cellular growth in some culture phases. Additionally, recombinant protein production is influenced by the available carbon source and the amount of $pCO_2$ in the culture medium. When growing on glucose, the increase in the $pCO_2$ concentration produced a down-regulation of central carbon metabolism by directing the carbon flux toward acetate accumulation; as a result, cellular growth and the overall GFP yield decreased. However, the maximum specific rate of GFP synthesis occurred with acetate as the main available carbon source, despite the low activity in the other metabolic pathways. To maintain cellular functions, including GFP synthesis, carbon flux was re-distributed toward the tricarboxylic acid cycle and the pentose phosphate pathway to produce ATP and NADH. The thermodynamic analysis allowed demonstrating the feasibility of the simplified network for describing the metabolic state of a recombinant system.