## 1 Introduction  
The rapid growth of the global population and the intensification of global climate change have made the need for (new) protein sources in the future even more urgent. As a result, alternative protein sources such as algae or bacterial proteins are becoming increasingly important [1]. Traditional protein sources such as meat and dairy products face many challenges, including greenhouse gas emissions, resource consumption, environmental pollution, and animal welfare. Currently, resources for human nutrition are mainly dependent on agriculture, livestock, and aquaculture [2]. These human activities contribute to greenhouse gas emissions and the depletion of land resources [2]. Producing animal and dairy products to meet the growing demand for protein is ultimately unsustainable [3]. SCPs have shown significant advantages in terms of being unaffected by climate, soil characteristics, and available land [4]. SCPs are primarily edible single-celled microorganisms that are provided to humans or animals [5]. SCPs are produced by microorganisms such as yeast, bacteria, algae, and filamentous fungi. Yeasthas long been used as a good source of SCPs [6]. However, yeast has a high nucleic acid content and low cell wall digestibility [7,8]. Filamentous fungi are low in protein and grow slowly [8]. Among these microorganisms, bacteria have a higher protein content, faster growth rate, and are rich in amino acids [9]. In addition, carbon dioxide is generally a third-generation feedstock for biofuels [10]. Achieving CO\({}_{2}\) recycling would be an effective way to address current energy, resource, and environmental challenges [11]. Researchers are focusing on the conversion of anthropogenic carbon dioxide into high-value-added products [12]. Among them, the physical, chemical, and biological pathways are the most common methods used for carbon dioxide conversion [13]. Chemists have been designing and developing new catalysts for the conversion of CO\({}_{2}\) into fuels such as CO, CH\({}_{4}\), and CH\({}_{3}\)OH with high energy efficiency, but the portfolio needs to be further expanded [14,15]. In recent decades, the biological removal of CO\({}_{2}\) from the atmosphere has attracted much attention from researchers [13]. In the process of the biochemical fixation of carbon dioxide, the absorption of inorganic carbon dioxide molecules by microorganisms and their conversion into bio-based products are interesting directions to explore [13]. The absorption of organic matter by carbon dioxide through the use of the Calvin-Benson cycle, the Wood-Jungdal pathway, and the reducing tricarboxylic acid (TCA) cycle is a pathway that contributes to the biochemical fixation of carbon dioxide [16,17]. The autotrophic metabolism of _Cupriviadus reactor_ H16 drives efficient carbon dioxide fixation through the Calvin-Benson-Bassham (CBB) cycle [18]. _C. necator_ is grown under hydrogen, carbon dioxide, and oxygen conditions for reducing CO\({}_{2}\) in astronauts during space flights and for single-cell proteins used in animals [19, 20, 21]. Under autotrophic conditions, the protein of _C. nenactor_ contains more than 70% DW [22,23]. Currently, Novo-Nutrients(r), Kiverdi(r)Solar, and Foods(r) use biomass products metabolized by _C. necator_ commercially as feed for fish, livestock, and pets [24]. _C. necator_ is a facultative autotrophic bacterium that is capable of utilizing gluconate, fructose, various organic acids, and CO\({}_{2}\) as carbon sources [25]. Turning industrial exhaust gasses, which are mainly composed of CO\({}_{2}\) and CO, into valuable substances can reduce greenhouse gas (GHG) emissions from industrial activities and create economic value [26]. Researchers have been studying the stoichiometric equations and stoichiometric coefficients of hydroxide bacteria since their discovery [27,28]. Recent studies have shown that the cell mass yield, as well as the stoichiometry of autotrophic growth, varies over a reasonably wide range over time; in other words, with changes in cell density [29,30].